PRINCIPLES OF LOGIC 
 
ROEHAMPTON I 
 PRINTED BY JOHN GRIFFIN 
 
PRINCIPLES OF 
 LOGIC 
 
 By 
 
 GEORGE HAYWARD JOYCE, S.J. 
 
 M.A., ORIEL COLLEGE, OXFORD 
 
 PROFESSOR OF LOGIC, ST. MARY*S HALL, 
 
 STONYHUR8T 
 
 SECOND EDITION 
 
 LONGMANS, GREEN AND CO. 
 
 39, PATERNOSTER ROW, LONDON 
 
 FOURTH AVENUE & 3 oxH STREET, NEW YORK 
 BOMBAY, CALCUTTA, AND MADRAS 
 
PREFACE TO SECOND EDITION 
 
 IN issuing this new edition of my Principles of Logic I 
 welcome the opportunity it affords me of expressing my 
 thanks to my various critics for the very kind manner 
 in which the work was received. The friendly notices 
 accorded to it, not only by such as were in sympathy 
 with its general standpoint, but by those whose philo- 
 sophical position was altogether different, tend to show 
 that at the present time a new interest is felt in that 
 Scholastic system, whose principles it was my purpose 
 to defend. 
 
 Since the publication of the first edition of this work 
 the Traditional Logic has been the object of hostile 
 criticism. More than one writer of mark has maintained 
 that, as an analysis of our mental operations, it is entirely 
 worthless : that it is destitute of any claim to be regarded 
 as a science. Such an estimate, we are convinced, is only 
 possible because Logic has for so long been studied out 
 of all relation to that philosophy of which it forms an 
 integral part. A detailed fragment has been treated as 
 though it were an independent whole. Under such cir- 
 cumstances it could .hariily fail to be misinterpreted and 
 undervalued. "But 'when it is viewed in the light of the 
 principles of Schol'ist : cism its true value is seen. Its 
 validity as an analysis of thought becomes apparent, and 
 its claim to be a true science is put beyond all dispute. 
 
 For the purpose of the present edition the work has 
 been carefully revised, certain corrections have been made, 
 and a few sections have been re- written. 
 
 IV 
 
INTRODUCTION 
 
 THIS work is an attempt at a presentment of what is fre- 
 quently termed the Traditional Logic, and is intended for 
 those who are making acquaintance with philosophical 
 questions for the first time. Yet it is impossible, even in a 
 text-book such as this, to deal with logical questions save 
 in connexion with definite metaphysical and epistemolo- 
 gical principles. Logic, as the theory of the mind's 
 rational processes in regard of their validity, must neces- 
 sarily be part of a larger philosophical system. Indeed 
 when this is not the case, it becomes a mere collection of 
 technical rules, possessed of little importance and of less 
 interest. The point of view adopted in this book is that 
 of the Scholastic philosophy ; and as far as is compatible 
 with the size and purpose of the work, some attempt has 
 been made to vindicate the fundamental principles on 
 which that philosophy is based. 
 
 From one point of view, this position should prove a 
 source of strength. The thinkers who elaborated our sys- 
 tem of Logic, were Scholastics. With the principles of 
 that philosophy, its doctrines and its rules are in full 
 accord. In the light of Scholasticism, the system is a 
 connected whole ; and the subjects, traditionally treated 
 in it, have each of them its legitimate place. 
 
 When a writer adopts some other standpoint, it is in- 
 evitable that his Logic must be remodelled, if it is to be 
 in harmony with his philosophical principles. For some 
 parts of the traditional science, there will be no place 
 in his scheme. And though these subjects may find 
 treatment in his work, yet it will be manifest that 
 
vi INTRODUCTION 
 
 they are present as unwelcome guests, only tolerated out 
 of deference to custom and the exigencies of a popular 
 demand. In such a case, a young student may well be 
 excused, if he fails to grasp the bearing of the question at 
 issue. 
 
 From another point of view, it might seem that Scholas- 
 tic principles must be a source of weakness. Have not, 
 it will be asked, the universities, one and all, long since 
 discarded Scholasticism ? 
 
 That this is true of all those universities which have 
 submitted to secular influences, must be frankly admitted. 
 At our ancient seats of learning, there has been a complete 
 neglect of the great mediaeval philosophers, the repre- 
 sentatives of that once famous school. The names of 
 Albert the Great, of St. Thomas Aquinas, of Duns Scotus 
 are never mentioned. It is not that they are weighed 
 and found wanting. They are ignored. It is assumed 
 that there is nothing in them worth knowing. The prac- 
 tice of what certain German writers have termed ' the 
 leap over the middle ages (der Sprung uber das Mittelalter),' 
 has been universal. From Plotinus to Bacon has been 
 regarded as a blank in the history of philosophy. 1 
 
 Yet by common consent the period thus ignored was 
 one of intense philosophic activity. Metaphysical pro- 
 blems were discussed with an interest, a zeal, an acumen 
 since unknown ; and some of the greatest intellects the 
 world has ever seen were nurtured in the schools of the 
 day. Nor was the philosophy of the Scholastics one of 
 those immature systems, which arise when the mind of 
 man is called to grapple for the first time with the great 
 problems of the universe. These men had inherited the 
 two streams of Greek and Arabian thought. They had 
 
 ! * It is with pleasure we notice that at Oxford the Summa Theologica of St. 
 Thomas is now recommended to candidates for theological honours, and his 
 Summa, contra Gentiles has been made an optional subject in the school of 
 Littera humaniores. But this welcome change only testifies to the complete 
 neglect which has so long prevailed. 
 
INTRODUCTION vii 
 
 set themselves to master and to develop the conclusions 
 of Plato, of Aristotle, of Avicenna, of Averroes. They 
 were influenced not by the Peripatetic school alone, but 
 further by Stoicism, Neo-platonism, Augustinianism. 1 It 
 is significant that nearly every thinker, even of those 
 occupying a hostile position, who has devoted enough 
 time and attention to understand the matter, has 
 expressed his admiration for the great synthesis effected 
 by the Scholastic philosophers. 2 
 
 When, therefore, the Neo-Scholastics of to-day avail 
 themselves of the results attained in that epoch, no wise 
 man will consider that this is likely to impair the value 
 of their conclusions. They are but claiming their share 
 in the great inheritance of the past. 
 
 The deliberate ignoring of so famous a period, and one 
 so fruitful for the civilization of Europe, may well provide 
 matter for reflection. For continuity is the law of human 
 progress. Advance must ever be won by building on the 
 foundations laid by our predecessors. The nature of man, 
 as essentially social, involves his subjection to this law. 
 
 1 Cf. de Wulf, Scholasticism Old and New, trans, by P. Coffey, p. 45. Picavet. 
 Esquisse d'une histoire des philosophies medi&vales. 
 
 2 The opinions of two authors neither of whom can be accused of sympathy 
 with Scholasticism may be of interest. Professor Huxley writes as follows : 
 
 " The Scholastic philosophy is a wonderful monument of the patience and 
 ingenuity with which the human mind toiled to build up a logically consistent 
 theory of the Universe. . . . And that philosophy is by no means dead and 
 buried as many vainly suppose. On the contrary, numbers of men of no mean 
 learning and accomplishment and sometimes of rare power and subtlety of 
 thought, hold by it as the best theory of things which has yet been stated. And 
 what is still more remarkable, men who speak the language of modern philo- 
 sophy, nevertheless think the thoughts of the Schoolmen." Science and Culture, 
 Lect. 2. Universities, p. 41. Somewhat similarly von Hartmann speaks of 
 Scholasticism as " a wonderful and close-knit system of thought, of which none 
 can think lightly save those who have not yet overcome the bias of party- 
 feeling nor learnt to view things from an objective standpoint." Die Selbst- 
 zersetzung des Christenthums, p. 75. 
 
 It would not be difficult to multiply such testimonies from the great minds 
 of every century. Thus Hugo Grotius writes, ' Ubi in re morali consentiunt 
 [Scholastici] vix est ut errent.' De Jure Belli et Pads, Proleg : 52. Cf. also 
 Leibniz, Epist. ad Thomasium, 49, and Trots Lettres a M. de Montmort, Lettre 
 III. On the other hand the atheist Diderot says of Scholasticism, ' Cette 
 philosophic a 6t6 une des plus grandes plaies del'esprit humain." CEuvres, torn. 
 xix. p. 372. 
 
viii INTRODUCTION 
 
 Pascal has well said, " C'est grace a la tradition que toute 
 ' la suite des hommes pendant le cours de tant de si&cles 
 ' doit etre considered comme un meme homme, qui sub- 
 ' siste toujours et qui apprend continuellement." * The 
 attempt to break with the past, to dispense with what 
 former generations have accomplished, to pull down 
 what they have laboriously built and to make a fresh 
 beginning, has ever ended in failure. No forward step has 
 ever been taken in that way ; for so to act is to violate 
 a fundamental law of our nature. Movements thus 
 initiated have been retrograde, not progressive. 
 
 Yet this is what the men of the Renaissance strove to do 
 in regard to the Christian civilization of the middle ages. 
 They put aside as valueless the hardly-won results of five 
 centuries of strenuous effort. Of that great revolt against 
 the past, the repudiation of the traditional philosophy was 
 an integral part. 
 
 It was Descartes who first framed a new synthesis, 
 which in some measure filled the place once held by the 
 Scholastic system. He, more than any other man, has a 
 right to be regarded as the father of modern philosophy. 
 And it is not without its lesson to note that he assigns 
 as his reason for holding the philosophy of the School to 
 be worthless, that it was the work not of a single mind 
 but of many minds. 2 
 
 Since the days of Descartes, many another philosophical 
 system, idealist, sensationalist and materialist, has been 
 offered as a solution of the world's riddles. These systems 
 differ widely among themselves. But one common fea- 
 ture differentiates them all alike from Scholasticism. 
 They simplify the problem by the omission of some es- 
 sential element. This characteristic seems inseparable 
 from any system which severs itself from that which has 
 been aptly termed the main stream of European thought. 
 
 1 Preface to the treatise Du Vide. 
 a Descartes, Meditation I. 
 
INTRODUCTION ix 
 
 The factors, with which philosophy must deal, are three 
 God, the world, and the human soul. The Scholastic 
 philosophy faced the problem in its completeness : it 
 shirked no element of it. It is creationist, thus distin- 
 guishing between God as Absolute and Unconditioned 
 Being on the one hand, and the soul and the world as 
 Contingent Being on the other. As regards the soul, it is 
 spiritualist, not materialist ; and in relation to the pro- 
 blem of knowledge, it is objectivist, teaching that the 
 intellect is capable of valid cognition in regard of that 
 external order with which it is brought into contact by 
 the senses. 1 
 
 In the novel philosophies proposed as substitutes for 
 Scholasticism, sometimes one of the three factors, some- 
 times another, is omitted ; and thus the solution remains 
 unsatisfactory and inadequate. Some, as e.g. Materialism, 
 dispense both with God and the soul. In others, as in 
 that Neo-Hegelianism which finds the only conscious 
 life of the Divine in the human consciousness, God is set 
 aside, and the soul alone is kept. In others again, as in 
 the philosophy of Berkeley, the world is eliminated ; God 
 and the soul alone remain. 
 
 The rapid rise and fall of systems is but the natural 
 result of this. Men will not long rest satisfied with any 
 scheme which does not account for all the facts. The 
 pendulum of thought swings, with more, or it may be with 
 less velocity, but as surely as it is biassed by a single preju- 
 dice withholding it from any truth, it will continually 
 change the curve it traces, and move in succession to all 
 points of the compass. 
 
 Of the multiplicity of modern philosophies, which offer 
 themselves to our acceptance, not one can claim to be 
 
 1 Cf. deVfulf.Histoiredela Philosophic M edievale, p. 222. " Toute theorie 
 negatrice de la spirit ualite de Fame ou de la personalite humaine, ou de la 
 distinction essentielle entre Dieu et la creature, est a nos yeux, subversive 
 des principes fondamentaux de la scolastique. Voila pourquoi nous 
 n'hesitons pas a ranger parmi les adversaires de la scolastique quiconque 
 nseigne le materialisme, la migration des ames, 1'atheisme ou le pantheisme." 
 
x INTRODUCTION 
 
 more than the shibboleth of a school. We may recognize 
 and honour to the full, the great ability of the thinkers 
 who propounded them. But the task, which they set 
 themselves, was too great for their powers. As it is not 
 given to any man to reconstruct the whole of physical 
 science from its first foundations, so it is not given to any 
 to reconstruct philosophy. 
 
 It is not one of the least evils that have arisen from this 
 state of things, that many now look on philosophy as a 
 body of doctrines purely relative to a particular age. 
 Philosophical systems, they hold, must come and go like 
 the fashions of our dress. We should not regard them 
 as more than a convenient mode of representing facts. 
 As men at one period interpreted the universe on a basis 
 of Aristotelianism, so at the present age they do well to 
 adopt the thought-forms of other systems, and interpret 
 it in accordance with the doctrines of Kant or of Hegel. 
 
 Against the corrosive scepticism of such a view, Neo- 
 Scholasticism utters its protest. Philosophy is a science 
 the highest of the sciences. Just as in the natural 
 sciences, the long line of investigators gradually pushes 
 forward the frontiers of human knowledge, and age by 
 age increases the number of those truths which are the 
 permanent conquests of the human mind, so it is in philo- 
 sophy. Wherever a real advance has been made, that 
 advance is true for all time. The point has been well put 
 by Professor de Wulf. " The endeavour," he writes, " of 
 ' Neo-Scholasticism to re-establish and plant down deeply 
 ' among the controversies of the twentieth century, the 
 ' principles which animated the Scholasticism of the thir- 
 ' teenth, is in itself an admission that philosophy cannot 
 ' completely change from epoch to epoch : that the truth 
 ' of seven hundred years ago, is true to-day : that out and 
 ' out relativism is an error : that down through all the 
 ' oscillations of historical systems, there is ever to be met 
 ' with a philosophia perennis a sort of atmosphere of truth 
 
INTRODUCTION xi 
 
 ' pure and undiluted whose bright clear rays have lighted 
 ' up the centuries even through the shadows of the darkest 
 ' and gloomiest clouds . . . For ' if reason be aught but a 
 'deceptive aspiration after the absolutely inaccessible, 
 ' surely whatever has been brought to light, whatever 
 ' our ancestors have unearthed, and acquired in their 
 ' pioneer labours, cannot have proved entirely worthless 
 ' to posterity.' "* 
 
 It is not of course to be supposed that the Neo-Scholas- 
 ticism of to-day is in all points identical with the Scholas- 
 ticism of the middle ages. The astronomical physics 
 of the mediseval doctors were theoretically erroneous. 
 Moreover new questions have arisen, new difficulties 
 been suggested, new discoveries have been made. The 
 adversaries of to-day are not the adversaries against whom 
 the mediseval doctors were called to contend. In adapt- 
 ing our methods to the needs of the day, we do not discard 
 the principles of the Scholastics. But Neo-Scholasticism 
 belongs to the twentieth century, not to the thirteenth ; 
 and it employs the weapons of a new age. 
 
 It has seemed advisable to make this brief apology for 
 the standpoint adopted in this book, since in England com- 
 paratively little is known of the reaction towards Scholas- 
 ticism which has taken place in recent years. Abroad 
 its strength is better understood. The importance of the 
 philosophical works of men such as Mercier, de Regnon, de 
 Wulf, Nys, Farges, Domet de Vorges, Carra de Vaux, 
 Mandonnet, Seeberg, Asin y Palacios, is acknowledged 
 by all competent judges. 2 In England, for obvious 
 
 1 De Wulf, Scholasticism Old and New, trans, by Coffey, p. 161. 
 
 2 Mercier, Cours de Philosophic, Louvain 1897-1903 ; de Regnon, Metaphysique 
 des Causes, Paris 1886 ; de Wulf, Histoire de la Philosophic Medievale, Louvain 
 1900 ; Nys, Cosmologie, Louvain 1900 ; Farges, Etudes Philosophiques, Paris 
 1892-1907 ; Domet de Vorges, Abrege de Metaphysique, Paris 1906 ; Carra 
 de Vaux, Avicenne, Gazali, Paris 1900, 1904 ; Mandonnet, Siger de Brabant 
 et V Averroisme latin au xiiie Siecle, Fribourg-en-Suisse 1899 ; Seeberg, Die Theo- 
 logie des Johannes Duns Scoius, Leipzig 1900 : Asin y Palacios, El Averroisme 
 teologico de S. Thomas de Aquino, Saragoza 1904. To these we must add the 
 most valuable work Beitrdge zur Geschichte der Philosophic des Mittclalters edited 
 by C. Baumker and G. von Hertling, Mlinster. Ozanam's Dante et la philosophic 
 
xii INTRODUCTION 
 
 reasons, the movement has been less felt. But some at 
 least of those who have noticed it have not underrated its 
 significance. In regard to it Professor Case writes as 
 follows in his article on Metaphysics in the Encyclopedia 
 Britannica : " One cannot but feel regret at seeing the 
 * Reformed Churches blown about by every wind of doc- 
 ' trine, and catching at straws, now from Kant, now from 
 4 Hegel, and now from Lotze : or at home from Green, 
 4 Caird, Martineau, Balfour and Ward in succession, with- 
 4 out ever having considered the basis of their faith : while 
 4 the Roman Catholics are making every effort to ground 
 4 a Universal Church on a sane system of metaphysics. 
 ' However this may be, the power of the movement is 
 'visible enough from the spread of Thomism over the 
 "civilized world." * 
 
 My sincerest thanks are due to the Rev. G. S. Hitchcock 
 alike for many valuable criticisms and suggestions, and 
 for his kindness in reading the proof-sheets. I must fur- 
 ther gratefully acknowledge my obligations to the Rev. 
 M. Maher and the Rev. T. Rigby. If my work prove of 
 service to those for whose use it has been written, the 
 result will be in no small measure due to the generous 
 assistance accorded me by these and other friends. 
 
 catholique au xiii e siecle, Paris 1855, may also be mentioned, as a book appealing 
 to a wider circle of readers than the others we have named. 
 
 1 M. Picavet, professor at Sorbonne, no friend of the movement, writes 
 as follows in the Revue Philosophique for 1896 : " Les catholiques, unis par le 
 Thomisme, qu'ils completent avec une ample information scientifique, sent 
 devenus les maitres de la Belgique : on compte avec eux en Amerique et en 
 Allemagne : leur influence grandit en France, meme en Hollande et en Suisse-' 
 cited by Mercier, Origines de la Psych, contemp. c. 8. 
 

 CONTENTS 
 
 PART I 
 THE LOGIC OF THOUGHT 
 
 CHAPTER I 
 THE NATURE AND AIM OF LOGIC 
 
 PAGE 
 
 i. DEFINITION OF LOGIC i 
 
 2. DIVISIONS OF LOGIC 3 
 
 3. THE PLACE OF LOGIC IN PHILOSOPHY .... 5 
 
 4. SCOPE OF LOGIC 7 
 
 5. HISTORY OF LOGIC 8 
 
 Note. DIFFERENT VIEWS AS TO THE SCOPE OF LOGIC. u 
 
 CHAPTER II 
 THE CONCEPT : THE NAME : THE TERM 
 
 i. THE CONCEPT 15 
 
 2. REPUGNANT CONCEPTS 18 
 
 3. ADEQUATE, CLEAR AND OBSCURE CONCEPTS . 18 
 
 4. THE NAME AND THE TERM 19 
 
 5. CATEGOREMATIC AND SYNCATEGOREMATIC WORDS . 19 
 
 6. DIVISIONS OF TERMS 20 
 
 7. SINGULAR, GENERAL AND COLLECTIVE TERMS . 21 
 
 8. ABSTRACT AND CONCRETE TERMS 23 
 
 9. CONNOTATIVE AND NON-CONNOTATIVE TERMS . . 25 
 
 10. POSITIVE AND NEGATIVE TERMS 31 
 
 ii. ABSOLUTE AND RELATIVE TERMS 3 2 
 
 12. TERMS OF FIRST AND SECOND INTENTION ... 34 
 
 13. UNIVOCAL, EQUIVOCAL AND ANALOGOUS TERMS . 35 
 
 14. OPPOSITION OF TERMS 3 6 
 
 15. THE ' SUPPOSITIO ' OF THE TERM 37 
 
 xiii 
 

 xiv CONTENTS 
 
 CHAPTER III 
 THE JUDGMENT AND THE PROPOSITION 
 
 PAGE 
 
 i. THE PROPOSITION 39 
 
 2. ANALYSIS OF THE JUDGMENT 41 
 
 3. QUALITY OF PROPOSITIONS 46 
 
 4. QUANTITY OF PROPOSITIONS 46 
 
 5. THE FOURFOLD SCHEME OF PROPOSITIONS ... 50 
 
 6. ANALYTIC AND SYNTHETIC PROPOSITIONS ... 51 
 
 7. COMPLEX PROPOSITIONS 55 
 
 8. COMPOUND CATEGORICAL PROPOSITIONS .... 56 
 
 9. MODAL PROPOSITIONS 58 
 
 10. REDUCTION OF PROPOSITIONS TO LOGICAL FORM . 61 
 
 ii. HYPOTHETICAL PROPOSITIONS 63 
 
 12. DISJUNCTIVE PROPOSITIONS 65 
 
 CHAPTER IV 
 THE LAWS OF THOUGHT 
 
 i. THE LAWS OF THOUGHT 67 
 
 2. THE LAW OF CONTRADICTION 69 
 
 3. THE LAW OF IDENTITY 71 
 
 4. THE LAW OF EXCLUDED MIDDLE 73 
 
 5. OTHER VIEWS AS TO THE SOURCE OF THE LAWS OF 
 
 THOUGHT 75 
 
 CHAPTER V 
 
 DIAGRAMMATIC REPRESENTATION OF PROPOSI- 
 TIONS : OPPOSITION OF PROPOSITIONS 
 
 i. DIAGRAMMATIC REPRESENTATION OF PROPOSITIONS : 
 
 EULER'S CIRCLES 77 
 
 2. DISTRIBUTION OF TERMS IN A PROPOSITION ... 81 
 3. OTHER METHODS OF DIAGRAMMATIC REPRESENTA- 
 TION 82 
 
 4. THE OPPOSITION OF PROPOSITIONS 84 
 
 5. OPPOSITION AS A MEANS OF INFERENCE .... 88 
 6. CONTRADICTORY OPPOSITION OUTSIDE THE FOUR- 
 FOLD SCHEME 89 
 
 7. CONTRARY OPPOSITION OUTSIDE THE FOURFOLD 
 
 SCHEME 90 
 
CONTENTS xv 
 
 CHAPTER VI 
 IMMEDIATE INFERENCE 
 
 PAGE 
 
 i. IMMEDIATE INFERENCE 92 
 
 2. CONVERSION 93 
 
 3. ARISTOTLE'S PROOF OF CONVERSION 97 
 
 4. EQUIPOLLENCE OR OBVERSION 98 
 
 5. CONTRAPOSITION 99 
 
 6. INVERSION 101 
 
 7. TABLE OF RESULTS 102 
 
 8. OTHER VARIETIES OF IMMEDIATE INFERENCE . . 102 
 
 CHAPTER VII 
 THE IMPORT OF PROPOSITIONS 
 
 i. IMPORT OF PROPOSITIONS : PREDICATIVE VIEW . . 105 
 
 2. THE CLASS-INCLUSION VIEW 106 
 
 3. THE ATTRIBUTIVE VIEW 109 
 
 4. IMPLICATION OF EXISTENCE no 
 
 5. THE COMPARTMENTAL VlEW Il6 
 
 6. MR. BRADLEY ON THE PROPOSITION 117 
 
 7. IMPORT OF THE HYPOTHETICAL PROPOSITION . . 119 
 
 CHAPTER VIII 
 THE PREDICABLES 
 
 i. THE PREDICABLES 121 
 
 2. THE TREE OF PORPHYRY 129 
 
 3. ARISTOTLE'S PREDICABLES 131 
 
 4. THE CONTROVERSY ON UNIVERSALS 132 
 
 5. THE UNIVERSAL IN MODERN LOGIC 135 
 
 CHAPTER IX 
 THE CATEGORIES 
 
 i. THE CATEGORIES IN THEIR METAPHYSICAL ASPECT 137 
 
 2. THE CATEGORIES IN THEIR LOGICAL ASPECT. . . 142 
 
 3. THE CATEGORIES AND THE SCIENCES 144 
 
 4. THE CATEGORIES AS A CLASSIFICATION OF PREDI- 
 CATES 145 
 
 5. MILL'S SCHEME OF CATEGORIES 147 
 
 6. THE CATEGORIES OF KANT 148 
 
 7. THE CONCEPT OF BEING . ,.>... 149 
 
xvi CONTENTS 
 
 CHAPTER X 
 DEFINITION AND DIVISION 
 
 PAGE 
 
 i. DEFINITION 150 
 
 2. VARIOUS KINDS OF DEFINITION 152 
 
 3. LIMITS OF DEFINITION 159 
 
 4. RULES OF DEFINITION 159 
 
 5. LOGICAL DIVISION 161 
 
 6. RULES OF DIVISION 165 
 
 7. DIVISION BY DICHOTOMY i6j6 
 
 8. VARIOUS KINDS OF DIVISION 168 
 
 CHAPTER XI 
 THE CATEGORICAL SYLLOGISM (I) 
 
 i. THE CATEGORICAL SYLLOGISM 169 
 
 2. RELATION OF PREMISSES TO CONCLUSION IN REGARD 
 
 TO TRUTH 172 
 
 3. GENERAL RULES OF THE SYLLOGISM 172 
 
 4. FIGURES AND MOODS OF THE SYLLOGISM, . . . 177 
 
 5. SPECIAL RULES OF THE FOUR FIGURES . . . . 179 
 
 6. THE MNEMONIC LINES 181 
 
 7. REDUCTION 182 
 
 8. SUPERIORITY OF FIG. i . . . 186 
 
 CHAPTER XII 
 THE CATEGORICAL SYLLOGISM (II) 
 
 i. CANON OF SYLLOGISTIC REASONING 187 
 
 2. THE FOURTH FIGURE 191 
 
 3. EXPRESSION IN SYLLOGISTIC FORM .... 193 
 
 4. PROGRESSIVE AND REGRESSIVE SYLLOGISMS . . . 194 
 
 5. VALIDITY OF THE SYLLOGISM 195 
 
 6. MATHEMATICAL REASONING 199 
 
 7. INFERENCES OTHER THAN SYLLOGISTIC .... 200 
 
 8. MR. BRADLEY'S THEORY OF INFERENCE .... 201 
 
 CHAPTER XIII 
 HYPOTHETICAL AND DISJUNCTIVE SYLLOGISMS 
 
 i. MIXED HYPOTHETICAL SYLLOGISMS 203 
 
 2. REDUCTION OF HYPOTHETICAL SYLLOGISMS . . . 206 
 
CONTENTS xvii 
 
 PAGE 
 
 3. THE DISJUNCTIVE SYLLOGISM ....... 207 
 
 4. THE DILEMMA ..... ..... 209 
 
 5. ANSWERING THE DILEMMA ........ 212 
 
 CHAPTER XIV 
 INDUCTION 
 
 i. THE NATURE OF INDUCTION ....... 215 
 
 2. CAUSE AND CONDITION ...... ... 219 
 
 3. THE AIM OF INDUCTIVE ENQUIRY ..... 222 
 
 4. RECOGNITION OF THE CAUSAL RELATION ... .223 
 
 5. THE INDUCTIVE SYLLOGISM ....... 228 
 
 6. PERFECT AND IMPERFECT INDUCTION ..... 231 
 
 CHAPTER XV 
 THE UNIFORMITY OF NATURE 
 
 i. THE UNIFORMITY OF NATURE ....... 235 
 
 2. J. S. MILL ON THE UNIFORMITY OF NATURE . . 241 
 
 3. " CESSANTE CAUSA, CESSAT EFFECTUS'" .... 246 
 
 4. UKITY OF NATURE .......... 248 
 
 CHAPTER XVI 
 ENTHYMEME : SORITES : ANALOGY 
 
 i. ENTHYMEME ............ 252 
 
 2. THE ARISTOTELIAN ENTHYMEME ...... 253 
 
 3. CHAINS OF REASONING ......... 255 
 
 4. EPICHIREMA ............ 256 
 
 5. SORITES ............. 257 
 
 6. ANALOGY . . ........... 259 
 
 CHAPTER XVII 
 
 FALLACIES 
 
 i. THE TREATMENT OF FALLACIES IN LOGIC . . . 264 
 
 2. WHAT ERRORS ARE RECKONED AS FALLACIES . . 265 
 
 3. ARISTOTLE'S LIST OF FALLACIES ...... 267 
 
 4. EQUIVOCATION ........... 268 
 
 5. AMPHIBOLOGY ... ........ 269 
 
 6. COMPOSITION AND DIVISION ....... 270 
 
 7. ACCENT ...... ........ 272 
 
xvill CONTENTS 
 
 PAGE 
 
 8. FIGURE OF SPEECH 272 
 
 9. ACCIDENT 274 
 
 10. CONFUSION OF ABSOLUTE AND QUALIFIED STATE- 
 MENT 275 
 
 ii. IGNORATIO ELENCHI 276 
 
 12. PETITIO PRINCIPII 278 
 
 13. FALLACY OF THE CONSEQUENT 279 
 
 14. FALSE CAUSE 280 
 
 15. MANY QUESTIONS 281 
 
 16. MILL'S CLASSIFICATION OF FALLACIES .... 282 
 
 PART II 
 
 APPLIED LOGIC, OR THE METHOD OF 
 SCIENCE 
 
 CHAPTER XVIII 
 APPLIED LOGIC AND THE LOGIC OF THOUGHT 
 
 i. SCIENCE AND PHILOSOPHY 289 
 
 2. THE SUBDIVISIONS OF PHILOSOPHY 293 
 
 3. LOGIC AND METAPHYSICS 298 
 
 4. THE BREACH WITH THE PAST 300 
 
 5. BACON 304 
 
 6. MILL 306 
 
 CHAPTER XIX 
 OBSERVATION AND EXPERIMENT 
 
 i. THE FUNCTION OF OBSERVATION AND EXPERIMENT. 310 
 
 2. IN WHAT OBSERVATION CONSISTS 311 
 
 3. CONDITIONS OF OBSERVATION . 313 
 
 4. EXPERIMENT 315 
 
 5. NATURAL EXPERIMENTS 317 
 
 6. RELATIVE ADVANTAGES OF OBSERVATION AND EX- 
 PERIMENT 317 
 
CONTENTS xix 
 
 CHAPTER XX 
 METHODS OF INDUCTIVE ENQUIRY 
 
 PAGE 
 
 i. THE FOUR EXPERIMENTAL METHODS .... 320 
 
 2. FURTHER ILLUSTRATIONS OF THE METHODS . . . 325 
 3. THE FUNCTION OF THE METHODS IN PROVING A LAW 
 
 OF NATURE 330 
 
 4. CRITICISM OF MILL'S CANONS 333 
 
 CHAPTER XXI 
 EXPLANATION 
 
 i. EXPLANATION 337 
 
 2. EXPLANATION BY REGRESSIVE REASONING . . . 339 
 
 3. EXPLANATION BY HYPOTHETICAL DEDUCTION . . 341 
 
 4. HYPOTHETICAL DEDUCTION AND INDUCTION . . . 343 
 
 5. EXPLANATION AS EMPLOYED BY NEWTON . . . 344 
 
 6. NEWTON'S RULES OF PHILOSOPHIZING 349 
 
 CHAPTER XXII 
 HYPOTHESIS 
 
 i. HYPOTHESIS 354 
 
 2. ORIGIN OF HYPOTHESIS 357 
 
 3. CONDITIONS OF A LEGITIMATE HYPOTHESIS . . . 359 
 
 4. VARIOUS KINDS OF HYPOTHESES 361 
 
 CHAPTER XXIII 
 
 QUANTITATIVE DETERMINATION: ELIMINATION OF 
 
 CHANCE 
 
 i. MEASUREMENT 363 
 
 , 2. METHODS OF APPROXIMATION 367 
 
 3. CHANCE 369 
 
 4. ELIMINATION OF CHANCE 372 
 
 5. PROBABILITY 373 
 
 CHAPTER XXIV 
 
 CLASSIFICATION 
 
 i. CLASSIFICATION 380 
 
xx CONTENTS 
 
 PAGE 
 
 2. ARTIFICIAL CLASSIFICATION . . 382 
 
 3. THE DOCTRINE OF NATURAL SPECIES 384 
 
 4. NATURAL CLASSIFICATION 389 
 
 5. CLASSIFICATION BY SERIES 393 
 
 CHAPTER XXV 
 METHOD 
 
 i. SCIENTIFIC METHOD 395 
 
 2. THE METHODIC PURSUIT OF TRUTH 398 
 
 3. PHILOSOPHIC TERMINOLOGY 400 
 
 4. DESCARTES' RULES OF METHOD 402 
 
 5. LEIBNIZ'S VIEWS ON METHOD 404 
 
PRINCIPLES OF LOGIC 
 
 PART: i 
 
 THE LOGIC OF THOUGHT 
 
 N.B. The student is recommended to reserve the passages 
 marked with an asterisk (*) for a second reading of the work. 
 
 CHAPTER I. 
 
 THE NATURE AND AIM OF LOGIC. 
 
 i. Definition of Logic. Logic maybe defined as the 
 science which directs the operations of the mind in the 
 attainment of truth. 
 
 What do we mean by truth ? An assertion is said to 
 be true when it corresponds to the reality of which the 
 assertion is made. But the verbal statement is merely 
 the outward expression of the thought within. It is 
 our thoughts which are properly said to be true or errone- 
 ous. For present purposes, therefore, we may define 
 truth as the conformity of the intellect with its object. 
 Thus if I see a white horse, and judge ' That horse is 
 white/ my judgment is said to be true, because my 
 thought corresponds with the thing about which I am 
 judging. 
 
 The aim of all our mental operations is to attain 
 true judgments. If I endeavour to establish a geometri- 
 cal proposition, my object is to arrive in the end at a 
 judgment, which is in conformity with reality. Now 
 there are certain definite ways in which, and in which 
 alone, our thinking faculty must proceed if it is to achieve 
 
 1 B 
 
A PRINCIPLES OF LOGIC 
 
 its task of faithfully representing the real order. Reflec- 
 tion enables us to observe the operations of the mind ; 
 and hence we are able to know and to catalogue these 
 common types of mental action. In this way we learn 
 the rules, which we must needs observe in reasoning, 
 if we are to arrive at a true result. For, as experience 
 shows us, it is very easy to argue in a way that will bring 
 us, not to truth, but to error. It was a boast of the 
 Sophists in ancient Greece that they could make the worse 
 appear to be the better cause. They effected this end 
 by skilfully violating the rules which men must observe, 
 if their conclusions are to be true. 
 
 Another definition may be given of Logic, in which 
 the science is considered in a different aspect. Logic is 
 the science which treats of the conceptual representation 
 of the real order ; in other words, which has for its subject- 
 matter things as they are represented in our thought. 
 The difference between this definition and that which we 
 gave in the first instance, is that this definition expresses 
 the subject-matter of Logic, the former its aim. We 
 shall find as we proceed that the science can scarcely be 
 understood, unless both these aspects are kept in view. 
 
 The work of Logic therefore is not to teach us some 
 way of discovering new facts. This belongs to the 
 special sciences, each in its own sphere. It assists us in 
 the attainment of truth, because it treats of the way in 
 which the mind represents things, and thus shows us 
 what are those general conditions of right thinking, 
 which must be observed whatever be the subject which 
 occupies us. 
 
 Where we have a systematic body of securely estab- 
 lished principles and of conclusions legitimately drawn 
 from these principles, there we have a science. Thus in 
 the science of Astronomy we start from certain general 
 laws, and have a body of conclusions derived from these. 
 Mere facts not brought under general laws do not consti- 
 tute a science. We are rightly said to have a science of 
 Logic, for, as we shall see, it consists of a body of princi- 
 ples and legitimate conclusions, such as we have described. 
 
THE NATURE AND AIM OF LOGIC 3 
 
 2. Divisions of Logic. The simplest act of the mind 
 in which it can attain truth is the judgment the act by 
 which the mind affirms or denies something of something 
 else. That which is affirmed (or denied) of the other is 
 called an attribute : that to which it is said to belong 
 (or not to belong) is called a subject. Hence we may 
 define a judgment as the act by which the mind affirms 
 or denies an attribute of a subject. 
 
 A judgment however gives the mind a complex 
 object : for it involves these two parts subject and 
 attribute. We must therefore take account of a more 
 elementary act of the mind than judgment, viz. : Simple 
 Apprehension. Simple apprehension is the act by which 
 the mind without judging, forms a concept of something. 
 Thus if I should conceive the notion of a triangle, with- 
 out however making any judgment about it, I should 
 be said to have formed a simple apprehension of a tri- 
 angle. The words true or false cannot be applied to 
 simple apprehensions, just as we cannot say that the 
 words in a dictionary are true or false. Some philoso- 
 phers indeed deny that the mind ever forms a simple 
 apprehension ; they hold that in every case some judg- 
 ment is made. We need not enter into this question. 
 We can at least analyse the judgment into simple appre- 
 hensions : for every judgment requires two concepts, one 
 in which the mind expresses the subject, and the other in 
 which it expresses the attribute. Thus in the example 
 given above, I must have a concept of horse, and one of 
 whiteness, in order to say ' The horse is white.' These 
 are the elements which go to constitute the complex act 
 of judgment, and they can be considered in isolation 
 from it. Logic therefore must deal with the concept. 
 
 There is a third process of the mind, namely Reason- 
 ing or Inference. This is defined as, the act by which 
 from two given judgments, the mind passes to a third 
 judgment distinct from these, but implicitly contained 
 hi them. Thus if I say : 
 
 (All roses wither in the autumn ; 
 \ This flower is a rose ; 
 
4 PRINCIPLES OF LOGIC 
 
 Therefore : This flower will wither in the autumn; 
 or if I argue : 
 
 'Whatever displays the harmonious ordering of many 
 parts is due to an intelligent cause ; 
 
 The world, displays the harmonious ordering of many 
 parts ; 
 
 Therefore : The world is due to an intelligent 
 
 cause ; 
 
 I am said in each case to infer the third judgment. An 
 inference of the form which we have employed in these 
 examples, is called a syllogism. The two judgments 
 given are known as the premisses. The judgment de- 
 rived from them is the conclusion. 
 
 It is of these three acts of the mind that Logic treats : 
 and the science falls correspondingly into three main 
 divisions, the Logic (i) of the Concept, (2) of the Judg- 
 ment, (3) of Inference. 
 
 Since Logic deals with thought, it necessarily takes 
 account to some extent of language the verbal expres- 
 sion of thought. It does so however from quite a 
 different point of view to that of Grammar. Grammar 
 is concerned with words as such. It is the art by which 
 the words employed in significant speech are combined 
 according to the conventional rules of a language. Hence 
 in it each of the nine parts of speech is treated indepen- 
 dently, and rules are given for their respective use. On 
 the other hand, the simplest object of which Logic takes 
 account is the Concept. In its consideration of words, 
 therefore, it does not deal with any of those parts of 
 speech, which taken by themselves are incapable of 
 giving us an independent concept. It is conversant not 
 with nine, but with two forms only of significant utter- 
 ance, viz.: the Name, the verbal expression of the Concept, 
 and the Proposition, the verbal expression of the Judg- 
 ment. 1 The proposition consists of three parts. These 
 
 1 Cf. Boethius, IntroducL ad Syll. Cat. (Migne P. L. vol. 64, col. 766. A), 
 and De Syll. Cat. lib. I. (ibid. col. 766. D). Another important difference 
 between Logic and Grammar is to be found in the fact that Logic is concerned 
 with but one mood the Indicative, Grammar with all the moods equally, 
 Seo below, Ch. 3, i. 
 
THE NATURE AND AIM OF LOGIC 5 
 
 are, (i) the Subject that of which the assertion is made : 
 (2) the Predicate that which is affirmed or denied of the 
 Subject : and (3) the Copula the verb is or are which 
 connects the Subject and the Predicate. The Subject 
 and the Predicate are called the Terms (from the Latin 
 terminus a boundary) of the proposition : and the 
 predicate is said to be predicated of the subject. 
 
 3. The Place of Logic in Philosophy. The sciences 
 fall into two broad divisions, viz.: the speculative and 
 the regulative (or normative] sciences. In the specu- 
 lative sciences, philosophic thought deals with those 
 things which we find proposed, to our intelligence in the 
 universe : such sciences have no other immediate end 
 than the contemplation of the truth. Thus we study 
 Mathematics, not primarily with a view to commercial 
 success, but that we may know. In the normative 
 sciences, on the other hand, the philosopher pursues 
 knowledge with a view to the realization of some practical 
 end. ' The object of philosophy,' says St. Thomas of 
 Aquin, ' is order. This order may be such as we find 
 already existing ; but it may be such as we seek to bring 
 into being ourselves.' x Thus sciences exist, which have 
 as their object the realization of order in the acts both 
 of our will and of our intellect. The science which deals 
 with the due ordering of the acts of the will, is Ethics, 
 that which deals with order in the acts of the intellect 
 is Logic. 
 
 The question has often been raised, whether Logic is 
 a science or an art. The answer to this will depend 
 entirely on the precise meaning which we give to the word 
 ' art.' The mediaeval philosophers regarded the notion 
 of an art as signifying a body of rules by which man 
 
 1 St. Thomas in Ethic. I. lect. i. Sapicntis est ordinare. . . . Ordo 
 autem quadrupliciter ad rationem cornparatur. Est enim quidam ordo quern 
 ratio non f acit scd solum considerat, sicut est ordo return naturalium. A lius 
 autem est ordo quem ratio considerando facit in proprio actu, puta cum ordinal 
 concept us suos ad invicem et signa conceptuum quac sunt voces significativae. 
 Tertius autem est ordo quem ratio considerando facit in operationibus volunta- 
 tis. Quartus autem est ordo quem ratio considerando facit in exterioribus 
 rebus, quarum ipsa est causa, sicut in area et domo. 
 
6 PRINCIPLES OF LOGIC 
 
 directs his actions to the performance of some work. 1 
 Hence they held Logic to be the art of reasoning, as well 
 as the science of the reasoning process. Perhaps a more 
 satisfactory terminology is that at present in vogue, 
 according to which the term ' art/ is reserved to mean a 
 body of precepts for the production of some external 
 result, and hence is not applicable to the normative 
 sciences. 
 
 Aesthetics, the science which deals with beauty and 
 proportion in the objects of the external senses, is now 
 reckoned with Ethics and Logic, as a normative science. 
 By the mediaeval writers it was treated theoretically 
 rather than practically, and was reckoned part of Meta- 
 physics. 
 
 It may be well to indicate briefly the distinction be- 
 tween Logic and two other sciences, to which it bears 
 some affinity. 
 
 Logic and Metaphysics. The term Metaphysics some- 
 times stands for philosophy in general : sometimes with 
 a more restricted meaning it stands for that part of 
 philosophy known as Ontology. In this latter sense 
 Metaphysics deals not with thoughts, as does Logic, but 
 with things, not with the conceptual order but with the 
 real order. It investigates the meaning of certain 
 notions which all the special sciences presuppose, such 
 as Substance, Accident, Cause, Effect, Action. It deals 
 with principles which the special sciences do not prove, 
 but on which they rest, such as e.g., Every event must have 
 a cause. Hence it is called the science of Being, since its 
 object is not limited to some special sphere, but embraces 
 all that is, whether material or spiritual. Logic on the 
 other hand deals with the conceptual order, with thoughts. 
 Its conclusions do not relate to things, but to the way 
 in which the mind represents things. 
 
 Logic and Psychology. The object of Psychology is 
 the human soul and all its activities. It investigates 
 
 1 St. Thomas in An. Post. /., lect. i. ' Nihil enim aliud ars esse videtur, 
 quam certa ordinatio rationis qua per determinata media ad debitum finem 
 actus humani perveniunt.' 
 
THE NATURE AND AIM OF LOGIC 7 
 
 the nature and operations of intellect, will, imagination, 
 sense. Thus its object is far wider than that of Logic, 
 which is concerned with the intellect alone. And even in 
 regard to the intellect, the two sciences consider it 
 under different aspects. Psychology considers thought 
 merely as an act of the soul. Thus if we take a judg- 
 ment, such as e.g., ' The three angles of a triangle are 
 together equal to two right angles,' Psychology considers 
 it, merely in so far as it is a form of mental activity. 
 Logic on the other hand, examines the way in which this 
 mental act expresses the objective truth with which it 
 deals ; and if necessary, asks whether it follows legiti- 
 mately from the grounds on which it is based. Moreover, 
 Logic, as a regulative science, seeks to prescribe rules 
 as to how we ought to think. With this Psychology 
 has nothing to do : it only asks, What as a matter of 
 fact is the nature of the mind's activity ? 
 
 4. The Scope of Logic. Logicians are frequently 
 divided into three classes, according as they hold that 
 the science is concerned (i) with names only, (2) with 
 the form of thought alone, (3) with thought as represen- 
 tative of reality. 
 
 (1) The first of these views that Logic is concerned 
 with names only, has found but few defenders. It 
 is however taught by the French philosopher Condillac 
 (1715-1780), who held that the process of reasoning con- 
 sists solely in verbal transformations. The meaning of 
 the conclusion is, he thought, ever identical with that 
 of the original proposition. 
 
 (2) The theory that Logic deals only with the forms of 
 thought, irrespective of their relation to reality, was 
 taught among others by Hamilton (1788-1856) and Mansel 
 (1820-1871). Both of these held that Logic is no way 
 concerned with the truth of our thoughts, but only with 
 their consistency. 
 
 In this sense Hamilton says : " Logic is conversant with 
 the form of thought, to the exclusion of the matter" 
 (Lectures, I. p. 15). By these logicians a distinction is 
 
8 PRINCIPLES OF LOGIC 
 
 drawn between ' formal truth/ i.e., self-consistency 
 and ' material truth/ i.e., conformity with the object ; 
 and it is said that Logic deals with formal truth alone. 
 
 On this view Mill well observes : " the notion of the 
 ' true and false will force its way even into Formal Logic. 
 ' . . . We may abstract from actual truth, but the 
 ' validity of reasoning is always a question of condi- 
 ' tional truth, whether one proposition must be true 
 ' if the others are true, or whether one proposition can 
 ' be true if others are true " (Exam, of Hamilton, p. 399). 
 
 (3) According to the third theory, Logic deals with 
 thought as the means by which we attain truth. Mill, 
 whom we have just quoted, may stand as a representative 
 of this view. " Logic/' he says, " is the theory of valid 
 * thought, not of thinking, but of correct thinking " 
 (Exam, of Hamilton, p. 388). 
 
 To which class of logicians should Aristotle and his 
 Scholastic followers be assigned ? Many modern writers 
 rank them in the second of these groups, and term them 
 Formal Logicians. It will soon appear on what a mis- 
 conception this opinion rests, and how completely the 
 view taken of Logic by the Scholastics differs from that 
 of the Formal Logicians. In their eyes, the aim of the 
 science was most assuredly not to secure self-consist- 
 ency, but theoretically to know how the mind represents 
 its object, and practically to arrive at truth. 
 
 The terms Nominalist, Conceptualist, and Realist 
 Logicians are now frequently employed to denote these 
 three classes. This terminology is singularly unfortun- 
 ate : for the names, Nominalist, Conceptualist and Realist, 
 have for centuries been employed to distinguish three 
 famous schools of philosophy, divided from each other 
 on a question which has nothing to do with the scope of 
 Logic. In this work we shall as far as possible avoid 
 using the terms in their novel meaning. 
 
 5. History of Logic. It was Aristotle (384-322 
 B.C.) who laid the foundations of the science by treat- 
 ing logical questions separately from other parts of 
 
THE NATURE AND AIM OF LOGIC 9 
 
 philosophy. Six of his treatises are concerned with the 
 subject : they cover almost the whole ground. 
 
 1. The Categories, a treatise on the ten primary classes 
 
 into which our concepts of things are divided. 
 
 2. De Inter pretatione, a treatise on terms and pro- 
 
 positions. 
 
 3. Prior Analytics, a treatise on inference. 
 
 4. Posterior Analytics, a treatise on the logical analysis 
 
 of science. 
 
 5. Topics, a treatise on the method of reasoning to 
 
 be employed in philosophical questions, when 
 demonstrative proof is not obtainable. 
 
 6. Sophistical Refutations, an account of fallacious 
 
 reasonings. 
 
 This group of treatises was afterwards known as the 
 Organon. It should, however, be noticed that they are 
 separate works. Aristotle himself had no single word 
 to signify the whole of Logic, and it seems doubtful 
 whether he viewed it as a single science. The name 
 Logic was introduced byZeno the Stoic (about 300 B.C.). 
 
 The successors of Aristotle added but little of perman- 
 ent value to his great achievement. Enduring import- 
 ance however attaches to a small treatise by the Neo- 
 platonist Porphyry (233-304 A.D.) entitled the Isagoge or 
 Introduction to the Categories of Aristotle. 
 
 In a certain sense the name of Boethius (B. Severinus 
 Boethius 470-525 A.D.) constitutes a landmark in the 
 history of Logic : for it was through the medium of his 
 translation of the Organon, and his commentaries on the 
 Categories and the Isagoge, that the works of Aristotle 
 and Porphyry were available for educational purposes 
 in Western Europe from the sixth to the thirteenth 
 century. 1 Through this period some knowledge of Logic 
 was widely possessed, as it was one of the seven liberal 
 arts Grammar, Dialectic i.e., Logic, Rhetoric, Geometry, 
 
 1 Two works attributed to St. Augustine were also recognized authorities 
 at this period. St. Augustine's interest in the science was not shared by all 
 the fathers. We are told of St. Ambrose, that he used to exclaim A Logica 
 Augustini, liber a me Domine. 
 
io PRINCIPLES OF LOGIC 
 
 Arithmetic, Astronomy, and Music of which higher 
 education was held to consist. 
 
 At the beginning of the thirteenth century the numer- 
 ous other treatises of Aristotle, and the works of his 
 Arabian commentators Avicenna (Ibn Sina 980-1037 
 A.D.) and Averroes (Ibn Roshd 1126-1189 A.D.) were 
 translated into Latin, and gave an immense impetus to 
 philosophic study. The mediaeval Scholastics availed 
 themselves of these works, to build up a thoroughly sys- 
 tematic science of Logic. It may perhaps be said that 
 their main advance on Aristotle's treatment lay in the 
 greater accuracy with which they discriminated the 
 respective spheres of Logic and Metaphysics, and in 
 their more precise arrangement of the various parts of 
 Logic itself. 
 
 The i5th and i6th centuries witnessed the decadence 
 of Scholasticism, and in 1620 an attack was made on 
 the very foundations of the Aristotelian Logic by 
 Francis Bacon in his Novum Organum. Much of his 
 criticism was ill-founded, since he believed that the pur- 
 pose of Logic was to provide men with a means towards 
 making discoveries regarding the laws and phenomena 
 of nature. Yet it was of service in calling fresh atten- 
 tion to the theory of Induction, a part of Logic to which 
 too little attention had been given by the later Scholastics. 
 
 Since the time of Bacon the whole question of Induc- 
 tion has been very fully discussed by writers on Logic. 
 The most eminent of these among English thinkers was 
 John Stuart Mill (1806-1873), whose treatment of the 
 subject long held rank as the classical work on Induction. 
 Many of the points, however, raised by these writers 
 do not strictly speaking belong to the province of Logic. 
 For, influenced by Bacon, they have dealt not merely 
 with Induction as a process of thought, but also with a 
 very different subject, namely the general theory of 
 scientific investigation. It was indeed natural that a 
 keen interest should be felt in this question. The rapid 
 growth and multiplication of the physical sciences dur- 
 ing the last three centuries could not but lead to the codi. 
 
THE NATURE AND AIM OF LOGIC n 
 
 fication of their rules and to reflection on their methods, 
 in other words to the formation of a philosophy of 
 evidence. Such a science was impossible in the middle 
 ages, ere the great era of physical investigation had 
 dawned. At the present day the treatment of this 
 subject forms a part of every work on Logic. By many 
 writers it is termed Material or Inductive Logic, the tradi- 
 tional part of the science receiving by way of distinction 
 the name of Formal or Deductive Logic. These names are 
 misleading. The traditional Logic was, as we have seen 
 ( 4), not purely formal. And though the treatment of 
 Induction, properly so called, by many of the mediaeval 
 writers was inadequate, yet they all regarded it as falling 
 within their scope. We have therefore preferred to 
 designate the two portions of this volume The Logic of 
 Thought and Applied Logic or the Method of Science 
 respectively. Induction as a process of thought, finds 
 its place in the first of these two divisions. 
 
 NOTE TO CHAPTER I. 
 DIFFERENT VIEWS AS TO THE SCOPE OF LOGIC. 
 
 * The difference of opinion as to the true scope of Logic is far 
 wider than would appear from the triple division given in 4, 
 which is that usually recognized in logical text-books : and special 
 names are now employed by logicians to indicate the point of 
 view from which the science is treated. Moreover the threefold 
 division is, as we have noticed, open to the further objection 
 that it compels us to group the Scholastic logicians either with 
 the school of Mansel or with that of Mill, though they have ^ttle 
 enough in common with either of these. It seems, therefore, 
 desirable to enter somewhat more into detail on the subject. 
 In this note we give an explanation of the special designations 
 referred to, viz. : Scholastic Logic, Formal Logic, Symbolic Logic, 
 Inductive Logic, Transcendental Logic, Logic of the Pure Idea, 
 Modern Logic. The notice in each case is necessarily very brief. 
 The purpose of the present work would render a more detailed 
 account of the systems out of place. As far as possible we have 
 availed ourselves of citations from authors representative of 
 the various views, in order to elucidate the meaning of the dif- 
 ferent terms. 
 
 (i) Scholastic Logic. We have explained above that the 
 Scholastic or Traditional Logic holds the subject-matter of the 
 
11 PRINCIPLES OF LOGIC 
 
 science to be the conceptual representation of the real order. 
 This may be otherwise expressed by saying that it deals with 
 things, not as they are in themselves, but as they are in thought. 
 Cardinal Mercier says : " There are two sciences whose object is 
 1 in the highest degree abstract, and hence universal in its applica- 
 ' bility. These are Metaphysics and Logic. The object of 
 ' Metaphysics is Being considered in abstraction from all in- 
 ' dividual determinations and material properties, in other words 
 the Real as such. . . . Logic also has Being for its object. . . . 
 ' It must not however be thought that Logic and Metaphysics 
 ' consider Being from the same point of view. . . . The object 
 1 of Metaphysics is the thing considered as a real substance en- 
 ' dowed with real attributes. The object of Logic is likewise 
 ' the thing, but considered as an object of thought endowed with 
 ' attributes of the conceptual order " (Logique, 23 [ed. 3]). 
 
 (2) Formal Logic. The characteristic of this school is to con- 
 sider the mental processes in entire abstraction from the relation 
 which the concept bears to the real order. Logic, says Dean 
 Mansel, " accepts as valid, all such concepts, judgments and 
 ' reasonings, as do not directly or indirectly imply contradictions : 
 ' pronouncing them thus far to be legitimate as thoughts, 
 ' that they do not in ultimate analysis destroy themselves " 
 (Proleg. Logica, p. 265). Mr. Keynes abstains from deciding 
 whether Formal Logic constitutes the whole of the science, but 
 says in its regard : " The observance of the laws which Formal 
 1 Logic investigates, will not do more than secure freedom from 
 'self-contradiction and inconsistency" (Formal Logic, i). 
 
 (3) Symbolic Logic is a further development of Formal Logic. 
 It is thus defined in Baldwin's Diet, of Philosophy. ' Symbolic 
 ' logic is that form of logic in which the combinations and relations 
 ' of terms and of propositions, are represented by symbols, in 
 ' such a way that the rules of a calculus may be substituted for 
 ' actively conscious reasoning.' Mr. Venn, its ablest exponent 
 in this country, claims for it the great advantages, that it " gene- 
 ' ralizes the processes of the ordinary Logic," showing them as 
 particular cases of wider problems dealing with relation (Sym- 
 bolic Logic, Introd. pp. xxi,-xxiii.) . Though the subject has 
 engaged the attention of several able men, it has no claim yet 
 to be considered a science. Almost every investigator has 
 adopted his own system of symbolic notation. It should further 
 be mentioned, that many thinkers believe that although it affords 
 scope for much ingenuity, it cannot possibly contribute in any 
 way whatever to our knowledge of the reasoning process. 
 
 (4) Inductive, Empirical, Material or Applied Logic is a science 
 developed on the basis of the views set forth in Bacon's Novum 
 Organum. Mill terms it " a general theory of the sufficiency of 
 ' Evidence," and " a philosophy of Evidence and of the Investi- 
 
THE NATURE AND AIM OF LOGIC 13 
 
 ' gation of Nature" (Exam, of Hamilton, p. 402). "Every 
 ' one,' he says, ' who has obtained any knowledge of the physical 
 ' sciences from really scientific study, knows that the questions 
 ' of evidence presented . . . are such as to tax the very highest 
 ' capacities of the human intellect " (ibid.) : and he severely 
 calls to task those who hold " that the problem which Bacon 
 ' set before himself, and led the way towards resolving, is an 
 ' impossible one . . . that the study of Nature, the search for 
 ' objective truth, does not admit of any rules." Granted that 
 there be such a science it must belong, he urges, to Logic, " for 
 ' if the consideration of it does not belong to Logic, to what science 
 ' does it belong ? " (ibid. p. 400). It is manifest that the science 
 Mill here describes, differs essentially from Logic, as heretofore 
 it had been understood. This philosophy of evidence deals, 
 not with thought, but with things as they are in the real order ; 
 and its function is to prescribe the due methods of enquiry in 
 each several science, not merely in the physical sciences as 
 this passage might suggest. H. Spencer with more consistency 
 than Mill refuses altogether the name of Logic to the traditional 
 science of that name, and prefers to term it the Theory of Reason- 
 ing (Psychology, pt. vi., c. viii.). 
 
 (5) Transcendental Logic is the name given by Kant to the 
 most fundamental portion of his Critical Philosophy. Kant 
 started with the assumption that all our knowledge, whether 
 sensitive or intellectual, is internal to the mind, that we have 
 no immediate knowledge of the external world. He further 
 assumed that the material of all our knowledge can be nought 
 but successive pulses of sensation without unity of any kind. 
 If these purely subjective feelings undergo such a transmuta- 
 tion within us as to present to our experience an orderly world 
 of matter and motion, this must be in virtue of an a priori ele- 
 ment an internal mechanism providing certain ' forms ' according 
 to which we perceive, think and reason. In the Transcendental 
 Aesthetic the work in which he treats of sensible perception 
 he endeavours to shew that space and time are the ' forms ' of 
 our sensitive faculty, while the pulses of sensation constitute its 
 matter. In the Transcendental Logic he deals with the ' forms ' 
 of intellect (Transcendental Analytic), and of reasoning (Trans- 
 cendental Dialectic] . The intellectual ' forms ' will be noticed 
 in Ch. 9 below. He gave them the name of Categories, a term 
 employed in a very different sense by Aristotle and his followers. 
 They are " the regular lines imposed by the intellect, on which 
 ' sensations settle down with unities, orders, sequences, identi- 
 ' ties " (Wallace, Kant, p. 70). The problems raised in the 
 Transcendental Dialectic fall outside the scope of the present 
 work. 
 
 (6) Logic of the Pure Idea. This is the name given by Hegel 
 
14 PRINCIPLES OF LOGIC 
 
 to his system. It will be sufficient for us to advert in the briefest 
 manner to this philosophy, with which we are only concerned 
 because of its bearing on Modern Logic. Its salient feature is 
 the identification of Logic and Metaphysics. Hegel would not 
 admit the existence of two orders an order of thought and an 
 order of reality. Thought, according to him, constitutes reality. 
 Hence the science of the real Metaphysics, is to be found in 
 Logic the science of thought : " Logic in our sense coincides 
 'with Metaphysics" (Wallace, Logic of Hegel, p. 38). The Uni- 
 verse has its origin in the inner necessity of the categories of 
 thought. But thought in its fullest development the thought 
 of the Whole or the Absolute Idea passes over into reality. 
 Thought becomes things, and realizes itself as the universe 
 which we know. 
 
 Hegelianism is in fact a form of Pantheism. In it things are 
 thoughts, and these thoughts are a Divine Mind evolving itself 
 in the process of the Universe. 
 
 (7) Modern Logic. The treatment of logical problems known 
 by this name owes its origin to the Hegelian philosophy. It is 
 plain that thinkers who deny the distinction between the order 
 of things external to us, and the order of thought within, were 
 bound to institute a new enquiry into the nature of those mental 
 acts, which had hitherto been regarded as representative of the 
 real order. The principal exponents of Modern Logic in England 
 are Mr. Bradley and Mr. Bosanquet : their work, however, is 
 very largely based on that of the eminent German logicians 
 Lotze and Sigwart. According to Mr. Bosanquet the only dif- 
 ference between Logic and Metaphysics lies in the aspect under 
 which they view the same subject matter. " I make no doubt," 
 he says, " that in content Logic is one with Metaphysics, and 
 ' differs if at all simply in mode of treatment, in tracing the 
 ' evolution of knowledge in the light of its value and import, 
 ' instead of attempting to summarize its value and import apart 
 ' from the details of its evolution " (Logic, I. 248). The opera- 
 tions of the mind judgment and reasoning are according to 
 this view regarded as vital functions, by which ' the totality we 
 ' call the real world ' is intellectually constituted. The task of 
 Logic is to analyse the process of constitution (ibid. p. 3). 
 
CHAPTER II. 
 
 THE CONCEPT : THE NAME : THE TERM. 
 
 i. The Concept. We have already explained what 
 are the grounds, on which Logic takes cognizance of the 
 Concept. Considered in isolation, the concept is not an 
 act by which the mind attains truth. It can neither be 
 termed true nor false. But concepts are the material of 
 which our mental acts, true and false, consist. Every 
 judgment of necessity contains two concepts. Hence 
 the treatment of the concept is fundamental in the science 
 of Logic. And in every science it is of vital importance 
 that the primary notions should be accurately grasped. 
 There is truth in that saying of Aristotle's, which in the 
 middle ages had passed into a proverb : " What is at the 
 ' beginning but a small error, swells to huge proportions 
 ' at the close." x 
 
 In the first place it is necessary to distinguish carefully 
 between the Concept or intellectual idea properly so 
 called, and the Phantasm or mental picture. Whenever 
 I think of an object, I simultaneously form a sensible 
 picture of it in my imagination. If for instance I judge 
 that ' Fishes are vertebrate,' or that ' The sun is 
 round,' I cannot do so without imagining to myself a 
 sensible representation of a fish, or of the sun. Some- 
 - times, indeed, as when I think of some abstract subject, 
 such as ' virtue,' the image of the mere word ' virtue ' 
 will serve my purpose : but some image is requisite, 
 nor does the intellect ever operate save in connexion 
 with a phantasm. 2 
 
 1 De Caelo, I. c. 5. rb lv apxy [UKpbv tv rrj reXevrrj yiveral Tra^^ycdes. 
 Parvus error in principio fit magnus in fine. 
 
 z The term 'phantasm' ((f>dvTu<r/j.a.) is Aristotle's. Thus in De Anima, III. 
 c. 8, he tells us that " when we contemplate anything, we are forced to con- 
 
16 PRINCIPLES OF LOGIC 
 
 This mental picture is however very different from the 
 concept. This will be easily understood, if we notice 
 that to judge ' The sun is round/ I must in thought have 
 separated the attribute of ' roundness ' from the thing I 
 term ' the sun.' No sensible image can effect such a 
 separation. It can only picture the single object ' a 
 round sun/ If again I say, ' This glass is transparent/ 
 I have in thought separated the attribute ' transparency ' 
 from the thing ' glass/ This power of separation requires 
 a higher faculty than that of the imagination, namely 
 the faculty of thought or intelligence. It is the intellect 
 alone that has this wonderful power of distinguishing 
 two things which in nature are inseparably conjoined, of 
 severing its roundness from the sun, its transparency from 
 the glass. Thus I can look at a single object, e.g., the 
 paper I am using, and consider separately its whiteness, 
 its smoothness, its oblong shape, its opacity, etc. 
 
 The mind's power of thus separating in thought things 
 which in the real order are one, is known as its power of 
 abstraction. 
 
 The characteristic feature by which the Concept differs 
 from the Phantasm, is its universality. A Concept is 
 equally representative of all objects of the same character. 
 Thus if I see a circle drawn on a black-board, the concept 
 which I form of that geometrical figure will express not 
 merely the individual circle before me, but all circles. 
 The figure I see is of a definite size, and is in a particular 
 place. But my mind by an act of abstraction omits these 
 individual characteristics, and forms the concept of a 
 circle as it is enunciated in Euclid's definition. This 
 concept is applicable to every circle that ever was drawn. 
 When however I form the phantasm of a circle/my phan- 
 tasm must necessarily represent a figure of particular 
 dimensions. In other words the concept of the circle 
 is universal : the phantasm is singular. Similarly, if I 
 form a concept of ' man/ my concept is applicable to all 
 
 template it in conjunction with a phantasm " (Srav re dewprj, 
 
 <f)dvTao-/jid TI Beajpelv) : and he proceeds to distinguish carefully between the 
 
 phantasm and the concept (v67jfj.a). 
 
THE CONCEPT : THE NAME : THE TERM 17 
 
 men. But a phantasm of a man must represent him as 
 possessed of a certain height, with certain features, with 
 hair of a definite colour, etc. 
 
 We have only to consider any object to see that all the 
 concepts which we can form of it, have this universal char- 
 acter. Thus, glancing out of the window, I see a garden - 
 roller. My mind conceives it as a roller, as cylindrical, 
 as iron, as dusty, cold and so on. Every one of these 
 concepts is universal, and thus applicable to any other 
 thing which resembles the roller in that one attribute, 
 no matter how much it may differ from it in others. 
 The concept of ' roller ' is equally applicable to the 
 ponderous machine with which the county-council repairs 
 the highways : that of ' cylindrical ' expresses perfectly 
 the shape of the candle on my mantel-piece : while the 
 concept of ' cold ' is appropriate to the water in the 
 neighbouring fountain. These various concepts are not, 
 of course, so many isolated units in the mind. They unite 
 to form a single composite concept. But that composite 
 concept is a universal, and would express all similar 
 rollers. 1 
 
 It must not be thought that the intellect has no means 
 of knowing individuals. It knows the individual by 
 advertence to the phantasm from which the universal 
 idea is abstracted 2 But the work of the intellect, as 
 distinct from that of sense , is to express the individual 
 object of sense-perception in a series oi universal con- 
 cepts. Thus it is the intellectual faculty which enables 
 at. to conceive the individual Socrates as a ' man,' or 
 as a ' vertebrate/ or as a ' father.' 
 
 1 The doctriue of this section is insisted on by Aristotle. " The universal 
 ' nature is evident to the intelligence, the individual to sense-perception. 
 ' For the intelligence deals with what is universal, and sense-perception with 
 ' what is particular (6 fjv yap \6yos rou Ka66\ov, i) 82 afodrjons rod Kara 
 1 [j.pos)," Physics, I. c. 5, 8. " The phantasm is as the perceptions of sense, 
 ' save that it is without material embodiment (rd yap (pavTaa/mara &<nrep 
 ' alaQ'/i/j.aTa tan irXrjv fiivev #X?7s)," De Anima, III. c. 8. For a further 
 consideration of the point, see Maher, Psychology (6th ed.), 235-238. 
 
 2 Vide St. Thomas, de Anima, III. lect. 8. The interpretation here given 
 by St. Thomas of the passage d^ Anima, III. c. 4, 7, is not only in full accord 
 with Aristotle's general doctrine, but is substantially the same as that pro- 
 posed by Themistius and by Simplicius. Cf. Rodier, Traite de I'dme, I.e. 
 Cf. also De Veritate, Q. II. Art. 6. 
 
 C 
 
r 8 PRINCIPLES OF LOGIC 
 
 2. Repugnant Concepts. Concepts are said to be 
 repugnant, when, as mutually exclusive, they cannot he 
 united in one composite concept. 
 
 It is not all concepts which can be brought together 
 to form a composite concept such as those described in 
 the last section. There are some which are incompatible, 
 so that the one necessarily postulates the exclusion of 
 the other. These are known as repugnant concepts. 
 Thus it is impossible to form the concept of ' a thinking 
 stone ' : for the concept of ' a stone ' expresses lifeless 
 matter, and the concept ' thinking ' expresses living 
 intelligence. Just as in the real order a thing cannot 
 both live and not live, so in the order of thought such a 
 thing is inconceivable. 
 
 The difference between what is inconceivable and what 
 is unimaginable should be carefully noted. There are 
 many things, that cannot be represented in our imagina- 
 tion, which nevertheless contain no repugnance as for 
 instance, colour to the blind from birth. On the other 
 hand, some things are quite inconceivable, and hence 
 impossible, of which I can form some kind of image. 
 Perhaps, it is possible to imagine a thinking stone. 
 
 3. Adequate, Clear and Obscure Concepts. A concept is 
 said to be adequate when it represents distinctly all the notes which 
 go to make up an object. It is plain that in regard to individual 
 things such concepts are impossible. We cannot form a concept 
 representing every characteristic of even the smallest flower. 
 We can however have adequate concepts of mathematical 
 figures in their universal aspect. Euclid's definitions express 
 adequate concepts of the figures with which they deal. A 
 concept is clear when, although it does not represent all l.he 
 notes of an object, it yet contains a sufficient number to dis- 
 tinguish that object from any other. Thus our knowledge of 
 nature may be very limited, but our concepts of the chief tribes 
 of animals have a degree of definiteness amply sufficient to en- 
 able us accurately to distinguish one from another. A concept 
 is obscure when our knowledge is insufficient to distinguish the 
 object of thought from other things. Thus a man may have 
 a general idea of what is meant by prudence and by fortitude 
 and may nevertheless be incapable of distinguishing prudence from 
 timidity, fortitude from rashness. 
 
THE CONCEPT: THE NAME: THE TETCM 19 
 
 4. The Name and the Term. We have intimated 
 (Ch. i, 2) that Logic takes account not only of thought, 
 but of language the verbal expression of thought. Hence 
 after the consideration of the Concept, we must say some- 
 thing of the Name. A Name is a word or group of words 
 which by convention signifies the concept of the speaker, 
 and the object of that concept. It is of importance to 
 observe that the name is immediately significative of 
 the concept, and only mediately of the thing : that is to 
 say, it is the name of the thing in question, because 
 the concept, which it immediately expresses, is the con- 
 cept of that thing. That this is so may be easily seen. 
 I can give the same name to many different indi- 
 viduals, because the same universal concept expresses 
 them all. Socrates, Plato, Peter, Paul are each of them 
 termed man. For one and all, in virtue of similar char- 
 acteristics, are truly represented by the same concept. 
 
 Names signify the particular characteristics contained 
 in the concept, which they express, but they are the names 
 of the thing, which the concept represents to us. 
 
 The Name is the expression of our thought, considered out 
 of all relation to its position in a proposition. Since Logic con- 
 siders names merely in so far as they are actual or possible terms, 
 we shall, in dealing with the distinctions which we are about 
 to enumerate, speak of them as distinctions of terms. The 
 distinction immediately following constitutes an exception for 
 reasons that will appear. 
 
 5- Categorematic and Syncategorematic Words. It 
 
 is plain, that it is not every word, which can be used as 
 a term. Many can only be so used in conjunction with 
 other words, e.g., in, but, well, me. Hence, we at once 
 distinguish words into two classes : 
 
 A Categorematic word is one, which can be used as a 
 term without being accompanied by any other word. 
 
 A Syncategorematic word is one, that can only enter 
 into a term in conjunction with other words. 
 
 These expressions are derived from the Greek words 
 Karyyopeiv to predicate, and crw together with. 
 
 Substantives, Pronouns, Adjectives and Participles 
 
20 PRINCIPLES OF LOGIC 
 
 are categorematic words. It will be noticed, however, 
 that adjectives and participles can only be predicates : 
 they cannot stand as the subject of a sentence, except 
 where there is ellipsis of the substantive. If we say, 
 ' The unjust shall perish/ ' unjust ' stands for ' unjust 
 men.' 
 
 Adverbs, Prepositions, Conjunctions, and Interjections 
 are syncategorematic. We can it is true employ them 
 as the subjects of those propositions in which we speak 
 of the mere words themselves ; as for instance, if we say, 
 ' When is an adverb of time/ ' When is a word of four 
 letters/ But in this case we use them in a different sense, 
 namely as signifying the mere vocal sound, or the written 
 characters. 
 
 A term which is composed of categorematic and syncate- 
 gorematic words, is spoken of as a many- worded term. 
 Terms consisting of a single categorematic word are 
 known as single-worded terms. 
 
 The student should be on his guard against speaking 
 of syncategorematic terms. If a word is said to be 
 syncategorematic, it is thereby affirmed to be incapable 
 of being a term. 
 
 6. Divisions of Terms. We enumerate here the 
 various divisions of terms. It should be observed that 
 every term may receive a place in each of the divisions, 
 since the various divisions are based on different principles. 
 What are called the logical characteristics of a term, are 
 expressed by referring it to its due position under each 
 head. All the divisions are of considerable logical 
 importance. 
 
 (1) General and Singular Terms. 
 
 (2) Concrete and Abstract Terms. 
 
 (3) Connotative and Non-connotative Terms. 
 
 (4) Positive and Negative Terms. 
 
 (5) Absolute and Relative Terms. 
 
 (6) Terms of First Intention and Terms of Second 
 Intention. 
 
 (7) Univocal, Equivocal and Analogous Terms. 
 
THE CONCEPT: THE NAME: THE TERM 21 
 
 7- Singular, General and Collective Terms. 
 
 A Singular term is one which can be used in the same 
 sense of only one individual thing. Such, for instance, 
 are ' the present king of Spain,' ' the capital city of 
 Italy,' ' Walter Scott.' To this class belong all proper 
 names. A Proper Name is a word whose sole purpose 
 is to denote an individual thing. Other Singular terms 
 which are not proper names, are called significant Singular 
 terms, since they tell us something about the object. 
 They are formed by using General terms, and restricting 
 them to designate but one of the many individuals to 
 which they might be applied. Thus ' king ' is a term 
 applicable to a number of individuals in history : but 
 if I say ' the present King of Spain,' I limit the sense 
 of the term to one of the class. A frequent way in which 
 terms are thus restricted, is by mentioning the time 
 and place to which reference is made. In the instance 
 just employed, the particular reference of the term ' king ' 
 is thus indicated. A proper name on the other hand 
 tells us nothing about the object. Its one purpose is 
 to serve as a distinguishing mark. Many proper names 
 indeed once had a meaning. But in so far as they are 
 used as proper names, the meaning they had is dis- 
 regarded, and they are employed solely for the purpose 
 of identification. 
 
 A General or Universal term is one which can be used 
 in the same sense distributively of many things. A term 
 is said to be used ' distributively ', when it can be applied 
 to each of the objects taken separately. Thus ' man,' 
 ' soldier,' ' Englishman,' ' white,' ' black,' are affirmed 
 of each of the objects to which they are applied. 
 
 It is not requisite that there should actually be a 
 plurality of objects, to which the name is applied. It 
 suffices, that it should be capable of such application. 
 Thus ' six-masted steam-ship ' is a term, which for very 
 many years was applicable to one ship only, ' The Great- 
 Eastern ' : but there was nothing in the nature of things 
 to prevent the existence of an indefinite number of six 
 masted steam-ships. 
 
 
22 PRINCIPLES OF LOGIC 
 
 It will be well to give careful attention to the way in 
 which these General terms are formed. The mind, 
 when considering some object, attends to some feature 
 in it, which is, or may be, precisely similar to features 
 present in other objects : and it abstracts from all other 
 features save this. Thus I may look at the ink in my 
 bottle, and abstracting from its liquid state, its taste, 
 etc., may consider it simply as black. The ink has 
 many other qualities besides this. It is, moreover, an 
 individual thing, and as such must have something in 
 it, which is absolutely peculiar to itself, and is possessed 
 by nothing else. But all this, my concept and the term 
 which manifests the concept do not express. The term 
 ' black ' may indeed be said to include implicitly all the 
 other qualities, for it does not exclude the supposition 
 that the subject which is black, possesses also many 
 other attributes. If the word ' black/ like the word 
 ' blackness,' involved the exclusion of everything save 
 the attribute of blackness alone, we could not say, ' The 
 ink is black/ just as we cannot say, ' The ink is black- 
 ness/ The term ' black ' neither excludes, nor explicitly 
 expresses the other attributes. 
 
 Then follows another step. I observe that my concept 
 of ' black ' is equally representative of all other black 
 objects. Mentally there is nothing to distinguish the 
 representations of an indefinite number of black things, 
 in so far as they are black. The same concept expresses 
 all. It is a Universal concept, and the word signifying 
 it is a General term. 
 
 It is thus that all our General terms arise. For 
 instance, experience shows us certain animals possessing 
 peculiar characteristics common to all alike. We group 
 the more marked of these characteristics into a concept, 
 e.g., that of a horse : and wherever we see an animal 
 possessed of these features, we term it a horse. The 
 characteristics thus expressed in a common concept 
 are styled the Intension or Comprehension of the General 
 term : the individuals to which the term is applicable 
 are said to constitute its Extension. Since the time of 
 
THE CONCEPT : THE NAME : THE TERM 23 
 
 Mill, English writers have more usually employed the 
 words Connotation and Denotation to signify respectively 
 Intension and Extension. 
 
 A Collective term is one that is applied to a group of 
 similar objects, the term not being applicable to the 
 objects taken singly. A Collective term may be either 
 a proper name, or a significant Singular term, or a General 
 term. Thus the term ' army ' is collective, since it is 
 predicable of the soldiers taken as a group, and not 
 singly. It is also a General term, for it is applicable to 
 many different armies. ' The National Portrait Gal- 
 lery ' is a Collective term signifying the pictures taken 
 together as a group. It is also a significant Singular 
 term. ' The Alps ' is a Collective term, which is a proper 
 name. 
 
 It is requisite to a Collective term that the objects 
 should be capable of being considered from some point 
 of view common to all. Thus the members of a family, 
 though differing in many points, are alike as sharers in 
 one home. For this reason, the definition requires that 
 there should be ' similar objects.' 
 
 The names of substances, such as ' water,' ' gold/ 
 ' lead,' are sometimes spoken of as Substantial terms. 
 When they are used to signify all the water or gold that 
 exists, they may be ranked as Singular terms. When 
 they are employed to signify different portions of the 
 substance, they become General terms. 
 
 8. Abstract and Concrete Terms. 
 
 An Abstract term is the name of a nature or attribute 
 considered in separation from the subject in which it 
 inheres, e.g., whiteness, height, ebullition, humanity. 1 
 
 A Concrete term is a name which expresses a nature 
 or attribute as inherent in a subject, e.g., white, high, 
 ebullient, man. 
 
 1 Subject in these definitions is used in a different sense from that in which 
 we have hitherto employed it. Hitherto we have been speaking of the sub- 
 ject of a proposition the subject of predication, as it is termed by logicians. 
 But real things are also termed the subjects of the qualities which inhere in 
 them : they are subjects of inhesion. It is in this sense that the word is 
 here used. 
 
24 PRINCIPLES OF LOGIC 
 
 We have already when speaking of the Concept ( i) 
 dealt with the abstractive power of the mind, in virtue 
 of which it is able to sever an attribute from the subject 
 in which it inheres, and to form such concepts as that 
 of ' whiteness.' Light will be thrown on this mental 
 operation, if we notice the distinction between a Sub- 
 stance and an Accident. A Substance is a thing which 
 can possess independent existence, as e.g., Peter, Paul, 
 man, lion. An Accident can only exist as inhering in 
 a Substance, e.g., whiteness, prudence, transparency. 
 In the Abstract concept we represent Accidents as 
 though they were isolated from the subject in which 
 they inhere. 
 
 The basis for this way of conceiving them, is found in 
 the fact that the Accident which inheres in a Substance 
 is not identical with the Substance. The whiteness of 
 the animal is not the animal itself. The colour of the 
 animal might alter, and yet the animal would be the 
 same individual as before. Hence the mind is naturally 
 led to conceive the quality as an independent entity, 
 as something which the animal has, and by which it is 
 determined and qualified. 
 
 But it is not Accidents alone which are expressed by 
 Abstract terms. By an act of the mind the substantial 
 nature itself can be represented in this abstract form, 
 as though it were an accidental determination. Thus 
 we form the concept of ' humanity/ though there is no 
 real distinction between the individual Peter and his 
 human nature. 
 
 Since these terms represent a single feature of the 
 whole entity, as if it existed independently and in isola- 
 tion, they possess a logical characteristic to which atten- 
 tion was called in the last section, viz. : that they cannot 
 be predicated of the subject to which they belong. We 
 can say, ' The horse is white ' : for the concrete term 
 ' white/ though it expresses but one attribute, yet 
 implicitly includes the whole object. We cannot say, 
 ' The horse is whiteness/ for the abstract term positively 
 excludes the subject in which it inheres. We can say 
 
THE CONCEPT: THE NAME: THE TERM 25 
 
 ' Socrates is man.' But we cannot say ' Socrates is his 
 humanity ' : for the abstract form of the word shows 
 that the characteristics, which Socrates has in common 
 with other men, in virtue of which he is called ' man/ 
 are alone to be considered, to the exclusion of those 
 which are proper to himself. 
 
 Abstract terms have no plural. The plurality that 
 a quality may have in the real order, it acquires in virtue 
 of the concrete individuals, in which it inheres. Hence 
 when we conceive it in isolation, we have no means of 
 conceiving it multiplied. Where plural forms are used, 
 as when we speak of ' enthusiasms ' or * ineptitudes,' 
 we merely mean the various instances in which the 
 quality was realized. The quality as abstract, is in- 
 capable of multiplication. It follows from this that 
 the only Abstract terms which are general, are those 
 which embrace a whole group of qualities. Thus * virtue ' 
 is a general Abstract term including ' justice/ ' pru- 
 dence/ ' temperance/ ' fortitude/ etc. But these latter 
 names are all singular. 
 
 Mill finds fault with " a practice, which if not introduced by 
 1 Locke, has gained currency chiefly from his example, of apply- 
 ' ing the expression ' Abstract name ' to all names, which are 
 ' the result of abstraction or generalization, and consequently 
 ' to all general names." The term ' Abstract name ' is, as Mill 
 notices, restricted by traditional usage to such as are con- 
 sidered in the present paragraph. Its application to General 
 terms is a mistake. On the two kinds of abstraction see 
 St. Thomas, Summa Theol. I. Q. 40, Art. 3. 
 
 9- Connotative and Non-Connotative Terms. This 
 distinction is one of the traditional divisions of terms. 
 Its signification in recent English Logic is, however, 
 altogether different from that which it used to bear. 
 The change is due to Mill, who imposed a new mean- 
 ing on the old terminology. The former sense of 
 the words has fallen almost altogether into oblivion 
 among English writers, and on the other hand much 
 has been written on the distinction in its novel sense. 
 We shall therefore deal in the first place with the terms 
 
26 PRINCIPLES OF LOGIC 
 
 in their recent acceptation, and subsequently add an 
 account of their traditional meaning. 
 
 The definitions given by Mill are as follows : 
 A Connotative Term is one which denotes a subject 
 and implies an attribute. A Non-connotative Term is 
 one which denotes a subject only, or an attribute only. 
 
 (i) Connotative Terms. We have already mentioned 
 ( 6) that the word Connotation is understood by logi- 
 cians to mean the characteristics signified by a name : 
 the word Denotation, to mean the individual objects 
 to which it is applicable. Every term which possesses 
 both these features is termed Connotative. Thus ' horse/ 
 ' man/ ' the Czar/ ' courageous/ are Connotative terms. 
 They are applicable to individual objects, and they are 
 given to these objects, because certain definite char- 
 acteristics signified by the name are present in them. 
 
 Not all the characteristics possessed by the individuals 
 in question enter into the connotation of the name. 
 The characteristics which constitute the connotation 
 are those only, because of which the name is given, and 
 in the absence of any of which it would be refused. Thus, 
 though before the discovery of Australia all swans of 
 which the civilized world had experience were white, 
 no one dreamed of refusing the name swan to the newly- 
 discovered black variety. Nor do we deny the name 
 of cat to Manx cats because they lack a tail. But the 
 absence of a single essential attribute would deprive the 
 object of its right to the class-name. Were an animal 
 discovered, otherwise like the horse in appearance, but 
 with cloven feet, it should not be termed a horse. 
 
 The explanation just given assumes that words possess 
 a fixed and precise meaning. This is of course an ideal 
 not altogether realized. The English language, perhaps 
 even more than others, is lacking in this scientific pre- 
 cision. Yet it will usually be found that among the 
 educated, there are definite and assignable characteristics 
 implied by a name, in default of which it is not applied 
 to an individual. It is true that'this connotation may 
 
THE CONCEPT: THE NAME: THE TERM 27 
 
 vary. Our knowledge as to the real nature of things 
 increases ; and thus we insensibly alter the significa- 
 tion of a name. Mediaeval writers would have under- 
 stood the term ' whale ' as connoting a special kind of 
 fish. We have learnt that the whale is not a fish but a 
 mammal. There are comparatively few things, as to 
 which we are sure that we possess the ultimate connota- 
 tion. In the case of mathematical figures, we know it, 
 for the law determining the construction of a geome- 
 trical figure is within our mental grasp. But even when 
 a connotation is susceptible of change, these changes 
 are not arbitrary. Science only calls on us to alter the 
 connotation of a term, when it has found some more 
 fundamental characteristic, in relation to which, those 
 hitherto reckoned as its connotation are merely deri- 
 vative. Thus the advance of knowledge is ever tending 
 to greater fixity of connotation, to the discovery of 
 what the name ought to mean. 
 
 Two other views as to the connotation of a term call 
 for mention, though neither of them is defensible. 
 
 Some writers have held that all the attributes possessed 
 by the object of the name, whether they are known or 
 unknown, constitute its connotation. This is the view 
 of Prof. Jevons : " A term taken in its intent (i.e. conno- 
 ' tation) has for its meaning the whole infinite series of 
 ' qualities and circumstances, which a thing possesses." 
 It is plain that if the term primarily represents the 
 concept, its connotation must concern the thing as it is 
 known, not the thing in its objective reality. The mean- 
 ing of the term is what the thought represents to us. 
 
 Others have held that it should be taken to signify 
 all that we know about the thing at the present time. 
 But many of these attributes are quite unimportant, 
 and their absence would never cause us to refuse the 
 name to an object. Hence it is manifestly inaccurate 
 to speak of them as the meaning of the term. The only 
 satisfactory account of connotation is that which takes 
 it to signify the fundamental characteristics, which 
 determine the application of the term. 
 
28 PRINCIPLES OF LOGIC 
 
 It is frequently given as a rule that, ' As connotation 
 ' increases, denotation decreases : and as denotation 
 'increases, connotation decreases.' This however must 
 be rightly understood. The rule is only true when we 
 are dealing with a number of classes arranged in hier- 
 archical subordination. Thus in the series, Animals 
 vertebrates mammals felidae lions, we have such a 
 series. The connotation of ' vertebrate ' is greater 
 than that of ' animal ' : the denotation is less. The 
 connotation of ' lion ' is the greatest of all : its denota- 
 tion is least. 
 
 Except where we are dealing with such classes, the 
 rule is not verified. Thus I may increase the connota- 
 tion by adding some attribute, which is found in every 
 member of the class, as for instance crow black crow. 
 Here no change takes place. Again the denotation of 
 a term is increased by the birth of new individuals : 
 but this makes no change in the connotation. It is, 
 moreover, inaccurate to state the rule in mathematical 
 language, thus : " Connotation and denotation vary 
 1 in inverse ratio." There is no mathematical relation 
 between the two. One alteration in connotation may 
 make an immense change in denotation, as e.g. zebra 
 tame zebra. 
 
 (2) Non-connotative Terms. The first kind of Non- 
 connotative terms mentioned by Mill are those which 
 denote a subject only, not connoting any attribute. 
 This group consists solely of proper names. These are 
 merely distinguishing marks of the individuals, and are 
 not held conditionally on their retaining certain definite 
 qualities. Connotative names on the other hand are 
 changed when the quality changes : the man we once 
 called ' thin,' we afterwards call ' stout.' For Connota- 
 tive names primarily signify the characteristic or quality, 
 and secondarily the individual object to which they 
 are applied. It is entitled to the name, because it pos- 
 sesses the quality. Proper names have no meaning in 
 this sense. A man cannot claim a proper name because 
 he possesses certain qualities. However zealous a 
 
THE CONCEPT : THE NAME : THE TERM 29 
 
 philanthropist he may be, he cannot ask us to call him 
 Lord Shaftesbury. 
 
 This point has been contested by Mr. Bradley and 
 others, on the ground that names grow to acquire a 
 connotation, and that the name of a friend recalls his 
 qualities to my mind. It is true that it may recall them. 
 But they do not therefore constitute the connotation 
 of the name. The proper name designating an individual 
 recalls his qualities by association. So far are they 
 from forming its connotation that though the individual 
 may lose them, he will not thereby lose his title to his 
 name. 
 
 It has been further urged that many proper names 
 do in fact signify definite attributes. Thus ' John 
 Smith ' is said to signify ' man ' and ' Teuton/ Has 
 then every male Teuton a right to term himself John 
 Smith ? And is not ' John Smith ' in all probability 
 the proper name of not a few negroes ? It can scarcely 
 be urged that this name is really significative of attributes. 
 Again, it is true that many proper names of places and 
 families originally indicated the possession of certain 
 attributes, e.g., ' Norfolk/ ' Edinburgh/ ' Southampton/ 
 ' Grosvenor.' But these have long lost all connexion with 
 the meaning they once had. Nor can any argument 
 be drawn from the fact that it is possible to use such 
 terms as ' a Don Quixote ' as connotative. Such a use 
 indicates that the word has ceased to be a proper name. 
 
 The other kind of Non-connotative terms are Abstract 
 names. These signify an attribute only. The question 
 has been raised whether these terms are rightly reckoned 
 as non-connotative. Several logicians maintain that 
 there is no term without denotation. They hold that 
 Abstract terms denote an object, namely the quality 
 which they connote ; that their denotation and conno- 
 tation coincide. A consideration of what the denota- 
 tion of a term truly is, will shew that this view cannot 
 be admitted. The denotation consists of the real objects 
 expressed by the concepts. Now there is nothing in 
 the real order corresponding to the Abstract term. In 
 
30 PRINCIPLES OF LOGIC 
 
 that term our concept represents the attribute as though 
 it were an independent entity. That is to say, it repre- 
 sents it in a way in which no attribute can exist in the 
 real order. These terms therefore have no denotation. 
 
 * The meaning attached to this division of terms by the 
 Scholastic logicians was altogether different from that which 
 we have just discussed. They distinguish them as follows : 
 
 A Connotative term is one which expresses an attribute as qualify- 
 ing a subject. 
 
 A Non-connotative term is one which expresses a nature or attri- 
 bute as an independent entity. 
 
 All adjectives are connotative terms : for each adjective signifies 
 some special attribute as qualifying some person or thing. Thus 
 ' courageous ' signifies the attribute of ' courage ' as determining 
 some subject. ' Prudent ' similarly signifies the attribute of 
 ' prudence ' as qualifying a person. l On the other hand all 
 substantives, as ' man,' ' father,' ' humanity,' ' paternity,' sig- 
 nify some entity that is conceived as independent and not as 
 the qualification of a subject. 
 
 The logical value of the distinction depends on the difference 
 that there is in the real order between Substances and Accidents. 
 Substances are expressed by nouns-substantive. Accidents on 
 the other hand are expressed by adjectives : for an accident is 
 not an independent entity, but a mere qualification of a sub- 
 stance. Hence a distinction between them is necessary in the 
 conceptual representation of the real order : and this distinc- 
 tion is expressed by the Non-connotative and the Connotative 
 term. Yet, as we have already had occasion to notice, the 
 power of the intellect enables it to conceive things otherwise 
 than as they actually exist. It can conceive the accident as 
 though it were an independent entity. 2 When it does so it em- 
 ploys the abstract term, and that term is a substantive and is 
 non-connotative. 
 
 The Scholastic distinction is therefore philosophically justified. 
 It corresponds to a fundamental difference in our mental con- 
 ceptions, and the logic of the concept would be incomplete 
 without it. 
 
 Mill, as an adherent of the Empiricist school, rejected the 
 distinction between substance and accident. There was there- 
 
 1 These Connotative terms when considered in relation to the character- 
 istic, the presence of which they signify, and from which they are etymologically 
 derived, were called Denominatives (-n-apuvvfjia. Categ. c. i, 5, c. 8, 27). 
 The abstract attribute was termed the Denominant. ' 
 
 2 The abstract term does not represent the accident as a substance, but 
 simply as an independent determination. Only concrete terms can repre- 
 sent substance. 
 
THE CONCEPT: THE NAME: THE TERM 31 
 
 fore no place in his logic for a division of terms which involved 
 its recognition. He solved the difficulty that thus presented 
 itself, by putting all general terms signifying substances on a 
 par with adjectives, and transferred them en bloc to the class 
 of connotative names. The resulting division is devoid of philo- 
 sophical value. A division of terms in the science of Logic must 
 express different ways of conceiving the real order : and when 
 a class of terms is designated by a common name, this should 
 indicate that all these terms are conceived in a similar manner. 
 This is certainly not the case in regard to Mill's Non-connotative 
 terms. Proper names and Abstract names have conceptually 
 nothing in common. Proper names are not significant of any 
 concept at all : they simply denominate individual objects of sense- 
 perception. 
 
 10. Positive and Negative Terms. 
 
 A Positive Term is one which signifies the presence 
 of some attribute. 
 
 A Negative Term is one which signifies the absence 
 of some attribute. 
 
 Thus as examples of Positive terms, we may take 
 ' living/ ' present/ ' equal ' ; and as examples of Nega- 
 tive terms ' lifeless/ ' absent/ ' unequal/ ' not-man/ 
 ' nonentity/ A special class of Negative terms is con- 
 stituted by what are called Privative Terms. These 
 express the absence of the attribute in an object in which 
 it might have been expected to exist, as for instance ' blind/ 
 ' dumb/ It would be correct to speak of some animal- 
 culae as ' sightless ' or ' eyeless/ but not as ' blind ' : 
 for the term ' blind ' implies the absence of sight where 
 it is normally to be found. 1 
 
 It should be noted that very many Negative terms, such 
 as, e.g., 'impatient/ 'careless/ 'inhospitable/ are under- 
 stood to imply the presence of positive qualities, opposite 
 to those designated by the corresponding Positive terms. 
 There is, however, one class of Negative terms to which no 
 possible positive signification can adhere, and which have 
 as Mr. Keynes says, ' a thorough-going negative character. 
 These are terms of the form ' not-man/ ' not-white/ 
 They denote everything which does not possess the 
 
 1 On Privative terms see St. Thomas, SummaTheol. i. Q. 33, Art. 4, ad. 2. 
 
32 PRINCIPLES OF LOGIC 
 
 positive quality to which the negation is attached. They 
 are called Infinite (Le. Indeterminate) terms (nomen 
 infinitum, ovo/ma aopurrov). The name was given them 
 by Aristotle, because they do not fulfil the natural 
 purpose of the name, which is to designate some deter- 
 minate character or some definite individual. They 
 are wholly indeterminate in their signification : the 
 term ' not-man ' is equally applicable to what is real and 
 to the unreal. I can say ' A horse is not-man,' and ' A 
 griffin is not-man.' 
 
 Certain recent logicians have denied that it lies within 
 our power to form a concept of ' not-man.' They assert 
 that we cannot hold together in a single thought things 
 which have nothing in common. It is quite true that 
 we cannot hold together things which have nothing in 
 common, by means of a positive concept. We can 
 however do so by a negative concept. The logical 
 significance of the Negative term lies in this very fact, 
 that it witnesses to our power to conceive the absence 
 of some quality as though it were a positive reality. 
 We conceive negations as though they were real things : 
 we give them conceptual realization. The very fact 
 that these terms can stand as the subject or predicate 
 of a sentence is a proof that there is a thought cor- 
 responding to them. 1 Were it not for this power of 
 conceiving by negations, we should have no thought 
 corresponding to the word ' nothing.' It is true we cannot 
 imagine ' nothing ' : but we can conceive it. The pro- 
 position ' Created Being was once nothing ' gives an 
 intelligible sense. Similarly we can form concepts of 
 not-man,' ' not-white.' 
 
 ii. Absolute and Relative Terms. 
 
 An Absolute term is a name, which in its meaning 
 implies no reference to anything else. 
 A Relative term is one, which, over and above the 
 
 1 ' Quia tamen [nomen infinitum] significat per modum nominis quod 
 potest subjici et praedicari, requiritur ad minus suppositum in apprehen 
 sione." St. Thomas in Periherm. lect. 4, If. Excludit quaedam. 
 
THE CONCEPT : THE NAME : THE TERM 33 
 
 object it denotes, implies in its signification another 
 object also receiving a name from the same fact which 
 is the ground of the first name. 
 
 We are all familiar with certain names which are 
 given in pairs ; so that if an object exists, to which one 
 of the two may be applied, we know that there must 
 also be an object to which the other may be applied. 
 Such are ' parent, child/ ' master, servant/ ' king, 
 subject/ ' husband, wife/ ' equal, equal/ etc., etc. If 
 it can be truly affirmed of any one that he is a parent, 
 then there is also some one of whom the term ' child ' 
 is predicated. If there is a master, there must also be 
 a servant. Such terms are known as Relative terms : 
 and each is said to be the correlative of the other. When 
 a term does not involve a correlative, it is known as 
 Absolute. 
 
 It should be carefully observed that the mere fact 
 of a relation between two objects, does not make their 
 names Relative names. Peter and Andrew are not 
 Relative names, though the two men be brothers. For 
 a name to be Relative, it must be such as to express a 
 concept in which the relation is the object of thought. 
 Now I can conceive Peter, without thinking of him as 
 a brother : his brotherhood may be altogether outside 
 my mind's field of vision. But if I think of him as 
 brother, then in my thought I necessarily refer him to 
 the person whose brother he is, and my thought is a 
 relative concept. The Relative term for the case in 
 question must be one that signifies such a relative con- 
 cept. It must express Peter precisely under the aspect 
 of his connexion with Andrew : it must be the term 
 'brother' (Categ. c. 7, 8). 
 
 A Relative term may be concrete or abstract. If 
 the name signifies the related object, we have the con- 
 crete relative, e.g., ' master/ ' father.' If we express 
 the relation in separation from the object to which it 
 belongs, it is abstract, e.g., ' dominion/ ' paternity.' 
 Abstract relatives have their correlative terms. Thus 
 ' paternity ' corresponds to ' filiation/ ' dominion ' to 
 
 D 
 
34 PRINCIPLES OF LOGIC 
 
 ' subjection/ the ' friendship ' of the one friend to the 
 ' friendship ' of the other, the ' equality ' which is pre- 
 dicated of one of two equals, to that which is predicated 
 of the other. 
 
 The logical significance of this division of terms will 
 not have escaped notice. We are here dealing with a 
 special way in which the mind can represent the real 
 order. It is capable on the one hand of representing 
 its object in isolation : and on the other it can represent 
 it in the light of the connexion by which it is related 
 to something else. Further, it can fashion relations, 
 even when they do not exist in the real order. Thus it 
 can conceive a thing, which is viewed under one aspect, 
 as ' identical ' with itself viewed under another aspect. 
 Yet in the real order there can be no such thing as a 
 relation of ' identity.' To have a real, as distinguished 
 from a merely conceptual relation, there must be two 
 things, not one only. 
 
 12. Terms of First and Second Intention. This 
 distinction has been omitted by many of the recent 
 English logicians. 1 It is, however, of the highest import- 
 ance ; and the student who has thoroughly grasped its 
 significance, will find his labour in the study of Logic 
 much lightened. 
 
 A term of First Intention is one which is applicable 
 to the object, as it exists in the real order. 
 
 A term of Second Intention is one which is applicable 
 to the object, only as it exists in the conceptual order. 2 
 
 Of the terms which may be predicated of an object 
 as signifying its attributes, not all belong to it as it is 
 in the real order. Some belong to it only in so far as 
 it is represented in the mind. Thus I may not only 
 say, ' The oak is a forest-tree,' ' The oak is deciduous ' ; 
 but I may go on to say, ' The oak is the subject of my 
 
 1 See however an accurate account by Sir William Hamilton in Edinburgh 
 Review, vol. 57, p. 210. " The distinction," he there says, "is necessary to be 
 ' known, not only on its own account as a highly philosophical determination, 
 ' but as the condition of any understanding of the Scholastic Philosophy." 
 
 2 Cf. St. Thomas, Opusc. 39, De Natura Generis, c. 12. 
 
THE CONCEPT : THE NAME : THE TETCM 35 
 
 judgment/ ' The oak is a universal concept.' Here, 
 as is manifest, I have two totally different orders of pre- 
 dicates. One sort belongs to the object in its own natural 
 mode of existence : the other belongs to it in so far as 
 it is represented conceptually, in so far that is, as it is 
 realized in the logical order. To this class of terms 
 belong many with which we shall have to deal in sub- 
 sequent chapters, such as genus, species, major, minor 
 and middle term, etc. These two orders of predicates 
 are called respectively terms of First Intention and 
 terms of Second Intention. The terminology will be 
 understood, when it is remembered that intentio is a 
 word used by the mediaeval logicians to signify ' an 
 act of the mind.' The first act of the mind is that by 
 which the mind conceives and knows the thing as it is 
 in the real order : the second act of the mind is that by 
 which it knows the thing as it is in the conceptual order. 
 The reason why we claim that the distinction is of 
 primary importance, is that Logic is wholly concerned 
 with the consideration of things as they are in the con- 
 ceptual order, with things as they are mentally repre- 
 sented, and hence as they are subjects, predicates, 
 universal terms, etc. It is not concerned with the real 
 order as such, but with the manner in which the mind 
 represents that real order. Hence Logic is wholly con- 
 cerned with Second Intentions : and it was not without 
 cause that the mediaeval logicians defined it simply 
 as the Science of Second Intentions. 
 
 Thus St. Thomas, Opusc. de Universalibus, c. 2, ' Logica princi- 
 ' paliter est de secundis intentionibus.' Scotus, Super Univer- 
 salia Porphyrii, Q. 3, quotes the saying that ' Logic deals with 
 ' Second Intentions as applied to First,' which he attributes to 
 Boethius. It is however said not to occur in that author's works. 
 Goudin (1640-1695) says, ' Omnes Thomistae assignant ens 
 ' rationis seu secundas intentiones pro objecto formali Logicae.' 
 Logica Maj. Quaest. Prae. Art. i. This distinction first appears 
 in the works of the Arabian commentators on Aristotle. 
 
 13- Univocal, Equivocal and Analogous Terms. 
 
 A Univocal Term is one which is always employed with 
 
36 PRINCIPLES OF LOGIC 
 
 the same intension. An Equivocal term, on the other 
 hand, is one which can be used to express two entirely 
 different meanings, as e.g. the word ' bit ' is used to 
 signify either a morsel or part of a horse's harness. Equi- 
 vocal terms are of no logical importance. Properly speak- 
 ing an equivocal term is not one but two terms. An 
 Analogous Term is one which is employed to express 
 meanings partly, but not wholly, the same. These terms 
 are of two kinds, (i) One class do not, for our purpose, 
 differ from Equivocal terms. The word ' healthy ' may 
 serve as an example. As applied to a man, it means that 
 his physical condition is satisfactory. As applied to food, 
 it signifies, not that the food is physically sound, but that 
 it is calculated to produce health in man. The two 
 meanings here, are as distinct as those of an Equivocal 
 term. (2) The other class of Analogous terms must be 
 carefully noticed. These terms do not, it is true, like 
 Univocal terms, convey precisely the same meaning 
 wherever they are employed. When an Analogous term 
 is applied to objects between which the analogy exists, 
 its meaning in the two cases is in so far different, that the 
 characteristic signified is present in different grades. Yet 
 we can express both forms of the characteristic in ques- 
 tion by a single concept, because there exists between 
 them a likeness of proportion (ai/aXo-yio), When for 
 instance we say that God is the ' cause ' of the world, and 
 that the sculptor is the ' cause ' of the statue, the word 
 ' cause ' is analogous. God causes the world in a differ- 
 ent sense from that in which the sculptor causes the 
 statue. Yet owing to the proportional resemblance be- 
 tween the two cases, we can form an Analogous concept, 
 and employ an Analogous term. Similarly the word * thing ' 
 is analogous. W T e say that a man is a ' thing/ and that 
 a thought is a ' thing ' ; but a man and a thought are 
 not things in the same sense. 
 
 14. Opposition of Terms. Terms can be opposed to 
 each other in the following ways : 
 
 (i) Contradictory Opposition is the opposition between 
 
THE CONCEPT : THE NAME : THE TERM 37 
 
 a term and its negation, e.g. 'man, not-man,' 'white, 
 not-white.' It is characteristic of this opposition that 
 the two terms are not merely mutually exclusive, but 
 they are exhaustive of all possible things. Everything, 
 no matter what it be, whether it be matter or spirit, 
 real or unreal, is either white or not white. 
 
 The opposition which exists between Repugnant terms 
 ( 2), e.g. between ' red ' and ' white/ is a special case of 
 Contradictory Opposition. The reason they exclude each 
 other, lies in the iact that while both are colours, they are 
 colours of different species. What is red cannot be also 
 white. It is not -white. 
 
 (2) Contrary Opposition is the opposition between two 
 classes, which are furthest removed from each other among 
 those which belong to the same genus. Such are, for 
 instance, ' white, black/ ' pious, impious/ ' kind, cruel/ 
 This opposition arises because our concepts of certain 
 series of qualities represent them as passing by gradation 
 from one extreme to the other : there is no abrupt tran- 
 sition such as is found to exist between contradict opies. 
 Where this gradation of qualities is found, the extremes 
 are known as contraries. 
 
 Many logicians speak of Contradictory opposition as 
 formal, because it can be symbolically represented as 
 * A, not-A ' : Contrary opposition they term material, 
 because we are unable to say whether two terms are con- 
 traries, unless we know the actual things which they 
 signify. On the view of Logic which we are defending, 
 there is no room for this distinction. The mental pro- 
 cesses which can be symbolically represented, do not 
 differ in any essential from those which cannot. The 
 mind recognizes Contrary opposition between the con- 
 cepts ' pious ' and ' impious/ ' white ' and ' black/ 
 precisely in the same manner as it recognizes the Contra- 
 dictory opposition between ' A ' and ' not-A/ 
 
 15. The 'Suppositio' of the Term. Even where 
 vo are dealing with one and the same univocal term, 
 there are various ways in which it may be construed. 
 
3 8 PRINCIPLES OF LOGIC 
 
 The same term may stand for something different. 
 These various uses of the term were termed by the Latin 
 logicians its suppositiones, (from supponere, ' to stand 
 for'). Although a little repetition may be involved, 
 it will be well to distinguish here the principal among 
 the different ways in which a term may be used. 
 
 (1) Collective and Distributive use. When anything is 
 affirmed or denied of a plural subject, the predicate may 
 apply either to the individuals, who constitute the subject, 
 taken separately, or to them taken as a group. The 
 former is known as the distributive use (suppositio dis- 
 tributiva) of the term ; the latter as the collective use 
 (suppositio collective^ . The propositions, ' The citizens 
 raised a monument to the dead statesman,' and ' The 
 citizens voted in the election,' will sufficiently illustrate 
 the two cases. 
 
 (2) Real and Logical use. This distinction depends 
 on whether the speaker refers to the object as it is in the 
 real order, or as it is in his concept. Thus, if I say " The 
 King of England is at Windsor," the use is real (suppositio 
 realis). If I say, " ' The King of England ' is the sub- 
 ject of my sentence," the use is logical (suppositio logica). 
 
 (3) ' Suppositio materialist When a word is taken to 
 signify simply the spolcen sound, or the written symbol, 
 it is said to be used in its suppositio materialis, e.g. 
 " ' To run ' is a verb." " ' Run ' is a word of three letters.''* 
 
CHAPTER III. 
 
 THE JUDGMENT AND THE PROPOSITION. 
 
 i. The Proposition. As the Term is the external 
 expression of the Concept, so the Proposition is the 
 expression of the Judgment. The Proposition may 
 be defined as a verbal expression in which we affirm 
 or deny an attribute of a subject (de Inter p. c. 6, i). 
 It is also sometimes defined as a verbal expression 
 enunciating a truth or falsity (de Interp. c. i) : for it 
 is characteristic of every proposition that it must be 
 either true or false. The form of the proposition is 
 5 is (or is not) P, e.g. ' The lion is vertebrate/ ' Caesar is 
 not alive.' 
 
 A proposition of the kind we have described, is commonly 
 known as the Categorical Proposition, to distinguish it 
 from Conditional propositions. In these we do not assert 
 the attribute of the subject absolutely : we merely affirm 
 that, given certain conditions, it belongs to it. In regard 
 to the Categorical proposition, the following points are 
 to be noted : (i) It is always in the indicative mood. 
 In the other grammatical moods, the mind does not judge 
 that the attribute belongs to the subject, but expresses 
 a wish that it may be so, or gives an injunction that it 
 should be so. In the indicative alone we affirm (or deny) 
 the attribute of the subject. Thus we have, ' The messen- 
 ger is speaking/ ' May the messenger speak ! ' ' Speak, 
 messenger ! ' So too it is only when the attribute is 
 affirmed of the subject that the mind reaches truth or 
 falsity. For truth is attained when the mind assigns to 
 the subject an attribute which belongs to it in the 'real 
 order. (2) The logical proposition is always stated in 
 
4 o PRINCIPLES OF LOGIC 
 
 the present tense. Our purpose in Logic, as we have seen, 
 is to study the mode in which the mind represents the 
 real order. As regards this the question of present, past 
 or future is purely accidental. The time-determination 
 does not affect the mental representation as such. Hence 
 differences of tense so necessary in the use of language 
 for practical ends have no place in Logic. (3) The 
 logical predicate is always separated from the copula. 
 In the language of common life, we frequently express 
 them in one word, as for instance, ' The bird flies/ In 
 Logic we must say, ' The bird is flying.' 
 
 This same process must be performed whenever we get 
 mutilated expressions, such as * Wolf ! ' ' Fire ! ' ' Rain ! ' 
 For Logic demands that every sentence, whatever its 
 grammatical form, shall be so analysed and expressed, 
 as to represent as closely as possible the intellectual act. 
 Sir W. Hamilton stated this in what is sometimes termed 
 Hamilton's Postulate, viz. : ' Logic postulates to be allowed 
 'to state explicitly in language, whatever is implicitly 
 ' contained in thought/ Our three mutilated expres- 
 sions may be respectively resolved into, ' A wolf is near/ 
 ' A fire is burning/ ' Rain is falling/ 
 
 We must carefully distinguish between the ' is ' of the 
 copula, and the same word when it means * to exist/ 
 The copula does not signify that the subject exists. 1 
 I may say ' A chiliagon is a geometrical figure/ even 
 though no chiliagon has ever existed. The copula in 
 affirmative sentences denotes the objective identity of 
 the subject and predicate : they are expressions repre- 
 senting one and the same object. In negative sentences 
 the copula 'is not' signifies the objective diversity of 
 the terms : the predicate is not applicable to the object 
 denoted by the subject. I may say, ' The lion is verte- 
 brate/ because the term ' vertebrate ' is rightly applied 
 to the same object as the term ' lion/ I cannot say 
 ' The octopus is vertebrate/ This relation between the 
 subject and predicate of the proposition, arises immedi- 
 
 1 The question of the ' Implication of Existence ' in the copula, will be 
 more fully dealt with in Ch. 7. 
 
THE JUDGMENT AND THE PROPOSITION 41 
 
 ately from the nature of the mental act which the pro- 
 position represents the judgment. In every affirmative 
 judgment the two terms are different mental expressions 
 of the same object. The same object is expressed in one 
 concept as ' lion/ in another as ' vertebrate/ But the 
 object which I conceive as ' octopus/ I cannot conceive 
 also as ' vertebrate/ Hence the judgment, ' The octopus 
 is vertebrate/ is impossible. 
 
 Here we see how totally Scholastic Logic differs from 
 Formal Logic. Strictly, Formal Logic should take no 
 account of the content of the subject and predicate. To 
 it every judgment is simply 5 is P. Scholastic Logic 
 rejects any judgments in which the concepts do not repre- 
 sent the same objective reality, e.g. ' Men are circles/ 
 ' Cows are lions/ In these the two notions are repugnant 
 the one to the other. The judgment is impossible. 
 
 2. Analysis of the Judgment. Although as we have 
 seen, the subject and predicate of the judgment are 
 different concepts of the same thing, it is important to 
 bear in mind that it is the subject which directly ex- 
 presses the thing, i.e. that to which attributes belong. 
 The predicate expresses the thing as qualified by a par- 
 ticular attribute or form.' 1 Whenever we fix our attention 
 on a thing, our mind immediately commences to abstract 
 the attributes from the object of thought, and affirm 
 them of it one by one. It judges : ' The thing is hard 
 is black is brittle, etc/ 2 Here the predicate in each 
 case is the attribute or form not indeed the attribute 
 considered in separation from the object in which it 
 inheres, i.e. hardness, blackness, etc., but considered as 
 qualifying the thing. It is easy to see how such judg- 
 ments develop into more complex ones. The hard, 
 
 1 Cf. St. Thomas, Summa Theol. I. Q. 13, Art. 12. 
 
 2 " Cost done grace a 1'abstraction intellectuelle que les choses sont ai- 
 ' firmables les unes des autres, et peuvent faire fonction de predicat dans les 
 'propositions." Mercier, 31. Similarly Themistius, commenting on Arist. 
 De Anima, III. vi. 2, says ' 17 i^ev yap ws v <pavTdcTai TOT fiadifovTa ~2(i}Kpd.Tr)v, 
 ' 6 vovs de oicupe? XU^HS /J.et> rbv S., x w P<* ^ TO fiadtfa ' " The sense-faculty 
 ' gives us the phantasm of Socrates walking as a single whole : the intellect 
 ' abstracts, and separates Socrates on the one hand from is walking on the 
 other." Them. 202, 10 cited in Rodier, Traite de I'dme, II. 471. 
 
42 PRINCIPLES OF LOGIC 
 
 brittle thing will be called ' coal ' : and the judgment 
 will take predicates of a less primary character. 1 
 
 A judgment is said to be true when the form expressed 
 by the predicate is really found in the object denoted 
 by the subject. Thus, if I see some object, e.g. Socrates, 
 and I judge ' Socrates is walking/ my judgment is a true 
 one if the attribute ' walking/ which I affirm of Socrates 
 in thought, does in fact belong to him in the real order. 
 Hence truth is defined as the conformity of the mind with 
 its object. For in every true affirmative judgment the 
 mental concept expressed in the predicate is in con- 
 formity with a real attribute belonging to the external 
 object. As regards negative judgments the case is some- 
 what different. In them we declare that the form ex- 
 pressed in the predicate is not to be found in the object 
 to which the judgment refers. Yet in a somewhat wide 
 sense we can say that in negative judgments also the 
 mind is conformed to its object. In judging a form not 
 to belong to an object which in fact does not possess it, 
 my mind is in correspondence with reality. But nega- 
 tion is a secondary and subsidiary form of truth. In 
 affirmation there is perfect correspondence between the 
 mental form expressed in the predicate and the object- 
 ive reality. 2 
 
 Grammatically the subject does not always take the 
 first place. It is the meaning of the proposition, not 
 the arrangement of the words, which tells us which is the 
 subject and which the predicate. The term which quali- 
 fies or defines the other, whether it comes first or last, is the 
 predicate. Thus in the words, ' Blessed are the meek/ 
 it is the meek who form the logical subject. 
 
 We have stated in the previous section that the copula 
 expresses the objective identity of the subject and predi- 
 cate. We must now enquire why this identity is expressed 
 by the verb ' to be/ 
 
 The reason will appear if we examine what is meant by 
 
 1 When the attribute expressed by the predicate is not something perceived 
 by the senses, the process of judgment is not by direct abstraction. Experi- 
 ence and education store the mind with concepts of numerous attributes. 
 On one ground or another we recognize the presence of one of these in the 
 subject, and judge, e.g., ' Caius is a cowurd,' ' iUil'ous is wise.' 
 
 2 Cf. St. Thomas, /. Sent. XIX. Q. 5, Art. i, ad i. 
 
THE JUDGMENT AND THE PROPOSITION 43 
 
 the ' being ' of an object. If we speak of the real order, 
 we can at once distinguish two senses of the term. The 
 ' being ' of an object may signify (i) its existence, that 
 in virtue of which the thing is : or it may signify (2) 
 the nature of the thing that in virtue of which it is what 
 it is. Thus for instance we say of Socrates that he is a 
 man : of Bucephalus, that he is a horse. And many other 
 characteristics than these may be affirmed of each of them. 
 For it is plain that besides the essential nature ' man ' 
 or ' horse/ numerous other qualities go to make an indi- 
 vidual object what it is. Size, colour, etc. etc., all go to 
 constitute the complete entity. 
 
 In considering the * to be ' of the copula, we are how- 
 ever not concerned directly with the real order, but with 
 its representation in the mind. Our words are the mani- 
 festation of our thoughts, and when we speak of things, 
 we speak of them as they are mentally represented. 
 Now when our mind forms a judgment concerning an ob- 
 ject, the function of the copula is to declare that some 
 attribute belongs to that object, to tell us what the object 
 is. In other words the ' to be ' of the copula represents 
 not the ' being ' of existence, but the second sense of 
 ' being/ that namely in which it means the nature of the 
 thing. This will appear still more plainly if we reflect 
 that we can make a series of true judgments about an 
 object, irrespective of whether it exists or not. Our 
 judgment, e.g. that 'the horse is a quadruped' would be 
 true even were the last member of the species equus ex- 
 tinct. Indeed so little has the ' is ' of the copula to do 
 with existence, that when we desire to affirm the fact of 
 existence, we do not employ the subject-copula-predicate 
 sentence at all, but simply say ' Socrates is.' l 
 
 But here we must call attention to a point of very great 
 importance. It will be remembered that when discuss- 
 
 1 It should be noticed that existence adds no new note or determination 
 to the nature of a finite being. The nature is complete in all its characteristics 
 apart from the actuality which existence confers. Hence our concept of the 
 nature is complete without respect to the question, whether the thing exists 
 If it were possible to have Singular concepts, the concept, say of Socrates, 
 would be the same in all its determinations, whether he existed or not. 
 
44 PRINCIPLES OF LOGIC 
 
 ing Negative terms (Ch. 2, q) we saw that we are able to 
 conceive as though they were real entities, things which 
 are in fact simply the negations of entities. And thus 
 we find that in many of our judgments, the predicate is 
 not a quality or determination in the real order. It is a 
 mere negation, which in the conceptual order I conceive 
 as though it were a positive characteristic, as e.g. in 
 the proposition, ' The horse is riderless/ ' To be riderless ' 
 is no positive characteristic of the horse. Sometimes 
 both subject and predicate are of this character : for 
 instance, ' Blindness deprives men of much happiness/ 
 Here not merely is a privation conceived as if it were a 
 real subject ; but a purely negative result is conceived 
 as a positive action. 
 
 From this it will easily appear that we cannot strictly 
 speaking say that the ' is ' of the copula expresses that the 
 subject is determined in some way : for the predicate 
 may not be a real determination at all. It expresses that 
 the subject is conceived as determined in some way. As 
 we have already said, it expresses the objective identity 
 of subject and predicate. 
 
 Mill gravely informs us that his father was the first 
 among philosophers to notice that ' to be ' in the sense of 
 ' to exist/ has not the same signification as when it means 
 to be some specified thing, as ' to be a man ' ; and adds 
 that Aristotle and all the ancients believed it to have a 
 common meaning wherever used. "The fog/' he adds, 
 ' which rose from this narrow spot diffused itself at 
 ' an early period over the whole surface of Metaphysics " 
 (Logic, Bk. I. c. 4, i). Mill frequently falls into error 
 when criticizing the philosophy of Aristotle and his 
 followers, with whose writings he was but imperfectly 
 acquainted. Nowhere perhaps is he more astray than 
 here. Not merely was the distinction carefully noted 
 by Aristotle l : but the various senses of ' Being ' was 
 one of the points most canvassed in the writings of the 
 Scholastics. 
 
 1 Thus in Soph. Elenchi, C. 5, he says, ou yap ravrbv dt>ai rt ri Kal eu/cu air\3s 
 (' To be something is not the same as to be.') Cf. de Interp. c. n, 9, 10. 
 
THE JUDGMENT AND THE PROPOSITION 45 
 
 It remains to be noticed that a judgment is a single act 
 of the mind. No mistake could be greater than to repre- 
 sent it as three separate acts, corresponding respectively 
 to subject, copula and predicate. Such a view might 
 seem to be implied, when it is said that in affirmation we 
 have the conjunction, in negation the separation of two 
 concepts. But it is manifest that a synthesis, in which 
 we recognize a relation of identity, and a separation in 
 which we judge that such a relation is absent, are alike 
 single acts. 1 
 
 Certain points which remain to be considered in regard 
 to the Scholastic theory of the judgment, must be dealt 
 with later. 2 
 
 * The following two citations will shew that the view we have 
 taken of the ' being ' expressed by the copula, as referring to 
 the nature of the object as conceived, is that held by St. Thomas 
 and his great commentator Cajetan : 
 
 " Sciendum est quod Esse dicitur tripliciter. Uno modo 
 'dicitur Esse ipsa quidditas vel natura rei, sicut dicitur quod 
 ' definitio est oratio significans quid est esse : definitio enim quid- 
 ' ditatem rei significat. Alio modo dicitur Esse ipse actus essen- 
 ' tiae. . . . Tertio modo dicitur Esse, quod significat veritatem 
 ' compositionis in propositionibus, secundum quod est dicitur 
 ' copula : et secundum hoc est in intellectu componente et divi- 
 'dente." St. Thomas in I. Sent. dist. 33, Q. i, Art. i, ad. i. 
 
 Cajetan takes as an example the proposition ' Navis est sine 
 gubernatore,' and says : " Navis caret gubernatore nullo intellectu 
 ' considerante : absentia tamen gubernatoris nullum esse sub- 
 ' stantiale aut accidentale ponit in navi. Unde navem esse sine 
 ' gubernatore, extra animam non est aliquod, sed non esse guber- 
 'natam. Acquirunt autem esse privationes et negationes ex 
 ' hoc quod intellectus intelligens privationes per habitus, et nega- 
 ' tiones per affirmationes, format in se ipso rei carentis aliquo modo 
 'idolum quoddam. Verbi gratia cum intellectus format in se 
 ' idolum quoddam navis gubernatore carentis, quod est ipsa pro- 
 ' positio mentalis, non-praesentia gubernatoris quae extra animam 
 ' nil ponit, in anima fit ens per hoc quod intellectus fecit ipsam 
 ' propositionis terminum aliquem." Comment, in De Ente et 
 Essentia, c. i. 
 
 The same view is implied in Aristotle's well known distinction 
 
 1 On the unity of the act of judgment Aristotle is explicit. He calls it 
 " a synthesis of concepts as though they were but one " (yvvdecris TIS 
 v orjfJ.aTO}v owrTrep v &VTUV), de Anima, III. c. 6, 41. 
 
 2 See below, Ch. 7, i, Ch. 9, 4, Ch. 10, 5. 
 
46 PRINCIPLES OF LOGIC 
 
 between 'being,' in the real order, and ' being' which signifies 
 truth, Met. V. c. 4, i. 
 
 3. Quality of Propositions. In every proposition P 
 must be either affirmed or denied of 5. This alternative 
 determines the Quality of the proposition, which must 
 be either (i) affirmative, or (2) negative. This 
 division is ultimate. Some logicians have, it is 
 true, endeavoured to reduce all propositions to the 
 affirmative form by writing 5 is not-P. But the 
 difference cannot be thus bridged. 5 *s not-P is, of course, 
 equivalent to S is not P. But they differ the one from the 
 other : since in S is not P we deny the positive concept P 
 of S, and in 5 is not-P we affirm the negative concept 
 not-P of 5. The negative and affirmative forms remain 
 radically distinct. 
 
 Kant admits three forms, Affirmative, Negative, Infinite, 5 
 is P, S is not P, S is not-P. His motive in assigning the In- 
 finite judgment to a separate class, instead of reckoning them 
 with the Affirmatives to which they rightly belong, seems to 
 have been the desire that his scheme of Categories should pre- 
 sent an harmonious appearance. A triple division was required 
 in its other portions, and a triple division must perforce be found 
 for the Quality of judgments. 
 
 4. Quantity of Propositions. In any affirmation or 
 negation, P may be affirmed or denied, (i) of all the 
 objects denoted by the subject-term, e.g. ' All men are 
 mortal ' ; or (2) of only some of these objects, e.g. 
 ' Some men are negroes ' : or (3) there may be no sign 
 to mark whether the predicate refers to some only or to 
 all, e.g. ' Pleasure is not a good ' : or (4) the subject 
 may be a singular term, e.g. 'Socrates is wise/ 'The 
 highest of the Alps has been scaled.' These various 
 alternatives lead to the division of propositions according 
 to quantity. 
 
 A Universal proposition is one, in which the predicate 
 h affirmed (or denied) of a subject, taken in its whole 
 extension and distributively. 
 
 We have already explained (Ch. 2, 14) that when a sub- 
 
THE JUDGMENT AND THE PROPOSITION 4; 
 
 ject is employed distributively, the predicate is affirmed 
 of every individual denoted by the subject. When we 
 say, ' All sparrows are winged/ we mean that every indi- 
 vidual sparrow is possessed of wings. A proposition 
 in which the subject is understood collectively is not uni- 
 versal. Thus the proposition, ' All the slates covered the 
 roof/ is not a universal proposition. The predicate is not 
 affirmable of each individual denoted by the subject, 
 but of the individuals as forming one group. Hence, 
 whenever the word All (and not Every) is employed to 
 qualify the subject, care must be taken to observe whether 
 it be understood collectively or distributively. 
 
 It is plain that though the Affirmative Universal is of 
 the form All S is P, the Negative Universal will not be 
 All S is not P, but No S is P. The form All S is not P 
 does not exclude P from each and every individual S, as 
 at once appears in the proposition ' All soldiers are not 
 generals/ If, however, I say, ' No Englishmen are 
 negroes/ I exclude the attribute from every member 
 of the class. 
 
 The employment of the plural in a universal proposition, e.g. 
 ' All men are mortal/ may possibly mislead the student into 
 supposing that in the subject the intellect conceives a number 
 of individuals. This is, of course, impossible. The mental act 
 is more truly represented by the Latin form ' Omnis homo est 
 mortalis.' The subject of the judgment is the universal nature 
 ' man/ not a number of individuals. The adjective ' All ' does 
 not multiply the concept, but signifies that to whatever entity 
 the nature ' man ' belongs, to that entity the attribute ' mortal ' 
 also belongs. 
 
 A Particular proposition is one in which the predicate is 
 affirmed (or denied) of a part only of the extension of the 
 subject. 
 
 The form of the Particular proposition is Some S are 
 (or are not) P ; for instance, ' Some soldiers are brave/ 
 ' Some rich men are not generous/ The sense, in which 
 the word ' some ' is here used, differs in certain respects 
 from that in which it is ordinarily employed. In ordinary 
 use, when we speak, e.g. of ' some ' men, we are under- 
 
48 PRINCIPLES OF LOGIC 
 
 stood to mean more than one, and also to exclude the 
 supposition that what we say may be true of all men. 
 ' Some ' means ' several but not all.' In Logic, the ' some ' 
 of a particular proposition, may be used even where the 
 predicate might be truly affirmed of all : and it may be 
 used also even if there be but one individual to whom it 
 could be applied. Thus I may say, ' Some birds have 
 wings/ even though it be the case that all birds possess 
 them : and ' Some men are eight feet high/ though in 
 fact there be but one such man. ' Some ' leaves the 
 extension to which reference is made wholly indeter- 
 minate. * 
 
 The essential distinction then between Universal and 
 Particular propositions lies in this, that Universals deal 
 with the whole class, Particulars with .an indeterminate 
 portion of the class. And here it is well to call attention 
 to the fact, that universal propositions are of two sorts. 
 The majority of them cannot be attained by mere enu- 
 meration of instances. Some indeed can. I can arrive at 
 the universal truth, that ' All the apostles were Jews/ by a 
 process of counting. But propositions of this character 
 are of minor moment. Enumeration will not serve me 
 in regard to such propositions as, ' All men are mortal/ 
 ' All birds are oviparous/ Here, I refer not merely to 
 an incalculable number of past instances, but also to the 
 future. All laws of nature known to science are proposi- 
 tions of this character. The aim and object of scientific 
 enquiry is to establish such universal truths. 
 
 How is it that we can affirm a predicate of individuals, 
 which have not come within our experience ? The ex- 
 planation lies in the fact, that in these propositions we 
 know the predicate to be invariably connected with the 
 universal class-notion employed in the subject. In a 
 later part of Logic, we shall consider how we reach this 
 
 1 The reason for this is easy to see. When the word has the significance 
 " some only," it is really equivalent to two propositions, one affirmative, 
 one negative. When it is used in reference to certain definite individuals, 
 A. B. C., it is equivalent to so many singular judgments. It is only in its 
 indeterminate reference that it is an independent and elementary thought- 
 form. 
 
THE JUDGMENT AND THE PROPOSITION 49 
 
 knowledge. It is sufficient here to observe that to what- 
 ever individuals the notion ' man ' is applicable, the predi- 
 cate ' mortal ' is applicable also. In virtue of their 
 being men, they possess the attribute of mortality. The 
 universality of these propositions rests not on enumera- 
 tion, but on our knowledge of the constant connexion 
 between the concepts of the subject and predicate. 
 
 It remains to consider Indesignate and Singular pro- 
 positions. 
 
 Indesignate propositions are such as have no sign of 
 quantity. As far as form is concerned, they may be 
 universal, or they may be particular. If I say, ' Old 
 men are melancholy,' it does not appear, whether I am 
 speaking of all old men, or of some only. Hence indesig- 
 nate propositions have no place in Logic, until a sign of 
 quantity is affixed to them. In some cases indeed the 
 Indesignate is used to signify that the predicate is con- 
 nected necessarily with the subject, e.g. ' Man is mortal/ 
 Here the proposition is of course equivalent to a universal. 
 For these judgments in which the Indesignate form stands 
 not for individuals, but for the class-nature, some authors 
 employ the convenient term Generic judgments. But 
 it should be observed that we do not know their universal 
 character from the logical form, but from our previous 
 acquaintance with the matter under consideration. Very 
 often the Indesignate is used for what are termed moral 
 universals, as in the example already given, ' Old men are 
 melancholy.' A moral universal admits exceptions, and 
 hence is logically a particular. 
 
 The Singular proposition is, as we have said, one whose 
 subject is either a significant Singular term or a proper 
 name. These propositions present some anomalies. On 
 the one hand, the individual object is a member of a 
 class, and it appears incongruous to treat it as though it 
 were itself a class. On the other, the definition of a 
 Universal proposition is applicable to them, for the predi- 
 cate is affirmed of the subject in its whole extension, 
 the extension in this case being restricted to a single indi- 
 vidual. 
 
50 PRINCIPLES OF LOGIC 
 
 Modern logicians have resolved to treat this proposition 
 as a Universal, and it will be convenient to adhere to that 
 arrangement. 
 
 The older logicians classify the Singular proposition 
 separately, and assign it neither to the Universal nor to the 
 Particular. 1 This was, it would seem, the more scientific 
 course. For the Universal and Particular are distin- 
 guished by the manner in which the concept employed as 
 subject is understood in regard to extension. But as we 
 have explained above (Ch. 2, i), we have no singular con- 
 cepts. Hence there is a fundamental difference between 
 such a proposition as, ' All men are mortal/ and ' Socrates 
 is a philosopher.' 
 
 Propositions whose subject is a Collective term are 
 Singular propositions. Thus if I say, ' All the apples filled 
 the bowl/ it is clear that I refer to this group of apples 
 considered as a single object. 
 
 5. The Fourfold Scheme of Propositions. The 
 
 last paragraph has shown us that the two fundamental 
 forms of the proposition are the Universal and the 
 Particular. In one of these two, every known truth 
 can be expressed. For the assertion made is either 
 known to hold good of the subject in its whole extension, 
 or not. If it is known to hold good, we use the 
 Universal proposition. If it does not hold good as regards 
 the whole extension of the subject, or if, though it holds 
 good, we do not know this to be the case, we use the 
 Particular. This distinction, combined with that based 
 on quality, gives us the fourfold scheme, viz. : Universal 
 Affirmative, Particular Affirmative, Universal Nega- 
 tive, Particular Negative. These are respectively indi- 
 cated by the letters, A.I.E.O. These letters are the 
 vowels of the two Latin words, Affirmo (I affirm) and 
 Nego (I deny). The first vowel in each stands for 
 the Universal, the second vowel for the Particular. 
 
 1 Cf . St. Thomas, Opusc. 44, Summa Totius Logicae, de Interp. c. 6. (This 
 Opusculum, though found among the works of St. Thomas, is from another 
 hand.) 
 
THE JUDGMENT AND THE PROPOSITION 51 
 
 Another notation, which is found convenient, is SaP, SiP, 
 SeP, SoP : this notation has symbols for the subject 
 and predicate, as well as for quantity and quality. Hence, 
 our four propositions may be thus expressed. 
 
 All 5 are P. A. SaP. 
 
 Some 5 are P. /. SiP. 
 
 No 5 are P. E. SeP. 
 
 Some 5 are not P. 0. SoP. 
 
 6. Analytic and Synthetic Propositions. This dis- 
 tinction is based on the fact that each of our Judgments 
 is based on one or other of two very different motives. 
 The point will best be elucidated by a few examples. 
 If we consider the following propositions, ' The angles 
 of every triangle are equal to two right angles/ ' The 
 whole is greater than its part,' ' Every square has 
 four sides/ and compare them with such propositions 
 as ' Water freezes at 32 Fahrenheit/ ' Some cows are 
 black/ we shall at once recognize that there is a differ- 
 ence between the two classes. We are, indeed, certain 
 of the truth of all these propositions. But our certainty 
 has a different motive in the first class, and in the 
 second. In the case of the first class of Judgments, as 
 soon as we consider the concepts of the subject and 
 predicate, we see that they are necessarily bound to- 
 gether. A triangle must have its angles equal to two 
 right angles ; otherwise it would not be what we mean 
 by a triangle. Were we told of any figure that its interior 
 angles were greater or less than two right angles, we 
 should be justified in affirming that it was not, and 
 could not under any circumstances be a rectilinear tri- 
 angle. In the same way the intension of the concepts 
 ' whole ' and ' part ' excludes the supposition of a whole 
 that is not greater than its part ; for the meaning of 
 the term ' whole/ is ' that which consists of parts.' In 
 regard to the second class, the motive of our assent is 
 very different. It is experience that has led to my 
 conviction that water freezes at 32 F., and that certain 
 cows are black. There is nothing in my notion of ' cow ' 
 
52 PRINCIPLES OF LOGIC 
 
 which prescribes ' blackness,' nor in my notion of ' water/ 
 which compels me to think of it as possessing this par- 
 ticular freezing-point at the sea-level. In neither of 
 these propositions are the two concepts linked together 
 in virtue of their intension. 
 
 The former class of propositions is termed Analytic, 
 the latter Synthetic. 
 
 The definition of Analytic and Synthetic pro- 
 positions is differently given by Scholastic philosophers 
 on the one hand, and by the greater number of Logicians 
 since the days of Kant, on the other. The difference is 
 of primary importance in philosophy. We place the 
 Scholastic definitions first. 
 
 An Analytic proposition is one, in which either the 
 predicate is contained in the intension of the subject, 
 or the subject in the intension of the predicate. 
 
 A Synthetic proposition is one in which the connexion 
 of subject and predicate is not involved in the intension 
 of the terms. 
 
 It will be seen that Analytic propositions are of two 
 kinds. The first kind consists of those in which the 
 predicate is a term signifying either the whole intension, 
 or part of the intension of the subject. Such is the 
 proposition, ' Every square has four sides.' The second 
 kind consists of those in which the predicate is an attri- 
 bute which results necessarily from the nature of the 
 subject. 1 For where this is the case the subject is found 
 in the intension of the predicate. An example is fur- 
 nished by the proposition, ' A triangle is a figure having 
 its interior angles equal to two right angles.' The 
 predicate here is not found in the intension or defini- 
 tion of ' triangle.' But it is an attribute which neces- 
 sarily results from and is involved in tl.e characteristics 
 of a triangle. And if we desire to define the attribute 
 ' having its interior angles equal to two right angles,' 
 
 1 An attribute which is thus connected with the subject by necessary 
 resultnncy is termed a property of that subject. The term will be fully dis- 
 cussed in Ch. 8, i. 
 
THE JUDGMENT AND THE PROPOSITION 53 
 
 we can only do so by stating that it is ' a quantitative 
 measure proper to the angles of a triangle.' * 
 
 It is not however necessary that the connexion of the 
 attribute with the subject should be evident on the 
 first consideration. Many steps may be necessary. 
 Every geometrical theorem gives us an Analytical pro- 
 position as its conclusion. The connexion between 
 subject and predicate is involved in the intension of the 
 terms : but we must often take a long series of steps 
 before the necessity of that connexion becomes manifest 
 to us. 2 
 
 The modern definitions are as follows : 
 
 An Analytic Proposition is one, in which the predicate 
 is contained in the definition of the subject. 
 
 A Synthetic proposition is one, in which the predicate 
 is not contained in the notion of the subject. 
 
 So prevalent have these definitions become, that in 
 any public examination at the present day, a question, 
 involving these terms, would certainly employ them 
 in this latter sense. 
 
 * (a) We have spoken of the differences between the two 
 definitions as of vital moment. The Kantian division of Analytic 
 and Synthetic propositions relegates to one class propositions, 
 our knowledge of which depends wholly on experience of the 
 individual case, such as ' This book is bound in cloth,' and pro- 
 positions such as, ' The square on the hypotenuse of a right- 
 angled triangle is equal to the sum of the squares on the remain- 
 ing sides.' Neither of these, Kant tells us, can be discovered 
 by analysis. For he considers only the case, in which the pre- 
 dicate is found by the analysis of the subject, and entirely 
 
 1 Analytic Propositions were termed by the Scholastics ' Proposition's 
 per se notae.' Cf. Arist. An. Post. I. c. 4, 3, and St. Thomas, in An. Post. 
 I. lect. x. " Primus modus ejus quod est per se est quando praedicatur de- 
 finitio de aliquo definite, vel aliquid in definitione positum : . . . secundus 
 modus dicendi per se est quando subjectum ponitur in definitione praedicati, 
 quod est proprium accidens ejus." Cf. also De Anima, II. lect. 14. 
 
 " If without axioms it is impossible to infer," says Mr. Bradley, " I won- 
 ' der where all the axioms can have come from " (Principles of Logic, p. 227). 
 There is no mystery about axioms. They are Analytic propositions in which 
 the connexion of subject and predicate is immediately evident. Cf . St. Thomas, 
 Sum-ma Theol. I. Q. 2, Art. i. " Ex hoc aliqua propositio est per se nota, 
 ' quod praedicatum includitur in ratione subjecti. ... Si igitur notum sit 
 ' omnibus de praedicato et de subjecto quid sit, propositio erit omnibus per 
 se nota." 
 
54 PRINCIPLES OF LOGIC 
 
 ignores the case, in which the subject-term is revealed by an 
 analysis of the predicate. What account then is to be given 
 of our conviction as to the truth of such propositions as that 
 relating to the square on the hypotenuse ? If they are not analy- 
 tic, two hypotheses only are possible. Either (i) we accept 
 them on a dictate of our understanding, of which no account 
 can be given. They are synthetic a priori. This is Kant's solu- 
 tion. Or (2) their truth is a conclusion, at which we arrive from 
 an examination of individual instances, but we possess no ground 
 for saying, that they must be true, that e.g. every right-angled 
 triangle has the property described. This is Mill's solution. 
 
 (b) There have been three theories as to the object of Analytic 
 propositions. Mill (following Hobbes) holds that they are con- 
 cerned with the meaning of names only, and terms them Verbal 
 propositions. Leibniz held that they are concerned with our 
 concepts. The Scholastics taught that they are truths relating 
 to things, though known through our concepts, and expressed 
 in words. Professor Case well says, " The division of propositions 
 ' into verbal and real is defective. A verbal is not necessarily 
 ' opposed to a real proposition, a predicate does not cease to be 
 ' characteristic of a thing by becoming the meaning of its name, 
 ' and there are some propositions which are verbal and real, 
 ' such as, all bodies are extended, the whole is greater than its 
 ' part. . . . Sometimes the same analytical judgment is at once 
 ' real, notional and verbal, e.g. the whole is, is conceived, and 
 ' means that which is greater than its part " (Physical Realism, 
 p. 340). 
 
 (c) It is sometimes said, that every synthetic judgment be- 
 comes analytic with the growth of our knowledge, that e.g. 
 'George III. died in 1820,' is an analytic judgment to one who 
 knows the history of that period. The argument is quite fallaci- 
 ous. The facts, which occur to an individual member of a class, 
 are not necessary notes of his nature, forming the connotation 
 of the concept which expresses it. In the first place, of indi- 
 viduals as such we have no concepts : all concepts are universal 
 (Ch. 2, i). And secondly, even were it possible to have a con- 
 cept expressing the essential nature of the individual, the purely 
 contingent facts relating to him would not be part of it. Of 
 course, if I form a complex concept applicable to George III., such 
 as e.g, ' The King of England at the beginning of the nineteenth 
 century,' and to this add the note ' who died in 1820,' then I 
 may form the analytic proposition, ' The King of England at 
 the beginning of the nineteenth century, who died in 1820, 
 died in 1820.' But the value of an analytic proposition of this 
 kind is not great. 
 
 (d) Analytic propositions are also termed Essential, Explica- 
 tive, a priori, Verbal ; and correspondingly, synthetic proposi- 
 
THE JUDGMENT AND THE PROPOSITION 55 
 
 tions are known as Accidental, Ampliative, a posteriori, Real. 
 On this whole subject, Professor Case's Physical Realism, pp. 
 334-353, may be consulted with advantage. 
 
 7. Complex Propositions. Complex propositions are 
 such as have a complex term for their subject or 
 their predicate. By a complex term is understood a 
 many-worded term, consisting of two or more distinct 
 parts, so that it expresses, not merely the nature of the 
 thing denoted, but also one or more qualifications 
 belonging to it, e.g. ' the white knight,' ' the roller 
 which is in my garden/ and the like. These qualifi- 
 cations are often (as in the second of the instances 
 just given), expressed by subordinate clauses, introduced 
 by a relative. Yet it is manifest that, even if a 
 complex term involves two or three such clauses, the 
 term is but one, and constitutes a single subject or 
 predicate, as the case may be. 
 
 Two forms of complex propositions are ordinarily 
 distinguished by logicians. The distinction is gram- 
 matical, not logical, and is given in order to put us on 
 our guard against ambiguity. 
 
 (1) Propositions with an explicative qualification. In 
 these the qualification belongs to every individual signi- 
 fied by the general name, to which it belongs. Thus 
 in the proposition, ' Whales, which are mammals, are 
 aquatic animals/ the relative clause is applicable to 
 every individual, that is signified by the general name 
 ' whales/ 
 
 (2) Propositions with a restrictive (or determinative) 
 qualification. In these, the qualification restricts the 
 signification of the general name to a certain part of 
 its denotation. Thus in the sentence, ' All nations, 
 that have been civilized, have cultivated philosophy/ 
 the qualification does not belong to all the members of 
 the class indicated. Not all nations are civilized. 
 
 The time determination involved in the use of the 
 past and future tenses of the verb, is a special form of 
 complexity in the proposition. This however, as we 
 
5 6 PRINCIPLES OF LOGIC 
 
 have noted, Logic is enabled to disregard. Another 
 constantly recurring form is that produced by the 
 employment of transitive verbs, followed by an object, 
 e.g. ' Brutus slew his benefactor,' which gives as the 
 logical predicate, the complex term ' a slayer of his 
 benefactor/ 
 
 8. Compound Categorical Propositions. It often 
 happens that what grammatically is a single assertion, 
 is resolvable into two or more propositions, each 
 with its own subject and predicate. In such cases, 
 we have the Compound Categorical Proposition. Pro- 
 positions of this kind are divided into two classes, 
 those whose character is apparent from their gram- 
 matical structure (aperte composite), and those in which 
 the grammatical form does not manifest their composite 
 nature (occulte compositi). These latter are termed 
 Exponibles. 
 
 (a) Propositions compound in form. Of these there 
 are three classes : 
 
 1. Copulative propositions. These are affirmative pro- 
 positions, in which there are two or more subjects or 
 predicates or both. Hence they are resolvable into a 
 number of independent affirmative propositions : e.g. 
 ' Peter and Paul ended their days at Rome.' This is 
 equivalent to ' Peter ended his days at Rome. Paul 
 ended his days at Rome.' 
 
 2. Remotive propositions. These are negations simi- 
 larly united. The conjunctions employed will be such 
 as the negative form demands. For example, ' Neither 
 riches nor honours can banish anxiety ' ; this sentence 
 may be resolved, ' Riches cannot banish anxiety. Hon- 
 ours cannot banish anxiety.' ' No Mohammedan will 
 eat swine's flesh or drink wine.' This, in its logical 
 expression, becomes, ' No Mohammedan will eat swine's 
 flesh. No Mohammedan will drink wine.' 
 
 3. Discretive or Adversative propositions. Here we 
 have either tw6 affirmative propositions, or an affirma- 
 tive and a negative proposition, connected by an adver- 
 
THE JUDGMENT AND THE PROPOSITION 57 
 
 sative conjunction, such as but, although, yet. Thus : 
 ' William I. was brave but not magnanimous/ This 
 gives us the two propositions ' William I. was brave. 
 William I. was not magnanimous.' 
 
 (b) Exponible propositions. In these, as we have 
 said, there is nothing in the grammatical structure of 
 the sentence to indicate that it is equivalent to more 
 than one logical proposition. Here also, three classes 
 are ordinarily enumerated. 
 
 (1) Exclusive propositions. These contain a word, 
 such as ' alone/ attached to the subject, and thus exclud- 
 ing the predicate from any other subject than this 
 one. Hence two propositions are necessary to declare 
 the full meaning, one to affirm the predicate of this 
 subj ect, and another to deny it of all others. For instance, 
 ' God alone is omnipotent.' This is equivalent to 
 ' God is omnipotent. No other is omnipotent.' 
 
 (2) Exceptive propositions. In these, the subject term 
 is restricted in its application by a word such as except 
 save, which excludes a portion of its denotation e.g. 
 ' All the crew save one were drowned.' Here again, 
 two exponent propositions are needed, the one denying 
 the predicate of the excepted part, the other affirming 
 it of the remainder. The example just given will become, 
 ' One of the crew was not drowned. The remaining 
 members were drowned.' 
 
 If the order of the terms is altered, then both Exclusives and 
 Exceptives may be expressed by a single exponent. ' Only 
 God is omnipotent,' will become ' All that is omnipotent is God ' ; 
 and ' All the crew save one were drowned/ will be ' The portion 
 of the crew that was not drowned was one man.' But if the 
 original order is to be preserved, two propositions are necessary. 
 The reasons which justify a change of order will be dealt with 
 in Ch. 5. 
 
 (3) Inceptive and Desitive propositions. In these a 
 statement is made as to the commencement or ending 
 of something ; e.g. ' Printing became customary after 
 ' the fifteenth century,' ' Paganism ceased in England 
 ' about the year 700 A.D/ These are resolved by two 
 
58 PRINCIPLES OF LOGIC 
 
 propositions, one relating to the state of things before 
 the time indicated, and one relating to what occurred 
 subsequently. Thus the first example will become 
 * Printing was not customary before the close of the 
 fifteenth century. Printing was customary after that 
 date.' 
 
 9. Modal Propositions. The Modal proposition 
 affords us another case in which the traditional ter- 
 minology differs from that in vogue since the days of 
 Kant. Here too we shall first explain modality as 
 understood by the Scholastic philosophers, and then 
 deal with the Kantian account. 
 
 The characteristic of the Modal, is that the copula 
 undergoes modification, in order to express the manner 
 in which the predicate belongs to the subject. There 
 are propositions, in which the attribute affirmed belongs 
 to the subject by strict necessity. Thus ' mortality ' 
 is an attribute that is necessarily connected with the 
 subject ' man/ In other cases the element of necessity 
 is absent. ' To be learned ' is affirmable of some men 
 only. It is not an attribute belonging necessarily to 
 the nature ' man.' The pure categorical draws no dis- 
 tinction between these cases. We employ the same 
 copula ' is,' whether the connexion is necessary or con- 
 tingent. But in the Modal proposition, the nature of 
 the connexion between attribute and subject receives 
 expression. 
 
 It has been frequently objected, that this whole ques- 
 tion belongs not to Logic but to Metaphysics. Thus 
 Sir W. Hamilton says, " Necessity, Possibility, etc. . . . 
 ' do not relate to the connexion of the subject and pre- 
 ' dicate ... as terms in thought, but as realities in 
 ' existence : they are metaphysical, not logical condi- 
 ' tions." This objection rests on a misconception as to 
 the province of Logic. Necessity and Possibility as 
 objective facts, belong to the real order. But as men- 
 tally expressed by us, they belong to the logical order ; 
 and a treatise on Logic would be incomplete without 
 
THE JUDGMENT AND THE PROPOSITION 59 
 
 some mention of the manner in which the mental judg~ 
 ment represents these metaphysical conditions. 
 
 The relation of the attribute to the subject is, objec- 
 tively, determined by one of three modes. These are 
 (i) the Necessary, in which the attribute belongs neces- 
 sarily to the subject. This is expressed by a proposi- 
 tion of the form, ' Men are necessarily mortal/ ' Equila- 
 teral triangles are necessarily equiangular.' (2) The 
 Impossible : in this case the predicate is repugnant to 
 the subject, e.g. ' It is impossible for irrational creatures to 
 exercise free will.' And (3) the Possible (or Contingent). 
 In this case the predicate belongs to the subject in some 
 instances, while in other instances it is not found with 
 it. Thus e.g. ' It is possible for a man to be a gram- 
 marian.' The conjunction of the two attributes involves 
 no impossibility, but on the other hand is not necessary. 
 This relation may be asserted from two points of view. 
 We may assert the possibility of the connexion between 
 subject and predicate, and express the proposition as it 
 is expressed above. Or we may declare the possibility 
 of their separation : and in this case the proposition 
 will take the form, ' It is possible for a man not to be a 
 grammarian.' Hence though there are but three modes, 
 there are four fundamental forms of Modal propositions, 
 as there are four fundamental forms of Categorical. 
 
 A difficulty is occasioned by the fact that ambiguity 
 attaches to the word ' possible.' ' Possible ' may have 
 the sense in which we have just explained it. It may 
 however, include in its signification the Necessary also ; 
 for if a predicate belongs necessarily to a subject, we can 
 say with truth that that subject is capable of receiving 
 it. 1 If all triangles must have three angles, it is true to 
 say that it is possible for a triangle to have three angles. 
 
 1 Summa Totius Logicae, Tract. 6, c. 13. " Notandum quod possibile 
 1 dupliciter potest sumi : vel in toto suo significato, et tune comprehendit 
 ' necessarium et contingens. . . . Alio modo, sumitur solum pro contingen- 
 tibus." Similarly Aristotle tells us that 'possible' when used in regard of 
 what is necessary, is employed in a distinct sense ' TO yhp hvayKaiov d/muvtifjius 
 fr5tx.ecr(>ai Myoftev,' An. Prior. I. c. 13, x. On this subject see also De 
 Interp. c. 13, 9. 
 
60 PRINCIPLES OF LOGIC 
 
 And similarly the assertion that it is possible for a subject 
 not to have such and such a predicate, may have a 
 sense in which it includes the Impossible. 
 
 The Modal may be expressed in two forms. In the 
 first of these, the mode itself constitutes the predicate, hav- 
 ing for its subject the proposition whose copula it affects, 
 e.g. ' That man should be mortal is necessary/ ' that a 
 bird should have gay plumage is possible/ Modals of 
 this form are all singular, since the subject is not a term, 
 but a proposition taken as a whole. Nevertheless the 
 modes of necessity and impossibility are a sure sign that 
 the proposition in question is universal ; while on the 
 other hand the mode of possibility, in the sense of merely 
 possible (as distinguished from the case in which possibil- 
 ity is predicated of a necessary judgment) is indicative 
 of a particular proposition. In the second forms of the 
 Modal the mode qualifies the copula itself : e.g. All trian- 
 gles are necessarily three-angled. Modals of this form are 
 not singular but take their quantity from their subject. 
 
 * Kant's division of Modals is based, not on the objective 
 relation of the predicate to the subject, but on the subjective 
 certainty of the thinker. He divides judgments into the Problem- 
 atic, i.e. ' 5 may be P,' the Assertoric, i.e. ' 5 is P,' and the Apo- 
 dictic, i.e. ' 5 must be P.' Of the problematic judgment he 
 says that it expresses " a free choice of admitting such a pro- 
 ' position, and a purely optional admission of it into the under- 
 ' standing." The assertoric judgment " implies logical reality or 
 'truth." The apodictic gives us the same judgment as the asser- 
 toric, when it is recognized as determined by the formal laws 
 of the understanding, and therefore as subjectively necessary 
 (see Ch. i. note (5)). In regard to this division it may be said 
 in the first place that such a proposition as ' 5 may be P ' is of 
 no value to the logician. It is a mere declaration of ignorance, 
 and not a judgment at all. Secondly, since the apodictic judg- 
 ment enunciates the same truth as the assertoric, merely in- 
 volving that the speaker recognizes more clearly the subjective 
 necessity under which he lies of thus judging, there is no reason 
 why he should not express the assertoric in the same form as 
 the apodictic ' S must be P.' The root error of this view is the 
 failure to see that the copula is not a mere mental act of union, 
 but expresses the objective connexion between the subject and 
 its attribute in the real order (see Ch. 9, 4). 
 
THE JUDGMENT AND THE PROPOSITION 61 
 
 The influence of the Kantian system is to be seen in many 
 recent logicians. We are not infrequently told that when a 
 truth is styled ' necessary,' nothing more is meant than a ' neces- 
 sity of thought,' and that the term has no reference to the real 
 order. Mr. Bradley tells us, " a necessary truth is really an 
 inference, and an inference is a necessary truth " (Principles, 
 p. 221). Similarly Mr. Bosanquet writes, "Every necessary 
 ' truth must, in so far as it is necessary, present itself as the 
 'conclusion from an antecedent " (Logic, II. 222). Such a view 
 as this must needs be fatal to any hope of attaining certitude 
 in philosophy or science. The existence of any necessary first 
 principles is denied. But where there are no necessary principles, 
 there can be no necessity in the conclusion derived from them. 1 
 
 10. Reduction of Propositions to Logical Form, The 
 
 sentences employed in literature and in ordinary conver- 
 sation exhibit considerable variety of form and complexity 
 of structure. It is possible however to analyse them and express 
 them in the shape of A E I O propositions. This process is 
 styled their reduction to logical form. By submitting sentences 
 to this analysis we reach the simple elements of thought, which 
 are contained in them. It is plain that this is very different 
 from grammatical analysis into parts of speech. That process 
 is concerned not with thoughts but with words. The preceding 
 paragraphs should have rendered the task of reduction com- 
 paratively easy. Its essential feature is to obtain propositions, 
 consisting of (i) a subject with the sign of quantity attached ; 
 (2) a copula, which must be of the form is or are (or is not, are 
 not], and (3) a predicate. 
 
 We find the subject by putting to ourselves the question, Of 
 what or of whom is this statement made ? 
 
 We find the quantity of the subject by asking, 7s the assertion 
 made of the whole extension of the subject, or of but part of it ? 
 
 We find the predicate by enquiring, What is it that is asserted 
 of the subject ? 
 
 These three points must always be considered, whenever the 
 analysis of a sentence is attempted. Two other cautions may 
 be added. First, that it is well, whenever it is possible, to ex- 
 press the predicate as an attribute, i.e. adjectivally, in order to 
 bring out the true meaning of the proposition : e.g. the form 
 ' All flattery is to be avoided ' is better than ' All flattery is a 
 thing to be avoided.' Secondly, that wherever it is necessary 
 to introduce a time determination, this must be done in the 
 predicate as in No. (7) below. The copula must always be in 
 the present tense. 
 
 1 Cf. Rickaby, General Metaphysics, p. 180. 
 
62 PRINCIPLES OF LOGIC 
 
 A few examples will illustrate the process : 
 
 (1) 'Fools despise wisdom.' 
 
 This will become, ' All fools are despisers of wisdom ' (A ) . 
 
 (2) 'All's well that ends well.' 
 
 This will be, 'All that ends well is well' (A). 
 
 (3) ' Firm at his dangerous post he stood.' 
 
 This in logical form is, ' He is standing firm at his dan- 
 gerous post ' (A). 
 
 (4) ' As a man sows, so shall he reap.' 
 
 Here we have a relative sentence. The two clauses of these 
 propositions give us the terms of a relation. Where the words 
 ' As ... so ' are employed to introduce the clauses, the relation 
 is one of likeness. The analysis gives us, 
 
 ' In every instance, the character of a man's harvest is like 
 the character of his sowing ' (A). 
 
 If the words ' Where . . . there ' are used, we have a 
 relation of place: if 'When . . . then,' a re]ation of time. 
 
 (5) 'Where thy treasure is, there will thy heart be also.' 
 Logically, this is, ' In every instance, the place of your treasure 
 
 is the place of your heart ' (A ) . 
 
 (6) 'Love is akin to madness.' 
 
 Here the subject is used without any sign of quantity, but 
 clearly stands for the whole denotation of the term. The pro- 
 position becomes, ' All cases of love are akin to madness.' 
 
 Where we have compound or exponible propositions, they 
 need resolving into their component parts, e.g. : 
 
 (7) ' Lions and tigers once lived wild in Europe, but not now. ' 
 This gives us four propositions. 
 
 ' Some lions are animals, that once lived wild in Europe ' 
 
 (/). 
 
 ' Some tigers are animals, that once lived wild in Europe ' 
 
 (I)- 
 
 ' No lions are living wild in Europe now ' (E) . 
 ' No tigers are living wild in Europe now ' (E) . 
 
 (8) 'Only the just enjoy peace of mind.' 
 This is resolved into : 
 
 'Some of the just are enjoying peace of mind' (/). 
 
 ' None, who are not just, are enjoying peace of mind ' (E). 
 
 (9) ' All save he had fled.' 
 
 Here we have a case, where the full force of the proposition 
 cannot be brought out in the analysis, since we have no uni- 
 versal term by which to designate all the remainder. The re- 
 duction gives : 
 
 ' He is not fleeing ' (E) . 
 
 ' Some (the rest) are fleeing ' (/). 
 
 (10) 'The great is not good, but the good is great.' 
 Notice should be taken of the ' reduplicative ' use of the word 
 
THE JUDGMENT AND THE PROPOSITION 63 
 
 great ' in the first clause. It signifies ' the great as such,' or 
 the great, just in so far as it is great.' This must be expressed 
 in the analysis : 
 
 ' The great, merely in virtue of its greatness, is not good ' 
 
 (). 
 
 'The good is great' (A). 
 
 Other Signs of Quantity* It will be useful to mention a few 
 other modes of expressing Quantity besides those we have already 
 noticed. 
 
 A. The universal affirmative is occasionally denoted by the 
 expressions, Any, Whoever, He who, Always, In every case. 
 I may be denoted by A few, Certain, Often, Generally, Most. 
 E may be expressed by the word Never. 
 
 has equivalents in A few . . . not, Not a// ... are, All . . . 
 are not, Few, Certain . . . not. 
 
 The word Most has been placed as one of the equivalents of 
 I. The proposition ' Most S's are P ' signifies that ' Some (more 
 than half) S's are P,' but does not necessarily imply in addition 
 that ' Some S's are not P.' It merely signifies that the majority 
 of instances have been examined, and found to possess the attri- 
 bute P. Thus we might say, ' Most English flowering-plants 
 are dicotyledonous,' without desiring to commit ourselves to 
 any opinion as to the whole flora : or again, after looking at 
 seven cards out of a hand at whist, we might say, ' Most of the 
 cards in this hand are court-cards,' knowing that it was possible 
 they might all prove to be so. Similarly we might say, ' Few 
 English flowering-plants are monocotyledonous,' even if we 
 were ignorant whether there were any of that character. Hence 
 Few is commonly reckoned as merely a sign of the proposition 
 O. 1 The words Hardly any, Scarcely any are also regarded as 
 equivalent to O. The use of All with a negative to signify O 
 should be carefully noticed. ' Not all the crew were lost,' will 
 be expressed ' Some of the crew were not lost.' 
 
 Special note should be taken as to whether the terms, to which 
 words such as All, A few, etc. etc. are attached, are used dis- 
 tributively or collectively (Ch. 2, 14). Wherever the use is 
 collective the proposition is singular. ' All the men built a raft ' 
 is a case in point. The proposition may be expressed, ' The 
 whole body of men is building a raft.' 
 
 ii. Hypothetical Propositions. Besides the Cate- 
 gorical propositions which we have hitherto been 
 considering, there is another class of judgments called 
 
 1 The difference between A few and Few is to be observed. A few is equiva- 
 lent to some. " Few," says Mr. Keynes, " has a negative force. And ' Few 
 S's are P ' may be regarded as equivalent to ' Most S's are not P.' " 
 
64 PRINCIPLES OF LOGIC 
 
 Conditional. These are distinguished from Categoricals 
 by the fact that in them the predicate is not asserted 
 absolutely of the subject. They are divided into two 
 classes, termed Hypothetical and Disjunctive. In the 
 present section we are concerned with the Hypothetical. 
 
 A Hypothetical Proposition is one in which the predi- 
 cation made in one proposition, is asserted as a conse- 
 quence from that made in another. The proposition 
 on which the truth of the other depends, is called the 
 Antecedent : that which follows on its admission, is 
 called the Consequent. Thus in the proposition, ' If 
 the shepherd be negligent, the sheep go astray/ the 
 antecedent is ' If the shepherd be negligent ' ; the conse- 
 quent is ' the sheep go astray.' It will be seen that 
 neither part of the proposition is independently asserted 
 as true. We do not affirm that ' the shepherd is negli- 
 gent/ nor yet that ' the sheep go astray/ It is the 
 nexus between the two, the dependence of consequent 
 on antecedent, which is affirmed. 
 
 There are two forms in which the hypothetical sen- 
 tence may be expressed. These are (i) If A is B, C is 
 D, and (2) If S is M, it is P. Judgments constructed 
 according to the first formula, may usually by a little 
 manipulation be expressed in the second form also. 
 But it is incorrect to say that the latter is a more funda- 
 mental type than the former. 
 
 Hypothetical of the second form, can be expressed 
 categorically, by substituting in the place of ' If S is 
 M, it is P/ the form ' All 5 that is M is P/ or ' All SM 
 is P.' Similarly for the categorical ' All S is P/ we may 
 write, ' If anything is S, it is P.' 
 
 Some writers on Logic have maintained that the categorical 
 and hypothetical propositions are in fact equivalent. There 
 can be no doubt that this opinion is erroneous. In the categorical 
 we state unconditionally that 5 is P. In the hypothetical we 
 state that S is P, if certain conditions are fulfilled. The con- 
 stituent parts of the categorical are related as subject and attri- 
 bute : the parts of a hypothetical are related as reason and 
 consequent. Nor is it only the mental forms that are different. 
 The fact to be expressed positively demands one form to the 
 
THE JUDGMENT AND THE PROPOSITION 65 
 
 exclusion of the other. Such propositions as ' Gold is yellow, ' 
 and ' If the King comes, a salute will be fired,' are distorted 
 when they are expressed as 'If anything is gold, it is yellow,' 
 and 'The case of the King's arrival is a case of firing a salute.' 
 In regard to the employment of the one form in place of the 
 other, Professor Case has well said : " Taking the carelessly ex- 
 ' pressed propositions of ordinary life [logicians] do not perceive 
 ' that similar propositions are often differently expressed, e.g. 
 ' ' I being a man am mortal,' and ' If I am a man I am mortal ' : 
 ' and conversely that different judgments are often similarly 
 ' expressed. In ordinary life we may say ' All men are mortal,' 
 '. . . ' All candidates arriving five minutes late are fined.' . . . 
 ' But of these universal propositions, the first expresses a cate- 
 'gorical belief . . . the other is a slipshod expression of the 
 ' hypothetical belief, ' If any candidates arrive late, they are 
 'fined.'' Encycl. Brit. (loth ed.), vol. 30, p. 333, Art. Logic. 
 
 Quantity and Quality of Hypothetical. All hypo- 
 thetical propositions are affirmative. If .we desire to 
 meet a hypothetical with its negation, we must deny 
 what it affirms. That is to say we must deny the nexus 
 between the antecedent and consequent. This is done 
 by the form ' Although 5 is M, it need not be P.' The 
 negative of * If he is poor, he is uneducated/ is ' Although 
 he is poor, he may not be uneducated.' These negative 
 forms, however, are not themselves hypotheticals : for 
 they do not assert the dependence of consequent on 
 antecedent. 
 
 There can be no differences of quantity in hypothe- 
 ticals, because there is no question of extension. The 
 affirmation, as we have seen, relates solely to the nexus 
 between the two members of the proposition. Hence 
 every hypothetical is singular. 
 
 12. Disjunctive Propositions. 
 
 A Disjunctive Proposition is one which makes an 
 alternative predication. 
 
 Disjunctives like Hypotheticals are of two forms : 
 (i) Either A is B, or C is D ; and (2) S is either P or 
 Q, e.g. ' Either the general was incompetent or his sub- 
 ordinates were disobedient,' ' Religions are either false 
 or true.' 
 
 F 
 
66 PRINCIPLES OF LOGIC 
 
 It has been much disputed whether the alternatives 
 in a disjunctive are mutually exclusive or not : in other 
 words, whether we not only know that one must be true, 
 but also that if the one is true, the other is certainly 
 false. Thus supposing we are aware that ' 5 is either 
 P or Q,' and are then informed that '5 is P,' can we 
 conclude that S is not Q ? We shall consider this point 
 in a subsequent chapter. 1 
 
 The Disjunctive can be expressed by means of Hypo- 
 thetical propositions. If it be maintained that the dis- 
 junction is exclusive, we need two hypothetical propo- 
 sitions to represent a disjunctive, viz., (i) If 5 is P, it is 
 not Q. (2) If 5 is not P, it is Q. If the mutual exclu- 
 siveness be denied, a single hypothetical will suffice, 
 viz., ' If 5 is not P, it is Q.' 
 
 Quantity and Quality of Disjunctives. By virtue of 
 their form all disjunctives are affirmative. The alter- 
 native is necessarily asserted. However, a difference 
 in quantity is possible. The proposition may be of 
 the form ' All S are P or Q ' ; or it may be particular, 
 as, ' Some 5 are P or Q.' 
 
 A form of proposition termed by the Scholastics Conjunctive 
 gives us what is practically the negative form of the Disjunctive. 
 Its formula is ' S is not bothP and Q,' ' The King is not both at 
 London and Windsor.' 
 
 The whole terminology of Conditionals is in confusion. We 
 have followed that preferred by Hamilton (Logic, I. 236) and 
 subsequently by several other authors. Some logicians make 
 hypothetical the genus, and give the name conditional to those 
 we have called hypothetical. This division is found in Whately 
 and is accepted by Mill (I. 91). Perhaps the most satisfactory 
 division is that of Boethius. He terms the genus conditionalis 
 or hypothetica indifferently, and calls the species respectively 
 conjuncta (connexa) and disjuncta. 
 
 1 See below, Ch. 14, 4. 
 
CHAPTER IV. 
 
 THE LAWS OF THOUGHT. 
 
 i. The Laws of Thought. In each science there are 
 certain principles or laws, which are recognized as 
 fundamental within that science. Every conclusion 
 which it claims to have demonstrated, depends for its 
 validity on the truth of those principles. Such for 
 instance are the definitions of Euclid in regard to 
 Geometry (the science of abstract spatial extension), 
 and the laws of motion in regard to the science of Mechan- 
 ics. In each case the principles have their own sphere 
 of application. They are principles of this or that 
 science, and beyond it they are not operative. There 
 are, however, certain laws, which are not confined within 
 the limits of any one of the special sciences, but which 
 apply to all that is, to all that has a right to the name of 
 Being or Thing. For instance the law of causality which 
 lays down that every event must have a cause, is such a 
 principle as this. It is not a law of one of the special 
 sciences, but is true of all things. It belongs to that 
 universal science of Metaphysics or Ontology, of which 
 something has been said in Ch. i, 3. 
 
 Just as there are laws which apply to the whole realm 
 of Being, to the real order in its full extent, so too there 
 are laws which govern the whole of the conceptual order, 
 and on which depends the validity of every judgment, 
 whatever it may be. These are the Laws of Thought, 
 which form the subject of the present chapter. They 
 are three in number : 
 
 (i) The Law of Contradiction, viz. : Contradictory 
 judgments (e.g. A is B, A is not B) cannot both be 
 true. 
 
68 PRINCIPLES OF LOGIC 
 
 (2) The Law of Identity, viz. : Everything is what it is. 
 
 (3) The Law of Excluded Middle, viz. : Of two contra- 
 
 dictory judgments (A is B y A is not B) the one 
 must be true, the other false. 
 
 These three laws we shall proceed to consider in detail. 
 But first, it will be well to ask ourselves in what sense 
 they are termed laws. For the word * law ' is used in 
 various senses. In its primary signification it means an 
 ordinance imposed by a legitimate superior on the body 
 politic, and carrying with it an obligation of obedience. 
 But it is also employed to signify a uniform mode of 
 acting observed by some natural agent. In this sense 
 we use the term ' laws of nature/ e.g. the law of gravita- 
 tion, the law that water under a certain pressure freezes 
 at 32 F., etc. Laws of nature are only called laws by 
 analogy : there is of course, no question here of the 
 obedience which one will ought to yield to another. The 
 law is simply our description of the way in which the 
 agent does in fact act. It tells us what is, not what ought 
 to be. In yet another meaning we use it to denote a 
 norm or standard, to which we must conform in order to 
 achieve some end. Thus we may speak of the laws of 
 perspective. If we wish our drawing to be accurate, we 
 must observe them. Otherwise, we shall not attain our 
 object. 
 
 It is in this last sense that we employ the word, when we 
 speak about the laws of thought. It is certainly the case 
 that we are unable to judge a pair of contradictory pro- 
 positions to be true, if we are conscious of the contra- 
 diction. But it not infrequently happens that men 
 unconsciously hold opinions, which are really contradic- 
 tory the one of the other, though because they are 
 expressed in different words, or from some confusion of 
 mind, their mutual opposition is not recognized. Hence 
 the laws of thought cannot strictly be termed laws in 
 the second of the senses we have noticed above. But 
 since in all our mental judgments our end and object 
 is to attain truth, they are rightly termed laws in the last 
 
THE LAWS OF THOUGHT 69 
 
 sense mentioned : for if they are not observed, our judg- 
 ments are not true but false. 
 
 2. The Law of Contradiction. The form in which 
 we have given the principle of Contradiction, ' Con- 
 tradictory judgments cannot both be true/ is that in 
 which, with various slight modifications it is several 
 times enunciated by Aristotle. 1 He, moreover, is care- 
 ful to point out that where judgments are contradic- 
 tory to each other, the predicate must be referred 
 to the subject in the same way in each, and the point 
 of time must be identical. " A refutation," he says, 
 " occurs when something is both affirmed and denied 
 ' of one and the same subject . . . and when it is denied 
 ' in the identical respect, relation, manner and time, 
 ' in which it has been affirmed." z It might be true to 
 say both that ' the prime minister is capable/ and that 
 ' the prime minister is not capable/ if the capacity re- 
 ferred to was in the one case capacity for government, 
 in the other capacity for writing Greek verse : or if we 
 were speaking of different periods in his life. 
 
 Mill adopts a more cumbrous phraseology. He words 
 the law as follows : ' The affirmation of an assertion and 
 the denial of its contradictory are logical equivalents, 
 which it is allowable and indispensable to make use of as 
 logically convertible" (Exam, of Hamilton, p. 414). 
 
 This law, as we have said, is a ruling principle of the 
 whole conceptual order. It applies to ah 1 that is thought. 
 But the order of thought of conceptual Being is 
 essentially a representative order. It manifests the order 
 of things. And this law of thought is the conceptual 
 expression of a fundamental necessity of the real order : 
 to the logical principle corresponds a metaphysical princi- 
 ple. This metaphysical law may be stated : " The same 
 attribute cannot at one and the same time both belong 
 and not belong to the same thing "(Arist. Met. III., c. 3, 10). 
 
 1 Met., III., c. 6, 10. aSvyaroit TTJV OLVT'I.<P<L<TLV a\t]0fi'<rdai 8,/J.a /caret rov 
 avrov. 
 
 * Soph. Elenchi. c. 5, 5. eXeyxos ^ev yap avTL<f>affLS rou avrov xai fros . 
 Kara rat/ro Kal 7r/>6$ rai/rd Kal u'cratrrws Acal iv ra> avr xp^V- 
 
70 PRINCIPLES OF LOGIC 
 
 Another form in which it is frequently expressed, is : 
 " It is impossible for the same thing both to be and not 
 to be, at the same time." l How closely the logical princi- 
 ple represents the metaphysical will at once be seen, if 
 we express the former as : " The same attribute cannot 
 at one and the same time be both affirmed and denied 
 of the same thing." But the student should be careful 
 to distinguish the various expressions of the law, and when 
 dealing with logical questions not to state the principle 
 in a metaphysical form, nor vice versa. 
 
 This law Aristotle declares to be the first of all axioms, 
 and the most certain of all principles (Met. X., c. 5, i). 
 
 * The question will doubtless suggest itself, on what grounds 
 this is asserted to be the first of all axioms. A brief examination 
 will show us that the principle of Contradiction is the first Analy- 
 tic proposition, which we attain through an analysis of our most 
 primary notion the notion of ' Being ' or ' thing.' 
 
 This notion, which we apply equally to all entities whatever, 
 calls for a brief consideration. 
 
 We are accustomed to name objects from their various deter- 
 minations and perfections. We term one man a ' runner,' be- 
 cause the perfection denoted by the word ' to run,' characterizes 
 him, and we call another a ' painter ' for a similar reason. Further, 
 we apply these denominatives to them, even though the per- 
 fection is not at the moment in a state of actualization. The 
 man is called a ' runner ' or a ' painter,' not because he is actually 
 running or painting, but because he has the capacity to elicit 
 these acts. ' Being ' is a denominative of this type. It is 
 applied to objects in virtue of that primary perfection signified 
 by the verb ' to be,' as understood in the first of the senses men- 
 tioned in Ch. 3, 2, namely ' to exist.' The notion which expresses 
 this primary characteristic of ' Being ' or ' actuality,' is clear to 
 us from the dawn of our intelligence. It is absolutely simple. 
 We cannot explain it by any that is simpler : for its simplicity 
 is ultimate. Indeed were there not primary notions of this kind, 
 it would be impossible to explain anything. The mind would 
 be lost in an infinite regress, as it endeavoured to find some idea 
 which did not itself need elucidation. 
 
 What then is the Analytic proposition which unfolds the 
 intension of this term, which is the first principle to emerge from 
 the consideration of our primary concept ? Its very simplicity 
 
 1 It is to be observed that the principle of Contradiction is a modal pro- 
 position de impossibili, and the principle of Excluded Middle a modal de 
 necessario (Ch. 3. 9). 
 
THE LAWS OF THOUGHT 71 
 
 prohibits our explaining it otherwise than by declaring its differ- 
 ence from its opposite, viz. that it is essentially opposed to 
 non-existence. 1 Yet we cannot state the principle as ' A Being 
 is that which is not non-existent,' for as we have noticed, ' Being ' 
 is applied not merely to that which does at present exist, but 
 to such objects of thought as we see can exist. A chiliagon may 
 be termed a ' thing ' or a ' Being.' Our proposition must be 
 expressed, ' A Being which is, cannot at the same time not be ' ; 
 or as otherwise phrased, ' It is impossible for the same thing 
 both to be and not to be at the same time.' Here then we have 
 the principle of Contradiction, as the first of principles derived 
 by analysis from the primary notion. 
 
 In regard of each Being, however, we must consider not merely 
 its existence, but its nature : that which makes it what it is. 
 The principle may be enunciated not merely in reference to the 
 former, but to the latter : for the nature of an entity determines 
 the mode of its existence. As thus expressed, we get the form ; 
 ' The same attribute cannot at the same time both belong and 
 not belong to the same thing.' The logical expression, as we 
 have seen, is identical with this, save that it refers to the mental 
 act by which we judge about the thing : ' The same attribute 
 cannot at the same time be both affirmed and denied of the same 
 thing.' 
 
 3. The Law of Identity. This principle is often 
 stated in the form A=A. This, however, is manifestly 
 a formula, and not the enunciation of a philosophic 
 principle. Locke (Essay, Bk. 4, c. 7) enunciates it as 
 ' Whatever is, is/ and this form appears to be philoso- 
 phically correct. Like the principle of Contradiction, 
 this law is an Analytic proposition explicative of 
 the concept of Being. Its connexion with that princi- 
 ple will appear plainly if we express it as ' A Being which 
 is, is.' In this form we see that the only difference be- 
 tween the two is that in the one case we affirm that things 
 which exist, exist : in the other, that things which exist, 
 cannot not exist. 
 
 Like the principle of Contradiction also, it may be 
 enunciated in reference to the nature, which determines 
 the existence. Leibniz has given expression to the law 
 
 1 On Being and Not-being as the primary concepts of the understanding, 
 see St. Thomas, Opusc. 44, Summa Totius Logicae, Tract 3, c. I, U Ad viden- 
 dum. Cf. Summa Theol. I., Q. n, Art. 2. ad 4. 
 
72 PRINCIPLES OF LOGIC 
 
 in this form. He words it ' Everything is what it is.' 
 Leibniz's form will serve us also for the logical order, if 
 it be understood as signifying that every subject of pre- 
 dication is what it is, i.e. that whatever attribute is 
 affirmed of any subject, is in fact an attribute of that 
 subject. 
 
 Mill somewhat unnecessarily introduces the question of 
 verbal expression. He enunciates the law as : " Whatever 
 is true in one form of words, is true in every other form 
 of words, which conveys the same meaning " (Exam, of 
 Hamilton, p. 409). 
 
 It is the universal practice at present to treat the princi- 
 ple of Identity separately from the principle of Contra- 
 diction. Scholastic authors, however, do not admit its 
 claim to rank as a really independent principle. At most 
 they admit that it is a rudimentary form of the principle 
 of Contradiction. 1 They urge that the predicate of an 
 Analytic proposition must in some way explicate the 
 notion of the subject. This principle does not do so. 
 The predicate and the subject are the same concept. It 
 is mere tautology. 
 
 There is, it may be owned, some force in this objection. 
 The principle tells us nothing. Yet we must remember 
 that Being is a concept which does not admit of analysis 
 properly so called. Hence perhaps justification may be 
 found for a tautologous principle here, which could not 
 be adduced in any other case. The form is permissible, 
 because it is indicative of the fact, that we have arrived 
 at the limits of all explanation. But in order for the 
 principle to convey any information, and to be of any 
 service, it must be developed into the law of Contradic- 
 tion. 
 
 * The separate treatment of the two principles first became 
 usual after the time of Leibniz. It is true that Parmenides the 
 Eleatic (circa B.C. 490) had enunciated the principle Being is 
 (eov e/A/xei'cu) as the foundation of his philosophy. But Aristotle 
 
 1 Cf. Pesch. Instit. Logicae, vol. 3, 1230. Ad usum principii identitatis 
 quod attinet, illud a Peripateticis nunquam in sua propria forma adhibit um 
 videmus. Est enim vagum et indetcrniinatum, et priiicipiorum potius radicem 
 coiitirict et germen imperfectum. 
 
THE LAWS OF THOUGHT 73 
 
 umphatically affirms that the law of Contradiction is the first 
 of all principles : and his decision for long went undisputed. 
 Among mediaeval authors the Spanish Scotist Antonius Andreae 
 (ob. 1320) argues that the first place should belong to the princi- 
 ple ' Every Being is a Being ' (Omme Ens est Ens, Qq. in Met. 
 IV., Q. 4). But the authority both of St. Thomas (Met. IV., lect. 
 6) and of Scotus (Quaest. sup. Met. IV., Q. 3) was against him : 
 and he is expressly refuted by Suarez (Disp. Met. III., 3). 
 Leibniz however makes the principle of Identity, which he gives 
 as ' Everything is what it is/ the first of the primitive truths 
 of reason which are affirmative, and the principle of Contra- 
 diction, ' A proposition is either true or false ' the first of the 
 negative truths (Nouv. Ess. IV., 2, i). He further says, "the 
 statement that a thing is what it is, is prior to the statement 
 that it is not another thing " (Nouv. Ess. IV., 7, 9). Here as 
 it would seem, is the real ground for the introduction of the 
 principle of Identity as distinct from that of Contradiction. It 
 appeared impossible that the primary analytic principle should 
 be negative. If however, the view taken in the last section is 
 accurate, the negative form is the necessary consequence of the 
 primary character of the principle. We can only explain the 
 perfectly simple by distinguishing it from that which it is not. 
 
 4. The Law of Excluded Middle. Aristotle enunciates 
 this principle in the form given above, " Of two contra- 
 dictory judgments, the one must be true and the other 
 false " (Met. III., c. 8, 3, 4). He says also, " Be- 
 tween the two members of a contradiction, there is no 
 middle term" (Met. III., c. 7, i). 1 
 
 As a metaphysical principle, it is stated, ' A thing must 
 either be or not be/ The truth of this is evident from 
 the immediacy of the opposition between being and not- 
 being. The truth of the logical principle is capable of 
 demonstration as follows. Where we have two contra- 
 dictories, we have affirmation and negation, is and is not. 
 If the member which constitutes the mental judgment 
 corresponds with the reality, whether it be in affirmation 
 or negation, then the mind has attained truth. Should 
 it, however, not be in conformity with its object, the 
 judgment is false. That is to say, the mind has either 
 
 1 avdyKrj yap TTJS dTi0dcrews ddrepov elvai TO fj.bpi.ov a\r)0s . . . Qarepov 
 yap [J.tpos rrjs dfrt^dcrews \f/vdos <?Tt.v (III., C. 8). 'AXXd /J.T]V ovdt ^cra|u 
 ovdev (III., c. 7) : and see Cat., c. 10, 31-40. 
 
74 PRINCIPLES OF LOGIC 
 
 judged that what is, is not, or that what is not, is. Wher- 
 ever, therefore, the judgment is false, the contradictory 
 judgment, whether it be the affirmative is, or the nega- 
 tive is not, will be true. Hence of two contradictories, 
 the one must be true, the other false. 1 
 
 The close connexion between the logical principle and 
 the metaphysical at once appears, when we reflect, that 
 in affirmation, we are attributing a certain conceptual 
 being to the subject ; in negation, we assert that it does 
 not possess this being (Ch. 3, 2). All contradictories 
 therefore present the alternative between being and not 
 being. 
 
 The way in which the principle is expressed by certain 
 logicians, " Of any two contradictory predicates, one 
 ' must belong to every subject," is unsatisfactory. It 
 supposes that the predicates, and not the propositions, 
 are contradictory to each other, and is represented by 
 the formula, ' A is either B or not-B/ But, as we have 
 seen, the primary form of negation is the negative 
 judgment, not an affirmative judgment with a negative 
 predicate ; and in the expression of a fundamental law, 
 it is the primary form that we need. Mill employs the 
 following formula : " It is allowable to substitute for the 
 denial of either of two contradictory propositions, the 
 assertion of the other " (Exam, of Hamilton, p. 416). 
 
 It should be carefully noted that the law of Excluded 
 Middle is in no way concerned with Contrary terms. 2 
 We have explained Contrary terms as those which ex- 
 press the widest possible difference among classes belong- 
 ing to the same genus, e.g. ' white, black/ * convex, 
 concave/ ' love, hatred.' There is, of course, a mean 
 between terms such as these. Objects possessed of any 
 
 1 Arist. Met. III., 7, i ; St. Thomas, in Met. IV., lect. 16. 
 
 * Mr. Bosanquet's views as to negation lead him into this error. He holds 
 that negation qua, negation is void of all significance, and that the true value 
 of a negative judgment is to be sought in its positive content. Hence he 
 concludes that the principle of Excluded Middle relates to contraries (Logic, 
 II. 210). A full treatment of the import of the negative judgment and of 
 the relation between contradictory and contrary propositions, will be found 
 in St. Thomas, Opusc. 33, De Quatuor Oppositis, cc. i, 2. 
 
THE LAWS OF THOUGHT 75 
 
 other variety of colour are neither white nor black ; a 
 plane surface is neither concave nor convex ; and indiffer- 
 ence is neither love nor hatred. It is manifest, however, 
 that an object must be either white or not white, convex 
 or not convex ; and that in regard to any particular 
 individual, it is either true that we do or that we do not 
 feel love towards him. 
 
 The principle has not passed unchallenged. Mill, in the 
 interests of the empiricist philosophy, declared the law to be a 
 mere generalization from experience. We have no grounds, he 
 thought, for regarding it as necessary. Indeed he goes further, 
 and maintains that "it is not even true except with a large 
 ' qualification. . . . ' Abracadabra is a second intention,' is neither 
 ' true nor false. Between the true and false there is a third possi- 
 ' bility, the Unmeaning." Such an argument can scarcely be 
 treated as serious. An unmeaning proposition is not a judg- 
 ment at all. Of more moment perhaps is the Hegelian objec- 
 tion. The very basis of the Hegelian philosophy is the recon- 
 ciliation of opposites. Becoming is supposed to owe its origin 
 to the union of Being and Not-Being, and the whole of Nature 
 is regarded as constituted by this dialectic development. Hegel 
 himself argues against the principle of Excluded Middle by point- 
 ing out that between + A and - A lies A. As against this view, 
 it is urged that in Hegel's system the opposites are in fact con- 
 traries not contradictories, and that the individual does not 
 owe its origin to them, but that they are obtained by abstraction 
 from the individual. Thus if it be urged that at dawn we can 
 say with equal truth ' It is day ' and ' It is not day,' and that 
 the state of dawn is constituted by these opposites, it is answered 
 that the two moments are not, as alleged, contradictory opposites, 
 but the contraries ' dark ' and ' light ' : and that dawn is 
 not in any sense constituted by a dialectic development out of 
 darkness and light, though we can mentally abstract these 
 concepts from the state of dawn. 
 
 * 5. Other Views as to the Source of the Laws of Thought. 
 
 In other schools of philosophy, very various accounts are 
 given as to the nature and origin of these laws. It seems well 
 to notice here three theories differing widely from that set forth 
 in the preceding sections. These views respectively regard the 
 laws of thought (i) as subjective laws of the understanding, of 
 whose objective, validity, however, we can have no rational 
 guarantee, (2) as principles determining the growth of that ' ex- 
 perience,' which men erroneously distinguish into thought on 
 
76 PRINCIPLES OF LOGIC 
 
 the one hand, and things on the other hand, (3) as mere generaliza- 
 tions from experience. 
 
 The first view is that of Kant. Among English logicians it 
 is explicitly taught by Mansel. He tells us that the principles 
 of thought are " laws under which the mind is compelled to 
 ' think, and which it cannot transgress, otherwise than ne- 
 ' gatively by ceasing to think at all." "It may be," he adds, 
 " that the conditions of possible thought correspond to con- 
 ' ditions of possible being, that what is to us inconceivable is 
 ' in itself non-existent. But of this, from the nature of the 
 'case, it is impossible to have any evidence " (Proleg. Logica, 71, 
 72). It is needless to point out that such a view as this leads 
 directly to philosophic scepticism. 
 
 The second view is represented by Mr. Bosanquet. We have 
 already (Ch. i, note (7)) called attention to the theory held by 
 the neo-hegelian school of logicians, according to which the 
 operations of the mind are vital functions by which the so-called 
 ' real ' world has been constituted. It is under this aspect Mr. 
 Bradley regards the laws of thought. He holds that we cannot 
 say that these principles are merely laws of thought, if by that 
 we mean thought as distinguished from things : " Since a separa- 
 ' tion between intelligence and experience is purely fictitious, 
 ' there is nothing to be gained by cutting down the content of 
 ' these principles to a minimum in the hope of restricting their 
 ' reference to thought as opposed to things." They are " the 
 animating principles of growth " which govern the development 
 of experience : and if we recognize them as " postulates of know- 
 ledge," this is because " on analysis of experience, they are 
 ' found to be active factors in it from the first " (Logic, II. 205- 
 207). 
 
 Mill (Logic, I., p. 308. Exam, of Hamilton, p. 417) explicitly 
 repudiates the view that these principles are subjective laws of 
 the thinking faculty. He holds that they are conclusions derived 
 from a constant experience of their truth. We have never as 
 a matter of fact known any case where two contradictories 
 have been simultaneously true. Hence we rightly lay down a 
 general but empirically discovered principle to that effect. As 
 for the law of Excluded Middle, we have already seen that he 
 holds that it needs qualification before it can be admitted as 
 universally true. It must, he admits, be owned that " we cannot 
 ' now conceive the opposite of these laws to be true. But this 
 ' inconceivability is of little value as a criterion of truth to 
 ' those who know how artificial, modifiable, the creatures of 
 ' circumstances and alterable by circumstances, most of the sup- 
 ' posed necessities of thought are." Constant experience of 
 one character is, in his view, sufficient to lead us to regard its 
 opposite as inconceivable. 
 
CHAPTER V. 
 
 DIAGRAMMATIC REPRESENTATION OF PROPOSITIONS : 
 OPPOSITION OF PROPOSITIONS. 
 
 i. Diagrammatic Representation of Propositions : 
 Euler's Circles. It might well seem that the task of repre- 
 senting by a diagram the mental act of judgment, necessar- 
 ily involved an impossibility. Take, for instance, a simple 
 proposition such as, ' The orange is round.' How, it may 
 be asked, can there be any material representation of so 
 essentially a psychical act as the abstraction of ' round- 
 ness ' from the concrete object ? Or how can any figure 
 express a universal concept ? If indeed we proposed to 
 represent the proposition as it is mentally conceived, these 
 objections would be unanswerable. But we may, if we 
 will, consider not the mental judgment, but, what is a 
 very different thing, the extension of the terms constitut- 
 ing the judgment. In extension we have to do not with 
 the conceptual order, but with the real : and hence 
 diagrammatic representation ceases to be intrinsically im- 
 possible. If the terms be thus understood, the proposi- 
 tion is viewed not as expressing a relation of attribute to 
 subject, but as expressing a relation between two classes. 
 The proposition ' All men are mortal/ will be looked on as 
 a statement of the relation that exists between the class 
 ' man ' and the class ' mortal things/ This is, of course, 
 a purely artificial method of treating the proposition. 
 But the student will find it, in many respects, helpful, 
 provided that he bears in mind that the diagrams exhibit- 
 ing the relations of the classes, represent things and not 
 thoughts. 
 
 The most usual method employed, is that entitled 
 
78 PRINCIPLES OF LOGIC 
 
 Euler's Circles. It was devised by the Swiss logician 
 Euler (1707-1803). In it 5 and P are represented each 
 by a circle, the circle standing for the collection of objects 
 denoted by the term. By the aid of these circles, the 
 various relations compatible with each of the four pro- 
 positions A.E.I.O are all of them capable of diagram- 
 matic expression. 
 
 FIG. 
 
 FIG. 2. 
 
 A propositions. The proposition S a P will be repre- 
 sented either by Fig. i or by Fig. 2. The class signified by 
 the subject may fall within the extension of the predicate 
 term, as in ' All men are mortal/ ' All triangles are plane 
 figures.' In this case, Fig. i accurately represents the 
 relation of the two classes. Or the extension of the two 
 terms may be identical, as in ' All men are rational ani- 
 mals ' ; ' All equilateral triangles are equiangular/ In 
 this case, the two circles must be coincident, and Fig. 2 
 is representative of the proposition. 
 
 FIG. 3. 
 
 E propositions. In every proposition of the form 
 5 e P, we deny that the two classes have any members 
 
DIAGRAMMATIC REPRESENTATION 79 
 
 in common. The one class is declared to fall altogether 
 outside the other, e.g. ' No fishes have lungs/ ' No scalene 
 triangles are equiangular.' Hence these propositions 
 are represented by Fig. 3. 
 
 I propositions. Figs. 4 and 5 show us the two cases 
 of the proposition 5 i P, in which it is some and not all 
 
 FIG. 4. FIG. 5. 
 
 of the class S, which fall within the class P. Fig. 4 repre- 
 sents the case in which there exist other members of the 
 class P besides those which are found within the extension 
 of S. ' Some men are black ' will serve as an example. 
 There are many objects belonging to the class ' black/ 
 which are not men. Fig. 5 stands for the case in which 
 there are no members of the class P, save those which 
 are also 5. ' Some elements are metals/ ' Some men are 
 Aryans/ are instances of such propositions. 
 
 But S i P does not exclude the truth of S a P : for, 
 as will be remembered, ' some ' in a particular proposition 
 is understood to mean, ' some, it may be all/ It is true 
 to say, ' Some equilateral triangles are equiangular/ 
 even though every equilateral triangle be such. The 
 mere form of the proposition does not tell us which rela- 
 tion in fact exists between the two classes denoted by the 
 terms. Hence not merely Fig. 4 and Fig. 5, but also 
 Fig. i and Fig. 2 may be the relation to which the I propo- 
 sition refers. When this proposition is used, there are 
 four possible cases. 
 
 propositions. In propositions of the form S o P, 
 we assert that some of the objects denoted by the object 
 
80 PRINCIPLES OF LOGIC 
 
 term, fall outside the extension of the predicate. When 
 it is the case that while some are outside, some also fall 
 within the extension of P, then the S o P proposition will, 
 like 5 i P, be represented by Figs. 4 and 5. Fig. 4 repre- 
 sents the case, in which P not only has some members 
 within the class S, but also some outside it, e.g. ' Some 
 men are not black.' Fig. 5 gives us the class in which P 
 is a class falling entirely within S, e.g. ' Some men are 
 not Aryans.' 
 
 But here too, the form of the proposition is compatible 
 with the case when the classes are mutually exclusive, 
 and when they have no members in common, e.g. 
 " Some scalene triangles are not equiangular." Where it 
 is thus employed, the classes will stand in the relation 
 represented by Fig. 3. For the S o P proposition there 
 are, therefore, three possible cases. 
 
 For a diagrammatic scheme to be thoroughly satisfac- 
 tory, it is usually stated that three conditions must be 
 fulfilled : 
 
 (1) The relation expressed by the diagram must be 
 
 evident, as soon as the principle of representa- 
 tion is understood. 
 
 (2) Each diagram must represent one relation and only 
 
 one. 
 
 (3) Each proposition in the schedule of propositions, 
 
 must be represented by one diagram alone. 
 
 Euler's circles have been found fault with on the ground 
 that they fail to fulfil this condition. The reason of this 
 failure is easy to understand. Diagrammatic representa- 
 tion is only possible in regard to extension. The true 
 function of the proposition is not however to express 
 the extension of the terms, but the inherence of an attri- 
 bute in a subject. There are five possible relations be- 
 tween the extension of two classes, and there are but four 
 fundamental propositions. Hence it would be idle to 
 look for a perfect system of representation. 
 
 Other systems of representation have been suggested 
 by various writers on Logic : but by the nature of the 
 case none of them is really satisfactory. Two of these 
 
DIAGRAMMATIC REPRESENTATION 81 
 
 methods we shall describe. But first it is necessary to 
 deal with the distribution of terms in a proposition, a 
 point that will be found to have important bearings on 
 several questions in Logic. 
 
 2. Distribution of Terms in a Proposition. A term 
 is said to be distributed in a proposition, when from 
 the form of the proposition we know that it must be 
 taken in its whole extension. When the form of the 
 proposition is not such as to indicate that the whole 
 extension is referred to, it is said to be undistributed. 
 
 If we consider the affirmative propositions A and 7, 
 we shall see that neither of them distributes the predicate. 
 When we say, ' All equilateral triangles are equiangular,' 
 it is true that the predicate ' equiangular ' refers here to 
 all equiangular triangles ; for there are no equiangular 
 triangles besides those that are equilateral. But we do 
 not know this from the form of the proposition. The 
 judgment ' All crocodiles are amphibious/ is of precisely 
 the same form, and here the predicate does not refer 
 to all amphibious creatures, but only to those which are 
 crocodiles. 
 
 The same reasoning holds good in the case of the pro- 
 position 7. We cannot tell from the form of the proposi- 
 tion, whether the whole extension of the term employed 
 in the predicate is referred to or not. In the proposition 
 ' Some flowers are fragrant/ the predicate is not taken 
 in its full extension. In the proposition ' Some mammals 
 are whales/ every member of the class ' whale ' falls 
 within the reference of the term : for whales are a small 
 class contained within mammals. But we could not 
 discover this from the form of the proposition. 
 
 In the negative propositions E and 0, the reverse is the 
 case. The subject of a proposition is excluded from the 
 whole extension of the class signified by the predicate 
 term. Thus if I say, ' No fishes are amphibious/ I ex- 
 clude the subject ' fishes/ from the whole class of amphi- 
 bious creatures. If I say, ' Some European nations are 
 not Aryan/ I exclude the European races of which I 
 
 G 
 
82 PRINCIPLES OF LOGIC 
 
 speak in the subject from the whole extension of the class 
 denominated ' Aryan/ 
 
 As regards the subject it is plain that it is distributed 
 in all universal propositions, and left undistributed in all 
 particular propositions. Universal propositions, of their 
 very nature, refer to the whole class signified by the 
 subject term. 
 
 Hence we have the following rules, which should be 
 carefully noted : 
 
 Universal propositions (A.E) distribute their subject. 
 
 Negative propositions (.0) distribute their predicate. 
 
 It will be noticed that E distributes both its terms, 
 while on the other hand / distributes neither subject nor 
 predicate. 
 
 * 3. Other Methods of Diagrammatic Representation. Other 
 ways of representing the proposition by means of dia- 
 grams have been suggested by various logicians. To two of 
 these systems we call attention here. They are (i) that pro- 
 posed by the German logician Lambert (1728-1777), and (2) that 
 of which Dr. Venn makes use in his Symbolic Logic. 
 
 (i) Lambert's method. Lambert employed a system in which 
 two horizontal straight lines, one above the other, represent the 
 terms of the proposition. The lower represents the subject, 
 the higher the predicate. Should the term be undistributed, 
 the line is partly continuous and partly dotted. If it be distri- 
 buted, there is no dotted portion. When the proposition is 
 affirmative, the continuous part of the predicate line is imme- 
 diately above the continuous part of the subject line : when it 
 is negative the continuous portions are not one above the other, 
 but are separated by a small interval. The forms of the four 
 propositions, will thus be : 
 
 P - P 
 
 5 S. 
 
 The figure here given for I is not that suggested by Lambert 
 
 himself, but one proposed in lieu of it by Dr. Venn. Lambert's 
 
 p _ 
 own figure is ' which, as Dr. Venn observes, "might con- 
 
 o ........ 
 
 ' sistently be interpreted to cover the case of * No 5 is P,' as well 
 ' as suggesting the possibility of there being no 5 at all " (Sym- 
 bolic Logic, p. 431). 
 
 In regard to this system, it may be said that it certainly ful- 
 
DIAGRAMMATIC REPRESENTATION 83 
 
 fils the requirements of having but one diagram for each pro- 
 position, and of being based on a simple and clear principle of 
 representation. Yet all will feel that it gives but little assistance. 
 The value of diagrams lies in the fact that they are able to repre- 
 sent to us the relation between the extension of the classes 
 denoted by the terms, a concrete point of view that often 
 assists the beginner. The same form of proposition, however, 
 is, as we have seen, significative of a variety of such relations. 
 Hence if we employ but one figure, it must necessarily be am- 
 biguous. As soon as we seek to represent the undistributed 
 term, we have to confess our ignorance of what the relation in 
 extension really is. We do not know where the line should 
 stop. The chief utility of the figure is thus lost. 
 
 (2) Dr. Venn's method. The sj^stem employed by Dr. Venn 
 is only available for the representation of universal propositions. 
 Circles are employed in this scheme, but the use made of them 
 is quite different to what we have seen in the Eulerian diagrams. 
 The primary diagram consists of two intersecting circles x and y. 
 This provides us with four compartments, viz., x which isy (xy), 
 X which is not y (xy), y which is not x (xy), and things which 
 are neither x nor y (xy}. This last compartment is sufficiently 
 represented by the blank space outside the circles. 
 
 FIG. i. 
 
 The method now proceeds on Dr. Venn's view that all uni- 
 versal propositions may be adequately represented by denying 
 the existence of certain classes. Thus, ' All x is y ' is adequately 
 represented by the denial that there is any x which is not y : 
 ' No yt is y ' denies that there is any x which is y : ' All x is all 
 y ' denies (a) that there is any x not y, and (b) that there is any 
 y not X. The representation of the propositions is effected by 
 shading out the compartment, whose existence is denied. The 
 following diagrams represent the propositions just mentioned : 
 
 FIG. 2. FIG. 3. 
 
84 PRINCIPLES OF LOGIC 
 
 ] 
 xy. 
 
 Fig. 2. ' All is y ' excludes xy. Fig. 3. ' No x is y ' excludes 
 '. Fig. 4. 'All x is all y' excludes xy and xy. The system 
 
 FIG. 4. 
 
 lends itself to the representation of universal propositions with 
 more than 2 terms, e.g. " All x is y or z." In this case, we have 
 to introduce a new circle intersecting all the compartments already 
 existing, and thus doubling their number : for the use of 3 
 terms will entail a need of eight compartments, viz., xyz, xyz 
 xyz, xyz, xyz. xyz, xyz, xyz. ' All x is y or z ' denies the existence 
 of the compartment xyz (Fig. 5). 
 
 X 
 
 FIG. 5. 
 
 The utility of the system is materially diminished by its being 
 applicable solely to universal propositions. Moreover, the view 
 that we can obtain an adequate representation of affirmative 
 universals by denying the existence of classes, is one to which, 
 as we shall show later (Ch. 7, 5), serious objections maybe urged^ 
 
 4. The Opposition of Propositions. 
 
 The Opposition of Propositions is the relation which 
 exists between propositions having the same subject 
 and predicate, but differing in quantity, or in quality, 
 or both. 
 
 The various differences give rise to four kinds of opposi- 
 tion. 
 
 The difference may be in both quality and quantity. 
 In this case it must be either between an A proposition 
 and an proposition, or else between an E proposition 
 
OPPOSITION OF PROPOSITIONS 85 
 
 and an I proposition. Opposition of this character is 
 styled contradictory. 
 
 The difference may be in quality alone. Here two 
 cases arise ; for the propositions in question may be 
 either universal or particular. The opposition between 
 two universal propositions differing in quality (A and E) , 
 is termed contrary. That between two particular pro- 
 positions, which differ in quality (/ and 0), is termed 
 
 subcontrary. 
 
 Where two propositions differ in quantity only, the 
 opposition between them is said to be subaltern. Thus 
 there is said to be subaltern opposition between A and / 
 and between E and 0. Of these the universal proposi- 
 tion is termed the subalternant, and the particular the 
 subalternate. 
 
 It is plain that this last relation is merely termed oppo- 
 sition by a conventional usage of that word. A universal 
 and a particular of the same quality, can hardly be said 
 to be opposed in the natural sense of the term, for the truth 
 of the universal carries with it the truth of the particular. 
 When A is true, / must be true. Indeed even in regard 
 to sub-contrary opposition, Aristotle says that it is merely 
 verbal : for the truth of one is compatible with the truth 
 of the other, e.g. ' Some men are just/ ' Some men are 
 not just/ 
 
 The relations just explained are set out in the figure 
 commonly called the square of opposition. 
 
 A contraries E 
 
 subcontraries Q 
 
86 PRINCIPLES OF LOGIC 
 
 We shall now proceed to examine the various kinds 
 of opposition in detail : 
 
 (1) Contradictory Opposition. Of two contradictory 
 propositions, the one must be true, the other must be 
 false. For example, the two propositions, ' All crows are 
 black/ ' Some crows are not black ', can neither be both 
 true, nor both false. This will be easily seen by the aid of 
 Euler's circles. The A proposition is represented by Fig. 
 i or Fig. 2 in which no part of the circle 5 falls outside the 
 limits of the circle P. In the proposition, either a part 
 or the whole of 5 falls outside P. It is plain that S 
 must either be such that no part is outside P, or such that 
 part is outside. Hence either A or must be true. 
 On the other hand it cannot be such that it both has 
 no portion outside P, and at the same time, some por- 
 tion outside P. Hence either A or must be false. 
 
 Contradictory opposition is the only form, of which it 
 is the case that if one of the propositions is true, the other 
 is false, and if one is false the other is true. Hence it is 
 said to be the most perfect form of opposition. The 
 characteristic to which we have just adverted, gives to 
 this kind of opposition a special importance in controversy, 
 to which we shall refer in the following section. 
 
 The rule of contradictory opposition is easily proved 
 from the laws of thought. In every case of contradic- 
 tion, we have judgments which are opposed as A is B, 
 A is not B. Thus in the judgments, ' All crows are black/ 
 ' Some crows are not black/ the negative proposition denies 
 that the attribute ' black ' belongs to each and all of those 
 individuals, of which it has been asserted : B is asserted 
 and denied of one and the same A . But the law of Contra- 
 diction has shewn us that where we have two propositions 
 of this form, one must be false : and the law of Excluded 
 Middle has taught us that one must be true. 
 
 (2) Contrary Opposition. Propositions which are op- 
 posed as contraries, cannot both be true, but may both be 
 false. Thus it cannot be at the same time true that 
 ' All metals are heavier than water/ and that ' No metals 
 are heavier than water.' For if it be true that there are 
 
OPPOSITION OF PROPOSITIONS 87 
 
 no metals heavier than water, then we may most certainly 
 assert the proposition : ' Some metals are not heavier 
 than water.' This, however, is the contradictory of ' All 
 metals are heavier than water/ Hence the judgment, 
 ' No metals are heavier than water/ excludes the truth of 
 the judgment, ' All metals are heavier than water/ 
 
 It is possible for each of two contraries to be false. For 
 to assert that both can be false together, is simply to 
 assert that their two contradictories can be simultaneously 
 true : that is, that the propositions I and can be true 
 together. But we have already seen that this can be the 
 case. It may be alike true that, ' Some men are black/ 
 and that, ' Some men are not black/ 
 
 A consideration of Euler's diagrams will confirm the 
 accuracy of these conclusions. The A proposition (Figs, 
 i or 2) shews us the circle S with no part of it outside P : 
 the E proposition shews us the two circles entirely 
 separated. These cannot both be the case at the same 
 time. But it may happen that neither is the case. For 
 5 may be partly within, and partly without P. 
 
 (3) Sub-contrary Opposition. Propositions, which are 
 opposed as sub-contraries, cannot both be false, but may 
 both be true. They cannot both be false ; for in that case, 
 their two contradictories, viz., A and E, would both be 
 true. And this we have shewn to be impossible. They 
 may both be true. For, as has just been said, there is no 
 impossibility involved in asserting both, ' Some men are 
 black/ and, ' Some men are not black/ For this reason 
 the older logicians refused the name of opposition both 
 to subcontrary and subaltern propositions (Summa 
 Totius Logicae, Tract 6, c. 8). 
 
 Here again Euler's circles serve us as illustrations. 
 The / proposition is represented by Figs, i, 2, 4, and 5 : 
 the proposition by Figs. 3, 4 and 5. Hence Figs. 4 
 and 5 represent cases where / and are simultaneously 
 true. But if I is false, the contradictory proposition E 
 must be true : and this being the case, Fig. 3 alone will 
 represent the relation of the terms. Similarly if is false, 
 the contradictory A must be true : and the relation of 
 
8g PRINCIPLES OF LOGIC 
 
 the terms must be represented by Figs, i or 2. But Fig. 3 
 is incompatible with either of these. 
 
 (4) Subaltern Opposition. In regard to subaltern pro- 
 positions, the truth of the universal involves the truth 
 of the particular, but not vice versa ; and the falsity of 
 the particular involves the falsity of the universal, but not 
 vice versa. The truth of these rules is easily seen. If A 
 is true, then I is certainly true. It is commonly said that 
 the truth of 7 follows from that of A by the law of Iden- 
 tity. It would perhaps be more accurate to say that it 
 needs no proof, as the same attribute is asserted of indivi- 
 duals, of which it has already been affirmed. 
 
 It is, however, clear that the truth of / does not involve 
 the truth of A. Some men may be black, and yet it 
 may not be the case that all men are so. 
 
 The falsity of the particular involves the truth of its 
 contradictory, e.g. If / is false, E is true. But the con- 
 tradictory of the subaltern is the contrary of the subal- 
 ternant. If then it be admitted as true, the universal 
 subalternant proposition is false, e.g., E being admitted as 
 true, A must be false. But if it be the universal which be 
 false, and the contradictory particular be true, it does not 
 follow that the subaltern of the universal is false. For two 
 sub-contraries may be true together. 
 
 The explanations already given of the use, which may 
 be made of Euler's circles, have probably been sufficient 
 to enable the student to notice how these rules also are 
 illustrated by them. 
 
 5- Opposition as a Means of Inference. We have 
 hitherto been treating of opposition as a relation ex- 
 isting between two propositions. But it will not have 
 escaped notice that it also provides us with a means, 
 by which we may pass from a statement as to the 
 truth or the falsity of a given proposition to a statement 
 as to the truth or falsity of other propositions related to 
 the first by the various kinds of opposition. The follow- 
 ing table from Mansel (Aldrich, p. 52) enumerates the 
 inferences, which we may thus draw : 
 
OPPOSITION OF PROPOSITIONS 89 
 
 1. If A is true ; is false, E false, / true. 
 
 2. If A is false ; is true, E unknown, / unknown. 
 
 3. If E is true ; / is false, A false, true. 
 
 4. If E is false ; / is true, A unknown, unknown. 
 
 5. If / is true ; E is false, A unknown, unknown. 
 
 6. If / is false ; E is true, true, A false. 
 
 7. If is true ; A is false, E unknown, I unknown. 
 
 8. If is false ; A is true, / true, E false. 
 Thus from the truth of a universal (Nos. i and 3), or 
 
 from the falsehood of a particular (Nos. 6 and 8) we may 
 infer the quality of all the opposed propositions : but 
 from the falsehood of a universal (Nos. 2 and 4) and from 
 the truth of a particular, we can only infer the quality 
 of its contradictory. 
 
 Since we argue directly from the truth of to the false- 
 hood of A, contradictory opposition acquires primary 
 importance in controversy. By the production of a single 
 negative instance, a whole general statement is at once 
 confuted. The generalization is destroyed, not by show- 
 ing that all its parts, but that one alone, is untrue. 
 
 6. Contradictory Opposition outside the Fourfold 
 Scheme. We have seen that it is characteristic of contra- 
 dictory propositions that the one must be false, the other true. 
 This is often assumed as the general definition of contra- 
 dictories : and in that case it is possible to find a contra- 
 dictory to every proposition, and not simply to those 
 which can be placed in a square of opposition. 
 
 Exponible propositions are contradicted by a disjunc- 
 tive asserting that at least one or other of the exponents 
 is false. Thus the contradictory of ' All the crew save 
 one were drowned/ is ' Either the remainder of the crew 
 were not drowned, or the one in question was not saved.' 
 It is plain that unless a disjunctive is used, it is possible 
 for both propositions to be false. Thus, supposing the 
 proposition to have been denied in the form, ' All the 
 crew save one were not drowned/ both the original asser- 
 tion and the negation would be untrue, if the facts were 
 that not even one of the crew was saved. 
 
90 PRINCIPLES OF LOGIC 
 
 The contradiction of propositions containing a numerical 
 assertion, depends on how they are to be understood. 
 When they are understood as conveying an exact com- 
 putation, a disjunctive must be used. Thus the contra- 
 dictory of the proposition, ' Fifteen candidates are pre- 
 senting themselves/ will take the form, ' Either more or 
 fewer than fifteen candidates are presenting themselves/ 
 
 Sometimes numerical statements must be understood 
 in the sense to signify that the proposition is true of at 
 least that amount : and then the disjunctive form is not 
 required. For instance the assertion ' The age of Henry 
 Jenkins of Swaledale was 169 years/ is contradicted by, 
 The age of Henry Jenkins of Swaledale was less than 169 
 years.' 
 
 Any proposition, however complicated, may be contra- 
 dicted by prefixing ' It is false that.' This method of 
 contradiction may, for instance, be usefully employed if 
 we are called on to deal with such a sentence as the follow- 
 ing : " This policy, being foolish and ill-considered, could 
 not, under any circumstances, have succeeded." 
 
 Opposition of Singular Propositions. In Ch. 3 we 
 called attention to the fact that although the Singular 
 proposition is frequently reckoned as a special type of 
 the Universal judgment, yet strictly speaking it stands 
 by itself and is neither universal nor particular. This 
 appears plainly when it is considered in relation to our 
 present subject. In the square of opposition it has no 
 place. If the original terms be retained, it admits of one 
 kind of opposition alone, viz., a contradictory. ' Caesar was 
 killed on the Ides of March/ ' Caesar was not killed on 
 the Ides of March/ are contradictories in the sense ex- 
 plained in the present section. One of the two proposi- 
 tions must be true, the other false. 
 
 7. Contrary Opposition outside the Fourfold Scheme. 
 
 The extended signification given to the term ' contra- 
 dictory ' necessitates a corresponding extension in the 
 employment of the term * contrary.' A contradictory, 
 as just explained, is a proposition asserting j-ist sufficient 
 
OPPOSITION OF PROPOSITIONS 91 
 
 to render the original statement false. A contrary is 
 accordingly understood as a negative which goes further 
 than this, denying more than is absolutely necessary to 
 destroy the proposition it rebuts. Contraries thus ex- 
 plained, possess the property which characterizes the 
 contraries of the square of opposition, that both may be 
 false, but both cannot be true. But it will be seen that 
 the sense in which the term is used, has been very 
 materially altered. Where the term ' contrary ' signifies 
 the opposition between E and A, a contrary proposition 
 is one which denies the truth of every case embraced by 
 the opposed judgment. In the secondary signification 
 with which we are now concerned, this sense is altogether 
 absent. Any form of denial, which goes further than 
 what is barely sufficient, is reckoned as a contrary. Thus, 
 where a disjunctive is needed as a contradictory, the 
 denial of either one of the members taken singly, is counted 
 as a contrary. For instance the proposition, " All house- 
 holders, and they alone, are voters," receives contrary 
 denial either by the proposition, ' Some householders 
 are not voters/ or by ' Some others besides householders 
 are voters.' 
 
CHAPTER VI. 
 
 IMMEDIATE INFERENCE. 
 
 i. Immediate Inference. Immediate Inference may 
 be denned as a process by which from a single given 
 judgment, we derive another, whose truth is implied 
 in the former. It thus differs essentially from syllo- 
 gistic inference (Ch. i, 2), in which the mind passes 
 from two truths already known to a third truth distinct 
 from either of them. In the syllogism there is a real 
 advance in knowledge. The conclusion is not formally 
 contained in either premiss taken separately. Here 
 however, we have no advance in knowledge. The 
 conclusion of an immediate inference declares some fact 
 already formally asserted in the premiss. If we have 
 understood the premiss, we already know the conclusion. 
 On this ground the name of Inference is sometimes 
 denied to Immediate Inferences. Mr. Bradley even 
 says : "As long as you keep to categorical affirmatives, 
 ' your conversion or opposition is not rational but 
 ' simply grammatical " (Principles^. 392). The question 
 as to whether these processes have a right to the 
 name of Inference, must depend on the precise meaning 
 we attach to that term. If it is understood to signify 
 an advance in knowledge, and this would appear to 
 be the more correct sense, it is wrongly applied", to 
 them. If however it includes any mental transition 
 from a datum to something involved in that datum, 
 its use here is justified. For it is certainly erroneous 
 to say that the change is purely grammatical. Take, 
 for example, so simple an Immediate Inference as 
 that by which we pass from ' Some men are not 
 wise/ to ' Some men are not-wise.' The change is 
 
IMMEDIATE INFERENCE 93 
 
 not a mere question of grammar, but a question oi 
 conceptual expression. In the predicate of the conse- 
 quent, in lieu of the positive concept ' wise/ we employ 
 a negative concept, i.e. a totally different mental form 
 (Ch. 2, 9) ; and the new judgment, instead of separating 
 subject and predicate by negation, conjoins them by 
 affirmation. In all Immediate Inferences the changes 
 are of a similar character : the same truth is enunciated, 
 but the conceptual expression undergoes transformation. 
 Thus we are justified in asserting in our definition that 
 it is a process by which we pass from one judgment to 
 another. 
 
 By some authors, Opposition is treated under Imme- 
 diate Inference, since, as was said in Ch. 5, 5, a knowledge 
 of what is involved in Opposition enables us to draw 
 certain immediate inferences. Here we have followed 
 the more usual plan of giving separate treatment to the 
 subject of Opposition, as being concerned primarily 
 not with inference, but with the system of relations 
 which hold between the four propositions of the square. 
 
 The inferences of which we are about to treat are (i) 
 Conversion, (2) Equipollence or Obversion, (3) Contra- 
 position, (4) Inversion, (5) Some forms of minor import- 
 ance. In several recent English works these five kinds 
 of Immediate Inference are contrasted with Opposition 
 under the name of Eductions. 
 
 2. Conversion. 
 
 Conversion is a process of immediate inference in 
 which from a given judgment we infer another, hav- 
 ing the predicate of the given judgment for its subject, 
 and its subject for predicate. Thus we pass by con- 
 version from a proposition of the form S is P to one of 
 the form P is S. The original proposition is known as 
 the Convertend : the inferred proposition as the Converse. 
 
 The philosophical justification of this transposition is to be 
 found in the significance of the logical judgment, as explained 
 in Ch. 3, i, 2. We there saw that the copula denotes the 
 identity of the subject and predicate, as being two mental ex- 
 
94 PRINCIPLES OF LOGIC 
 
 pressions of one and the same reality. Of these two mental 
 expressions, the subject is understood as signifying the thing, 
 the predicate as the thing qualified by some determining charac- 
 teristic some ' form of being ', which we assert of the thing. 
 Manifestly when the subject is a significant term, it, no less 
 than the predicate, contains some determining characteristic. 
 If e.g. we say, ' This bronze object is spherical,' the term ' bronze,' 
 no less than the term 'spherical/ expresses an attribute belong- 
 ing to the thing. Hence we may say that the proposition declares 
 the coinherence in the same subject of the two ' forms of being ' 
 expressed by the terms, though the form signified by the subject 
 is assumed, that signified by the predicate is asserted. This 
 coinherence of forms may, as regards truth, be expressed in 
 either order indifferently. In Logic we are concerned with 
 things as known to us, and our knowledge in regard to the forms 
 may take either order. It is as true to say, ' That running thing 
 is a dog,' as it is to say, ' That dog is running.' It follows that 
 we may legitimately transpose the order of the terms, and may 
 replace a proposition of the type 5 is P, by one of the type P i S, 
 provided we are careful that the converse should not assert the 
 coinherence of S and P in relation to any entity which was out- 
 side the scope of the original proposition. 
 
 The following rules are given to ensure the validity of 
 conversion : 
 
 (1) The converse must be of the same quality affir- 
 
 mative or negative as the convertend. 
 
 (2) No term may be distributed in the converse, which 
 
 was not distributed in the convertend. 
 
 The reason of Rule i is obvious. In every affirmative 
 proposition the two terms are different mental expressions 
 of the same object or objects. The inferred proposition 
 in a conversion, refers to the identical object to which the 
 premiss referred, and employs the same terms. It is then 
 manifestly impossible that it should be negative : for a 
 negative proposition asserts that one of the terms is in- 
 admissible as a mental expression of the thing in question. 
 In the same way it is equally impossible that a negative 
 proposition should, after conversion, appear as an affirma- 
 tive. 
 
 As regards Rule 2, we have already pointed out (Ch. 5, 
 2) that where a term is undistributed, there is nothing 
 in the form of the proposition to show that it is to be 
 
IMMEDIATE INFERENCE 95 
 
 understood of the whole class of objects belonging to 
 the extension of the term. If then, after conversion, a 
 term previously undistributed is distributed, more is 
 asserted in the converse than was contained in the 
 convertend. If we add anything, we are going beyond 
 the point to which our warrant extends. Even if what 
 we say be true, we shall not have drawn it from the 
 original proposition. It will not be an inference. Ex- 
 amples of this will appear in the case of the A proposition, 
 which we are now about to discuss. 
 
 (a) Conversion of A propositions. In A propositions 
 the predicate is undistributed. Hence we cannot 
 convert All S is P into the form All P is S. To do 
 so would be to violate the rule which we have just 
 explained. A glance at Fig. I of Euler's circles, will 
 shew us the fallacy which would be contained in 
 this. Such a conversion might well involve the assertion 
 
 that the larger class lay within the smaller. Because 
 we can say, ' All men are animals/ it does not follow 
 that, ' All animals are men.' We must therefore be 
 careful to keep P undistributed in the converse, which 
 will thus appear as Some P is 5, ' Some animals are 
 men/ This kind of conversion is known as Conversio 
 per accidens or sometimes as conversion by limitation. 
 It is true that in certain cases the conversion of All S 
 is P to the form All P is S may give us a true result. 
 Thus it is not only true that " All right-angled triangles 
 ' have the square on the hypotenuse equal to the sum 
 ' of the squares on the two sides containing the right 
 ' angle," but the converse proposition may be asserted 
 in the form All P is S. This however does not appear 
 from the form of the original proposition, and cannot 
 be inferred from it. We learn it from other sources. 
 
PRINCIPLES OF LOGIC 
 
 (b) Conversion of E and I propositions. In E and I 
 
 propositions, there is no need to change the quantity 
 of the proposition, which we convert. No S is P becomes 
 No P is 5, and Some S is P is converted to the form Some 
 P is S. Conversion of this character is known as simple 
 conversion. In converting these propositions, in this 
 way no rule is violated. The proposition 5 e P distributes 
 both its terms. Hence the converse P e S does not dis- 
 tribute what was undistributed in the convertend. Simi- 
 larly 5 iP has both subject and predicate undistributed ; 
 and the same is true of its converse, P i S. Euler's 
 circles will assure us as to the correctness of the process. 
 S e P is represented by Fig. 3. Thus if we say ' No plant 
 
 FIG. 3. 
 
 FIG. 4. 
 
 FIG. 5. 
 
 is capable of sensation/ we exclude one class altogether 
 from the other. Hence the converse also must deny 
 any union between them. It will be ' No being capable 
 of sensation is a plant.' 5 i P is represented by Figs. 
 4 and 5. It is manifest that in either case we may with 
 perfect truth frame a proposition of the form P i S. If 
 we have affirmed, e.g. ' Some Europeans are English- 
 men ' (Fig. 5), we may also say, ' Some Englishmen are 
 Europeans.' Should, however, 5 i P be employed where 
 S aP might have been used, there too, as we saw in dis- 
 cussing the A proposition, we may legitimately convert 
 to P i S. 
 
IMMEDIATE INFERENCE 97 
 
 (c) The proposition and conversion. The propo- 
 sition does not admit of conversion consistently with 
 the observance of the rules. The proposition S o P is 
 particular negative : as such its subject is undistributed, 
 its predicate distributed. Conversion would necessitate 
 that the proposition should be of the form P o S. But 
 in P o 5, the predicate 5 must be distributed. This 
 is impossible, as it is undistributed in the convertend. 
 Fig. 5 will render this clear. Because we have said 
 ' Some Europeans are not Englishmen/ we cannot 
 conclude, ' Some Englishmen are not Europeans.' The 
 place of conversion in regard to this proposition, is 
 filled, as will be seen, by Contraposition. 
 
 (d) Conversion of Singular propositions. Only those 
 singular propositions in which the predicate as well as 
 the subject is a singular term, are capable of conversion. 
 In all others the transposition of the terms alters the 
 grammatical form, but not the logical. We may express 
 the sentence ' Plato was a philosopher/ as ' One of the 
 philosophers is (was) Plato ' ; but Plato is still the subject 
 that of which something is said. On the other hand 
 where both terms are singular, either of the two may 
 legitimately take the place of subject, e.g. ' The man 
 coming towards us is Socrates/ Such propositions are 
 converted simply. 
 
 It will not have escaped notice that when it is desired to con- 
 vert a proposition, it is absolutely necessaiy first to express it 
 in full logical form, with subject, copula and predicate, and 
 with the sign of quantity prefixed. Otherwise mistakes are 
 bound to occur : and a proposition, such as, e.g. ' The indus- 
 trious usually become wealthy/ will be converted to the form 
 ' The wealthy usually become industrious.' The proposition 
 should first be expressed as ' Some (most) of the industrious are 
 men who become wealthy ' ; and the converse will then appear 
 correctly as : ' Some men who become wealthy are industrious.' 
 
 * 3. Aristotle's Proof of Conversion. The following proofs 
 to establish the validity of the process of conversion, are given 
 by Aristotle in An. Prior /., c. 2, 2, 3. 
 
 (i) E propositions. If No S is P, then it will follow that No 
 
 H 
 
98 PRINCIPLES OF LOGIC 
 
 P is S : for if not, let it be supposed that something of which 
 P can be predicated, say C, is S. Then since C is both 5 and P, 
 it follows that Some S is P. This however is the direct contra- 
 dictory of our datum ; therefore it, and the supposition on 
 which it is based, are false. 
 
 (2) A propositions. If All S is P, it will follow that Some P 
 is S. For if it be supposed that this is false, then No P is S. 
 But we have already shewn that when No P is S, it follows that 
 No S is P. But this result is incompatible with our datum that 
 All S is P. 
 
 (3) 7 propositions. If Some S is P, it will follow that Some 
 P is S. For if not, then No P is S. But this involves that No 
 S is P. 
 
 It is manifest that every step in this proof rests upon the Laws 
 of Thought. 
 
 4. Equipollence or Obversion. 1 
 
 Eauipollence or Obversion is a process of immediate 
 inference in which the inferred judgment, while retain- 
 ing the original subject, has for its predicate the con- 
 tradictory of the original predicate. The original pro- 
 position is termed the Obvertend, the inferred pro- 
 position the Obverse. It is evident that as in the 
 Obverse we have substituted for the original predicate 
 its contradictory term, we must also change the 
 quality of the proposition : thus, we pass from 5 is P 
 to 5 is not not-P. The rule for the process may be 
 stated : 
 
 Change the quality of the proposition, and substitute 
 for the predicate its contradictory term. 
 
 The process is applicable to all the four fundamental 
 propositions. The subjoined table will shew the equipol- 
 lent forms of each : 
 
 Original proposition. S a P S i P S e P S P. 
 Obverse. S eP S o P S a~P S i P. 
 
 The following will serve as examples : 
 
 1 Equipollence is the term employed by the majority of the Latin writers, 
 and among English logicians has the authority both of Mill and Mansel. The 
 use of the term Obversion in this sense, appears to be due to Bain. By Hamil- 
 ton it is used as synonymous with Conversion (Logic, I. 262). The process 
 is briefly touched on by Aristotle, de Interp., c. 10, 15. 
 
IMMEDIATE INFERENCE 99 
 
 Original proposition. Obverse. 
 
 All men are mortal. No men are not-mortal. 
 
 No philosophers are prao All philosophers are not- 
 
 tical. practical. 
 
 Some judges are just. Some judges are not not- 
 
 just. 
 
 Some ministers are not wise. Some ministers are not- 
 wise. 
 
 Where it is possible to find a single word, which accu- 
 rately expresses the sense of the contradictory term, 
 such a word should be employed in place of it. Thus 
 in these examples, we may with advantage use the 
 words ' immortal/ ' unpractical/ ' unjust/ ' unwise ' 
 in lieu of ' not-mortal/ etc. 
 
 The validity of the process is proved by the Laws of 
 Thought. The law of Contradiction shews us that if 
 All S is P, then No S is not-P : for according to this 
 principle, if anything is P, it is thereby proved not 
 to be not-P. The Ob version of the negative judgment, 
 follows from the Law of Excluded Middle. 5 must be 
 either P or not-P : and since we know No S is P, we 
 conclude that All S is not-P. 
 
 A consideration of the diagrams will confirm these 
 conclusions. Thus, if we assert that ' All men are 
 mortal/ the circle representing ' men ' falls within the 
 limit of the circle representing ' mortal.' It is thus 
 apparent that no part of the circle ' men ' is to be found 
 in the space which denotes ' non-mortals.' 
 
 Obverted Converse. Among the immediate infer- 
 ences which can be derived from the four fundamental 
 propositions, must be reckoned not only the Obverse 
 forms of the propositions themselves, but the Obverted 
 Converse. This will be as follows : 
 
 Converse. -^ * 2. -P * S P e $_ none - 
 
 Obverted Converse. P o S P o S P a S none. 
 
 5. Contraposition. 
 
 Contraposition is a, process of immediate inference 
 
TOO PRINCIPLES OF LOGIC 
 
 in which from a given judgment another judgment is 
 inferred, having for its subject the contradictory of the 
 original predicate. The rule to obtain the contra- 
 position of a proposition may be shortly stated : 
 
 Convert the Obverse of the proposition. 
 
 The proposition, ' All reptiles are vertebrates ' has 
 as its Obverse, ' No reptiles are non-vertebrates ' : the 
 Contrapositive will therefore be 'No non- vertebrates 
 are reptiles.' Similarly, the proposition ' Some right 
 actions are not agreeable/ will become after Contra- 
 position, ' Some not-agreeable things are right actions/ 
 
 The following table will shew the forms assumed by 
 the various propositions : 
 
 Original proposition. S_a P SiP S_e P Sjo P. 
 Contrapositive. P e S none P i S P i S. 
 
 It will be seen that the I proposition has no Contra- 
 positive. For after Obversion it becomes 5 o P, and this 
 proposition does not admit of Conversion. 
 
 The E proposition becomes by Obversion S a P. This 
 on Conversion, must change its quantity to particular. 
 Hence here we have what has been termed Contrapositio 
 per accidens. 
 
 Obverted Contrapositive. 1 It is plain that each of the 
 Contrapositives is itself capable of Obversion. We 
 can in each case alter the quality of the proposition, 
 and change the predicate to its contradictory term. 
 This will give us : 
 
 Contrapositive. P e S none P i 5_ P i S. 
 
 Obverted Contrap. P a S none P o S P o S. 
 
 1 It will be observed that the Obverted Contrapositive retains the quality 
 of the original proposition. The older Latin logicians considered Contra- 
 position merely as a method for obtaining the conversion of the terms, and 
 as deriving its importance from the fact that in this way it was possible to 
 convert the proposition. They called it not Contrapositio, but Conversio 
 per Contrapositionem. Hence they reserved the name for the obverted- 
 contrapositive, since it alone follows the rule of Conversion that the quality 
 remains unchanged. Cf. e.g. Sylv. Maurus (Quaest. Phil. I., p. 65). In this 
 they followed Boethius, DC Syll. Cat. I. (P. L. vol. 64, c. 807). Contraposition 
 is recognized by Aristotle in Topics, II. 8. 
 
IMMEDIATE INFERENCE i0r 
 
 6. Inversion. 
 
 Inversion is a process of immediate inference, in 
 which from a given judgment another judgment is 
 inferred, having for its subject the contradictory of the 
 original subject. We have seen how to pass from a pro- 
 position having 5 for its subject, to propositions having 
 P or P for their subjects. We now proceed to enquire 
 whether it be possible to pass to one having 5 for its 
 subject. 
 
 The process of obtaining such a proposition must be 
 similar to that employed in the other methods of imme- 
 diate inference, viz. : Conversion and Obversion. The 
 mode in which we arrive at the Inverse of S a P is shown 
 in the left hand column below. It will be observed 
 that the first step taken is to obvert. In the right hand 
 column we have a similar process, but commencing 
 with Conversion : and it is seen that after two steps we 
 find ourselves with the proposition P o S to be converted. 
 This however is impossible ; and hence it appears that 
 we cannot find the Inverse by that route. 
 
 5 a P. S a P. 
 
 By Obversion S_e P. By Conversion P i S. 
 
 By Conversion P e S. By Obversion P o S. 
 
 By Obversion P a 5. By Conversion 
 
 By Conversion S i P. 
 
 By Obversion S o P. 
 
 In the case of the proposition S e P, it will be found 
 on experiment that if we commence with Obversion, 
 we are again met with the difficulty of an proposition 
 demanding Conversion. If however we commence with 
 Conversion, we pass through the series 5 e P, P e S, P a S, 
 S i P, which gives us the required proposition. 
 
 In the case of 7 and propositions, experiment will 
 shew that in no case is it possible to get an Inverse 
 form. 
 
 Our results may be tabulated thus : 
 
 Original proposition. 50 P S i P S^e P S o P. 
 
 Inverse. 5 o P none S i P none. 
 
tf>2 PRINCIPLES OF LOGIC 
 
 Obverted Inverse. Just as we have seen that it is 
 possible to obtain obverted forms of the Converse and 
 Contrapositive, so we may obvert the Inverse forms 
 which we have just reached. The Obverse of S o P 
 will be S~i P ; that of S i P will be S" o P. 
 
 7. Table of Results. We may summarize the results 
 at which we have arrived as follows. 
 
 A I E 
 
 Original proposition. S aP S i P S eP S o P. 
 
 Obverse. SeP SoP S aP Si P. 
 
 Converse. PiS PiS PeS 
 
 Obverted Converse. ?i^ PoS PaS 
 
 Contrapositive. PeS_ PiS PiS. 
 
 Obverted Contrapositive. Pa S P_oS PoS. 
 
 Inverse. SoP S_iP 
 
 Obverted Inverse. SiP SoP 
 
 8. Other Varieties of Immediate Inference. 
 
 (1) Immediate inference by added determinants is a 
 
 process of immediate inference, which consists in limiting 
 both the subject and predicate by the same determinant. 
 The formula for the process will be 5 is P, therefora 
 Sa is Pa. For instance, ' A statue is a work of art ' ; 
 therefore ' A beautiful statue is a beautiful work of 
 art/ ' A statue by Canova is a work of art by Canova.' 
 This form of immediate inference is only possible, when 
 the determinant qualifies the terms under precisely 
 the same aspect. Thus, I cannot argue that because 
 'A prizefighter is a man,' therefore 'A good prizefighter 
 is a good man.' In this case ' good ' as qualifying ' man,' 
 signifies that the man realizes in himself the ideal 
 of man ; that is, he lives in accordance with the prescrip- 
 tions of his rational nature. As qualifying ' prize- 
 fighter,' the word ' good ' merely means that he realizes 
 in himself the ideal of a prizefighter ; that is, he possesses 
 in a high degree the art of knocking other men down. 
 
 (2) Inference by omitted determinants. Here we have 
 an inference, in which from a proposition affirming of 
 
IMMEDIATE INFERENCE 103 
 
 a given subject an attribute qualified by a determinant, 
 we infer a proposition affirming of the same subject 
 the attribute without qualification. Thus, from ' Men 
 are rational mortals/ we conclude ' Men are mortals.' 
 A fallacy may arise here, if the determinant is such as 
 to alter the meaning of the predicate. Thus, we cannot 
 argue from ' Spiritualistic manifestations are pretended 
 facts,' to ' Spiritualistic manifestations are facts.' 1 
 
 (3) Immediate inference by complex conception. This 
 process is closely analogous to inference by added 
 determinants. It consists in employing both the subject 
 and predicate of the original as parts of a more complex 
 conception. ' Bronze is a metal,' therefore ' A statue 
 in bronze is a statue in metal.' ' A negro is a man,' 
 therefore ' The death of a negro is the death of a man.' 
 In these cases, the subject and predicate of the original 
 proposition are not determined by what is introduced, 
 but are themselves employed as determinants. Falla- 
 cies may, of course, arise here, similar to those we have 
 already examined. Thus, we cannot infer from ' All 
 judges are lawyers,' that therefore ' A majority of the 
 judges is a majority of lawyers/ 
 
 (4) Immediate inference by converse relation is a 
 process of inference, by which from a proposition stating 
 the relation in which Q stands to 5, we infer another 
 proposition stating the converse relation in which 5 
 stands to Q. The terms are transposed, and the relative 
 name which was attributed to the previous subject, is 
 consequently replaced by the correlative, which is attri- 
 butable to the new subject. Thus, from ' Socrates 
 was the husband of Xantippe,' we conclude ' Xantippe 
 
 1 Venn, Symbolic Logic, p. 286. This form of immediate inference is two 
 or three times discussed by Aristotle, delnterp.,c. n, 8, Topics, II., c. u, 4 
 Soph. Elenchi, c. 25. 
 
 The principle governing its application was by the Latin logicians 
 stated in the form : A dicto secundum-quid valet illatio ad dictum 
 simpliciter, quando determinatio non est diminuens. St. Thomas, Opusc. 
 35, deFallaciis, c. n, de Potentia, Q. 9, Art. 5, obj. 2. See also Ch. 17, 10 
 below. 
 
 Mr. Bradley's criticisms (Principles, p. 394) would appear to indicate that 
 he has overlooked Aristotle's discussion of the point. 
 
104 PRINCIPLES OF LOGIC 
 
 was the wife of Socrates ' : from ' Onesimus was the 
 slave of Philemon/ to ' Philemon was the master of 
 Onesimus/ 
 
 Some of the Formal logicians have denied that this 
 mode of immediate inference falls within the province 
 of Logic. There is, they urge, no necessary law of 
 thought, by which we pass from ' A is the father of 
 B ' to ' B is the child of A.' To do so, it is necessary 
 to be acquainted with the meaning of the terms. The 
 process cannot be symbolically represented. 
 
 From the point of view of the Formal logician the 
 objection has much force. But to the Scholastic logi- 
 cian, who holds that the object of Logic is the conceptual 
 expression of the real, it presents no difficulty. Who- 
 ever employs the relative concept ' father ', must have 
 in his mind the correlative ' child,' and hence can pass 
 by immediate inference from ' A is the father of B,' 
 to ' B is the child of A! The inference is expressly 
 recognized by Aristotle (Categ., c. 7, 6). 
 
 Immediate inference by modal consequence. By this 
 method of inference, we conclude from the fact that 
 something is necessary, to the fact that it is possible. 
 For instance from the proposition * It is necessary for 
 an equilateral triangle to be equiangular/ to ' It is 
 possible for an equilateral triangle to be equiangular.' 
 At first sight there appears a difficulty in concluding 
 from necessity to possibility. But if it is not the case 
 that what is necessary is possible, then by the principle 
 of Excluded Middle, the contradictory is true, and we 
 must say that it is impossible (de Interp., c. 13, 9). 
 As this conclusion is false, we recognize that what is 
 necessary is also possible, and similarly that whenever 
 we can assert that something is impossible, we can also 
 assert that it is possible for this not to be. In this case, 
 we use the words in the second of the two senses noted 
 in Ch. 3, 9. 
 
CHAPTER VII. 
 
 THE IMPORT OF PROPOSITIONS. 
 
 i. Import of Propositions Predicative View. In 
 
 this chapter we shall be occupied in considering 
 various theories as to the precise nature of the relation 
 expressed in the mental act of predication. We have 
 already in Ch, 3, i, 2, Ch. 6, 2 explained our own view 
 on this subject in some detail. For it was not possible 
 to treat of the proposition, or of the process of con- 
 version, without first indicating how the relation between 
 subject and predicate should be understood. Briefly 
 to recapitulate what we have said, both the subject 
 and predicate express the object of the judgment under 
 some aspect, the subject however being construed to 
 signify the thing, the predicate some attribute which 
 we affirm (or deny) of the thing. The copula declares 
 that the object expressed by the subject, and that ex- 
 pressed by the predicate are identical. Further, inas- 
 much as the judgment deals with the object as it is 
 known, and as in regard to our knowledge there is no 
 fixed order as to which aspect of an object we know first, 
 a judgment may reverse the natural order of predication. 
 What is naturally a mere attribute, may stand as the 
 subject ; what is naturally the subject, may be affirmed 
 as though it were the attribute. Thus we may have a 
 case in which a proper name, a name whose special office 
 it is to denote the individual concrete thing, stands in 
 iiie place of the attribute, as when we say, ' That object 
 coming this way, is Socrates.' Logically, this transpos- 
 ition of the natural order is perfectly legitimate. For 
 the function of the predicate is simply to tell us what 
 the subject is ; and when we define the subject to be 
 
io6 PRINCIPLES OF LOGIC 
 
 this or that particular individual to be the man Socrates, 
 this is most certainly done. 
 
 That there is a natural order of predication will easily be seen 
 on recalling the distinction between substance and accident 
 (Ch. 2, 7). Clearly it is the substance which supports the 
 accidents. They determine it, and characterize it : the sub- 
 stance is not something which determines and characterizes 
 them. It possesses independent existence. They exist as its 
 determinations, and not in their own right. Hence Aristotle 
 rightly says that though we can express our proposition in such 
 a form as, ' The object coming this way is Callias,' such an order 
 of the terms is not natural but per accidens. * 
 
 The same is true where the subject is not an accident, but a 
 substantial term of wider generality, e.g. 'That man is 
 Socrates.' 2 
 
 This view of the proposition according to which the 
 subject is understood as the thing and the predicate as 
 the attribute, or as it is sometimes put, in which the 
 subject is construed in extension, and the predicate in 
 intension, is known as the Predicative View. 
 
 During the past century the most diverse theories 
 on this point have been held by logicians. The principal 
 of these we shall proceed to examine. In the course 
 of the discussion, we shall be brought across another 
 problem, which of recent years has afforded matter for 
 debate, the question namely, whether a categorical 
 proposition implies that things corresponding to its 
 terms actually exist. 
 
 2. The Class-inclusion View. Those who interpret 
 the proposition on the class-inclusion view, hold that 
 both subject and predicate are conceived in exten- 
 
 1 An. Prior I., 0.27, 3. See also An. Post. I., c. 22, 2, where he points 
 out that such a proposition as ' That white object is a stick ' is predication 
 per accidens, since ' the white ' did not become a stick, but vice versa. On 
 this St. Thomas comments as follows. " Subjectum fit hoc quod praedicatur 
 ' de ipso sicut de subjecto. . . . Cum ergo non sit verum dicere quod Album 
 1 fiat lignum, manifestum est quod album non est lignum proprie et per se 
 ' loquendo. Sed si hoc concedatur Album est lignum, intelligitur per accidens, 
 ' quia scilicet illud particulare subjectum, cui accidit album, est lignum. Iste 
 ' ergo esC sensus hujusmodi praedicationis in qua subjectum praedicatur de 
 'accidente," in An. Post. I., lect. 33. 
 
 Jevons (Principles of Science, p. 39) has completely misunderstood Aristotle's 
 meaning on this subject. 
 
 a See below, Ch. 8, i. 
 
THE IMPORT OF PROPOSITIONS 107 
 
 sion. They believe the true significance of a proposition 
 is to assert that the objects denoted by the subjec; are 
 included in, or excluded from the class signified by the 
 predicate, e.g. ' Men are mortal ' asserts that all men 
 fall within the class ' mortal/ The predicate on this 
 interpretation must necessarily be read collectively as 
 signifying the whole class considered as a unit. A dis- 
 tributive use would be impossible. All men are included 
 within mortal things, as these constitute a whole : they 
 are not included within them, each taken separately. 
 The subject on the other hand may be either collec- 
 tively or distributively used. 
 
 We have already pointed out that in regard of the 
 real order, inclusion in a class is involved in affirmative 
 propositions, and exclusion from a class in negations : 
 and that it is due to this that we are able to frame a 
 scheme of diagrams corresponding to the four funda- 
 mental propositions. But the question before us, is not 
 whether the proposition does or does not indicate the 
 existence of classes in the objective order : but whether 
 this is the relation conceived by the mind, and verbally 
 expressed by the subject copula and predicate. 
 
 A fatal objection to the theory is the fact, that were 
 it true, we should not express our propositions in the 
 form ' All men are mortal.' They would assume some 
 such form as ' All men are included among mortals.' 
 If ' mortals ' signifies the class of mortal things, it is 
 inaccurate to say ' All men are mortal.' Every man is 
 not the class ' mortal.' On the other hand, on the predi- 
 cative view, the subject, copula and predicate are the 
 natural mode of statement : for ' mortal ' is a true 
 expression of what men are. It is sometimes indeed 
 urged that there are a certain number of propositions, 
 which are naturally understood in this way, namely 
 those which are sometimes termed ' judgments of classi- 
 fication,' e.g. ' Lions are Felidae,' ' Daisies are Com- 
 positae.' It is, however, quite inaccurate to say that 
 here we affirm a relation between two classes. By 
 1 Lions are Felidae,' we signify that every lion has the 
 
io8 PRINCIPLES OF LOGIC 
 
 attributes that mark a Felis. The copula here has no 
 inclusive signification. It declares the identity between 
 each of the things denoted by the subject, and the same 
 things differently conceived in the predicate. No argu- 
 ment can be drawn from these propositions in support 
 of the class-inclusion view. 
 
 * Quantification of the Predicate. This is a special form of 
 the Class-inclusion view, which we owe to Sir W. Hamilton. At 
 one time it was accepted by several logicians of note, as e.g. 
 Dr. Thomson, and Dr. Baynes. It has long since been recognized 
 to be quite untenable, and possesses only historic interest. Hamil- 
 ton held that the essential function of a proposition is to com- 
 pare two notions in respect of their quantity (Logic, II., p. 257). 
 If this be so, it follows as a matter of course that the quantity 
 of the predicate, even though not expressed, must be known. 
 This, he maintained, is in fact the case, so that mentally at least 
 the predicate, like the subject, is always either universal or sin- 
 gular. The scheme of fundamental propositions becomes con- 
 sequently eightfold, as follows : 
 
 f All 5 is all P. U. e.g. All triangles are all trilateral. 
 
 (All 5 is some P. A. e.g. All triangles are some figures. 
 
 rSome 5 is all P. Y. e.g. Some figures are all triangles. 
 
 - Some 5 is some P. /. e.g. Some triangles are some ir- 
 
 regular figures. 
 
 rNo 5 is any P. E. e.g. No triangles are any squares. 
 
 (No 5 is some P. 77. e.g. No triangles are some figures. 
 
 /'Some 5 is not any P. O. e.g. Some figures are not any 
 
 triangles. 
 1 Some 5 is not some P. u>. e.g. Some triangles are not some 
 
 I figures. 
 
 The theory has nothing to recommend it. In thought we do 
 not quantify the predicate. We may e.g. affirm that ' All rhino- 
 ceroses have a single horn,' without reflecting in any manner 
 on the extent of the class, whose members are single-horned. 
 Further, a list of eight propositions each expressive of a different 
 relation between the classes, is impossible. There are but five 
 such relations possible, as we saw in our consideration of Euler's 
 circles. If the essential function of the proposition is to express a 
 quantitative relation there must be five forms, and no more. The 
 redundancy of the eightfold scheme appears as soon as it is ex- 
 amined. A and 17 express the same relation. Y and O correspond 
 in a similar manner. Finally the proposition <D conveys no infor- 
 mation whatever about the relation between the classes. It is 
 compatible with any of the other forms, even with U. ' All 
 
THE IMPORT OF PROPOSITIONS 109 
 
 dogs are all latrants ' (U) ; but it is equally true that ' Some 
 dogs (terriers) are not some latrants (mastiffs).' 
 
 Equational View. Professor Jevons held that the proposition 
 signified not inclusion, but an equation between the extension 
 of the subject and that of the predicate. There is, he tells us, 
 exact analogy between mathematical equality, and the relation 
 of subject and predicate (Principles of Science, p. 68). He would 
 express the proposition in this form : 
 Common Salt = Sodium Chloride. 
 Chlorophyll = green colouring matter of plants. 
 
 A difficulty however arises when the predicate denotes a wider 
 class than the subject. Here if the equation is to be correct, 
 we cannot write ' Men = mortals.' Nor is it more satisfactory 
 to write ' Men = some mortals.' For by ' some mortals,' we 
 might indicate quite another part of the extension of the class 
 ' mortal,' than that to which ' man ' is equated. Hence Jevons 
 employs the form ' Men = men mortals.' 
 
 This view is open to the objections we have urged against the 
 Class-inclusion view. We do not think of the predicate in quan- 
 tity. Hence as an explanation of the mental act of judgment, 
 the theory is valueless. Moreover the representation of the 
 proposition as an equation, does away with the fundamental 
 distinction between subject and predicate. And if the sign (=) 
 is to be understood in its usual sense, then all predication is re- 
 duced to the form 5 is equal to P. Here the words ' equal to ' 
 form a constituent part of the predicate. It is manifest how- 
 ever, that in the great majority of our judgments we are concerned 
 not with a relation of equality but of identity, and that our 
 predicate is not 'equal to P,' but P. 
 
 3. The Attributive View. On this view both subject 
 and predicate are read in intension : and the import of 
 the proposition is held to be that the attributes signified 
 by the subject are accompanied by those signified by the 
 predicate. Mill is ordinarily regarded as the principal 
 supporter of this view, but, as will be seen, he supports it 
 under certain important qualifications. He points out, 
 that where we have a general proposition such as * All 
 men are mortal/ we do not mean that the attribute signi- 
 fied by the predicate is possessed by a certain number of 
 individuals, whose possession of it we have verified. Most 
 of the individuals signified by such a subject are not 
 known to us. From this he concludes that the import 
 of the judgment is simply that the attributes of the 
 
no PRINCIPLES OF LOGIC 
 
 predicate constantly accompany the attributes of the 
 subject, and that the proposition just quoted should be 
 interpreted, ' Mortality constantly accompanies the attri- 
 butes of man ' (Logic, L, c. 5, 4). 
 
 Mill is correct when he says that we can only form 
 things into classes on the ground that they possess 
 common attributes. Yet it by no means follows from 
 this, that the true import of a proposition is simply 
 that the attributes of the predicate always (or some- 
 times) accompany those of the subject. The subject in 
 such a judgment as ' All men are mortal/ is conceived 
 as concrete : we do not conceive the abstract notion 
 ' humanity/ but ' man/ Of this concrete subject, we 
 affirm that since it is qualified by mortality, it is mortal. 
 Not only therefore is he wrong in his explanation of 
 the subject, but he is in error too as regards the 
 copula. The copula does not express concomitance, it 
 tells us what the subject is. 
 
 Mill in fact makes admissions, which in great measure 
 deprive his argument of its force. ' It is true/ he says 
 ' that we usually construe the subject of a proposition 
 in extension/ And in regard to propositions, in which 
 the subject is non-connotative, he owns that their import 
 is that the individual thing denoted by the subject, 
 has the attributes connoted by the predicate. More- 
 over, when he interprets the proposition ' All men are 
 mortal/ in the form ' Whatever has the attributes 
 connoted by the subject, has also those connoted by the 
 predicate/ he practically concedes all that is required. 
 We have here for subject, not the mere intension, viz.: 
 the abstract attributes, but an indefinite number of 
 concrete things, ' Whatever entity has the attributes/ 
 
 These admissions should not however lead us to sup- 
 pose that Mill had abandoned the Attributive view for 
 the traditional interpretation. A theory which reduced 
 general propositions to statements about the coexistence 
 and sequence of attributes, was in harmony with his 
 general philosophic position. 
 
THE IMPORT OF PROPOSITIONS IIT 
 
 4. Implication of Existence. It has been a matter 
 of much discussion among recent logicians, whether in a 
 categorical proposition, the existence of objects corre- 
 sponding to the subject and the predicate, is implied. 
 The question seems to have first been raised explicitly 
 by the German philosopher Herbart (1776-1841). Very 
 various views have been taken. Ueberweg (System of 
 Logic, 68) teaches that all propositions imply the exist- 
 ence of the subject, save those in which the predicate 
 is such as to abolish the subject-notion, e.g. " An abso- 
 lutely greatest number is impossible." Mill (Logic, I., 
 p. 124) holds that analytic propositions do not involve 
 the existence of their subjects, but that synthetic pro- 
 positions do so. Mr. Keynes and Dr. Venn alike teach 
 that universal propositions have no such implication, 
 but that where a particular proposition is used, some- 
 thing corresponding to the subject must exist. This 
 may appear strange in the face of such a judgment as 
 ' Some griffins have long claws.' But we are told that 
 the existence need not be in the physical universe ; it is 
 in the * universe of discourse.' It will be necessary briefly 
 to examine this notion of the ' universe of discourse.' 
 
 (i) Universe of discourse. As first employed, the 
 phrase signified no more than that by a convention our 
 propositions, as verbally expressed, are restricted in 
 their reference. 1 Thus if I say, ' No one now wears 
 chain-armour,' I refer only to soldiers. Actors are not 
 under consideration ; and hence soldiers might be said 
 to constitute my universe of discourse. 
 
 As used now however, the phrase has taken a different 
 signification. We are told that things, which do not 
 exist in the actual physical universe, can exist in ' the 
 universe of mythology,' ' the universe of folk-lore,' ' the 
 universe of the imaginable,' ' the universe of heraldry.' 
 These various forms of existence are called ' empirical ' 
 to distinguish them from logical existence, which belongs 
 to mere objects of thought. 2 
 
 1 De Morgan, Formal Logic, c. iv. 
 
 * Keynes, Formal Logic, Part II., c. 7- Venn, Symbolic Logic, p. 127. Cf. 
 Bradley, Appearance and Reality, p. 367. 
 
H2 PRINCIPLES OF LOGIC 
 
 It is scarcely necessary to bring serious arguments 
 against this view. It is rightly termed by Mr. Wolf 
 " an extravagant conception, which does not really 
 ' mean what it seems to mean " (Studies on Logic, p. 71). 
 It may however be well to indicate to what these 
 various universes really amount. Now in the first place 
 it is evident that if a thing possesses actual existence at 
 all, it exists in this physical universe. The griffins of 
 heraldry exist. At the present day, they are usually 
 made of paint and pasteboard. We need not expect 
 to find them in any other world than this. Many indeed 
 of the objects, concerning which we form judgments 
 have no actual existence at all. They are mere objects 
 of thought. The idea by which they are represented, 
 exists as a physical fact : but the object thought of 
 belongs not to the real but to the conceptual order. 
 A distinction should however be drawn between two 
 classes of such ideal entities. Some of the objects of 
 thought about which judgments are framed, and pro- 
 positions enunciated, are mere creatures of the imagina- 
 tion ; these, we imagine as existing in the physical uni- 
 verse conditioned by place and time. Thus I may say 
 ' The wrath of the Homeric gods is terrible,' ' Hamlet 
 was Prince of Denmark/ ' The upas-tree is the tree, 
 the mere approach to which involves death/ But in 
 all these cases the subject as verbally expressed is ellip- 
 tical. The full form of the judgment would be ' The 
 wrath of the gods imagined and described by Homer, 
 is terrible/ The second class of objects possessing 
 merely conceptual existence is of far more moment. 
 Here we are not concerned with individuals pictured 
 by the imagination. This class consists of entities, 
 which though they do not exist, are not repugnant to 
 the constitution of the physical universe ; and which 
 are expressed in universal concepts. Such for instance 
 are those mathematical figures, which have never, so 
 far as we know, existed, but whose nature and properties 
 can be accurately determined. Here our proposition 
 needs no amplification : it is true as it stands. We 
 
THE IMPORT OF PROPOSITIONS 113 
 
 may affirm that, ' Some geometrical figures are chiliagons,' 
 and the accuracy of the statement is indisputable. This 
 point will appear clearly in what follows. 
 
 (2) Implication of existence. Having now determined 
 that if an entity exists at all, whether as matter or as 
 spirit, it exists in this physical or actual universe and 
 not in another, we may the more securely face the 
 question, whether or not existence is implied in cate- 
 gorical propositions. 
 
 There can be no doubt, that the categorical form 
 as such, contains no such implication. We have already 
 pointed out (Ch. 4, 2) that our concepts, while they 
 accurately represent the nature of the thing conceived, 
 abstract altogether from the question of its existence. 
 In regard to the subject they tell us what it is, they do 
 not tell us that it is. If then our concept represents the 
 nature of some entity, and we abstract one of the notes 
 which determine its nature, and affirm this note of the 
 entity, our judgment is true even should the thing in 
 question be a mere ' possible.' Even should e^ery 
 animal perish from the face of the earth, we cannot hold 
 that it would be untrue to affirm mortality of animal, 
 and that the assertion would become true once more 
 if animals were again created. 1 It is this that explains 
 and justifies propositions, such as ' All chiliagons have a 
 thousand angles.' The proposition is true even though 
 the chiliagon has never existed : for the predicate affirmed 
 is one that necessarily belongs to the subject which my 
 concept represents. 
 
 It is plain that such propositions may be formed both 
 as universals and particulars. I may say, ' All chiliagons 
 have a thousand angles/ or I may say ' Some plane 
 figures are chiliagons.' 
 
 We do not, however, mean to assert that there are 
 no categorical propositions, which imply the existence 
 of their subject terms. We have merely asserted that 
 the categorical form as such does not imply it. There 
 are certain classes of categoricals, which by reason of 
 
 1 Bradley, Principles, p. 47. 
 
 I 
 
1 14 PRINCIPLES OF LOGIC 
 
 what is affirmed in them, do contain such an implication. 
 Thus (i) all propositions, in which existence is actually 
 predicated, of course, signify the existence of the subject, 
 e.g. God exists. (2) Wherever the predicate affirms 
 that the subject has acted, or has been the recipient of 
 an action, the proposition implies the existence of the 
 subject. We may define an entity, and assert of it the 
 properties, which flow from its nature, even though it 
 has never existed. But we cannot truthfully affirm 
 that it has acted, unless it has existed. The mere nature 
 cannot act. Propositions such as ' Brutus slew his 
 benefactor/ ' The meteor fell to the earth,' certainly 
 imply the existence of their subjects. And (3) the judg- 
 ments, in which a demonstrative pronoun is attached 
 to the subject, may be said to fall within the same cate- 
 gory. The pronoun is a sign that we are concerned 
 with a subject, which is not merely existing but under 
 observation. 1 
 
 * It has been maintained by several logicians of eminence, 
 that the view which we have been defending, reduces the cate- 
 gorical to a hypothetical, and that on our showing ' All 5 is P,' 
 should be read ' All 5 (if 5 exists) is P,' and ' Some 5 is P,' should 
 be read ' Some 5 (if S exists) is P.' 2 To this we may reply, 
 ' All S (if 5 exists) is P ' is a quite inaccurate representation 
 of the proposition as we understand it. The existence of 5 is 
 wholly outside the scope of the categorical as such. The pro- 
 position ' All 5 is P ' may indeed have been reached through 
 experience of existing things, e.g. ' All crows are black ' : but 
 it may have been reached by a process of purely intellectual 
 conception, e.g. ' All chiliagons have a thousand angles.' The 
 information which it communicates, concerns the nature, and 
 
 1 It is a mistake to suppose that this question was not raised by the Scho- 
 lastics. The following citation deals with it succinctly. " Ab est tertio 
 ' adjacente, ad est secundum adjacens, in enunciationibus contingentibus recte 
 ' concluditur : ut Si mortui sunt miseri, ergo mortui sunt. Atqui veto in pro- 
 ' nunciatis necessariis non item. Non enim necessario infertur Homo est ani- 
 ' mal, ergo homo est." Sanderson, Logica, p. 103 (ed. Antwerp, 1589). The 
 author of this work, John Sanderson, Canon of Cambray, had been Logic- 
 reader at Cambridge, but became one of the exiles for religion under Elizabeth. 
 The book is dedicated to Cardinal Allen, and contains prefatory verses by 
 Gregory Martin, B. Edmund Campion and other members of that notable 
 group of scholars. 
 
 2 Venn, Symbolic Logic, pp. 135-137. 
 
THE IMPORT OF PROPOSITIONS 115 
 
 the nature alone : and the proposition is true, if it accurately 
 expresses what the nature is. Chiliagons are possible entities, 
 not actually existing things. Similarly, when we say, ' Some 
 geometrical figures are chiliagons,' the last thing that we intend 
 to assert, is that ' If any geometrical figures exist, some of these 
 figures are chiliagons.' 
 
 Implication of Existence and Immediate Inference. The bear- 
 ing of the various views as to the implication of existence, upon 
 the processes of immediate inference, has been discussed with 
 customary thoroughness by Mr. Keynes. It will be sufficient 
 to summarize the conclusions to which he is brought, as to the 
 effect respectively of the traditional doctrine here defended, and 
 of his own doctrine. 
 
 In regard to his discussion of the traditional doctrine, it is to 
 be noted that he starts from the presupposition that the pro- 
 positions are to be interpreted according to the explanation we 
 have just rejected, viz.: ' All S is P ' as equivalent to ' All S (if 
 5 exists) is P.' Starting from this erroneous hypothesis he 
 argues (a) that the conversion of A is invalid. From ' All 5 
 (if there be any 5) is P,' we cannot conclude that ' Some P (if 
 there be any P) is 5.' Similarly the conversion of 7 is invalid. 
 The invalidity of these conversions involves (b) that the contra- 
 position of E and O, and (c) that the inversion of A and E are 
 also invalid. In regard to the doctrine of Opposition, (d) Con- 
 tradiction does not hold good. For ' All 5 is P ' merely denies 
 that there are any 5 not P ; and ' Some 5 is not P ' asserts that, 
 ' If there be any 5, some are not P.' Where S does not exist 
 in ' the universe of discourse,' both these propositions may be 
 true. Finally (e) Contrariety does not hold good. ' All 5 is P,' 
 and ' No 5 is P ' may both be true : for it is alike the case that 
 there are no SP's and no 5 not-P's, when 5 is not found in the 
 ' universe of discourse.' 
 
 These conclusions are all based on the erroneous interpreta- 
 tion of the proposition. Interpreted as we have understood it, 
 all the processes of immediate inference are valid. 
 
 In regard to his own view, viz. : that universal propositions 
 have no existential implication, but that particular propositions 
 imply the existence of their subjects, he arrives at the following 
 results : 
 
 (a) The conversion of A is invalid, for the same reason as was 
 given above : and similarly (b) the contraposition of E, and 
 (c) the inversion of A and E are invalid. The conversions of 
 E and I are valid. These results may be summarized by saying 
 that we may infer a universal from a universal, and a particular 
 from a particular, but not a particular from a universal. In 
 regard to Opposition (d) Subalternation manifestly does not 
 hold good, and (e) Contrariety for the reasons alleged above is 
 
u6 PRINCIPLES OF LOGIC 
 
 invalid. (/) Sub-contrariety is invalid also : for where S is not 
 found, both sub-contraries may be false. 
 
 Mr. Keynes holds that these results, notwithstanding the 
 havoc they make in the doctrine of immediate inference, are 
 more satisfactory than those of the traditional view, since they 
 secure the validity of the two important processes of (i) contra- 
 diction, (2) simple conversion. But, as we have seen, his estimate 
 of the traditional view is vitiated by the initial mistake as to 
 the interpretation of the proposition. 
 
 * 5. The Compartmental View. Our discussion on the 
 implication of existence in propositions will, we trust, throw 
 some light on the theories as to their import, which we have yet 
 to discuss. The view we propose to consider in the present 
 section, owes its origin to Dr. Venn. Mr. Keynes also has ac- 
 cepted it. Dr. Venn, when dealing with the import of proposi- 
 tions, calls attention to the fact that, though it is quite impossible 
 to admit that universal propositions should be understood as 
 signifying the existence of their subjects, yet all of them do 
 imply that certain things do not exist. If I affirm ' All x is y,' 
 the assertion certainly contains the information that no such 
 things as xy exist. Thus ' All men are mortal ' has the non- 
 existential implication, ' No non-mortal men exist.' Hence he 
 urges that "in respect of what such a proposition affirms, it can 
 ' only be regarded as conditional, but in respect of what it denies, 
 ' it may be regarded as absolute. The proposition ' All x is y ' 
 ' . . . declares the non-existence of a certain combination, viz. : 
 ' of things which are both x and not-y. But it does not tell us 
 ' whether there is any y at all ; or if there be, whether there is 
 ' also any #." 
 
 This view has been called the Compartmental view, because 
 its characteristic feature is that the essential import of the uni- 
 versal proposition is regarded as consisting in the fact that it 
 empties a definite compartment. ' All x is y ' empties the com- 
 partment xy ; ' All y is x,' the compartment xy ; ' No x is y,' 
 the compartment xy. The affirmative import, ' If there are 
 such things as x, then all the x's are y,' is regarded as a 
 secondary and derivative implication. 
 
 Those who have found no reason to disagree with what was 
 said in our last section , will not be prepared to accept this view. 
 We maintain in the first place, that the categorical proposition, 
 ' All x is y,' is in no sense a conditional proposition, but the 
 direct affirmation of an attribute in relation to a known subject. 
 Secondly, we maintain that it is not the case that the negative 
 form is the primary import, and the so-called conditional affirma- 
 tive form the secondary ; but on the contrary, the negative 
 form is a mere inference from the affirmative form. 
 
THE IMPORT OF PROPOSITIONS 117 
 
 A further objection may be raised on the ground that the 
 non-existential interpretation is quite inadequate as representing 
 the true import of the proposition. When discussing Dr. Venn's 
 system of diagrams (Ch. 5, 3) we promised to say something 
 on this point. The negative, ' There are no xy,' merely tells us 
 that at the present time there happen to be no x's that are not 
 y. It does not in any way imply that whenever and wherever 
 an x is found, that x is always y. It is this surely, which is the 
 point of real importance. Yet the theory tells us that not this, 
 but the comparatively unimportant ' There are no xy,' is the 
 true and primary significance of the proposition. 
 
 The treatment of the particular proposition is equally unsatis- 
 factory. In contrast with the universal, it is asserted it does 
 imply the existence of its subject. "If it did not do so," says 
 Dr. Venn, " it would have absolutely nothing certain to tell 
 ' us ... it can extinguish no class, and establish no class, and 
 ' has therefore no categorical information to give us." It is 
 quite true that existentially the particular proposition can extin- 
 guish no class, and establish no class ; but a judgment such as 
 'Some figures are chiliagons,' is most assuredly categorical, and 
 informs us that there is a class of possible entities, which have 
 the definite characteristic of having a thousand sides. It is 
 urged on behalf of Dr. Venn's interpretation, that only thus do 
 we get perfect contradiction between the universal and the 
 particular. ' All x is y ' and ' Some is not y ' are true contra- 
 dictories, if they respectively mean ' No xy exists ' and ' Some 
 xy exists.' Of these one must be false ; the other must be true. 
 But to this it may be replied that the ordinary interpretation 
 of the two judgments provides us with contradiction, when 
 rightly understood, and that the contradiction here is obtained 
 by making the universal mean far less, and the particular far 
 more, than rightly understood they do mean. 
 
 The German logician, F. Brentano, held the same view in a 
 more extreme form. He urged that the ordinary mode of stat- 
 ing the A.E.I.O propositions was logically indefensible, and 
 that the correct forms should be : 
 
 A . There is not an immortal man (= All men are mortal) ; 
 
 E. There is not a live stone (=No stones are living) ; 
 
 /. There is a sick man (=Some men are sick) ; 
 
 O. There is an unlearned man (=Some men are not learned). 
 
 The existential significance of the copula would, he claimed, 
 thus appear plainly. Such a theory carries its own refutation 
 with it. It is manifest to any one who reflects, that as a matter 
 of fact we do not think in these forms. 
 
 * 6. Mr. Bradley on the Proposition. Mr. Bradley defines 
 judgment as ' the reference of an ideal content to reality.' The 
 
n8 PRINCIPLES OF LOGIC 
 
 true subject of a judgment is, he tells us, not the grammatical 
 subject, but the reality itself. The whole judgment is of the 
 nature of a predicate representing attributes which are referred 
 to the real world. Thus, "in ' A precedes B,' this whole relation 
 ' A-B is the predicate, and in saying this is true, we treat it as 
 ' an adjective of the real world. It is a quality of something 
 ' beyond mere A-B. But if this is so, the reality to which the 
 ' adjective A-B is referred, is the subject of A-B " (Principles, 
 Bk. I., c. i, 17). If this view be correct, and the two terms of 
 the judgment form in fact a single predicate, it follows, of course, 
 that the copula is meaningless. Mr. Bradley accepts the con- 
 clusion. In its ordinary acceptation, he tells us, the copula is ' a 
 superstition.' The traditional account of the judgment, that 
 it is a synthesis of ideas, he rejects as manifestly false. Not 
 only is it the case, he urges, that one idea is sufficient for a judg- 
 ment, as when I point to an animal in motion, and say ' Run- 
 ning ' ; but further, did judgment consist in a synthesis of ideas, 
 it would be confined to a sphere of unreal universals. " When 
 ' I say ' Gold is yellow,' then certainly some fact is present to 
 ' my mind. But universal gold and universal yellow are not 
 'realities " (Principles, Bk. I., c. 2, 5). Hence he concludes that 
 the true account of judgment is to be found in saying that we 
 refer the ideal content of our assertion to the real order. 
 
 Mr. Bradley's arguments are of little weight. In the proposition 
 ' Gold is yellow,' those who hold the term ' Gold ' to be the true 
 subject, are not bound to interpret the judgment as meaning 
 no more than that the universal idea of gold is qualified by the 
 universal idea of yellowness. On their showing, it means that 
 that which the concept of gold represents, namely the real entities 
 for which it stands, are qualified by the real determination ' yellow,' 
 But the real entity is not the subject of the intellectual judg- 
 ment, any more than the real determination is a predicate. 
 ' Subject ' and ' predicate ' belong to the thing as conceived. 
 The concepts are, it is true, universal : they omit the individualiz- 
 ing notes of the several pieces of gold. But they do not deny 
 their presence : they merely abstract from them. Thus the 
 term ' Gold ' can be used as representative of every piece of that 
 metal. Further, since we possess knowledge, not merely through 
 the concepts of the intellect, but through the senses which per- 
 ceive the individual, we may employ the universal concept to 
 designate a particular individual, by using the demonstrative 
 pronoun and saying ' This gold is yellow.' 
 
 The contention that we can express a judgment by a single 
 word without either subject or copula, has already been criti- 
 cized (Ch. 3, i). An expression such as ' Running 1 ' is a mere 
 mutilated proposition. It is an abbreviated sentence, and 
 represents the mental judgment 'That object is running.' 
 
THE IMPORT OF PROPOSITIONS 119 
 
 7. Import of the Hypothetical Proposition. In 
 
 Ch. 3, 2, we saw that the explanation of the Cate- 
 gorical judgment was to be found in the comparison of 
 ' being ' in the conceptual order, with ' being ' in the 
 real order. A somewhat similar comparison will afford 
 us the clue to the meaning of the hypothetical propo- 
 sition. The latter expresses the dependence of the conse- 
 quent on the antecedent in the order of conceptual 
 being. If the mind admits the antecedent, it must 
 perforce admit the consequent. In the real order, effects 
 depend on causes, properties on the natures from which 
 they flow. The conceptual order is not thus limited. 
 The mind argues from effect to cause, from property 
 to substance, as well as from cause to effect and from 
 substance to property. It not only judges that ' If 
 the bomb explodes, the king will be killed/ but that ' If 
 the flags are half-mast high, the king is dead.' What is 
 a very remote effect in the real order, is often the imme- 
 diate antecedent in the conceptual order. The Scholastics 
 accurately distinguished between what is anterior in 
 the order of being (prius in or dine reali), and what is 
 anterior in the order of thought (prius in or dine logico). 
 Thus if we argue from the existence of a finite world 
 to the existence of God, in the logical order God is pos- 
 terior to the world, though in the real order the world 
 depends on Him. It is of the utmost importance that 
 the distinction should be borne in mind, for in the study 
 of Logic we are explicitly concerned with the mode in 
 which the order of thought deals with the order of reality. 
 The terms Ground and Reason are sometimes employed 
 to express that on which something depends in the 
 order of thought, in contrast with the term Cause which 
 signifies that on which something depends in the real 
 order. To the followers of the Idealist school the mani- 
 fest difference between conceptual dependence and real 
 dependence presents a problem for which they are unable 
 to offer any satisfactory solution. They reduce the whole 
 world to relations expressed by thought : and their 
 philosophical principles would appear to involve that 
 
120 PRINCIPLES OF LOGIC 
 
 the death of the king depends just as much and just 
 as little on the position of the flag, as on the explosion 
 of the bomb. Thus Mr. Bosanquet tells us that apart 
 from temporal succession which is " the natural differ- 
 entia of causation " he " cannot see how the relation of 
 conditioning differs from that of being conditioned " 
 (Logic II. 262, 264). 
 
 * Truth of the Hypothetical Propositions. In recent works 
 on Logic somewhat lengthy discussions have been devoted to 
 the question as to how a hypothetical judgment can be said to 
 be true. 1 It may well be the case that neither the antecedent 
 nor the consequent taken separately are true. Yet somehow 
 we attribute truth to the assertion in its entirety. In what 
 sense can it be said to correspond with reality ? 
 
 To solve this question we must distinguish two classes of 
 hypo the ticals. In regard to the first of these classes, its truth 
 depends on the fact that the real order does not consist solely 
 of what is actual. Besides what is actually real, there are real 
 potentialities. An acorn is actually an acorn and nothing more : 
 but potentially it is an oak tree. Hence it is true to say, ' If 
 this acorn is planted, it will become an oak.' For its nature is 
 such, that given suitable conditions, it must necessarily develop 
 according to definite laws. Similarly we find systems such as 
 law and social custom, which determine what would happen, under 
 definite conditions, even though those conditions have never 
 occurred, e.g. ' If the king were to arrive, a salute would be 
 fired.' Our judgments are true, not because they correspond 
 to what is, about which we make no assertion but because 
 they correspond to what would be. 
 
 The second class may be illustrated by the judgment, ' If the 
 souls of brutes are spiritual, they are immortal.' Here the 
 judgment depends for its validity, not on a potentiality, but on 
 the generic categorical proposition, ' The spiritual soul as such 
 is immortal.' This principle, being universal, abstracts from 
 time and place. It is therefore capable of application in regard 
 to any time and any place. If the judgment ' B as such is C,' 
 is known, then we may assert regarding any given object, ' If 
 that object is B, it is C.' Such a judgment must be true, for 
 it is merely an application of a principle already acknowledged. 
 
 1 Cf. e.g. Bradley, Principles, Bk. I., c. 2, 49, 50. 
 
CHAPTER VIII. 
 
 THE PREDICABLES. 
 
 i. The Predicables. 
 
 The Predicables are the various relations in which 
 universal terms may stand to the subjects of which 
 they are predicated. The account of the Predicables 
 given by the Scholastic philosophers, is derived from 
 the Isagoge of Porphyry (Ch. i, 5). Porphyry's treat- 
 ment of the subject differs from that of Aristotle in one 
 or two details, which we shall explain in a subsequent 
 section. It is however, as it explicitly professes to be, 
 in full accord with the principles of his philosophy. 
 
 The Isagoge enumerates five possible relations, which a 
 universal term holding the position of predicate, may 
 bear to the subject of which it is predicated. It may 
 stand as the Genus, or the Species, or the Differentia, 
 or as a Property, or an Accident of the entity, of which 
 it is affirmed. 
 
 Before explaining these terms it is important to point 
 out that the Porphyrian account of the Predicables, 
 depends on a fact strongly emphasized by Aristotle (Categ., 
 cc. 2, 5) that the ultimate subject of all predication is the 
 individual. We may of course form propositions such 
 as ' Man is mortal/ in which the subject is not an indi- 
 vidual, but a general term. But ' man ' can only stand 
 as the subject of this proposition, because it is itself cap- 
 able of being predicated of the singulars, ' Socrates/ 
 ' Plato/ etc., etc. ' Man ' has no existence save in so 
 far as individual men exist ; and it is because it can be 
 affirmed of the individual, that the general term is able 
 
122 PRINCIPLES OF LOGIC 
 
 to become a subject of attribution. This distinction 
 between the singular term, denoting the individual 
 substance, e.g. Socrates, and the universal term ' man/ 
 which expresses the class-nature of Socrates, Aristotle 
 marked by the names Primary and Secondary Substances. 
 The individual is the Primary Substance : the class- 
 nature he called Secondary Substance. 
 
 It is evident therefore, that when we are considering 
 the case of some general term employed as the predicate 
 of a proposition, e.g. the term ' animal ' in ' Man is an 
 animal,' we may consider the relation of ' animal/ not 
 merely to its subject ' man/ but to the ultimate subject 
 of predication, namely individual men such as Socrates, 
 Plato, etc. 
 
 Similar considerations will be of force in regard to 
 those abstract terms which signify a quality. Amongst 
 these also there are general terms such as ' colour/ 
 ' virtue/ and the like, which are sometimes found as the 
 subject of propositions. But here too, the right of a 
 general term to stand as a subject, is due to the fact that 
 it is itself used as a predicate of the individual quality, 
 e.g. of ' whiteness/ as exhibited in the individual object. 1 
 So that both in the case of substances, and in the case of 
 abstract qualities, we are able to consider all general 
 terms in reference to their ultimate subject. 
 
 We may now proceed to consider the five predicables 
 we have enumerated above. 
 
 (i) Species. If we take an individual substance, e.g. 
 Socrates, we shall see that among the predicates which 
 can be affirmed of him, there is one which expresses his 
 class-nature, viz. : man. What now is the compre- 
 hension of the term which signifies this class-nature ? 
 It consists of what we may call the constitutive notes or 
 characteristics of that nature. By the word ' constitu- 
 
 1 Arist. Categ., c. 2, 3. " In short, individuals and whatever is numerically 
 ' one, cannot be predicated of a subject. Nothing however prevents them 
 4 in some cases, from inhering in a subject. Thus, an individual instance of 
 4 the science of grammar is one of those entities that inhere in a subject, 
 ' but it is not predicated of any subject." 
 
THE PREDICABLES 123 
 
 live/ we signify those notes which are requisite to make 
 the entity the kind of thing it is, which make it repre- 
 sentative of the type to which it belongs. Thus the com- 
 prehension of the term man is ' rational animal.' For 
 man not only possesses all the notes of the wider class 
 animal, but also the distinctive note of rationality. 
 An entity in which these notes are found is a man. If 
 one of these were absent he would be no longer such. 
 The concept which thus expresses the constitutive notes 
 by which the individual is what he is, is said to represent 
 the essence (ova-La) of the individual. Two other terms 
 were also employed to signify the essence. It was called 
 the quiddity (TO ri rjv elvai), because it is by the term 
 which declares the essential nature, that we reply to the 
 question, What is it ? (quid sit), in regard to any object. 
 It was also called the species (eZSo?), i.e. characterizing 
 form. We may therefore define the species as the sum of 
 the essential attributes of an entity. Or, since we are here 
 considering it as constituting one of the relations which 
 may exist between predicate and subject, we may put 
 the matter thus : Whenever the predicate expresses the sum- 
 total of the essential attributes of the subject, it is said to 
 be the species of the subject. Thus, if I affirm the proposition 
 ' Bucephalus is a horse,' ' horse ' is said to be the species 
 of Bucephalus, since the concept of ' horse/ has for its 
 comprehension the full class-nature of its subject. 
 
 When it is said that the notes expressed by the species 
 are those which make the thing what it is, we must not be 
 supposed to signify that these concepts give us some pecu- 
 liar insight into the inner constitution of class-natures. 
 It is only in the case of mathematical figures, as e.g. of 
 the triangle or circle, by reason of their extreme simplicity, 
 that our minds can represent the actual constitutive prin- 
 ciple of their object. Here indeed our concepts are ade- 
 quate (Ch. II, 3). In regard to natural classes all we can 
 do is to form concepts representing certain characteristic 
 notes that distinguish one class from another. We must 
 be content that our concepts shall be clear. 
 
 Though the primary signification of the word ' species' 
 
124 PRINCIPLES OF LOGIC 
 
 is as we have just explained, that name is often applied 
 to a term, not in reference to the essential nature which 
 it expresses, but in reference to the individual objects 
 which possess that nature : in other words, it is taken 
 not in intension, but in extension, and denotes the group 
 of objects of which it can be predicated. In this sense 
 it is almost synonymous with the word ' class.' And we 
 shall see that though the definition given above is the more 
 philosophically accurate, another based on the extensive 
 signification is frequently employed. 
 
 (ii) Genus. Among the notes constitutive of the specific 
 notion, there are some which are common both to the 
 class in question and to other classes. Thus the notes 
 indicated by the term ' animal ' are common alike to 
 man, and to the various tribes of brutes. A term signifi- 
 cative of this part of the essence, provides us with a 
 predicate, which stands to the subject in a different rela- 
 tion from that occupied by the species. Such a predicate 
 is said to express the genus of its subject. A genus may 
 thus be defined as that part of the essence of the subject 
 which it has in common with other species. Thus ' ani- 
 mal ' is a generic concept in relation to the various species 
 ' man,' ' lion,' ' horse,' etc. ; * triangle ' is generic in 
 relation to ' equiangular,' ' isosceles,' and ' scalene/ 
 
 When it is said that the genus expresses the notes 
 common to several species, we must not be understood 
 to signify that an essence is a collection of attributes, 
 that are mutually independent, and separable one from 
 another. Such a view would be quite foreign to the truth. 
 The species differs from the genus because it is the nature 
 as completely determined, whereas the genus is incom- 
 pletely determined. Thus the notion ' triangle ' is less 
 completely determined than that of * isosceles triangle.' 
 But ' isosceles ' and ' triangle ' are not two different attri- 
 butes in the sense that it is possible to have the note 
 ' isosceles ' existing apart from a triangle. Nor can we 
 have a triangle which is not either isosceles, equilateral, or 
 scalene. But we can form a generic concept of ' triangle,' 
 because our intellect can abstract from the determining 
 
THE PREDICABLES 125 
 
 characteristics, and merely represent what is common 
 to the three species. 
 
 Genus, like species, may be understood in extension. 
 And so understood, it will merely be a wider class, of 
 which the various species are sub-classes. The two terms 
 may in consequence be thus denned : 
 
 A genus is a wider class consisting of narrower classes. 
 
 A species is a narrow class included in a genus. 
 
 It is evident that just as ' animal ' is a genus, under 
 which ' man ' is a species, so we may find higher genera 
 above ' animal.' ' Man ' ' animal ' ' living Being ' 
 ' corporeal substance/ form an ascending scale of Genera. 
 It is this fact that frequently renders it convenient to 
 understand the terms in the meaning expressed by these 
 extensive definitions : for this definition of species makes 
 the term applicable to each sub-class, as referred to the 
 class above it. As ' man ' is a species in relation to 
 ' animal,' so ' animal ' is a species in relation to ' living 
 Being,' and so on. When the intensive definition is 
 employed, ' man ' alone of all the series could be called a 
 species. The higher classes are none of them predicated 
 of any subject as its whole essence. It is only in refer- 
 ence to individuals that such a predicate is found 
 Isag., c. 2, 21, 22). But if we accept the extensive 
 definition, then in the hierarchy of classes, all save the 
 highest are species. This highest class is termed a 
 summum genus. And all save the lowest class, which is 
 known as an infima species, are genera. 
 
 (ill) Differentia. 
 
 The differentia is that part of a specific essence by which 
 it is distinguished from other species of the same genus. 
 Just as the mind can abstract what is common 
 to various species, and express it in the concept of the. 
 genus, so it can by abstraction form a concept of that por- 
 tion of the specific essence which is distinctive of it. This 
 part of the nature is termed the differentia. Thus, ' ra- 
 tional ' is the differentia, which together with the genus 
 ' animal,' constitutes the specific nature * man.' Simi- 
 larly it is by the respective differentiae that ' triangle ' 
 
126 PRINCIPLES OF LOGIC 
 
 becomes ' equilateral triangle/ ' isosceles triangle/ ' scalene 
 triangle.' What we have said as to the genus, will show 
 that in the real order the genus and the differentia are 
 not two different parts of the nature. We cannot in the 
 real order separate between a triangle and its equiangu- 
 larity. It is the mind alone which can distinguish the 
 differentiating form from the indeterminate generic 
 nature, and can view the triangle and its form as equian- 
 gular or isosceles, as distinct. Thus there is a great dif- 
 ference between the essence of a thing in the real order, 
 and the logical essence of which we are here treating. 
 In the real order the parts which make the thing to be 
 what it is are real parts. Socrates is a man because he 
 possesses a human soul and body. The parts of the 
 logical essence on the other hand are not real parts but 
 conceptual parts the incompletely determined genus 
 and the determining differentia. 
 
 Each species in the ascending scale, is marked off from 
 the other classes contained under its genus by a differentia. 
 The differentia of the infima species is termed a specific 
 differentia. The others are known as generic differentiae. 
 
 (iv) Property. Besides the notes which go to make 
 the essence, which we have hitherto been considering, 
 many other attributes may be predicated of a subject. 
 Some of these are directly and necessarily connected 
 with the essential characteristics. These are termed 
 properties (propria 18 ia), and are thus denned : 
 
 A property is an attribute which does not form part of 
 the essence of its subject, but results necessarily from that 
 essence. These properties are not reckoned as forming part 
 of the essence, because they are derivative qualities, not 
 primary. But the fact that they follow from it by result- 
 ancy, ensures that they are found wherever that nature 
 is present, that they are found nowhere else, and that 
 they are constant. Hence the extension of the specific 
 property is precisely the same as the extension of the 
 species. The classical example is the faculty of laughter 
 in man. This is immediately dependent alike on the 
 intelligence and the corporeal structure of human nature. 
 Similarly, his power of intelligent speech, and his practice 
 
THE PREDICABLES 127 
 
 of cooking his food, have been assigned as properties of 
 man. Besides the specific properties, there will be others, 
 which result from the generic notes of the nature. These 
 will, of course, not be limited to the species, but will be 
 coextensive with the genus to which they belong. 
 
 (v) Accident. The fifth of the predicables embraces 
 all those attributes, which are unconnected with the 
 essence. It is thus defined : 
 
 An accident is an attribute, which neither is part of 
 the essence, nor necessarily results from the essence of the 
 subject. 1 Accidents are separable or inseparable accord- 
 ing as the subject is ever found without them or not. 
 Where we are speaking of accidents in relation not to 
 a single individual, but to a whole species, the inseparable 
 accident is one which is found present in every individual 
 of the class ; the separable is one found only in certain 
 members. It may well be asked what it then is, which 
 distinguishes an inseparable accident from a property. 
 If an attribute is found to belong to all the members of a 
 species, should we not rank it as a property, not as an 
 accident ? Porphyry replies that the inseparable acci- 
 dent is found present in other species besides the one in 
 question. The property on the contrary is peculiar to 
 its own species (/sag., c. 16, 4). Thus the black colour 
 of the crow is an inseparable accident. If an entity 
 should be found lacking an attribute of this character, it 
 would not on that account be placed in a different species 
 (ibid. c. 5, 2). This was in fact what occurred when the 
 black swans of Australia were discovered. No one re- 
 garded them as entitled to a different specific name, though 
 they were without what had heretofore been regarded as 
 an absolutely constant characteristic. 
 
 In the case of accidents, not of the species but of the 
 
 1 The term. Accident as signifying the fifth practicable has a different sense 
 from that in which it was employed in Ch. 2, 7, Ch. 7, i. There we used 
 it to denote a real entity whose connatural mode of existence is by inherence 
 in substance. Such entities are termed Real Accidents. As a predicate it 
 signifies a predicate which stands in a certain relation to the subject of the 
 proposition. These are termed Logical Accidents. The relation belongs to 
 the logical order. 
 
128 PRINCIPLES OF LOGIC 
 
 individual, separable and inseparable accidents are other- 
 wise distinguished. An inseparable accident is one which 
 belongs to the subject at all times, e.g. ' To be a Mantuan ' 
 is an inseparable accident in regard to Virgil. A separ- 
 able accident is one, which can only be predicated of its 
 subject at certain times. Thus if it be affirmed, ' Virgil 
 is writing poetry/ this is a separable accident. 
 
 Besides the five Predicables we have mentioned, Por- 
 phyry (Isag., c. 2, 37) notices the case in which a singular 
 term is predicated of a subject, e.g. ' Socrates is the son 
 of Sophroniscus/ This, however, has no claim to constitute 
 a separate Predicable. The primary praedicabilia 
 terms which can be predicated of something are 
 necessarily universal. They express some attribute 
 which can be affirmed of a subject : and the attribute or 
 nature is always universally conceived. A singular term 
 that is predicated, is not one of the primary predicable 
 terms. We form the singular term by limiting some 
 universal notion in regard of place and time. 
 
 It may be easily shewn, that setting aside the case of 
 the singular predicate, the list is exhaustive. For when 
 an attribute is predicated of a subject, it must either 
 belong to that subject by strict necessity or not. If it is 
 not one of the necessary attributes, it is an accident. 
 If, on the other hand, it is a necessary attribute, it either 
 belongs to the constitutives of the essence, or is an attri- 
 bute resulting necessarily from the essence. In the latter 
 case it is a property. Should it belong to the constitu- 
 tives of the essence, it must either be the whole essence, 
 in which case it is a species : or it must be that part of 
 the essence which is common to other classes the 
 genus : or finally the part of the essence peculiar to 
 the species, viz. : the differentia. 
 
 * We have pointed out above that the separation of the genus 
 and differentia is the work of the mind : and that in the thing 
 itself we cannot distinguish two parts, one of which is ' triangle,' 
 the other ' isosceles.' From this it would seem to follow that 
 the differentia must implicitly involve the presence of the genus, 
 that, e.g. the form of the figure as isosceles, necessarily supposes 
 
THE PREDICABLES 129 
 
 that the figure determined is a triangle. Such in fact, is the 
 teaching of Aristotle. The specific differentia, he tells us, gives 
 us the essence. 1 Yet a difficulty may here suggest itself. 
 ' Rational,' it may be urged, does not involve ' man.' Do we 
 not speak of 'rational desires/ 'rational actions' etc., etc.? 
 To this it is replied that the term ' rational,' as predicated on 
 the one hand of man, and on the other of actions and desires, 
 is analogous and not univocal. As applied to man it signifies 
 that his substantial nature itself is distinguished from that of 
 all other animals by the faculty of reason. As used of desires 
 and actions it merely signifies such desires and actions as are 
 directed in accordance with what reason prescribes as right. 
 In this sense the attribute is purely accidental, and in no sense 
 constitutive of a natural class. Eating with a view to preserve 
 health is a rational action, because directed by reason ; but as 
 a natural act it does not differ from the same act as performed 
 by the lower animals. It may be further noted that the term 
 ' rational ' as signifying the differentia of man, must not be 
 understood as synonymous with ' intelligent.' Not man alone, 
 but God and the angels possess intelligence. ' Rational ' 
 denotes an intelligence of a particular kind, viz. one that is 
 dependent on sense perception and arrives at its conclusions by 
 discursive reasoning (Cf. St. Thomas, De Pot. Q. ix., art. 2, ad. 10). 
 The case is somewhat similar as regards the term ' living.' It 
 has been objected that the attribute ' living ' belongs not merely 
 to certain corporeal substances but to all incorporeal beings. 
 It is replied that the life animating a body and rendering it 
 capable of immanent action, and the life of a pure spirit are 
 totally dissimilar. The differentia ' animate ' is found in cor- 
 poreal substances alone. Yet the fact that many terms, which 
 in their primary signification denote a differentia, have in their 
 various analogous senses a wider reference, explains how it is 
 that in several passages Aristotle tells us that the term signifying 
 the differentia is not convertible with the species since it may 
 be common to more species than one (Cf. e.g. Top. I. c. 8, 3). 
 
 2. The Tree of Porphyry. After what has been 
 said in the last section, the figure commonly termed the 
 tree of Porphyry needs no explanation. It shews us 
 the series of species and genera from the highest genus 
 down to the lowest species, together with the differentiae, 
 which go to constitute each species. 
 
 1 Met. VI., c. 12, 9. d BTJ OVTWS x ei > (fxivepov STJ Sri -fj reXevrata 8ia<f>opari 
 oixria TOU irp6.yfjt,a.TO$ &TTCU Kal 6 6/>i0yi6s. Cf. St. Thomas, Opusc. 39, De 
 Natura Generis, c. 8. " Tota namque constituitur definitio ex ultima differen- 
 tia." But with these passages, compare Topics, VI. c. 6, 10, and St. Thomas, 
 Opusc. 26, De Ente et Essentia, c. 3. The differentia implies the genus as the 
 subject of which, and of which alone it is a determining principle : but it is 
 not a logical whole containing the genus. 
 
 K 
 
I 3 
 
 PRINCIPLES OF LOGIC 
 Substance 
 
 Corporeal 
 
 Animate 
 
 Sensible 
 
 Rational 
 
 Socrates 
 
 Incorporeal 
 
 Inanimate 
 
 Insensible 
 
 Irrational 
 
 Plato, etc. 
 
 It is evident that schemes may be drawn up to repre- 
 sent the genera and species, not merely of substances as 
 in the tree of Porphyry, but also of those attributes, 
 which qualify substance, but which can be conceived in 
 abstraction from it. The following scheme gives us the 
 divisions of abstract figure. It will be observed that a 
 separate line is not given for the differentiae, since in 
 this case our language does not possess different terms 
 for the differentia and the species. 
 
 I 
 
 Plane 
 I 
 
 Figure 
 J 
 
 Solid 
 
 I 
 
 Rectilineal 
 
 Curvilinear 
 
 r 
 
 Triangles 
 
 I II I 
 
 Quadrilaterals, Pentagons, etc., etc. 
 
THE PREDICABLES 
 
 * 3. Aristotle's Predicables. The fivefold division of 
 Porphyry is in accord with the principles of the Aristotelian 
 philosophy. Yet Aristotle himself gives us a scheme arranged 
 on a different system. The Porphyrian scheme is, as we saw, 
 based on the principle that the ultimate subject of predication 
 is the individual, and that it is in consequence, possible to frame 
 an ascending scale of genera and species corresponding to the 
 order of nature. Though this is part of the teaching of Aristotle, 
 yet he does not base his division of predicables upon it, but 
 solely on the relation between 5 and P, considered without 
 regard to their position in the scale of being. It is thus that 
 he explains his system : 
 
 " Whenever a predicate is affirmed of any subject, the predi- 
 ' cate must either be coextensive with the subject or not. If 
 
 * it be coextensive, the predicate is either the definition * of the 
 ' subject or a property. If it gives us the essence, it is the 
 ' definition ; if not, a property. For we have explained the 
 ' property, as that which is coextensive with the entity to which 
 ' it belongs, while not forming part of its essence. If however, 
 
 * the predicate be not coextensive, it must either form part of 
 ' the attributes comprised in the definition of the subject or not. 
 ' If it be one of those attributes, it is either a genus or a dif- 
 ' ferentia, since the definition is composed of the genus and the dif- 
 'ferentiae. If it is not one of the attributes contained in the 
 ' definition, it is clear that it is an accident " (Topics, I., c. 8, 
 2, 3). 
 
 This gives us the following scheme. 
 
 (1) Definition. \ / Containing the essen- 
 
 Coextensive with tial attributes. 
 
 (2) Propria. subject. ^ Containing attributes 
 
 not belonging to es- 
 sence. 
 
 Containing some por- 
 tion of essential at- 
 tribute. 
 
 Containing attributes 
 not connected with 
 the essence. 
 
 In this system of Predicables, there are two points which 
 call for notice. 
 
 (i) The omission of the species. This is readily explained if 
 the principle on which the system is constructed be kept in view. 
 The only case in which a predicate can express the species is, 
 
 1 The definition is ordinarily expressed by the proximate genus and its 
 differentia. Thus the definition of man is ' rational animal ' ; that of animal 
 is ' sensitive living- being.' 
 
 I 
 
 (3) Genera and 
 Differentiae. 
 
 (4) Accidents. 
 
 Not coextensive with 
 subject. 
 
1 32 PRINCIPLES OF LOGIC 
 
 as we saw, when the subject is an individual, e.g. ' Socrates is 
 a man.' But as regards the relative extension of the terms, the 
 species does not differ from the genus : neither of them is co- 
 extensive with the subject. Hence Aristotle reckons the species 
 here under the head of genus. Nor does the fact that he declares 
 the genus only to express part of the essential attributes, militate 
 against this explanation. For the species, though expressing 
 all the constitutive notes of the type, the whole class-essence, 
 cannot give us the essence of the individual with the differentia 
 which separates him from others of the same species. 
 
 (2) The ranking of the differentiae with the genus as differing 
 in extension from the subject. In Topics, IV., c. 2, n he says 
 that the differentia is ' either coextensive with the species or 
 exceeds it in extension.' This is the more accurate statement. 
 Occasionally we have a term which expresses the determining 
 principle of a particular species as such, e.g. ' isosceles ' in regard 
 to ' triangle.' More often our term is common to various species. 
 Thus the term ' intelligent ' or ' rational ' may be employed as 
 the differentia of man, and may also be predicated of spiritual 
 beings. 
 
 * 4. The Controversy on Universals. The full discussion of 
 the Predicables renders it necessary that we should deal with 
 the question as to what it is that the universal term really signi- 
 fies. If for instance we consider the terms ' man,' ' white,' 
 ' round,' we see that each of these has a perfectly stable meaning, 
 which it retains wherever it is employed. Yet though the mean- 
 ing be thus invariable, the term ' man ' is predicated, and rightly 
 predicated, of different individuals of Socrates, and of Plato, 
 of Mill, and of Kant. What is this human nature which is one, 
 and yet stands in the same relation to every member of the 
 class, which though it is one, belongs at the same time to many 
 individuals ? * Various answers have been given to this question. 
 We may hold (i) that this common nature is something real. 
 Those who give this answer are termed Realists. We may say (2) 
 that the common nature is merely a thought in the mind without 
 objective counterpart in the real order. The adherents of this 
 doctrine are known as Conceptualists. 2 Or we may say (3) that 
 the only common element is the name, given to a variety of 
 
 1 Met., VI. C. 13, 2. TOVTO yap \eyeTca Ka66\ov 8 ir\elo(riv virdpxfiv 
 TrtyvKev. ' We call Universal that whose nature it is to belong at once to 
 many.' 
 
 8 Among modern logicians Hamilton and Mansel were Conceptualists. As 
 such also may be reckoned the Idealist logicians, whose theory of knowledge 
 is based on the doctrines of Kant and Hegel. Among the medieval philo- 
 sophers, this was the teaching of William of Ockham (1280-1349) and his 
 school. They were at that period known as Nominalists. But their tenets 
 on this point agreed with those of the modern Conceptualists. 
 
THE PREDICABLES 133 
 
 objects because of some real or fancied resemblance. This view 
 is that of the Nominalists. 1 
 
 That this is a philosophical problem of the very first importance 
 will appear at once, when it is observed that every scientific 
 principle relates to the universal. A merely particular fact is 
 of no value in science. Facts attain their value, when they can 
 be related to some law. But a general law is a law affirmed 
 about the universal nature. If then we hold that in the real 
 order there is nothing corresponding to the universal term : 
 that for instance, when we assert that water at the sea-level 
 freezes at 32 F., the assertion relates merely to a concept in 
 the mind, or to the meaning of the word ' water ' : our philosophy, 
 in that case, discredits the assured results of science. 
 
 The only satisfactory answer that the problem has received, 
 is that afforded by the doctrine known as Moderate Realism. 
 
 We have already (Ch. 2, i) called attention to the manner 
 in which the concepts of the intellect abstract from the individual- 
 izing conditions of the object of thought. Our senses distinguish 
 individual entities, even though they be precisely similar to each 
 other. But the mind seizes not on what is individual, but on what 
 is characteristic : and it recognizes that the characteristics which 
 it represents in thought, may be reproduced in an indefinite num- 
 ber of individuals. Take, for instance, the concepts formed by 
 the mind if a sovereign is presented to sense. It conceives it 
 as gold, as yellow, as lustrous. It is true that when these notes 
 are first conceived by the mind, they are not at once viewed as 
 universal : that is to say they are not referred to a number of 
 similar objects. But the mind has only to reflect on the nature 
 of the concept, and it immediately sees that the idea, e.g. of 
 yellow, would serve to express not only the gold under observa- 
 tion, but any number of other things, provided they were similar 
 in that particular respect. Whenever we are brought into 
 contact with several objects presenting similar features, this 
 universality is forced upon our notice. We frame a concept 
 representing the notes they have in common, and abstracting 
 from all others. We see that it is one and the same concept 
 which represents them all, and that the name expressive of these 
 notes may be affirmed of each. Thus my concept ' man ' repre- 
 sents the characteristics common to all men ; and the nature 
 represented by the concept may be affirmed of every one. 
 
 It may however be asked, whether it is not my concept of 
 man, rather than the nature of man, which I affirm of the in- 
 dividual. It is manifest that I affirm the nature, not the con- 
 
 1 Nominalism has been the traditional doctrine of the English sensationalist 
 school from the days of Hobbes. It finds its most notable representative in 
 Mill. 
 
134 PRINCIPLES OF LOGIC 
 
 cept. I could not say ' Socrates is a man,' if the predicate signi- 
 fied my concept. It signifies the nature represented in my 
 concept. 
 
 Nor can it be urged that on this explanation, we affirm the 
 identity of Socrates with what at most is only a part of his being, 
 abstracted from the remainder : that on our showing we assert 
 ' Socrates is human nature.' The concept ' man ' while ex- 
 pressly representing the notes only that are common to all men 
 alike, does not exclude the remaining notes. It does not signify 
 ' human nature,' but ' a being possessed of human nature.' Im- 
 plicitly it includes all the other notes of the individual of whom 
 it is affirmed. 
 
 Our conclusions now enable us to answer the question, which 
 we proposed to ourselves at the beginning of the section, viz.: 
 What is the human nature, which we think of as at one and 
 the same time one and many ? We reply that this characteristic 
 of multiplicity in unity, belongs to the nature as and only as it 
 is conceived in the intellect ; and that it consists simply in the 
 fact that one and the same concept represents all the members 
 of the class in question. But though we know the nature in a 
 universal concept, yet the nature itself, which my mind makes 
 known to me, and which I affirm regarding the subject of my 
 judgment, is in the real order, and it is found in the objects of 
 which it is affirmed. 1 Hence the laws of science, and all our 
 general statements are affirmed, not (as the Nominalists tell us) 
 merely about the common name which stands as subject, nor 
 yet (as the Conceptualists would have it) about our concepts, 
 but about the objects themselves, in which the common charac- 
 teristics are found. It is as maintaining this position that the 
 adherents of the traditional Scholastic doctrine are rightly termed 
 Realists. 
 
 It is therefore of prime importance to notice the distinction 
 between what is termed the direct and the reflex universal. The 
 direct universal is simply the nature abstracted from individualiz- 
 ing conditions, and as thus abstracted affirmable of a subject, 
 e.g. the nature ' man ' which we can affirm of Socrates. But 
 when by an act of reflection, we consider this nature as it is 
 mentally conceived, we see that it is affirmable of each and every 
 
 1 St. Thomas tells us that that which the mind contemplates is the nature : 
 the concept is that in which it knows the nature. " Substantia ergo rei est id 
 quod intellectus intelligit." Opusc., 40, De Potentiis Anitnae. " Istud ergo sic 
 ' formatum et expressum in anima dicitur verbum interius, et ideo compara- 
 ' tur ad intellectum non sicut id quo intellectus intelligit, sed sicut in quo in 
 ' telligit, quia in isto sic expresso et formato videt naturam rei intellectae." 
 Opusc. 12, De Differentia Verbi Divini et Humani. " [Verbum interius] est 
 ' tanquam speculum in quo res cernitur." Opusc. 13, De Natura Verb* 
 Intellects. 
 
THE PREDICABLES 135 
 
 man that it belongs to all, that it is one and many. This is 
 the reflex universal. 1 
 
 It will now be apparent how necessary is the discussion of 
 this question to the understanding of the Predicables. For 
 the five Predicables are simply the five possible divisions of the 
 universal thus mentally conceived as being one and many. They 
 give us the five relations in which a class-notion can stand to 
 the things within the class, or as we may otherwise put it, in 
 which a predicate can stand to the subject of which it is affirmed. 
 A universal term in the predicate, must, as we have seen, be 
 Species, Genus, Differentia, Property or Accident. These five 
 therefore are Second Intentions (Ch. 2, n). They are terms 
 which can only be affirmed of the nature as it is in the conceptual 
 order : they do not belong to the object in the real order. We 
 cannot argue because Socrates is a man, and man is a species, 
 that therefore Socrates is a species. For Socrates is a man in 
 the real order, while man is a species in the conceptual order 
 alone. 
 
 The above account has shewn that this Moderate Realism 
 the prevalent view among the Scholastic philosophers, bore no 
 resemblance to Exaggerated Realism, the extravagant doctrine 
 according to which the universal has objective existence in the real 
 order as a universal, and the species and the genus are held to 
 be real things beyond the individuals of which they are asserted. 2 
 St. Thomas again and again rejects such a view in express terms, 
 and tells us that his own teaching is identical with that of the 
 two great Arabian Aristotelians, Avicenna and Averroes. 3 
 Nevertheless English writers on Logic, as a rule fail even to 
 mention this view, and represent the Scholastics as ordinarily 
 teaching the objective reality of universals. An error on so 
 fundamental a point as this, should render the student very 
 cautious in accepting any criticism which such writers may pass 
 on the Aristotelians of the middle ages. 
 
 * 5. The Universal in Modern Logic. The view of the 
 universal taken by Mr. Bradley and Mr. Bosanquet is 
 radically different from any of the theories as to its nature, 
 which we have hitherto considered. According to this 
 view it consists in "a persistent identity in difference" 
 
 1 On Direct and Reflex Universals, see Maher, Psychology, Ch. 14, pp. 294 
 and sqq. (ed. 6). 
 
 2 Exaggerated Realism is famous as the doctrine of Plato. A somewhat 
 similar view was maintained by William of Champeaux (d. 1121). 
 
 3 The following will serve as a typical passage. Opusc. 39, De Natura 
 Generis, c. 5. "In re igitur nihil est commune multis, quia quidquid est in re 
 4 est singulare, uni soli communicabile. Quod autem commune est, dicitur per 
 intellectuni. Intellectus enim facit universalitatem in rebus, ut dicit Com- 
 mentator [i.e. Averroes] supra librum de Anima." 
 
1 36 PRINCIPLES OF LOGIC 
 
 (Bosanquet, II., p. 92). This identity is not understood as a 
 conceptual identity expressing things, which are in the real order 
 not the same but similar, but as a real identity. "If we say 
 'that A and B are alike," says Mr. Bradley, " we must be taken 
 ' to mean that they are so far the same. ... If A and B for 
 ' instance both have lungs or gills, they are so far the same " 
 (Principles, Bk. II., Pt. i, c. 6, 3). " What seems the same, is 
 the ' same and cannot be made different by any diversity " (ibid. 
 5). The belief, he urges, that there is no reality except exclu- 
 sive particulars, is not proved. It is "a mere inherited pre- 
 * conception which has got to think itself a real fact " (ibid. 8). 
 Similarly Mr. Bosanquet tells us that " Mortality is affirmed of 
 ' all individual men in virtue of a oneness of nature running through 
 ' them all : and therefore we must take individual unity to be a 
 'matter of degree, and to be wholly absent in no content that 
 'can be presented to thought as designating a subject of judg- 
 'ment" (Logic, I., p. 148). This view, that universality involves 
 identity is a natural result of the Hegelian philosophy, which, 
 as we have seen, denies the existence of any distinction between 
 thought and things. A further development of the same doc- 
 trine is to regard the concrete individual as a universal. The 
 finite individual is universal, says Mr. Bradley, because it is 
 " the identity of its own internal diversity " (Principles, Bk. I. 
 c. 6, 38). (Cf. Bosanquet, I., p. 210.) 
 
 There are thus two fundamental errors in the theory. First, 
 distinct things are asserted to be identical, because, under a cer- 
 tain aspect, they can be expressed by one and the same concept. 
 Secondly, the real identity of an individual thing in virtue of 
 which it persists through changes and is the bond of many attri- 
 butes, is confused with the conceptual identity of the universal. 
 A theory of Logic based on errors such as these, whatever be 
 the subtlety with which it be defended, must needs be radically 
 fallacious. 
 
CHAPTER IX. 
 
 THE CATEGORIES. 
 
 i. The Categories in their Metaphysical Aspect. 
 The Categories (or Predicaments) may be considered 
 both as belonging to the real order, and as belonging to 
 the conceptual order, in other words, both metaphysic- 
 ally and logically. It will be convenient to treat of Ihem 
 under their metaphysical aspect first, and to deal with 
 their logical aspect afterwards. 
 
 Viewed as belonging to the real order, they were termed 
 by the Scholastics the ten summa genera of things the 
 ten classes, to one of which all things whatever could be 
 referred. But in this account of the Categories, the word 
 ' things ' must be rightly understood. In ordinary dis- 
 course, by things we mean substances : and a division 
 of things into classes would signify a classification of 
 substances. This is not what is meant here. The word 
 ' things ' includes accidents as well as substances. For 
 accidents are real entities, though they cannot exist apart 
 from substances. It is one thing to be a horse, another 
 to be black, another to be carrying a rider. Yet Buce- 
 phalus may be all these things at one and the same time. 
 It is in this sense we must understand the word, when 
 we term the following list a classification of ' things/ 
 
 1. Substance : natures which exist not as mere deter- 
 
 minations, but in their own right, e.g. Socrates, 
 man, animal. 
 
 2. Quantity : the spatial extension, 'height, breadth of 
 
 a substance. 
 
 3. Quality : determinations which characterize the 
 
 nature. 
 
138 PRINCIPLES OF LOGIC 
 
 Aristotle in the Categories distinguishes four kinds of qualities, 
 viz. : 
 
 (1) Habits and Dispositions, i.e. determinations of the nature 
 
 itself, e.g. knowledge in the intellect, health in the body. 
 
 (2) Capacity and Incapacity, i.e. determinations of the active 
 
 powers, e.g. the capacity to walk. The term Incapacity 
 signifies not the total absence of the determination, but 
 its possession in an undeveloped and immature degree. 
 
 (3) Passive Qualities, i.e. determinations consequent on or 
 
 productive of physical change, e.g. the sensible qualities of 
 cold, heat and colour. 
 
 (4) Figure, i.e. determinations of quantitative extension. 
 
 It should however be observed that these four classes are not 
 put forward by Aristotle as mutually exclusive, nor even as 
 necessarily exhaustive (Categ., c. 8, 3, 6, 23). They merely 
 embody the distinctions recognized in the current vocabulary 
 of the Greek language. 
 
 4. Relation : the order which holds between one sub- 
 
 stance and another. Thus two substances may be 
 alike in quality, equal in quantity, the same in specific 
 nature. 
 
 5. Place : position in relation to surrounding space, 
 
 e.g. at London, in Westminster Abbey. 
 
 6. Time : position in relation to the course of events, 
 
 e.g. last year. 
 
 7. Posture : the relative position of parts in the object 
 
 itself, e.g. sitting, lying down. 
 
 8. Habit : the determinations accruing from the physi- 
 
 cal adjuncts, which belong to the full integrity of 
 the substance as a necessary equipment for its work 
 in Nature, e.g. armed, cloaked. 
 
 9. Action : the production of a change in some other 
 
 object, e.g. digging, 
 
 10. Passion : the reception of change from some agent, 
 e.g. being struck. 
 
 These ten Categories may be illustrated in the case of 
 an individual. We find that in order that the individual 
 may fill his place as a part of Nature, he must be deter- 
 mined in all these ten ways. Here, for instance, is some 
 one whom I know. As man, he is substance something 
 that is not a determination, but can receive determina- 
 
THE CATEGORIES 139 
 
 tions. As regards quantity, he is six feet high. Among 
 his qualities it may be noted that he is (i) a mathema- 
 tician, (2) a skilful carver, (3) swarthy, (4) square- 
 shouldered. He closely resembles his father, to whom he 
 is thus related by the relation of likeness. He is in the 
 city of York (place) ; and it is October, 1907 (t'me). 
 He is stooping (posture) ; dressed in cloth, and provided 
 with a hammer and chisel (habit) ; he is carving wood 
 (action), and his tool has just cut him (passion). 
 
 In what sense are the nine categories of Accidents called 
 ' things ' ? How can we regard the quality of swarthi- 
 ness or the relation of likeness as ' a thing ' ? If indeed 
 we are speaking of these accidents considered as separ- 
 ate entities, then they are not things at all : there is no 
 such thing as ' walking ' or ' sitting ' or ' health ' existing 
 independently. These accidents are said to be, not be- 
 cause they possess existence themselves, but because the 
 concrete subject is what it is, through them. 1 The con- 
 crete subject is walking, and is healthy. Hence, as Aris- 
 totle says, " They are called ' things,' because in their 
 * respective ways, they determine that which is a thing in 
 ' the sense of being a substance." 2 
 
 In speaking of the Categories as the ' summa genera of 
 things/ we have employed a traditional expression. But 
 their nature would perhaps be more clearly indicated, by 
 calling them the ten modes of being in which an individual 
 thing is realized. For the various kinds of determination 
 the classes of ' things ' differ one from another by 
 the mode of being, which they confer on the individual. 
 
 It is now clear why there is not one summum genus only, 
 viz. : Thing or Being, of which these classes are subor- 
 dinate species. Genus and species are only found, when 
 the various classes can be expressed in a common uni- 
 vocal concept, and are distinguished by specific differen- 
 
 1 St.Thomas, Summa Theol, I., Q. 45, Art. 4. " Illiproprie convenit Esse, quod 
 ' habet Esse, et est subsistens in suo Esse. Formae autem et accidentia et alia 
 ' hujusmodi, non dicuntur entia quasi ipsa sunt, sed quia eis aliquid est : ut 
 'albedo ea ratione dicitur ens, quia ea subjectum est album." 
 
 2 Met., VI., C. I, 2. TO. 5' dXXct X^yercu 8vra T$ TOV ourws 6vros TO. ptv 
 iroff6ri]Ta.s e&>at, rd 8t Troi^TTjras, TCI 5 irdOr), TO 5 #XXo n TOIOVTOV. 
 
I 4 o PRINCIPLES OF LOGIC 
 
 tiae. There is no univocal concept of ' thing/ nor can 
 we find differentiae, by which the notion is determined. 
 ' Thing ' is an analogous term. It has a different mean- 
 ing as applied to each of the ten categories : and though 
 we can form a universal notion expressive of Thing in 
 general, it possesses the universality of an analogous, not 
 of a univocal concept. For the same reason there is no 
 common genus ' Accident.' The nine kinds of accident 
 are irreducible. 
 
 It has been asserted by some authorities that the 
 order of the Categories is based on no intelligible princi- 
 ple, that Aristotle apparently drew up his list in a hap- 
 hazard fashion. 1 
 
 Most assuredly, this would be a very extraordinary 
 feature in a doctrine to which Aristotle recurs so fre- 
 quently. As a matter of fact those who say this, have 
 missed a most important feature in the doctrine of the 
 Categories. The order in which they are enumerated, 
 reveals to us the law governing the synthesis of forms in 
 the individual. This will easily be seen on considera- 
 tion. The substantial nature gives us as it were the start- 
 ing point. In virtue of this, the thing possesses inde- 
 pendent existence, and is the kind of thing it is. But 
 the substantial nature cannot exist without those acci- 
 dental forms which constitute the complement of its 
 being. 2 Of these the first is magnitude or extension 
 the second Category. Physical qualities presuppose 
 extension : they are supported by the substance as 
 extended. From these three primary Categories result 
 three kinds of relation, which give an order and harmony 
 in the manifold of the universe, viz.: likeness of quality, 
 equality of quantity, sameness of specific form. The 
 remaining categories are extrinsic determinations. They 
 add nothing to the entity itself. But in the physical 
 universe, each entity is determined not merely by its 
 
 1 Thus Dr. Wallace says (Outlines of the Philosophy of Aristotle, p. 25), " These 
 ten Categories would seem to be arranged on little or no principle." 
 
 2 The order of the Categories is of course an order of relative subordination, 
 It is in no sense an order of time. St. Thomas, Opusc. 63 in Boeth, de Trin. 
 Q. 5- art. 3. 
 
THE CATEGORIES 141 
 
 inherent characteristics, but by its status as a part of the 
 whole. It must be at a definite point in space, and at a 
 definite period in time. Its own parts are disposed either 
 after one order, or after another. Further, in the case 
 of man, a special Category arises that of habit. For 
 man, unlike the beasts, is not fully equipped by Nature. 
 The incompleteness of his equipment is a necessary con- 
 sequence of his intelligence. Irrational creatures are 
 provided with the instruments and the extraneous cover- 
 ing requisite to enable them to attain the ends to which 
 instinct guides them : for these ends are confined within 
 definite limits. Man in virtue of his intelligence pursues 
 ends which are unlimited in their range. Hence his 
 equipment cannot be a natural endowment, but must be 
 the work of the inventive reason (Summ. Theol. I. q. 76, 
 art. 5, ad. 4). 
 
 The entity is now determined as a part of Nature. But 
 between the different physical substances there is mutual 
 interaction. Hence arise the two last Categories, action 
 and passion. 
 
 * It is often asserted that the last six Categories are all rela- 
 tions, that they have no right to be reckoned as independent 
 classes. It may be of interest to indicate in a very brief manner 
 on what grounds St. Thomas would have founded the claims of 
 these Categories to independence. 
 
 In regard to the Category of place, it is true that when we state 
 where an object is, we do so by indicating its relation to other 
 bodies. But the thing is not constituted in place by these re- 
 lations. It is possessed of these relations because it is in this 
 place. Local position itself is not a relation. For us the place 
 of a thing is denned by its distance from certain assigned points. 
 Thus the place of an object in a room is denned by its distance 
 from the enclosing walls : the place of an object in the air by its 
 height above such and such a spot on the earth's surface. The 
 case of time is analogous to that of place. This, too, is an ex- 
 trinsic determination irreducible to one of any other kind. ! 
 As concerns posture, a change of position among the various parts 
 of one and the same thing, cannot be called a change of relations : 
 for here also we have but one substance, not two. The Category 
 of habit would indeed be reducible to relation, if man could be 
 
i 4 2 PRINCIPLES OF LOGIC 
 
 looked on as a complete substance related to the extraneous sub- 
 stance which is predicated of him. But, as we have seen, as 
 a part of Nature he is incomplete until he has received the 
 additional determination conferred by the adjacent ' habit.' 
 Action and passion include relations, but are differentiated from 
 that Category, inasmuch as they further involve the production 
 of change, or its reception. 
 
 It may be noted that there has always been considerable 
 divergence of opinion among Scholastic authors regarding the 
 value of this tenfold division, and as to whether certain of the 
 number can justly be reckoned as independent classes. The 
 reader may be referred to the treatment of the subject by Domet 
 de Verges, Abrege de Metaphysique, II., cc. 25-36. 
 
 2. The Categories in their Logical Aspect. In theii 
 logical aspect the Categories are no longer modes oi 
 real being : they belong to the conceptual order. It 
 is as thus regarded that they belong properly to our 
 subject. They claim our attention as a classification of 
 things as mentally represented. 
 
 It is under this aspect that Aristotle treats the Cate- 
 gories in his famous work known by that name. As thus 
 understood, they are defined as the orderly classification 
 of genera, species, and individuals from the summa genera 
 to the individual entities. 1 The treatment of this subject 
 .belongs of course to the Logic of the Concept, not to the 
 Logic of the Judgment. 
 
 Things in the real order are all singular. The sub- 
 stances, qualities and quantities which are found in the 
 external world cannot be universals. The singular alone 
 exists. But when we pass to the order of knowledge we 
 find not merely things singular but things universal. Our 
 intellect shews us universal natures such as man, animal, 
 substance. These terms signify real substances, for they 
 can one and all be affirmed of the concrete individual : 
 and what is identical with the individual is real. Yet at 
 the same time they are universal ; though as universal 
 they exist in our mind alone. In precisely the same 
 
 1 Joan, a S. Thoma. (1590-1644), Log., Q. 14, Art. i. " Praedicamentum nihil 
 'aliud est quam series seu co-ordinatio praedicatorum superiorum et inferiorum ab 
 ' uno supremo genere quod praedicatur de omni inferiori, usque ad individuum 
 quod subjicitur omni superiori." Cf. Suarez, Disp. Met., XXXIX. Proem. 
 
THE CATEGORIES 143 
 
 way, the mental order reveals to us not merely the singu- 
 lar quality this whiteness, but the universal quality colour. 
 The store of these conceptual representations of the real 
 order which at any time is found in our minds, constitutes 
 the elements into which our knowledge is resolvable. They 
 are that out of which our mental furniture is built up. 
 Of them our judgments and our reasonings are all formed. 
 
 A careful scrutiny of the character of these concepts 
 reveals the fact that they stand in a hierarchical subor- 
 dination one to another. Some are such that they can- 
 not be predicated universally of any other ; some again, 
 while they can be predicated of others, can themselves 
 stand as the subjects of predication : while a last group 
 can only occupy the position of predicates, and are 
 incapable of receiving predication (An. Prior /., c. 27, 
 2) . The first of these three classes consists of individual 
 things singulars. In the second are found all those 
 universal terms, which themselves stand as species to 
 wider generic conceptions. In the third class are the 
 summa genera alone. Thus we can say, ' Socrates is a 
 man/ ' Man is vertebrate/ ' Vertebrates are animals ' : 
 but we cannot reverse the order and say, ' Animals are 
 vertebrates/ ' Vertebrates are men/ l Of what funda- 
 mental importance in Logic is this law, in virtue of which 
 the wider concept is predicated of the more restricted, 
 we shall see in subsequent chapters. 
 
 It further appears that this hierarchical arrangement 
 falls into distinct groups, the groups we have desig- 
 nated as the Categories. We cannot predicate a term be- 
 
 1 This point is well put by Mr. Joseph (Introd. to Logic, p. 236). " We say 
 ' that diamonds glitter, rather than that some glittering things are diamonds : 
 ' that blue is a colour, rather than that a colour is blue. To say that a colour 
 ' may be blue is natural enough : just as it is to say that a stone may be a dia- 
 ' mond : but still we predicate the genus of the species, and not the species of 
 ' the genus : it is not the genus colour, but colour in some particular case ; not 
 ' the genus stone, but some particular mineral that is blue or that is diamond. 
 ' Commonly, except where they are mere coincident attributes, the predicate 
 'is a wider term or more generic than the subject in judgment." The fact to 
 which Mr. Joseph here calls attention, viz. : that when we say ' Some stones 
 are diamonds,' we are predicating the species of individuals, not of the genus, 
 at once appears, if we reflect that we cannot say, ' Stone (as such) is diamond,' 
 ' The triangle (as such) is equilateral.' 
 
I 4 4 PRINCIPLES OF LOGIC 
 
 longing to one Category of another, except where the two 
 determinations happen to belong to one subject. The 
 natures expressed by the different Categories, are funda- 
 mentally distinct. 1 
 
 The investigation of the conceptual order has thus 
 revealed the fact that it is not a chaos of concepts, but 
 that, no less than the real order, it is governed by definite 
 laws. This discovery must ever rank as one of the great- 
 est results of Aristotle's genius. 2 
 
 Each Category then consists, as we have said, of an 
 ordered series of terms significative of a special mode of 
 being, commencing with the term that designates the 
 summum genus, and ending with singular terms, e.g. this 
 man. Each series develops into a tree of Porphyry. But, 
 as we have noted on more than one occasion, the univer- 
 sals of the Categories must not be confused with the uni- 
 versals of the Predicables. In the Predicables we view 
 the universals as universals : we consider in what relation 
 the abstracted and universal nature stands to the sub- 
 jects of which it is predicated. Thus the Predicables are 
 all terms of Second Intention. The Categories on the 
 other hand are terms of First Intention. We are con- 
 cerned only with the nature expressed, and not with the 
 character of the nature so far as universal. As belong- 
 ing to the Category of substance the nature ' man ' is 
 not ' a species/ but is ' rational animal.' 
 
 3. The Categories in their Relation to the Sciences. 
 
 The important bearing of the predicamental lines on 
 
 1 Hence as arranged in ascending series according to their several categories, 
 the terms belonging to the nine genera of accidents are expressed in the ab- 
 stract, not in the concrete form, e.g. as ' prudence,' ' virtue,' not ' prudent,' 
 * virtuous.' The latter form expresses the accident as qualifying something 
 else. Thus ' white ' signifies some substance which is qualified by whiteness. 
 It is by the abstract term alone that we can signify the accident as a deter- 
 mination distinct from the subject in which it inheres (vide Pesch. Inst. Log., 
 1449). We do not, however, as has been objected, transform the accident 
 into a substance by employing the abstract term. The concrete term alone 
 expresses the subsistent reality which belongs to substance (S. Thomas, 
 Summa TheoL, I., Q. 3, ad. 3). 
 
 2 The Categories provide a complete classification of concepts. Negative 
 and Privative terms belong to the category to which belongs the positive term, 
 by means of which they are conceived. Terms of Second Intention belong 
 to the Category of Relation. 
 
THE CATEGORIES 145 
 
 those organized bodies of knowledge which we term 
 sciences, should not be overlooked. In any such line, 
 the concepts in their ascending scale of wider and wider 
 generality furnish us with so many distinct objects of 
 scientific consideration. Provided that our abstractions 
 are not arbitrary, but are grounded on the nature of 
 things, the objects expressed by the several concepts have 
 each of them a group of attributes peculiar to itself. 
 Thus in the series horse-equidae-ungulate-mammaL-verte- 
 brate, etc., each of the types expressed has many distinc- 
 tive properties. These properties are affirmed of the 
 type in a system of true universal, i.e. generic judgments : 
 e.g. ' Equidae as such tread only on the hoof upon the last 
 phalanx of the third digit.' The group of generic judg- 
 ments known in regard of any object, constitutes the 
 science of that object. 
 
 It is not merely in regard of substances that the pre- 
 dicament has this function. In other Categories also, 
 science organizes itself in our mind on this basis. Thus 
 quantity continuous quantity extension plane surface 
 triangle, provide us with so many heads of scientific 
 knowledge. Did science in any case reach its unattain- 
 able ideal, it would consist of the accurate definition of 
 some object thus universally conceived, together with 
 the complete series of attributes predicable of it, whether 
 as constituting its own properties or as belonging to it 
 in virtue of some type higher in the scale. Thus the 
 Categories provide us with the principle on which the 
 analysis of the sciences must be based. They shew how 
 the various sciences are correlated in our mind : and they 
 shew how their respective objects are distinguished from 
 each other, either as falling within different Categories, 
 or as differentiated by various degrees of abstraction. 
 The Posterior Analytics of Aristotle, which we have de- 
 scribed above (Ch. i, 5) as a treatise on the logical analy- 
 sis of science, throughout considers the sciences under 
 this aspect and in the light of these principles. 
 
 4. The Categories as a Classification of Predicates. 
 
 The Categories may further be viewed in their bearing 
 
 L 
 
146 PRINCIPLES OF LOGIC 
 
 on the logical proposition. As such they form a classifi- 
 cation of possible predicates. It is under this aspect they 
 are introduced by Aristotle in his Topics (I., c. 9). 
 And it is as thus conceived that they have received the 
 name of Category (/caryyopia, tcaryyopeiv to predicate), 
 and its Latin equivalent Predicament. The very purpose 
 of the proposition, is to tell us what the subject is to 
 assert some form of being in its regard. Since then the 
 Categories are our mental representations of ' being ' in 
 its various modes, it follows of necessity that the predi- 
 cates of all propositions may be grouped according to 
 the particular kind of ' being ' asserted, in other words 
 according to the ten Categories. 1 
 
 From this it appears that the doctrine of the Categories 
 throws a new and most important light on the meaning 
 of the ' is ' of the copula. The discussion as to the import 
 of the proposition, is in fact incomplete, apart from the 
 doctrine of the Categories. The copula, as we saw, signi- 
 fies that the subject is (or is not) determined in some way. 
 The Categories shew us that it does not express one mode 
 of determination only, but a variety, according to the 
 different modes of ' being/ According to the predicate 
 employed, it signifies that the subject is determined either 
 substantially, or quantitatively, or qualitatively, or by 
 some relation, etc., etc. 2 Nothing can be more errone- 
 ous than to hold that the determination is always of one 
 kind. 3 This is the mistake which we have noticed on 
 the part of those who hold the equational theory as to 
 the import of propositions. They regard the copula as 
 always signifying that the subject is determined by a 
 relation of equality. 
 
 1 Cf. St. Thomas in Met., V., lect. 9. " Propter hoc ea in quae dividitur ens 
 'primo, dicuntur esse praedicamenta quia distinguuntur secundum diversum 
 'modum praedicandi." 
 
 2 St. Thomas, Opusc. 39, De Natura Generis. " Eorum autem quae praedican- 
 ' tur, quaedam significant quid, quaedam quantum, quaedam quale, et sic de 
 ' ceteris : ideo oportet quod unicuique modo praedicandi ' esse ' idem significet : 
 ' ut cum dicitur ' homoest animal,' esse significet substantiam, cum vero dicitur 
 ' homo est albus,' esse significet qualitatem, et sic de aliis praedicamentis." 
 Cf. in Met., V. lect. 9. 
 
 3 Such a theory of the copula may be found in Sidgwick's Fallacies, p. 53. 
 
THE CATEGORIES 147 
 
 It may at first sight appear inaccurate to speak of the pre- 
 dicate as determining the subject, when it is a more generic term 
 within the same category. We do not determine the subject 
 when we say, e.g. ' Man is an animal,' ' A triangle is a plane 
 figure ' : for the predicate in these cases shews us the same 
 nature as the subject but more abstractly conceived. But it 
 must be remembered that in any proposition the predicate alone 
 is understood in comprehension, the subject being understood 
 in extension without formal advertence to the attributes it 
 connotes. Hence even where the predicate is a generic term, it 
 is conceived as one of the attributes or determinations belonging 
 to the subject. 1 
 
 * 5. Mill's Scheme of Categories. Mill, after enumerating 
 the Categories of Aristotle, remarks that " the imperfections 
 'of this classification are too obvious, and its merits not 
 'sufficient to reward a minute examination." He therefore 
 proposes to " recommence under better auspices, the attempt 
 ' made with such imperfect success by the great founder of 
 ' logic." 
 
 After a lengthy discussion, the following is the scheme he 
 gives us. It should be premised that the point of view is alto- 
 gether metaphysical. It is a list of things, and is not proposed 
 in any way as a classification of concepts : 
 
 " (i) Feelings, or States of Consciousness.' 
 
 ' (2) The Minds, which experience those feelings.' 
 
 ' (3) The Bodies or external objects, which excite certain of 
 ' those feelings, together with the powers or properties whereby 
 1 they excite them : these last being included rather in com- 
 * pliance with common opinion, and because their existence is 
 ' taken for granted in the common language from which I can- 
 'not prudently deviate, than because the recognition of such 
 ' powers or properties as real existences appears to be warranted 
 ' by sound philosophy. 
 
 ' (4) The Successions, and Coexistences, the Likenesses and 
 ' Unlikenesses between feelings or states of consciousness." 
 
 It would be beyond the scope of this work to enter upon a 
 criticism of Mill's metaphysical views. It must be sufficient 
 to note that this scheme is not even consistent with his own 
 philosophical position. He holds strongly that the mind has 
 no reality save that of the feelings which it experiences : that 
 it has no substantial existence of its own. He has, therefore, 
 no justification for placing minds in a separate category from 
 feelings. The same is true in regard to bodies. Bodies, as 
 existing realities apart from the sensations by which we are 
 
 1 Cf. Joan, a S. Thoma., Logica, II., Q. 5, Art. 2, ad. 4. 
 
148 PRINCIPLES OF LOGIC 
 
 conscious of bodies, are, according to him, a figment of the 
 imagination. They too then should have been relegated to 
 the category of Feelings. Relations fare no better. He tells 
 us that no relation is anything but our feeling of such a relation. 
 The philosophy of Mill, is in fact incompatible with any scheme 
 of Categories at all : for it reduces a reality of whatever kind 
 to mere subjective feeling. 
 
 * 6. The Categories of Kant. Kant, as we have noted 
 (Ch. i, note (5)), assumed as certain the hypothesis that the 
 data of knowledge consist solely in the subjective states 
 of our own mind : and further that these states are mere 
 instantaneous and unconnected feelings, neither in time nor 
 in space. The problem, therefore, before him was to explain 
 how, if these are our data, our experience can present us with 
 the world such as we know it. The result, he held, is due to 
 subjective principles of our cognitive faculties, which operating 
 on the unconnected mental impressions, fashion them within 
 us into the appearance of a world. The internal knowledge 
 thus afforded, is all we can hope to possess. It is due, he taught, 
 to the sensitive faculty that our impressions appear in time and 
 space. The intellectual faculty, also, provides twelve ' forms ' 
 of its own, corresponding to the twelve different species of judg- 
 ments. 1 These twelve 'forms' he termed Categories. They 
 are shewn in the following list : 
 
 Forms of Judgment. Categories. 
 
 I. Quantity. 
 
 1. Singular (This S is P) i. Unity. 
 
 2. Particular (Some S is P) 2. Plurality. 
 
 3. Universal (All S is P) 3. Totality. 
 II. Quality. 
 
 4. Affirmative (S is P) 4. Reality. 
 
 5. Negative (S is not P) 5. Negation. 
 
 6. Infinite (S is not-P) 6, Limitation. 
 III. Relation. 
 
 7. Categorical (S is P) 7. Substance and 
 
 Attribute. 
 
 8. Hypothetical (If S is P, Q is R) 8. Cause and Ef- 
 
 fect. 
 
 9. Disjunctive (S is P or Q) 9. Reciprocal Ac- 
 
 tion. 
 
 1 Kant believed that all thought is judgment, and that for that reason the 
 various kinds of judgment must necessarily shew the various modes in which 
 it is possible for the intellect to shape our knowledge. 
 
THE CATEGORIES 149 
 
 Forms of Judgment. Categories. 
 
 IV. Modality. 
 
 10. Problematic (S may be P) 10. Possibility and 
 
 Impossibil- 
 ity- 
 
 11. Assertoric (S is P) n. Existence and 
 
 Non - exist- 
 ence. 
 
 12. Apodictic (S must be P} 12. Necessity and 
 
 Contingency. 
 
 Thus, by way of illustration, if I judge that ' All men are mor- 
 tal,' this is not, as I fondly imagine, because there is an actual 
 world outside me, in which there is a race of men, all of whom 
 have this attribute of mortality : it is because within my mind 
 the four Categories of Totality, Reality, Substance and Accident, 
 and Existence and Non-existence, have shaped my knowledge, 
 and have thus produced a judgment which is universal, affirma- 
 tive, categorical, and assertoric. 
 
 We are not called on here to enter on a discussion of the Kantian 
 philosophy. But apart from the more fundamental errors with 
 which the system may be charged, the scheme of Categories, 
 considered as an analysis of logical judgments, contains, as we 
 have already pointed out (Ch. 3, 3, 9), serious imperfections. 
 
 * 7. The Concept of Being. We have already noted ( i) 
 that the term Being cannot be the summum genus in regard to 
 the Categories, inasmuch as it is predicated of the ten classes 
 in distinct though analogous senses. It seems desirable to 
 indicate the true relation of this concept to these classes. The 
 Categories express as we have seen the nature or essence of things : 
 they tell us what the thing is. The infima species gives us the 
 complete nature : the higher classes express it as less completely 
 determined. The concept of Being on the other hand has no- 
 thing to do with the essence : it is concerned with the existence. 
 When I affirm Being of a subject, I mean that that subject can 
 exist in rerum natura. The concept of existence can have no 
 place in a scheme, which, while it expresses essences in their 
 different degress of determination, prescinds from the question 
 as to whether they exist or not. 
 
 That this view of the concept Being is the true one may be 
 seen from the following consideration. In regard to the nature 
 of an object our knowledge progresses from the indeterminate 
 to the determinate. We recognize that it is corporeal substance : 
 then that it is a living animal : finally we arrive at the complete 
 type. There is no advance whatever in regard to our recognition 
 of it as Being. From the first we realize that it is a Thing it exists. 
 No increase of knowledge can reveal a higher degree of existence, 
 
CHAPTER X. 
 
 DEFINITION AND DIVISION. 
 
 i. Definition. We are concerned in this chapter 
 with two processes, both of which belong, not to the 
 Logic of the Judgment, but to that of the Concept. 
 Neither Definition nor Division, however, can be satis- 
 factorily treated, unless the Predicables have previously 
 been explained. This, therefore, seems to be the most 
 convenient place at which to deal with them. 
 
 The definition of an object is the declaration of its 
 essential characteristics. Hence, a definition is given 
 in the form of a proposition, in which the object defined 
 stands as the subject, and the essential characteristics 
 form the predicate. It is this predicate which is the 
 definition properly so called. The discussion of the 
 question belongs, as we have said, to the Logic of the 
 Concept : for considered as a mental act, the definition 
 is the concept which expresses the true nature of the 
 thing defined. 
 
 It is carefully to be observed that the definition is 
 concerned with the nature of a thing. For by some 
 logicians it is explained as being simply the connotation 
 of the subject term, as it is understood by competent 
 thinkers, Now it is, of course, the case that whenever 
 the essential characteristics of a thing its true nature, 
 are known, these will constitute the intension of its 
 name. Thus the intension of the term ' triangle,' is 
 ' a plane figure contained by three straight lines.' But 
 it will often happen that a name is applied to a group 
 of objects, which we are perfectly able to identify by 
 certain common properties they possess, while at the 
 same time, we are ignorant of their real nature. Thus, 
 
DEFINITION AND DIVISION 151 
 
 for instance, when a new disease, e.g. the sleeping sick- 
 ness, makes its appearance, doctors recognize it and 
 give it a name, long before they are able to define it. 
 The term in this case, has a connotation, viz.: the symp- 
 toms by which the disease is known : but we have not 
 yet found the definition of the thing. The true definition 
 must do more than enable us to recognize it. It must 
 unfold its nature. 
 
 Aristotle expressed this, by saying that the definition 
 gives us the ' why ' of the thing. 1 The definition ' Man 
 is a rational animal/ is a case in point. If we are asked 
 what makes Socrates a man, we reply that he possesses 
 these characteristics. It is not because he is ' a tool- 
 using animal/ that he is a man, nor yet because he is 
 ' an animal that cooks his food/ though these statements 
 are true. He is a man because he is a rational animal. 
 The ideal definition will then contain the essential char- 
 acteristics. To what extent we are able actually to 
 realize this ideal in our definitions, we shall see when 
 we study the various kinds of definition. 
 
 Definition is always of the universal. Nature gives 
 us general classes, and phenomena which occur subject 
 to general laws. The individual members of these 
 classes, the individual instances of the phenomena, 
 are all different : each has accidental characteristics, 
 by which it differs from every other. The aim of defini- 
 tion is to seize on the type, which is constant amid all 
 this variety. One attack, e.g. of sleeping sickness, or 
 of malarial fever, differs from another in a hundred 
 particulars, in duration, in intensity, in collateral 
 effects, etc., etc. These are of no importance to the defini- 
 tion ; for it is concerned alone with what is essential 
 with the permanent type. 2 
 
 Hence definition is rightly said to be the aim of science. 3 
 
 1 An. Post. II., c. 2, 5. 'fiffTrep o$v \yo(j.ev rb rl tcrnv eldtvai ravrb 
 tern Ko.1 Sia rl OTLV. Cf. ibid. c. 8, i. 
 
 * An. Post. II., c. 13, 19. 
 
 8 Cf. Rabier, Logique, p. 180. La definition, au sens de concept resumant 
 la science, est la fin de la science. Mercier, op. cit., 153. La definition est 
 avant tout un moyen d'asseoir les bases de la science. 
 
152 PRINCIPLES OF LOGIC 
 
 Science has achieved its object, when it has accurately 
 determined the nature of some substance, or the law 
 of some phenomenon. 
 
 It is often said that all definition should be by genus and dif- 
 ferentia. There are indeed certain cases in which we can assign 
 the genus and differentia, understanding those words as they 
 were employed in connexion with the Predicables. In some 
 cases, however, this is impossible. Thus an eclipse can be de- 
 fined, but it has not properly speaking a genus or differentia. 
 Hence these terms are here employed with a certain amount of 
 latitude. Genus should be understood as meaning no more 
 than such attributes as are common alike to the class of objects 
 in question, and to other classes : differentia signifies the notes 
 which are proper to the class, and distinguish it from others. 1 
 
 2. Various Kinds of Definition, (i) Real and 
 Nominal. In the last section we shewed in what a 
 Real definition consists. It is an expression which 
 declares the nature of a thing. A Nominal defini- 
 tion on the other hand, is an expression declaring 
 the meaning of a word. Some logicians, as we have 
 already noticed, have maintained that no definitions 
 are intended to do more than this ; that one and all 
 they merely unfold the connotation of terms. Aristotle 
 considers this question at length, and distinguishes two 
 kinds of Nominal definitions. In the first place, there 
 are (i) definitions of names which signify imaginary 
 objects, to which nothing either actual or possible corre- 
 sponds. We may find an example in the definition of 
 a dragon as ' a serpent breathing flame/ An impossible 
 self-contradictory concept cannot provide us with a 
 Real definition : for that must state the essence. An 
 essence -which contains repugnant characteristics is no 
 essence at all. 2 Indeed the expression, ' A dragon is a 
 
 1 Cf. Joan, a S. Thoma., Logica, Bk. II., c. 3. "Deftnitio fit per genus et 
 4 differentiam ; et cum haec conditio non solum complectatur defmitionem 
 ' essentialem, in qua proprie invenitur genus et differentia, sed etiam descrip- 
 e tivam et accidentalem in qua non est proprie genus et differentia, sed aliquid 
 ' loco illius ; ideo intelligitur nomine generis aliquid commune, nomine differentiae 
 'aliquid distinctivum particulare." 
 
 2 An. Post. II., c. 7, 2. rb yap M dv, ovdels oWev 8 n ivrlv, dXXd ri 
 /j.tv cry/mivei o \6yos r) rb oj/o/xa, QTO.V eforw Tpayt\a<j>os t ri 8' 2< 
 
DEFINITION AND DIVISION 153 
 
 serpent breathing flame,' is elliptical. Fully stated, 
 the proposition should be ' A dragon (as imagined by 
 the writers of fables) is a serpent breathing flame ' 
 (Ch. 7. 4). 
 
 Aristotle further reckons as Nominal definitions, (2) 
 those in which we are unable to assign the essential 
 properties of a thing, and are merely able to indicate 
 it by a description. Thus, the definition of thunder, 
 as ' a noise in the clouds,' is nominal : nominal, because 
 it describes what is meant, and yet does not unfold the 
 nature of the object (An. Post. II. , c. 10, i, c. 8, 7). 
 
 All Nominal definitions, therefore, do not deny exist- 
 ence to their objects. In this latter class existence is 
 presupposed. But in Aristotle's view, none save those 
 which express the essential characteristics, can rightly 
 be termed definitions of the thing. This distinction 
 of Real and Nominal has largely fallen into disuse for 
 reasons to be mentioned presently. But it should be 
 carefully noticed, for the principle it embodies is one 
 of importance. 
 
 * Mill holds strongly to the position that definitions are merely 
 explicative of names. Hence he is led to consider at some length 
 the alleged importance of definitions. Is it the case, he asks, 
 that some sciences, e.g. Geometry, are deduced from statements 
 as to the meaning of names ? His answer is that the sciences 
 are not derived from the definitions at all, but from the implied 
 postulate of the existence of the thing in question. Thus the 
 definition of triangle " obviously comprises not one but two 
 ' propositions, perfectly distinguishable. The one is, ' There 
 ' may exist a figure bounded by three straight lines ' ; the other, 
 ' ' And this figure may be termed a triangle.' The former of 
 ' these propositions is not a definition at all. The latter is a 
 ' mere Nominal definition. It is the former which is the basis 
 ' of all reasoning about the triangle." 
 
 Mill's analysis is here at fault. Often it is true we do pre- 
 suppose the existence of the object. This occurs when, previous 
 to definition, the existence of the object has been manifested to 
 us. For instance men knew that the relative motion of earth 
 and sun existed as a fact, long before they knew how to define 
 it. When at length, it was expressed in a definition accurately 
 setting forth the law of the process, they then possessed a sure 
 basis for reasoning. But the ground of reasoning was not tho 
 
154 PRINCIPLES OF LOGIC 
 
 existence of the phenomenon, nor even the nature of the pheno- 
 menon in itself, but its nature as known in other words, the 
 definition. Mill has combined the postulate of existence and 
 the definition of the nature, in his first proposition : and then 
 he triumphantly points to a second proposition, which is neither 
 postulate nor definition, and styling it a definition, informs us 
 that it cannot be made the foundation of a train of reasoning. 
 As a matter of fact in the case of a triangle, the postulate of 
 existence is unnecessary, since the statement of its essential 
 characteristics is quite sufficient for the mind to recognize that 
 we are dealing with a possible essence. It is not the existence 
 of objects, but their essences that are the foundation of science : 
 many mathematical figures have never existed. When the 
 essence is once known, we can deduce the properties which flow 
 from it. From the definition of a right-angled triangle Pytha- 
 goras deduced Euclid, I., 47. 
 
 (ii) Essential Definitions. These are the definitions 
 which are formed by genus and differentia in the stricter 
 sense. Such for instance is our definition of man as ' a 
 rational animal/ Such too are our definitions of mathe- 
 matical figures. The limits by which a plane figure 
 is bounded, constitute its specific differentia. ' A plane 
 figure contained by three straight lines/ is the essential 
 definition of a rectilinear triangle. 
 
 In the case, however, of every other natural type 
 except man, it is impossible to obtain an Essential defi- 
 nition. The specific differentia, from which its peculiar 
 properties flow, is unknown to us. While we recognize 
 that the substantial principle, which determines the 
 distinctive characteristics of, e.g. a lion, must needs be 
 totally different from that of a horse, we can never 
 hope to penetrate to any knowledge of the two principles, 
 except in so far as they are manifested by their properties. 
 We must then be content with definition by properties, 
 or as it is often called : 
 
 (iii) Distinctive Definition. It is at definitions of this 
 kind that the student of natural history or of physical 
 science, aims. He seeks to state the most characteristic 
 properties of the type with which he is dealing. 1 More- 
 
 1 Cf. Arist. De Amma, I., C, I, 8. rcl crt^/Se/ST/Kora, (ru^tySaXXerai ^ue-yct //.epos 
 npds r6 fltevai rb ri e<m, ' The knowledge of the properties contributes in a 
 
DEFINITION AND DIVISION 155 
 
 over he recognizes that he can scarcely hope to attain 
 finality in his quest. For the number of distinctive 
 properties in every natural type is vast, and it is always 
 possible that he may discover some property of primary 
 moment hitherto overlooked. 
 
 These definitions are of the highest importance in 
 science. For it is on them that is based the scientific 
 classification of natural types. This application of 
 definition will form the subject of a later chapter. 
 
 It is because these Distinctive definitions are the 
 only definitions attainable in the case of natural classes, 
 that Aristotle's division of Real and Nominal defini- 
 tions has been discarded. It would be manifestly un- 
 satisfactory if a class of definitions, which, within their 
 own sphere, are the highest result of science, were ranked 
 as merely Nominal, because they fail to reveal the specific 
 essence of the nature. Yet between the Distinctive 
 definition which states properties only, and the Essen- 
 tial definition which unfolds the essence, there is a 
 great difference. For wherever we possess the Essential 
 definition we can reason from the essence to the pro- 
 perties. But we cannot from the properties given in 
 the Distinctive definition, conclude to the essence. 
 Moreover, the same substance under different circum- 
 stances, manifests itself by different properties. Thus 
 the properties of phosphorus are totally different from 
 those of what is termed amorphous phosphorus : while 
 it is needless to point out how much those of carbon, 
 graphite and diamond differ from each other. Yet in 
 each of these cases, we are supposed to be dealing with 
 the same substance, manifesting itself by different 
 properties when affected by different conditions. 
 
 (iv) Genetic Definitions give us neither the essential 
 nature of the thing nor its properties, but the elements 
 which, taken in conjunction, result in its produc ion. 
 
 great measure to a knowledge of the essence ' : and St. Thomas, Opusc. 26, 
 DC Ente et Essentia, c. 5. In rebus enim sensibilibus ipsae differentiae essen- 
 tials nobis ignotae suht : unde significantur per differentias accidentales 
 quae ex csscntialibus ormntur, sicut causa significatur per suuin effectum. 
 
i$6 PRINCIPLES OF LOGIC 
 
 The term is most frequently used in reference to certain 
 mathematical definitions, which express the nafure of 
 a figure by a statement of the manner in which it may 
 be constructed. Thus a circle may be denned, as a figure 
 formed by the revolution of a line in a plane round 
 one of its extremities. Here the several segments 
 gradually traced by the line are not themselves a circle. 
 Yet when the process is complete, and all the parts are 
 seen in conjunction, they constitute a circle. But the 
 employment of Genetic definitions is by no means limited 
 to this special case. The definitions employed in chem- 
 istry are of this type, as, e.g. the definition of water as 
 ' two atomic weights of hydrogen chemically combined 
 with one of oxygen/ For these definitions do not 
 inform us regarding the qualities of the substance. 
 They tell us what constituents are requisite to its pro- 
 duction. 
 
 (v) Causal Definitions are of two kinds, (a) One class 
 defines by indicating the Final cause or purpose of 
 the object (Arist, Met., VII., c. 2, 7, 8). This form of 
 definition is the one ordinarily used in the case of the 
 works of human ingenuity. We define a clock by saying 
 that it is ' a mechanism destined to indicate the hours 
 of the day/ a stirrup by terming it ' a metal hoop for 
 the purpose of supporting the foot when riding.' 
 
 (b) The other class of Causal definitions defines by 
 stating the Efficient cause. It may often happen that 
 the most satisfactory explanation of the nature of the 
 thing, is given in this manner. Thus since the days of 
 Koch, who first discovered that certain diseases were due 
 to the presence of specific microbes, it is a true definition 
 of anthrax (wool-sorter's disease) to say that it is ' an 
 illness caused by the introduction into the body of the 
 bacillus anthracis.' Some things, e.g. natural products, 
 can hardly be defined in any other way. We naturally 
 define the double cocoa-nut as ' the fruit of the tree 
 Lodoicea Seychellarum , ' 
 
 (vi) Accidental Definitions. These are employed to 
 define those sub-classes, which do not constitute distinct 
 
DEFINITION AND DIVISION 157 
 
 species. Thus a negro may be defined by his colour as 
 ' a black man/ even though colour be an accident and 
 not a property of the nature. These are, however, 
 rather to be regarded as descriptions, than as definitions. 
 (vii) Analytically-formed and Synthetically-formed 
 Definitions. This distinction has been employed by 
 recent logicians : it is only applicable when definitions 
 are regarded not as declaring the nature of the thing, 
 but simply as stating the meaning of the word. If the 
 definition gives the recognized intension of the term, it is 
 said to be analytically-formed. It, however, sometimes 
 happens that a special meaning is attached to a word, 
 which hitherto it has not borne. Such for instance is the 
 employment of the term ' wave ' by physicists, as signify- 
 ing ' a change periodically recurring in time and space.' 
 When a new definition of this character is introduced, it 
 is said to be synthetically-formed. 1 
 
 The Aristotelian doctrine of the four causes throws 
 considerable light on this long list of definitions. Every 
 material thing has four causes the efficient, the final, 
 the formal, and the material cause. The meaning of these 
 terms may be illustrated in the case of a statue. The 
 efficient cause of the statue is the sculptor : the final 
 cause is the motive, be it honour or profit, that leads him 
 to execute the work. These are known as the extrinsic 
 causes. The formal and material causes are termed 
 intrinsic, since they are internal constitutive principles 
 of the thing itself. The formal cause is the determining 
 principle which gives the thing its specific character. 
 The shape of the statue, e.g. Apollo, Julius Caesar, 
 Charles I . , may be viewed as such. In a natural entity such 
 as e.g. a man, or any one of the animals, the formal 
 cause is not, of course, the mere external shape. The 
 unifying principle of the material object, that which makes 
 it to be the kind of thing it is, is the vital principle, the 
 soul. The material cause is the substratum to which 
 
 1 Vide Ueberweg, 61. The distinction was first given by Kant, Logic, 
 100. He however interprets it somewhat differently. 
 
158 PRINCIPLES OF LOGIC 
 
 the formal principle gives its character. In the statue 
 it is the marble. 
 
 We stated above that the true definition always gives 
 us the cause of the thing defined. Definitions are formed 
 from each of the four causes which we have mentioned. 1 
 Sometimes a more satisfactory explanation is given by 
 assigning one cause rather than another : sometimes 
 only one cause is fully known to us. The definitions 
 drawn from the efficient and final causes have been ex- 
 plicitly noticed in our list, and need not be further 
 discussed. Essential definition is definition by the for- 
 mal cause. We are not speaking here of the formal 
 cause in the real order, which is, as we have seen, the 
 soul. But we can form an abstract notion of ' humanity/ 
 expressing those attributes alone, in virtue of which an 
 individual is a man. In the conceptual order this 
 ' humanity ' is viewed as though it were a formal cause 
 by which the individual is constituted man. He may 
 have many other attributes : he may be a Greek, a 
 philosopher, etc., etc. But it is only those attributes 
 which belong to his ' humanity/ which make him a man. 
 The definition ' rational animal ' expresses the notes 
 which are found in this formal cause. 2 
 
 Finally Genetic definition is definition by the material 
 cause. Even when the conjunction of constitutive parts 
 does not, as in the case of chemical combination, result 
 in internal changes, the parts always stand to the whole 
 in the relation of material cause. For taken separately 
 they lack the distinctive attributes of the thing in ques- 
 tion. It is only to the whole produced by their conjunc- 
 tion, that the attributes belong. 3 
 
 1 Cf. St. Thomas, An. Post. II., lect. 4. 
 
 8 The abstract specific essence conceived as though it were a form, was 
 termed the forma totius. On this subject see St. Thomas, Opusc. 26, 
 De Ente et Essentia, c. 3, and An. Post. II., lect. 20. In the latter passage 
 St. Thomas guards his readers against supposing that ' humanitas ' is some- 
 thing real, common to the various members of the species ' homo,' and points 
 out that it belongs to the conceptual order, ' Socrates est similis Platoni in 
 humanitate, non quasi una humanitate numero in utroque existente.' 
 
 3 For this aspect of the material cause, see An. Post. II., c. n, 1,2. 
 Physics, II., c. 3, 7. 
 
DEFINITION AND DIVISION 159 
 
 3. Limits of Definition. It is manifest that the 
 highest genera will be incapable of definition properly 
 so called. We cannot assign any higher genus under 
 which they may fall. Much more is this the case 
 with concepts such as Being, Unity and the like, 
 which transcend the limits of the highest genera, 
 and are found in all of them. At the other end of the 
 scale, there can be no definition of individuals. They 
 can only be described, not defined : for definition is 
 always of the universal. Further it is impossible to define 
 the simple qualities which are the immediate data of sense- 
 perception, e.g. sweetness, cold, whiteness, pain, etc. 
 The purpose of definition is to unfold the nature of the 
 object by an analysis. Here there is no room for analysis. 
 These are the elements from which knowledge begins. 1 
 We can, of course, enumerate the properties of such 
 qualities, as when, e.g. we say that red is the colour 
 which manifests itself through vibrations varying from 
 360 billions to 500 billions per second. But this is not 
 properly speaking a definition : for apart from this 
 information we have a perfectly clear conception of the 
 colour itself. 
 
 4. Rules of Definition. We must now consider the 
 traditional rules of definition. These are four in 
 number : 
 
 (i) The definition must be adequate to its object ; 
 erring neither by excess nor defect. It must, that is, be 
 applicable to every member of the class defined, and to 
 no other objects. It must thus be convertible with the 
 class name. We constantly come across definitions which 
 are too wide or too narrow. Thus the definition, ' Logic 
 is a machine for combating fallacy,' is far too narrow. It 
 reduces the whole science to what is, in fact, one of the 
 least important of its properties. Mill's definition of 
 
 1 Hence it follows, as both Aristotle and St. Thomas point out, that we can- 
 not define the terms of a definition in infinitum. " Definitiones habent priuci- 
 ' pium et finem, quia non est ascendere in infinitum in generibus, sed accipitur 
 ' quasi primum genus generalissimum : nee etiam est descendere in infinitum 
 'in speciebus, sed est stare in specie specialissima." De Anima, I., lect. 8. 
 
160 PRINCIPLES OF LOGIC 
 
 eloquence as ' the power of influencing the feelings by 
 speech or writing/ is too wide. It is possible to influ- 
 ence men's feelings by speech without eloquence. So too, 
 to define religion as ' the totality of man's relations 
 with God,' is to err by excess. 
 
 (2) The definition must not be obscure. This rule must 
 not be misunderstood. It does not signify that the defini- 
 tion must in no case appear obscure to the uninstructed. 
 Sometimes the elements of the definition may to the 
 uninstructed be less comprehensible than the thing 
 defined. In a scientific definition, e.g. of lightning, or 
 a philosophic definition, say of free-will, obscurities are 
 unavoidable. 1 A definition is the result of long study, 
 and many definitions will, to those whose minds are 
 unprepared for them, seem more obscure than the thing 
 they profess to explain. When the mind of the learner 
 has been prepared by the requisite instruction, he will 
 realize that in the definition, he has received the summarized 
 results of science. Such definitions do not really offend 
 against this rule ; for they are true analyses of the 
 phenomenon into its simpler elements. In regard to this 
 class of definitions, the purpose of the rule is to forbid 
 ambiguous and metaphorical expressions. 
 
 Where, however, the definition is intended to serve as 
 a brief explanation for those not versed in the special 
 subject under consideration, it is requisite that it should 
 be couched in simple terms. Those who violate this 
 rule, are said to explain obscurum per obscurius. 
 
 (3) The definition must not be tautologous. This fault 
 is committed when the subject of the definition reappears 
 either explicitly or implicitly in the defining predicate. 
 Thus to define a horse as ' a member of the species equus/ 
 would convey no information whatever. This rule is 
 violated when we have what is termed circulus in defini- 
 endo, e.g. ' A day is a period of time consisting of twenty- 
 four hours/ and ' An hour is a twenty-fourth part of a 
 
 1 Rabier, Logique, p. 198. 'Les trois quarts des definitions 6tant donnees 
 d'emblee, seront pour qui les entend pour la premiere fois, Verba et voces prae- 
 tereaque nihil ... a moins cependant qu'elles ne soient une suggestion d'idees 
 bizarres ou fausses.' Cf. An. Post. II., c. 13, 19, 20. 
 
DEFINITION AND DIVISION 161 
 
 day/ It is not, however, regarded as a circular defini- 
 tion when, in the case of two relative terms, each appears 
 in the definition of the other ; since their concepts are 
 mutually dependent. We cannot define ' antecedent ' 
 without mention of ' consequent/ nor ' consequent ' 
 without mention of ' antecedent.' x 
 
 (4) The definition must not be negative if it can be 
 positive. We are not to define wisdom by saying that 
 it consists in the ' avoidance of folly ' ; nor health as 
 ' the absence of sickness.' 
 
 There are two cases where positive definitions cannot 
 be given. The first of these is when we have to define 
 objects which are incorporeal or unextended. Our 
 cognitive faculties have direct knowledge only of what is 
 corporeal and extended. We are therefore compelled to 
 define the unextended by negative expressions. 2 We 
 define a line as ' length without breadth ' ; a point as 
 ' that which has no parts ; ' 3 a spirit as ' an immaterial 
 substance.' The second case occurs in regard to nega- 
 tions and privations. These consist essentially in the 
 mere absence of a positive quality, and hence must be 
 defined in that manner. Blindness is ' the absence of 
 sight in an animal usually found with that sense.' 
 Darkness is ' the absence of light/ 
 
 5. Logical Division. 
 
 A Logical Division is the analysis of a logical whole 
 into its parts ; in other words, the analysis of a genus 
 into its species. It is expressed in a proposition in which 
 the generic term occupies the place of subject, while 
 the subordinate species are enumerated disjunctively in 
 the predicate, e.g. ' Substance is either corporeal or 
 incorporeal/ ' Quantity is either continuous or discrete/ 
 
 1 Topics, VI., c. 4, 13. 
 
 Cf. St. Thomas, Summa Theol., I., Q. u, Art. 2, ad. 4. 
 
 8 This definition (oO /xepos ovdtv) is that of Euclid. Fault has been found 
 with it on the ground that it contains no positive element at all. A point 
 has position, and belongs to continuous quantity. Aristotle, An. Post. I., 
 c. 27, defines it any/ATI obffla. 0er6s : and St. Thomas, Summa TheoL, I., Q. 52, 
 Art. 2, ' Punctum est indivisibile habens situm.' Pythagoras had also 
 denned it by its positive aspect as ' a unit having position 
 Cf. Arist., De Anima, I., c, 4, 7. 
 
 M 
 
1 62 PRINCIPLES OF LOGIC 
 
 ' The Vertebrate is either amphibian or reptile or bird or 
 fish or mammal/ 1 
 
 Logical divisions are ordinarily distinguished into (i) 
 Natural, and (2) Artificial. A Natural division (divisio 
 per se) is based on the essential modifications of the 
 constitutive attributes ; while on the other hand an 
 Artificial division is one based on the modifications of 
 a few attributes, or even of a single one. The older logi- 
 cians distinguished three kinds of such artificial divisions, 
 which they termed divisiones per accidens? 
 
 (1) Divisions of substances according to the presence 
 
 of some accidental quality, e.g. ' Men are either 
 Europeans, or Asiatics, or Africans, or Americans, 
 or Australians, or Polynesians/ 
 
 (2) Division of an accidental quality according to the 
 
 substances in which it is found, e.g. ' Beings with 
 vocal organs are either men or brutes/ 
 
 (3) Division of things having some accidental quality 
 
 according to the modifications of some other acci- 
 dental quality, e.g. ' Inhabitants of Scotland are 
 either English-speaking, or Gaelic-speaking, or 
 bilingual/ 
 
 The generic notion which forms the subject of a logical 
 division is necessarily indeterminate. It expresses no 
 one of its subordinate species in particular : but it must 
 be realized in one or other of these species. For this 
 reason the division is correctly expressed by a disjunctive 
 proposition. The subordinate species are termed mem- 
 bers of the division. Each of them removes the indeter- 
 mination of the genus in some manner : and it is the 
 variety of mode in which the indetermination is actualized 
 that constitutes the difference of species. The charac- 
 teristic whose varieties thus modify the indeterminate 
 genus is called the basis of the division (fundamentum 
 divisionis) . 
 
 1 Definition and Division may be distinguished by saying that the purpose 
 of the former is to reply to the question Quid sit? (What is the thing ?), and 
 the purpose of the latter to reply to the question Quotuplex sit ? (In how many 
 forms is the thing realized ?). 
 
 8 Boethius, De Divisione, ed. Migne, col. 877. 
 
DEFINITION AND DIVISION 163 
 
 The essential difference between divisio per se and the 
 divisiones per accidens, lies in the fact that in the forme r 
 the genus is divided into the species which are naturally 
 subordinate to it, and belong to its own category. In 
 the latter the differentiating note is something accidental 
 to the genus and belonging to some other category. 
 
 It is most important to observe that in logical division 
 we are not concerned with extension. The species are not 
 parts of the genus because each of them contains a certain 
 number of individuals, which taken all together consti- 
 tute the larger class. The relation of logical whole and 
 logical part arises entirely from the indeterminateness of 
 generic nature as realized in the conceptual order, and 
 the determination of the subordinate species. The whole 
 contains its parts potentially : in other words, it is cap- 
 able of being determined by various differentiae to each 
 of them. Thus the notion ' triangle ' contains potentially 
 ' equilateral,' ' isosceles ' and ' scalene.' 1 To a logical 
 whole of this kind belong two noticeable characteristics, 
 viz., (i) it is found in each of its parts. 2 As the whole 
 contains the part potentially, so the part contains the whole 
 actually. The generic nature ' triangle ' is actually con- 
 tained in the specific notion ' scalene triangle.' And (2) 
 it is, as we saw when treating of the Categories (Ch. 9, 2), 
 predicable of all its parts. 3 The generic notion is pre- 
 dicated of the specific notion, not the specific notion of the 
 generic. We say, ' Mammals are vertebrates,' not ' Verte- 
 brates are mammals.' 
 
 A further point to be noticed is that logical division 
 properly so called stops short at the ultima species. It 
 is by sense, not by intellect that we distinguish the indi- 
 vidual members of a species : the function of the intellect 
 is to reveal unity in multiplicity. The division of the 
 universal by its own differentiae stops short at the com- 
 
 1 On the logical whole, cf. Hamilton, Logic, I., pp. 204-207. 
 
 2 Cf. St. Thomas, Summa TheoL, I., Q. 77, Art. i, ad. i. Totum enim univer- 
 sale adest cuilibet parti secundum totam suam essentiam et virtutem, ut 
 animal homini et equo. 
 
 8 Arist., Met. IV., c. 26, a. 
 
r64 PRINCIPLES OF LOGIC 
 
 plete specific nature. 1 Yet though this is the case a 
 looser terminology is sometimes found : and the expres- 
 sion ' logical part ' is applied to all subordinates of the 
 class-notion, whether they be subordinated as species to 
 a genus, or as individuals to a species. Owing to the 
 convenience of this terminology, we shall occasionally 
 employ it. 
 
 Several recent logicians, failing to distinguish between 
 the science of the conceptual order and the sciences which 
 deal with the real order, have identified logical division 
 with the general theory of Classification. The subject 
 of Classification will occupy us when we come to consider 
 the Method of Science. It deals mainly with the prin- 
 ciples on which the student of the real order should co- 
 ordinate the types offered by Nature to his contempla- 
 tion. The co-ordination of these types is effected through 
 long and careful comparison of numerous individuals, the 
 results of the comparison being registered in definitions. 
 As the definitions are framed, the mutual relationships 
 of the natures as conceptually expressed reveal them- 
 selves as a logical division. Together with the attain- 
 ment of a scientific classification of real things, we attain 
 a logical division in regard to our concepts. The whole 
 and the parts in the two cases, are widely different. The 
 one is a whole of many concrete individuals, the other whole 
 is a single generic nature. The treatise on Classification 
 belongs to the natural sciences ; that on logical divi- 
 sion belongs to the science of the conceptual order. 
 
 Subdivision. It is evident that each of the subordin- 
 ate species enumerated in an act of division, may itself 
 be subjected to a similar process. This is called a sub- 
 division. These subdivisions are of importance to 
 science. For it is by a series of subdivisions that syste- 
 matic classifications are mentally represented. Hence, 
 our knowledge of the elaborate classifications, which play 
 so large a part in many sciences, is summed up in logical 
 divisions. 
 
 1 Joseph, Introduction to Logic, p. 116. Thus Aristotle terms the ultimae 
 species 'indivisible.' An. Post. II., c. 13, 6, XP*) 5^ ... SieXet? TO 
 yevos ci$ r& &TO/J.O. rtf ei'Set rd 
 
DEFINITION AND DIVISION 165 
 
 Co-division occurs when a single class is variously 
 divided by divisions founded on different bases (funda- 
 menta divisionis). Thus, e.g. 'man' may be divided 
 according to political divisions, or according to racial 
 divisions. The classes founded on the two systems 
 will manifestly not be in accord with each other. 
 
 In the proposition, the mind views the subject and 
 predicate as standing in the relation of logical part to 
 logical whole. Indeed the term subjective part is used as 
 synonymous with that of logical part. 1 This relation 
 between subject and predicate is manifest in regard to 
 those propositions in which the predicate belongs to the 
 same category as the subject, e.g. ' Mammals are verte- 
 brates.' But even the propositions in which the terms 
 are of different categories, e.g. * Tigers are ferocious,' 
 may be thus regarded. The subject is regarded as a 
 species subordinated to the predicate in virtue of a divisio 
 per accidens. This aspect of the proposition will be found 
 to be of great logical importance, and should by no means 
 be overlooked. 2 
 
 6. Rules of Division. The rules of Division are 
 variously enumerated. The following four rules are 
 ordinarily accepted : 
 
 (1) Each act of division must have but one basis. The 
 violation of this rule involves either that some members 
 appear in more than one species, or that some are alto- 
 gether omitted. Usually, both faults occur. Thus, if 
 we divide American citizens into Republicans, Democrats, 
 and Immigrants, many citizens wiU be found to have a 
 place in two classes, while others, who are, it may be, 
 little interested in politics, will not be included under any 
 of the species enumerated. 
 
 (2) The constituent species must together be equal to 
 the genus. The rule prescribes that the division should 
 
 1 The term Subjective part is a little wider in its reference than Logical part. 
 An individual is a subjective part in regard to the species. 
 c Cf. the important passage, S. Thomas, Sumtna Theol., I., Q. 85, Art. 5. ad. 3. 
 
166 PRINCIPLES OF LOGIC 
 
 be complete, that none of the subclasses should be 
 omitted. If, e.g., we divide men into Aryan, Semitic, 
 and Hamitic races, we leave out many varieties, and the 
 genus is not exhausted. 
 
 (3) The constituent species must be mutually exclusive. 
 This condition is fulfilled, if the first rule be observed. 
 Since the division is constituted by different determina- 
 tions of the indeterminate generic notion, it follows that 
 as long as one basis is adhered to, one determination is 
 necessarily exclusive of the other. Thus, if we divide, 
 e.g., the genus ' nation ' into English, French, German, 
 etc., etc., it is plain that the members of this division 
 considered as nations are mutually exclusive. This is 
 true, even if it be the case that certain individual men have 
 a right to citizenship in more than one country. 
 
 (4) Each step in a continued division must be a proxi- 
 mate one (Divisio ne fiat per saltum). When this rule is 
 neglected, some species are omitted. The rule would, 
 for instance, be broken, if after dividing quantity into 
 continuous and discrete, we should at once proceed to 
 divide continuous quantity into triangles, quadrilaterals, 
 etc., etc. By neglecting the step, in which continuous 
 quantity is first divided into plane and solid, we should 
 have omitted all the species of solid figures. 
 
 7. Division by Dichotomy. This name has been 
 given to a method of division consisting of successive 
 steps, in each of which a division is made into two classes 
 according to the presence or absence of some given attri- 
 bute. By thus repeatedly subdividing, it was held 
 that we might arrive at last at a fully determined notion 
 of the last species. Plato advocated this method of 
 division as a means of discovering definitions. 1 Thus the 
 definition of man, might be supposed to be reached by 
 successive subdivisions of the notion of substance. 
 Aristotle severely criticized this view of Plato's, and 
 hence some mention of clichotomous division is found 
 in most logical treatises. 2 
 
 1 Cf. Plato, Protagoras, 332. Phaedrus, 266. 
 
 8 Cf. An. Prior I., c. 31. De Part. Anim., I., cc. 2, 3. 
 
DEFINITION AND DIVISION 167 
 
 Regarded as a method of finding the definition of an 
 object, it is clearly useless. In order to know to which 
 member of the division we should assign the entity, we 
 must already know its definition to that extent. Thus, 
 unless we knew that man is corporeal, it would avail 
 nothing to divide substance into corporeal substance and 
 incorporeal substances ; for we should not know under 
 which member we should class man. 
 
 Again the method is invalid, because the mere absence 
 of an attribute, is no basis on which to constitute a class. 
 Let us consider what is involved in dividing a class A into 
 AB and A non-B. One of two things must be the case. 
 Either (i) we know that in this class there are real 
 objects marked by the absence of B. If this be so, these 
 objects have their own specific differentiae. In all prob- 
 ability they belong to many different species, and to rank 
 them all together as A non-B, is calculated to mislead 
 people into supposing they have a generic unity. More- 
 over, if we distinguish the class A non-B by subsequent 
 division, the species will appear in their wrong position 
 in the classification. For they will not be placed where 
 they should be placed, viz., as co-ordinate species with 
 the class AB. Or (2) we may be supposed to be unaware 
 of the existence of other objects save those we are con- 
 sidering. In that case, we shall, at each step of the 
 division, be introducing a class, whose very existence is 
 doubtful. At this rate, our dichotomous division might 
 be carried to any length. We might divide men into men 
 with wings (if any) and men without wings. 
 
 Division by dichotomy is ranked by Kant (Logic, 
 113) as a method which is applicable in purely formal 
 Logic, and which is entirely independent of material con- 
 siderations. Mansel has rightly pointed out that this is 
 not so. 1 We cannot, e.g., divide animal into irrational 
 and rational, unless we know that there are rational and 
 irrational animals. We cannot divide any generic notion 
 into two classes, unless we are acquainted with the 
 determinations which that notion is capable of receiving. 
 
 1 Proleg. Logica, pp. 192, 193. 
 
1 68 PRINCIPLES OF LOGIC 
 
 8. Various Kinds of Division. We have seen that 
 logical division is the analysis of a logical whole into 
 its parts. With a view of rendering quite distinct the 
 difference between this kind of division and the other 
 processes which are so termed, Boethius in his Liber de 
 Divisione calls the attention of his readers to the other 
 cases in which a whole is resolved into its parts. The 
 following are those now usually mentioned in this con- 
 nexion. They differ but very slightly from those enumer- 
 ated in his list. 1 
 
 (1) Physical partition, as e.g. the partition of a house 
 
 into its parts roof, bricks, timber, glass, etc. 
 
 (2) Metaphysical distinction, viz., of the genus from the 
 
 differentia, as when we distinguish between the 
 ' animality ' and the ' rationality ' in man. The 
 term is sometimes employed to signify further the 
 distinction of the qualities of an object, e.g. between 
 the colour, fragrance, shape, etc., of an orange. 
 
 (3) Distinction of faculties, e.g. of the soul into memory, 
 
 intellect, and will. 
 
 (4) Distinction between the various meanings of a term, 
 
 e.g. between ' church ' as a building, and ' church ' 
 as signifying the whole body of the faithful. 
 
 1 Boethius, op, cit., ed. Migrie, col. 877, 878 ; and cf. S. Thomas, Summa 
 Theol., I., Q. 76, Art. 8. 
 
CHAPTER XL 
 
 THE CATEGORICAL SYLLOGISM (l.). 
 
 i. The Categorical Syllogism. We have now 
 discussed the Logic both of the Concept, and of the 
 Judgment. It remains for us to treat of the third 
 of the mental processes mentioned at the beginning 
 of this work (Ch. i, 2), viz., Reasoning or Mediate Infer- 
 ence. This has already been defined as the process by 
 which from certain truths already known, the mind passes 
 to another truth distinct from these. The two principal 
 forms of inference are termed deduction and induction 
 respectively. In deduction, the mind passes from the 
 more general to the particular or the individual. In 
 induction, we argue from the individual or particular to 
 the general. It is with the former of the two, that we 
 are at present concerned. 
 
 The deductive inference is known as the syllogism. 
 A syllogism is defined as an inference by which, from 
 two given propositions, we proceed to a third proposition 
 the truth of which follows from these two as a necessary 
 consequence. 1 Thus I may argue : 
 
 'All mammals are vertebrates. 
 All horses are mammals.' 
 Therefore, All horses are vertebrates. 
 This syllogism, consisting, as it does, of three A propo- 
 sitions, may be represented by the formula : 
 
 M a P. 
 S a M. 
 S a P. 
 
 1 Arist. An. Prior /., c. i, 5. 2v\\oyiff(j.bs d &m \6yos tv 
 re/3oJ' TI rdv Kei/j.evui' e dvdyKtjs ffvfj.f3a.lvei rif ravra elvcu. 
 
170 PRINCIPLES OF LOGIC 
 
 The two given propositions are known as the premisses 
 (Trporaa-eis, praemissae) ; that which follows from them 
 as the conclusion (o-viuLTrepacrju.a, conclusio) or consequent. 1 
 
 In all deductive inference, we argue, as has been just 
 stated, from the more general to the less general. Hence, 
 one at least of the premisses must be a universal proposi- 
 tion. And the essence of syllogistic reasoning lies in the 
 application of a general principle to a case that falls 
 under it. In the example just given, it will be seen that 
 the general principle, ' All mammals are vertebrates/ is 
 applied to the particular case of the horse. 
 
 It is evident that no inference is possible unless there 
 is a term which is common to the two premisses. This 
 term is known as the middle term (TO /*ror). Aristotle 
 gives us two reasons for his selection of this name. 
 The middle term, he says, is the term which is itself con- 
 tained in one of the others (P), while the remaining term 
 (S) is contained in it. The relation of which he here 
 speaks, is that of logical part to logical whole. The middle 
 term is a logical part in regard to one of the other terms, 
 and a logical whole in regard of the third. A logical part, 
 as we saw in Ch. 10, 6, stands to its whole in the relation 
 of a subordinate concept to one that is more general. It 
 cannot be too clearly recognized that this is what is 
 meant by the terms ' whole ' and ' part ' in this connexion. 
 The relation belongs, not to extension, but to the hierarchi- 
 cal subordination of species and genus in the conceptual 
 order. When we predicate one term of another, it is the 
 wider notion which is the predicate : the genus is affirmed 
 of the species. Hence, since the middle term is subject 
 of one premiss, and predicate of the other, it is a logical 
 part in relation to the term predicated of it, a logical whole 
 
 1 Some of the earlier writers employ a different terminology, calling the 
 two premisses respectively the sumptio (or sumptum) and the assumptio. " Quo- 
 'niam omnis syllogismus ex propositionibus texitur, prima vel propositio vel 
 ' sumptum vocatur : secunda vero dicitur assumptio : ex his quae infertur 
 'conclusio nuticupatur." Boethius, De Syll. Hypoth, (Migne, t. 64, col. 
 
 844). 
 
 2 An. Prior /., c. 4, 3. KO.\W 8t ^aov pkv o KOJ. CLUTO ev d\Ay nal a\/\o tv 
 
 , o KO.L ry dfoei firtrtu peaov. Cf. also c. 41, 5- 
 
THE CATEGORICAL SYLLOGISM (I) 171 
 
 in relation to the term of which it itself is predicated. 1 
 Aristotle in his treatment of the syllogism ever keeps in 
 view the typical case in which the terms stand in this 
 order. It is entirely erroneous to say, as do many logi- 
 cians, that he looked on the terms of the syllogism in their 
 extension, and called the middle-term by that name 
 because in extension it lay between the two others. 
 
 The second reason, which Aristotle gives, is that the 
 middle term is such by position. This reason is of less 
 moment, and need not detain us. It rested on the Aristo- 
 telian method of stating the syllogism. Where we say 
 M is P, and S is M, therefore S is P, he employed the form, 
 P is predicated of M, M is predicated of S, therefore P 
 is predicated of S. 
 
 Regarding a syllogism of the same character as the 
 standard type, the term which is subject in the conclusion 
 is aptly known as the minor term, and the term which is 
 predicate in the conclusion as the major term. These 
 names are adhered to even in negative conclusions, and 
 in other cases where the relation of whole and part, is 
 not found. The major and minor terms are sometimes 
 spoken of as the extremes (TO. aKpa). The premiss in 
 which the major term occurs, is called the major premiss : 
 that which contains the minor term is called the minor 
 premiss. 
 
 A distinction is sometimes drawn between the matter 
 and form of a syllogism. The matter of the syllogism 
 consists of the terms and propositions employed in it. 
 The form lies in the special arrangement of the terms in 
 the three propositions, in virtue of which the conclusion 
 follows from the premisses by necessary consequence. 
 It is evident that a syllogism may be formally valid, 
 while in regard to the matter, every proposition may be 
 untrue. The greater part of the Logic of the syllogism, 
 is concerned with the form alone. We treat of the vari- 
 ous ways in which a process of reasoning may be con- 
 
 1 An. Prior I., c. I, 7. TO Se eV 6Xy elvat Zrtpov ere'pw xal rb /card TTOLVT^ 
 K.a.Triyopeitfda.1 darepov Odrepov Tavrbv cffriv. ' To say that one thing is 
 contained in another as a whole, is the same as to say that the second can be 
 predicated universally of the first.' 
 
17* PRINCIPLES OF LOGIC 
 
 structed so as to conclude validly. It is chiefly because 
 this important branch of Logic deals wholly with the self- 
 consistency of our thought with securing conclusions 
 consistent with their premisses, that the Formal logi- 
 cians were led to hold that Logic deals only with self- 
 consistency, and abstracts altogether from the question 
 of truth. The answer to this contention is that the theory 
 of syllogistic form, is but one portion of Logic ; and that 
 even in it, we treat of formal truth only as a means by 
 which the mind passes from true premisses to a true 
 conclusion. 
 
 2. Relation of Premisses to Conclusion in regard to 
 Truth. It is quite possible that false premisses may 
 furnish a true conclusion. Thus if I argue, ' All mam- 
 mals are vertebrates, All owls are mammals, therefore 
 All owls are vertebrates/ the minor premiss is false, 
 yet the conclusion is true. The way in which this occurs, 
 
 is easily seen from the diagram. I assert that S is P, 
 because it is M. It is true that 5 is P, but it is not so 
 because of the reason alleged. A conclusion of this kind 
 is said to be true per accidens ; i.e. its truth is not con- 
 nected with the reason assigned in the argument. 
 
 Hence it appears that we cannot argue that the pre- 
 misses must be true because the conclusion is true. On 
 the other hand, if the premisses are true, and the argu- 
 ment is rightly stated, we may be sure that the conclu- 
 sion is true. For a conclusion legitimately drawn, con- 
 tains nothing that is not implicitly contained in the 
 premisses (An. Prior //., c. 2, i, c. 4, 13). 
 
 3. General Rules of the Syllogism. The following 
 
THE CATEGORICAL SYLLOGISM (I) 17 > 
 
 eight rules hold good of all syllogisms, in whatever form 
 they may be stated 1 : 
 
 I. Relating to the structure of the syllogism. 
 
 Rule i. A syllogism must contain three, and only 
 
 three, terms. 
 Rule 2. A syllogism must consist of three, and only 
 
 three, propositions. 
 
 II. Relating to quantity. 
 
 Rule 3. The middle term must be distributed in 
 one, at least, of the premisses. 
 
 Rule 4. No term may be distributed in the con- 
 clusion, which is not distributed in a premiss. 
 
 III. Relating to quality. 
 
 Rule 5. No conclusion can be drawn, where both 
 premisses are negative. 
 
 Rule 6. If one premiss be negative, the conclusion 
 must be negative : and to prove a negative 
 conclusion, one of the premisses must be nega- 
 tive. 
 
 IV. Corollaries. 
 
 Rule 7. No conclusion can be drawn, where both 
 
 premisses are particular. 
 Rule 8. If one premiss be particular, the conclusion 
 
 must be particular. 
 
 We shall now deal with each of these rules separately. 
 Rule i. This rule prohibits what is known as an ambigu- 
 ous middle. We have stated above (Ch. 2, 12) that an 
 equivocal term is really equivalent to two terms. Hence, 
 when the middle term is equivocal, and is employed in 
 different senses in the two premisses, we have not three 
 terms but four. The following example will serve to 
 
 1 The following mnemonic verses, summing up the rules of the syllogism 
 are traditional in English works on Logic : 
 
 Distribuas medium, nee quartus terminus adsit, 
 Utraque nee praemissa negans, nee particularis, 
 Sectetur partem conclusio deteriorem, 
 Et non distribuat, nisi cum praemissa, negetve. 
 
 The third line, to the effect that the conclusion must always follow the inferior 
 alternative, signifies that where one premiss is negative, the conclusion is 
 negative, and where one is particular the conclusion is particular. Negation 
 is regarded as inferior to affirmation, and the particular as inferior to the 
 universal. 
 
r 7 4 PRINCIPLES OF LOGIC 
 
 illustrate what is meant. ' Beings, who are not free, are 
 incapable of sin, Slaves are beings who are not free, 
 therefore Slaves are incapable of sin/ Here the word 
 ' free ' in the major premiss denotes the freedom of the 
 will, in the minor premiss civil freedom. 
 
 The example, given in Ch. 8, 4, ' Man is a species, 
 Socrates is a man, therefore Socrates is a species/ provides 
 us with another case of ambiguous middle. The term 
 ' man ' is not equivocal. But when a term is employed 
 in the one case in reference to the real, in the other in 
 reference to the conceptual order, ambiguity necessarily 
 arises. 
 
 Rule 2. The second rule follows immediately from the 
 definition of a syllogism, which states that it is an infer- 
 ence, in which from two given propositions, we pass to a 
 third proposition. There are, as we shall see, forms of 
 argument, which contain a number of propositions. These 
 are not syllogisms, though they consist of syllogisms. A 
 syllogism must have but three propositions. 
 
 Rule 3. The object of the third rule is to guard against 
 the fallacy known as undistributed middle. It prescribes 
 that in one premiss at least the middle term should refer 
 to the whole of its extension. The reason for this is 
 obvious. In the syllogism, we discover the relation exist- 
 ing between the major and minor terms, by comparing 
 each with the middle term. It is therefore absolutely 
 essential that the term of comparison should be the same 
 in both cases, otherwise we have no means of comparing 
 major and minor. When the middle term is undistri- 
 buted, we have no guarantee that both propositions refer 
 
 to the same part of the extension. This may be seen in 
 the accompanying diagram. I may assert with truth 
 
THE CATEGORICAL SYLLOGISM (I) 175 
 
 that 5 is M, and that Pis M. But I am not justified in 
 concluding that 5 is P. Hence premisses, such as ' All 
 men are mortal, All negroes are mortal/ give no ground 
 for the conclusion that ' All negroes are men/ though 
 that proposition happens in fact to be true. This appears 
 at once, if in place of the term ' negroes ' we substitute 
 the term ' birds ' or ' fishes/ 
 
 Rule 4. The reason for this rule is obvious. It forbids 
 us to go beyond our data, and assert more in the conclu- 
 sion than is warranted by the premisses. It can be vio- 
 lated both as regards the minor and the maj or term. When 
 the major term receives illegitimate distribution in the 
 conclusion, that is, when the conclusion takes it in its 
 whole extent, though the premisses gave information 
 about a part only, the fallacy is termed illicit process 
 of the major. Should it be in the case of the minor term 
 that the error occurs, it is known as illicit process of the 
 minor. As an instance of the former, we may take the 
 following argument, ' All men are beings with an immor- 
 ' tal destiny, Brutes are not men, therefore Brutes are 
 ' not beings with an immortal destiny.' The invalidity 
 of such an argument is manifest, if we take an example 
 which is precisely similar, save that the conclusion is false : 
 e.g. ' All men are animals, Brutes are not men, therefore 
 ' Brutes are not animals.' Illicit process of the minor 
 maybe illustrated by, ' No birds are viviparous, All birds 
 ' are bipeds, therefore No bipeds are viviparous.' In this 
 syllogism the premisses only, justify us in concluding, 
 ' Some bipeds are not viviparous.' 
 
 Rule 5 forbids that both premisses should be negative. 
 Should this occur, we have no means of drawing a con- 
 clusion. In a negative premiss, we deny the connexion 
 of the middle term with the extreme contained in that 
 premiss. If both extremes are declared to be uncon- 
 nected with the middle term, we have no means of com- 
 paring them. We cannot say whether they are found 
 conjoined or not. 
 
 Certain recent logicians have called in question the universa 
 validity of this law. Prof. Jevons (Principles of Science, p. 63) 
 gives us the following syllogism as an exception to it : 
 
176 PRINCIPLES OF LOGIC 
 
 What is not metallic is not capable of powerful magnetic in- 
 fluence. 
 
 Carbon is not metallic. 
 
 .'. Carbon is not capable of powerful magnetic influence. 
 Mr. Bradley concurs with Prof. Jevons. " The fact remains," 
 he says, " that from two denials you somehow have proved a 
 further denial." The solution to the difficulty will be easily 
 seen, when it is observed that if the proposition, ' Carbon is not 
 metallic ' is taken as it stands, we have no middle term. In 
 the major premiss we have ' what-is-not-metallic,' and in the 
 minor ' metallic.' The mind replaces this proposition with the 
 equivalent affirmative, ' Carbon is a-thing-which-is-not-metallic,' 
 and the syllogism concludes without breach of rule. 1 
 
 Rule 6. The reason for the sixth rule is evident. When 
 the one premiss is affirmative, and the other negative, 
 the connexion of one extreme with the middle term is 
 asserted, the connexion of the other extreme with the 
 same term is denied. It follows that the conclusion 
 must necessarily deny that the two extremes are con- 
 nected inter se. The truth of the second part of the rule, 
 viz. : that a negative conclusion involves a negative 
 premiss, is shewn in a similar way. If the conclusion 
 denies the connexion of the two extremes, this cannot be 
 because both of them are connected with one and the 
 same middle term : it must be because the one is con- 
 nected with this term, and the other is not. 
 
 Rule 7. This rule may be proved by examining the 
 possible cases of two particular premisses, and testing 
 them by the preceding rules. Since there are but two 
 particular propositions, / and 0, the possible combina- 
 tions are limited to three //, 10, 00. 
 
 Of these the first // contains no distributed term, 
 and hence violates Rule 3. The third 00 gives us two 
 negative premisses, and thus contains a breach of Rule 5. 
 The combination 10 has one term alone distributed, 
 viz. : the predicate of 0. But it is necessary that two 
 terms, the middle and the major, should be distributed 
 in the premisses. A distributed middle is required by 
 
 * The difficulty is of respectable antiquity. Ueberweg, 106, calls attention 
 to its solution by Boethius, in Lib. de Interp., Ed. 2** (ed. Migne, t. 64, 
 c. 551) ; and Boethius refers us back to Alexander of Aphrodisias. 
 
THE CATEGORICAL SYLLOGISM (I) 177 
 
 Rule 3 ; and a distributed major is also needed, for, since 
 the conclusion must be negative by Rule 6, the predicate 
 must be a distributed term. 
 
 Rule 8. The rule that, if one premiss is particular, the 
 conclusion is particular, is also proved by an examina- 
 tion of cases. The possible combinations are four, AI, 
 AO, El, EO. Since EO contains two negatives, it may 
 be disregarded. A I contains but one distributed term. 
 Since the middle term must be distributed, it follows that 
 no term is distributed in the conclusion. The conclusion 
 therefore cannot be universal. AO and El both contain 
 two distributed terms. One of these must be the middle 
 term. Hence one term alone is distributed in the 
 conclusion. But the conclusion must necessarily be 
 negative, since in both cases there is a negative premiss. 
 But the universal negative E has both terms distributed. 
 The conclusion therefore, since it has but one distributed 
 term, can only be particular. 
 
 4. Figures and Moods of the Syllogism. 
 (i) Figure is the form of the syllogism as determined 
 by the position of the middle term in the two premisses. 
 
 The arrangement of figures now usual supposes that in 
 stating the premisses, we are already aware which of the 
 extremes is to be the subject of the conclusion, and which 
 is to be the predicate, in other words, which of our two 
 propositions is the minor premiss, and which the major. 
 This gives us a fourfold division, (i) In the first figure, 
 the middle term is subject in the major premiss, and 
 predicate in the minor premiss. (2) In the second figure, 
 the middle term is predicate in both premisses. (3) In 
 the third figure, the middle term is subject in both pre- 
 misses. (4) In the fourth figure, the middle term is predi- 
 cate in the major, and subject in the minor premiss. 
 The figures are represented by the following forms : 
 Fig. i. Fig. 2. Fig. 3. Fig. 4. 
 
 M P P M M P P M 
 
 S M S M Af_S M S 
 
 S P S P S P 5~P 
 
 N 
 
178 PRINCIPLES OF LOGIC 
 
 * For many centuries logicians employed a division of figures 
 in which no account was taken as to which premiss contained 
 the major term and which the minor. Nothing was considered 
 save the position of the middle term, and three figures only were 
 recognized, which were thus distinguished (i) Fig. i, M, subject 
 in the one premiss, predicate in the other, (2) Fig. 2, M, predicate 
 in both, (3) Fig. 3, M, subject in both. The figures may be 
 represented as follows : 
 
 (i) (2) (3) 
 
 MB B M MB 
 
 AM AM MA 
 
 The first of these figures, however, necessarily provides two vari- 
 eties, according as we make A or B the subject of the conclusion. 
 The forms in which B, the term which is predicate in its premiss, 
 becomes the subject in the conclusion, are those which, accord- 
 ing to the system now in vogue, constitute the fourth figure. 
 This arrangement was that of Theophrastus, a disciple of Aris- 
 totle. It differs a little from Aristotle's own treatment of the 
 figures, in a point which will be mentioned in Ch. 1 2, 2 below. 
 The Theophrastean arrangement is still preferred by many 
 logicians. 
 
 (ii) Mood is the form of a syllogism as determined by 
 the quantity and quality of its premisses. Since there are 
 but two premisses in a syllogism, and each of these must 
 be one of the four propositions, A,E,I,0, it follows that 
 there are but sixteen possible arrangements of premisses, 
 from which the mood of the syllogism can be selected, 
 viz. : 
 
 AA IA EA OA 
 AI // El 01 
 
 AE IE EE OE 
 
 AO 10 EO 00 
 
 Not all of these sixteen combinations, however, can 
 be employed in the premisses of a syllogism. The rule 
 of the syllogism prohibiting two negative premisses, 
 excludes four of the sixteen, viz. : EE, EO, OE, 00. 
 Four also are excluded by the rule, which tells us that 
 two particular premisses give no conclusion, viz. : //, 
 10, 01, 00. The last of these had already been rejected 
 on the previous count. Of the nine remaining cases, one, 
 IE, can be shewn to involve an illicit process of the major 
 
THE CATEGORICAL SYLLOGISM (I) 179 
 
 term. For since it contains a negative premiss, the con- 
 clusion must be negative. A negative conclusion distri- 
 butes its predicate, and hence necessitates that the major 
 term should be distributed in its premiss. But in IE, 
 no term is distributed in the major premiss, I. Therefore 
 a conclusion drawn from these premisses must needs be 
 vitiated by an illicit process of the major. 
 
 The possible moods are therefore eight in number, 
 and consist of the' combination El, and the seven possible 
 combinations, which contain the premiss A. We must 
 now examine, which of these moods may be employed 
 in the several figures. 
 
 5. Special Rules of the Four Figures. Though, as we 
 have seen, there are eight possible moods, not all of them 
 can be employed in each figure. Every figure has its 
 own special rules, involved in the arrangement of terms 
 peculiar to it, and only admits those moods which conform 
 to these rules. In this section, we shall deal with the 
 rules of the four figures in succession. 
 Figure i. 
 
 M P 
 S_M 
 T~P 
 
 Rules, (i) The minor premiss must be affirmative. 
 (2) The major premiss must be universal. 1 
 
 (1) If the minor premiss were negative, the conclusion 
 would be negative. A negative conclusion requires that 
 the major term should be distributed in the conclusion, 
 and therefore in the major premiss also. But the major 
 term is predicate in its premiss : hence were it distri- 
 buted, the premiss must be negative. Thus we should 
 have two negative premisses. 
 
 (2) Since the minor premiss is affirmative, the middle 
 term in that premiss is undistributed. It must therefore 
 be distributed in the major premiss. In that premiss, it 
 
 1 The older logics give us these rules in the following mnemonic hexameter 
 Sit minor affirmans, major vero generalis. 
 
i8o PRINCIPLES OF LOGIC 
 
 stands as the subject : the subject is distributed in univer- 
 sal propositions alone. 
 
 Rule (i) excludes the moods AE and AO, and Rule (2) 
 excludes I A and OA. There remain therefore four avail- 
 able moods in this figure, viz. : A A, AI, EA, EL Or, if 
 we express them with the letter denoting the conclusion 
 to be drawn from them, AAA, EAE, All, EIO. 
 Figure 2. 
 
 P M 
 
 S M 
 
 S P 
 
 Rules, (i) One premiss must be negative. 
 (2) The major premiss must be universal. 1 
 
 (1) Since the middle term is predicate in both pre- 
 misses, were both affirmative, it would not be distributed 
 in either. Therefore one must be negative. 
 
 (2) Since the conclusion is negative, the major term is 
 distributed. It must therefore be distributed in its 
 premiss. In the major premiss, it stands as subject. The 
 distribution of the subject involves a universal proposition. 
 
 Here Rule (i) excludes A A, AI, IA\ and Rule (2) 
 I A and OA . The valid moods of this figure will therefore 
 be EAE, AEE, EIO, AGO. 
 Figure 3. 
 
 M P 
 M S 
 S P 
 
 Rules, (i) The minor premiss must be affirmative. 
 (2) The conclusion must be particular. 2 
 
 (1) The former of these rules is established by the same 
 considerations as shewed the necessity of an affirmative 
 minor premiss in Fig. i. A negative minor would involve 
 a negative major, and therefore there would be two nega- 
 tive premisses, contrary to the fifth rule of the syllogism. 
 
 (2) Since the minor is affirmative, its predicate is undis- 
 tributed. This predicate is the minor term. The con- 
 
 1 Una negans esto, major vero generalis. 
 
 2 Sit minor affirmans, conclusio particularis. 
 
THE CATEGORICAL SYLLOGISM (I) 181 
 
 elusion therefore has an undistributed subject, and thus 
 is particular. 
 
 The valid moods of this figure are six in number, AAI, 
 IAI, AH, EAO, OAO, EIO. 
 
 * Figure 4. 
 
 P M 
 M S 
 S P 
 
 The fourth figure, as will be seen in the sections which follow, 
 is both theoretically and practically of very minor importance. 
 Its rules however are somewhat more complex than those of 
 the other figures. 
 
 Rules, (i) If the major is affirmative, the minor must be 
 universal. 
 
 (2) If the minor is affirmative, the conclusion must be par- 
 ticular. 
 
 (3) If the conclusion is negative, the major must be universal. 
 A breach of Rule (i) would involve undistributed middle : 
 
 a breach of Rule (2) an illicit process of the minor ; and of Rule 
 (3) an illicit process of the major. 
 There are five valid moods, AAI, AEE, IAI, EAO, EIO. 
 
 6. The Mnemonic Lines. The nineteen moods, whose 
 validity we have established, are enumerated in the 
 following mnemonic lines. It will be noticed that the 
 moods are expressed in succession by the vowels of each 
 word. Thus the mood AAA is signified by Barbara, 
 EAE by Celarent. The significance of the consonants 
 will be explained in 7 : 
 
 Barbara, Celarent, Darii, Ferioque prioris, 
 Cesare, Camestres, Festino, Baroco, secundae. 
 Tertia Darapti, Disamis, Datisi, Felapton 
 Bocardo, Ferison, habet. Quarta insuper addit 
 Bramantip, Camenes, Dimaris, Fesapo, Fresison. 1 
 Five of these moods, viz. Barbara, Celarent, Cesare, 
 Camestres, and Camenes, give universal conclusions. We 
 
 1 These particular mnemonics in an earlier form (Ch. 12, 2, note) occur 
 first in the work of William Shyreswood (d. 1249). They are contained also in 
 the Summulae Logtcales of Petrus Hispanus, afterwards Pope John XXI. 
 (d. 1277)- This was one of the most widely known of mediaeval logical 
 treatises, and through it they acquired universal notoriety. Many others of 
 the old mnemonics are found in this work. 
 
i8z PRINCIPLES OF LOGIC 
 
 may however, if we will, draw from the premisses a con- 
 clusion that is particular ; since there is nothing to pre- 
 vent us from asserting less than our premisses would 
 warrant. These moods, Barbari, Celaront, etc., are known 
 as subaltern moods. They are, of course, of no import- 
 ance. 
 
 The name of strengthened syllogisms is occasionally 
 given to the moods, Darapti, Felapton, Bramantip, and 
 Fesapo, for the reason that in each of them, the same 
 conclusion could be obtained by a particular premiss in 
 lieu of one of the universal premisses employed. In 
 Darapti, Felapton, and Fesapo, the middle term is twice 
 distributed. In Bramantip, the major term is distri- 
 buted in the premiss, and undistributed in the conclusion. 
 The remaining fifteen moods are termed fundamental 
 syllogisms. 
 
 7. Reduction. Aristotle held that only in the first 
 figure is the validity of our conclusion absolutely evident. 
 Figs. 2 and 3 he regards as valid, but as destitute of the 
 peculiar evidential quality, which marks Fig. i. That 
 alone is the perfect (re'Aeio?) syllogism. The others are im- 
 perfect (areXels). Their conclusiveness is only manifest, 
 when after the conversion of one or other of the premisses, 
 the syllogism is rearranged in some mood of the first figure. 
 This process was called Reduction by the Scholastics, and 
 may be defined as the process by which a syllogism in 
 one of the imperfect figures is expressed as a syllogism 
 of the first figure. 
 
 The names of the various moods as they are given in 
 the Mnemonic lines, " Barbara, etc./' are constructed on 
 an ingenious plan, so as to indicate the moods of the first 
 figure, to which they are to be reduced, and what opera- 
 tions are necessary to achieve the result. 
 
 It will be observed that every name begins with one 
 of the four letters, B, C, D, or F. These initial ietters 
 signify respectively that the mood in question is to be 
 reduced to Barbara, Celarent, Darii or Ferio. Of the 
 consonants composing the body of the word, the letters 
 
THE CATEGORICAL SYLLOGISM (I) 183 
 
 S, p, m, c are employed to tell us what changes are re- 
 quired to obtain a syllogism in one of these four moods : 
 S (= simpliciter] signifies that the premiss indicated 
 by the preceding vowel must be converted simply. 
 p (= per accidens) signifies that the preceding premiss 
 
 must be converted per accidens. 
 
 m (= muta), that the premisses are to be transposed. 
 C ( = per contradictor iam propositionem) , that the reduc- 
 tion is to be indirect or per impossibile. 
 These four letters were, therefore, not selected arbi- 
 trarily, but in each case denote the Latin name of the 
 process employed. 
 
 One or two examples will illustrate the application of 
 these methods. We give first a syllogism in Cesare of the 
 second figure : 
 
 No Englishmen are negroes. 
 All Hottentots are negroes. 
 .;. No Hottentots are Englishmen. 
 The letter s in Cesare tells us that the major premiss 
 must be converted simply, the initial C indicating that 
 the syllogism will be in the mood Celarent of Fig. i. The 
 process may be symbolized 
 
 P e M M e p 
 
 S a M S a M 
 
 S e P S~TP 
 
 The conversion of the major premiss gives us, 
 No negroes are Englishmen. 
 All Hottentots are negroes. 
 .-. No Hottentots are Englishmen. 
 The following example is in Disamis. Here we have 
 to convert the major premiss, and to transpose the order 
 of the two premisses. Moreover, the resulting conclusion 
 in Fig. i is not the actual conclusion of the syllogism in 
 Disamis, but, as the final s indicates, is shewn to be equi- 
 valent to it by simple conversion. 
 
 Some murderers are unsafe companions. 
 All murderers are men. 
 /. Some men are unsafe companions. 
 Here the symbolic representation becomes, 
 
1 84 PRINCIPLES OF LOGIC 
 
 M i P^^M a S 
 M a S^-P i M 
 S i P P i S 
 
 The syllogism as expressed in Darii will therefore be, 
 All murderers are men. 
 Some unsafe companions are murderers. 
 
 .*. Some unsafe companions are men. 
 
 By conversion this conclusion is shewn to be equivalent 
 to the conclusion of the Disamis syllogism. 
 
 This process, which gives us a syllogism in the first figure 
 precisely equivalent to the original syllogism, is termed 
 Direct or Ostensive Reduction. There are, however, two 
 moods, Baroco (Fig. 2) and Bocardo (Fig. 3), to which it 
 cannot be applied. In these moods, another method, 
 that of Indirect Reduction, is employed. This consists in 
 admitting by way of hypothesis that the conclusion of the 
 mood may be false, and in showing by a syllogism in 
 Barbara that this supposition involves the falsity of one 
 of the original premisses. The original premisses, how- 
 ever, are ex hypothesi known to be true. Hence we are 
 forced to admit that the conclusions in Bocardo and 
 Baroco are valid. Thus, we may take the following syllo- 
 gism in Baroco, 
 
 All whales are aquatic animals. 
 
 Some mammals are not aquatic animals. 
 
 .-. Some mammals are not whales. 
 
 If the conclusion is false, its contradictory must be 
 true, i.e. we must admit that ' All mammals are whales.' 
 We now form a syllogism in Barbara, using as our premisses 
 this proposition, and that one of the original premisses 
 which is a universal affirmative. This gives us, 
 All whales are aquatic animals. 
 All mammals are whales. 
 
 /. All mammals are aquatic animals. 
 
 This conclusion is, however, the contradictory of the 
 original premiss, ' Some mammals are not aquatic ani- 
 mals,' and is therefore false. But the error does not lie 
 in the reasoning, for that is in the first figure. One of the 
 premisses must therefore be false. The premiss ' All 
 
THE CATEGORICAL SYLLOGISM (I) 185 
 
 whales are aquatic animals ' is, however, given as true. 
 The premiss ' All mammals are whales ' is consequently 
 the erroneous one ; and since it is false, its contradictory, 
 the original conclusion of the Baroco syllogism, is true. 
 This method of indirect Reduction may be applied to 
 any mood, in lieu of the ostensive process. Let us take, 
 
 M eP 
 e.g., a syllogism in Felapton, M a S. If the conclusion 
 
 S o P. 
 S o P be false, S a P is true. We may now form a 
 
 S a P 
 syllogism in Barbara M a S But M a P is inconsistent 
 
 M a P. 
 
 with the original premiss M e P, and is therefore false. 
 It follows that the supposition S a P is false, and that 
 S o P is true. 
 
 Indirect Reduction is the only method employed by 
 Aristotle for dealing with Baroco and Bocardo. If, 
 however, we make use of Obversion, they may be treated 
 ostensively. The mnemonic words Faksoko and Doksa- 
 mosk, indicate the necessary operations for the direct 
 reduction of syllogisms in Baroco and Bocardo to Ferio 
 and Darii respectively. The letter k signifies the ob ver- 
 sion of the preceding premiss. The combination ks 
 signifies that the premiss must be first obverted, and then 
 converted. The following syllogism will serve as an 
 illustration : 
 
 Some ministers are not straightforward. 
 All ministers are privy-councillors. 
 /. Some privy-councillors are not straightforward. 
 This will become : 
 
 All ministers are privy-councillors. 
 Some men, who are not straightforward are ministers. 
 Some men, who are not straightforward are privy- 
 councillors. 
 
 * Further employment of Reduction. Aristotle also shews us 
 (An. Prior I., c. 7, 4) how Darii and Ferio may be reduced re- 
 spectively to Barbara and Celarent. It may appear remarkable 
 that he should think that these moods gain anything by reduc- 
 
186 PRINCIPLES OF LOGIC 
 
 tion, since he explicitly recognizes them as being among the 
 ' perfect ' moods of the syllogism. But his reason will be seen, 
 if we remember that the two universal moods alone give us 
 what he holds to be the absolutely typical inferential process. 
 In them the subject and middle-term are related as logical part 
 and logical whole, while the major-term either contains the 
 middle or absolutely excludes it. In the particular moods we 
 no longer have three universal concepts. The minor is particu- 
 lar : and particular propositions always depend in the last resort 
 on sensible experience. 1 Only a universal judgment can become 
 the object of an entirely intellectual intuition. For this reason 
 a syllogism in which one premiss is particular does not attain 
 to what in Aristotle's view is the absolute standard of the in- 
 ferential process of the intellect. 
 
 The method of reduction Aristotle here employs, is somewhat 
 cumbrous. A simpler method is possible. We may illustrate 
 it in the case of Darii. IfSiP be false, 5 e P is true. This may 
 be converted to P e S, and ob verted to Pa's. We may now, by 
 employing one of the original premisses form the syllogism in 
 
 PaS 
 Barbara M a P which gives the conclusion M a S or M e S, 
 
 MaS 
 
 equivalent to 5 e M, the contradictory of the original premiss 
 5 i M. Ferio may be dealt with in a precisely similar way. 
 
 8. Superiority of Pig. 1. Not only does the first figure excel the 
 others as a mode of inference. It has two other characteristics 
 which render it superior to them, (i) By its means we may 
 arrive at conclusions in all the qualitative and quantitative 
 varieties that are possible. We are not limited to negatives as 
 in Fig. 2, nor to particulars as in Fig. $. 2 More important still, 
 is the fact, that by it we can obtain a universal affirmative con- 
 clusion, viz. in Barbara. When we consider how great an im- 
 portance attaches to conclusions of this character, we see at 
 once that its utility exceeds that of all the other figures. Every 
 argument in which we bring a special case or type of case under 
 a general rule, is an argument in Barbara whether our subject 
 be Mathematics, Physics, Ethics, Law or what not. If the 
 student will, for instance, be at the pains to analyse a short pro- 
 position of Euclid, he will find that each step of advance is a 
 syllogism in this mood. 
 
 1 An. Post. I., c. 24, 15, v) f'-^v KaffoXov vo'irfi, i] 5e /card /*epos cts alaQ<]<ri.v 
 reXeura. " The universal proposition is the object of intellectual intuition ; 
 the particular ends in sense-perception." 
 
 2 An. Prior I., c. 5, 15. 
 
CHAPTER XII. 
 
 THE CATEGORICAL SYLLOGISM (ll.). 
 
 i. Canon of Syllogistic Reasoning. We stated in 
 the last section that Aristotle held the first figure to be 
 the only one in which the conclusiveness of the inference 
 is absolutely evident. His Scholastic followers expressed 
 the principle, which governs the reasoning of the figure, 
 in a canon to which they gave the name of the Dictum 
 de Omni et Nullo. This they held to be the fundamental 
 principle of the reasoning process. It may be thus 
 stated : Whatever is affirmed (or denied) universally 
 of any subject is thereby affirmed (or denied) of every 
 logical part of that subject. The Dictum is based on a 
 passage of Aristotle, and accurately represents his theory 
 of inference, though his expression of it does not give 
 it as the ultimate canon of reasoning. 1 
 
 It must be carefully noticed that in this principle, the 
 subject of which the affirmation or denial is made, is 
 not regarded as a collection of individuals. This would 
 
 1 The principle is thus given by John of St. Thomas, who may be taken as 
 fairly representative of the Thomistic school. Quidqvid universaliter dicitur 
 de aliquo subjecto, dicitur de onini quod sub tali subjecto continetur : quidquid 
 negatur de aliquo subjecto, negatur et de omni contento sub tali subjecto (Logica 
 Pars /., Lib. 3, c. x). The various forms in which it is stated, differ but slightly 
 from each other. Cf. St. Thomas An. Post. /., lect. 9. Scotus, Sup. Lib. 
 I. Priorum, Q. 7. The actual words of Aristotle, which it represents, are 
 found in An. Prior I., c. I, 8. Keyopev 8 TO Kara TT&VTOS Karriyopelffdac OTO.V 
 l^yS^ 77 Aa/3eti> rCjv TOV vTroKeifj.evov, Kad' o5 ddrepov ou Xex^crercu * /cat TO Kara 
 fjir)8cvbs uxrairrws. ' We say that an attribute is predicated of All a subject, 
 ' when there is no one of the parts of the subject, of which the attribute is 
 ' not predicated ; and similarly in the case, in which it is predicated of None." 
 The passage explains the significance of the universal proposition, which con- 
 stitutes the major premiss. As Scotus says (I.e.), it gives us the Nominal 
 definition (quid nominis) of the universal. 
 
 Some recent writers have erroneously identified Arist., Cat., c. 3, i with 
 the Dictum de Omni et Nullo. On the true meaning of that passage, see a 
 valuable note in Mr. Joseph's Introduction to Logic, p. 275. 
 
 187 
 
1 88 PRINCIPLES OF LOGIC 
 
 reduce inference to a barren tautology : for if the subject 
 is regarded as a collection of individuals, no inference 
 is required to affirm the attribute of them taken singly. 
 The general proposition has already affirmed it of each. 
 Such judgments as these, which are really a matter of 
 counting heads, are called Enumerative judgments. 
 In the Dictum the universal subject is the species or 
 genus as such, the logical whole. This appears clearly 
 if we state the proposition in the generic form, * Man is 
 vertebrate/ ' The salmon has scales,' ' The nightshade 
 is poisonous/ Our reason for employing the prefix 
 ' All/ is to emphasize the distributive force of the subject, 
 not to show that our knowledge is to be viewed as the 
 result of an enumeration. It is possible to attain a 
 knowledge of the species without knowing each member 
 of the class. We cannot have experimental knowledge 
 of all men, or of all salmon, or all plants of nightshade. 
 There is therefore no tautology, when we infer from 
 the logical whole to one of its parts. 1 
 
 It is manifest that all reasoning in Fig i, is of this 
 type : the major premiss affirms (or denies) some attri- 
 bute of a universal subject in its distributive accepta- 
 tion, e.g. ' All mammals have lungs.' The minor premiss 
 states that some class or some individual is a subordinate 
 of this universal subject. The conclusion affirms the 
 attribute of the class or the individual in question. 
 
 The Dictum is an immediate deduction from the 
 principle of Contradiction. Were we to assert any 
 attribute of a generic whole, and then deny it of some 
 part of this whole we should violate that primary law 
 
 1 That the Scholastics understood the universal terms constituting the subject 
 and the predicate, not as classes reckoned in extension, but as logical wholes, 
 may be seen from the following passage from Versorius Parisiensis, a Scholastic 
 commentator on Petrus Hispanus. When dealing with the Dictum de Omni 
 et Nullo, he distinguishes as follows, between the two expressions employed 
 by Aristotle (An. Prior I., c. i, 8) of the universal proposition. " Primo scien- 
 ' dum quod ' dici de omni ' est conditio praedicati in ordine ad subjectum . . . 
 ' sed ' esse in toto ' est conditio subjecti in ordine ad praedicatum, quia sub- 
 1 jectum est in praedicato sicut pars subjectiva in toto suo universali." Petrus 
 Hispanus (Venice, 1597), p. 217. If the subject is a pars subjectiva of the 
 predicate it must be viewed as a logical unity, and not as a collection, even 
 though it be qualified by the term ' All.' 
 
THE CATEGORICAL SYLLOGISM (II) 189 
 
 of thought. We should simultaneously assert an A 
 and an proposition. 
 
 Why, it may be asked, did Aristotle regard the first 
 figure as the only one possessed of perfect evidence ? 
 The answer must be that in this figure alone is the natural 
 synthesis of the terms given in the premisses themselves. 
 The premisses of the first figure give us ' 5 is a logical 
 part of M, M a logical part of P.' The subordination 
 of the concepts, gives us the synthesis we require ; and 
 we pass at once to ' 5 is a logical part of P.' The transi- 
 tion from the mental acts which constitute the premisses, 
 to the conclusion, is spontaneous, immediate, and neces- 
 sary. 
 
 In Figs. 2 and 3, the premisses do not give us the 
 terms in the order of subordination which we need. 
 The synthesis we are seeking, is not offered to us in the 
 mere conjunction of the premisses. The scheme of 
 Fig. 2 makes both S and P subordinate to M : that of 
 Fig. 3 gives us M as a logical part of S and P. Hence 
 the logical relation of the terms 5 and P is not given to 
 us in the premisses themselves. Doubtless our data 
 are sufficient for us to draw the conclusion which de 
 facto we do draw. But the mental operation here is 
 not the perfect process of inference : for in that the 
 premisses are two causative principles whose mere con- 
 junction in the mind gives us the conclusion as an imme- 
 diate result^ It was for this reason that Aristotle was 
 led to regard these forms as imperfect, and to maintain 
 that only in Fig. i does the full necessity of the inferential 
 act appear. It need not however be supposed that he 
 believed Reduction to represent the actual working of 
 
 1 Aristotle tells us that the premisses are the material cause of the conclusion, 
 at yrofleaeis TOU av/jLirepd t/^taros u>s r6 e r>0 atria, tonv. II. Phys. 3, 7 
 cf. Met. IV., c. 2, 7. They are the material cause in a sense analogous to that 
 in which the parts are the material cause of the whole. Thus e.g. the parts 
 of a circle separately are merely the material of the circle : but set together 
 in due order they result in the circle. In this sense in An. Post. II., c. u, i 
 he calls the material cause to ' rb rlvuv &VTWV &.vd~/Ky TOUT' elvai.' The 
 similarity between this definition and that of the syllogism (p. 169, note) is 
 patent. The premisses taken separately are mere ' material ' : but taken 
 together they give a complete inference. 
 
TOO PRINCIPLES OF LOGIC 
 
 the mind in reasoning. We employ, it can hardly be 
 
 doubted, Figs. 2 and 3 as independent instruments of 
 
 thought. Where e.g. we have such premisses as, 
 
 All heliotrope is sweet-smelling. 
 
 This flower is not sweet-smelling, 
 
 we need not convert the negative premiss : we recog- 
 nize that any other conclusion than ' This flower is not 
 heliotrope ' would involve a contradiction. But. the 
 process by which the premisses result in the conclusion 
 is not the connatural inferential process of the mind. 
 That is only found when the three concepts which to- 
 gether constitute the object of the intellectual act, stand 
 in such a relation to each other, as themselves to give 
 us the logical relation of the terms of the conclusion. 1 
 
 It is asserted by many recent logicians that Aristotle 
 was in error in holding the first figure to be the only 
 one in which the inferential process is absolutely evident. 
 Independent canons are given for the other figures : 
 and the whole process of Reduction is declared to be 
 useless. The following canons are among those which 
 have been suggested. 
 
 Fig. 2. Dictum de diverso. " If a certain attribute can 
 be predicated affirmatively or negatively of every member 
 of a class, any subject of which it cannot be so predicated, 
 is not a member of that class" (Mansel, Aldrich, p. 84). 
 
 Fig, 3. (I) Dictum de excmplo. " If a certain attribute 
 can be affirmed of any portion of the members of a class, 
 it is not incompatible with the attributes of that class " 
 (ibid.) 
 
 (II) Dictum de excepto. " If a certain attribute can 
 be denied of any portion of the members of a class, it 
 
 1 No argument can be drawn against the doctrine of Reduction from those 
 syllogisms in the third figure, in which the middle term is a singular term the 
 syllogismus expositorius, e.g. Socrates is poor, Socrates is wise.'. Some wise 
 men are poor. This is not an inferential process at all, but an appeal to ex- 
 perience in a particular case. The mind does not pass to a new truth it did 
 not possess. " Syllogismus expositorius non est vere syllogismus, sed magis 
 ' sensibilis demonstratio, seu resolutio facta ad sensum, ad hoc quod conse- 
 ' quentia quae vera est secundum intellectualem cognitionem, declaretur in 
 ' sensibili." St. Thomas, Opusc. 43, De Natura Syllogism*. It is in that manner 
 that it is employed by Aristotle in the proof of Fig. 3. 
 
THE CATEGORICAL SYLLOGISM (II) 197 
 
 is not inseparable from the distinctive attributes of 
 that class " (ibid.) 
 
 Fig. 4. Considerable difficulty has been found in dis- 
 covering any principle, which shall serve as a canon for 
 this figure. Lambert's Dictum de reciproco runs as 
 follows : " If no M is B, no B is this or that M : if C is 
 or is not this or that B, there are Bs which are or are 
 not C." 
 
 Those who reject Aristotle's doctrine, regard the 
 syllogism from a totally different point of view, and in 
 most cases appear to be ignorant as to the nature of his 
 theory of inference. 1 In the canons just cited, the 
 general proposition is a mere statement about the " mem- 
 bers of a class " taken in extension. The idea of the 
 terms of the premisses as objects of thought related one 
 to another as logical whole and logical part, was quite 
 foreign to them. It is easy enough to draw up canons 
 on the basis of extension. But if the canons are to be 
 strictly logical in their character, it may be questioned 
 whether any save that of the first figure can claim to be 
 absolutely self-evident. 
 
 Mill rejects the Dictum de omni on the ground that 
 it " merely amounts to the identical proposition that 
 ' whatever is true of certain objects, is true of each of 
 ' those objects " (II., c. 2, 2). He prefers the canon 
 " Whatever is a mark of any mark, is a mark of that 
 ' which this last is a mark of." In regard to this it 
 is sufficient to say that in the conceptual order we are 
 not concerned with things and marks, but with subjects 
 and attributes. The principle is not a logical principle 
 at all. 2 
 
 * 2. The Fourth Figure. The Fourth Figure calls for 
 
 1 The Aristotelian theory of the syllogism fell into almost complete oblivion. 
 It is interesting however to note that it was explained and defended by the 
 eighteenth century Scottish writer Lord Monboddo. See Dugald Stewart's 
 Philosophy of the Human Mind, vol. II., ch. 3, I. 
 
 2 Many recent Scholastic writers give the principles : ' Quae sunt eadem 
 uni tertio sunt eadem inter se : Si ex duobus unum cum iertio identicum est, 
 alterum non est, neque inter se ilia duo identica esse possunt.' But in the logical 
 order the subject and predicate are not the same. The identity is in the real 
 order, not the conceptual. To justify the syllogism we need a principle refer- 
 ring to thought not things. 
 
192 PRINCIPLES OF LOGIC 
 
 separate treatment. It corresponds to no natural process 
 of inference. The premisses tell us that ' A is a logical part 
 of B, B a logical part of C ' ; and we are asked to regard 
 a conclusion in which C is subordinate to A, as a normal 
 working of the mind on a parity with a conclusion in Fig. i. 
 It may safely be asserted that the mind never acts in this 
 way : though, of course, the conclusion that C is in part 
 subordinate to A, is not invalid. Three of the moods (Braman- 
 tip, Camenes, Dimaris), are in fact simply the first three moods 
 of Fig. i with the conclusion converted. The two remaining 
 moods (Fesapo, Fresisori) are not of this character. But they 
 need not therefore be relegated to a special figure. Aristotle 
 (An. Prior I., c. 7) views them as cases of Fig. i, in which the minor 
 
 premiss is a universal negative, a W-- ' Here, he says, a con- 
 clusion can be obtained, if the premisses be converted : but in 
 the conclusion the minor term will be predicated of the major, 
 
 M eS. 
 viz. P i M The arrangement made by his disciple Theophrastus, 
 
 .-. P o S. 
 
 was, it would appear, more satisfactory. He recognizes the 
 possibility, not merely of the normal conclusion in Fig. i, ' 5 is 
 subordinate to P,' but also of the abnormal but valid conclusion, 
 ' P is subordinate to S.' This adds the five moods in question 
 to the four Aristotelian moods of Fig. i, but reckons them in a 
 different class. This system was followed by the mediaeval 
 logicians, who termed them Indirect Moods of Fig. 1.1 It is 
 stated that Galen was the first to rank them apart as an inde- 
 pendent mode of reasoning. But this method did not become 
 prevalent till the decadence of Scholasticism, when excessive 
 attention was paid to the mechanical arrangement of terms and 
 premisses, and philosophic considerations were neglected. 2 
 
 Aristotle's conception of the figures of the syllogism is perhaps 
 best understood, if they be considered in their application to the 
 mental organization of our knowledge along the predicamental 
 lines (Ch. 9, 3). In Fig. i, employing a genus as middle term 
 we establish a connexion between a species on the one hand, 
 and on the other either a property of the genus or some higher 
 
 1 The mnemonic lines as given by Petrus Hispanus follow this arrange- 
 ment : 
 
 Barbara, Celarent, Darii, Ferio. Baralipet 
 
 Celantes, Dabitis, Fapesmo, Frisesmo. Deinde 
 
 Cesare, Camestres, Festino, Baroco. Darapti. 
 
 Felapton, Disamis, Datisi, Bocardo, Ferison (Petrus Hisp., Venice, 1597, 
 p. 249). 
 
 8 On Fig. 4, vide Joseph, Introduction to Logic, pp. 301-305. Ueberweg, 
 103. 
 
THE CATEGORICAL SYLLOGISM (II) 193 
 
 genus under which it falls : in Fig. 2 we shew the negative re- 
 lation between species which do not fall under the same genus ; 
 in Fig. 3 we shew the relation which holds between two genera, 
 if the same species is subordinate to both. This last relation 
 can, of course, only give a particular conclusion. 
 
 3. Expression in Syllogistic Form. The student will 
 find it a valuable exercise to throw into syllogistic 
 form some of the reasonings he may meet with in 
 the books which he reads, and in ordinary conversation. 
 Whenever we conclude from a general principle to 
 a particular case which falls under that principle, 
 the argument is syllogistic, though the syllogism may 
 not be expressed in full. An argument stated with its 
 full paraphernalia of major, minor, and conclusion may 
 be compared to a specimen beetle set out for exhibition. 
 When at large and alive, it is not accustomed to display 
 its members in a manner so convenient for the entomo- 
 logist. Nor do we, either in the spoken or written word, 
 express every step of our argument. We may omit one 
 of the premisses, leaving our hearers to supply it. Or 
 we may state the premisses, and leave the hearer to 
 draw the conclusion for himself. Or we put one member, 
 not as a judgment, but as a rhetorical question. One 
 or two examples will serve to illustrate the point: 
 
 'This undertaking is doomed to failure. No enterprise suc- 
 ceeds whose promoters lack foresight and prudence.' 
 This may be expressed by the syllogism, 
 
 No enterprise, whose promoters lack foresight and prudence, 
 
 is successful. 
 
 This undertaking is an enterprise, whose promoters lack fore- 
 sight and prudence. 
 
 /. This undertaking will not be successful. 
 The following example is a little more complex : 
 
 ' There is a real reason for distrusting many common-sense 
 judgments, since these are largely the general opinion 
 of men based on mere sense-perception, without the 
 correction which mature reflection affords.' 
 The syllogistic expression will be : 
 
 All general opinions, based on mere sense-perception and with- 
 out, etc., etc., are to be distrusted. 
 
 O 
 
194 PRINCIPLES OF LOGIC 
 
 Many common-sense judgments are general opinions, based 
 
 on mere sense-perception, etc., etc. 
 
 .-. Many common sense judgments are to be distrusted. 
 The next example provides a case in which one of the members 
 is expressed as a rhetorical question : 
 
 ' Can any general, whose army is disheartened, attain victory? 
 That was his case ; and there lay the cause of his failure/ 
 This will become : 
 
 No general whose army is disheartened is victorious. 
 He was a general whose army was disheartened. 
 .. He was not victorious. 
 
 4. Progressive and Regressive Syllogisms. 
 
 Progressive Syllogisms are those in which we reason 
 from a cause to its effect. Regressive Syllogisms are 
 those in which we reason from the effect to the cause. 
 
 Thus I may argue from the ascent of the mercury in the 
 
 tube of a barometer, to the conclusion that it must be 
 
 subject to atmospheric pressure. Or I may argue from 
 
 a previous knowledge of the existence of atmospheric 
 
 pressure, to the ascent of the mercury as a necessary 
 
 result. The Regressive syllogism will take the form : 
 
 A liquid, which (under the given circumstances) 
 
 ascends in an exhausted tube, must be subject to 
 
 atmospheric pressure. 
 
 The mercury of a barometer is a liquid which ascends 
 
 under the circumstances stated. 
 .*. The mercury of a barometer is subject to atmospheric 
 
 pressure. 
 
 A Progressive syllogism will proceed in the converse 
 way : 
 
 What is subjected to atmospheric pressure will (under 
 
 given circumstances) ascend in the tube. 
 The mercury of the barometer is subjected to atmo- 
 spheric pressure. 
 /. The mercury of the barometer will ascend in the 
 
 tube. 
 
 In Progressive syllogisms it is the middle term which 
 expresses the cause. 
 
 The cause from which we conclude to the effect may 
 be either the immediate or the remoter cause. Thus, if 
 
THE CATEGORICAL SYLLOGISM (II) 195 
 
 I argue that Socrates is capable of sensation because he 
 is a man, I argue from a remoter cause. He is endowed 
 with the capacity to feel, not because he belongs to the 
 narrower class ' man,' but because he belongs to the 
 wider class ' animal.' It is in his being an animal that 
 we find the immediate cause of his sensation. 
 
 When we know a thing through its immediate cause, 
 our knowledge of it is of a higher character than when we 
 reach it in any other way. It is when we know the 
 precise immediate cause of a thing, the reason why it 
 takes place, that we regard ourselves as fully under- 
 standing it. 
 
 In the syllogism in which we argued that the mercury 
 must rise in the barometer because of the presence of 
 the atmosphere, our reasoning was based on the efficient 
 cause. But each of the four causes (Ch. 10, 2) may be 
 employed in a Progressive argument (An. Post. II., c. n). 1 
 
 The syllogism is thus seen to afford us an inference 
 based on our knowledge of law. It is our knowledge of a law 
 which enables us to infer either from effect to cause, or 
 cause to effect. A syllogism in which the major premiss 
 is a mere enumerative judgment, is an inference of an- 
 other and far inferior kind. Arguments such as, e.g. 
 ' All the apostles were Jews ; St. Paul was an apostle ; 
 /. St. Paul was a Jew,' have for those who know the 
 grounds on which the major is based, no right to the 
 name of reasoning. For those who themselves have 
 made the enumeration, there is no passage from one 
 truth to another. They knew the conclusion before 
 they asserted the major. 2 
 
 5. Validity of the Syllogism. It is necessary for us 
 to consider a view taken by certain logicians, belonging 
 
 1 Syllogisms in which the middle term is the immediate cause of the attri- 
 bute which constitutes the major, are styled by Aristotle Syllogisms of the 
 Cause (<rv\\oyiff(j.ol rov 5i6n). All others are classed as Syllogisms of the 
 Fact (<rv\\oyiff/j.oi TOV 8n). Cf. An. Post. I., c. 13. It is Syllogisms of the 
 Cause which he regards as the true syllogisms of science : in them alone our 
 mental expression of things is in harmonious correspondence with the order 
 of Nature. 
 
 2 On the two kinds of universal, see Summa Totius Logicae, Tract 9, c. 2. 
 
ip6 PRINCIPLES OF LOGIC 
 
 to the Empiricist school, to the effect that the syllogism 
 as a method of inference, is formally invalid. The most 
 conspicuous recent logician who has adopted this posi- 
 tion is Mill. In this section we shall notice the objec- 
 tions which he urges against the syllogism, and the 
 account of the mind's process in reasoning which he 
 regards as presenting a more satisfactory analysis. 
 
 He argues that the major premiss, if literally inter- 
 preted, is a manifest begging of the question. In it, 
 we assert the very fact, which in the conclusion, we 
 profess to prove. The conclusion, as we state it, con- 
 tains nothing new : it is merely a reassertion of what 
 we have already affirmed in the major. " In every 
 ' syllogism, considered as an argument to prove the con- 
 1 elusion, there is a petitio principii. When we say, 
 ' ' All men are mortal, Socrates is a man, therefore Socrates 
 ' is mortal/ it is unanswerably urged by the adversaries 
 ' of the syllogistic theory, that the proposition Socrates 
 ' is mortal, is presupposed by the more general assump- 
 ' tion, All men are mortal : that we cannot be assured 
 ' of the mortality of all men, unless we are already assured 
 ' of the mortality of every individual man " (Logic, Bk. 
 II., c. 3, 2). It is clear, that if this be admitted, we 
 do not reach the conclusion that Socrates is mortal 
 from the major premiss, but on some other grounds. 
 Mill holds that the true grounds for our conclusion, are 
 in every case to be found in individual facts. We argue 
 from the deaths of individual men, of John and Thomas 
 and every other person in whose case the experiment 
 has been fairly tried, that the person of whom we 
 are speaking is mortal like the rest. We may indeed 
 pass through the stage of asserting that All men are 
 mortal, but we need not do so : not one iota is added 
 to the proof by interpolating a general proposition. 
 Indeed, experience assures us, that as a matter of fact, 
 we habitually do reason from particulars, without the 
 interpolation of the general proposition. " All our 
 * earlest inferences are of this nature. . . . The child, 
 ' who, having burnt his fingers, avoids to thrust them 
 
THE CATEGORICAL SYLLOGISM (II) 197 
 
 ' again into the fire, has reasoned or inferred, though 
 ' he has never thought of the general maxim, Fire burns. 
 ' . . . He is not generalizing : he is inferring a particular 
 ' from particulars " (ibid. 3). 
 
 From these considerations, Mill concludes that the 
 reasoning process is but ill represented by the syllogistic 
 form. The true and universal type of ratiocination 
 may be thus expressed, " Certain individuals have a 
 ' given attribute : an individual or individuals resemble 
 ' the former in certain other attributes : therefore they 
 ' resemble them also in this attribute." 
 
 If then, there is no inferential process in the descent 
 from the major premiss to the conclusion, where, it may 
 be asked, does the inference take place, when we use the 
 syllogism in argument ? Mill tells us that the whole 
 of the inferential process is found in the assertion of 
 the major premiss. The assertion of the universal pro- 
 position shows that the grounds on which we draw an 
 inference in regard of some one individual, are sufficient 
 for us to infer the same conclusion in regard to any indi- 
 vidual, who, in certain attributes, resembles the cases 
 we have observed. A general proposition serves not 
 merely to preserve in the memory the particular facts 
 it records, but also to contain our inference from these 
 facts. But " the inference is finished when we have 
 
 * asserted that all men are mortal. What remains to 
 
 * be performed afterwards is merely deciphering our 
 ' own notes " (ibid. 3). 
 
 Nevertheless, while denying the claim of the syllogism 
 to be a correct analysis of reasoning, Mill holds those 
 who look on it as useless, to be mistaken. The universal 
 statement renders us cautious in our inferences. Were 
 we not to make use of it, we might easily, in cases in 
 which we feel a special interest, give way to the natural 
 inclination to draw a conclusion in accordance with 
 our wishes. The universal proposition shews us that 
 " the experience, which justifies a single prediction, 
 ' must be such as will bear out a general theorem " 
 (ibid. 5). It may well be that this general theorem 
 
198 PRINCIPLES OF LOGIC 
 
 is manifestly untrue. Hence we discover our error by 
 a reductio ad impossibile. 
 
 Our criticism on this theory shall be confined to three 
 issues : 
 
 (1) It is not the case that the universal proposition 
 is a mere record of individual facts, together with an 
 inference to other particulars. The true universal pro- 
 position, (for we are not here concerned with the enumera- 
 tive judgments mentioned in i) relates, not to a collec- 
 tion of observed instances, but, as we have often said, 
 to the nature regarded in the abstract. When e.g. we 
 say, ' The cow is a ruminant/ we mean that the attribute 
 ' ruminant ' belongs to the nature of the cow, and is to 
 be found in any number of individuals, past, present or 
 future, in whom that nature is realized. The Empiricist 
 school deny that we possess this power of intellectual 
 abstraction. By so doing they cut away the foundations 
 of Logic. 
 
 (2) It is erroneous to say that the whole inference is 
 finished, when we have asserted the major premiss. 
 The major premiss may be well known to us, while, 
 through ignorance of the minor, we may be unaware of 
 the conclusion. I may have learnt that all mammals 
 breathe through lungs, and yet because I imagine that 
 a whale is a fish, I may not be aware that whales breathe 
 through lungs. It is true that the major universal 
 proposition, asserting that all mammals breathe through 
 lungs, covered the fact that whales do so. But inference 
 has to do, not with the facts as they are in the real order, 
 but with our knowledge of the facts. And if I do not 
 know that whales breathe through lungs, I certainly did 
 not infer it when I made the assertion that all mammals 
 breathe through lungs. It may even happen that I 
 know both the major and the minor premiss, and yet 
 may be ignorant of the conclusion. For unless I think 
 of the two premisses together unless I make the syn- 
 thesis, I may never reach the conclusion involved in 
 them. 1 
 
 1 Cf. An. Prior //., c. ax, 9. 
 
THE CATEGORICAL SYLLOGISM (II) 199 
 
 (3) If we examine the nature of the inference, by 
 which we pass from particulars to a conclusion about 
 another particular which resembles them, we shall 
 find that a universal proposition is involved. We argue 
 from one case to another, because they possess certain 
 common attributes. That is to say, we base our conclu- 
 sion on these attributes. But this involves a universal 
 proposition applicable to each and every case in which 
 such attributes are present. 
 
 * 6. Mathematical Reasoning. Several recent logicians 
 have maintained that much of the reasoning employed in 
 mathematics is not syllogistic. As cases in point they allege 
 inferences of the following character, common enough in 
 geometry and in arithmetic : 
 
 The triangle ABC is equal to the triangle DEF. 
 The triangle GHI is equal to the triangle DEF. 
 /. The triangle GHI is equal to the triangle ABC. 
 and 
 
 12=7 + 5, 12=20 8, .-. 7 + 5=20 8. 
 
 Here, it is argued, the process is clearly non-syllogistic. Our 
 data do not give us a subject-attribute relation, but a relation 
 between two quantities. The argument if carefully inspected, 
 has four terms, not three. And the principle on which the 
 reasoning is based, is not a canon of the syllogism, but the axiom 
 ' Things which are equal to the same thing are equal to each 
 other.' 
 
 We believe this view to be erroneous. In the first place the 
 data most certainly give us a subject-attribute relation : for 
 this is inseparable from judgment. We predicate the attribute 
 ' equal to DEF ' of the two subjects ABC and GHI. Secondly, 
 it is impossible that the axiom ' Things which are equal to the 
 same thing, etc., etc.' should be a principle of inference. It is 
 a truth relating to the real order, not to the conceptual. It is 
 necessary to the inference, but it is not a canon governing the 
 inferential process itself. A canon of inference must have ex- 
 plicit reference to the conceptual order. Here, as elsewhere, we 
 find our ultimate justification in the Dictum, which tells us that 
 what is predicated of the logical whole, may be predicated of 
 its parts. Doubtless, in practice we do not need so to arrange 
 our data as to show how the argument is justified by its con- 
 formity with this canon. The mind has no more need of this 
 than it has of reduction. But if this be required of us, the argu- 
 ment must be evolved in the form : 
 
200 PRINCIPLES OF LOGIC 
 
 Any two quantities, each of which is equal to the same third 
 
 quantity, are equal to each other. 
 ABC and GHI (as being equal to DEF) are two quantities 
 
 each of which is equal to the same third quantity. 
 .*. ABC and GHI are equal to each other. 
 
 7. Inferences other than Syllogistic. Some defenders 
 of the syllogism have gone so far as to maintain 
 that there is no such thing as non-syllogistic infer- 
 ence. They represent the syllogism as the only legiti- 
 mate form of reasoning, and hold that whenever the 
 mind infers, it must of necessity proceed syllogistic- 
 ally. If we restrict the term inference to signify the 
 derivation of a truth from propositions in which it is 
 implicitly contained, this is true. In the syllogism, and 
 in the syllogism alone, is the conclusion implicitly con- 
 tained in given premisses. But inference is frequently 
 used in a wider sense, to include also the derivation of a 
 conclusion from concrete facts by an act of the critical 
 judgment. When a jury after weighing a mass of evi- 
 dence acquit or condemn a man accused of burglary, 
 they may be rightly said to infer. But their concern has not 
 been to find out what is implicitly contained in certain 
 propositions, but to find out what is involved in certain 
 concrete facts. They decide that these facts are com- 
 patible or incompatible, as the case may be, with the 
 man's innocence. Their conclusion is simply a critical 
 estimate of what the facts involve. Cardinal Newman 
 has discussed this form of inference at length in the 
 Grammar of Assent. But the difference between the two 
 forms of reasoning was familiar to St. Thomas, and is 
 carefully noted, by him more than once. 1 
 
 * Mr. Bradley, dealing with this question, gives the following 
 as specimens of non-syllogistic inference : (i) A is to the right 
 of B, B is to the right of C, therefore A is to the right of C : 
 (2) A is due north of B, B is due west of C, therefore A is north- 
 
 1 St. Thomas holds that as these inferences are solely concerned with particular 
 facts, they are effected by the vis cogitativa, in which sense and intellect meet 
 See Summa TheoL, II. II ae ., Q. 2, Art. i. 
 
THE CATEGORICAL SYLLOGISM (II) 201 
 
 west of C, etc., etc. In regard to these, we believe him to be 
 mistaken. It seems to be indubitable, that in these cases, as in 
 the mathematical inferences considered in the last section, the 
 mind relies on an unexpressed, but self-evident first principle. 
 It is as self-evident that what is locally to the right of an object, 
 which is situated to the right of a third entity, is itself to the 
 right of that entity, as that things which are equal to the same 
 thing are equal to each other. 
 
 * 8. Mr. Bradley 's theory of Inference. The view taken 
 by Mr. Bradley as to Universals (Ch. 8, 5) will have to some 
 extent prepared the reader for his theory regarding the 
 closely connected question of inference. " Inference," he tells 
 us, " rests on the principle that what seems the same, is the 
 ' same " (Principles, p. 264). In virtue of this ' axiom,' wherever 
 we have two premisses with a common term, we are able to 
 effect ' an ideal construction,' which unites the two judgments 
 into an individual whole, and so permits the mind to pass to 
 the assertion of a new relation. " The premisses . . . are two 
 ' or more judgments, and the operation on these data will con- 
 ' sist in joining them into a whole. We must fasten them to- 
 ' gether, so that they cease to be several, and are one construc- 
 ' tion, one individual whole. Thus instead of A B, B C, we 
 ' must have A B C " (ibid., p. 236). " If we are to construct, 
 ' we must have identity of the terminal points. Thus in A B, 
 1 B C, B is the same, and we connect A B C. The operation 
 'consists in the extension and enlargement of one datum by 
 ' others, by means of the identity of common links. . . . Hav- 
 ' ing thus turned our premisses into one whole we proceed to 
 ' our conclusion by mere inspection. . . . By inspection we 
 ' discover and select a new relation, and this intuition is the 
 ' conclusion. ... It is useless to lay down rules for either 
 * part of this process. . . . No models for construction can 
 'possibly be invented" (ibid., pp. 237-8). x 
 
 The view taken by Mr. Bosanquet differs in various respects 
 from Mr. Bradley's theory. He rejects the account of the pro- 
 cess as a ' construction.' He is, however, at one with Mr. Bradley 
 in holding that inference depends on a real identity shared by 
 the various differences of a common universal. " It is possible," 
 he says, " to proceed from content to content, because the world 
 ' as known consists of universals exhibited in differences, and 
 
 1 Mr. Bradley's respect for the theory of the syllogism is small. He denies 
 that a major premiss is necessary in inference. " Begotten by an old meta- 
 ' physical blunder, nourished by a senseless choice of examples, fostered by 
 ' the stupid conservatism of logicians, this chimaera has had a good deal more 
 ' than its day." " The syllogism itself like the major premiss is a superstition." 
 " Perhaps we may say that a man who cannot use more than three terms in 
 ' reasoning, is unlikely to do much in any subject " (Principles, pp. 228-9). 
 
202 PRINCIPLES OF LOGIC 
 
 ' the contents from which and to which we proceed, are not 
 ' shut up within their respective selves, but depend on a per- 
 ' vading identical character or universal, of which they are the 
 'differences" (Logic, II., p. 2). The simplest example of an 
 inference through a universal he finds in the syllogism in which 
 the middle term is a proper name, as when we argue that since 
 Socrates is both good and a Greek, therefore a Greek may be 
 good (ibid. p. 200). l 
 
 As we have already pointed out, this view that things which 
 can be brought under the same universal are united by a per- 
 vading identity, is based on the confusion of the real and con- 
 ceptual order. In the real order the things are similar, not identi- 
 cal. But in virtue of the abstractive power of the intellect, we 
 can prescind from individual varieties and represent them by 
 a common concept. This universal concept enables us to make 
 statements valid in regard to all objects to which it may be 
 applied, and thus provides us with a basis for inference. 
 
 1 The reader will not need to be reminded that the Scholastic authors denied 
 that there was any inferential process in these syllogismi expositorii: see p. 
 190, note. 
 
CHAPTER XIII. 
 
 HYPOTHETICAL AND DISJUNCTIVE SYLLOGISMS. 
 
 i. Mixed Hypothetical Syllogisms. Syllogisms, in 
 which one or both of the premisses are hypothetical 
 propositions, are termed hypothetical syllogisms. If 
 both premisses are of this character, the syllogism is 
 known as a Pure Hypothetical. This is of far less im- 
 portance than the Mixed Hypothetical Syllogism. The 
 latter is defined as a syllogism, in which the major premiss 
 is a hypothetical proposition, and the minor premiss a 
 categorical proposition either affirming the antecedent 
 or denying the consequent of the major. The following 
 formulas show the character of the reasoning : in Ex. 
 i, the antecedent is affirmed ; in Ex. 2, the consequent 
 is denied. 
 
 Ex. i. If A is B, it is D. or If A is B, C is D. 
 
 A is B. A is B. 
 
 .-. A is D. .'. C is D. 
 
 Ex. 2. If A is B, it is D. or If A is B, C is D. 
 
 A is not D. C is not D. 
 
 /. A is not B. /. A is not B. 
 
 The affirmation of the antecedent, and the denial of 
 the consequent constitute the two moods of the mixed 
 hypothetical syllogism. These are known as the modus 
 ponens (or the constructive hypothetical syllogism), and 
 the modus tollens (or the destructive hypothetical syllogism) 
 respectively, these names being derived from the canon 
 of the syllogism, which is thus stated : 
 
 To posit the antecedent is to posit the consequent ; and 
 to sublate the consequent is to sublate the antecedent. * 
 
 It is more convenient to employ the terms ' posit ' and 
 
 1 Posito antecedente ponitur consequens : sublato consequente tollitur 
 antccedens. 
 
204 PRINCIPLES OF LOGIC 
 
 ' sublate,' in this connexion, than ' affirm ' and ' deny. 
 For the antecedent may contain a negative ; and in this 
 case the proposition positing it, will also be of negative 
 quality. To speak of negative propositions as affirma- 
 tions, could only cause confusion. This feature is illus- 
 trated by the following syllogism, 
 
 If the doctor is not skilful, he will cause this 
 
 patient much pain. 
 He is not skilful. 
 
 /. He will cause this patient much pain. 
 Here we posit the antecedent by a negative sentence. 
 It is further to be observed that when the consequent 
 is denied, the conclusion will be the contradictory, not 
 the contrary, of the antecedent it denies. Thus in the 
 syllogism, 
 
 If all men were actuated by the highest motives, the 
 
 sanction of punishment would be unnecessary. 
 The sanction of punishment is not unnecessary ; 
 we can only conclude that ' Some men are not actuated 
 by the highest motives.' It would be fallacious to argue 
 that none are so actuated. 
 
 There are two fallacies to which these syllogisms are 
 liable. These are (i) the fallacy of denying the ante- 
 cedent, and (2) the fallacy of affirming the consequent. 
 From the fact that the antecedent can be denied, we 
 cannot conclude to the falsity of the consequent : for 
 it may well be that the same result may take place, but 
 owing to some other cause. I cannot argue thus : 
 
 If his rifle is damaged, he will fail to hit the bull's- 
 eye. 
 
 His rifle is not damaged. 
 /. He will not fail to hit the bull's-eye. 
 Similarly, to assert the truth of the consequent affords 
 us no ground for concluding to the truth of the ante- 
 cedent. We cannot, for instance, argue 
 
 If the novel possesses real literary merit, it will be 
 
 widely read. 
 It will be widely read. 
 /. It possesses real literary merit. 
 
HYPOTHETICAL AND DISJUNCTIVE SYLLOGISMS 205 
 
 This fallacy has, at all times, been one of the most fre-^ 
 quent pitfalls in men's ordinary reasonings. The old 
 proverb, Cucullus non facit monachum, warns us that, 
 though it is safe to argue that because a man is a monk, 
 he will wear a habit, there is risk of error, when we con- 
 clude if he wears a habit, therefore he must needs be a 
 monk. 
 
 The fallacy of denying the antecedent is often said 
 to be equivalent to illicit process of the major, and that 
 of affirming the consequent to undistributed middle. 
 It is in fact the case, that if we express the major of a 
 Barbara syllogism as a hypothetical judgment, the 
 fallacies of illicit major and undistributed middle will 
 be thus represented. For example, ' Every man is a 
 biped ; this bird is a biped : .*. This bird is a man,' will 
 become, ' If anything is a man, it is a biped : this bird 
 is a biped : .*. This bird is a man.' But it cannot be said 
 there is any real equivalence. The error in thought is 
 not the same. Moreover the transformed categorical 
 syllogism is only in appearance a hypothetical syllogism. 
 It has no true right to the name : for the minor affirm- 
 ing the consequent, contains a term ' bird,' which is not 
 found in the major. In the true hypothetical, the minor 
 introduces no new terms. 
 
 Several logicians of eminence, amongst others Kant, Hamilton 
 and Bain, have held that the mixed hypothetical syllogism is 
 an Immediate and not a Mediate Inference. The reason for 
 this view, is that in the hypothetical we have only two distinct 
 clauses, both 'of which appear in the major. Hence it has 
 been argued that the true mode of stating the hypothetical 
 syllogism is, 
 
 If A is B, C is D. 
 .'. A being B, C is D. 
 
 The view cannot be maintained. The judgment ' A is B, 
 is not part of the conclusion, but is one of the data. From the 
 conditional statement, ' If the afternoon prove fine I shall go 
 for a walk,' we cannot draw as a conclusion the judgment that 
 ' The afternoon is fine.' The data of the syllogism are two in 
 number, and neither is sufficient alone. 
 
 Pure Hypothetical Syllogism. In the Pure Hypothetical 
 
206 PRINCIPLES OF LOGIC 
 
 Syllogism, as has already been observed, all the propositions are 
 hypothetical. The argument is of the form : 
 
 If C is D, E is F. 
 
 If A is B, C is D. 
 
 .'. If A is B, E is F. 
 
 Since the hypothetical proposition admits no variety as re- 
 gards quantity or quality, but is necessarily both affirmative 
 and singular, this syllogism has but one form and no more. 
 
 2. Reduction of Hypothetical Syllogisms. In 
 
 these syllogisms, the modus ponens may without diffi- 
 culty be reduced to the modus tollens, and vice versa. 
 All that is required is to substitute the negation of the 
 consequent for the antecedent, and the negation of the 
 antecedent for the consequent. Thus, 
 
 Modus ponens Modus tollens 
 
 If A is B, C is D t may be expressed If C is not D, A is 
 
 not B. 
 
 A is B. A is B. 
 
 .-. C is D. .-. C is D. 
 
 It will be seen that the second form is a true Modus 
 tollens, since the conclusion ' C is Z)/ contradicts the 
 antecedent of the major premiss. 
 
 Reduction to categorical form. It is sometimes said 
 that all these syllogisms can be reduced to categorical 
 form. In regard to this point, the essential difference 
 between the two classes of proposition must be borne 
 in mind. The categorical proposition gives us two con- 
 cepts related as subject and attribute : the hypothe- 
 tical proposition gives us two judgments related not as 
 subject and attribute as a thing and its determina- 
 tion, but as reason and consequent. It may safely 
 be said that to express the one in terms of the other, is 
 to do violence to our thought. This appears plainly 
 in the following example. 
 
 If the opium habit is innocuous, the whole medical 
 
 faculty is deluded. 
 The whole medical faculty is not deluded. 
 
 /. The opium habit is not innocuous. 
 
 A syllogism of this character cannot naturally be 
 
HYPOTHETICAL AND DISJUNCTIVE SYLLOGISMS 207 
 
 expressed as a categorical. The result, it is true, is 
 sometimes achieved, as follows : 
 
 The case of the opium habit being innocuous is a 
 case of the whole medical faculty being deluded. 
 
 The case of the whole medical faculty being deluded 
 
 is a supposition not to be admitted. 
 .'. The case of the opium habit being innocuous is a 
 supposition not to be admitted. 
 
 But it is lightly urged that the altered major premiss 
 has no meaning, unless it is translated back into its 
 hypothetical significance. The latter clause does not 
 really express an attribute of the former. The mind 
 must understand the two clauses as reason and conse- 
 quent, whatever be the clumsy phraseology we elect to 
 employ. Hence, there is here no reduction properly 
 so called. The mental process remains the same. It 
 is the words only that have been changed. And the 
 result of the change is thoroughly misleading, since it 
 induces us to regard as identical, processes which are 
 fundamentally distinct. 
 
 3. The Disjunctive Syllogism, (a) Import of the Dis- 
 junctive Judgment. Before explaining the disjunctive 
 syllogism, a word must be said as to the import of the 
 disjunctive judgment. This point could not be conven- 
 iently treated in Ch. 7, where the import of categoricals 
 and hypothetical was discussed : for, as we have seen 
 (Ch. 10, 5), one form of the disjunctive expresses the 
 relation of the genus to its constituent species, and in 
 consequence, cannot be understood till the nature of 
 that relation has been explained. The disjunctive 
 proposition is of two kinds. One may be termed the 
 Disjunctive of Logical Division. In it the subject is a 
 generic whole, while the predicate is formed by the dis- 
 junctive enumeration of the subordinate parts. This 
 form of the judgment has been discussed sufficiently 
 already. The other kind may be termed the Disjunctive 
 of Ignorance. In this we affirm that one out of two (or 
 more) predicates which we enumerate, belongs to the 
 
208 PRINCIPLES OF LOGIC 
 
 subject. Our knowledge is sufficient for us to assert 
 that the truth lies with one of these alternatives, but 
 we do not know with which : e.g. ' This curve is either 
 a circle or an ellipse/ ' He is either very thoughtful or 
 very stupid/ In disjunctives of this class the subject 
 is not the logical whole but a subordinate part. It is 
 the function of the predicate to express the whole, as 
 in the categorical sentence : but we are in doubt to 
 which of two logical wholes the subject should be re- 
 ferred. 1 
 
 Logicians have disputed as to whether in a disjunctive 
 judgment the members of the disjunction are mutually 
 exclusive. In other words, when we assert ' 5 is P or 
 Q,' do we intend to exclude the supposition that some 
 particular 5 may be both at the same time ? In regard 
 to the first class of disjunctives, the mutual exclusiveness 
 is quite evident. The species must be distinguished 
 from each other. But in regard to the disjunctives of 
 ignorance, it would seem that the mere form of the propo- 
 sition gives us no assurance on the point. If I say ' He 
 must be very clever or very painstaking/ I can hardly 
 be understood to exclude the supposition that the person 
 in question may be both. Often however the members 
 of the disjunction are formed by repugnant terms, e.g. 
 ' The horse was either bay or chestnut.' Here we have 
 mutual exclusion : but it is not due to the disjunctive 
 form as such. 
 
 (b) The Disjunctive Syllogism. This may be defined as 
 a syllogism in which the major premiss is a disjunctive 
 proposition, and the minor a categorical proposition, 
 either affirming or denying one member of the opposition. 
 It is to be noted that this syllogism has no application 
 in regard to the first of the two forms of disjunctive 
 proposition. It is concerned with the Disjunctive of 
 Ignorance alone. The argument has two moods, called 
 respectively the modus ponendo tollens and the modus 
 tollendo ponens. The affirmation in the minor premiss 
 
 1 The form 'Either A is JB, or C is D,' is also a case of the Disjunction of 
 Ignorance. 
 
HYPOTHETICAL AND DISJUNCTIVE SYLLOGISMS 209 
 
 of one of the two alternatives, gives us the modus ponendo 
 tollens : the denial of an alternative, the modus tollendo 
 ponens. The following formulas illustrate these cases : 
 Modus ponendo tollens. Modus tollendo ponens. 
 
 S is either P or Q. S is either P or Q. 
 
 S is P. S is not P. 
 
 .'. S is not Q. .-. 5 is Q. 
 
 The modus ponendo tollens is only valid in those cases, 
 in which the members of the disjunction are known to 
 be mutually exclusive. Otherwise it would be impos- 
 sible to conclude from the presence of one alternative 
 to the absence of the other. The modus tollendo ponens 
 is always valid. 
 
 4. The Dilemma. The Dilemma is an argument 
 in which both the hypothetical and the disjunctive 
 judgment are employed. It is defined as an argument 
 in which the major premiss is a compound hypothetical 
 proposition, and the minor a disjunctive. In actual 
 use the disjunctive is often placed first. Its chief import- 
 ance arises from its effectiveness as a rhetorical weapon. 
 The disjunctive apparently exhausts the alternatives 
 open to the adversary ; and the hypothetical, which 
 follows, shows that each one of them leads him to an 
 unwelcome conclusion. Hence it is not surprising that 
 this argument was first analysed and explained by 
 rhetoricians. 1 Where three alternatives are offered, we 
 have the Trilemma : where four, the Tetralemma. Like 
 other hypothetical syllogisms it has a constructive and a 
 destructive form, according as the disjunctive proposition 
 affirms that one of the antecedents must be true, or that 
 one of the consequents must be false. Moreover both 
 the Constructive and the Destructive Dilemma may be 
 Simple or Complex. In the Simple Constructive, the 
 consequents of the two hypothetical clauses are identical. 
 In the Complex Constructive they are different. It is 
 manifest that in a Constructive Dilemma, there can be 
 no question of the antecedents being identical : for 
 
 1 See Ueberweg, 123. 
 
 P 
 
zio PRINCIPLES OF LOGIC 
 
 were they so, they could not be disjunctively asserted 
 in the minor. In the destructive form, the opposite 
 is the case. The Simple Destructive has but one ante- 
 cedent ; the Complex Destructive has two. The following 
 formulas show their varieties : 
 
 (1) Simple Constructive. If A is B, E is F : and if 
 
 C is D, E is F. 
 Either A is B, or C is D. 
 /. E is F. 
 
 (2) Complex Constructive. If A is B, E is F : and if 
 
 C is Z), G is #. 
 Either ^ is B, or C is D. 
 /. Either E is F, or G is #. 
 
 (3) Simple Destructive. If ^4 is B, E is F, and G 
 
 is #. 
 Either is not JP, or G is 
 
 not H. 
 .*. ^4 is not B. 
 
 (4) Complex Destructive. H A is B, E is F : and if 
 
 C is Z), G is H. 
 Either E is not F, or G is 
 
 not H. 
 
 /. Either ^4 is not B, or 
 C is not D. 
 
 (i) We may find a suitable illustration of the Simple Con- 
 structive Dilemma in the argument by which Empson, the 
 notorious agent of Henry VII., is said to have always been able 
 to prove that his victim was capable of paying a large amount 
 into the treasury : 
 
 If the accused lives at a small rate, his savings must have 
 
 made him very rich : if, on the other hand, he maintains 
 
 a large household, his expenditure proves him to be 
 
 wealthy. 
 
 But either he lives at a small rate, or he maintains a large 
 
 expenditure. 
 
 .*'. He is rich, and consequently can pay heavily to the king. 
 This piece of reasoning was known, as the reader will remember, 
 as ' Empson's fork,' a name, which is a striking parallel to the 
 expression, which speaks of a man as being impaled on the horns 
 of a dilemma. The argument leaves no escape. Whichever 
 alternative is selected, the result is equally disagreeable, 
 
HYPOTHETICAL AND DISJUNCTIVE SYLLOGISMS 211 
 
 (2) As an example of the Complex Constructive Dilemma, we 
 may take Tertullian's argument against the methods employed 
 by Marcus Aurelius in his persecution of the Christians : 
 
 Either the Christians have committed crimes, or not. 
 If they are guilty of crimes, your refusal to permit a public 
 enquiry is irrational ; if they have committed no offence, 
 it is unjust to punish them. 
 /. Your conduct is either irrational or unjust. 
 Unfortunately from the time of Nero to the present day, 
 neither justice nor reason have weighed much with the perse- 
 cutors of the Church. 
 
 (3) The following may serve to illustrate the Simple Destruc- 
 tive : 
 
 If he would pass the straits unharmed, he must escape both 
 
 Scylla and Charybdis. 
 But either he will not escape Scylla, or he will not escape 
 
 Charybdis. 
 /. He will not pass the straits unharmed. 
 
 (4) This example of the Complex Destructive Dilemma is 
 given by some authors : 
 
 If he were intelligent, he would see the worthlessness of his 
 
 arguments ; if he were honest, he would own himself wrong. 
 
 But either he does not see that his arguments are worthless ; 
 
 or seeing it, he will not own himself in the wrong. 
 /. Either he is wanting in intelligence, or he is dishonest. 
 
 The student will observe that the premiss of the Simple 
 Destructive form differs in a material point from the 
 Simple Constructive. In the Destructive Dilemma, 
 the consequent is copulative, not disjunctive : ' If A is 
 B, C is D and E is F.' The reason for this is, that were 
 the two consequents alternatives, the denial of one or 
 other of them in the minor premiss would not necessarily 
 involve the falsity of the antecedent. An argument 
 can, of course, be constructed, in which the consequents 
 are disjunctive, and both are denied in the minor : 
 If A is B, either C is Z), or E is F. 
 C is not Z), nor is E, F. 
 
 .*. A is not B. 
 
 According to our definition, which postulates a dis- 
 junctive minor premiss as essential to the argument, 
 this is not a true dilemma. It should however be noticed 
 that not a few logicians (e.g. Hamilton, Thomson, Ueber- 
 
212 PRINCIPLES OF LOGIC 
 
 weg, etc.), hold it to be such, and adopt a different defini- 
 tion of the argument. Thus Mr. Joseph (Introd. to Logic, 
 p. 331) defines the dilemma as "an argument offering 
 'alternatives, and proving something against an adver- 
 ' sary in either case." The point is not of first-class 
 importance. We have preferred the view, which re- 
 quires the disjunctive minor premiss, since the separate 
 treatment of this argument seems to demand that its 
 form should be one and the same in all its varieties. 
 
 5. Answering the Dilemma. We have already called 
 attention to the great value of the Dilemma to the 
 rhetorician. It is, therefore, not surprising that attention 
 should have been paid to the manner in which it should 
 be answered. Three ways of dealing with it are enu- 
 merated : 
 
 (1) Taking it by the horns. Here the person against 
 whom it is brought, accepts the alternatives offered 
 him, but shows that they do not involve the consequents 
 attributed to them in the major. Where this is shown 
 in respect of only one of the alternatives, he is said to 
 take the dilemma by one horn. Thus, in the Complex 
 Destructive given in the last section, the controversialist 
 against whom such a dilemma was urged, would probably 
 reply that he would willingly admit himself to be intel- 
 ligent, but that it by no means followed he would recog- 
 nize his arguments as invalid : that, on the contrary, 
 he knew them to be valid. 
 
 (2) Escaping between the horns. This is the method 
 adopted, when it is shown that the disjunction is not 
 complete, and that another alternative remains. For 
 example, suppose it to be pointed out to some man, 
 that he must vote either for the conservative or the 
 liberal candidate in some election, and that in either 
 case he would materially injure his business prospects 
 by giving offence to a section of his clients. He might 
 reply that there was yet another possibility, for it might 
 happen that he would be enjoying a well earned holiday 
 abroad at the time of the election. 
 
HYPOTHETICAL AND DISJUNCTIVE SYLLOGISMS 213 
 
 (3) Rebutting the Dilemma. The Dilemma is said to 
 be rebutted, when reply is made by another Dilemma, 
 in which the same alternatives are taken, but are shown 
 to involve consequents fatal to the original argument. 
 It is, for instance, not difficult to construct a rebutting 
 argument to meet Empson's ' fork.' 
 
 If the accused lives at a small rate, his economy is 
 evidence of his poverty : if he has maintained 
 a large expenditure, that must needs have im- 
 poverished him. 
 
 But either he lives at a small rate, or has main- 
 tained a large expenditure. 
 /. He is poor and is incapable of paying much to 
 
 the king. 
 
 To rebut the argument, the two consequents are trans- 
 posed, and their quality changed. Where the original 
 Dilemma gives us, 
 
 If A is B, E is F ; and if C is Z), G is H. 
 But either A is B, or C is D. 
 .-. Either E is F, or G is H, 
 the new argument is of the form, 
 
 If A is B, G is not H : and if C is D, E is not F. 
 But either A is B, or C is D. 
 .-. Either G is not H, or E is not F. 
 
 One or two celebrated dilemmas of the ancients still retain 
 their fame as par excellence the classical examples of this argu- 
 ment. Of these, the best known is the ' Litigiosus.' It is re- 
 lated that Protagoras the Sophist agreed to train one Euathlus 
 in the art of rhetoric, the condition being that only half the fee 
 should be paid at the time : the payment of the remainder was 
 to depend onEuathlus's success in his first law-suit. Should he 
 fail, the fee was to be forfeited. Euathlus delayed to undertake 
 any suit, and eventually Protagoras himself summoned him 
 before the court. He urged the following dilemma against 
 him : 
 
 If this case is decided in my favour, you must pay me by 
 order of the court : if it is decided in your favour, you 
 must pay me under the terms of our agreement. 
 But it must be decided either in my favour, or in your favour. 
 .-. You are in any case bound to pay me. 
 
2T4 PRINCIPLES OF LOGIC 
 
 This argument was met by Euathlus as follows : 
 
 If the case is decided in your favour, I am free by the 
 terms of the agreement : if it is decided in my favour, I 
 am free by order of the court. 
 
 But it must either be decided in your favour, or in my favour. 
 .*. I am in any case discharged of my debt. 
 
 How this knotty question should be solved, is still dubious. 
 Perhaps, it should be said that this case was not contemplated 
 by the terms of the original compact, and should have been 
 dealt with independently of it. But various solutions to the 
 puzzle have been suggested. The judges, we are told, left the 
 case undecided. 1 
 
 1 For a list of the more famous of such dilemmas with references to the 
 authorities where they are found, vide Hamilton, Logic, I. 466. 
 
CHAPTER XIV. 
 
 INDUCTION. 
 
 i. The Nature of Induction. In the chapters on 
 the Categorical Syllogism, we dealt at some length with 
 the subject of deductive reasoning. We saw how it is 
 the process by which the mind passes from a general 
 principle to a particular case, which falls under that 
 principle. In order, therefore, to employ Deduction at 
 all, the mind must have reached the knowledge of some 
 universal truth. The question now arises, how do we 
 come to the knowledge of these general truths. We 
 must reply to this enquiry, by drawing a distinction, 
 between such as are analytic, and such as are synthetic 
 in character. The source of our universal analytic 
 judgments need cause us no difficulty. In these pro- 
 positions the necessary, and therefore universal, con- 
 nexion of subject and predicate, appears on the analysis 
 of the notions themselves. Every object of which the 
 subject can be affirmed, is necessarily such that of it the 
 predicate too can be affirmed. Thus, for instance, when- 
 ever we can term a figure a regular hexagon, we can 
 also affirm that each of its angles equals 120. It is 
 with the other class of general truths, with those namely 
 that are synthetic, that Induction, the subject of our 
 present chapter, is concerned. In these judgments 
 the predicate is found to belong to the subject not by 
 the analysis of the notions, but by experience. Induc- 
 tion is the legitimate derivation of universal laws from 
 individual cases. 
 
 Here, it at once appears, there is a problem for solu- 
 tion. Our experience is limited to a comparatively 
 
 215 
 
216 PRINCIPLES OF LOGIC 
 
 small number of individual cases. Yet in many instances, 
 we hold ourselves justified in asserting a universal law 
 of nature, which embraces not merely the cases we have 
 observed, but all other members of the same class. We 
 say that ' All diamonds are combustible/ ' All potassium 
 floats in water/ though in each of these cases the number 
 of instances observed is infinitesimal compared with 
 the full number of which the assertion is made. It 
 may even happen that the carefully tested observation 
 of a single case is held sufficient to justify a universal 
 conclusion of the kind to which we refer. 
 
 Every law of nature may be viewed as expressing a 
 relation of cause and effect. Now, when is it that after 
 the examination of a few instances in which a certain 
 effect is found to occur, we hold ourselves justified in 
 asserting a universal law attributing this effect to a 
 certain cause ? It is when we are certain that we are 
 giving the name of cause to that which is in fact the 
 reason of the effect, and not to some circumstance, which 
 although in these instances it is found in connexion 
 with the effect, is not itself the true reason why the effect 
 occurs. When we have discovered the precise quality 
 in virtue of which the effect is produced, we say with 
 confidence that, given these circumstances, this quality 
 will always have this same result. Thus to take a 
 familiar example, a few experiments with hydrogen and 
 oxygen satisfy us that these elements produce water, 
 not in virtue of anything peculiar to the individual 
 instances, but simply because of their character as 
 hydrogen and oxygen : and we have no hesitation in 
 holding that they will always produce water. 
 
 The logical process by which we pass to this universal 
 conclusion is purely abstractive. Should a result a be 
 produced, we endeavour to determine the particular 
 characteristic A, by which it is effected : and then 
 neglecting all that belongs to the instances simply as 
 individuals, we affirm that A as such produces a. This 
 is very different from saying that a concrete object, 
 which among many other qualities has the quality A 9 
 
INDUCTION 217 
 
 is the cause of a. For we abstract one quality, namely 
 A from all others, and we assert that it is from this that 
 a proceeds. But by the very fact that A is thus ab- 
 stracted, it is no longer conceived as individual : it is 
 the object of a universal concept. Our statement is 
 not that this particular A is the cause of a, but that the 
 nature A is such, that (given similar circumstances to 
 those under review), it has a as its effect. Thus in the 
 instance cited, we say that hydrogen and oxygen as 
 such produce water. This process is not ratiocinative. 
 We do not argue from premisses to conclusion. Our 
 work is done when we have separated the essential from 
 the non-essential, when we have discovered the true 
 causal relation. 1 
 
 The difficulty of Induction may therefore be said to 
 be practical rather than logical. The passage of the 
 mind from the data of sense to a universal principle, 
 does not admit a variety of forms, as does the syllogism. 
 But as the history of science may tell us, the discovery 
 of universal laws is no easy matter. The complexity 
 of the physical order is prodigious : the circumstances 1 
 which affect the operation of natural causes, are so 
 multifarious, and their accurate determination sur- 
 rounded by so many difficulties, that the progress of 
 human knowledge is slow, and its victories won at the 
 cost of prolonged toil. We may illustrate the diffi- 
 culties of determining a causal relation by an example. 
 Let us suppose that a certain herb produces favourable 
 results on patients suffering from a particular illness. 
 Can it therefore be assumed that the plant possesses 
 definite curative properties in regard to that illness ? 
 May there not be something peculiar to the constitution 
 of the patients in question, owing to which the result 
 
 1 Cf. Ueberweg, 129. " The formation of valid inductions is very closely 
 ' related to the formation of notions according to their essential attributes. . . . 
 ' For a great number of properties and relations stand in a causal nexus with 
 ' the essential attributes of the object of which the notion is formed : on this 
 ' causal nexus depends the validity of the induction. From this comes the 
 ' logical right to refer properties to the whole species which have been observed 
 ' in single individuals of a species, in so far as they are not evidently conditioned 
 ' by mere individual relations." 
 
2i8 PRINCIPLES OF LOGIC 
 
 is produced ? Even granted that it can be shewn that 
 in this region the results are invariably favourable, can 
 we be sure that the relation between the medicine and 
 the ailment would be the same in a different climate ? 
 Further, is the result due to the plant as such, or can 
 we discover some special constituent in it, to which and 
 to which alone the curative effect should be attributed ? 
 Even an example so simple as this, will suffice to show 
 us how difficult is the problem before us, when we 
 undertake to separate what is essential from what is 
 non-essential in a physical process. 
 
 It is often stated that Induction depends altogether 
 on the great principle of the Uniformity of Nature, to 
 the consideration of which our next chapter will be 
 devoted. This principle may be stated as follows : 
 
 All relations of cause and effect are constant and uniform ; 
 or in other words, The same cause will under the same 
 circumstances always produce the same effect ; and reci- 
 procally, effects of the same kind are the results of the same 
 cause. The logicians who tell us that Induction depends 
 on this principle, usually signify that it is actually em- 
 ployed in the inferential process by which we arrive at 
 our universal conclusion. They assert that the Uni- 
 formity of Nature is the major premiss of all Induction, 
 and that our conclusion is reached by a syllogism of 
 the following type : 
 
 Every relation of causality is constant. 
 
 A and a in the instances examined, are related as 
 cause and effect. 
 
 /. The relation between A and a as cause and effect 
 is constant. 1 
 
 It is easy to see that this explanation is erroneous. 
 The minor premiss in this syllogism is itself the statement 
 of a universal law. For if, when it is said that in the 
 instances examined A is the cause of a, it be still left 
 
 1 This formula is given by Rabier. He denies that it is strictly speaking 
 syllogistic, since the minor term is particular in the premiss, and universal 
 in the conclusion. This distinction, however, depends on the manner of formu- 
 lation. Logique, p. 149. Cf. Mill, Logic, Bk. III. c. 3, i. Bain, Induction, 
 c. a, I. 
 
INDUCTION 219 
 
 uncertain whether a was really due to A as such or to 
 some other circumstance peculiar to the individual 
 instance, we have no ground for a universal conclusion. 
 The meaning must therefore be that A as such is the 
 cause of a. But when this is asserted, we have already 
 left the individual instance far behind, and have by 
 abstraction reached our universal law. 
 
 The assertion that Induction depends on the Uniform- 
 ity of Nature may however be understood in another 
 sense. It may merely signify that in that principle, 
 we have the guarantee that our universal judgment 
 will be verified in fact. Our judgment that A as such 
 is the cause of a, would help us but little, unless we 
 further knew that in the real order the same cause does 
 actually always produce the same effect. The principle 
 corresponds to the logical process. Just as in our act 
 of abstraction we judge that the universal nature A is 
 intrinsically connected with a, so the metaphysical 
 principle assures us all A 's must produce the same effect, 
 whatever that may be. 
 
 Once again, it must not be thought that the principle 
 of Uniformity is the canon of Induction in the sense in 
 which the Dictum de Omni is the canon of deductive 
 reasoning. It does not reply to the question, How does 
 the mind pass to the conclusion that the nature A is 
 necessarily connected with the effect a ? ; but to the 
 question, Does the same real cause always produce the 
 same effect ? It belongs to a different order to the 
 order of things, and not to the order of thought. 
 
 2. Cause and Condition. The last section has shewn 
 us that every induction depends upon the accurate 
 determination of cause and effect. It is not possible to 
 lay down a universal law, until we have discovered the 
 precise nature of the relation in the case with which we 
 are dealing. Yet here a difficulty meets us. How can 
 we, considering the complexity of Nature, say what is 
 the cause of any phenomenon, and what is not ? As I 
 write at my table, can I really say what is the cause of 
 
220 PRINCIPLES OF LOGIC 
 
 the letters I form on the paper ? Am I the cause ? May 
 not the paper manufacturer, or the maker of pens, or 
 the carrier who brings me my materials, all claim to be 
 the cause ? Could I write, if it were not for the laws of 
 gravity ? Must we, in fine, own that it is a hopeless 
 task to fix on anything special, as the cause par excellence 
 of a certain effect, or is it possible to distinguish between 
 cause and condition ? 
 
 How are we to define a Cause ? Many and various 
 are the definitions offered us. One that is given by Dr. 
 Thomson (Laws of Thought, p. 218), seems to come very 
 near what we really signify by that term. " We mean," 
 he says, " by the cause of a thing, the sum of the facts 
 ' to which it owes its being." A definition practically 
 identical with this, was in fact frequently employed by 
 the Scholastics. But since this formula is, as will appear, 
 open to a certain ambiguity, it seems preferable to avail 
 ourselves of another expression having the same signifi- 
 cance, and define a cause as that which makes a thing to 
 be what it is. 1 
 
 Let us consider our definition as it is verified in the 
 four causes enumerated in Ch. 10, 2. Once again the 
 example of the statue will serve our purpose. Most 
 assuredly, we may say that (i) the final cause the 
 purpose for which the statue was carved has made it 
 what it is. Its special characteristics are determined 
 in reference to this. The statuary will make it in a 
 different manner, if he intends it to fill a niche over an 
 altar, and if he intends it to stand on a column fifty feet 
 high. Of (2) the efficient cause the statuary himself 
 it is hardly necessary to speak. Every detail of the 
 carving is his work. His brain conceived it ; and his 
 hand executed it. He too has made it what it is. Simi- 
 larly, in regard to (3) and (4), the intrinsic causes. If 
 made of a different material, it would be something 
 
 1 The cause is defined as ' Id quod influit esse in rent,' and as ' Id quo res 
 est id quod est.' The two definitions may be rightly regarded as equivalent ; 
 for that which makes a thing to be, is the same as that which makes it what 
 it is. No agent can be the cause of the existence, which is not also the cause 
 of the nature. 
 
INDUCTION 221 
 
 different from what we now see : while its dependence 
 on the formal cause is yet more intimate. Of the form, 
 even more than of the matter, may it be said that it 
 makes the statue what it is. 
 
 It is, of course, the case that in various ways, the 
 statue may be said to owe its being to other agencies. 
 A ship brought the marble from Italy ; an English 
 workman did the ' rough-nobbling/ Yet a very little 
 consideration will show us that there is a great difference 
 between the way in which the object owes its being to 
 the ship or to the skilled workman, and to the four 
 causes we have specified. Some other mode of convey- 
 ance might have been substituted for the ship, without 
 causing the least difference in the characteristics of the 
 statue. Granted that similar marble can be obtained 
 in England, the statue would be qualitatively identical, 
 whether the block came thence or from Italy. In other 
 words, in the case of the ship we have to do with an 
 agency which does not make the object what it is, which 
 exercises no determining effect on its special character- 
 istics. But to do this, is the distinctive mark of a cause : 
 there is not a single characteristic of the statue which 
 has not been received from one of its causes, and they 
 are its causes only in so far as they communicate these 
 characteristics to it. The ship is not a cause, but a 
 condition. A condition is that which in one way or another 
 enables the causes to act in the production of the effect, but 
 which does not make the thing what it is. 
 
 There is one special kind of condition, which merits 
 separate mention since the name of cause is often applied 
 to it. If, for instance, I strike a match, it is quite true 
 that the friction by which I light the flame, is a condition 
 rather than a cause. The same result might have been 
 produced in many ways a sure sign that the effect 
 does not owe its characteristics to those of the action in 
 question. Heat, percussion, the application of certain 
 chemical agents would have had the same result. My 
 action merely put the forces, that were present in the 
 match, in the state required for the exercise of the causa- 
 
222 PRINCIPLES OF LOGIC 
 
 live powers they possessed. Yet undoubtedly this act 
 has a special character, since it communicated the impulse, 
 which set free these forces. Other conditions may be 
 requisite for one reason or another ; but they do not, 
 as does this one, set in motion the whole process. They 
 are in no sense the origin of the effect. In virtue of this 
 originative character, a condition, such as this, is not 
 without reason known as the determining cause (causa 
 determinants). 1 
 
 3. The Aim of Inductive Enquiry. It may be asked, 
 which of the various causes we have enumerated, is the 
 object of inductive investigation. To this it must be 
 replied, that it is not in all cases the same. Sometimes 
 the knowledge of one cause, sometimes that of another, 
 is important to us ; and very frequently it happens, 
 that Nature has only put the knowledge of one cause 
 within our reach. As Professor Case has well put it, 
 " Man has to fasten on Nature as best he can. He 
 ' knows more about present facts than about past causes : 
 ' and when he knows causes, it is sometimes the efficient 
 ' cause, as in the mechanics of the forces by which bodies 
 ' act on one another : sometimes the material cause, 
 ' as when the chemist knows the elements out of which 
 ' a body is composed, without having discovered the 
 ' force of chemical affinity so-called, by which they 
 ' compose it : sometimes again the final cause, as in 
 ' morals, where we know for what end we act, without 
 ' fully understanding the voluntary, nervous, and mus- 
 ' cular forces by which we perform our actions." * 
 
 Often indeed, what we wish to discover is the deter- 
 mining cause. For instance, it had long been known 
 that in unisexual plants, fertilization takes place by the 
 communication of pollen from one plant to another. 
 But the method of communication remained a problem 
 for science to resolve, till the determining cause was 
 discovered in the insects that pass from one plant to 
 
 1 De Regnon, Metaphysique des Causes, pp. 129, 207, 596. 
 
 8 Lectures on the Method of Science (ed. by T. B. Strong), p. 5. 
 
INDUCTION 223 
 
 another. When our search is motived by a practical 
 end, the knowledge of the determining cause may be of 
 far greater moment to us than that of the causes properly 
 so-called : for what we desire to know is not so much 
 the inner nature of the phenomenon, as how to bring it 
 about, or how to prevent it. Thus, for instance, if we 
 desire to prevent the spread of some epidemic, to increase 
 the productivity of soil, etc., etc., in all such cases, it is 
 the determining cause, rather than any other, which is 
 the object of the scientist's search. 
 
 Colloquially, the word cause is used in a loose sense. 
 It may be applied to any one of the antecedent conditions, 
 in the absence of which the event would not have taken 
 place, and on which for some reason it may be desirable 
 to lay stress. We say that the construction of a railway 
 in the neighbourhood, is the cause of the increase in the 
 value of land. But the mere construction of the railway 
 would not in itself increase the value, unless the railway 
 were such as to bring the neighbourhood into connexion 
 with some populous centre. Inductive enquiry is not 
 concerned with causes in this popular sense : and we 
 must be on our guard against confusing the word as 
 thus colloquially employed, with its more accurate 
 signification. It is the failure to draw this distinction, 
 which alone has given plausibility to the erroneous 
 assertion contained in not a few works on Logic, that 
 there is no difference, scientifically speaking, between 
 cause and condition. 
 
 4. Recognition of the Causal Relation. The pre- 
 ceding sections have, it is hoped, given the reader a 
 clear notion as to the object of inductive investigation. 
 We must now examine the way, in which the mind recog- 
 nizes a relation between a cause and its effect. 
 
 There are certain cases, in which this recognition is 
 easy, and after considering a few concrete cases of the 
 causality in question, we are able without hesitation 
 to abstract the relation ; and thus from the particular 
 instances, induce a general proposition. We say ' a 
 
2i 4 PRINCIPLES OF LOGIC 
 
 few cases,' for ordinarily a single instance leaves us in 
 doubt, whether there may not be some error in our 
 observation. Were we convinced that we had avoided 
 this danger, one instance would suffice us. 1 It is an 
 induction of this kind, if, for instance, I see the impression 
 made by my foot on the sand, and judge that as often 
 as a human foot is pressed on this yielding material it will 
 make a mark like this : and conversely, that such a mark 
 must be the effect of a human foot. I do not pass to my 
 conclusion by a syllogism. I see my foot make and leave 
 its impression : and my mind recognizes the relation 
 between the shape of the foot as cause and the shape of 
 the impression as effect. In the knowledge of this causal 
 relation it has the ground for a universal conclusion. 
 Robinson Crusoe, like other men, had formed this induc- 
 tion. So when he saw the footprints on the shore, he knew 
 for certain that there was another man on the island. 
 
 We are often able to understand the nature of the 
 causal relation the reason why such an effect should 
 follow from such a cause, even when the action is of a 
 less simple character than in the case just described. 
 The cause of malarial fever long escaped observation 
 because of its minuteness. But as soon as its origin 
 was discovered in a special microbe, and the activity of 
 this microbe in the body had been studied, the nature 
 of the relation which united the malady and its cause 
 was evident. When it was known what havoc this 
 minute creature worked among the blood-corpuscles, 
 it immediately became evident how the illness followed 
 from its cause. Here too, the mind abstracts the rela- 
 tion, and induces a universal law that wherever this 
 cause operates, this effect must follow. 
 
 1 " Great scientists rarely mistake the worth of a significant fact, though 
 ' only occurring once. It is said that Sir C. Bell would not repeat the famous 
 ' experiment that established the difference between the motor and sensory 
 ' nerves, so much did his feelings recoil from causing animals to suffer. . . . 
 ' The Abb Haiiy lets fall a piece of quartz, and merely by observing the 
 ' fracture, he concludes that he has discovered a law of nature. ... So in 
 ' a thousand cases. The knot then is not in the repetition itself, but in the 
 ' fact of the coincidence : only the repetition evidently adds much to the 
 ' value of the coincidence." Janet, Final Causes (English trans.), p. 431, 
 
INDUCTION 225 
 
 Yet there are a vast number of cases, in which we 
 can see no reason why a particular effect should follow 
 rather than some other, and in which therefore the causal 
 relation cannot be recognized, as it is recognized in these 
 examples. This is especially noticeable in regard to 
 physical constituents, considered as the cause of the 
 resulting compound. There is no resemblance between 
 hydrogen and oxygen on the one side, and water on the 
 other. The properties of the effect bear no likeness to 
 the properties of the cause. Again, we cannot hope to 
 discover any reason to account for the properties possessed 
 by the different natural substances. Why, for instance, 
 should galena crystals be cubical while quartz crystallizes 
 in hexagonal prisms ? Why should gold resist the 
 action of solvents, which are efficacious against other 
 metals ? Why should sulphur, when heated, first liquefy, 
 then thicken, and then liquefy again ? In all these 
 cases, our experience assures us as to the fact of the rela- 
 tion. But why such a cause should produce such a 
 result, remains altogether concealed from us. We must 
 be content to know the bare fact that such and such 
 things are causes of such and such effects. We analyse 
 water, and hydrogen and oxygen are found : we syn- 
 thesize hydrogen and oxygen, and the result is water. 
 
 In saying that our knowledge in these cases relates 
 not to the reason of the causal connexion but to the fact, 
 we must not be thought to mean the singular fact as 
 perceived by sense. The fact here is recognized by the 
 intellect. In the singulars which sense perceives, the 
 intellect recognizes and abstracts the universal rela- 
 tion. 
 
 In thus determining experimentally a causal connexion, 
 it is usually the case, even more than where the nature 
 of the causal relation is recognized, that a number of 
 experiments is necessary, before the law is looked on as 
 established. But here too the repetition is not itself 
 part of the logical process. It is preliminary to it. It 
 is merely a guarantee that we have not been deceived 
 in the nature of the experiment. If for instance we 
 
 Q 
 
226 PRINCIPLES OF LOGIC 
 
 suppose the experiment to be the synthesis of hydrogen 
 and oxygen, with a view to establishing for the first 
 time the universal truth that these are the causes of 
 water, we should repeat the experiment under a variety 
 of circumstances, in order to satisfy ourselves that no 
 other ingredient but hydrogen and oxygen was present 
 in our synthesis, that the result was not due to something 
 peculiar to the individual case. When once we are satis- 
 fied that the fact is as we conceive it, then we proceed 
 to our induction. We induce from the securely estab- 
 lished fact that in such and such concrete cases water 
 has been produced from these elements, a universal 
 conclusion. We assert that hydrogen and oxygen are 
 causally related to water ; and the assertion is made, 
 not of the individual particles of hydrogen and oxygen 
 with which we experimented, but of hydrogen and oxygen 
 as such, of these elements viewed in abstraction from 
 individualizing conditions. 
 
 The value of the instances to produce conviction will 
 depend almost entirely on the intellect which considers 
 them. Evidence which to the untrained mind has no 
 meaning, will reveal with certainty a universal law to 
 one who is already versed in the subject under considera- 
 tion. An investigator of this kind sees the evidence in 
 the light of a hundred facts previously known. He 
 may recognize that the suggestion contained in the 
 evidence, is precisely what these facts would lead him 
 to expect, or he may see that either it or they must be 
 false. The manifestation of the universal law by the 
 particular case, cannot be made to depend altogether 
 on the nature of the evidence. It depends also on the 
 mind to which it is presented. What is sufficient for 
 the mind well stored with knowledge is insufficient for 
 the tyro. 
 
 It will follow from what has been said that it is impos- 
 sible for us to give a canon or a series of canons, which 
 shall be to Induction what the Dictum de omni is to 
 Deduction. We can do no more than describe in general 
 outline the principal ways in which evidence of a causal 
 
INDUCTION 227 
 
 connexion presents itself, and thus to indicate what may 
 be termed methods of inductive enquiry. This subject 
 however does not belong to Logic strictly so called, but 
 to the Method of Science : for the logical ground of the 
 induction is not altered by the different manner in which 
 the evidence appears. We shall therefore defer its 
 consideration to the second part of this work. 
 
 To sum up, Induction is not a syllogistic, but a purely 
 abstractive process. It becomes possible as soon as we 
 see in the individual instance (or instances) of the cause 
 in question, that the effect is not due to some accidental 
 circumstance, but that it belongs essentially to the type. 
 And this is known either (i) by rational insight into the 
 nature of the connexion between cause and effect, or 
 (2) by rational recognition of the fact of the causal 
 connexion. 
 
 * The induction of the universal from the particular in the 
 manner we have described, is succinctly taught by Aristotle, 
 An. Post. /., c. 31. 
 
 "It is owing to our inability to apply our senses, that certain 
 ' questions remain unsolved. For could we but see what takes 
 ' place, we should not still be seeking a solution. Not indeed 
 ' that the mere act of sight would give us scientific knowledge ; 
 ' but sight would be the means through which we should attain 
 ' the universal. Thus if we saw the perforations in the glass, 
 ' and the light-particles coming through, the cause of its illuminat- 
 ' ive power would be manifest. Sense would perceive the in- 
 ' dividual instance, and the intellect would recognize that this 
 ' was a universal law." 
 
 In this passage Aristotle should not be understood as approv- 
 ing the theory of light which he mentions. He uses, as is his 
 wont, a contemporary opinion as an illustration. 
 
 A similar passage occurs An. Post. II., c. i, 4. 
 
 In the well-known chapter An. Post. II., c. 19 he treats the 
 case in which we draw our universal conclusion from the observ- 
 ation of a number of particulars. The memory of many in- 
 dividual instances constitutes, he tells us, one Experience (e/ATreipt'a) : 
 this Experience results in the possession of an abstract universal 
 principle in the mind. Since the passage itself is so compressed 
 as to stand in need of some exposition, we prefer to give in 
 its place the lucid commentary of St. Thomas : 
 
 " Ex memoria multoties facta circa eandem rem in diversis 
 tamen singularibus, fit experimentum : quia experimentum nihil 
 
228 PRINCIPLES OF LOGIC 
 
 aliud videtur, quam accipere aliquid ex multis in memoria re- 
 tentis. Sed tamen experimentum indiget aliqua ratiocinatione 
 circa particularia, per quam confertur unum ad aliud, quod est 
 proprium rationis. Puta cum talis recordatur quod talis herba 
 sanavit multos a febre, dicitur esse experimentum quod talis 
 herba sit sanativa febris. Ratio autem non sistit in experimento 
 particularium : sed ex multis particularibus in quibus expertus 
 est, accipit unum commune quod firmatur in anima, et con- 
 siderat illud absque consideratione alicujus singularium, et hoc 
 accipit ut principium artis et scientiae. Puta diu medicus con- 
 sideravit hanc herbam sanasse Socratem febrientem, et Pla- 
 tonem et multos alios singulares homines : cum autem sua 
 consideratio ad hoc ascendit, quod talis species herbae sanat 
 febrientem simpliciter, hoc accipitur ut quaedam regula artis 
 medicinae. . . . Posset autem aliquis credere quod solus sensus 
 vel memoria singularium sufficiat ad causandum intelligibilem 
 cognitionem principiorum, sicut posuerunt quidam antiqui non 
 discernentes inter sensum et intellectum : et ideo ad hoc ex- 
 cludendum Philosophus subdit, quod cum sensu oportet prae- 
 supponere talem naturam animae quae posset pati hoc, id est 
 sit susceptiva cognitionis universalis " (An. Post. II., lect. 20). 
 The reader will observe that in these passages no use is made 
 of the term Induction. The word experimentum (e/xTrei/na) 
 takes its place. 
 
 5. The Inductive Syllogism. The Inductive Syllogism 
 is a special mode of arguing from the particular to the 
 general, different from Induction properly so-called. 
 The principle of this method of inference is that an 
 attribute which is affirmed (or denied) of all the logical 
 parts, may be affirmed (or denied) of the logical whole. 
 The validity of the argument depends on our certainty 
 that we have overlooked no one of the parts. Hence 
 this mode of reasoning is only available for the cases in 
 which we are dealing with the several species of a genus. 
 The individuals belonging to a species cannot be counted : 
 their number is indefinite. 1 But the species are always 
 limited in number. 
 
 The syllogism may be represented by the following 
 formula : 
 
 1 Aristotle held the number of individuals in a species to be infinite. Hence 
 when he tells us that the enumeration of the parts must be complete, he evi- 
 dently supposes that we are dealing with species, not with individuals. 
 
INDUCTION 229 
 
 S p S 2y S 3 are P. 
 S lt S 2 , 5 3 alone are M 
 .-. All M is P. 
 
 The conclusion here is represented not as in the formula 
 of the deductive syllogism ' All S is P,' but as ' All M 
 is P.' For the purpose of this syllogism is to establish 
 the general proposition, which in the deductive syllogism 
 stands in the major premiss. Hence Aristotle calls it 
 an argument by which we prove the major term to be true 
 of the middle term, by means of the minor term (An. Prior. 
 //., c. 23). This method of proof is not infrequently 
 employed by Euclid, when he establishes his proposition 
 for the separate cases, in which the supposition he makes 
 can be realized. The twentieth proposition of his third 
 book is of this character : its conclusion may be expressed 
 as an Inductive syllogism : 
 
 The angle at the circumference of a circle is half the 
 size of the angle at the centre on the same arc, (i) when 
 the centre of the circle is within the angle at the circum- 
 ference, (2) when it is on one of its sides, (3) when it is 
 outside of it. 
 
 But these three cases are the only cases in which it is 
 possible to have an angle at the centre and an angle at 
 the circumference on the same arc. 
 
 .-. The angle at the circumference is always half the 
 size of the angle at the centre on the same arc. 1 
 
 An Inductive Syllogism, if we do no more than shew 
 that P is found in each of the logical parts severally, 
 does not give us a universal proposition in the full and 
 complete sense of the word. It does not show us that 
 there is a law connecting M with P : for the reason why 
 P belongs to the several parts of M may be different 
 in the different cases. It is an Enumerative judgment, 
 though one valid of an indefinite number of individuals. 2 
 
 1 Cf. Ueberweg, 128. 
 
 2 Aristotle points out its enumerative character in An. Post. /., c. 5. He 
 supposes the case of a man who has proved of the equilateral, the isosceles, 
 and the scalene separately, that the interior angles of each are equal to two 
 right angles. This man, he says, cannot be really said to know that all tri- 
 angles, as such, have this attribute. " ov ykp 77 rplywvov ol6ev t oti5 TTP 
 
230 PRINCIPLES OF LOGIC 
 
 In order that it should be more than this, it would be 
 necessary to shew that the reason for the inherence of 
 P is the same in regard to all the parts of M. 1 
 
 The example of this Syllogism, given by Aristotle has often, 
 owing to the brevity of its expression, caused some perplexity. 
 It is as follows : 
 
 Man, horse, ass ... are long lived. 
 
 Man, horse, ass . . . are animals without bile. 
 
 /.All animals without bile are long lived. 2 
 
 The example at first sight presents two considerable difficul- 
 ties. In the first place the minor premiss as it stands, is mani- 
 festly untrue. In the second place, a complete enumeration 
 of animals without bile, would appear impossible. As a matter 
 of fact, by the expression ' without bile,' Aristotle doubtless 
 signifies that the animals in question have no excess of choleric 
 humours a different thing from being totally without bile. 3 
 Further the assertion should be understood, not of animals in 
 general, but of the more highly organized animals : for in An. 
 Post. II., c. 17, 7 he restricts it to quadrupeds. Thus a com- 
 plete enumeration would not present insuperable difficulties. 
 
 In another passage Aristotle gives the following, as exemplify- 
 ing an inductive argument : " If we know that the skilful steers- 
 ' man is best, and the skilful driver, and so on, we may conclude 
 ' that the man who is skilful is best at every occupation." 4 But, 
 it would be misleading to employ this here as an illustration. 
 For it is given as an example of dialectical argument, in which 
 demonstrative certitude being unattainable, we must be con- 
 tent with probabilities. It is by no means intended as a typical 
 instance of the argument in its perfect form. 
 
 rpiywvov, d\\' ^ /car' aptdfj-bv ' KO.T 'elSos 8' otf irav." I.e. 5. (" For he does 
 ' not know the attribute to belong to the triangle, as such : nor does he know 
 ' it to belong to all triangles, except in so far as ' all ' is understood of mere 
 ' numerical reckoning. He does not know it to be a property of the species.") 
 He describes this proof ( i) as that which occurs " orav rvyx^-g 8" ws tv /xe/> 
 6\ov ^0' $ deiKwrai." (" When it happens that our proof concerns a whole, 
 not as a whole, but in its logical parts.") 
 
 1 Euclid is generally able to do this. The proposition may require different 
 constructions : but the same proof mutatis mutandis is ordinarily employed. 
 
 2 An. Prior II., c. 23, 2 ; cf. An. Post. II., c. 17, 7 ; DePart. Anim.IV., c. 2. 
 8 The reader will not need to be reminded of the importance attached in 
 
 ancient physiology, to the four humours, on which the temperament of the 
 individual sanguine, choleric, melancholic, or phlegmatic was held to de- 
 pend. Of this doctrine Wundt says, " Psychology borrowed the doctrine of 
 * the four temperaments from the medical system of Galen. And though the 
 ' theory of the humours, which was its physiological basis is now obsolete, 
 yet the distinction of the temperaments seems to have been derived from 
 'acute psychological observation," Psychologic, III., 637. 
 4 Topics, I., c. 12. 
 
INDUCTION 231 
 
 The Inductive Syllogism resembles a syllogism in 
 Fig. 3 with a universal instead of a particular conclusion. 
 This is legitimate, since the enumeration is known to 
 be complete. The minor is sometimes expressed in the 
 form ' S t , S 2 , 5 3 are all M.' This form is however inad- 
 missible. It suggests that the significance of the copula 
 here is different from its ordinary import : that it 
 means ' S 19 S 2 , S 3 constitute Af/ J If this were the 
 meaning, the conclusion would be illegitimate. M would 
 be used collectively in the minor premiss, and distribut- 
 ively in the conclusion. 
 
 6. Perfect and Imperfect Induction. The term Per- 
 fect Induction is employed to signify the process by 
 which we affirm a given attribute of all the individuals 
 belonging to a class, and then proceed to affirm it of 
 the class as a whole. Thus I may assert of each of the 
 apostles taken separately, that he was a Jew, and so 
 pass to the general proposition, ' All the apostles were 
 Jews/ The process may, of course, be drawn up in the 
 form of an Inductive Syllogism. But it differs widely 
 from it. The enumeration there is of logical parts. 
 It is an intellectual process : for it is not by sense-per- 
 ception that we sum up the equilateral, the isosceles 
 and the scalene as completing the list of possible triangles. 
 But in Perfect Induction the enumeration is purely 
 sensible. It is a simple counting of heads. Further, 
 the conclusions obtained are of different value the one 
 from the other. A general proposition obtained by 
 Perfect Induction is a mere summary ; and though 
 inferences may be drawn from it, yet this general pro- 
 position presupposes the knowledge of every so-called 
 conclusion. On the other hand the conclusion of an 
 Inductive Syllogism is true of an indefinite number of 
 individuals, and affords us a solid basis for inference to 
 new facts. 
 
 When we draw a universal conclusion after enumerat- 
 ing some members only of a class, we are said to employ 
 
 1 Hansel, Aldrich, App. G- 
 
232 PRINCIPLES OF LOGIC 
 
 Imperfect Induction. A conclusion drawn in this way 
 is of such a precarious character as to be valueless, unless 
 we have grounds for supposing some causal connexion. 1 
 But if we have reason to believe the attribute to be 
 causally connected with the subject, we are relying on 
 something else than mere enumeration. It may illus- 
 trate how liable to frustration are conclusions drawn in 
 this manner, if we remember how at one time, experi- 
 ence seemed to indicate that all bodies expand under 
 the influence of heat, and contract when exposed to cold. 
 Numbers of cases had been examined in which the rule 
 was verified, though no reason could be assigned why 
 it should be so. As we are well aware, exceptions are 
 found to this rule. Water expands instead of contract- 
 ing, when it fails below 39*4 F. ; and similarly, india- 
 rubber, clay and certain other substances, contract 
 under the influence of heat. Had a universal conclu- 
 sion been drawn in this case by Imperfect Induction, it 
 would have proved false. 
 
 * It is commonly stated in English text-books of Logic, that 
 the Scholastic philosophers knew of no inductive process save 
 Perfect and Imperfect Induction, and that they believed that 
 our certainty as to the laws of nature, was based on mere enu- 
 meration. We have already had occasion to point out how 
 cautiously we should receive what our popular logicians say of 
 Scholastic philosophy. It may indeed be owned that the subject 
 of Induction received far less attention from the mediaeval 
 writers than it merits. Yet to say that they believed our know- 
 ledge as to the laws of nature, to rest on a process of Imperfect 
 Induction by mere enumeration, argues a remarkable want of 
 acquaintance with their writings. There is indeed a considerable 
 variety of opinion among the Scholastics on this subject. But 
 
 1 This point is forcibly put by Leibniz. " Nam si universalia nihil aliud 
 sunt quam singularium collectiones, sequetur scientiam nullam haberi per 
 demonstrationem (quod et infra colligit Nizolius) sed collectionem singular! um 
 seu inductionem. . . . Certitude perfecta ab inductione sperari plane non 
 potest, additis quibuscunque adminiculis, et propositionem bane Totum 
 magis esse sua parie sola inductione nunquam perfecte scimus. Mox enim 
 prodibit, qui negabit ob peculi arena quandam rationem in aliis nondum ten- 
 tatis veram esse, quemadmodum ex facto scimus Gregorium a S. Vincentio 
 negasse totum esse majus sua parte, in angulis saltern contactus : alios in 
 infinite : et Thomam Hobbes (at quern virum ?) coepisse dubitare de pro- 
 positione ilia Geometrica a Pythagora demonstrata, et hecatombae sacrificio 
 digna habita : quod ego non sine stupore legi." Leibniz, De Stilo Philosophico 
 
INDUCTION 233 
 
 the more eminent amongst them base our certainty in regard 
 to natural laws on the principle, that when the operation of 
 some natural agent produces regularly and habitually some par- 
 ticular result, this result is not due to an accidental circumstance, 
 but is an effect having for its cause the specific nature of the 
 agent. In other words, they held the enumeration of instances 
 to be of value, inasmuch as it enables the investigator to judge 
 that the phenomenon a is really connected with the nature 
 A, and not merely with some circumstance incident to this 
 individual instance of A . The instances thus understood, do not 
 constitute the premisses of a universal conclusion. They are 
 the condition of our act of abstraction, ' A as such is followed 
 by a.' Anything more remote than this from the doctrine 
 which is usually asserted to have been held by the whole body 
 of Scholastic philosophers, can hardly be imagined. 
 
 The error seems to have arisen from the fact that the most 
 famous of the Scholastics (St. Thomas, Albert the Great, Scotus) 
 do not employ the term Induction as the distinctive name of 
 the inference by which we establish universal laws of nature. 
 Following the terminology of Aristotle, noticed at the end of 
 4, they call it the proof from experience (e/x7rei/oia, experimentum, 
 experientia). The significance of the term Induction was some- 
 what vague. It covered all argument from the particular to 
 the general. Hence (as e.g. in Scotus, An. Prior II., Q. 8) it might 
 include this meaning among others. But it was more usually 
 employed to denote the formal process of Perfect Induction 
 arranged as an Inductive Syllogism. Moreover it was some- 
 times pointed out, that our argument might be thrown into the 
 form of an Inductive Syllogism : for though the enumeration 
 was incomplete, yet in these few instances we have equivalently 
 seen all. It was by a later generation that the term Induction 
 was restricted to its present signification. Incautious readers, 
 finding in certain passages the Inductive Syllogism described as 
 the formula of inductive argument, jumped too hastily to the 
 conclusion that the mediaeval philosophers rested their know- 
 ledge of the laws of nature on no basis but enumeration. 
 
 We have already cited St. Thomas on this subject, in 4. 
 The reader will see that his words imply the view we have here 
 taken. The following brief extracts will show that the position 
 of Albertus Magnus and of Scotus was the same as that of St. 
 Thomas. " [Propositiones] experimentales autem sunt quas 
 accipimus intellectu orto ex sensu, sicut scimus . . . quod 
 scamonea purgat choleram et quod vinum inebriat : sensus 
 enim apprehendit inebriationem post potationem vini saepius 
 
 Nizolii, Op. phil. (Erdmann), p. 70. Leibniz's own view wc*ild seem to have 
 been that criticized in i above, according to which the uniformity of Nature 
 is a major premiss in a syllogistic reasoning. 
 
234 PRINCIPLES OF LOGIC 
 
 factam, et percipit intellectus quod hoc vini virtute accidit : 
 et si esset casuale non contingeret saepissime : et sic in intellectu 
 generatur illius rei scientia firma, de qua non est dubium," Alb. 
 Mag. An. Post. I., Tract i, c. 2. " Quamvis sentire non est 
 scire, nee universale est sensibile, sicut in ante habitis dictum 
 est, sed sensibile per abstractionem fit universale, quod in nobis 
 est principium scientiae." An. Post. II., Tract i, c. 3. 
 
 Scotus writes as follows, " De cognitis per experientiam dico 
 quod licet experientia non habeatur de omnibus singularibus, 
 sed de pluribus, nee quod semper sed quod pluries, tamen ex- 
 pertus infallibiter novit quod ita est, et quod semper, et in om- 
 nibus : et hoc per istam propositionem quiescentem in anima : 
 Quidquid evenit ut in pluribus ab aliqua causa non libera, est 
 effectus natumlis illius causae." I. Sent. Dist. 3, q. 4, n. 9. 
 Cf. also De Regnon, Metaphysique des Causes, pp. 40-54. 
 
CHAPTER XV. 
 
 THE UNIFORMITY OF NATURE. 
 
 i. The Uniformity of Nature. In this chapter we 
 consider the principle of the Uniformity of Nature, or 
 as it is sometimes termed, the Uniformity of Causation. 
 That principle, as we saw in the preceding chapter, 
 assures us that the same cause will, under the same cir- 
 cumstances, always produce the same effect : and that 
 effects of the same kind are to be referred to the same 
 cause. It was further pointed out that this principle 
 is not a logical principle. It belongs to the real order : 
 it tells us about the nature of things, not about the way 
 in which we think and reason. Yet Logic can scarcely 
 be adequately treated without discussing it. It is insuffi- 
 cient to show how the general proposition ' A as such, 
 is the cause of a,' is abstracted from the particulars of 
 experience, unless we also show that in the order of 
 reality, Nature prescribes that given A, a shall follow. 
 
 The principle as we have enunciated it, must be under- 
 stood with a qualification. It refers exclusively to the 
 material universe governed by natural laws. Hence 
 it can claim no higher degree of necessity than belongs 
 to the constitution of this natural order. The Power 
 which established the universe can suspend the opera- 
 tion of its laws, and bring it about that a given cause 
 shall produce an abnormal effect, or no effect at all. 
 This is expressed in Scholastic philosophy by saying 
 that the principle of Uniformity is physically necessary, 
 not metaphysically. 
 
 We propose in the following paragraphs to explain 
 (i) the reasons which justify us in holding that the uni- 
 formity of Nature is physically necessary ; and (2) the 
 
 136 
 
236 PRINCIPLES OF LOGIC 
 
 limits of physical necessity, and the grounds it affords 
 for scientific certainty. 
 
 (i) It will be remembered that when we considered 
 the distinction between cause and condition, we saw that 
 all the properties of the effect come to it from one or 
 other of its causes. The Hermes of Praxiteles could 
 never have possessed its beauty of form, had not Praxi- 
 teles conceived that form in his imagination : it would 
 never have possessed the durability which has preserved 
 it to our own days, had its material cause been clay and 
 not marble. The connexion between cause and effect 
 is not a mere time sequence of antecedent and consequent. 
 We can find in the cause the reason of every characteristic 
 that the effect possesses : and it is by the action of the 
 cause that they are all communicated to the effect. 
 
 It is further manifest that every agent acts according 
 to its nature, and can act in no other way. When we 
 see the young cuckoo appear in the nest of the starling, 
 we never dream that it is the starling's offspring. We 
 do not gather grapes from thorns : and we should regard 
 a man as eccentric, to say the least, who told us that 
 he saw no reason why such things should not occur. 
 Bos locutus est in foro, says Livy : but even he regarded 
 it as a portent. The active powers are proportioned 
 to the nature of the agent : they are in fact the 
 connatural expression of that nature. Indeed we 
 only know the permanent nature through the mani- 
 festation of its active powers. The nature or essence 
 for nature is but another term for essence is the prin- 
 ciple which determines the character of these powers. 
 Moreover unless an agent possesses free-will, it must 
 act in a manner not merely in accordance with its nature, 
 but absolutely prescribed by that nature. It cannot 
 give what it has not : it must give what it has. This 
 does not mean that it will act in the same way in every 
 variety of circumstances in which it may be placed. 
 The action involves a relation to the object acted on, and 
 hence depends not merely on the agent but on the 
 patient. But it does involve that where the relation 
 
THE UNIFORMITY OF NATURE 237 
 
 of the agent to its surroundings is the same, there (unless 
 it be miraculously impeded) its action will be the same. 
 Thus the very concept of a natural agent devoid of free- 
 will, involves that under the same circumstances, its 
 action will be of the same kind : and precisely similar 
 considerations show that similar effects must be referred 
 to causal agencies of the same kind. In other words 
 the truth of the principle is evident from its terms. 1 
 
 (2) In order to deal with the question of the limits of 
 physical necessity, we must touch on a matter which 
 belongs properly to Natural Theology, viz. : the relation 
 of the First Cause to the created universe. The very 
 notion of a First Cause involves as its consequence that 
 He is not merely the cause of all things as regards their 
 origination, but that He continually sustains them in 
 being. Their persistence in being is, as it were, a con- 
 tinued creation. Were the conserving action of the 
 First Cause withheld they would fall back into nothing- 
 ness. This, moreover, holds good not merely in regard 
 to the existence of creatures, but to all exercise of active 
 power on their part. In acting, a creature obtains a 
 further realization of itself an extension of its being. 
 Hence as the First Cause is the ground of all reality, He 
 must needs be the fountain of all activity. No exercise 
 of causality can take place, save in so far as He com- 
 municates the power to act. He must concur in every 
 action. Without this concurrence, neither spiritual nor 
 material agents could perform any of those actions which 
 are connatural to them. Apart from this concurrence 
 the mind could not think nor could one body act upon 
 another. Again, the First Cause may confer on one of 
 these agents some new active power enabling it to produce 
 higher results than its natural endowments could effect. 
 From this it follows that though we may say truly that 
 the same cause must in like circumstances always pro- 
 
 1 Cf. St. Thomas, Summa Theol., Q. 41, Art. 2. "Effer+us assimilatur 
 formae agentis per quam agit. Manifestum est autem quod unius rei non 
 est nisi una forma naturalis per quam habet esse. Unde quale ipsum est, 
 tale facit." 
 
238 PRINCIPLES OF LOGIC 
 
 duce the same effect, the necessity of this principle is 
 hypothetical necessity. It supposes the First Cause to 
 preserve the ordinary operation of natural laws. 
 
 It has occasionally been asserted that to admit the 
 possibility of any interference in regard to the laws of 
 Nature, is to render the principle of Uniformity nugatory. 
 The objection might have weight if we represented the 
 Deity as interfering capriciously with these laws. So 
 far however is this from being the case, that the regu- 
 larity of Nature's order is recognized in Scholastic treatises 
 on Natural Theology as a mark of Supreme Wisdom. 
 This very regularity affords man a guide without which 
 he could not direct his life with a view to the future. 
 It is one thing to own that the Deity has power to suspend 
 His own laws, and that occasionally He does in fact sus- 
 pend them, when the striking manifestation of His power 
 may be for man's good. It is a very different thing to 
 hold that a capricious suspension of law is at any moment 
 likely to occur. In the long run, it is better that the 
 stern regularity of law should train men to rule Nature 
 by obeying her, than that they should constantly be 
 able to obtain exceptions in their favour. 
 
 We have asserted that there is a higher kind of neces- 
 sity than belongs to physical law. This is termed meta- 
 physical necessity. It is not like physical necessity, 
 hypothetical, but absolute. In it there is no scope for 
 miraculous intervention. Axioms such as the principle of 
 Causality that Whatever comes into being must have a cause, 
 and the principle of Contradiction that, It is impossible for 
 a thing both to be and not to be at the same time, together with 
 all the truths of Mathematics possess this higher degree 
 of necessity. What, it may be asked, justifies the dis- 
 tinction ? The answer must be that these principles 
 are metaphysically necessary, because they are altogether 
 independent of any physical process. In some cases we 
 see that certain concepts statically considered, stand in 
 a relation of identity (or difference) under pain of a con- 
 tradiction in terms. To assert that the same thing can 
 at the same time both be and not be, is to assert what is 
 
THE UNIFORMITY OF NATURE 239 
 
 self-contradictory, in other words, meaningless. In other 
 cases a causal relation is involved in the very nature of 
 the abstract concept, apart from any dynamic efficiency. 
 This is exemplified in the case of geometrical figures and 
 their resultant properties. A figure which has three 
 sides must of necessity have three angles. Here no 
 physical activity is in question, and consequently the 
 cause produces its effect by an absolute, and not a 
 merely hypothetical necessity. Where no physical pro- 
 cess is involved, to suppose a cause without its connatural 
 effect, is to suppose a contradiction : and even divine 
 power cannot produce what is self-contradictory. 
 
 Since the principle of uniformity is evident from the 
 mere consideration of the concepts involved, it might 
 seem that we possess in it an analytical proposition, yet 
 one which differs from other analytical judgments in 
 being liable to frustration. Undoubtedly an analytical 
 proposition can be framed regarding the uniformity of 
 Nature. But this proposition must express the condition 
 which we have just noticed, and it will take the form : 
 ' A natural agent devoid of free-will, granted the normal 
 concurrence of the First Cause,, must in similar circum- 
 stances always produce the same effect/ The principle 
 thus enunciated possesses the absolute necessity belonging 
 to all analytical judgments. The necessity of the laws 
 of nature themselves is not absolute but hypothetical. 
 
 It may perhaps be urged that if the truth of the princi- 
 ple were thus readily apparent, it would be more univers- 
 ally recognized as necessarily valid. Yet savages look for 
 capricious action on the part of natural phenomena, 
 and children recognize the truth of the multiplication 
 table more easily than that of this principle. To this it 
 may be replied that even where analytical principles are 
 concerned, not all are immediately self-evident. Every 
 conclusion in pure mathematics is analytical : yet many 
 of these are unintelligible to the untrained mind. To real- 
 ize the necessary character of the principle in question, 
 we must see what is involved in the concept of a natural 
 agent devoid of free-will. The untutored mind, anthropo- 
 
240 PRINCIPLES OF LOGIC 
 
 morphic in all its representations, is apt to attribute 
 free-will not merely to animals but even to the powers 
 of Nature. In so far as children and the uneducated 
 do as a matter of fact expect the same cause to act in 
 the same way, this may be attributed partly to the 
 influence of experience, and partly to the growing capa- 
 city to distinguish between the free and the determined 
 agent. 
 
 We have throughout treated both parts of the prin- 
 ciple, alike that which asserts that similar causes produce 
 similar effects, and that which asserts that similar effects 
 are to be referred to similar causes, as equally valid. 
 Philosophically this is so. But it must be borne in mind 
 that not uncommonly the object of scientific search is 
 a determining cause, and not a cause properly so called. 
 Moreover agents altogether diverse may possess some 
 similar characteristic in virtue of which they produce 
 similar effects. Here strictly speaking the same cause 
 is operative in all. But in common parlance, we speak 
 of the effect as due to different causes. 
 
 A few lines should perhaps be added as to the exception made 
 in regard to the will of man. On what grounds, it may be asked, 
 is the exception made ? If all action depends on the nature of 
 the agent, must not human action do the same ? Each man 
 has his own character partly inherited, partly the result of his 
 past life. Will not the character of his act depend on the cir- 
 cumstances in which he is placed ? If we make an exception 
 here, are we not arguing altogether arbitrarily ? 
 
 It would, of course, be out of place to enter on the subject of 
 free-will in a logical text-book. It must suffice to point out that 
 our argument is only valid for such agents as, ex hypothesi, are 
 not free. To extend it to the human will without first discover- 
 ing whether that will be free or not, would be arbitrary. It 
 would be to prejudge the whole case. We cannot argue from 
 the mode in which natural agents act to the mode in which the 
 will acts. For the human soul is unlike them. It is spiritual, 
 and the mode of its action must be discovered by an appeal to 
 the testimony of consciousness, and not by a mere analogy 
 drawn from natural agents. 1 
 
 1 On Free-Will see Maher's Psychology, c. xix., pp. 394-424. 
 
THE UNIFORMITY OF NATURE 241 
 
 2. J. S. Mill on the Uniformity of Nature. Mill, of 
 all logicians, is the one who has devoted most attention 
 to the enquiry into the process, by which the mind comes 
 to know laws of nature. He recognizes that apart 
 from a belief in the uniformity of causation, such know- 
 ledge is impossible, and makes this principle the founda- 
 tion of all inductive inference. Thus, he tells us (Logic, 
 Bk. III., c. 3, i) "We must first observe that there is 
 ' a principle implied in the very statement of what Induc- 
 tion is . . . namely that what happens once, will under 
 ' a sufficient degree of similarity of circumstances happen 
 'again'' ; and he says (ibid.) "Every induction may be 
 ' thrown into the form of a syllogism, by supplying a 
 ' major premiss. If this be actually done, the principle 
 ' which we are now considering, that of the uniformity 
 ' of the course of nature, will appear as the ultimate 
 ' major premiss of all inductions." 
 
 In the present section, we shall deal shortly both with 
 his explanation of the principle, and with his account 
 of the manner in which we arrive at a knowledge of 
 it. His theory is, of course, based on the Empiricist 
 philosophy, of which he was a leading exponent. 
 
 He terms the principle the Law of Causation, and tells 
 us that it is " the truth, that every fact which has a 
 
 * beginning, has a cause " (c. 5, i). But in the following 
 section he enunciates it more fully, thus : " The law of 
 ' Causation ... is but the familiar truth, that invari- 
 ' ability of succession is found by observation to obtain 
 ' between every fact in nature, and some other fact 
 ' which has preceded it ... the invariable antecedent 
 
 * is termed the cause : the invariable consequent the 
 ' effect " (ibid. 2). 
 
 The explanation which Mill gives to the principle rests 
 entirely on the meaning which he attaches to the terms 
 ' cause ' and ' effect.' 
 
 The causal relation, as conceived by him, is totally 
 different from the account we have given of that relation 
 in the last chapter. According to his view, the whole 
 question is one of succession in time, of before and 
 
 R 
 
242 PRINCIPLES OF LOGIC 
 
 after. The cause does not exert any influence on the 
 effect. He expressly desires that the causes treated of 
 by him, should not be viewed as possessed of efficiency : 
 " the causes with which I concern myself, are not efficient 
 ' but physical causes " (ibid. 2). He finds fault with 
 the Greek philosophers, because " they wished to see 
 ' the reason why the physical antecedent should produce 
 ' this particular consequent . . . they were not content 
 ' merely to know that one phenomenon was always 
 ' followed by another " (ibid. 9). A cause in fact, in 
 no wise differs from a condition : " The cause, philoso- 
 phically speaking, is the sum total of the conditions, 
 ' positive and negative, taken together . . . the negative 
 ' conditions may be all summed up under one head, 
 ' namely, the absence of counteracting causes " (ibid. 
 3). Yet it should be carefully noted that mere in- 
 variability of succession is not sufficient to constitute 
 a relation of causality, unless the succession is also 
 unconditional, that is to say, unless it would take place 
 whatever supposition we may make in regard to all 
 other things : " Invariable sequence is not synonymous 
 with causation, unless the sequence, besides being invari- 
 able, is also unconditional." 
 
 There are various points in this account which call 
 for criticism : 
 
 (i) The reduction of efficient causality to a mere 
 time-relation, is totally contrary to reason. Reason 
 tells us that a thing which begins to exist, cannot possibly 
 have its existence from itself, it cannot be self-created ; 
 hence it must receive existence from something else. 
 That this must be so appears plainly, if it be remembered 
 that before a thing exists, it is nothing ; and what is 
 nothing cannot give itself existence. Hence, everything 
 which comes into being, must have, not a mere ante- 
 cedent in time, but an efficient cause which is the reason 
 why it exists. In one case alone is there no need of an 
 efficient cause, namely in the case of the First Cause, 
 Who has never come into being, but has existed from all 
 eternity. 
 
THE UNIFORMITY OF NATURE 243 
 
 (2) The identification of cause and condition is inad- 
 missible. We have dwelt at length on the difference 
 between these two (Ch. 14, 2), and it is unnecessary to 
 discuss the point again. It is clear that any account 
 of causation, which fails to distinguish them, must be 
 fundamentally misleading. 
 
 (3) The theory is inconsistent with itself. On the 
 one hand the relation between cause and effect is reduced 
 to succession in time. On the other, we are told that 
 we must be cognizant of the unconditional character of 
 the connexion, i.e. that it will take place, whatever suppo- 
 sition we choose to make about other things. It is, 
 however, evident, that if we are able to affirm that the 
 connexion is ' unconditional/ we must know of some 
 bond linking the consequent to the antecedent, some 
 reason why this consequent must follow this antecedent, 
 and that we have passed far away from a mere record 
 of sequences. 
 
 (4) Another inconsistency is to be found in his de- 
 scription of the cause as the ' invariable antecedent/ 
 This can only mean, that whenever a particular effect 
 occurs, it is always the result of the same cause. But 
 such a view contradicts a doctrine, on which Mill lays 
 great stress, that of the plurality of causes. "It is 
 'not true," he tells us, "that the same phenomenon is 
 'always produced by the same cause : the effect a may 
 ' sometimes arise from A sometimes from B. . . . Many 
 ' causes may produce motion : many causes may produce 
 'death/' 
 
 The doctrine of the plurality of causes is, of course, 
 due to the fact that Mill's theory did not admit of his 
 distinguishing between determining causes, and causes 
 properly so called. 
 
 (5) Finally, it should be noticed that he has confused 
 two entirely distinct principles, (a) the principle of cau- 
 sality that everything which begins to be must have an 
 efficient cause ; and (b) the principle of uniformity. The 
 latter includes in its reference all cause?, efficient, formal, 
 material, final. Each one of these will, under similar 
 
244 PRINCIPLES OF LOGIC 
 
 circumstances, produce the same effect. The former 
 relates expressly to efficient causation. There is no 
 need for a thing, which begins to be, to have an antecedent 
 material cause. Were it so, either creation could never 
 have taken place, or matter must have always existed. 
 
 We must now consider Mill's account of the grounds, 
 on which we accept this principle, ' the major premiss 
 of all induction/ in virtue of which our knowledge as 
 to the laws of nature is based on something firmer than 
 simple enumeration. It is evident that an empiricist 
 philosopher cannot, as we have done, base it on the 
 nature of things. To this school, the sole sources of 
 knowledge are individual sense-experiences ; and a 
 general truth does but summarize a number of such 
 experiences. 
 
 The Uniformity of Nature, Mill tells us, is itself dis- 
 covered " by the loose and uncertain method of simple 
 'enumeration " (Ch. 21, 2). The principle is, he holds, 
 gathered from a number of particular uniformities 
 observed in nature, which justify us in regarding the 
 law as of universal application. But before the estab- 
 lishment of the wider principle, these particular uni- 
 formities, on which it was based, had not the same 
 certainty as now belongs to laws of nature. For since 
 they could not receive confirmation from the principle 
 of uniformity, antecedently to its establishment they 
 were merely based on the enumeration of instances. 
 
 Mill recognizes that he will be accused of inconsistency 
 in thus first contrasting the uncertainty of simple enu- 
 meration, with the certainty derived from the principle 
 of uniformity, and then teaching that the former is the 
 foundation of the latter : and it certainly looks as if he 
 were building an immoveable house on a moveable 
 foundation. But he argues that the inconsistency is 
 only apparent, because the uncertainty of simple enumera- 
 tion is due to the possibility that the empirical law 
 which our observations establish, may be true only 
 within certain limits of place, time and circumstance. 
 
THE UNIFORMITY OF NATURE 245 
 
 Where the subject-matter of a generalization is so wide 
 " that there is no time, no place, and no combination 
 * of circumstances, but must afford an example of its 
 ' truth or falsity, and it be never found otherwise than 
 ' true," then we may regard the generalization in question 
 as possessing all the force of a scientific law. 
 
 Few thinkers now attempt to defend this theory. 
 Two points in it call for special notice : 
 
 (1) Unless the uniformity of nature be already pre- 
 supposed, how can we be sure that any of the particular 
 uniformities, on which it is based, have any right to that 
 name ? We may, for instance, regard it as a case of 
 such a uniformity that hemlock is poisonous. The evi- 
 dence, on which we rely, is the effect produced by the 
 plant on a number of individual men. But in estimating 
 the evidence, unless we rely on the general principle, 
 what guarantee have we that the poisoning was not due 
 to different causes in the different cases, although the 
 symptoms were so similar. To prove the principle, even 
 on Mill's own shewing, we must presuppose it. 
 
 (2) Human experience has extended over a minute 
 portion of space, through a few thousands of years, and 
 the records of that experience are fragmentary and some- 
 times uncertain. If our grounds for holding the prin- 
 ciple of uniformity be nothing more than the imperfectly 
 recorded successions observed by men on this one small 
 planet, it is as insecurely based as ever was an induc- 
 tion by simple enumeration. Indeed, Mill himself owns 
 that he sees no reason why the law should hold good ' in 
 'distant parts of the stellar regions ' (Ch. 21, 4). Pre- 
 cisely the same reasons would suggest that we have no 
 satisfactory grounds to rely on it for any time beyond 
 the present. 
 
 It is worth noting that some Empiricists boldly renounce all 
 attempt to prove this principle. Thus Bain, Deductive Logic, 
 App. D, "The fact generally expressed as Nature's Uniformity 
 ' is the guarantee, the ultimate major premiss of all Induction. 
 ' . . We can give no evidence for this uniformity." So Hux- 
 ley, Life of Darwin, II., p. 200, " The one act of faith in the con 
 
246 PRINCIPLES OF LOGIC 
 
 ' vert to science, is the confession of the universality of order, 
 ' and of the absolute validity, in all times and at all places, of 
 ' the law of causation. This confession is an act of faith, be- 
 ' cause by the nature of the case, the truth of such proposition^ 
 ' is not susceptible of proof." To adopt this attitude, is to 
 renounce the hope of finding any secure basis for physical science. 
 Well might Bain speak of it as " the leap in the dark." 
 
 One or two terms employed by Mill in his discussion of this 
 question should be observed, as they are occasionally employed 
 by others also. The intermixture of effects occurs when two or 
 more causes combine to produce a complex effect. Sometimes 
 this joint effect is of the same kind as the separate laws. This 
 constitutes the Composition of Causes ; and the effect is called 
 a Compound Effect. Sometimes as in chemical compounds 
 the effect is totally unlike the causes. This is called Combina- 
 tion of Causes, and the effect, a Heteropathic Effect. 
 
 3. " Cessante causa, cessat effectus." If it can be 
 
 shewn that cause and effect are ever absolutely contem- 
 poraneous the one with the other, it is evident that a 
 theory, which reduces the causal relation to mere time- 
 sequence must fall to the ground. Hence, Mill is led 
 to devote some space (Ch. 5, 6) to the discussion of this 
 possibility. He quotes against himself the Scholastic 
 saying " Cessante causa, cessat effectus (When the cause 
 ceases to operate, the effect ceases)/' 1 and says, " the 
 ' necessity for the continued existence of the cause to 
 ' the continuance of the effect, seems to have been a 
 ' once generally received doctrine. . . . Yet there 
 ' were at all times many familiar instances of the con- 
 ' tinuance of effects long after their causes had ceased. 
 ' . . . A ploughshare once made remains a ploughshare, 
 ' without any continuance of heating and hammering, 
 ' and even after the man who heated and hammered 
 ' it, has been gathered to his fathers." This criticism 
 is indicative of the temper in which Mill approached the 
 consideration of any Aristotelian doctrine. It never 
 seems to have occurred to him, that he must have failed 
 to understand the meaning of the axiom, and that in 
 
 1 Vide Arist., Met. V., c. 2, and Phys. II. , c. 3, 13, and St. Thomas's com- 
 mentaries on these two passages. 
 
THE UNIFORMITY OF NATURE 247 
 
 the absurd sense which he attributed to it, it could not 
 have been a dogma of the schools. 
 
 A review of its true meaning will help us in the further 
 elucidation of the causal relation. Let us take Mill's 
 own example of the ploughshare, and consider what 
 part the various causes hold in regard to it. 
 
 The efficacy of two among the causes the final and 
 the efficient ceases, as soon as the thing is made. It 
 becomes what it is through them. But as soon as we can 
 say of it that it is, it depends on them no longer : their 
 work is at an end. On the other hand, the material and 
 formal causes are what make it to be a ploughshare. 
 Had it been made not of iron, but of some yielding sub- 
 stance, it would not be a ploughshare at all ; and if it 
 should be melted down and lose its shape, it would 
 cease to be one. 
 
 We have then two kinds of cause the Causa in fieri 
 (Cause of becoming) and the Causa in esse (Cause of 
 being), each with its own proper effect. If either of 
 these two causes ceases to operate, its effect ceases. 
 This does not mean that when the smith dies, the plough- 
 share ceases to be : for the smith is not, as we have said, 
 the cause of its being. He is, strictly speaking, only 
 the cause of the change, by which the iron is transformed 
 into the new shape. If, while the change is going on, 
 he ceases to exercise his causality, the process of change 
 stops. But when he has done his task, it remains : for 
 it is no longer in a transition state. It is an existing 
 thing, and depends on other causes. 
 
 There are causes which may be said to be at one and 
 the same time causa in fieri and causa in esse to their 
 effects. Thus the sun both calls into being and sustains 
 in being the ray of light which proceeds from it : and 
 the pressure of the atmosphere both causes the mercury 
 to ascend in the exhausted tube, and sustains it in that 
 position. Yet these instances are useful chiefly as illus- 
 trations. The effects in question are mere accidental 
 modifications. No created cause is both causa in fieri 
 and causa in esse to any complete entity ; and this fact 
 
248 PRINCIPLES OF LOGIC 
 
 reveals to us that created agents realize but in an im- 
 perfect manner the full concept of a cause. On the 
 other hand the great First Cause God Himself is 
 alike causa in fieri and causa in esse to the whole universe. 
 He called it into being, and sustains it in every instant 
 of its existence. To imagine otherwise would be to 
 imagine that it could possess existence in its own right, 
 and not as an effect communicated from Him. 1 
 
 Each effect then is dependent on the cause which 
 produces it, in so far as they are related as cause and 
 effect. If the cause ceases to exercise its causality, the 
 effect no longer takes place. This does not imply that 
 cause and effect are one and the same. We call atten- 
 tion to this, unnecessary as it may appear to do so, for 
 such a view seems to be implied by the words of certain 
 recent writers. It is plain that if cause and effect are 
 the same, then the effect, if it be caused at all, must be 
 caused by itself a supposition that is self-contradictory. 
 Further, not only are the two distinct, but though the 
 action of the cause is contemporaneous with the effect, 
 yet the efficient cause itself must be prior to the effect. 
 The cause must exist before it can act. 
 
 * 4. Unity of Nature. The principle which we have termed 
 the Uniformity of Nature, is by some logicians spoken of as the 
 Unity of Nature. This name is preferred by those adherents of 
 the Idealist philosophy, who form what is called the Neo-Hegelian 
 School. The name Unity of Nature, is regarded by these writers, 
 as better indicating the reason why, in our experience, things 
 appear as governed by uniform laws and as conforming to uni- 
 form types. The most eminent exponent of the Neo-Hegelian 
 doctrine was the late Prof. T. H. Green : and it is his teaching 
 on the point that we shall have in view in the present section. 
 
 1 Cf. St. Thomas, Summa Theol, I.,Q. 104, Art. i, " Omnis effectus dependet 
 a sua causa secundum quod est causa ejus. Sed considerandum est quod 
 aliquod agens est causa sui effectus secundum fieri tantum, et non directe 
 secundum esse ejus : quod quidem convenit in artificialibus et in rebus naturali- 
 bus. Aedificator enim est causa domus quantum ad ejus fieri, non autem 
 directe quantum ad esse ejus. . . . Sicut igitur fieri rei non potest remanere, 
 cessante actione agentis quod est causa effectus secundum fieri : ita nee esse 
 rei potest remanere cessante actione agentis quod est causa effectus non solum 
 secundum fieri, sed etiam secundum esse. . . . Ideo Augustinus dicit ' Virtus 
 ' Dei ab eis quae creata sunt regendis si cessaret aliquando, simul et illorum 
 ' "essaret species, omnisque Natura concideret.' " 
 
THE UNIFORMITY OF NATURE 249 
 
 The Idealist school, as we have already noted, does not ad- 
 mit the difference between thought and reality. Its defenders 
 hold it as indubitable, that we know nothing save what is within 
 us, and that all the objects of our experience are states of our 
 own consciousness. Further, not merely are the objects of 
 knowledge within the mind, they are also the work of the mind. 
 Apart from the activity of the spiritual principle which we term 
 mind or intellect, there could be nothing in our consciousness 
 save transitory sensations. It is the intellect, and the intellect 
 alone, which transforms what in themselves are simply subjective 
 feelings into an orderly world of matter and motion. 
 
 The objects of knowledge, it is urged by Prof. Green, them- 
 selves testify to their intellectual origin. If we ask of ourselves, 
 in what any object really consists, we shall find that it is wholly 
 constituted by relations ; " Abstract the many relations from 
 1 the one thing, and there is nothing. They being many, deter- 
 1 mine and constitute its definite unity. It is not the case that 
 * it first exists in unity, and then is brought into various rela- 
 ' tions. Without the relations it would not exist at all " (Green, 
 Prolegomena, 28). Now relations are essentially the work of 
 the mind : as relations they can only exist for a mind, and in 
 a mind. For every relation involves the mystery of the many 
 in one, a mystery that is inexplicable, unless we admit that 
 it is mind which thus unites them. Thus two entities united 
 by a relation of succession, in so far as they are related, exist 
 not successively but together i.e. in a mind. " Of two objects 
 ' which form the terms of a relation, one cannot exist as so related 
 ' without the other, and therefore cannot exist before or after 
 ' the other. For this reason the objects between which a relation 
 ' exists, even a relation of succession, are just so far as related 
 ' not successive. In other words a succession always implies 
 ' something else than the terms of a succession . . . which can 
 ' simultaneously present to itself objects as existing not simultane- 
 'ously, but one before the other" (ibid. 31). 
 
 The question now arises, what can be the meaning of the 
 distinction, which men are accustomed to make between the 
 real and the unreal ? The unphilosophic mind is apt to hold 
 that the unreal and the real, fancy and fact, are distinguished 
 as being the one the work of the mind, the other possessed of 
 an independent existence of its own. This distinction is now 
 seen to be untenable. For on the one hand, the real itself con- 
 sists but in relations, which are themselves mental ; on the 
 other the ' unreal ' if it be really the work of the mind, consists 
 equally in relations, and has no less a claim to be looked on as 
 real (ibid. 12). Is then the distinction drawn by common- 
 sense wholly without meaning ? No. " If from the futile 
 ' question, What is the real ? which we can only answer by saying 
 
250 PRINCIPLES OF LOGIC 
 
 ' that the real is everything, we pass to one more hopeful 
 ' How do we decide whether any particular event or object is 
 ' really what it seems to be ? ... the answer must be, that 
 ' we do so by testing the unalterableness of the qualities which 
 'we ascribe to it." 
 
 Reality then consists in a certain ' unalterable set of relations,' 
 by which the spiritual principle within us constitutes the objects 
 of our experience. But to say that the mind organizes our ex- 
 perience in unalterable relations, is to say that Nature is governed 
 by uniform laws. The uniformity of Nature is therefore involved 
 in the very difference between reality and unreality, and is thus 
 a postulate of all knowledge. " That there is an unalterable 
 ' order of relations ... is the presupposition of all our enquiry 
 'into the real nature of appearances " (ibid. 26). It is thus 
 seen that the uniformity of the world as known by us, is due 
 to the unity of the spiritual principle which constitutes it. Hence 
 the expression Unity of Nature may justly be looked on as more 
 philosophic than the commoner phrase Uniformity of Nature. 
 
 In all this there is not a little which calls for criticism. The 
 theory we have summarized contains, we believe, several funda- 
 mental errors. It is based on three main positions : (i) that 
 relations can only have a mental existence, (2) that individual 
 objects consist solely in relations, and (3) that the real differs 
 from the unreal as being an unchangeable, as contrasted with 
 a changeable, order of relations. We shall examine these points 
 in succession. Grave objections may be urged against each of 
 them. 
 
 (1) It is true, as Prof. Green points out, that relations involve 
 the mystery of the many in one. A relation is a link, a bond 
 of connexion : it is according to the old definition " an order 
 ' that holds between one thing and another (or do unius ad aliud)." 
 There is in every relation a unity of the manifold, a multiplicity 
 of that which is one. We may freely own that this is inexplicable 
 without a combining intelligence : and yet we may deny alto- 
 gether that the ordered entities must needs exist only in an 
 intelligence. When things are united by a relation of succession, 
 the mind which thus related them, must indeed have grasped 
 them in a single thought : but as regards their own existence, 
 they are not simultaneous but successive. All the motions in 
 the working of a watch, are related to each other. Yet these 
 motions do not exist simultaneously : they follow each other. 
 Although therefore the world of our experience is bound by a 
 myriad relations, this lends no support to the theory that it 
 exists only in and for a mind. It merely proves that it owes 
 its origin to an intelligent First Cause. 
 
 (2) It is difficult to understand how it can be maintained 
 
THE UNIFORMITY OF NATURE 251 
 
 that an individual consists solely in relations. The accuracy 
 of the definition of relation as ' an order holding between one 
 thing and another ' can, we think, hardly be disputed. The 
 intelligence recognizes that this, and nothing else, is what it 
 means by relation. Now the entities which are thus connected, 
 are not themselves connexions. They are substances or quanti- 
 ties or qualities. It is true that every substance and every attri- 
 bute is, for one reason or another, bound by relations to others. 
 It is related as agent to patient, as patient to agent, as similar, 
 as antecedent, as consequent and so on. But it is not con- 
 stituted by the relations. On the contrary its own distinctive 
 character is the ground of these relations. Had it not certain 
 characteristic qualities, there could be no relations. To empty 
 all the other categories of being and to reduce everything to 
 relation, is as unphilosophic as is the Empiricist doctrine which 
 admits no reality save sensation alone. 
 
 (3) The question at issue as to the distinction between the 
 real and the unreal, is misstated by Green, owing to his Idealist 
 assumptions. He has, of course no difficulty in showing that 
 a thought even if it be erroneous, is a real thought : and from 
 this he concludes that the figments of the imagination and er- 
 roneous judgments are " as real as anything else " (op. cit. 22). 
 But this conclusion is only valid on the hypothesis that the 
 conceptual order embraces all existence. And this has never 
 been proved, and cannot be proved. On the contrary it is an 
 hypothesis which is contrary both to reason and to the testimony 
 of our cognitive faculties. These alike testify to the existence 
 of a twofold order, the real and the conceptual. And when men 
 speak of a judgment or an imagination as ' unreal,' what they 
 mean is, that though the objects represented exist in thought, 
 yet in that real order which thought should represent, there is 
 nothing to correspond to these creations of the mind. 
 
 We conclude therefore that the Idealist theory of an unalter- 
 able order of relations breaks down at every point, and affords 
 us no means whatever by which we may account for the Uni- 
 formity of Nature. Idealism no less than Empiricism leaves 
 physical science destitute of any basis. 
 
CHAPTER XVI. 
 
 ENTHYMEME : SORITES : ANALOGY. 
 
 i. Enthymeme. The fundamental methods of infer- 
 ence have now been discussed. The forms of argument 
 with which we are concerned in this chapter, do not 
 exhibit any new process of the mind. All save one, viz. : 
 Analogy, are purely syllogistic : and Analogy is resolvable 
 into an induction followed by a deduction. Yet because 
 the structure of these forms differs in certain particulars 
 from the standard type, it is convenient to treat them 
 in a separate chapter. 
 
 An Enthymeme is a syllogism, abridged by the omission 
 of one premiss or of the conclusion. The Enthymeme 
 is the usual manner in which syllogistic reasoning is 
 verbally expressed. It has already been pointed out 
 that, though we think in syllogisms, whenever we reason 
 from a general principle to a special case, yet we do not 
 ordinarily express each of the three constituent judg- 
 ments. We are usually satisfied when our words are 
 sufficient to bring our meaning home to our hearers 
 with clearness and precision : and this can be done by 
 employing the Enthymeme in lieu of the fully-stated 
 syllogism. We have only to read any page of reasoned 
 thought, to assure ourselves that the shorter form is 
 employed more frequently than the longer and complete 
 form. Indeed it is precisely this fact, which rendered 
 necessary the section on the expression of arguments in 
 syllogistic form (Ch. 12, 3) . It is plain, therefore, that the 
 distinction between the Enthymeme and the Syllogism 
 is purely one of language, and in no sense one of thought. 
 
 According as omission is made of the major premiss, 
 the minor premiss, or the conclusion, the Enthymeme 
 
ENTHYMEME : SORITES : ANALOGY 253 
 
 is said to be of the first, second or third order. The 
 following brief examples are given by Hamilton : 
 
 The Syllogism. Every liar is a coward. 
 
 Caius is a liar. 
 /. Caius is a coward. 
 
 Enthymeme of the First Order. Caius is a liar. 
 
 /. Caius is a coward. 
 
 Enthymeme of the Second Order. Every liar is a coward. 
 
 .*. Caius is a coward. 
 
 Enthymeme of the Third Order. Every liar is a coward. 
 
 Caius is a liar. 
 
 The Enthymeme of the third order, which merely 
 states the premisses, and leaves it to the hearers to 
 draw the conclusion, is indeed often far more effective 
 rhetorically, than the explicit syllogism would be. 
 
 Similar omissions may be made in the hypothetical 
 syllogism. Our meaning is abundantly clear when we 
 say, ' He will see the notice in the Times ; so he will 
 hear of something to his advantage/ even though we do 
 not insert the hypothetical major implied. Hence, we 
 may have Enthymemes of the three orders in these 
 syllogisms also. 
 
 * 2. The Aristotelian Enthymeme. By Aristotle the term 
 Enthymeme is used in a different sense. It is, he tells us, ' a 
 rhetorical syllogism ' (Rhet., I., c. 2, 8). He recognized that 
 though the processes of reasoning are always fundamentally the 
 same, yet the manner in which we apply them, will differ greatly 
 according to the class of questions treated. " An educated 
 'man," he says at the commencement of the Ethics, " will always 
 ' look for just so much precision of argument as the matter in hand 
 'admits." Some account therefore of this ' rhetorical syllogism ' is 
 desirable in Logic, if only that we may see how, even when 
 demonstrative reasoning is impossible, its place is filled by some- 
 thing closely analogous. 
 
 The perfect syllogism is the method of reasoning appropriate 
 to science. Scientific conclusions are worthless, unless we can 
 appeal to some indubitable and universal principle. In any 
 other case, they would not carry conviction. But in rhetoric 
 our object is not primarily to convince the mind, but to sway 
 the will. Hence when the orator appeals to a principle, it is 
 
254 PRINCIPLES OF LOGIC 
 
 sufficient for him if it is verified in the majority of cases, and 
 so affords a reasonable motive to his audience for coming to the 
 decision he desires. Where such principles are not to be had, 
 the orator points to some fact, which may serve as a sign or 
 evidence that his view is correct. Nor does he usually trouble 
 himself to secure anything resembling conclusive proof. 
 
 The Enthymeme, therefore, is defined as a syllogism from 
 likelihoods or signs. 1 The likelihood is a proposition, which is 
 usually true, and thus affords a basis for a probable conclusion. 
 An instance of such an argument is to be found in a well-known 
 clause in the will of the late Mr. Cecil Rhodes : 
 
 Those who live secluded from the world are as children in 
 
 business affairs. 
 Resident fellows of colleges live secluded from the world. 
 
 .. They are as children in business affairs. 
 
 A piece of reasoning, which would not preclude some fellows 
 of colleges from being highly capable in such matters. 
 
 The sign is some fact, which affords evidence either for the 
 truth of some general principle or for the existence of some other 
 fact. The argument here may fall into any figure of the syllo- 
 gism, and is of very different value in the different cases, (a) If 
 the sign is an effect of the fact in question, and an infallible 
 indication of its presence, the syllogism is in Fig. i, and is 
 perfectly conclusive. 
 
 Wherever there is smoke, there is fire. 
 That house is giving out smoke (s). 
 
 .-. That house contains a fire. 
 
 (ft) The sign maybe an individual instance (or instances), from 
 which we conclude to the existence of a general law, e.g. ' The 
 wise are good, for Pittacus is good.' This is in fact a syllogism 
 in Fig. 3, and if analysed, is seen to be of this form : 
 Pittacus is good (s). 
 Pittacus is wise. 
 
 .-. The wise are good. 
 
 The argument is invalid, since there is an illicit process of the 
 minor. The legitimate conclusion is only that ' Some wise men 
 are good.' We meet with this argument, when we are told that 
 ' Hume, Reid and Hamilton were Scotsmen, and therefore Scots- 
 men in general are metaphysicians.' 
 
 (y) When the argument from the sign falls into the second 
 figure, it is of less value still ; since the premisses do not justify 
 even a particular conclusion. For instance, 
 
 Murderers tremble in the presence of the murdered man, 
 This man trembles in the presence of the murdered man, 
 
 /. This man is the murderer. 
 
 1 'Ei'flifywj/ia fj.tv o5v eori ffv\\oyi<r/JL6s 4 elxdruv r) o"r)fj.eiuv (An. Prior II., 
 C. 27, 2>. 
 
ENTHYMEME: SORITES: ANALOGY 255 
 
 In countries where it is the custom to confront the suspected 
 man with the body of the victim, this particular Enthymeme 
 still appears to carry some weight. 
 
 The etymological meaning of the word ' enthymeme ' would 
 seem to be 'the result of an act of reflection.' It is used to 
 signify a thought suggested by a person or thing. 1 Hence, as 
 Mansel says, " the term is naturally enough applicable to the 
 ' suggestions or persuasive arguments of rhetoric, as distin- 
 ' guished from the demonstrations of science." How it ceased 
 to bear this meaning, and was employed by logicians to signify 
 the abbreviated syllogisms considered in i, is not so clear. 
 Possibly the explanation may be found in a passage, in which 
 Aristotle says that, if one of the premisses is well known to the 
 audience, the orator should omit that premiss. 2 
 
 3. Chains of Reasoning. In any sustained argu- 
 ment, the syllogisms form a connected series, the conclu- 
 sion of one being used to form the premiss of another. 
 When this occurs, we are said to have a chain of reasoning, 
 or as it is sometimes called a Polysyllogism. The syllo- 
 gism, whose conclusion becomes the premiss of the other, 
 is termed the Prosyllogism : the name of Episyllogism 
 is given to that which borrows its premiss from the other. 
 Should three syllogisms be thus connected, the second 
 is an episyllogism as regards the first, a prosy llogism in 
 relation to the third. 
 
 The following poly syllogism may serve as an example. 
 
 (1) Those who prefer the greater to the lesser good, are wise. 
 Those who sacrifice temporal things to gain eternal, prefer 
 
 the greater to the lesser good. 
 
 (2) /. Those who sacrifice temporal things to gain eternal, 
 
 are wise. 
 
 The martyrs were men who sacrificed temporal things 
 to gain eternal. 
 
 (3) /. The martyrs were wise. 
 
 The eighteen Carthusians were martyrs. 
 .'. The eighteen Carthusians were wise. 
 
 In this instance, it is the major premiss which is in 
 each case supplied by the Prosyllogism. The following 
 
 1 Sophocles, Oed. Col. 292, 1199, vide Mansel, Aldrich., p. 216. 
 
 1 TO 5t tv6ti/j.T}fji.a, 0-uAXoytoTids, (cat ^ 6\iywi> re xal TroAAa/a? e\a.Tr6vuv ?) ^ 
 &v o Tr/xSros (Ti/AAoyttr /u,6s * &v y&p rj n TOIUTUV yvd)ptfj.ov, ou8 Set X^yetr avrbs 
 yap TOVTO irpoo-Tldrjaiv 6 eUpoctT^s (Rhet. I., c. a, 13). 
 
256 PRINCIPLES OF LOGIC 
 
 example illustrates the case in which the minor premiss 
 is the one to be borrowed : 
 
 (1) All acts of aggression are unjust. 
 
 Napoleon's campaign against Russia was an act of ag- 
 gression. 
 .-. Napoleon's campaign against Russia was unjust. 
 
 (2) All unjust acts deserve to fail of their intention. 
 
 Napoleon's campaign against Russia was unjust. 
 .'. Napoleon's campaign against Russia deserved to 
 fail of its intention. 
 
 In each of the previous examples, we have proceeded 
 from the prosyllogism to the episyllogism ; and conse- 
 quently we have a Progressive reasoning. But it often 
 happens that another method is adopted. The final 
 conclusion is first stated ; the premisses, which establish 
 it, are then given as reasons ; and the proof of these 
 premisses follows in a similar fashion. Such a mode 
 of stating an argument is termed Regressive. Thus : 
 
 (1) Logic is deserving of study : for, 
 
 All the sciences are deserving of study, 
 And Logic is a science. 
 
 (2) Now, All the sciences are deserving of study : for, 
 Whatever assists to perfect the intellect is deserving of 
 
 study, 
 And all the sciences assist to perfect the intellect. 
 
 4. Epichirema. A syllogism is termed an Epi- 
 chirema, when to one or both of its premisses is annexed 
 a reason in support of it. Thus : 
 
 Whatever is spiritual is immortal ; for it is incapable of cor- 
 ruption. 
 
 The human soul is spiritual. 
 .*. The human soul is immortal. 
 
 It will be seen that the Epichirema is equivalent to a 
 regressive Polysyllogism : the Episyllogism is expressed 
 in full, the Prosyllogism appears as an Enthymeme. In 
 the example given, the Enthymeme, when written in 
 full, will be, 
 
 Whatever is incapable of corruption is immortal. 
 Whatever is spiritual is incapable of corruption. 
 Whatever is spiritual is immortal. 
 
ENTHYMEME : SORITES : ANALOGY 257 
 
 Where a reason is attached to one premiss alone, we 
 have a Single Epichirema : where both of the premisses 
 are thus supported, it is called a Double Epichirema. 
 
 5. Sorites. 
 
 The Sorites is a syllogism in the first figure with 
 many middle terms. 1 In this reasoning the principle 
 
 of the Dictum de Omni et Nullo, that ' whatever is 
 affirmed of any subject, is affirmed of each logical part 
 of that subject,' is extended in its application. The 
 terms which appear in the premisses, denote not three 
 alone, but a number of species arranged in serial sub- 
 ordination ; and the conclusion states that the lowest 
 term in the series is subordinate to the highest. Thus : 
 
 Socrates is a man ; 
 All men are mammals ; 
 All mammals are animals ; 
 All animals are living creatures ; 
 All living creatures are substances ; 
 .. Socrates is a substance. 
 
 An argument of this character may be analysed into 
 a number of regular syllogisms in the first figure, there 
 being as many separate syllogisms as there are middle 
 terms in the Sorites. Hence a Sorites is frequently 
 defined as a polysyllogism abridged by omitting the con- 
 clusions of the prosyllogisms. In the example we have 
 given, the analysis will be : 
 
 (1) Socrates is a man ; 
 
 All men are mammals ; 
 
 (2) /. Socrates is a mammal. 
 
 All mammals are animals ; 
 
 (3) /. Socrates is an animal. 
 
 All animals are living creatures ; 
 
 (4) /. Socrates is a living creature. 
 
 All living creatures are substances j 
 .-. Socrates is a substance. 
 
 It will be noticed that the first proposition is the minor 
 premiss of its syllogism, and that in each case, the omitted 
 
 1 This definition is given by Mr. Joseph, Introd. to Logic, p. 385. See also 
 Summa Totius Logicae, Tract 8, c. 4, " Et licet in tali discursu," etc. 
 
 S 
 
258 PRINCIPLES OF LOGIC 
 
 conclusion forms the minor premiss of the subsequent 
 episyllogism. This is termed the Aristotelian Sorites. 1 
 
 Aristotle himself does not treat of this mode of stating an argu- 
 ment ; though the discussion in which he shows that there 
 cannot be an infinite series of middle terms between the ultimate 
 subject and the summum genus may be held to imply it 
 (An. Post. II. , c. 20). Hamilton tells us that among the Greek 
 logicians of the Lower Empire, it was known by the name of 
 Complex Syllogism (crvAAoyicr^io? o-w^crds), and that the name 
 Sorites (<ru>po9 a heap) does not appear in any author before 
 Laurentius Valla (1415-1465). 
 
 There are two special rules for the Aristotelian Sorites: 
 
 (1) Only one premiss, and that the last, may be 
 negative. 
 
 (2) Only one premiss, and that the first, may be 
 particular. 
 
 The reasons for these rules are easy to see. (i) If any 
 other premiss except the last is negative, we break the 
 rule, which forbids a syllogism in Fig. i to have a nega- 
 tive minor premiss. For the first premiss of the Sorites 
 is itself a minor ; and any subsequent negation save 
 in the case of the last premiss, would involve a negative 
 conclusion, itself a minor premiss in its episyllogism. 
 The result would inevitably be an illicit process of the 
 major term. 
 
 (2) The second rule is involved in the first. Since 
 the minor premiss in each syllogism is affirmative, and 
 the syllogisms are of the first figure, it follows that, unless 
 we are to have an undistributed middle, the major 
 premiss must be universal. But every one of the pro- 
 positions, save the first, plays the part of a major premiss. 
 
 The two rules, then, are identical with the two special 
 rules of Fig. i, that the minor must be affirmative, the 
 major universal. 
 
 The second variety of Sorites differs from the first 
 only in the arrangement of the propositions composing 
 
 1 The Sorites is not a form of reasoning which frequently occurs. Dr. Watts, 
 however, in his Logic (1725), calls our attention to a well-known passage in 
 St. Paul, where the argument is thus stated, " For whom he foreknew, he 
 also predestinated, etc., etc." Rom. viii. 29, 30. 
 
ENTHYMEME : SORITES : ANALOGY 259 
 
 it. It is called the Goclenian Sorites, from Rodolphus 
 Goclenius, professor at Marburg, who first drew attention 
 to it in a work he published in 1598, on the Organon 
 of Aristotle. In this Sorites, we begin not with the 
 lowest of the logical parts, but with that which is imme- 
 diately subordinate to the summum genus. Thus : 
 
 All living creatures are substances j 
 All animals are living creatures ; 
 All mammals are animals ; 
 All men are mammals ; 
 Socrates is a man ; 
 /. Socrates is a substance. 
 
 When the argument, as thus stated, is analysed, it is 
 seen that it is the major premisses of the episyllogisms, 
 which are omitted, and not, as in the case of the Aristo- 
 telian Sorites, the minor premisses. This will necessitate 
 a restatement of the two special rules. They now 
 become : 
 
 (1) Only one premiss, and that the first, may be 
 negative. 
 
 (2) Only one premiss, and that the last, may be 
 particular. 
 
 These changes are necessary, since (i) here all the 
 premisses save the first are minor premisses ; hence a 
 negation in any of them would involve an illicit process 
 of the major. And (2) were any premiss, save the last, 
 particular, we should have a particular conclusion to 
 one of the prosyllogisms, and in consequence a particular 
 major premiss involving an undistributed middle. 
 
 6. Analogy. In Analogy (or as it is termed by Aris- 
 totle, Example (TrapaSciy/uLa)) we have to deal, not with a 
 logical form of comparatively little moment, such as 
 are those with which we have been hitherto occupied 
 in this chapter, but with a mode of inference, which we 
 not only employ constantly in the practical concerns of 
 life, but which has also pointed the way to many of the 
 discoveries of science. It is however a guide, which, 
 used without much caution, misleads instead of assisting. 
 
260 PRINCIPLES OF LOGIC 
 
 Analogy may be defined as an inference based on a 
 
 similitude. The formula for this mode of argument 
 may be thus represented : 
 5, is P. 
 
 S 2 resembles S t in being M. 
 .-. S 2 is P. 
 
 The following is the illustration, with which Aristotle 
 provides us : 
 
 The war of the Thebans against the Phocians proved 
 calamitous. 
 
 War between Athens and Thebes resembles the war of the 
 Thebans with the Phocians in being a war with a neigh- 
 bouring state. 
 
 War between Athens and Thebes will prove calamitous. 
 
 The value of the inference here depends altogether 
 on the supposition that there is a causal connexion 
 between M and P. If this be the case, the inference is 
 legitimate. If they are not causally related, it is falla- 
 cious ; for the mere fact that S 2 is M, would then give 
 us no reason for supposing that it was also P. But in 
 regard to this causal relation, we must have no more 
 than a supposition. Our grounds for believing it must 
 not justify certainty. As soon as we are certain that 
 M is the cause of P, our argument ceases to be an Analogy 
 and becomes a perfect syllogism. 
 
 The analogical argument may be said to contain both 
 induction and deduction. By an induction we conclude 
 from the instance S that ' All M are P ' ; and we then 
 argue deductively, ' All M are P, S 2 is M, .*. 5 2 is P.' 1 
 
 1 Aristotle thus describes the argument from Example : " The Example is 
 4 an inference, not from the logical parts to the logical whole [induction], nor 
 ' from the logical whole to its parts [deduction], but from part to part, when 
 ' both fall under a common genus, but one of the two is better known to us 
 4 than the other " (An. Prior II., c. 24, 3). Thus, in the illustration given, the 
 inference passes from S to S 2 , both being logical parts of the genus M. The 
 validity of the argument requires, as we have indicated, that P should be a 
 property resulting from the nature M, and should not be one of the differentiat- 
 ing characteristics of S t (cf. Trendelenburg, Elem. Log. Arist., 38). In the 
 same passage, Aristotle terms it an inference, " in which we prove the major 
 'term of the middle, by a term which resembles the minor." This description 
 applies to the inductive part of it alone. In that part, we conclude that the 
 major term (P) may be universally predicated of the middle (M), on the ground 
 that it is predicable of S it a term which resembles the subject of our eventual 
 conclusion S. 
 
ENf HYMEME : SORITES : ANALOGY 261 
 
 The inference from Example is termed by Aristotle 
 the Induction of Rhetoric, just as he regards the Enthy- 
 meme as representing Deduction, where rhetorical argu- 
 ment is concerned. It is in fact frequently applicable 
 in regard to those practical affairs, which form the subject 
 matter of deliberative consultation ; and in which Induc- 
 tion strictly so-called has no place. We often argue in 
 this way, when we apply the lessons of history. We may 
 well suppose, for instance, a Frenchman to have made 
 a forecast of the future on such grounds, when at a time 
 of complete political disorganization, he saw Napoleon 
 Bonaparte return to France as the general of a victorious 
 army. He would remember that Julius Caesar under some- 
 what similar circumstances, had seized supreme power 
 at Rome, and that on a smaller scale, Cromwell had done 
 the same in England. Analogy would suggest that 
 events would follow the same course in France. 
 
 The analogical argument is however not merely of 
 value in such matters as these. It has, as we have noted, 
 been one of the most fruitful sources of scientific dis- 
 covery. When two different classes of objects have 
 certain attributes in common, and one of the two is 
 further characterized by a property, which appears to 
 be in some way dependent on these attributes, the investi- 
 gator is led by Analogy to enquire whether the same 
 property is not to be found in the other class. It will 
 be sufficient here to give a single example of this scientific 
 analogy, since we shall have to return to the subject in 
 a later chapter. By way of illustration we may take 
 the inference which led to the discovery that lightning 
 is an electrical discharge. The discovery was made by 
 Franklin in 1749. The phenomena of electricity were 
 at that time only known to him through the small elec- 
 trical machines of the day. But he had noticed the 
 similarity between lightning on the one hand, and on 
 the other the sparks given off by the conductor of the 
 machine. In both cases the light is of the same colour, 
 the motion rapid, and conduction can be effected by 
 metal. It suggested itself to him, that lightning was 
 
262 PRINCIPLES OF LOGIC 
 
 electrical in its character, and was due to the clouds 
 being charged with electricity, just as the electrical 
 machine is charged. Were this so, then a conductor 
 sent among the clouds should, he judged, give off sparks, 
 precisely as does the conductor of the machine. The 
 experiment was tried. A kite was sent up during a 
 thunderstorm with a wire attached to it. The anti- 
 cipated result was obtained. The two phenomena proved 
 to resemble each other in this point also : the analogical 
 inference was correct. It is true that this inference 
 itself only concluded to the fact that the clouds would 
 give off electrical sparks. But this was sufficient to 
 establish a truth of vast moment, viz. : that lightning 
 was to be reckoned among electrical phenomena. 
 
 Mill devotes a chapter of his Logic (Bk. III. c. 20) to the sub- 
 ject of Analogy. He holds that the force of an analogical in- 
 ference, depends entirely on the number of points of similarity 
 between the two objects. Thus he says (I.e. 3), " Since the 
 ' value of an analogical argument, inferring one resemblance 
 ' from other resemblances without any antecedent evidence of a 
 ' connexion between them, depends on the extent of ascertained 
 ' resemblance, compared first with the amount of ascertained 
 ' difference, and next with the extent of the unexplored region 
 ' of unascertained properties : it follows that ... if after much 
 ' observation of B, we find that it agrees with A in nine out of 
 ' ten of its known properties, we may conclude with a probability 
 ' of nine to one that it will possess any given derivative property 
 ' of A." What has been said above will have shown that such 
 a basis for analogy presents many difficulties. The mere number 
 of resemblances, is in fact a point of little moment. The value 
 of the inference depends on the reasons, which we possess for 
 supposing that the characteristic common to the two objects 
 is really connected with the property in question. These reasons 
 must not, as we have already said, be such as to amount to cer- 
 tainty. They must be probable, not conclusive. But it is they 
 that are the true foundation of the argument : and where they 
 are wanting analogy becomes mere guess-work. Moreover, 
 Mill's demand that a comparison should be instituted between 
 the known points of agreement and difference on the one hand, 
 and ' the unexplored region of unascertained properties,' is 
 incapable of fulfilment. Since the region is unexplored, any 
 attempt to form an estimate of the number of properties which 
 it contains, must needs be fruitless. 
 
ENTHYMEME : SORITES : ANALOGY 263 
 
 Analogy is occasionally defined as an argument based on similar- 
 ity of relations. Of this kind is the inference which compares 
 various orders of citizens to the different parts of the human 
 body the head, the hands, the eyes, etc., and then reasons to 
 their respective duties. The whole basis of such an argument 
 is the similarity of relations between the group of citizens and the 
 state on the one hand, and on the other between the organ in 
 question and the body. This account of Analogy adheres closely 
 to the etymological meaning of the term (dva/Voyia), which was 
 used among the Greeks to signify numerical proportion. As a 
 definition it presents some inconveniences. The form of reason- 
 ing traditionally known as Analogy, is one which plays a very 
 important part. In many cases the resemblances on which it 
 is based, are not similarities of relations. Nothing would be 
 gained by restricting the use of the term to a narrower scope. 
 
CHAPTER XVII. 
 
 FALLACIES. 
 
 i. The Treatment of Fallacies in Logic. It might 
 perhaps seem that fallacies have no place in this work. 
 We have throughout treated Logic as the science which 
 deals with the conceptual representation of the real 
 order. So far, then, as an argument is fallacious, it is 
 no longer logical. It fails to conform to any of those 
 processes, which it is the work of Logic to explain. It 
 contributes but little to a knowledge of Logic, to be 
 warned against a syllogism whose middle term is ambi- 
 guous. For here we have not one of those legitimate 
 operations of the mind, with which the science is 
 concerned, but a mere counterfeit argument, whose 
 plausibility is due to the fact that the same vocal sound 
 represents two different ideas. 
 
 The chief reason why fallacies almost invariably form 
 a constituent part of treatises on Logic is historical. 
 The last portion of the Organon of Aristotle, the Sophistici 
 Elenchi, or Refutations of the Sophists, is concerned with 
 them. Hence it came about that subsequent writers 
 on the subject also included them within the scope of 
 their work. We shall realize why Aristotle treated 
 this point at some length, if we recall the circumstances 
 of his day. At that period, the pursuit of knowledge 
 depended far less on written books than on the spoken 
 word. Verbal intercourse or ' Discussion ' was not 
 merely the method of instruction, but also the method, 
 by which friends co-operated in the search for philosophic 
 truth, and by which controversy was carried on. There 
 were three main kinds of these reasoned discussions : 
 
FALLACIES 265 
 
 (1) The demonstrative arguments relating to some 
 special science, proposed by a teacher to learners. 
 
 (2) Friendly co-operation in the search for truth. 
 
 (3) Intellectual skirmishes between opponents. 1 To 
 this class, belonged the arguments of the Sophists. The 
 boast of these men was that they could defend either 
 side in any argument, and reduce their opponent to 
 discomfiture. To them reasoning was a means employed, 
 not for the discovery of the truth, but to win popular 
 applause and secure pecuniary gain. 2 
 
 It is therefore not to be wondered at, that Aristotle in 
 his logical treatises deals not merely with the internal 
 reason, but with argument as carried on between con- 
 tending parties. He discusses the methods, by which 
 in these verbal discussions, truth might be pursued, 
 the claims of suggested solutions tested, and the falla- 
 cious arguments of the Sophists avoided. These ques- 
 tions form the subject of the Topics and the Sophistici 
 Elenchi. 
 
 It is not, however, to be thought that the study of 
 fallacies is useless to ourselves. We have not indeed 
 a class of men prepared for a consideration to defend 
 either side of any thesis. But the art of making ' the 
 worse cause appear the better,' still has its adepts. 
 Politics, philosophy, certain aspects of religious contro- 
 versy, afford these men a field for the exercise of their 
 talents. Some acquaintance with the main types of 
 fallacy may be of real service in guarding us against 
 pitfalls. It is true, this alone will not ensure that we 
 shall detect the sophisms proposed for our acceptance ; 
 but it will undoubtedly render us more capable of doing 
 so. 
 
 2. What Errors are reckoned as Fallacies? It is 
 
 manifest that in treating of fallacies, we do not reckon 
 as such every error which, occurring in an argument, 
 could vitiate the conclusion. To such a task, there 
 
 1 Soph. Elenchi, c. 2, i. 
 
 8 For a discriminating account of the Sophists, see Grant's Ethics of Aristotle, 
 pp. 104-155. 
 
266 PRINCIPLES OF LOGIC 
 
 could be no possible termination. Moreover most of 
 such errors belong to some special science. Hence, 
 even if we consider the Art of Discussion as part of Logic, 
 it is not the function of Logic, but of the science to which 
 the error belongs, to indicate its falsity. The consideration 
 of erroneous premisses, is therefore excluded from the 
 treatment of fallacies. 
 
 Another class of errors is similarly excluded, because 
 their detection belongs to the special science, with the 
 matter of which the syllogism deals. In these, the 
 false conclusion occurs, not because the premisses are 
 wrong, but because some method of solution inappro- 
 priate to the case in question is applied in the reasoning. 
 Such, for instance, is the famous argument, relating to 
 Achilles and the tortoise. 1 
 
 Breaches also of syllogistic rule, such as undistributed 
 middle and illicit process of the major or minor term, 
 are further ruled out from the list of fallacies. A fallacy 
 must present a semblance of truth. But a syllogism, 
 in which these rules are violated, to men versed in the 
 art of dispute, lacked the essential qualities necessary 
 to recommend it. In these days, indeed, many of the 
 false arguments propounded for our acceptance, err 
 precisely in these respects. Perhaps the prevalence of 
 these errors has arisen, as de Morgan suggests, because 
 the study of Aristotelian Logic has been neglected, and 
 men scarcely know which forms of argument are conclu- 
 sive, and which are not. " The philosophers," he says, 
 " who made the discovery (or what has been allowed 
 
 1 In this fallacy, it was supposed that a race takes place between Achilles 
 and a tortoise, and that while Achilles slept, the tortoise gained a small start. 
 It was urged that Achilles could never overtake his rival. For if the tortoise 
 had a start of, say five yards, then during the time that Achilles was advancing 
 this distance, it would have made some further progress. In the same way, 
 while he was covering the new ground gained upon him, the tortoise would 
 still advance in front ; and so on, ad infmitwn. But no one, not even Achilles, 
 can cover an infinite number of distances, however small. Therefore Achilles 
 can never overtake the tortoise. Here the fallacy lies in an error relative 
 to the nature of motion. It is throughout supposed that it is composed of a 
 number of separate parts. It is in fact like space itself, continuous ; thus the 
 difficulty of traversing an infinite number of parts does not occur. (For 
 another solution see Lewes, Hist, of Philosophy, ist Epoch, c. 3.) 
 
FALLACIES 267 
 
 ( to pass for one) that Bacon invented a new species of 
 ' Logic, which was to supersede that of Aristotle, have 
 ' succeeded by false history, and falser theory, in driving 
 ' out from our system all study of the connexion between 
 'thought and language" (Formal Logic, p. 241). 
 
 The errors in argumentation, which are reckoned as 
 fallacies, are thus limited to those cases, in which we 
 have the appearance of a syllogism, whose premisses 
 are undeniable, and whose conclusion follows in due 
 form, but in which nevertheless we have a false con- 
 clusion. A fallacy may then be defined as a violation 
 of logical principle, disguised under a show of validity. 
 
 The following terms occasionally used as synonymous with 
 fallacy, should be noted. Sophism, a false syllogism fabricated 
 for the special purpose of deceiving others. Paralogism : this 
 word is explained by Hamilton (following Kant) as a fallacy, 
 of whose falsehood the employer is not conscious. It is more 
 frequently employed to signify a breach of the formal rules of 
 inference. Paradox, something contrary to received opinion. 
 
 3. Aristotle's List of Fallacies. Aristotle divided 
 fallacies into two groups. 
 
 (1) Those arising from the language (fallaciae in 
 dictione Trapa TV\V \e)iv.) 
 
 (2) Those in which the error arises from some other 
 source than the language (fallaciae extra dictionem 
 
 These were called by some of the Schoolmen, ' Falla- 
 cies in the matter ' (fallaciae in re), since in them the 
 source of the confusion is in the thing stated. 
 
 The following is the list of these two classes : 
 
 A. Fallacies in the language. 
 
 1. Equivocation. (Aequivocatio Trapa rrjv ofuavvfjiiav.) 
 
 2. Amphibology. (A mphibologia Trapa rrjv au(pi/3o\iav. ) 
 
 3. Composition. (Compositio Trapa rrjv crvvOecriv.) 
 
 4. Division. (Divisio Trapa -rrjv Siatpetriv.) 
 
 5. Accent. (Accentus Trapa Trjv rrpoo-wSiav.) 
 
 6. Figure of Speech. (Figura dictionis Trapa TO 
 
268 PRINCIPLES OF LOGIC 
 
 B. Fallacies in the matter. 
 
 1. Accident. (Accidentis wapa TO o-u/x/ 
 
 2. Confusion of absolute and qualified statement. 
 (A dicto secundum quid ad dictum simpliciter wapa TO 
 aw\u>s r} Try XeyeirOai.) 
 
 3. Refuting the wrong point. (Ignoratio Elenchi 
 wapa TY\V TOV eXey^ou ayi-oiav.) 
 
 4. Begging the question. (Petitio Principn wapa 
 TO ev dp'xy Xau/Sdveiv.) 
 
 5. Consequent. (Consequentis wapa TO ewofjLevov.) 
 
 6. False Cause. (Non Causa pro Causa wapa TO utj 
 
 # t tf \ 
 
 aiTiov ft)? aiTLov. ) 
 
 7. Many questions. (Plurium Interrogationum wapa 
 TO TO. Suo eaoT^jmaTa eV woielv. 
 
 * The list of the fallacies in the language, Aristotle tells us, 
 is exhaustive, including all which can arise from the words em- 
 ployed in the argument. 1 St. Thomas proves that this is so in 
 the following manner : There are, he says, three possible sources 
 of misapprehension as to the meaning of the language, (a) The 
 words employed may be really ambiguous. This gives us two 
 cases, viz. : (i) when the ambiguity belongs to a single word 
 (Equivocation), and (2) when it belongs to a phrase (Amphibology}. 
 (b) The second source of error occurs when the words are not 
 really ambiguous, but may be rendered so by a change of pro- 
 nunciation. This also gives us two cases, viz. : (i) when the quasi- 
 ambiguity is found in a single word (Accent), and (2) when it 
 belongs to a phrase (Composition and Division), (c) The am- 
 biguity may be due merely to the misunderstanding on the part 
 of the disputant (Figure of Speech). 2 
 
 4. Equivocation. Equivocation is the fallacy which 
 arises from the employment of the same word in different 
 senses. The premisses appear undeniable, for the context 
 determines the word in question to an appropriate sense ; 
 but we are brought to a false or unwelcome conclusion. 
 Many examples given in illustration of the fallacy are 
 simple enough. De Morgan supplies us with the fol- 
 lowing : 
 
 All criminal actions ought to be punished by law. 
 
 1 Soph. Elenchi, c. 4, i. 
 
 3 St. Thomas, Opusc. 35, de Fallaciis, c. 3. 
 
FALLACIES 269 
 
 Prosecutions for theft are criminal actions. 
 
 /. Prosecutions for theft ought to be punished by law 
 (op. cit. p. 241). 
 
 But it should be remembered that Equivocation covers 
 the case not merely of equivocal but of analogous terms. 
 Indeed it would seem to have been these that Aristotle 
 had specially in view. 1 Where the sophism is of this 
 character it may sometimes cause grave perplexity to 
 the student. Thus it might be argued : 
 
 Nothing can be a real cause that does not possess real 
 existence. 
 
 So-called final causes do not possess real existence. 
 
 /. So-called final causes are not real causes. 
 
 Here the analogous word ' cause ' brings us to a false 
 conclusion. The major premiss is not true of all causes. 
 A final cause exerts its causality, not in virtue of real 
 existence, but in so far as an intelligent efficient cause 
 sets it before him as his end-in-view. Yet the erroneous 
 major may easily win acceptance, because when causes 
 are spoken of, we ordinarily mean efficient causes. 
 
 5. Amphibology. Amphibology, or as it is now often 
 called, Amphiboly is identical with Equivocation, except 
 that here the error is due not to an ambiguous word, 
 but to the doubtful meaning of some phrase. The 
 reply alleged to have been given by the oracle to Pyrrhus 
 before his invasion of Italy, has appeared in almost all 
 logical treatises from the time of Boethius to our own 
 days as the typical example of this fallacy, and it can 
 scarcely be omitted : 
 
 ' A io te Aeacida Romanos vincere posse' 
 
 The form of the phrase is such that it may equally 
 well signify, ' I tell thee, son of Aeacus, that thou canst 
 conquer the Romans/ and ' I tell thee, son of Aeacus, 
 that the Romans can conquer thee/ 
 
 When one noun is qualified by another in the genitive 
 case, the relation between the two is left quite inde- 
 terminate, and can only be known from the context. 
 
 1 Soph. Elenchi, c. 7, i. 
 
270 PRINCIPLES OF LOGIC 
 
 Often the relation signified is that between the possessor 
 and the thing possessed. But frequently some very 
 different relation is in question, such as, e.g. that between 
 an author and his book. Thus some of the old logicians 
 give this example : 
 
 This is Aristotle's book. 
 What is Aristotle's belongs to Aristotle. 
 /. This book belongs to Aristotle. 
 
 The following instance may serve to show how amphi- 
 bology may give rise to a philosophical difficulty. 
 
 It is impossible that anything can be made out of 
 nothing (Ex nihilo nihil fit). 
 
 To create is defined as to make something out of 
 nothing. 
 
 .*. Creation is impossible. 
 
 Here the fallacy arises from the ambiguity of the 
 phrase ' to make out of nothing/ In the old axiom 
 Ex nihilo nihil fit, we mean that ' nothing ' cannot be 
 a substratum, out of which something is made ; in 
 other words, no one can turn nothing into something. 
 When, however, we define creation as ' to make out of 
 nothing,' we mean ' to make without any substratum 
 at all.' No impossibility is involved in this, as there 
 is in the idea of employing nonentity as a substratum. 
 
 6. Composition and Division. When one term of 
 a proposition consists of several words, these members 
 must sometimes be understood conjunctively, and some- 
 times disjunctively. Thus if we say, ' Five is two and 
 three,' the words ' two and three ' must be taken in 
 conjunction as constituting a single predicate. But 
 when it is stated that ' Bacon was a statesman and a 
 philosopher,' we have two separate predicates ; and 
 the sentence can be analysed into two propositions. 
 The fallacy of Composition occurs, when we join together 
 the members of such a term, in a case where they should 
 be kept separate. Thus if we argue, 
 
 Peers and ecclesiastics are excluded from membership 
 of the House of Commons. 
 
FALLACIES 271 
 
 Two men only are peers and ecclesiastics. 
 
 .*. Two men only are excluded from membership of 
 the House of Commons, 
 
 we commit this fallacy. For each of the two classes 
 is excluded, and it is not necessary that a man should 
 be alike a peer and an ecclesiastic, to be disqualified. 
 
 The fallacy of Division is the converse of the preceding. 
 The argument is vitiated by this fallacy when we separate 
 what should be taken together. Thus, 
 
 Heaven is the reward of all who love their friends 
 and forgive their enemies. 
 
 Caius loves his friends. 
 
 /. Heaven will be the reward of Caius. 
 
 An interesting example of the fallacy of Composition 
 is furnished by Mr. Bradley. In treating of the Disjunc- 
 tive proposition he lays it down as evident that the 
 expression ' A is b or c ' " cannot possibly answer to 
 'real fact. No real fact can be 'either or.'" On this 
 he bases a long and intricate discussion as to the real 
 meaning of the proposition. The alleged difficulty is 
 simply a case of this fallacy. The words ' either b or 
 c ' have been read conjunctively instead of disjunctively 
 (Principles, p. 122). 
 
 An instance of the fallacy to be found in one of Mill's works, 
 has become famous. It occurs in his Utilitarianism, when 
 he is seeking to establish that the summum bonum, after which 
 all men should strive, is the ' greatest happiness of the greatest 
 number.' He says, " Each person . . . desires his own happi- 
 ' ness. This being a fact, we have all the proof which the case 
 'admits of ... that each person's happiness is a good to that 
 ' person, and the general happiness, therefore, a good to the aggre- 
 'gate of persons." The argument involves a syllogism of this 
 character : 
 
 The happiness of a, b, c, d . . . is the happiness of the aggre- 
 gate of persons. 
 
 The individuals a, b, c, d . . . desire their own happiness (the 
 happiness of a, b, c, d . . .). 
 
 .*. Each several individual [should] desire the happiness of 
 the aggregate of persons. 
 
 Here in the minor premiss, as is evident, the predicate must be 
 understood in sensu diviso. In the major premiss however the 
 same term appears as subject in sensu composite. It is quite 
 
272 PRINCIPLES OF LOGIC 
 
 untrue that the happiness of a, b, c, d, etc., is the happiness of 
 the aggregate if they are taken severally and out of relation to 
 all others, as they are when we say that each desires his own 
 happiness. The conclusion is of course worthless. Moreover 
 it is further vitiated by another illegitimate alteration, which 
 we shall notice more particularly when we discuss the fallacy 
 known as Figure of Speech. For he slips into this error as well ; 
 and when he should draw the conclusion that all men do 
 as a fact aim at the general happiness, he concludes instead that 
 it is the end at which they should aim. 
 
 7. Accent. As to the fallacy of Accent, Aristotle 
 says, "Accentuation in unwritten discourse can hardly 
 ' furnish a fallacious reasoning, but only in written 
 ' controversy and criticism on the poets." 1 It would 
 appear that he only introduces it, in order to render 
 exhaustive his list of the errors, which can arise from 
 the language. Within the sphere to which he inclines 
 to restrict it, the ambiguity arising in this way often 
 makes it difficult to fix the precise thought, which an 
 author intended to express. For example the words 
 addressed by Cardinal Wolsey, when dying, to Sir William 
 Kingston, are thus printed by Dr. Brewer, the historian 
 of the reign of Henry VIII., " Had I but served my God 
 with as much zeal as I have served my king, He would 
 not have given me over in my old age to my enemies." 2 
 The stress on the word ' He ' gives a new significance to 
 the passage. If it be the true reading, Wolsey did not 
 speak of his deliverance into the hands of the Boleyn 
 faction as being a punishment inflicted upon him by 
 God ; he saw it as the act of an ungrateful master, and 
 contrasted it with the treatment he would have received 
 from God, had he made His service his chief aim. 
 
 8. Figure of Speech. This fallacy occurs when the 
 structure of a word or expression leads us erroneously 
 to suppose that its meaning is analogous to that of words 
 whose form is similar. 3 A term really belonging to one 
 
 1 Soph. Elenchi, c. 4 (Poste's trans.). 
 
 2 Brewer, Hist, of Henry VIII., p. 444. 
 
 3 We sometimes see it stated (cf. e.g. de Morgan, op. cit. p. 250) that the 
 fallacy is simply the grammatical mistake of giving a feminine adjective to 
 a masculine noun, whose termination happens to be one which is ordinarily 
 
FALLACIES 273 
 
 category may be understood as belonging to another : 
 quantity may be taken for substance, agent for patient, 
 and so on. No better example can be given than one 
 found in Mill's Utilitarianism, to which reference has 
 already been made in 6. In the same passage from 
 which our previous citation was taken, he says, " The only 
 ' proof capable of being given that an object is visible, 
 ' is that people actually see it. The only proof that a 
 ' sound is audible, is that people hear it. ... In like 
 ' manner, I apprehend, the sole evidence it is possible 
 ' to give that anything is desirable, is that people do 
 ' actually desire it." Here the whole force of the argu- 
 ment lies in the similarity of the words ' visible/ ' audible/ 
 ' desirable/ Yet ' visible ' and ' audible ' signify that 
 the object wseen or can be seen, and is heard, or can be 
 heard. But ' desirable/ though it implies that the 
 object can be desired, means much more, and deals with 
 the moral order ; for it signifies that the object ought 
 to be desired. 1 
 
 On identical grounds exception may reasonably be 
 taken to the use, by certain authors, of the term ' a per- 
 ception/ to signify an object perceived. The form of the 
 word ' perception ' is similar to that of terms such as 
 ' emotion/ ' passion/ etc., which denote subjective 
 affections, and hence paves the way to the fallacious 
 conclusion that the immediate objects of sense are likewise 
 subjective. 
 
 Aristotle includes under this fallacy all cases, where there is 
 an illegitimate transition from category to category. The follow- 
 ing example, which he gives, well illustrates how a Sophist might 
 succeed in putting an unskilled dialectician into a difficulty. 
 The question is first proposed, Whether a man must not have 
 lost that which he once had, and now has no longer. It is 
 readily conceded that it is so. The Sophist then argues : 
 
 He who has ten dice, and loses one, no longer has what he 
 
 once had, viz. : ten dice. 
 
 feminine (e.g. bona poeta), and the like. Such an error is not logical at all. 
 It is true that this case is mentioned by Aristotle ; but it should be remem- 
 bered that one of the objects of the Sophists was to make their opponents 
 ridiculous by driving them into grammatical solecisms. 
 
 1 In this argument, the fallacy carries us from one species of relation to 
 another totally different in kind. 
 
 T 
 
274 PRINCIPLES OF LOGIC 
 
 He who no longer has the ten dice he had once, has not neces- 
 sarily lost ten dice. 
 
 .-. He who no longer has what he once had, has not neces- 
 sarily lost it. 1 
 
 The fallacy lies in the fact that in the original question the 
 words ' to have no longer what he once had,' are understood of 
 an object considered independently. As applied to the dice, 
 ' what he once had ' signifies the collective body. Objects col- 
 lectively considered stand in mutual relation as members of a 
 group of such and such extent. If one be removed, this relation 
 is lost by each and all. Hence there is here an illegitimate 
 transition from ' substance ' to ' relation.' 
 
 9. Accident. The meaning of the term ' accident ' 
 as here employed, is somewhat different both from that 
 which it bears as applied to one of the Predicables, and 
 from that it has when it denotes the nine last Categories. 
 Here a predicate is said to be accidental to a subject, 
 when, and in so far as, it has not the same definition. 
 The form of the proposition ' S is P ' leads us to regard 
 5 and P as identical. They are so, if by this we mean 
 that they denote the same individual ; but considered 
 in regard to what they signify, they are different unless 
 their meaning, their definition, is the same. Viewed 
 from this aspect, two terms may stand to each other in 
 three relations. 2 They may (i) be synonymous, having 
 precisely the same definition, e.g. ' A sheath is a scabbard/ 
 Or (2) they may have definitions which are entirely 
 different, e.g. ' The horse is black.' Or again, (3) the 
 definitions may have something in common, e.g. ' Man is 
 animal/ ' Man is risible/ We cannot conclude that 
 what is true of the predicate, is true of the subject, unless 
 what is asserted of the predicate, belongs to it, precisely 
 in so far as its definition is identical with that of the 
 subject. 3 The fallacy of accident results from neglecting 
 this principle. Aristotle gives us various examples in 
 illustration. Thus the Sophist is represented as asking, 
 ' Do you know the man with his face muffled ? ' f I do 
 not/ ' Do you know Coriscus ? ' 'I do/ * The man 
 
 1 Soph. Elenchi, c. 22. 
 
 2 S. Thomas, Opusc. 35, c. 10. 
 
 8 Soph. Elenchi, c. 24, 2, c. 5, i. 
 
FALLACIES 275 
 
 with his face muffled is Coriscus. You have both asserted 
 and denied that you know Coriscus/ The solution of 
 the difficulty, as he points out, is that it is one thing 
 ' to be Coriscus/ and another ' to be with muffled face.' 
 It is perfectly possible at the same time to know ' Coriscus,' 
 and not to know ' the man with muffled face.' In the 
 same way, we may dispose of the sophism, ' That dog is 
 yours, and he is a father : therefore he is your father.' 
 The two terms ' yours ' and ' a father ' cannot be treated 
 as though they were one, merely because they refer to a 
 single individual. Of a similar character is the argument, 
 
 Risible is a property. 
 
 Man is risible. 
 /. Man is a property. 
 
 It is true that ' risible ' contains ' man ' as part of its 
 definition, because it is a property of ' man ' ; but it does 
 not follow that everything that can be affirmed of 
 ' risible/ can likewise be affirmed of * man.' 
 
 10. Confusion of Absolute and Qualified Statement. 
 
 This fallacy is commonly known as the fallacy Secundum 
 quid, from its Latin name, fallacia a dicto simpliciter 
 ad dictum secundum quid. A predicate is said to be 
 affirmed secundum quid, i.e. only in some particular respect, 
 when a word is added qualifying the application of the 
 predicate to the subject. Qualification may be of 
 two kinds. It may be such as to limit and to narrow the 
 reference of predicate to subject, so that it would be 
 false to affirm the proposition without mention of the 
 qualification. Or it may be one which, so far from limit- 
 ing the applicability of the predicate, presupposes the 
 truth of the unqualified assertion. Thus the proposition, 
 ' Gibbon is a great historian/ could not be true, were 
 not the absolute statement ' Gibbon is an historian/ 
 true. 1 But because it is the case that ' To offer up your 
 aged parents in sacrifice, is a duty among the Triballi/ 
 we cannot conclude that the same is a duty elsewhere. 2 
 
 1 See Ch. 6, 8 (2) above ' Inference by the omission of determinants.' 
 a Cf. Topics, II. c. ii. 
 
276 PRINCIPLES OF LOGIC 
 
 It is in regard to statements limited in this manner, that 
 there is danger of the fallacy secundum quid. This 
 limiting qualification may be such as to deny the reality 
 of the predicate, e.g. ' This coin is a false shilling,' ' A 
 centaur is an imaginary animal.' Or it may assign 
 some precise place, time, or respect, in reference to which 
 alone the assertion is made, e.g. ' Laudanum is conducive 
 to health in certain illnesses,' ' It is lawful to take life 
 in a just war,' etc., etc. 1 In none of these cases, can we 
 from the limited, infer the truth of the absolute statement. 
 A centaur is not an animal; nor is laudanum, speaking 
 ' absolutely,' conducive to health. 
 
 This fallacy may be said to be connatural to the race 
 of man. We are all apt to believe that what has been 
 found useful within our own narrow experience, must 
 needs be so to other men, and in other circumstances. 
 It is hard, for instance, to persuade an inhabitant of 
 this island that a nation can prosper and be happy, with- 
 out representative government and trial by jury. Indeed, 
 it is commonly said that we have in certain cases done 
 positive harm by imposing English methods on races, 
 to which they were unsuited. Our legislators, arguing 
 too hastily a dicto secundum quid ad dictum simpliciter, 
 judged that what was adapted to Englishmen would 
 be equally serviceable to the Hindoo. 
 
 ii. Ignoratio Elenchi. The name Ignoratio Elenchi 
 is now commonly applied to all cases, in which a man 
 establishes, not the point which he has undertaken to 
 prove, but some other conclusion. But the true signifi- 
 cance of the term is ' ignorance of the nature of refuta- 
 tion.' It is the fault committed in controversy by the 
 man who does not prove the true contradictory of the 
 statement advanced by his opponent, but something 
 which may be mistaken for it. A true refutation, as 
 we have already seen (Ch. 4, 2), only occurs when " the 
 ' same predicate is denied of the same subject in the 
 
 1 For a more detailed analysis of the various ways in which the predicate 
 is limited, see St. Thomas, Opusc. 35, c. n. 
 
FALLACIES 277 
 
 ' identical respect, relation, manner and time in which 
 ' it has been affirmed." l It is, for instance, not un- 
 common for the Catholic doctrine that the Pope is 
 infallible regarding matters of faith and morals, to be 
 attacked on the ground that it can be historically proved 
 that some Popes have been guilty of grave sin. Here 
 there is manifest ignoratio elenchi : for the statement 
 brought as a refutation, viz. : ' The Popes are not impec- 
 cable,' does not deny the same predicate as was affirmed 
 in the original proposition, ' The Popes are infallible.' 
 
 Within the sphere of philosophy, a good example is 
 afforded in a well-known passage of Berkeley, contained 
 in the Introduction to the Principles of Human Know- 
 ledge. He undertakes to prove that the mind is incapable 
 of forming general concepts ; and he does so as follows : 
 
 " I can imagine a man with two heads or the upper 
 'part of a man joined to the body of a horse. I can con- 
 ' sider the hand, the eye, the nose, each by itself abstracted 
 ' or separated from the rest of the body. But then what- 
 ' ever hand or eye I imagine, it must have some particular 
 ' shape or colour. ... I cannot by any effort of thought 
 'conceive the abstract idea above described." It is 
 plain that his reasons prove something quite different 
 from what he is seeking to establish ; for they only show 
 that we cannot form a universal phantasm, not that we 
 cannot conceive a universal idea. 
 
 Together with ignoratio elenchi we may class the argumentum 
 ad ignorantiam, where the speaker trusts to the ignorance of 
 his hearers for their acceptance of his statements : the argumen- 
 tum ad populum, the appeal not to reason but to popular pre- 
 judices : the argumentum ad verecundiam, in which the speaker 
 urges that the dignity of those who hold his opinion is such, that 
 his hearer should feel himself constrained to yield his opinion to 
 theirs : z the argumentum ad hominem, in which the previous 
 
 1 Soph. Elenchi, c. 5, 5. 
 
 2 The argumentum ad verecundiam should be carefully distinguished from 
 the perfectly legitimate argumentum ad auctoritatem. The latter relies, not 
 on the dignity of those who hold the opinion, but on their supremacy in the 
 particular matter under discussion. Thus in a question which concerns art, 
 a man but little versed in the subject, will rightly regard his view as inferior 
 to that of the great authorities on art. Similarly, hi questions of political 
 economy, statesmanship, religion, etc., etc. 
 
278 PRINCIPLES OF LOGIC 
 
 history of a man is urged as rendering it impossible that he 
 should with consistency hold certain views. 
 
 12. Petitio Principii. The term employed by Aris- 
 totle to denote this fallacy, signifies literally ' to assume 
 the very point proposed for debate at the outset.' Hence 
 our English expression ' to beg the question/ renders 
 the original sense with fidelity. For the question (quaes- 
 tio) is the name used by the old logicians for the conclu- 
 sion, which the disputant undertakes to prove, but for 
 which he has not yet advanced his arguments. It is, 
 of course, but rarely that it is possible for a man to 
 assume without any circumlocution the point at issue. 
 At the least, he must conceal the indecency of the pro- 
 ceeding by the employment of different words. Where 
 this is done, he may escape detection. It would perhaps 
 be possible at the present day to hear the thesis that 
 the House of Lords is out of date, supported by the argu- 
 ment that an upper chamber in England is an anachron- 
 ism. Aristotle enumerates five ways in which the ques- 
 tion may be begged. 1 The first of these is the case in 
 which the proposition itself is assumed. The example 
 just given will illustrate this method. The other four 
 are : (2) the assumption of a universal proposition which 
 involves the conclusion to be established : (3) if the 
 proposition needing proof is universal, the assumption 
 of a particular case involving it : (4) the assumption of 
 the truth of the conclusion in regard to each part of the 
 subject, of which as a whole it is to be proved : (5) the 
 assumption of a proposition, the truth of which carries 
 with it the truth of the one to be established. 
 
 Of these various kinds perhaps the second is the one 
 which affords the disputant the greatest facility for 
 escaping detection. 2 A notable instance is afforded by 
 the famous argument by which in the Monadology Leibniz 
 
 1 Topics, viii. c. 13. 
 
 2 Mr. Welton (Manual, 187), speaking of this form of Petitio Principit, 
 says : ' This was the sense in which the term was used by the Scholastics,' 
 apparently implying that they did not recognize the o'her f"*jr forms. In 
 this he is in error. Cf, e.g. St. Thomas, Opusc. 35, c. 13. 
 
FALLACIES 279 
 
 seeks to show that all material bodies are constituted 
 of simple and indivisible monads. He argues that what 
 is ' compound ' must needs be an aggregate of simple 
 substances ; hence, since we know that there are ' com- 
 pound ' substances, we know that there are simple 
 substances. 1 The argument relies on the supposed prin- 
 ciple, 'What is not simple is actually compound/ But 
 this is a mere assumption. For there is a third alterna- 
 tive, viz. : the continuous, which is not formed of actual 
 parts, i.e. of parts already separated from each other, 
 and yet is not a simple entity. 
 
 A well-known form of the fifth case is the circulus in argu- 
 mentando or vicious circle, in which of two correlative propositions, 
 each is made to depend for its proof upon the other. An in- 
 stance may be drawn from the works of Mr. Grant Allen, one 
 of the popularizers of the evolutionary hypothesis in its more 
 extreme forms. In his work The Evolutionist at Large, he ac- 
 counts for the development of brilliant plumage in certain species 
 of birds, on the ground that they have acquired an aesthetic 
 taste, owing to the fact that their food has to be sought among 
 bright fruits and flowers : while conversely, he accounts for 
 the development of the bright colours of the edible berries, on 
 the ground that they have ' assumed ' these hues, because the 
 birds which live upon them, have a taste for bright colours. 2 
 
 In this connexion we may mention the argument from silence. 
 This form of argument assumes that some event was unknown 
 to a writer, because none of his existing works mention it. Many 
 instances might be cited to show that conclusions thus based 
 really amount to petitio principii. Thus Theophilus of Antioch, 
 writing a defence of Christianity, does not once name Christ. 
 Tacitus does not mention the tragedies of Seneca, and Martial 
 and Statius never mention one another. 
 
 13. Fallacy of the Consequent. This fallacy is 
 ordinarily understood as denoting the illegitimate con- 
 clusion, which is drawn in a hypothetical syllogism 
 from the assertion of the consequent or the denial of 
 the antecedent : as for instance : 
 
 1 Monadologie, 2. II faut qu'il y ait des substances simples : puisqu'il 
 y a des composes : car le compost n'est autre chose qu'un amas ou aggrega- 
 tum des simples. 
 
 2 Cf. Fr. J. Gerard, Science and Scientists, pp. 84, 94. 
 
28o PRINCIPLES OF LOGIC 
 
 If a student is idle, he will have little acquaintance 
 with his subject. 
 
 This student has little acquaintance with his subject, 
 
 ,\ He is idle. 
 
 These errors have already been noticed in Ch. 13, i, and 
 there is no need to deal with them afresh. 
 
 * This explanation of the fallacy has a long tradition behind 
 it. It is not a novelty of the modern text-books, but has de- 
 scended to them from the mediaeval treatises. But it is not 
 identical with the Aristotelian account. Aristotle gives no 
 separate treatment in his logical works to the hypothetical syllog- 
 ism. It is therefore unlikely that he should deal with that error 
 in his enumeration of fallacies. As a matter of fact, the word 
 Consequent (kiro^vov] in his logical treatises, where it is of fre- 
 quent occurrence, has a different meaning from that now attri- 
 buted to it. It denotes any predicate, which is necessarily 
 involved in a subject. 1 Thus, in the propositions ' man is ani- 
 mal,' ' man is mortal,' both of the predicates are among the 
 cTro/xei/a of ' man.' The fallacy of consequent occurs, when we 
 treat the consequent as convertible with the antecedent. Rhe- 
 torical Enthymemes (of Fig. 3) are, he says, vitiated by this 
 fault, and he illustrates this by the syllogism : 
 
 Men of loose character dress elaborately. 
 This man dresses elaborately. 
 .. This man is of loose character.* 
 
 The fallacy, he says, is based upon a misapplication of the 
 axiom, ' two things, which are identical with the same thing, 
 are identical the one with the other.' Those who are unversed 
 in Logic, erroneously imagine that this relation is that which 
 obtains between the subjects and the predicate of their premisses. 
 Indeed, fallacies of the consequent, he adds, are a subordinate 
 species of fallacies of accident. The difference between them is 
 merely that in the latter, we are concerned with a single subject : 
 this we identify with its accident, and affirm of the accident 
 what really belongs to the subject alone. In fallacies of the 
 consequent we have two subjects, of which the same accident 
 is affirmed : and on these grounds we identify the subjects. 3 
 
 14. False Cause. Both the fallacy of non causa 
 pro causa and the following one of ' Many questions/ 
 though incident to disputation, as it was carried on at 
 ancient Athens, are not among those errors, into which 
 
 1 Cf. Bonitz in Arist. Met. A. 981, a. 27. * Soph. Elenchi, c. 5, 9. 
 
 3 Ibid. c. 6, 10. 
 
FALLACIES 281 
 
 the mind of man keeps falling, irrespective of time and 
 place. They may therefore be briefly treated. The 
 ' False Cause ' was employed by the Sophist, when he 
 desired to show that the statement of his opponent led 
 to an absurd result. In his own argument, however, 
 the absurd conclusion was not due to the statement of 
 his adversary. For although he had feigned to employ 
 this as one of his premisses, he had joined to it other 
 assertions ; and it was from these, and not from his 
 opponent's doctrine, that the reductio ad impossibile 
 was attained. Thus, if we suppose the Sophist's opponent 
 to have affirmed that the death-penalty for murder is 
 just, the Sophist might argue as follows : ' The position 
 ' leads to an absurdity : for granting that the death- 
 ' penalty for murder is just, and that punishment is to 
 * be held just in so far as it is efficacious as a deterrent, 
 ' then it follows that it would be equally just to inflict 
 ' the death-penalty for pocket-picking.' Here the original 
 statement has nothing to do with the conclusion obtained. 
 This follows from the principle that the justice of a pun- 
 ishment is measured by its efficacy as a deterrent, a 
 principle which is in no way connected with the state- 
 ment that the death penalty for murder is just. For 
 those who hold this, would almost certainly base it on 
 the very different principle, that the punishment must 
 be proportioned to the crime. The opponent would 
 therefore reply that the Sophist had alleged his state- 
 ment as the cause of the conclusion, though in fact it 
 was not so : that he was thus guilty of the fallacy Non 
 causa pro causa. 
 
 15. Many Questions. The fallacy of ' Many ques- 
 tions ' was rendered possible by the fact that in the 
 earlier days of dialectic disputation, a direct affirmative 
 or negative was required in answer to the questions 
 proposed by that one of the two disputants, who under- 
 took the task of confuting the positions advanced by 
 the other. The respondent might be put into a serious 
 difficulty if the question, though apparently single, 
 
282 PRINCIPLES OF LOGIC 
 
 was in fact complex, and required two answers, one 
 affirmative and one negative. Thus a question, such as 
 ' Do you not spend much of your time on the useless 
 study of Logic ? ' contains two members, viz. : ' Do you 
 spend your time on the study of Logic ? ' 'Is not that 
 study useless ? ' It cannot be answered by a single 
 reply. If the respondent attempts to do so, his opponent 
 has a manifest advantage. For should the answer be 
 affirmative, he assumes that it was intended as the 
 reply to the member, which needed the negative answer, 
 and should he receive a negative reply, he makes a 
 similar misapplication of that. Such questions are still 
 effective rhetorically, and many a schoolboy has felt 
 himself aggrieved on being asked by his master whether 
 he has not wasted his whole morning on cricket. Aris- 
 totle warns his disciples that they must insist on resolving 
 the question into its constituent parts, and replying to 
 each separately. 
 
 * It has been frequently asserted that the seven preceding 
 fallacies have no point in common, and that a logical error was 
 committed in referring them to a single group. It may be freely 
 conceded that the resemblance is of the slightest. Yet it seems 
 that there is a real justification for holding one and all to be due 
 to a confusion as to the thing stated (fallaciae in re}. In the 
 fallacy of Accident we take things which are merely conjoined 
 to be identical ; in Secundum quid, we confuse the limited with 
 the absolute ; in Ignoratio Elenchi, we take what is not opposed 
 to the original thesis to be opposed to it ; in Petitio principii, 
 we take the same fact asserted under two forms, to be two dif- 
 ferent truths ; in Consequent, we confuse the condition and the 
 conditioned ; in False Cause, we imagine what is not the reason 
 of the conclusion to be its reason ; in Many Questions, we accept 
 an interrogation referring to two facts, as though it had reference 
 to one. 1 
 
 16. Mill's Classification of Fallacies. It is necessary 
 to consider the classification of fallacies proposed by 
 J. S. Mill. This scheme is based on a different system 
 from that of Aristotle, and embraces a wider field of 
 errors. With a new classification, he, as a natural 
 
 1 St. Thomas, Opusc. 35, c. 9. 
 
FALLACIES 283 
 
 consequence, introduced a new terminology ; and this 
 has to a greater or less extent been adopted by many 
 subsequent writers on Logic. 
 
 The Aristotelian scheme was, as we have seen, a classi- 
 fication of the principal cases, in which statements not 
 in themselves untrue, are so presented to the mind, that 
 it is misled into forming a wrong judgment as to their 
 significance. Moreover, it only professes to enumerate 
 those difficulties, which are of such a character as to 
 occasion perplexity to a man of ordinary capacity. 
 " The dialectician," says Aristotle, " must enumerate 
 ' the sources of apparent proofs, apparent that is, not 
 ' to any ignoramus, but to people of average intelligence ; 
 ' for it would be an endless work to enquire into the 
 ' sources of every idiotic belief/' * It was further pointed 
 out, that the subject belongs properly, not to Logic, 
 but to the theory of discussion, which is itself one of the 
 subsidiary methods, by which we seek to arrive at truth. 
 Mill's view as to the place of fallacies in Logic is different, 
 as his view of Logic itself is different. Logic, he defines, 
 is the science of Evidence ; and precisely as the scientist 
 who investigates into the nature of health is bound to 
 treat of disease, so it is the duty of the writer on Evidence 
 to discuss " what are the most dangerous varieties of 
 ' Apparent Evidence, whereby persons are misled into 
 ' opinions for which there does not exist evidence really 
 ' conclusive " (Logic, Bk. V., c. 7, i). It follows that 
 the treatment of fallacies should be coextensive with 
 the science of Logic ; and proceeding on this principle, 
 he draws up a scheme of five different classes of fallacy, 
 viz. : 
 
 i. Fallacies of Simple Inspection. These errors are 
 antecedent to all evidence. The essential character 
 of the fallacy lies in the acceptance of erroneous 
 propositions as self-evident. 
 
 The remaining four classes fall under two heads 
 that in which the evidence is clearly conceived, but the 
 logical process is erroneous, and that in which the evi- 
 
 1 Soph. Elenchi, c. 9, (Poste's trans.). 
 
1*4 PRINCIPLES OF LOGIC 
 
 dence is confusedly apprehended. The former of these 
 two categories embraces the 2nd, 3rd, and 4th classes : 
 the latter gives us but one class, the fallacies of confusion. 
 Classes 2 and 3 are termed Inductive fallacies. 
 
 2. Fallacies of Observation. In these, the error lies 
 
 in not sufficiently ascertaining the facts on which 
 the theory is grounded. 
 
 3. Fallacies of Generalization. This class contains 
 
 (i) Illicit Inductions, and (2) False Analogies. 
 Deductive fallacies. 
 
 4. Fallacies of Ratiocination. To this class are to be 
 
 referred faults against the laws both of mediate 
 and immediate inference, together with the Aristo- 
 telian fallacies of Accident and Secundum quid. 
 Errors due to confused apprehension of evidence. 
 
 5. Fallacies of Confusion. The remaining Aristotelian 
 
 fallacies. 
 
 We shall deal briefly with such of these groups as 
 seem to call for notice. 
 
 The Fallacies of Simple Inspection are those errors 
 where " the proposition is embraced not as proved, 
 ' but as requiring no proof ; as a self-evident truth." 
 Some few of the instances cited by Mill are the vulgar 
 errors of the uninstructed or the superstitious, such as 
 the belief in pagan Rome that words of ill omen would 
 bring disaster. Were this all, there would scarcely 
 appear sufficient reason for the introduction of this 
 class. But it assumes some importance, as Mill relegates 
 to it a considerable number of philosophic principles, 
 with which he did not agree, as e.g. that the same effect 
 must be produced by the same cause. 
 
 Fallacies of Observation. The claim of errors in observa- 
 tion to a place in Logic, stands and falls with the Empi- 
 ricist view of the science. This theory, as we have 
 several times noticed, does not distinguish between 
 sense-perception and intellectual cognition. It follows 
 from this, that any science of knowledge must take 
 account of sense-perception ; and thus the Empiricist 
 Logic is bound to find room for some consideration of 
 
FALLACIES 285 
 
 errors arising from this source. These are distinguished 
 by Mill into fallacies of Non-observation and fallacies ot 
 Mai-observation. In regard to Non-observation, the 
 logician must give an answer to the question, " what 
 ' sorts of instances, or of circumstances in any given 
 ' instance, are most likely to escape the notice of observers 
 ' generally ? " (Logic, Bk. V., c. 4, i). The most frequent 
 source of such neglect, Mill rightly finds in preconceived 
 opinions. It is needless to point out how, when men 
 approach a subject with their minds strongly biassed 
 in one direction, they become almost incapable of judging 
 the evidence on the other side. A strong partizan in 
 politics will scarcely hold the balance even in estimating 
 the character of King James II. or of William of Orange. 
 Mai-observation differs from Non-observation, inasmuch 
 as in it the error " does not lie in the fact that something 
 ' is unseen, but that something is seen wrong.'' The 
 origin of these mistakes lies in the confusion of our 
 perceptions with the inferences which we draw from 
 what we have perceived. The inability to discriminate 
 between these is greatest among those of little mental 
 cultivation. But it probably has happened to all of 
 us to be convinced that we have seen and recognized 
 some" person whom we know, and afterwards to have 
 discovered that we were deceived by certain points of 
 resemblance, perhaps in themselves not particularly 
 important. We had in fact inferred from these points, 
 that the person we saw was our friend. 
 
 The most important among the Fallacies of Generali- 
 zation are the illicit inductions arising from simple 
 enumeration. These have been sufficiently adverted 
 to in Ch. 14, 6. 
 
 False Analogy provides us with a copious source of 
 error. Few things carry conviction to the mind so 
 much as a striking analogy, and few things can be more 
 misleading. Whenever a doctrine becomes widely 
 accepted, analogies are drawn from it to support views 
 which are concerned with matters not even remotely 
 connected with it. Of recent years, we have analogies 
 
286 PRINCIPLES OF LOGIC 
 
 drawn from the theory of Evolution for every conceiv- 
 able purpose. Thus for instance, in a valuable lecture 
 on Currency and Coinage, given in 1905 by Sir R. Temple, 
 the distinguished author throughout treats the history 
 of coinage from the point of view of evolution, and at 
 the close, writes as follows : "In very fact English 
 ' sixpences, French francs, and pieces of any similar money 
 1 one can mention ... are all like their owners them- 
 ' selves, in obedience to the natural law of heredity, the 
 'heirs of the ages." 1 Any comparison between the 
 law of natural heredity and the history of coinage, is 
 the merest metaphor. Hence the analogical argument, 
 The race of man is ever advancing in perfection. 
 Shillings and sixpences are like men in being sub- 
 ject to the law of heredity. 
 /. Shillings and sixpences are ever advancing in 
 
 perfection, 
 is from a logical point of view, almost grotesque. 
 
 As another example of false analogy, we may cite 
 the argument by which some of those interested in 
 abnormal mental states, have sought to explain as a 
 hypnotic phenomenon the power possessed by certain 
 saints of the Catholic Church to read the secret thoughts 
 of those with whom they spoke. The explanation 
 enabled them to represent the alleged miracles as 
 circumstances naturally incident to the condition of 
 persons subject to hypnotic influences. The argument 
 takes this form : 
 
 Some persons manifesting abnormal phenomena are 
 
 hypnotic. 
 The saints resemble the persons aforesaid in being 
 
 able to read the thoughts of others. 
 .*. The saints were hypnotic. 
 
 M. Henri Joly in his work, The Psychology of the Saints, 
 has well pointed out that the resemblance is entirely 
 superficial, and that in consequence the analogy is worth- 
 less. " St. Catherine of Sienna," he says, " St. Vincent 
 Ferrer, and St. Theresa divine the thoughts, not of those 
 
 1 Lectures on the Method of Science: edited by T. B. Strong, p. 215. 
 
FALLACIES 287 
 
 who dominate them, but of those whom they dominate. 
 They are rightly to be compared not to the hypnotized 
 but to the hypnotizer. But the latter, even Charcot 
 himself, . . . are the ' divined ' and not the diviners." l 
 In regard to the Fallacies of Ratiocination and Fallacies 
 of Confusion, it seems unnecessary to add to what has 
 already been said on the subject. The various faults, 
 which can be committed against the rules of immediate 
 and mediate inference, are by this time familiar to our 
 readers. And the foregoing sections of the present 
 chapter have, as it is hoped, sufficiently explained the 
 nature of Secundum quid and Accident and of the various 
 Fallacies of Confusion. 
 
 1 Joly, Psychology of the Saints, Eng. trans., p. 68. 
 
PART II 
 
 APPLIED LOGIC 
 CHAPTER XVIII. 
 
 APPLIED LOGIC AND THE LOGIC OF THOUGHT. 
 
 i. Science and Philosophy. In order to understand 
 the precise meaning of the term ' Applied Logic,' and 
 the connexion between the branch of knowledge thus 
 designated, and the Logic of Thought, it will be necessary 
 to explain with somewhat more detail than seemed 
 advisable in Ch. I., the relation between the Logic of 
 Thought and the sciences of the real order. The first 
 three sections of the present chapter are devoted to this 
 subject. In the present section, we treat of the distinc- 
 tion between Science and Philosophy, and of their mutual 
 relations. 
 
 What is a science ? We may define a science as an 
 organized body of truth regarding some special object 
 of thought. 1 By an object of thought, we do not signify 
 a concrete individual thing. The various and manifold 
 aspects of one and the same thing, which the mind can 
 distinguish the one from the other, constitute so many 
 different objects of thought. Thus, under its various 
 aspects, the same living plant is the object of different 
 sciences. It is studied by the chemist in regard to the 
 organic products resulting from it ; by the physiologist 
 in regard to its vital processes : the botanist considers 
 its structure, and its classification by genus and species. 
 Wherever the mind can abstract an aspect of the know- 
 
 1 " When we speak of ' the Sciences,' we moan what is sometimes more 
 ' definitely expressed as ' the special sciences ' a group of organized bodies 
 ' of general knowledge, each concerned with some aspect of the knowable 
 ' world." H. Sidgwick, Philosophy, its Scope and Relations, p. 4. 
 
290 PRINCIPLES OF LOGIC 
 
 able world, whose properties, principles, and causes 
 provide an organized body of knowledge, there we have 
 a science. 1 
 
 It will be observed that scientific knowledge, in virtue 
 of the fact that it is knowledge of the type considered 
 in abstraction from the individual, is always universal. 
 We consider, e.g. the characteristics of sulphur and of 
 radium, of the lily and of the date-palm in general : we 
 are not concerned with the individual peculiarities of 
 the specimen under examination, save in so far as it 
 illustrates a general law. Scientia est de universalibus 
 was a dictum of the ancients. And Mr. Sidgwick ex- 
 presses the same thought as follows : "To get a defini- 
 ' tion of science ... we must, I think, take the char- 
 ' acteristic of ' generality ' as the essential distinction 
 ' between scientific knowledge and merely ' historical ' 
 ' knowledge of particular facts. ... It is true that 
 ' we largely regard knowledge of particular facts e.g. 
 ' of the discovery of a new planet as scientific know- 
 ' ledge : but only, I think, in view of its relation to 
 'general knowledge" (op. cit. p. 8). 
 
 Now even had every special aspect of things been 
 made the object of a special science, the work of the 
 mind would still be incomplete. A great province of 
 knowledge would still be untouched. There are laws 
 and principles, which relate not to some restricted area 
 of the knowable, but which embrace in their reference 
 the objects of all the special sciences. The mind can 
 view the objects of all the sciences in common, can frame 
 a system of the knowledge which relates to them as thus 
 considered, and can thus attain to a universal science. 
 It is this universal science which we term Philosophy. 2 
 
 The special sciences depend for their very being on 
 the universal science. It provides the foundations on 
 which they rest. They can, it is true, develop many 
 details within their own provinces, organizing knowledge 
 
 1 Arist. An. Post. I., c. 10, 4. 
 
 a The word ' Philosophy ' is used in various significations. The meaning 
 here assigned is the traditional, and still, we believe, the most usual. For 
 a somewhat different account see Erdmann, History of Philosophy, Introd. 
 
APPLIED LOGIC AND THE LOGIC OF THOUGHT 291 
 
 and involving the facts in a rational system. They 
 carry us far beyond the mere rule of common-sense. 
 But they must postulate for it is beyond their province 
 to explain many facts and principles, a denial or false 
 explanation of which would ruin their whole system. 
 In order even to make a commencement, they must 
 accept as objectively real such facts as, e.g. the 
 movement of bodies in space, their duration in time, 
 the power of one material thing to act upon 
 another, the unity of a substance notwithstanding 
 its multiplicity of parts, the principles of mathe- 
 matics, the law of causality. Thus the intellect finds 
 itself forced to seek for a science having for its object 
 these facts of universal import. This science is Philo- 
 sophy. It is the part of Philosophy to deal with the 
 universal conditions of things, and so to explain them 
 that the account which it affords of them is consistent 
 with the facts of experience. When it does this, the 
 validity of the special sciences is vindicated. When in 
 lieu of explaining them, it explains them away, the 
 special sciences collapse. No science could lay claim 
 to be true, if the principles of mathematics, or the objec- 
 tive reality of local motion or of temporal duration, 
 were denied. Not one of its conclusions would possess 
 any validity. The sciences can no more divorce them- 
 selves from Philosophy than they can from common- 
 sense or experience. In the latter case they would 
 have no data, in the former they would have no justi- 
 fication. 
 
 Philosophy then is the science which treats of the 
 principles and the characteristics which belong to the 
 universe as a whole. 1 
 
 1 Cf. Arist., Met., I., c. i. TTJV 6i'0/j.ao/J.evr)v ffofoav irept ra irpdra atria Kal 
 ras apxas viro\a/ji.(3d.i>oviTi -rr&VTes. ' All regard philosophy as the science, 
 'which treats of primary causes and principles.' St. Thomas, commenting 
 on this passage of the Metaphysics, says, ' Sapientia est scientia quae considerat 
 'primaset universalescausas.' Mr. Sidgwick expresses himself to the same 
 effect, when he says (op. cit. p. 38), " As to Rational Theology, it seems to me 
 ' that the questions with which it deals . . . are primd facie philosophical 
 'questions . . . i.e. they belong to the contemplation of the universe as a whole.'' 
 Elsewhere, however, he explains philosophy somewhat differently. 
 
 Among recent philosophers, it is not uncommon to find Scienc distin- 
 
292 PRINCIPLES OF LOGIC 
 
 * The character of scientific knowledge. We have in the 
 present paragraph already noted one feature of scientific know- 
 ledge, viz. : its generality. Two other characteristics distin- 
 guish it from the majority of the assents we give. The assents 
 of true Science are certain. At the present day, indeed, the term 
 " science " is often used to signify the organized body of facts 
 experimentally known regarding some aspect of reality, as ex- 
 pressed in terms of the theory most generally accepted by those 
 who are experts in the matter in question. Thus, the body of 
 truths known about the phenomena of light, when expressed in 
 terms of the undulatory theory, is called the science of light. 
 Such an expression of the facts is of course provisional : it lacks 
 the full certainty of science strictly so called. There is no need 
 to quarrel with the terminology, which has extended the signifi- 
 cation of the word ' science ' to this case also. But it should 
 be noted that we have not here science in the fullest meaning of 
 the term. 
 
 Science as defined by the ancients, was further the knowledge 
 of things by their causes cognitio certa rei per propriam causam. 
 This demand has given occasion to much adverse comment. It 
 has been asserted that the Schoolmen admitted no knowledge 
 as scientific, except such truths as were capable of a priori demon- 
 stration. Some of the shallower spirits may perhaps have ex- 
 pressed themselves to this effect. But there is no reason what- 
 ever to attribute such an opinion to Aristotle or St. Thomas. It 
 rests on an altogether too narrow interpretation of the word 
 ' cause.' As we have seen, that term includes in its meaning 
 all the four causes enumerated by Aristotle. Thus understood, 
 such knowledge, as e.g. that sulphuric acid consists of hydrogen, 
 oxygen, and sulphur, is scientific knowledge of its nature, though 
 very incomplete and capable of immense extension. Indeed 
 
 guished from Philosophy, on the ground that Science is concerned with 
 Appearance alone, Philosophy or Metaphysics with the Reality, which lies 
 behind appearances. This distinction we owe to Kant, and by many writers 
 it is accepted without question. There are however 'signs of a return to 
 the traditional, and, as we hold, saner view. Thus, Mr. Sidgwick (op. cit. 
 p. 93) declines to distinguish Physics from Metaphysics on this basis, " be- 
 ' cause Physics regards its object as real, and itself requires the distinction 
 ' between Reality and Appearance." And somewhat similarly, Professor 
 Pringle-Pattison writes, ' It is hardly possible to open a scientific or semi- 
 ' philosophical work, without meeting the complacent admission that our 
 ' knowledge is ' only of phenomena.' Or the writer tells us that the science 
 * in question, so far as he is concerned, treats only of phenomena, the con- 
 ' sideration of the corresponding noumena being relegated to philosophy or 
 ' metaphysics. . . . [These writers] may rest assured that the best result 
 ' of this contemned metaphysics in modern times has been just this to ex- 
 ' plode the conception of such duplicate entities as they still cannot help 
 ' half believing in, and to repudiate in consequence the brand of that ' only ' 
 ' before phenomena ' (Scottish Philosophy, pp. 175, 176). 
 
APPLIED LOGIC AND THE LOGIC OF THOUGHT 293 
 
 it has been well observed, that according to this definition, science 
 begins as soon as we have the generalized notion of the object. 1 
 For, as we have pointed out in Ch.io, 2, the generalized notion, i.e. 
 definition of an object, is, logically considered, its formal cause. 
 
 2. The Subdivisions of Philosophy. We have already 
 explained (Ch. i, 3) that the Scholastic philosophers 
 divided the sciences into the speculative sciences (scientiae 
 speculativae) on the one hand, and the regulative or 
 normative sciences (scientiae practicae] on the other. 
 In the speculative sciences, our object is to know the 
 order of things in the universe, as it offers itself to our 
 contemplation. The normative sciences are concerned, 
 not with the knowledge of an already existing order, 
 but with the production of an order we desire to see 
 realized. This order may be in our own acts, or in ex- 
 ternal things. The sciences, which deal with the pro- 
 duction of order in our actions, are Logic and Ethics. 
 Logic treats of order in the acts of the intellect ; Ethics 
 of order in acts of the will. Both of these sciences are 
 rightly regarded as branches of philosophy ; since, as 
 we shall point out in the next section, both possess that 
 note of supremacy, which is philosophy's distinctive 
 characteristic. 
 
 In the present section, our purpose is to deal more 
 
 I The following passage from a little work, entitled Qu'est-ce que la Science ? 
 (Paris, 1906), by L. Bailie, professor at the Leonine University of Anagni, 
 throws light on this point ; and further indicates with considerable insight, 
 how it has come about that the acceptation of the term ' science ' has varied 
 so much at different periods. " En vertu meme de la definition qu'ils [Aristote 
 et S. Thomas] nous ont leguee, des qu'une proposition s'appuie solidement 
 sur 1'observation en la depassant par la generalisation, ou sur Tintuition 
 generalisatrice en 1'appliquant, elle commence a etre scientifique : mais elle 
 n'est jamais le dernier mot a dire sur le sujet. . . . 
 
 Le concept de science a toujours 6te, pour cette philosophie, un concept 
 analogique, et par suite infiniment souple malgre 1'apparente precision de sa 
 definition, susceptible de deVeloppements variables, opposes meme, et pour- 
 tant et c'est la le merite singulier de cette definition toujours en continuity 
 parfaite avec leur commune origine. 
 
 II arrive toutefois qu'en poursuivant trop exclusivement 1'un de ces d6- 
 veloppements, applicable seulement a 1'une des branches de la science, on 
 perd de vue rorigine de la notion et du concept primitif. ... De 1'arbre ou 
 Ton est monte on ne voit plus que la branche ou Ton est, ou bien on regarde 
 les autres rameaux comme des etrangers." Op. cit. p. 63. 
 
294 PRINCIPLES OF LOGIC 
 
 particularly with the threefold division of speculative 
 philosophy, which we owe to the profound insight of 
 Aristotle. 1 
 
 All science, as we have seen, considers primarily, not 
 the individual, but the general type the universal 
 nature, which our intellect abstracts from the singulars, 
 in which it is realized. By this, we do not intend to 
 assert that science is concerned only with our abstract 
 concepts, and not with things. This would be to fall 
 into the error of the Conceptualists. Science is con- 
 cerned with things, but solely in so far as the universal 
 type is found in them. 2 If the scientist devotes himself 
 to the study of the phenomena manifested by a par- 
 ticular electrical machine, or the motions of a particular 
 spinning-top, it is that he may discover laws of universal 
 import. Nor is his knowledge of the individual fact 
 scientific knowledge, save in so far as he, to use St. 
 Thomas's expression, ' applies ' the abstracted universal 
 to the particular case. There is not, nor can there be, 
 a science of particulars as such ; for the particular is in per- 
 petual flux. It is ever changing. We make some state- 
 ment about it ; and before the words are well out of our 
 mouth, they are no longer true. It was this, that led 
 Plato to suppose his world of super-sensible entities, 
 which were, he held, the true object of all scientific know- 
 ledge. The keener insight of Aristotle perceived that 
 the solution of the difficulty lay in another direction. 
 The object of science was not to be sought for in the 
 super-sensible world of Ideas, but in those universal and 
 stable types, which our intellect abstracts from the 
 
 1 See Arist., Met., V.,c. i. In this chapter Aristotle discusses the place of 
 Metaphysics in relation to the other sciences. 
 
 2 Cf. St. Thomas, Opusc. 63, in lib. Boethii de Trinitate, Q. 5, Art. 2* 
 ad. 4. ' Scientia est de aliquo dupliciter. Uno modo primo et principaliter 
 et sic scientia est de universalibus rationibus super quas fundatur. Alio 
 modo est de aliquibus secundario, et quasi per reflexionem quandam : et 
 sic de rebus illis est quarum sunt illae rationes, in quantum rationes illas 
 applicat ad res etiam particulares quarum sunt, adminiculo inferiorum virium.' 
 
 The ' application ' of the universal to the individual, which is here spoken 
 of, is of course in the conceptual order. When we affirm ' Socrates is a man,' 
 we mentally ' apply ' the form ' humanity ' to the individual Socrates. 
 
APPLIED LOGIC AND THE LOGIC OF THOUGHT 295 
 
 ever-changing singulars, and in the singulars themselves 
 so far as the type is realized in them. 1 
 
 Abstraction is the basis of science, and to the different 
 grades of abstraction must correspond distinct sciences. 
 There are, as Aristotle has shewn us, three such grades. 
 We may simply abstract from the individuating con- 
 ditions. Such is the abstraction we employ in all the 
 special sciences dealing with the material world. This 
 abstraction, moreover, is the foundation of the science, 
 which considers the general nature of material substance 
 subject to motion and change. This science, whose 
 object is the totality of material substances, may well 
 be termed Natural Philosophy. The ancients, following 
 Aristotle, called it Physics. 
 
 A further abstraction enables us to prescind altogether 
 from those sensible qualities which are the conditions 
 of all change and mutability, and to consider corporeal 
 substance solely as the subject of extended quantity. 
 The science which treats of bodies purely in so far as 
 endowed with quantity, is Mathematics. 2 
 
 1 The following passage will show that this ancient difficulty is with us yet : 
 ' In strict fact nothing ever is ; everything becomes, and turns our most con- 
 scientious predications into falsehoods. The real is here, there and every- 
 where, until we stop breathless in the chase, and point gasping. The ' eter- 
 nal truths ' unable to sustain the pace have long since ceased to reside with 
 us, and have gone down or up, (one really cannot be precise about directions 
 in these Copernican days,) into the TOTTOS vofjT6s, where it is possible to 
 preserve one's dignity without doing any work." F. C. Schiller, Axioms 
 
 as Postulates, 34. 
 
 Mr. Schiller's lively and agreeable style should not blind us to the fact 
 that he is drawing us back into a quagmire, from which Aristotle delivered 
 philosophic thought more than two thousand years ago. The error contained 
 here is identical with that which Heraclitus taught. Even in the early days 
 of Greek philosophy, it was quickly lecognized that such a doctrine does not 
 account for the facts. 
 
 2 It is not uncommon in the works of non-scholastic writers to find the 
 assertion that Mathematics deals with merely mental creations, and not with 
 the extended bodies of the real world. It is urged that the perfect circle 
 and the perfect square, which are the objects of Geometry, are mere figments 
 of the understanding to which nothing corresponds. To adopt this view is 
 to introduce into science an error of the most serious and far-reaching kind. 
 Geometry no less than the physical sciences deals with the real world. The 
 solution of the difficulty mentioned, lies in the fact that the intellect in iorm- 
 ing its concepts, finds its object not in the concrete individual the object of 
 sense-perception but in the type. The intellect grasps the principle of order 
 and harmony realized, however imperfectly, in the individual. The realization 
 of the type is conditioned by the material receiving it, a truth expressed 
 by the Scholastics in the phrase Quidquid recipitur, recipitur secundum moduli 
 
ap6 PRINCIPLES OF LOGIC 
 
 A third degree of abstraction yet remains. By this 
 we abstract from matter altogether, and consider those 
 universal notions and principles, which dominate all 
 Being ; these must be true as well of the spiritual as of 
 the material universe, since they hold good of things, 
 not in so far as they are material bodies, nor yet in so 
 far as they are endowed with quantity, but because 
 they are things. This highest degree of abstraction 
 gives us the science of Ontology or Metaphysics. It is 
 this science whose function it is to treat of the principles 
 of Contradiction and Causality, of the meaning of Being, 
 Unity, Perfection, Substance, Accident, Potentiality, 
 Actuality, and other such notions of absolutely universal 
 reference. This science alone enables us to ascend by 
 reason as distinct from revelation, from the contempla- 
 tion of the visible universe to some knowledge of the 
 First Cause, from whom all proceeds, from the creature 
 to the Creator. Hence it was not undeservedly termed 
 by Aristotle and his followers, the science of Theology. 1 
 
 recipientis. Thus the realization of geometrical forms is, as far as we know 
 always more or less imperfect, according to the nature of the material. A 
 plane surface as shewn on a black-board is very remote from the ideal. In 
 polished metal the imperfection is in some measure removed : but perfection 
 we cannot attain. Yet the intellect in the act of abstraction, seizes the type. 
 Hence Geometry deals not with figments, but with the real world : and a 
 proposition, e.g. in Trigonometry, gives us the real height of a real building. 
 
 A word may be added on the subject of discrete (arithmetical) quantity. 
 This is reached by a similar process of abstraction. Arithmetical number 
 is obtained by the division of continuous quantity into equal parts. The 
 unit is a portion of continuous quantity viewed as an undivided whole : and 
 number is produced by the repetition of the unit. Were the arithmetical 
 unit not of this nature, there could be no such things as fractions. The ex- 
 pression e.g. '123 is intelligible as applied to a line or other continuum, but 
 not so if applied to a quality or relation. On this subject see Summa Totius 
 Logicae, Tract 3, C. i. 
 
 1 ' Quaedam vero sunt speculabilia, quae non dependent a materia secun- 
 dum esse, quia sine materia esse possunt : sive nunquam sint in materia 
 sicut Deus et Angelus, sive in quibusdam suit in materia, et in quibusdam 
 non, ut substantia, qualitas, potentia et actus, unum et multa et hujusmodi : 
 de quibus omnibus est Theologia, id est, divina scientia, quia praecipuum 
 cognitorum in ea est Deus. Alio nomine dicitur Metaphysica, id est trans- 
 physica, quia post Physicam discenda occurrit nobis, quibus ex sensibilibus 
 competit in insensibilia devenire. Dicitur etiam Philosophia prima in quantum 
 scientiae aliae ab ea principia sua accipientes earn sequuntur.' St. Thomas, 
 Opusc. 63, in lib. Boethii de Trin. Q. 5, Art. i. It is a disputed point 
 whether the name ' Metaphysics ' was given for the reason here assigned, or 
 simply because Aristotle's work of that name came next to his treatise on 
 Physics. 
 
APPLIED LOGIC AND THE LOGIC OF THOUGHT 297 
 
 In this hierarchy of sciences, the inferior are, as we 
 pointed out in the preceding section, essentially dependent 
 for their justification on the higher and more abstract. 
 If the value of the higher science be impugned, nothing 
 can save the lower. The conclusions of Mathematics 
 are worthless, if Metaphysics cannot defend the principle 
 of contradiction ; and without the law of causality, it 
 is idle to argue in the special sciences from effects to 
 their causes. The long scientific calculations relative 
 to the phenomena of heat and light, are a mere intellec- 
 tual amusement, if the scientist be still doubtful whether 
 the truths of Mathematics have reference to objective 
 reality, or are fictions of the mind. And if Physics 
 cannot establish the validity of the laws of motion, it is of no 
 avail to look for certainty in the conclusions of Astronomy. 
 
 * In this paragraph, we have reckoned Logic with Ethics as 
 a regulative science, in this following the division given by St. 
 Thomas in Ethics /., 1. i (see p. 5, note). This arrangement 
 differs slightly from that of Aristotle. He did not reckon Logic 
 (TO, dyaAuriKa) as a science on a level with the other sciences, 
 but as an introduction to, and an instrument of the sciences. 
 His reasons are evident. That acquirement, which is requisite 
 to the right ordering of all those organized bodies of knowledge, 
 which we term sciences, seems to stand on such a different footing 
 from them, that it might easily appear best to relegate it to a 
 different category. Moreover, there was no place for it in Aristo- 
 tle's famous division of the sciences into ' speculative,' ' practical ' 
 and ' productive.' For by ' practical,' he did not denote pre- 
 cisely what we have signified by the more general term ' regula- 
 tive.' The function of a ' practical ' science is to determine 
 the will to choose the right course. The will being able to choose 
 either the right or the wrong, it is essential to us that it should 
 be guided by adequate knowledge. " In the practical sciences," he 
 says, "the principle ofaction is the choice of the will (rj Tr/oocupecns)." 1 
 Logic provides us with rules ; but it is not the choice of the will 
 that is determined by them. As soon as we grasp them, the 
 intellect spontaneously obeys them. Hence the Peripatetic 
 school regarded Logic not as a constitutive part of philosophy, 
 but as the instrument, by which we are able to attain science. 
 Accordingly they gave to Aristotle's logical treatises the name 
 of the Organon or Instrument. 2 
 
 1 Met., V., c. i, 5. 
 
 2 Ammonius the son of Hermias, in his comment on the Categories, tells 
 us that the Peripatetic and Stoic schools were distinguished by the place 
 
298 PRINCIPLES OF LOGIC 
 
 3. Logic and Metaphysics. At the commencement of 
 this work, two definitions of Logic were offered. It 
 was explained to be the science which directs the opera- 
 tions of the mind in the attainment of truth, and also as 
 the science of the conceptual representation of the real 
 order. The former definition indicates its scope as the 
 practical science, which regulates the operations of the 
 intellect. The latter declares the subject-matter, with 
 which it is conversant. It would be erroneous to term 
 it, * the science of the operations of the mind ' : for it 
 does not in fact consider the actual operations the 
 processes of conceiving, judging, and reasoning, but 
 the result of these processes. It considers things as 
 expressed in concepts and in judgments, and as made 
 known to us in conclusions resulting from premisses. 
 The subject of the science is, as we have seen in the course 
 of the foregoing pages, the characteristics which things 
 possess as thus expressed. It views things as possessed 
 of those properties, in virtue of which we term them 
 subject, predicate, genus, species, logical part, middle- 
 term etc., etc. ; and it is through the knowledge it gives 
 us of reality thus expressed, that it enables us to tread 
 the difficult path of reasoning securely. The character- 
 istics, which things possess solely in virtue of their 
 mental expression, were termed by the ancient logicians 
 Logical Entities (entia rationis} or Second Intentions 
 (Ch. 2, n). The former name contrasted them with 
 Real Entities (entia realia), by which name were signified 
 the actual substance and all those attributes, which it 
 possesses in the order of existence. In these writers, 
 Logic is frequently defined simply as the science which 
 treats of the ens rationis. 
 
 When Logic is seen to be the science, which treats of 
 
 assigned to Logic in their respective systems. The Stoics held it to be a 
 part of Philosophy, the Peripatetics regarded it as the instrument by which 
 we reach it. Trendelenburg, Elem. Log. Ar., p. 48. 
 
 St. Augustine De Civ. Dei, viii. reckons it as one of the speculative sciences. 
 On this St. Thomas says, " Logica non continetur sub philosophia speculativa 
 quasi principals pars, sed quasi quoddam reductum ad earn, prout ministrat 
 speculationi sua instrumenta." Opusc. 63, Q. 5, Art. i, ad. 2. 
 
 Cf. also Boethius, Comment, in Porph., Lib I. (Migne, P. L. t. 64, col. 74). 
 
APPLIED LOGIC AND THE LOGIC OF THOUGHT 299 
 
 things as they exist in the conceptual order, it at once 
 appears that there is a parallelism between Metaphysics 
 and Logic. They are the universal sciences. Meta- 
 physics is the universal science of the real order, the 
 science which investigates principles of universal appli- 
 cation, and the attributes common to all things which 
 are. Logic is no less universal in its reference. For 
 the range of the intellect is unlimited, and whatever 
 can exist, can also be an object of thought, and can thus 
 appear vested with the characteristics of the conceptual 
 order. As Metaphysics is the universal science of the 
 real order, so Logic is the universal science of the con- 
 ceptual order : it deals with those conditions which 
 are common to all things, in so far as they are thought. 1 
 The very fact that the provinces of these two sciences 
 are so different, and yet so closely parallel, renders it 
 essential for all who enter on their study to be on their 
 guard lest they should suppose that properties, which 
 belong only to the thing as thought, must belong to it 
 as it exists in the real order ; and conversely, lest, because 
 existence in the real order involves certain definite con- 
 ditions, they hold that things must needs exist under 
 the same conditions in the conceptual order. The his- 
 tory of philosophy is full of errors arising from this con- 
 fusion of the real and the logical. Plato, recognizing 
 the universality of the nature or essence as it is repre- 
 sented, affirmed the real existence of universal natures. 
 The Empiricists, taking their stand on the fact that in 
 the real order nothing can exist which is not individual, 
 denied that even in thought one and the same nature 
 could be repeated in a multiplicity of subjects. Kant, 
 seeing that we possess our knowledge of things through 
 
 1 Cf. St. Thomas, Opusc. 39, De Natura Generis, c. 4. " Sciendum 
 est ergo quod sicut in 4 Metaph. dicitur, Logicus et Metaphysicus circa omnia 
 operantur, differenter tamen. Sicut enim Primi Philosophi est loqui de Ente 
 in communi, ita et Logici. . . . Ens dupliciter dicitur scilicet naturae et ra- 
 tionis. Ens autem rationis proprie dicitur de illis intentionibus quas ratio 
 in rebus adinvenit : sicut est intentio generis et speciei quae non inveniuntur 
 in rerum natura, sed sequuntur actiones intellectus et rationis : et hujus- 
 modi ens est subjectum Logicae : et illud ens aequiparatur enti naturae, quia 
 nihil est in rerum natura de quo ratio non negotietur." Cf. in Met., IV., 
 lect. 4 ; in An. Post. /., lect. 20. 
 
300 PRINCIPLES OF LOGIC 
 
 udgments, in which the predicate notion expresses the 
 nature of the thing, taught that it is the act of judgment 
 itself, which confers on the phenomenon the nature 
 we attribute to it. That thinkers such as these con- 
 found one order with another, is a sufficient testimony 
 to the difficulty involved in an accurate analysis of the 
 mental processes in their relation to the real, and to the 
 marvellous acumen of the great Stagirite who laid so 
 securely the foundations both of Logic and Metaphysics. 
 
 If it is the distinctive mark of Philosophy to be supreme 
 in some department, the claim of Logic to be designated 
 a branch of Philosophy is sufficiently manifest. As 
 soon as it is seen to be the science which deals with the 
 representation of things in an intelligent subject, it is 
 evident that it is not one of those sciences which are 
 restricted in their range to some special sphere of being, 
 but that it is concerned with attributes which belong to 
 all things, both real and possible. The universality of 
 Ethics is closely analogous to that of Logic. Here too 
 we have to deal with an order of things, totally different 
 from that with which we are concerned in the sciences 
 of the real. The science which treats of the moral 
 obligations of a free self-determining agent, cannot be 
 brought into the same category as they. Ethics, in 
 dealing with these obligations, deals with them not in 
 regard of any particular circumstances, but as general 
 laws of universal reference, valid in all circumstances 
 in which the agent may be placed. It also therefore is 
 rightly termed philosophy. 
 
 4. The Breach with the Past. It must have seemed 
 to philosophers in the golden age of Scholasticism, that 
 the analysis of the sciences into their main divisions, 
 was a permanent achievement of the human mind a 
 step not to be retraced. Yet, as all are well aware, 
 between that age and this, a revolution has taken place 
 in European thought. In all the great seats of learning, 
 save where the influence of the Catholic Church is pre- 
 ponderant, the Aristotelian system no longer finds 
 
APPLIED LOGIC AND THE LOGIC OF THOUGHT 301 
 
 acceptance. It might indeed appear at first sight, that 
 the science of Logic had survived even in those places, 
 where the rest of the philosophy had been forsaken : 
 for to a large extent the form of the science popular in 
 England and Germany during the nineteenth century, 
 employs the same terminology, and treats of the same 
 matters as the historical form has ever done from Aristotle 
 through Aquinas, Scotus, Suarez to the modern Scho- 
 lastics. But the similarity is deceptive. Logic is but 
 one member of a whole, no part of which can stand with- 
 out the others. The rise of the modern sects in philo- 
 sophy was inevitably followed by a new theory of reason- 
 ing in which every feature of the ancient science was 
 altered beyond recognition. Hence it seems advisable 
 to say a little in regard to the history of the great change, 
 in order to explain how it has come about that the sub- 
 jects treated of in this second portion of our work, are 
 by many now regarded as part of the same science, 
 which treats of the concept, the judgment, and the 
 syllogism. 
 
 The chief cause of the downfall of Scholasticism, is 
 to be found in the intellectual movement of the Renais- 
 sance period. With the revival of classical studies, 
 and the fresh interest aroused in the civilizations of 
 Greece and Rome, a new set of subjects began to occupy 
 men's minds. They were captivated by the beauties 
 of the ancient literature, and by the living interest of 
 the works now first placed at their command. In their 
 enthusiasm for purity of style, they had nothing but 
 contempt for the Schoolmen and their mediaeval Latinity, 
 which had been produced to meet the philosophers' 
 need of a language at once clear, flexible and competent 
 to express the finer operations and results of thought. 
 And the scholastic discussions which emulous students 
 too often reduced to mere word-fencing, seemed far less 
 attractive than the myths of Plato. 
 
 While the zealots of the New Learning adopted an 
 attitude of aggressive antagonism to the old order, many 
 of the Scholastic doctors showed themselves equally 
 
302 PRINCIPLES OF LOGIC 
 
 unconciliatory. They did not imitate their great pre- 
 decessors of the thirteenth century, who when called 
 to face the intellectual ferment occasioned by the intro- 
 duction of the Arabian philosophy, had resolutely adopted 
 all that was good in the novel ideas. They regarded 
 the New Learning in the light of a connatural foe, and 
 by their hostility to all innovation, drove many men of 
 ability towards the opposite camp. 
 
 Amongst causes tending still further to weaken the 
 position of Scholasticism two others call for mention. 
 In the sixteenth century its defenders became too nar- 
 rowly occupied with the traditional Metaphysics and 
 Theology to the exclusion of other subjects. The earlier 
 Scholastics had by no means neglected the physical 
 sciences. The discoveries of Galileo owed a great debt to 
 the pioneer work of Ockham and Buridanus in this direc- 
 tion. The classical revival on the other hand contributed 
 nothing to the cause of physical investigation : its de- 
 votees had no interest to spare for such matters. Yet 
 owing to the reaction occasioned by it, it came about that 
 the majority of Scholastic writers cared for nothing save for 
 the old paths. And a school which has ceased to press 
 forward into new fields is bound to become decadent and 
 ultimately to succumb. The second influence of which we 
 have spoken, was the popularity enjoyed in the mediaeval 
 schools by Conceptualism. 1 The legitimate outcome 
 of this doctrine is Scepticism. Men trained in a Scholasti- 
 cism which offered them such a philosophy as this, might 
 well think that such a cause was hardly worth defending. 
 
 When the beginning of the seventeenth century was 
 reached, men scarcely knew what to believe. Some 
 philosophy men must have : but in the northern univer- 
 sities the credit of Scholasticism, for the time at least, 
 was gone. All confidence in it was lost. 
 
 Eventually, in the course of that century, two currents 
 of thought arose, to one or other of which we may assign 
 almost every thinker who has, since that period, exercised 
 
 1 In 1425 the heads of the university of Cologne were called before the 
 Elector to answer to the charge that they continued to teach the old-fashioned 
 views of St. Thomas, to the neglect of the more modern Conceptualism. 
 
APPLIED LOGIC AND THE LOGIC OF THOUGHT 303 
 
 commanding influence in Europe. These were Idealism 
 and Empiricism. Idealism had its origin in Descartes 
 (1596-1650). Though not himself an Idealist in the 
 full sense, his system was based on suppositions which 
 inevitably led to that doctrine. The philosophy of 
 Locke (1632-1704) gave rise to the Empiricist school. 
 Neither of these two doctrines is compatible with any 
 theory of Logic, in the sense in which Logic was under- 
 stood by the Aristotelian writers. With them, Logic 
 was the science of the conceptual representation of the 
 real. But Idealism denies the existence of the real, as 
 Empiricism does that of the conceptual order. We 
 cannot have a theory of the mode in which the mind 
 represents the real order, if there be no reality outside 
 thought. And such a science is equally impossible, if 
 concepts are a figment, and our only form of knowledge 
 is the perception by sense of concrete singulars. In the 
 hands of writers belonging to either of these schools, 
 the ancient science of Logic could hardly avoid being 
 roughly handled. It was inevitable that its boundaries 
 would become very uncertain, that, on the one hand, 
 parts of it would be discarded as meaningless, and on 
 the other, that to it would be assigned the treatment of 
 topics, which the Scholastics would not reckon as falling 
 within its province. 
 
 With Logic, as interpreted in an Idealist sense, we 
 are not now concerned. What is called Applied Logic 
 owes its incorporation into the treatises of the present 
 day as an integral part of the science, to the influence of 
 Mill, an empiricist. Though the subject is dealt with 
 in idealist works, yet its treatment there is due to the 
 influence exerted by Mill in establishing traditional 
 limits for the science. Yet before dealing with Mill's 
 theory, it is necessary to say something in regard to the 
 views of Francis Bacon (1561-1626). For although, as 
 Professor Minto has well said, it was by Mill that the attempt 
 was first made " to incorporate scientific method with 
 ' Logic, and add it as a new wing to the Aristotelian 
 ' building," yet it was in the Novum Organum of Bacon 
 
304 PRINCIPLES OF LOGIC 
 
 that this undertaking was suggested. That work has 
 always been regarded as a landmark in the story of the 
 revolt from Scholasticism. By its very title, the writer 
 challenged comparison for his book with the Organon 
 of Aristotle, and threw into strong relief his conviction 
 that the Logic, which ever since the days of Cicero had 
 been the groundwork of a liberal education, was of but 
 little worth, and that the time had come to supersede 
 it by something better. 
 
 5. Bacon. Francis Bacon lived at the very time 
 when the chaos of philosophical opinion was most com- 
 plete. Endowed with an intelligence naturally both 
 inquisitive and capacious, he turned it to every kind of 
 problem both philosophical and scientific, and believed 
 himself capable of solving all. In the fifth book of his 
 work De Augmentis Scientiarum he exposes a completely 
 new system of Logic. But by Logic he signifies some- 
 thing very different from the science his predecessors 
 had known by that name, as may be gathered from the 
 fact that he reckons Grammar, Rhetoric and the Art 
 of Memory as parts of Logic. The Scholastic Logic he 
 holds to be entirely useless ; he blames it especially for 
 recognizing no other Induction save that by simple 
 enumeration. This defect he undertakes to remedy by 
 setting forth a new Inductive Method. For this method 
 he makes the loftiest claims. Its discovery would, he 
 averred, do for science what the discovery of the compass 
 had done for navigation. Its efficacy was such, that 
 it would put the intelligence of all men on an equality. 
 Of this new science he does not treat in the De Augmentis : 
 it was reserved for another volume, the famous Novum 
 Organum. 
 
 The value of Bacon's Induction is intimately bound 
 up with certain philosophical views of his own. He 
 believed every substance to be an aggregate of simple 
 natures. Thus, gold unites the following natures : it 
 is heavy, yellow, malleable to a certain extent, etc., etc. 
 Each of these simple natures depends, he holds, on a 
 
APPLIED LOGIC AND THE LOGIC OF THOUGHT 305 
 
 certain special disposition of the component particles. 
 The disposition of the particles may thus be regarded 
 as the constitutive principle of a nature, and is termed 
 the Form of that nature. The aim of Induction is the 
 discovery of these ' Forms.' When we know wherein 
 the ' Form ' consists, we shall be able to induce the 
 simple nature corresponding to it on other substances. 
 Thus an acquaintance with the ' Forms ' of yellowness, 
 heaviness, etc., will enable us to unite them in another 
 substance, and so transform it into gold (II. v.). 
 
 In the Novum Organum Bacon prescribes what he 
 conceives to be the most suitable method for directing 
 our observations and our experiments to the discovery 
 of the ' Form.' This is his Inductive Method. The 
 first step is to draw up various tables containing respect- 
 ively (a) instances of the presence of the nature which 
 is the object of inquiry, (b) instances of its absence, (c) 
 instances in which it is present in varying degrees. The 
 method then proceeds by a series of exclusions. Thus 
 if we are seeking to find the Form e.g. of ' yellowness,' 
 and it be suggested that some particular internal char- 
 acter x be it, we forthwith examine our tables, and 
 should we find any case in which x occurs in the absence 
 of yellowness or in which a yellow object exists without 
 x, we know that x may be excluded from the list of 
 alternatives. Finally all forms but one are rejected, 
 and we know that this is the object of our search. 
 
 In regard to this method, we may say first, that it 
 has never been found of any service. It has been fruitful 
 of no discoveries. No man of science has ever used it. 
 Secondly, it is not in any way, as Bacon maintained it 
 was, a new logical process. The method is little more 
 than a direction to employ elimination in the discovery 
 of laws of nature. Logically the process is the old 
 disjunctive syllogism : 
 
 The form in question is a or b or c. 
 It is not a or b. 
 /. It is c. 
 
 The Novum Organum is not, in fact, a logical treatise 
 
 x 
 
306 PRINCIPLES OF LOGIC 
 
 on Induction at all. There is in it no attempt to deal 
 with the logical explanation of the mental act by which 
 we pass from the individual instances to the universal 
 principle. 
 
 Crucial Instance. This term employed by Bacon in describing 
 his method, has acquired sufficient note to claim separate ex- 
 planation. In the process of exclusion by which the Form is 
 discovered, the following case, he says, will occasionally occur. 
 Our choice will lie between two Forms only, to one or other of 
 which the nature must be attributed. In these circumstances 
 we may be fortunate enough to find an instance which absolutely 
 excludes one alternative, thus establishing the other. This he 
 calls an Instantia Crucis, taking the metaphor from the cross-posts, 
 which stand where two roads meet (Nov. Org., II. 36). The 
 expression has passed into the language, and when an experi- 
 ment shows one of two hypotheses to be false and thus estab- 
 lishes the truth of the other, it is termed a Crucial Experiment. 
 
 6. Mill. Mill took up the suggestion contained in 
 the Novum Organum. In his hands, Logic became a 
 science having for its primary object the proof of natural 
 laws. Like the older logicians, he tells us indeed, that 
 Logic is concerned with ' the attainment of Truth * 
 (Exam., p. 397) ; but he makes use of this expression in 
 a sense quite other than theirs. In his view, it contri- 
 butes to this end, not because it deals with the general 
 conditions of all intellectual representation, but because 
 it prescribes the methods by which we obtain evidence 
 for the laws of nature. The formal laws of the traditional 
 Logic are indeed admitted into the science, but in a 
 purely subordinate position. Their office is to secure 
 us against inconsistency and self-contradiction. In 
 this way, they fulfil a subsidiary, but not unimportant 
 function in the search for truth. 
 
 This theory of Logic is clearly laid down in the Exami- 
 nation of Hamilton. " The doctrine [of Sir W. Hamilton 
 ' assumes that with the exception of the rules of Formal, 
 ' that is, of Syllogistic Logic, no other rules can be framed, 
 ' which are applicable to thought generally abstractedly 
 ' from particular matter, . . . that the problem which 
 ' Bacon set before hjmself, and led the way towards 
 
APPLIED LOGIC AND THE LOGIC OF THOUGHT 307 
 
 ' resolving is an impossible one . . . that the study of 
 ' nature, the search for objective truth, does not admit 
 ' of any rules, nor its attainment of any general test 
 ' (p. 400)." And a little further on, Mill terms this 
 enquiry " a Philosophy of Evidence and of the Investi- 
 ' gation of Nature," and says of it, that if such a theory 
 be possible, " this must be Logic /car' e^o-giv, and any- 
 ' thing else called by the name, can be only ancillary to 
 'it." 
 
 It is true that in the introductory chapter to his Logic, 
 his account of the subject with which he is about to 
 deal, is more in harmony with the traditional view. 
 But though this be so, yet in the work itself, we find the 
 science treated, not in accordance with the sketch there 
 given, but with the theory set forth in the Examination 
 of Hamilton, which renders it abundantly clear that it 
 was thus in fact that he understood its scope. Professor 
 Carveth Read well says, " It appears to me that the 
 ' subject of those immortal volumes, is not the operations 
 ' of the mind, but primarily the Laws of Nature and 
 ' their Proof. . . . The highest Laws are the Axiom of 
 ' the Syllogism, the Law of Causation with its derivative 
 ' Canons of Experiment, the theory of Probabilities 
 ' and perhaps the doctrine of kinds : all of which are 
 ' plainly conceived by Mill to be Laws of Nature. Then 
 ' in the First and Fourth Books there is much discussion 
 ' of matters subsidiary to the discovery and proof of 
 ' Laws, such as Names and Naming, Definition, Classifi- 
 ' cation, etc. : and here again facts and the order of 
 ' Nature are the chief concern." 1 
 
 It will be plain to those who have followed the fore- 
 going paragraphs, that Mill was here combining two 
 things, which are absolutely incompatible, namely, a 
 science of the investigation of nature a branch of know- 
 ledge which relates to the real order, and the rules of 
 the traditional Logic, which concern the conceptual 
 order. No one can be blind to the importance of the 
 subject with which Mill was principally concerned, namely 
 
 1 Carveth Read, Theory of Logic, p. 7. 
 
308 PRINCIPLES OF LOGIC 
 
 the methodology of the sciences. The subject was one 
 which called for treatment, and had hitherto received 
 inadequate attention at the hands of philosophers. His 
 contributions to it were very great, and his work will 
 probably long rank as a classic. His error lay in regard- 
 ing this subject as one and the same science with the 
 theory of our mental processes. 
 
 It may possibly be asked of us, to what science could 
 we on the principles of Scholastic philosophy refer the 
 general theory of the methods of Science. To this ques- 
 tion, we reply that there is and can be no such general 
 theory of investigation, prescribing the method to be 
 followed in all Science. Each science proceeds upon 
 the method which its peculiar subject-matter demands. 
 Indeed, though Mill speaks of such a theory of scientific 
 method as one, yet he can only do so by regarding it as 
 concerned solely with the search for Physical Law. In 
 his Logic, he devotes a separate treatise to the Logic of 
 the Moral Sciences. And in the work of his disciple 
 Bain, we have the Logic of Chemistry, the Logic of Medi- 
 cine, the Logic of Mathematics. All this has no concern 
 with Logic properly so called. The outline of the 
 method to be followed in the various sciences, belongs 
 in each case to the science to which it refers, and 
 should be incorporated with it, not with Logic. 1 
 
 Reference has been made in Ch. i to the novelty, entitled 
 Symbolic Logic, in which mathematical methods are applied to 
 terms and propositions. If the analysis of the sciences, which 
 we have given, be correct, the pursuit can lead to no result of 
 any value. For it consists in nothing else than in the applica- 
 tion of principles belonging peculiarly to one science, to obtain 
 the solution of problems belonging to another. Of the Sym- 
 bolic Logician, as of the alchemist in Faust, it may be said that, 
 He fused and fused by rule and recipe 
 Things which by nature are antagonistic. 
 
 1 Cf. S. Thomas, in Met., II., lect. 5. Logica tradit communem modum pro- 
 cedendi in omnibus aliis scientiis. Modus autem proprius singularium scien- 
 tiarum, in scientiis singulis circa principium tradi debet. 
 ' ' Der in Gesellschaft von Adepten 
 Sich in die schwarze Kiiche schloss, 
 Und nach unendlichen Recepten 
 Das Widrige zusammengoss.' Faust, Act i, Sc. i. 
 
APPLIED LOGIC AND THE LOGIC OF THOUGHT 309 
 
 Indeed there was a slight chance that an alchemist would 
 obtain some solid result from his labours, though not perhaps 
 in the direction in which he looked for it. It is difficult to see 
 that Symbolic Logic can lead to anything. The root of the evil 
 lies in the confusion on the part of many men of great ability 
 as to the true character both of Mathematics and Logic. Thus, 
 e.g. Professor Whetham writes in Recent Developments of Physical 
 Science, p. 33, " The science of Mathematics has nothing to do 
 ' with natural phenomena. . . . The mathematician lives in a 
 ' purely conceptual sphere, and Mathematics is but the higher 
 ' development of Symbolic Logic." 
 
CHAPTER XIX. 
 
 OBSERVATION AND EXPERIMENT. 
 
 i. The Function of Observation and Experiment. 
 
 As we have already pointed out in the preceding chapter, 
 we are now concerned, not with a science of the con- 
 ceptual order, but with those of the real. We are not 
 considering what it is that justifies us in passing from 
 the premisses of a syllogism to its conclusion, or from 
 the experience of one or two particular facts to a uni- 
 versal judgment. All that belongs to the sphere of Logic 
 proper. We consider, with special reference to the sub- 
 ject we are studying, how we are to obtain our data, and 
 how we must apply to these data our knowledge of Logic, 
 in order to pass from them to the generalizations of 
 science. This study is termed Methodology. It is 
 in particular, with the methods of what are termed 
 the Natural Sciences, that we shall be dealing in the 
 following chapters. 
 
 The objects which Nature offers to our contemplation 
 are of two kinds. They are either static forms or dynamic 
 activities. The study of the former gives us the sciences 
 of natural types, e.g. systematic botany and zoology, 
 and in general what may be termed the classificatory 
 sciences. The latter give us the sciences of physical 
 law, e.g. chemistry, electricity, light, heat, etc. The dis- 
 cussion of the general methods employed in these two 
 great groups of sciences, involves the consideration of 
 the processes known as Observation and Experiment. 
 For it is through them that we attain that knowledge 
 of natural phenomena, which is the condition of scientific 
 advance. They give us our data : it is by their means 
 that we win from Nature a knowledge of her laws. 
 
OBSERVATION AND EXPERIMENT 311 
 
 Nature does not reveal her secrets readily. Her pro- 
 cesses are hidden and full of mysteries. We see enough 
 to recognize from the first that we stand in the midst 
 of an ordered cosmos, but what are the laws of that 
 cosmos, we know not. Why does the rainbow appear 
 in the sky after the shower ? and why do the same pris- 
 matic colours play upon the waterfall ? How is sound 
 transmitted to the ear, and light to the eye ? The threads 
 of that mysterious web may be unravelled by diligent 
 searching alone. Mere antecedence in time counts for 
 little in establishing a relation of cause and effect ; for 
 to every event, there are many antecedents ; and the 
 difficulty lies in determining which of these antecedents 
 is the true cause. For long it was believed that the 
 cause of the malaria was the poisonous air of the marshes, 
 since that was an antecedent of the illness. There was 
 needed a closer examination among the various ante- 
 cedents before the true cause was found. It is by the 
 help of Observation and Experiment, that Nature's 
 secrets are detected. We may at last find some case, 
 in which Nature's process stands revealed to our rational 
 insight, and we recognize the relation of cause and effect 
 connecting two phenomena. Or we may find the data of 
 an eliminative argument, and be able to assert that such 
 and such an antecedent hitherto believed to be the cause, 
 is not the cause, for we have observed a case where 
 in its absence the phenomenon nevertheless occurred. 
 
 2. In what Observation consists. Observation is 
 the application of our faculties to the accurate determin- 
 ation of natural phenomena. The faculties we employ 
 immediately are our external senses. But these do not 
 act alone. Man is essentially rational. He cannot, 
 even if he wishes, first apply his senses, as though they 
 were unintelligent machines, and then set to work to 
 use his reason. He cannot look out on Nature with the 
 dull gaze of vacancy. It is the intelligence of man, that 
 is the true observer ; and the senses are but instruments 
 of the observant mind. 
 
312 PRINCIPLES OF LOGIC 
 
 It is for this reason that observation is always and 
 necessarily selective. The mind cannot fix its attention 
 on the myriad aspects of reality which sense-perception 
 presents to it, but concentrates itself to take note of 
 some one point. Nor is this the only part played by 
 intelligence in Observation. Almost invariably, we 
 observe in order to reply to some question which has 
 proposed itself to our mind, and to see whether some 
 particular answer is the true one or not. In other words, 
 our observation is generally made in the light of some 
 hypothesis. But the putting to ourselves of a question, 
 and the suggestion of an answer, are alike the work of 
 the intelligence. 
 
 One of the most essential conditions of observation is 
 that the observer should most carefully distinguish 
 between the facts which his faculties reveal to him, and 
 those which he infers. Many of the facts which we 
 ordinarily speak of as facts of observation, contain what 
 may be loosely called inference, though it would be more 
 accurate to style it imagination. Thus, for example, 
 a man may assert with confidence that he has seen his 
 brother in the street. Yet what he really saw was, it 
 may be, a man resembling his brother in a few character- 
 istic notes. Imagination filled in what was lacking, 
 and he unhesitatingly judged that this was his brother. 
 If his observation was hastily made, the judgment may 
 well have been mistaken. Again men have often asserted 
 that a thing does not exist, merely because under circum- 
 stances in which they believed they would have seen it 
 if it did exist, they have failed to see it. Here, mani- 
 festly, the assertion is the conclusion of a hasty inference. 
 It may be that the phenomenon was such as their unaided 
 faculties were not capable of perceiving. Such errors 
 are characteristic of those who are unversed in scientific 
 observation. The scientific observer knows that true 
 observation, though intelligent, must be free from infer- 
 ential conclusions. 
 
 Though the external senses are the instrument given to us by 
 nature to observe the natural order, yet man's inventive power 
 
OBSERVATION AND EXPERIMENT 313 
 
 has found means to obtain auxiliary instruments, capable of 
 registering facts outside the ken of immediate sense-perception. 
 An interesting example is afforded in photography. The im- 
 pression made by a ray of light on the retina of the eye, reaches 
 its maximum in about r \ T th of a second, and after that time 
 ceases to increase, for the limits of sensibility have been reached. 
 Hence when the action of the ray is too faint for it to become 
 perceptible within that period, we are unable to see the object 
 whence it proceeds. It is not so, however, with the sensibility 
 of the photographic plate. Here the effect continues to accumu- 
 late as long as exposure continues. Thus many objects, which 
 to the naked eye are invisible, leave a permanent impression on 
 the photographic plate. This fact has proved of the utmost 
 value in science, since it permits us to obtain records of number- 
 less astronomical phenomena, which otherwise must have re- 
 mained undiscovered. To the same category of auxiliary instru- 
 ments belong microscopes, microphones, Rontgen-rays, etc. 
 
 3. Conditions of Observation. It is impossible to 
 draw up a set of practical rules to be followed in every 
 case of observation. As Mill has well said, " The extent 
 ' and minuteness of the observation which may be re- 
 ' quisite, and the degree of decomposition to which it 
 'may be necessary to carry the mental analysis, depend 
 ' on the particular purpose in view " (III. c. 7, i). We 
 can, however, indicate certain general conditions, which 
 the work of observation demands in those who undertake 
 it. These conditions are intellectual, physical and moral. 
 
 In the intellect, observation calls for the spirit of 
 inquiry the desire to know the reason of things, to have 
 an explanation of what we see. This spirit of inquiry 
 is as natural to the healthy mind, as is the appetite for 
 food and exercise to the body. It is to this desire to 
 find an explanation for things, that Aristotle rightly 
 attributes the origin of science and philosophy. 1 The 
 craving may, and often indeed does become atrophied. 
 But when this occurs, no mere excellence of the sense- 
 faculty will make a competent observer. 
 
 Physically, it is necessary that the sense or senses 
 employed, should be sound. Those who suffer from 
 
 1 Met., I., c. 2. Sict y&p TO 6av/j.deiv ol HvdpuTTQi. KO,\ vvv Ka.1 TO 
 
3 i4 PRINCIPLES OF LOGIC 
 
 colour-blindness cannot undertake observations, in which 
 the discrimination of colours is in question, nor can the 
 tone-deaf distinguish sounds. Yet if a man has once 
 possessed the faculty, and has been deprived of it through 
 illness or advancing years, he is not wholly debarred 
 from the work of the observer. He may observe with 
 the eyes of other men. For the faculty of imagination 
 enables him to reconstruct what they communicate to 
 him. Thus Arago, after blindness befell him, continued 
 his researches into the polarization of light, employing 
 the eyes of others to aid him in his work. 1 Where, how- 
 ever, the sense has never been possessed, there this 
 mediate observation is impossible ; for the imagination 
 is powerless to reproduce phenomena unlike to anything 
 of which we have had experience. 2 
 
 The chief moral requisite, which observation demands, 
 is impartiality. This condition is not one which it is 
 easy to fulfil. Jevons truly remarks that "it is not 
 ' easy to find persons who can with perfect fairness, 
 ' register facts both for and against their own peculiar 
 1 views " (Principles, p. 402). No one comes to the task 
 of observation unbiassed. Each investigator has opinions 
 and beliefs of his own ; he desires that his beliefs may 
 be confirmed, that he may not have to face the difficulty 
 of seeking new solutions to problems he regards as solved. 
 Indeed, in many cases the observation is actually prompted 
 by such a belief ; it is made because the observer is 
 confident that it will confirm some cherished hypothesis. 
 It requires great candour and openness of mind, for a 
 man thus situated to be impartial in his study of facts, 
 and to refrain from reading into them that which he 
 wishes to see. Yet it is the first duty of the observer 
 to accept the truth, whether it be welcome or unwel- 
 come. 
 
 Some writers exaggerate the sphere, within which 
 the observer is bound to preserve this openness of mind. 
 They have urged that it is his duty to regard all his 
 beliefs and convictions, metaphysical, religious and 
 
 1 Rabier, Logique, p. 98. 2 Cf. An. Post. /., c. 18, i. 
 
OBSERVATION AND EXPERIMENT 315 
 
 scientific, as liable to correction and revision as the 
 results of his observations may prescribe. 1 To hold 
 such a view as this, is to maintain that human knowledge 
 is built upon the sand, and that neither in philosophy 
 nor in religion have we found any foothold on the rock 
 of certainty. Were this so, all intellectual effort would 
 be futile indeed. But our case is not so desperate. Both 
 in the sphere of religion and in that of science, we are 
 in possession of irrefragable verities. Thus, to confine 
 ourselves to the natural order, a man would lack intelli- 
 gence, who should propose to hold the principle of contra- 
 diction or of causality as open to revision. We must 
 distinguish between what is certain, and what, although 
 probable and, it may be, supported by many facts, is 
 not yet fully established. It is the latter alone, not the 
 former, that the observer must be ready to relinquish. 
 For truth is consistent with itself. And when once 
 absolute certainty has been attained, then the supposition 
 of contradictory evidence becomes an absurdity. 
 
 4. Experiment. We have seen that the purpose 
 both of Observation and of Experiment in the sciences 
 of physical law, is to establish the existence of a causal 
 relation between an antecedent and a consequent, or 
 else to prove by elimination that some particular ante- 
 cedent is not the cause. Experiment only differs from 
 Observation, in so far as in Experiment we observe the 
 phenomenon under conditions which have been artificially 
 simplified. The necessity of this arises from the fact 
 that the conditions, as they occur in Nature, are extremely 
 complex. We should therefore be at a loss to distinguish 
 which of the many antecedents was the true cause of 
 the phenomenon, were it not possible to produce this 
 latter in circumstances carefully determined, and thus 
 
 1 " Le doute philosophique, dont il s'agit ici, ne consiste pas a douter de 
 la science elle-meme, ni de 1'esprit humain en general, mais a tenir momentanS- 
 ment comme douteuses et susceptibles d'etre redressees et corrigees par les 
 lecons de la r6alit6 toutes les opinions, soit religieuses, soit metaphysiques, 
 soit scimtifiques, que nous consid6rons d'ailleurs comme les plus justinees 
 et les plus certaines." Rabier, Logique, p. 103. 
 
316 PRINCIPLES OF LOGIC 
 
 to exclude the supposition that any causes are operative, 
 save those we are engaged in considering. A good 
 example of such artificial simplification is afforded by 
 the well-known ' guinea and feather ' experiment, in 
 which the two substances are placed in an exhausted 
 receiver, and allowed to fall from the top together. 
 They reach the bottom of the receiver at the same moment, 
 and thus demonstrate to us that when the resistance of 
 the air and other interfering influences are allowed for, 
 all bodies tend to the earth with equal rapidity. It is 
 plain that without some method of simplifying the con- 
 ditions, it would have been difficult, if not impossible, 
 to obtain conclusive evidence of this truth. 
 
 It will be seen that although Observation may take 
 place without set purpose, and indeed the history of 
 science records not a few famous discoveries made by 
 what may be called chance, Experiment necessarily 
 requires an hypothesis. Unless we frame some sup- 
 position, and make our experiment to the end that we 
 may know whether this supposition is correct or not, no 
 experiment can take place. To experiment is to question 
 Nature ; and our question must take some clearly defined 
 form. 
 
 The mere use of a scientific instrument does not in 
 itself constitute an experiment. We do not speak of 
 experimenting, but of observing with a microscope. To 
 make an experiment, it is not enough that the observer 
 himself should be set in new and special circumstances. 
 It is requisite that the object observed be placed under 
 new conditions, and further that these new conditions 
 should in some way modify its action. 
 
 In scientific investigation, it is not infrequently neces- 
 sary to make use of what is termed the Blind or Negative 
 Experiment. This is an attempt to show that not only 
 is A always followed by a, but that a is always preceded 
 by A : that a particular antecedent always involves 
 a particular consequent, and that this consequent never 
 occurs except when the antecedent in question has 
 preceded it. An example is afforded by a series of 
 
OBSERVATION AND EXPERIMENT 317 
 
 experiments which were undertaken in regard to the 
 origin of the sleeping-sickness of Uganda. A series of 
 careful observations were first made which appeared to 
 establish that the disease was due to a certain microbe 
 communicated to the blood by the bite of the tsetse fly. 
 But a further series of experiments was undertaken, in 
 which it was shown that even where all the other con- 
 ditions, which usually accompany the disease, were present, 
 yet if this microbe was not communicated to the blood, 
 the disease never appeared. This last part of the investi- 
 gation constituted the Negative Experiment. 
 
 5. Natural Experiments. A Natural Experiment is 
 the name employed to denote those events, in which 
 the processes of Nature themselves produce special and 
 determinate conditions, under which the phenomenon 
 in question may be observed. Such events have proved 
 of great importance in many sciences. Astronomers 
 are indebted to these natural experiments for many of 
 their discoveries. An eclipse of the moon, such as we 
 have all of us witnessed, affords us a case in point. Here 
 the shadow cast upon the lunar disc shows us the shape 
 of the earth. Another interesting example may be 
 given, relating to visual perception. It had long been 
 disputed whether the defect to which colour-blindness 
 was due, was in the eye itself or in the brain. The doubt 
 was solved in the following manner. The affection is 
 occasionally hereditary ; and cases have been known 
 to occur, in which the vision of one eye is normal, while 
 the other suffered from ' red-green ' blindness. Now, 
 had the lesion been in the brain, this could not have 
 occurred. For each of the eyes is supplied with nerves 
 from either side of the brain, the nerves crossing each 
 other in what is called the optic chiasma. 1 
 
 6. Relative Advantages of Observation and Experi- 
 ment. In all cases, in which Experiment is possible, 
 there can be no room for comparison between it and 
 Observation, so complete is its superiority from the 
 
 1 Proc, Royal Society, vol. 31, p. 302, 1881. 
 
3 i8 PRINCIPLES OF LOGIC 
 
 scientific investigator's point of view. Its limitations 
 lie in the fact that a vast number of Nature's processes 
 cannot be imitated. In these cases, we must be content 
 to observe. Thus, we have no means of experimenting 
 where geological and cosmic forces are concerned. We 
 must be content to wait on Nature, and to learn from 
 her, as by her own methods she achieves her work in the 
 great laboratory. In the case of many phenomena, the 
 scientist is fortunate, who has the opportunity of con- 
 ducting an observation himself, and need not rely on 
 the reports of others. Few astronomers have been able 
 like Tycho Brahe to note the appearance of a temporary 
 star at the very hour when it commenced to shine in 
 the heavens. " This appearance of the star of 1572," 
 writes Herschel, " was so sudden, that Tycho Brahe, 
 ' returning one evening (nth November) from his labo- 
 * ratory to his dwelling-house, was surprised to find a 
 ' group of country-people gazing at a star, which he 
 ' was sure did not exist half an hour before. It was 
 ' then as bright as Sirius, and continued to increase till 
 ' it surpassed Jupiter when brightest, and was visible 
 ' at midday." 1 
 
 The advantages of Experiment over Observation are 
 to be found in the fact that we are enabled by it (i) to 
 produce, under varying conditions, a number of instances 
 of the phenomenon we desire to investigate, (2) to simplify 
 the conditions, (3) to produce new phenomena of a 
 similar kind. 
 
 (i) It is hardly necessary to dwell on the importance 
 of varying the conditions of the phenomenon. The 
 investigation, for instance, of the facts relating to the 
 crystallization of bodies would have presented immense 
 difficulties, had it not been in our power to reproduce 
 such phenomena experimentally. The science of elec- 
 tricity would probably never have emerged from infancy, 
 had it been possible to study it only during the thunder- 
 storm. 
 
 A multitude of instances does much too to protect us 
 
 1 Herschel, Outlines of Astronomy (nth edit.), p. 602. 
 
OBSERVATION AND EXPERIMENT 319 
 
 against the tendency already mentioned ( 3), which 
 leads us to see our own beliefs confirmed by the facts 
 we observe. When experiments are multiplied, in some 
 one or other we find a crucial instance proving that we 
 are in error. 
 
 (2) As experiment helps us to simplify the conditions 
 of the phenomenon, it enables us to exclude any circum- 
 stances that may operate as interfering causes. We are 
 thus able to control the phenomenon, and to obtain 
 certain knowledge instead of mere conjecture. Thus a 
 simplification, very similar to that of the guinea and 
 feather experiment, provides us with a proof that the 
 transmission of sound is due to vibration in the atmo- 
 sphere. A bell is struck in a vacuum, and no sound is 
 heard. 
 
 (3) Of the production of phenomena, similar to those 
 which Nature shews us, we have striking examples in 
 recent scientific investigation, in the famous experiments 
 by which Professor Dewar succeeded in liquefying and 
 freezing oxygen, hydrogen and air. These experiments 
 revealed to us a series of facts analogous indeed to those, 
 with which we are familiar, but which Nature uncon- 
 trolled affords us no opportunity of observing. 
 
 As we should be led to expect, having regard to the 
 immense advantages possessed by experimental investi- 
 gation, the sciences in which this has been possible, are 
 those in which the greatest progress has been made. 
 Mechanics, Physics and Chemistry all admit of experiment 
 to a very large extent. In Anatomy, Physiology, Meteor- 
 ology it can hardly be employed. It will not therefore 
 surprise us that the former group of sciences has 
 advanced far more rapidly than the latter. 
 
CHAPTER XX. 
 
 METHODS OF INDUCTIVE ENQUIRY. 
 
 i. The Four Experimental Methods. Our purpose 
 in this chapter is to describe the principal ways, in which 
 the evidence of a causal connexion manifests itself. We 
 shall thus be describing the manner in which scientists 
 are accustomed to direct their observations and experi- 
 ments, in order to win from Nature the secret of her 
 laws. For to know the various ways in which the evi- 
 dence of universal laws appears, is to know the methods 
 of scientific inquiry. As we have already said (Ch. 14, 
 4), it is not possible to lay down fixed canons of evidence, 
 prescribing the precise conditions under which we may 
 be certain as to the existence of a general law. For 
 what is satisfactory evidence in one case, is quite insuffi- 
 cient, when a subject of a different character is under 
 consideration. If on two or three occasions I hear a 
 wild bird of a certain kind give voice to a special song, 
 I rightly conclude that there is a causal connexion between 
 that species of bird and the soixg in question. But be- 
 cause it has occurred two or three times that a special 
 sort of food has been hurtful to me, I should be rash in 
 making an induction to a general law. In such a case, 
 the effect may be due to accidental circumstances. 
 Again, it is possible to test the evidence of a deductive 
 argument by a canon ; for in Deduction, the whole of 
 the evidence is contained in the two premisses of the 
 syllogism. In Induction, the evidence is not the mere 
 singular fact from which I abstract the law, but a number 
 of other facts recorded in memory, some of them 
 concerning the phenomenon about which the law is 
 
METHODS OF INDUCTIVE ENQUIRY 321 
 
 enunciated, and some concerning the surrounding 
 circumstances. 
 
 The discussion of these Experimental Methods, as 
 they are often termed, is in large measure due to the 
 important place they hold in Mill's Logic. He doubtless 
 took a mistaken view of them. He drew up elaborate 
 canons for them, and believed that they were so many 
 distinct processes of inductive reasoning. His treatment 
 has been the object of much criticism. Yet it should 
 be borne in mind, that though his analysis may be wrong, 
 the methods he attempts to formulate are from a prac- 
 tical standpoint those employed in scientific investigation. 
 We cannot therefore dismiss them from our consideration. 
 We must endeavour to determine what is their true 
 bearing on Induction. 
 
 The subject is usually discussed in relation to Mill's 
 treatment, and we shall not deviate from that practice. 
 We give here in tabulated form, his Methods with their 
 respective canons. An example is given in each case, 
 illustrating the application of the method in question : 
 
 I. Method of Agreement. 
 
 Canon. " If two or more instances of the pheno- 
 ' menon under investigation have only one circumstance 
 ' in common, the circumstance in which alone all the 
 ' instances agree, is the cause (or effect) of the given 
 'phenomenon" (III. c. 8, i). 
 
 Mill represents this method by a formula in which 
 the capital letters stand for antecedents, the small letters 
 for consequents. Granted that the two instances may 
 be symbolized respectively as ABC-abc, ADE-o^tf, then 
 we may conclude that A is the cause of a. 
 
 The Method may be illustrated by the following 
 example from Jevons. "Sir D. Brewster accidentally 
 ' took an impression from a piece of mother-of-pearl in 
 ' a cement of resin and bee's-wax, and finding the colours 
 1 repeated upon the surface of the wax, he proceeded 
 ' to take other impressions in balsam, fusible metal, 
 ' lead, gum arabic, isinglass, etc., and always found that 
 ' the iridescent colours are the same. He thus proved 
 
 Y 
 
322 PRINCIPLES OF LOGIC 
 
 ' that the chemical nature of the substance is a matter 
 ' of indifference, and that the form of the surface is the 
 ' real condition of such colours " (Principles, p. 419). 
 
 II. Method of Difference. 
 
 Canon. "If an instance in which the phenomenon 
 ' under investigation occurs, and an instance in which 
 ' it does not occur, have every circumstance in common 
 ' save one, that one occurring only in the former : the 
 ' circumstance in which alone the two instances differ 
 ' is the effect, or the cause, or an indispensable part of 
 'the cause of the phenomenon" (III. c. 8, 2). 
 
 Formula. ABC-abc, EC-be : whence it may be con- 
 cluded that A is the cause of a. 
 
 A good example is provided by the experiment referred 
 to above, in which a bell is struck in a vacuum, and no 
 sound is heard. In the first instance, the air is present 
 in the receiver, and the striking of the bell is clearly 
 audible. Here the presence of the air is denoted by A, 
 and the sound by a. The air is then removed by means 
 of an air-pump, and the removal of this antecedent is 
 seen to involve the removal of the consequent a. We 
 are thus assured that the air must at least play an 
 indispensable part in enabling us to hear. 
 
 Joint Method of Agreement and Difference. 
 
 This method is not reckoned by Mill as independent 
 of the preceding ones, and as constituting a distinct 
 method of proof. He holds it to be " a great extension 
 ' and improvement of the method of Agreement, but 
 ' not as participating in the more cogent nature of the 
 ' method of Difference." 
 
 Canon. " If two or more instances in which the 
 ' phenomenon occurs have only one circumstance in 
 ' common, while two or more instances in which it 
 ' does not occur, have nothing in common save the 
 ' absence of that circumstance : the circumstance in 
 ' which alone the two sets of instances differ, is the 
 ' effect or cause or an indispensable part of the cause 
 'of the phenomenon" (III. c. 8, 4). 
 
 It is of course to be understood that the instances in 
 
METHODS OF INDUCTIVE ENQUIRY 323 
 
 which the phenomenon does not occur, are of such a 
 character, that were it due to any other cause but the 
 circumstance in question, there would be good reason 
 to anticipate its appearance. Unless the instances were 
 thus relevant to the subject under consideration, they 
 would afford no grounds for a conclusion of any kind. 
 
 Formula. No formula is given by Mill. Mr. Welton 
 suggests the following : ABC-abc, ADE-ade, BT>M.-bdm, 
 CEO-ceo : whence we conclude that A is the cause of a. 
 
 In illustration of the method, we may take the investi- 
 gations made by Darwin in regard to the influence of 
 earthworms in the production of vegetable mould. 1 In 
 these investigations, a large number of observations 
 were made as to the formation of mould on soil of different 
 kinds. The development of the mould and the apparent 
 sinking of the objects on the surface, were carefully 
 noted. Notwithstanding the variety of circumstances, 
 the growth of the mould was a feature common to all 
 these instances. And as far as could be detected, the 
 one circumstance common to all alike was the presence 
 of earthworms in great quantities in the surface soil. 
 
 A number of cases were also examined, in which 
 there had been no increase of mould. The cases selected 
 were thoroughly relevant, for the land observed was 
 in the same districts as those which had provided the 
 positive instances. It was invariably found that either 
 from excessive dry ness, or for some other reason, the 
 soil here contained no earthworms. 
 
 These two classes of observations are those contem- 
 plated by the canon, and provide a large amount of 
 evidence for the conclusion that the action of the earth- 
 worms is causally related to the development of the 
 mould. To render the conclusion more certain, experi- 
 ments were undertaken to test the adequacy of the cause 
 to produce the effect. It was estimated that in cultivated 
 soil, earthworms exist in sufficient number to give between 
 seven-and-a-half to eighteen tons per acre of castings 
 
 1 Vide Welton, Manual, 154. Mr. Welton gives this example in a slightly 
 different connexion. 
 
324 PRINCIPLES OF LOGIC 
 
 every year. These results would yield a layer of mould 
 from an inch to an inch-and-a-half in thickness every 
 ten years. The cause is therefore fully adequate to 
 produce the effect attributed to it. 
 
 HE. Method of Residues. 
 
 Canon. " Subduct from any phenomenon such part 
 ' as is known by previous inductions to be the effect of 
 ' certain antecedents, and the residue of the phenomenon 
 ' is the effect of the remaining antecedents " (III. c. 8, 
 
 5). 
 
 Formula. If it be known that ABC-abc are causally 
 connected, and further that A is the cause of a, B of 6, 
 then we may conclude that C is the cause of c. 
 
 The method may be illustrated by the discovery of 
 the planet Neptune by Leverrier. Here the motions of 
 Uranus provided the clue. While their general features 
 were such as the position of the planet in the solar system 
 would prescribe, they presented nevertheless certain 
 residuary phenomena, which convinced the astronomer 
 that yet another planet existed, to whose influence they 
 must be attributed. This conclusion was shown to be 
 justified by the subsequent discovery of Neptune. 
 
 In cases such as this we do not, strictly speaking, attribute 
 the remaining consequent to the ' remaining antecedent.' We 
 are led by the presence of an unexplained element in the pheno- 
 menon we are considering, to seek its unknown cause. Hence, 
 it has been urged that Mill's canon is not applicable, and that 
 these cases should be regarded as exemplifying another rule, viz., 
 " When any part of a complete phenomenon is still unexplained 
 ( by the causes which have been assigned, a further cause for the 
 ' remainder must be sought' 1 The point need not detain us : 
 for we are not here concerned to vindicate the validity of Mill's 
 formula, but only to shew what modes of investigation his canons 
 were intended to describe. In explaining his Method of Residues, 
 he explicitly mentions as falling under it, those cases in which 
 " the agent C is an obscure circumstance not likely to have been 
 'perceived unless sought for" (III. c. 8, 5). 
 
 IV. Method of Concomitant Variations. 
 Canon. " Whatever phenomenon varies in any manner 
 * whenever another phenomenon varies in some par- 
 
METHODS OF INDUCTIVE ENQUIRY 325 
 
 ' ticular manner, is either a cause or an effect of that 
 ' phenomenon, or is connected with it through some fact 
 'of causation" (III. c. 8, 6). 
 
 Formula. The following expression is given by Mr. 
 Welton : A 1 BC- 1 6c, A 2 BC-0 2 fo, A 3 BC-# 3 fo : whence 
 we conclude that A is causally related to a. 
 
 It is in this manner that Albert the Great proves the 
 causal influx of the moon on the tides. The discovery 
 of the connexion between the moon on the one hand 
 and the ebb and flow of the tide on the other, had been 
 made by the Arabs : and from them the knowledge 
 had passed into Europe in the ninth century. Albert 
 in one of his works, argues the point against certain 
 opponents of the theory, and bases his conclusion on the 
 principle that the concomitance of phenomena is indicative 
 of causal connexion. 1 
 
 In a similar way Pascal showed that the column of 
 mercury in a barometer is sustained by the weight of 
 the atmosphere. In 1648 at the suggestion of Descartes, 
 he made a series of observations on the Puy-de-Ddme 
 mountain, which conclusively established that the height 
 of the mercury varied concomitantly with the different 
 altitudes at which the observation was taken. 2 
 
 2. Further Illustrations of the Methods. The illus- 
 trations given in the last section were selected in each 
 case because of their simplicity. In practice, however, 
 it usually happens that the determination of a relation 
 between cause and effect, involves the use of more than 
 one of the methods, and is by no means so simple and 
 straightforward a proceeding as these examples would 
 
 1 Albertus, De Proprietatibus Elementorum, lib. I. tract 2, c. 8. '* Contra 
 secundam autem sectam est, quod si moveretur mare quia spirat naturaliter, 
 sicut alia in quibus generantur venti et vapores spirituales ; et tune debet 
 fieri accessus et recessus per unura modum semper ; quia opera naturae sunt 
 uno modo : . . . tamen ejus contrarium videmus, quod sequitur motum 
 lunae, ad hoc quod posito aliquo ponitur et destructo destruitur et hoc causatur 
 ab ipso : sic autem videmus semper accessum maris poni et fieri quando luna 
 tangit circulum hemisphaerii : videbitur igitur causari ex motu lunae." Cf. 
 Scotus, Meteor, lib. ii. q. 2. 
 
 8 Haldane, Descartes, p. 310, 
 
326 PRINCIPLES OF LOGIC 
 
 lead us to suppose. This point is of importance in 
 considering the relation of the methods to Induction. 
 In this section, we give two instances of such scientific 
 investigation. 
 
 (i) Effect of radio-active substances on gelatin media. 
 Our first example is drawn from an enquiry bearing on 
 the alleged effect of radium in producing life. In 1906, 
 considerable interest was aroused in some experiments 
 made by Mr. Butler Burke to test the effect of radio- 
 active substances on gelatin media. He found that as 
 the result of their action certain ' bacteria-like ' cells 
 were obtained, containing a nucleus ; that they appeared 
 to be highly organized bodies ; and that after growing 
 to a certain point, they subdivided. 
 
 In order to test these results and discover whether 
 Mr. Burke was justified in supposing that living cells 
 had been produced, a series of experiments was under- 
 taken by Mr. Douglas Rudge. It is these experiments 
 which provide our example. 1 
 
 (a) In the first place, several samples of radium salts 
 were used. These differed in their degree of purity, 
 and it was seen that the rate and amount of growth did 
 not correspond to the amount of radmm present in the 
 sample. As radium salts contain a large admixture of 
 barium salts, it was thought possible that the latter, and 
 not the former, might be the agent which produced the 
 cells. It was found on experiment that barium salts 
 without radium, produced a growth which appeared 
 identical with that caused by the radium. 
 
 These experiments were, as is easily seen, negative 
 instances in the methods of Concomitant Variations 
 and of Difference. They appear to render it certain 
 that radium was not the cause of the cells. 
 
 (b) A s} stematic examination followed with all kinds 
 of metallic salt. It was found that those of barium, 
 lead and strontium were the only ones which resulted 
 in the appearance of the growth. These three metals 
 are those which form insoluble sulphates ; and the con- 
 
 1 Vide Proc. Royal Soc., Dec. 20, 1906, vol. 78. 
 
METHODS OF INDUCTIVE ENQUIRY 327 
 
 elusion suggested by the experiments, was that the 
 cells developed round precipitates, which were formed 
 owing to the presence of sulphur in the medium. 
 
 This group of experiments shows us the application 
 of the Method of Agreement. 
 
 (c) Instead of gelatin, other forms of meat-culture 
 were now tried, fixity being given to them by various 
 mucilaginous substances, such as starch, gum, etc. It 
 was found that if distilled water were employed, no 
 growth appeared, and that the growth was in all cases 
 proportionate to the amount of sulphur in the water. 
 Further, between thirty and forty specimens of gelatin 
 were tested, and with three exceptions, all proved to 
 contain enough sulphuric acid to give a distinct preci- 
 pitate. 
 
 In this case, the Method of Concomitant Variations 
 was again used ; but on this occasion, the result was 
 not negative but positive. 
 
 (d) Finally, experiments were made in gelatin, from 
 which all sulphuric acid had been removed, with the 
 result that no sign of growth manifested itself. 
 
 Having regard to the evidence furnished by the pre- 
 vious experiments, this last may be considered as an 
 application of the Method of Difference. 
 
 The final result of the whole investigation was entirely 
 to discredit the view that the phenomenon was in any 
 sense a vital process. It was shown (i) that the cells 
 form round a precipitate of insoluble sulphate, the growth 
 of the cell being dependent on the amount of sulphur 
 present ; and (2) that radium has no specific action in 
 forming cells. 
 
 (2) Possibility of spontaneous generation. As our second 
 instance, we give a short account of some experiments 
 carried out by M. Pasteur in his famous investigations 
 regarding this subject. 1 The spontaneous development 
 of life in substances undergoing decomposition, was 
 strenuously maintained by Pouchet and other scientists ; 
 
 1 Vide Guibert, In the Beginning (' Les Origines,' transl. by Whitmarsh), 
 c. 12 : and Rabier's Logique, pp. 138-141. 
 
328 PRINCIPLES OF LOGIC 
 
 and these experiments were undertaken by Pasteur in 
 order to shew that if sufficient precautions were taken 
 to exclude the germs which are so plentiful in the atmo- 
 sphere, no life would be developed, and no decomposition 
 take place. 
 
 (a) He first filled a flask with a liquid known to be 
 specially liable to decomposition. The long curved 
 neck of this flask was connected with a platinum tube 
 which passed over a flame. The liquid in the flask was 
 boiled, and at the same time, the platinum tube was 
 heated red-hot. The flask was then allowed to cool ; 
 but while it cooled the platinum tube was kept at its 
 high temperature, so as to ensure that the air which 
 entered the flask should be free from all germs. The 
 flask was then closed ; and it was found that no life 
 whatever was developed in the liquid. 
 
 Here we appear to have an instance of the method 
 of difference. ^For it seems that the sole circumstance 
 distinguishing this case from one in which decomposition 
 takes place, is the presence of germs in the air within 
 the flask. Exception was however taken to the con- 
 clusiveness of the experiment. It was urged that 
 spontaneous generation might depend on the presence 
 of certain conditions in the atmosphere, with which 
 the heating process had interfered. 
 
 (b) Recourse was therefore had to another experiment. 
 The air admitted into the flask was not transmitted 
 through a red-hot tube, but simply passed through a 
 cotton-wool stopper. The effect was found to be the 
 same. Further, in order to preclude any objections on 
 the score that cotton-wool, being an organic substance, 
 might have some peculiar effect in rendering the liquid 
 sterile, a similar experiment was made, in which the 
 stopper was not of wool, but of asbestos. 
 
 Here the method of agreement is exemplified. The 
 three cases we have considered, agree in so far that life 
 is produced in none of them, and they have but one 
 material circumstance in common, namely, the exclusion 
 of vital germs. 
 
METHODS OF INDUCTIVE ENQUIRY 329 
 
 (c) Yet it is to be noted that in each case the liquid 
 was first boiled. It might perhaps be said that this 
 boiling had made spontaneous generation impossible. 
 It was necessary to exclude this suggestion. M. Pasteur 
 therefore made a fresh experiment, this time with blood 
 obtained direct from the veins of healthy animals, so 
 that it was as yet free from all contamination ; he exposed 
 this blood to contact with air purified from vital germs. 
 Though blood is a substance, which readily decomposes, 
 no development of life took place. 
 
 This experiment may be regarded as completing the 
 application of the Method of Agreement. 
 
 (d) Finally an especially interesting group of experi- 
 ments was made in the following manner. Liquid was 
 enclosed in a number of flasks. The necks of all these 
 flasks were sealed over a blow-pipe, after all vital germs 
 that might be contained in it, had been destroyed by 
 boiling. The flasks were distributed in various places, 
 their necks broken, and the liquid exposed to the air. 
 It was found that the proportion of those in which putre- 
 faction took place to those which escaped, was just 
 what might have been anticipated, if, as was urged, 
 decomposition was due to germs floating in the air. In 
 a dwelling-room, in which the ordinary sweeping and 
 dusting of a household made the distribution of dust 
 general, not a flask escaped. In the open air of the 
 country, decomposition took place in eight out of twenty 
 flasks. On one of the lower spurs of Mount Jura, five 
 only out of twenty, became infected. And on the 
 Mer-de-glace, decomposition set in in one case, while 
 nineteen remained free. Had the development of life 
 been due, not to the chance distribution of germs, but 
 to spontaneous generation, it is difficult to see how such 
 results could have been obtained. Where the flasks 
 contained the same liquid, and were exposed to the 
 same conditions, either all would have developed life, 
 or none. 
 
 This final experiment may legitimately be reckoned 
 as falling under the Method of Concomitant Variations. 
 
330 PRINCIPLES OF LOGIC 
 
 3. The Function of the Methods in proving a Law 
 of Nature. It was shewn in Ch. 14, that the act of 
 Induction is immediately dependent on the recognition 
 by the intellect of a causal relation connecting two facts. 
 We pass to our universal conclusion, when the intellect, 
 considering the facts revealed by sense, apprehends the 
 precise characteristic, in virtue of which the agent pro- 
 duces such and such an effect. This may be other- 
 wise expressed by saying that Induction is possible, 
 when not only the complex elements which consti- 
 tute the phenomenon are perceived by the senses, but 
 when the mind also understands the relation uniting 
 them. 
 
 The question now arises as to how the Experimental 
 Methods, which we have been considering, assist us in 
 this task. It is of course evident that in themselves 
 the Methods are not logical processes. They are merely 
 special ways of arranging our data. They constitute 
 in each case a prerequisite to the mental act, by which 
 we make an inference from the facts. 
 
 The Methods aid us in two ways. They provide the 
 data for (i) Eliminative Syllogisms, (2) Induction. 
 
 Elimination must be carefully distinguished from 
 Induction properly so called. It is of value as an ancil- 
 lary process, but it is not Induction. Its importance 
 is due to that complexity of Nature, which provides so 
 many difficulties to the scientific investigator. When 
 we are seeking to discover the cause of some fact, it is 
 often the case that while we have good reason to suppose 
 the cause is one of several antecedents, there is nothing 
 to indicate with certainty, which of these it is. The 
 application of the Methods enables us to eliminate many 
 of these antecedents. For if it can be shewn (a) that 
 some particular phenomenon is present when the fact 
 in question is absent, or (b) that it is absent when the 
 fact is present, or (c) that its variations bear no relation 
 to variations observed in the fact, then w r e know that 
 it is not the cause at least not the complete and suffi- 
 cient cause of the fact. The arguments by which we 
 
METHODS OF INDUCTIVE ENQUIRY 331 
 
 reject these suggested causes, are deductive syllogisms 
 in Celarent : 
 
 No characteristic which is present when a is absent, 
 
 is the cause of a. 
 
 /3 is a characteristic, which is present when o is 
 absent. 
 
 .-. /3 is not the cause of a. 
 
 It has been maintained by some that the inductive 
 process consists essentially in Elimination ; that in a 
 valid Induction, the antecedents among which the cause 
 is to be looked for, are first tabulated and then succes- 
 sively eliminated until one only remains. This remain- 
 ing antecedent is then declared to be the cause. " The 
 ' essence of inductive reasoning," says Mr. Joseph, " lies 
 ' in the use of our facts to disprove erroneous theories 
 ' of causal connexion. It is ... a process of elimina- 
 ' tion. The facts will never show directly that a is the 
 ' cause of x : you can only draw that conclusion if they 
 ' show that nothing else is " (Introd., p. 395). This view 
 we believe to be untenable. An argument drawn in 
 this manner would remain for ever inconclusive. Where 
 conclusions have been based on such reasoning, they 
 have often proved to be incorrect. The list of antece- 
 dents was defective, and the true cause has been dis- 
 covered in some factor that had been overlooked. We 
 must not merely eliminate those antecedents which are 
 not the cause ; we must have positive grounds for assert- 
 ing that the effect proceeds from such and such a fact 
 and from no other. 
 
 The Methods provide us with the material not merely 
 for Elimination, but for Induction properly so called. 
 The object that we have in view in them, is so to simplify 
 our data, that we shall no longer be bewildered by their 
 complexity, but shall recognize the causal relation as it 
 is exemplified in the individual case. Our aim is to see 
 A producing , and this so clearly that the mind shall 
 affirm that a proceeds from A qua A, that is from A in 
 respect of its being A and nothing else. To quote some 
 words of Aristotle already cited (Ch. 14, 4) : "Not 
 
332 PRINCIPLES OF LOGIC 
 
 ' that the mere act of sight would give us scientific 
 ' knowledge ; but sight would be the means, through 
 ' which we should attain the universal." * Such, to 
 take a simple example, is the inductive process, when 
 after employing the Method of Difference, we induce 
 the general conclusion that gold is dissolved by aqua 
 regia. Previous to the application of the aqua regia, 
 there is no dissolution. It is applied, and the senses 
 show us dissolution taking place wherever the liquid 
 reaches. The intellect does not set to work eliminating, 
 but abstracts a general conclusion that gold as such is 
 dissolved by aqua regia. 
 
 In certain cases, the evidence of causation is provided 
 not by one, but by a series of observations. Pascal's 
 experiments as to the pressure of the atmosphere on the 
 barometer furnish us with a case in point. Taken 
 separately, each observation would have been insufficient 
 for his conclusion. If, however, a series of such observa- 
 tions be viewed together, as they are in fact viewed 
 when stored in the memory of the observer, the effect 
 on the mind is convincing. It recognizes the combined 
 testimony to the causal influx, and draws its universal 
 conclusion. 
 
 Without doubt, a vast number of our inductions are 
 only probable. We believe that we recognize one fact 
 as determining another, whereas in truth we have merely 
 some fallible signs of causality. Thus, when before 
 the discovery of gravitation, the ancients judged that 
 All heavy substances tend downwards, all light substances 
 upwards, 2 it appeared to them that the facts showed a 
 spontaneous tendency in light substances to rise above 
 the earth ; and they held that this motion must be 
 caused by the * lightness ' inherent in them. In such cases, 
 as we saw in Ch. 19, 2, imagination outruns observation. 
 We believe there is a relation of cause and effect, not 
 
 1 An. Post. /., c. 31. 8. oi/x^s eldores T$bpq.v, d\\' ws x oi/7 " ej T & Kado\ov IK 
 roO opav. 
 
 8 Cf. Arist. Physics, IV., C. 4, 21. ^Trei rb fjikv KOV<J>OV rb &va> 
 i, rb 
 
METHODS OF INDUCTIVE ENQUIRY 333 
 
 because its existence is evident, nor because, strictly 
 speaking, we infer it, but because at the suggestion of 
 certain signs we imagine it. Of this character was the 
 error described in the last section in regard to the activity 
 of radium. The cells arose on the application of the 
 radium salt. Here was a phenomenon which is one of 
 the signs of causality, though not an infallible sign. 
 Imagination did the rest. 
 
 It may be observed that the emendations suggested by various 
 authors for the Method of Difference, harmonize with the 
 account of the process we have offered. Thus Dr. Mellone pro- 
 poses that the canon should run as follows " When the addition 
 ' of the agent is followed by the appearance, or its subtraction by the 
 ' disappearance of a certain event, the other circumstances remaining 
 ' the same, that agent is the cause of the phenomenon." As we have 
 stated, we do not believe that it is possible to make any canon, 
 which can be rigorously applied as a test of causation. But 
 though this may not be strictly speaking a canon, it is at least 
 a description of the circumstances under which we are frequently 
 justified in drawing a universal conclusion. And the circum- 
 stances presuppose an abstractive, not an eliminative process. 
 Our conclusion is not reached by eliminating those circumstances 
 which are not the cause. But when we see the agent A produce 
 a, we abstract the characteristics in question, and say A as such 
 is the cause of a. 
 
 4. Criticism of Mill's Canons. Mill's view of the 
 Four Methods is very different from that which we have 
 sought to present. To him, they are not an analysis 
 of the circumstances, which in the physical sciences best 
 enable us to detect causal relations. They constitute 
 so many independent canons of reasoning, comparable 
 to the syllogism, but differentiated from it by the fact 
 that syllogistic reasoning is deductive, proceeding from 
 the general to the particular, while they are inductive, 
 guiding us from the particular to the general. " The 
 ' four methods," he writes, . . . " are the only possible 
 ' modes of experimental inquiry, of direct induction d 
 1 posteriori, as distinguished from deduction. . . . These, 
 ' with such assistance as can be obtained from deduction, 
 1 compose the available resources of the human mind 
 
334 PRINCIPLES OF LOGIC 
 
 ' for ascertaining the laws of the succession of pheno- 
 ' mena " (III. c. 8, 7). The hostile criticism which 
 his treatment of the subject has encountered, and of 
 which we are about to recapitulate the chief points, is 
 principally valid against this view of them. 
 
 In the first place, the reasoning of the methods as 
 described by Mill, is deductive. A general principle is 
 stated, and a particular case is brought under it. This 
 may be seen on an analysis of an argument under the first 
 of the canons : 
 
 Wherever in two instances of the phenomenon under 
 investigation, it is found that one circumstance alone 
 besides the phenomenon is common to both instances, 
 that circumstance is the cause of the phenomenon. 
 
 In the two instances abc, ade, in which the phenomenon 
 a appears, it is found that the circumstance A alone is 
 common to both instances. 
 
 .*. A is the cause of a. 
 
 All causal relations in Nature are constant. 
 
 A ... a is a. causal relation. 
 
 .*. The causal relation A ... a is constant. 
 
 It may be objected secondly, that if there are really 
 four canons of inductive reasoning, those canons should 
 be independent of one another. It should not prove 
 to be the case, that they are one and all based on the 
 same principle. If the canons can be shewn to be all 
 derived from one principle, they must be held to have for- 
 feited their claim to be so many distinct principles of 
 ratiocination. Now the inductive canons one and all 
 are based on the same law, viz., that when of two facts 
 the one can appear without determining the presence 
 of the other, there is between these two no causal relation. 
 This is the principle of the Method of Agreement. Here 
 a is shown not to be causally related to B or C or D or 
 E, because it can appear in their absence. Similarly, 
 in the Method of Difference, we show that neither B nor 
 C causes a ; for they can be present without it. And 
 
METHODS OF INDUCTIVE ENQUIRY 335 
 
 the reasoning of the other methods is of the same char- 
 acter. Mill himself frankly recognizes their intimate 
 connexion. He tells us in so many words, that the 
 " Method of Residues is in truth a peculiar modification 
 of the Method of Difference " (III. c. 8, 5) ; and in 
 another passage informs us that the Method of Conco- 
 mitant Variations may be identified either with the 
 Method of Agreement or with that of Difference (III. 
 c. 22, 4). The two chief methods, those of Agreement 
 and Difference are both, he tells us, methods of elimina- 
 tion (III. c. 8, 3). Under these circumstances, there 
 can be no justification for enumerating four canons of 
 reasoning. 
 
 The canons further suppose an unreal state of things 
 in Nature. For they apparently proceed upon the 
 assumption that we have a number of antecedents all 
 clearly determined, and a number of consequents of a 
 similar character. In reality, so manifold are the links 
 which unite natural agents, and so complex the process 
 of action and reaction, that the representation of the 
 antecedents by the symbols A, B, C, D y and of the conse- 
 quents by a, b, c, d is quite deceptive. We have, for 
 example, seen in the investigation as to the effects of 
 radio-activity, how difficulties at once arose from the 
 unexpected interaction of causes that had been over- 
 looked. If Nature could really be represented by Mill's 
 symbols, Induction would be a matter of little difficulty. 
 Again, the employment of the large and small letters, 
 would seem to indicate that we can detect at once which 
 fact is antecedent, and which is consequent. This is 
 frequently not the case. Thus, if a patient consults a 
 doctor, the doctor may often have reason to doubt where 
 to find the cause, and where the effect. If, for instance, 
 it appears that the patient is suffering from nervous 
 breakdown, and is also a prey to mental depression, it 
 may be hard to say whether the nerves are responsible 
 for the depression, or vice versa. Moreover, the use of 
 the same series of letters both for antecedents and conse- 
 quents certainly conveys the impression, that it can be 
 
336 PRINCIPLES OF LOGIC 
 
 no very recondite problem to find the a which corresponds 
 to A, the b which corresponds to B, etc. 
 
 From the point of view of Mill's own philosophical 
 position, yet another objection may be raised. His 
 doctrine of the Plurality of Causes renders it impossible 
 for him to regard the canons as valid methods of inferring 
 universal judgments. We may indeed conclude that 
 in this instance a is caused by A, but if the same effect 
 can follow from causes entirely different the one from 
 the other, we have no guarantee that our judgment is 
 true for any other case than the one under examination. 
 In all other instances, a may be caused by X, not by 
 A. A canon, which is always liable to frustration, is 
 of little value as a criterion of valid reasoning. 
 
CHAPTER XXI. 
 
 EXPLANATION. 
 
 i. Explanation. A thing is said to be explained, 
 when it is rendered intelligible when the mind acquires 
 a facility to grasp it, which it did not possess before. 
 This may be understood in two ways. The explanation 
 may have special reference to the particular mind to 
 which it is addressed. It may not be intended to throw 
 light on the nature of the thing itself, but merely by illus- 
 trations and analogies familiar to the hearer, to enable 
 him to grasp something, of which he has no experience. 
 Such are the explanations we give to children. But an 
 explanation may be such as to give us a real insight 
 into the nature of the fact explained. In this case, a 
 new light is thrown on the thing itself, and not simply 
 on this or that mind. It is with such explanations 
 that we are concerned in this chapter. 
 
 A law of nature is said to be explained, when it is 
 shewn to result from the operation of some wider law 
 or laws, from which it can be deduced. Thus the motion 
 of the moon round the earth was explained, when it 
 was proved to be due to the force we call terrestrial 
 gravity. Similarly, an individual fact is said to be 
 explained, when we are able to point out the laws which 
 have brought it about. Thus we explain the fall of a 
 tree in a storm, by indicating the looseness of the soil, 
 and the other circumstances, which in conjunction with 
 the force of gravity, rendered it unable to withstand 
 the stress to which it was exposed. There is indeed a 
 sense in which, when we explain an individual fact, we 
 are really explaining a law. For we are pointing out 
 
 337 
 
338 PRINCIPLES OF LOGIC 
 
 how it is a necessity of nature that every such tree situated 
 in similar circumstances should fall. In each case, we 
 explain by assigning the reason of the law or of the 
 event. For the mind regards a thing as intelligible 
 when it knows the cause which produced it. 1 
 
 It is manifest that this process must find a limit. We 
 soon arrive at laws, which we cannot account for by 
 bringing them under any law wider than themselves. 
 These we must accept as ultimate. They are truths 
 made known to us by the testimony of experience, but 
 for which no reason, in the sense of which we have spoken, 
 can be assigned. 
 
 * Logicians of the Idealist school, who take the view that 
 individual entities consist solely of relations (Ch. 15, 4), under- 
 stand Explanation somewhat differently. By these writers no 
 essential distinction is drawn between cause and condition, and 
 Explanation is to them the " ascertainment of necessary con- 
 ditions." A phenomenon is fully explained, " when the con- 
 ' ditions of every detail . . . are so fully and exactly known, 
 ' that not only a phenomenon of that general character, but 
 ' just this very phenomenon, with exactly these details, and in 
 ' exactly this amount, must follow from these conditions." 2 
 The conditions in question are in fact the relations, in which 
 the object is held to consist. Explanation is therefore the deter- 
 mination of the constitutive relations of the object or event. 
 
 Since every one of these relations is, as conceived by the mind, 
 universal, the analysis of the event into its constitutive relations 
 is described as a process of Generalization ; for by Explanation, 
 we bring to light, in each relation, some element which is common 
 to other phenomena. Every relation present in a phenomenon, 
 shows us some aspect, in which it agrees with many other 
 individuals. 
 
 The Explanation of the Idealist philosophers differs funda- 
 mentally from that described in the body of this section. Their 
 Explanation is not explanation of an effect by its cause, but of 
 a part by its whole, a very different thing. According to this 
 school, Nature is an organism a unit of which individual 
 things are but parts ; it is not an organization formed of things, 
 which are complete in themselves, though related one to the 
 
 1 Cf. Arist., An. Post. II., C. II, I. eirlffraadai oto/xefla $rav d8fjici> TTJV 
 aMav. " We believe ourselves to know a thing, when we are acquainted 
 with its cause." 
 
 2 Welton, Manual, 159. 
 
EXPLANATION 339 
 
 other. This difference is crucial. For it is impossible to under- 
 stand a part save in its relation to a whole ; and we cannot have 
 a correct idea of a part, unless we have a correct idea of the 
 whole, of which it is a part. In an organism, the parts are what 
 they are, because the organism is what it is. In an organization, 
 on the other hand, the whole is what it is, because the units, 
 out of which it is composed, are what they are. They must be 
 understood, before the whole can be understood. 
 
 If Nature is an organism of relations, not an organization 
 of related things, Explanation has no term or limit. All our 
 explanations are provisional ; nor can we attain to the true 
 explanation of any object or event, till we have grasped this 
 scheme of things entire ; l till we know alike the finite and the 
 Infinite, nay, if there be no radical difference between thought 
 and things, till our mind's vision surveys the whole of both 
 orders. In other words, Science is impossible. But if Nature is 
 an organized manifold, then Science begins with tasks that can 
 be measured, and every step forward is a permanent acquisition 
 of truth. 
 
 2. Explanation by Regressive Reasoning. We have 
 said that the task of Explanation is to assign the reason 
 of the law, with which we are concerned. Logical 
 principles indicate to us the way in which we must pro- 
 ceed. We must employ regressive argument from the 
 effect to the cause (Ch. 12, 4). We must show that 
 as regards the antecedent and the consequent we are 
 considering, their connexion is due to some cause of 
 wider generality. We are given S is P, and our object 
 is to prove that 5 is P, because it is M. This can only 
 be done by showing that the phenomenon P proves the 
 presence of the cause M. We must not merely establish 
 the proposition ' If M, then P,' but the reciprocal of 
 it, ' If P then M.' In other words, the proposition ' All 
 M is P ' must be simply convertible. We are thus 
 enabled to form the syllogism : 
 
 P is M. 
 S is P. 
 /. S is M. 
 
 1 " Ultimately, you may imagine, nothing can be known rightly, without 
 knowing all else rightly." Bosauquet, Logic, I. p. 393. 
 
340 PRINCIPLES OF LOGIC 
 
 In this way we demonstrate that the agent M is present 
 in every S, and so explain how it comes about that 
 ' All 5 is P.' To take a simple case, we may thus assign 
 the reason of the law that potassium floats in water. 
 
 Substances which float in water, have a specific gravity 
 less than that of water. 
 
 Potassium floats in water. 
 
 .*. Potassium has a specific gravity less than that of 
 water. 
 
 When the conclusion ' 5 is Af / is thus established, 
 the syllogism, by converting the major, may be restated 
 in the form : 
 
 M is P. 
 S is M. 
 .-. S is P. 
 
 In this form, the cause, and not the effect, is used as the 
 middle term. The order of nature is followed : we 
 prove the effect by the cause. 
 
 Substances, whose specific gravity is less than that of 
 water, float in water. 
 
 Potassium has a specific gravity less than that of 
 water. 
 
 .. Potassium floats in water. 
 
 These two methods of reasoning were known to the ancients 
 as the via resolutions, i.e. the analysis of a fact into its prin- 
 ciples, and the via compositions, i.e. the synthesis of principles 
 which determine the fact. In this connexion we may con- 
 veniently notice two other expressions employed, via inventionis 
 and via doctrince. The former is used to signify all reasoning 
 in which there is an advance from the known to the unknown, 
 whether by way of progressive or regressive argument (S. 
 Thomas, Summ. TheoL I. q. 79, art. 8, 9) The via doctrince is 
 the reasoned exposition of truth already attained. For this 
 purpose we naturally proceed by the progressive method from 
 cause to effect. 
 
 Science owes many of her greatest triumphs to re- 
 gressive argument from effect to cause. Professor Case 
 (Lecture on Scientific Method, p. 14) instances what is 
 perhaps the most famous of all Kepler's discovery 
 that the path of the planet Mars is an ellipse with the 
 
EXPLANATION 341 
 
 sun in one of the foci. The observations, which 
 formed the basis of the argument, Kepler owed in large 
 measure to Tycho Brahe. These observations revealed 
 certain regular movements of the planet, but what law 
 governed these movements was not apparent. Many 
 were the hypotheses that he tested, only to find that they 
 did not agree with the facts. At last the clue was found, 
 and he was able to deduce his conclusions in the following 
 manner : 
 
 Such and such positions are the properties of an 
 ellipse. 
 
 The orbit of the planet Mars has such and such 
 positions. 
 
 .'. The orbit of the planet Mars is an ellipse. 
 
 This argument deserves careful attention for two 
 reasons. In the first place, it has been misunderstood 
 by recent logicians, and several erroneous accounts 
 have been given of the reasoning involved. Whewell, 
 for example, has described it as an induction ; though 
 it is clear that the task before Kepler was to explain a 
 law, not to generalize from particular facts. But a 
 yet greater interest attaches to the argument in so far 
 as it signalizes for us the intimate connexion between 
 the science of the ancients and that Copernican astron- 
 omy, which is regarded as characterizing in an especial 
 manner the modern era. For the major premiss in the 
 reasoning of Kepler was a conclusion drawn from the 
 theorems of Conic Sections : and the science of Conies 
 was an inheritance from the days of classical antiquity. 
 Science did not spring suddenly into being at the close 
 of the middle ages, as some writers would have us believe. 
 The discoveries of the great scientists of the sixteenth 
 and seventeenth centuries were rendered possible by 
 the labours of their predecessors. 
 
 3. Explanation by Hypothetical Deduction. A dif- 
 ferent account of Explanation is given by some logicians. 
 It will be necessary for us to say something of this other 
 view, as it has exercised great influence on recent logical 
 
342 PRINCIPLES OF LOGIC 
 
 speculation, especially in England. According to this 
 theory, Explanation is achieved, not by regressive 
 reasoning from effects to causes, but by deduction from 
 a cause hypothetically suggested. Thus, if it is desired 
 to explain the law 5 is P, an hypothesis is ventured 
 that P may be due to M . The consequences of M are 
 then calculated by deduction, and they are compared 
 with P as manifested in experience. If it is found that 
 they agree, the hypothesis is thereby confirmed. The 
 process therefore consists of : 
 
 (1) The formation of an hypothesis to explain the 
 law or fact under consideration. 
 
 (2) Deduction : the hypothesis being treated as a 
 general principle from which conclusions are drawn. 
 
 (3) Verification : or comparison of these conclusions 
 with the facts of Nature. 
 
 This view of Explanation is that held by Mill. In his 
 account, it appears as a special case of what he terms 
 the Deductive Method. This Deductive Method is a 
 way, by which we are enabled in certain cases to deter- 
 mine the laws governing complex phenomena, in regard 
 to which we cannot apply Observation and Experiment. 
 These are all cases in which a Composition of Causes 
 has resulted in Intermixture of effects (Ch. 15, 2). The 
 application of the method supposes that we are acquainted 
 with the various simple laws which combine to produce 
 the complex result. Mill cites as cases in which the 
 method is employed, such problems as that of three 
 bodies gravitating together, and that of the path of a 
 projectile, when the causes affecting its velocity and 
 range are known. Here Observation and Experiment 
 are of no avail. But solutions, at least approximately 
 correct, may be obtained for these problems by De- 
 duction. 
 
 Hypothetical Deduction he regards as differing from 
 this process only in so far that our deductive calculation 
 is made, not from a known law, but from an hypothesis 
 provisionally assumed. The conclusion in the Deductive 
 Method, no less than that obtained from the hypothetical 
 
EXPLANATION 343 
 
 cause, must be verified by comparison with facts. With- 
 out this step, we may have overlooked some contributory 
 cause, and so vitiated our calculations. 
 
 Mill quotes as one of the most notable discoveries we 
 owe to the method of hypothetical deduction, Newton's 
 conclusions in regard to the system of the universe. 
 We shall show in a subsequent section that Newton's 
 discoveries were not made by this method, but by regres- 
 sive reasoning. But it can scarcely be doubted that 
 we owe this theory of Explanation to an erroneous 
 analysis of Newton's argument. 
 
 The mere fact that the conclusions drawn from our 
 hypothesis agree with the law we desire to explain, 
 does not, it is evident, constitute a proof that we have 
 discovered the cause of the law. We cannot argue ; 
 If M then P ; but P is true, .-. M is true. Hence Mill 
 rightly insists that not only must we shew that the 
 hypothesis accounts for the facts, but we must shew 
 that there is no other hypothesis which will do so. But 
 he fails to observe that if we can attain certainty on 
 this point, our argument, logically analysed, is no longer 
 a hypothetical deduction, but a strict regressive syllogism. 
 Our major premiss is no longer, ' M is cause sufficient 
 to account for P ' ; it is, ' P is an effect which proves 
 the presence of the cause M.' 
 
 Unfortunately, not all subsequent logicians have 
 insisted on the absolute necessity of proving that the 
 hypothesis proposed is the only one which will account 
 for the facts. Yet without this, the conclusions obtained 
 are logically worthless. 
 
 * 4. Hypothetical Deduction and Induction. We have seen 
 that it is impossible to accept Hypothetical Deduction as a true 
 account of Scientific Explanation. It can only be regarded as 
 an error on Mill's part. A worse mistake was to come. Jevons 
 identified Mill's Hypothetical Deduction with Induction. He 
 terms Induction " the inverse operation of deduction " (Princ., 
 p. 122). Deduction is the process, which starts from laws that 
 govern the combination of qualities, and infers the combinations 
 agreeing with these laws. In Induction, we have the combina- 
 
344 PRINCIPLES OF LOGIC 
 
 tions of qualities as our data, and our task is to determine the 
 laws governing the combinations. This is accomplished by 
 hypothetical deduction, in the three stages of (i) forming the 
 hypothesis, (2) deducing consequences, and (3) verification. 
 The value of inductions regarding laws of nature is, he holds, 
 never more than probable. To begin with, it is ordinarily possible 
 to form rival hypotheses as to the laws governing the combina- 
 tions, in such a way that each hypothesis will give results approxi- 
 mating in some degree to the facts. It would be necessary to 
 entertain all these rival hypotheses, and hold each of them to 
 be of value in proportion to their probability. Hence the induc- 
 tive inference, as regards its validity, is based on the mathematical 
 theory of probability. Moreover, even had we accurately deter- 
 mined the law in question, we have no ground for certainty as 
 to the uniformity of nature. As far as we can see, natural laws 
 are constant ; but reason cannot justify our conviction that it 
 must be so. Belief should never amount to certainty till the 
 experiment has been tried. 
 
 Jevons's theory that in Hypothetical Deduction we have the 
 true account of Induction, has, strange to say, found a wide 
 acceptance. Sigwart, Bosanquet and Welton may be men- 
 tioned among the adherents of this view. They part company 
 however with Jevons, in so far as he bases inductive argument 
 on the theory of probability. Certainty, they maintain, can be 
 reached by hypothetical deduction. For this view, there can 
 be no logical justification. 
 
 5. Explanation as employed by Newton. In this 
 section, we propose to consider the method of proof by 
 which Newton succeeded in establishing the universal 
 gravitation of matter according to the law of the inverse 
 square. In most recent works on Logic, some attention 
 has been devoted to this subject. Nor need we feel 
 surprised at this. It has been justly said by Whewell 
 that it was " indisputably and incomparably the greatest 
 ' scientific discovery ever made. . . . Any one of the 
 ' five steps . . . would of itself have been considered 
 ' an important advance ; would have conferred dis- 
 ' tinction on the persons who made it, and the time to 
 ' which it belonged. All the five steps taken at once 
 ' formed not a leap but a flight not an improvement 
 ' but a metamorphosis not an epoch but a termination." 1 
 
 1 Whewell, Hist, of Inductive Sciences (srd ed.), vol. 2, p. 136. 
 
EXPLANATION g 45 
 
 Moreover, this great discovery was precisely of the kind 
 with which we are now concerned. It did not consist 
 in the detection of some natural phenomenon never 
 yet observed, in the sense in which we speak of the 
 discovery of galvanic electricity, of argon, of the Rontgen- 
 rays. The work was essentially explanatory. A treat- 
 ment of Explanation might justly be held to be incom- 
 plete, which did not show how the account given of 
 the process, was borne out by this greatest of all explana- 
 tory reasonings. 
 
 There is another reason, as we have already noted, 
 for dealing with Newton's arguments. Several eminent 
 logicians have misunderstood the nature of the reasoning, 
 and on their erroneous interpretation have based a false 
 theory of Explanation. Our object here is to shew 
 that the method employed by Newton is simply the 
 regressive method, as we have described it in 2. 
 
 Of the five points into which Whewell divides the 
 discoveries connected with gravitation, we shall restrict 
 our attention to the two which may be regarded as the 
 principal, viz. : 
 
 (1) that the force by which the planets are attracted 
 to the sun, is in the inverse proportion to the square 
 of their distances : 
 
 (2) that the earth also exerts such a force on the moon, 
 and that this force is identical with terrestrial gravity. 
 
 In each case, it will appear that the method employed 
 was regressive reasoning from facts to their causes. 
 Newton takes the known motions of the heavenly bodies, 
 and argues directly from these to the nature of the force 
 which is necessary to produce them. 
 
 (i) The facts in the first of the cases we are about to 
 consider, were those which are contained in Kepler's 
 laws, viz. : 
 
 First law. The planets move in elliptical orbits round 
 the sun in one of the foci. 
 
 Second law. The areas swept by lines drawn from the 
 
346 PRINCIPLES OF LOGIC 
 
 sun to the planet, are proportional to the times employed 
 in the motion. 1 
 
 Third law. The squares of the periodic times are 
 as the cubes of the mean distances from the sun. 2 
 
 It had been surmised by several mathematicians that 
 an attractive force situated in the sun, and acting accord- 
 ing to a law of inverse squares, would account for these 
 motions. But the complexity of the problem baffled 
 their attempts at solution. Newton's genius triumphed 
 over the obstacles. His proofs rest upon the three 
 laws of motion. These he regarded as securely estab- 
 lished by induction. Basing his demonstrations on these 
 laws, he proved deductively two famous theorems in 
 mechanics : (a) Every body which moves in a curve, 
 and by a radius drawn to a point describes about that 
 point areas proportional to the times of description, is 
 urged by a centripetal force to that point (Princ.,Lib. 
 I, prop. 2) : (b) When the squares of the periodic times 
 are as the cubes of the radii (i.e. the mean distance 
 from the central body), the centripetal forces by which 
 the bodies tend to the centre are inversely as the squares 
 of the radii ; and the converse of this proposition is 
 also true (Princ., Lib. i, prop. 4, cor. 6). 
 
 These conclusions provided him with all that was 
 required to prove that the law of inverse squares governs 
 the planets in regard of their motion towards the sun. 
 The proof is given in the second proposition of Bk. III. 
 of the Principia. The proposition is as follows : 
 
 The forces, by which the planets are withheld from recti- 
 
 1 The accompanying figure may be taken to represent the course of a planet 
 
 round the sun ; and it may be supposed that the areas 
 ABS and CDS are equal. Then according to the law, 
 the time employed by the planet to cover the distance 
 between A and B, will be the same as that employed in 
 covering the shorter distance between C and D. For 
 the times are proportional, not to the distance covered, 
 but to the areas swept by the imaginary lines. 
 
 2 Thus the period of the earth's revolution round the sun is i year : that of 
 Saturn 30 years. The squares of these two periodic times are respectively 
 i and 900. The mean distance of the earth from the sun wi 1 ! therefore stand 
 to the mean distance of Saturn from the sun as the cube root of i to the cube 
 root of 900. In other words, the mean distance of Saturn is a little more 
 than nine times the mean distance of the earth. 
 
EXPLANATION 347 
 
 linear motion and retained in their orbits, tend to the sun ; 
 and these forces vary inversely as the squares of the distances 
 from the sun. 
 
 Proof of part i. Every body, which moves in a curve, 
 and by a radius drawn to a point describes about that 
 point areas proportional to the times of description, is 
 urged by a centripetal force to that point (Princ., Lib. i, 
 prop. 2). 
 
 The planets, by radii drawn to the sun, describe areas 
 proportional to the times of description (Kepler's 2nd 
 law). 
 
 .-. The planets are urged by a centripetal force to 
 the sun. 
 
 Proof of part 2. When the squares of the periodic 
 times are as the cubes of the radii, i.e. the distances, the 
 centripetal forces of the bodies will be inversely as the 
 squares of the radii, i.e. the distances (Princ., Lib. i, 
 prop. 4, Cor. 6). 
 
 The squares of the periodic times of the planets are 
 as the cubes of their mean distances from the sun (Kepler's 
 3rd law). 
 
 .*. The centripetal forces of the planets tending to 
 the sun are inversely as the squares of their distances 
 from the sun. 1 
 
 (2) The demonstration we have just considered may 
 be applied to the case of the moon in its relation to the 
 earth. Our data regarding its motion prove that it 
 also is subject to the law of inverse squares. But we 
 must now consider the further step which was taken, 
 when Newton shewed that the force which retains the 
 moon in her orbit is one and the same with the force 
 known to us as terrestrial gravity. It was this identifi- 
 cation that caused us to see in the courses of the stars 
 and the planets, a manifestation of the very same pheno- 
 menon which we witness when a stone falls to the earth. 
 
 1 On this demonstration, see the treatment in Professor Case's lecture on 
 Scientific Method as a Mental Operation, to which I am under great obliga- 
 tions. The translation of the proposition is that there given. 
 
348 PRINCIPLES OF LOGIC 
 
 In addition to what is required in the proofs with 
 which we have already dealt, this new argument involves 
 further presuppositions. These are stated in the first 
 two of Newton's Rules of Philosophizing, 1 which run as 
 follows. 
 
 First Rule. No more causes of natural things are to 
 be admitted than such as are both true (verae), and 
 sufficient to explain the phenomena of these things. 
 
 Second Rule. And therefore natural effects of the 
 same kind are to be referred as far as possible to the 
 same causes. 
 
 The importance of these rules to his argument will 
 appear in what follows. 
 
 The supposition that the force retaining the moon 
 in her orbit was none other than terrestrial gravity, 
 presented itself to Newton as an hypothesis. In order 
 to test the worth of that hypothesis, it was necessary 
 to know the precise amount of the force exerted on the 
 moon by the earth. This was easily susceptible of 
 determination. Without the influence of the earth, 
 the moon, if the first law of motion be true, would leave 
 her orbit, and pass away into space at a tangent. Hence, 
 the attractive force exerted by the earth on the moon 
 in one minute, is represented by the amount of deflection 
 from the tangent during that period of time. Newton 
 calculated that this amounted to very nearly 16 feet. 
 Allowing for the law of inverse squares, it could be shewn 
 that, if such be the attraction at the distance at which 
 the moon stands from the earth, the ' pull ' which would 
 be exerted, were the moon close to the surface of the 
 earth, would be precisely 16 feet in one second. This 
 is identical with the rate at which bodies are drawn to 
 the earth by terrestrial gravity. 2 Here then Newton 
 
 1 These rules will be dealt with in the next section. 
 
 2 The proof, by which Newton shews this, may be thus summarized. The 
 distance of the moon from the centre of the earth may be taken as equal to 
 sixty of the earth's radii. Since bodies at the surface of the earth are at a 
 distance of one radius from the centre, it follows by the law of inverse squares, 
 that the fall of the moon in one minute, were it close to the surface of the 
 earth, would not be 16 feet, but 16 feet x 6o 2 . What then would it be in one 
 second ? Galileo's discovery that the distances fallen by bodies vary as the 
 
EXPLANATION 34y 
 
 applies his two rules to establish his proof. We have 
 in the fall of the moon a phenomenon exactly similar 
 to the fall of bodies at the earth's surface. It must 
 therefore (Rule 2) be attributed to the same cause, viz., 
 gravity. For in thus explaining it, we are not intro- 
 ducing any merely hypothetical agent : we account 
 for it by a true cause, one that we know to be really 
 operative in nature, and to be adequate to the effect 
 (Rule i). 1 This gives us the following regressive syl- 
 logism : 
 
 Any material body which, on commencing to fall to 
 the earth, passes through a space equivalent to a fall of 
 16 feet in one second at the earth's surface, is urged to 
 the earth by gravity. 
 
 The moon is a material body whose fall to the earth 
 is of this character. 
 
 .-. The moon is urged to the earth by gravity. 
 
 Such is the proof by which Newton establishes the 
 second of those great discoveries to which we referred 
 above, namely that the force which the earth exerts 
 upon the moon is none other than terrestrial gravity. 
 
 6. Newton's Rules of Philosophizing. The ' Rules 
 of Philosophizing ' preface the third part of Newton's 
 Principia the part in which he unfolds his conclusions 
 as to the system of the universe. In them, he evidently 
 intends to lay down the fundamental principles which 
 have governed the reasoning of that treatise. They 
 are, in fact, a statement of what he held to be the true 
 method to follow in Natural Philosophy. When we 
 reflect that these rules were drawn up by one of the 
 greatest geniuses who ever lived, and in reference to a 
 series of reasonings which have influenced the thought 
 of the whole human race, we may be confident that 
 
 squares of the times, shows that to find the distance fallen in one-sixtieth 
 part of a minute, we must divide the distance fallen in a minute by 6o 2 . This 
 gives us 16 feet as the space, through which the moon would fall in one second, 
 were it close to the surface of the earth (Principia, Lib. Ill, prop. 4). 
 
 1 ' Propterea vis qua luna in orbe sua retinetur, si descendatur in superficiem 
 terrae, aequaliter evadit vi gravitatis apud nos, ideoque (per regulam I et II) 
 est ilia ipsa vis quam nos gravitatem dicere solemus" (ibid.). 
 
350 PRINCIPLES OF LOGIC 
 
 they merit the most careful consideration. They are 
 as follows : 
 
 Rule I. "No more causes of natural things are to be 
 admitted than such as are both true, and sufficient to 
 explain the phenomena of those things. 
 
 It is a saying of the philosophers that Nature does nothing 
 in vain, and to employ more means when less will serve 
 would be to act in vain : for Nature is simple, and is not 
 prodigal in unnecessary causes." 
 
 Rule II. " And therefore natural effects of the same 
 kind are to be referred as far as possible to the same 
 causes. 
 
 As for instance, respiration in man and beast : the fall 
 of stones in Europe and America : light in the fire on our 
 hearth and in the sun : the reflexion of light on the earth 
 and in the planets." 
 
 Rule HI. " Those qualities of bodies that can neither 
 be increased nor diminished in intensity, and which 
 are found to belong to all bodies within the reach of our 
 experiments, are to be regarded as belonging to all bodies 
 whatever/' 
 
 (In a somewhat lengthy comment, Newton points 
 out that it is on these grounds that we infer the extension, 
 hardness, impenetrability, and mobility of all bodies, 
 and the laws of motion themselves. ' And this/ he 
 adds, ' is the foundation of all [Natural] Philosophy/ 
 Further, an induction of this kind will enable us to 
 conclude that gravity belongs to every particle of matter ; 
 though, as it is capable of increase and diminution, it 
 cannot be regarded as an essential attribute of material 
 substance.) 
 
 Rule IV. "In experimental philosophy, propositions 
 collected by Induction from phenomena are to be regarded 
 as exactly true or as very nearly true, notwithstanding 
 any contrary hypotheses, until other phenomena occur, 
 by which they are made more accurate or are rendered 
 subject to exceptions. 
 
 This must be granted, lest conclusions based on induction 
 be denied in favour of hypotheses." 
 
EXPLANATION 351 
 
 The first two rules stand in close connexion with each 
 other. They may be considered together. 
 
 By what must be considered one of the strangest of 
 mistakes, these rules are frequently described as stating 
 the conditions requisite to a valid hypothesis. They 
 are in fact rules to ensure that the doctrines advanced 
 and the conclusions attained in Natural Philosophy, 
 should be free from the least suspicion of being based 
 on hypotheses. To ensure this, says Newton, we must 
 never assert that a phenomenon proceeds from any 
 cause, unless we know that this cause is a true cause, 
 actually existing in nature, and is such as would produce 
 the effect. Then, indeed, we may do so, for Nature is 
 not prodigal in unnecessary causes. It would be con- 
 trary to sound philosophy to suppose that there are 
 two natural forces each destined to produce precisely 
 the same effect. Hence the second rule follows as a 
 corollary of the first, and the examples indicate the use 
 which Newton intends to make of it as to the motions 
 of the moon in regard to the earth, and those of the 
 planets in regard to the sun. 
 
 The principle, to which he makes appeal as the basis 
 of the first rule, is derived from Aristotle, and is of fre- 
 quent occurrence in Scholastic philosophy. 1 It is grounded 
 on the evident fact that reason is everywhere apparent 
 in the world, that finality and purpose rule the whole 
 natural order. Hence, it is inadmissible to attribute 
 to Nature what would be a mark not of reason but of 
 unreason. The principle is fundamental in Newton's 
 argument. If its truth be denied, his reasoning loses 
 all conclusiveness. We can no longer assert that such 
 and such motions on the part of the moon furnish a proof 
 that it is swayed by gravity. It becomes perfectly 
 
 1 Arist., De Anima, III. c. 9, 6. et ovv fi-tyre fiydtv TJ 0tf<rts TTOIC? fid-njv, 
 airoXelTrei r&v avayKaliov. ' If then Nature does nothing in vain, and omits 
 nothing that is necessary . . .' Cf. S. Thomas, Opusc. 13, De Verbo Intellec- 
 tus. ' Natura non agit aliquid superfine.' It would seem to have been the 
 perception of this truth which led another great scientist, Clerk Maxwell, to 
 say that it would be " poor scientific taste " to choose the more complicated 
 of two equally well balanced scientific conceptions. 
 
352 PRINCIPLES OF LOGIC 
 
 reasonable to attribute them to another cause. All we 
 can say is that gravitation would be capable of accounting 
 for them. And with this, the keystone of the whole 
 proof is taken away. The reasoning becomes hypo- 
 thetical, and Newton's boast that his philosophy does 
 not consist of hypotheses becomes empty verbiage. It 
 is on the foundation afforded by this Aristotelian principle 
 that the cogency of the great argument depends. 
 
 The third and fourth rules summarize Newton's view 
 as to the true starting point in all our reasonings on 
 physical science, with special reference to the matter 
 dealt with in the treatise he is beginning. In the third 
 rule, he claims the right of inferring universal propo- 
 sitions as to corporeal substance by induction from 
 experience. Against such inductive conclusions, no 
 objections based on mere hypotheses, can, he urges, 
 have any weight. 
 
 These two rules should be compared with the following 
 passage from the Optics. " In Natural Philosophy the 
 ' investigation of difficult things by the method of Ana- 
 ' lysis, ought ever to precede the method of Composition. 1 
 ' This Analysis consists in making Experiments and 
 ' Observation, and in drawing general conclusions from 
 ' them by way of Induction, and admitting of no objec- 
 ' tion against the conclusions, but such as are taken 
 ' from experience or other certain truths. For hypo- 
 ' theses are not to be regarded in experimental philo- 
 'sophy. . . . And although the arguing from Experi- 
 ' ments and Observation be no demonstration of general 
 * conclusions : 2 yet it is the best way of arguing that 
 ' the nature of things admits of, and may be looked 
 ' upon as so much the stronger, by how much the induc- 
 ' tion is the more general. And if no exception occur 
 ' from phenomena, the conclusion may be pronounced 
 ' generally. But if at any time afterwards any excep- 
 
 1 By Analysis, Newton signifies all argument from effects to causes whether 
 by induction or regressive deduction : by Synthesis, the argument from 
 causes to their effects. The terms are more fully explained below, Ch. 25, i. 
 
 2 Demonstration is here used in its technical sense of syllogistic proof from 
 first principles of admitted certainty. 
 
EXPLANATION 353 
 
 ' tion shall occur from experiments, it may then begin 
 ' to be pronounced with such exceptions as occur." 1 
 
 The only difference between this passage on the one 
 hand and the rules on the other, lies in the fact that in the 
 Optics Newton is dealing with physical science in general, 
 while in the rules he speaks only of the inductions which 
 shew that some attribute is to be reckoned among the 
 properties of all corporeal substance. It is by such 
 inductions that the laws of motion are established, on 
 whose truth depends the value of his whole physical 
 system. The legitimacy of the principles expressed in 
 the rules, he regards as evident. And if these be granted, 
 a valid science is possible, grounded on rigorous reasoning 
 from facts to their causes. To labour at this is, he 
 holds, the true work of the Natural Philosopher. " Later 
 ' philosophers," he says, " feign hypotheses . . . for 
 'explaining all things mechanically . . . whereas the 
 ' main business of Natural Philosophy is to argue from 
 ' phenomena without feigning hypotheses, and to deduce 
 ' causes from effects till we come to the very first cause, 
 ' which certainly is not mechanical." 2 
 
 It will be evident from these citations that the method 
 employed by this greatest of scientific discoverers was 
 none other than that recognized by the Scholastic philo- 
 sophers. Most assuredly it was not the hypothetical 
 deduction attributed to him by recent logicians. 3 
 
 1 Newton, Optics, p. 380 (srd edit. 1721). 
 
 2 Newton, Optics. Qy. 28. 
 
 8 On Newton's Rules of Philosophizing, see Pemberton's View of Newton's 
 Philosophy (1728), Introduction, 22-25. 
 
 AA 
 
CHAPTER XXII. 
 
 HYPOTHESIS. 
 
 i. Hypothesis. 
 
 An hypothesis is a supposition made with evidence 
 recognized as insufficient, in order to account for 
 some fact or some law known to be real. In other 
 words, an hypothesis is a provisional or tentative 
 explanation. 
 
 Discovery is almost entirely dependent on hypothesis. 
 No man is likely to distinguish the law which lies hidden 
 behind the complex phenomena of experience, unless 
 he hazards an hypothesis, and then by observation and 
 experiment forces Nature to declare whether his hypo- 
 thesis is correct or not. The first task of the investigator 
 is to ask himself what various hypotheses, in themselves 
 possible, may be imagined, which are capable of account- 
 ing for the phenomena. Logic can teach no art of 
 making suitable hypotheses. The peculiar insight, which 
 enables a man to seize on the clue to Nature's secrets, 
 is a gift, a gift which may be cultivated, but not one 
 which can be communicated in a code of rules. 1 
 
 The method of investigation advocated by Francis 
 Bacon dispensed with hypotheses. He believed, as we 
 have seen, that to employ tables of presence, absence, 
 and presence in varying degrees, would provide a royal 
 road to discovery. The laws of nature would on the 
 application of this method reveal themselves, and all 
 men's minds stand on the same level. 2 Hypotheses 
 
 1 Cf. Aristotle's account of eiVroxta, An. Post. I., c. 34, Ethics, VI., c. 10. 
 
 2 Nov. Org. I., 61. " Our method of discovering the sciences is such as 
 to leave little to the acuteness and strength of wit, and indeed rather to level 
 wit and intellect." 
 
 364 
 
HYPOTHESIS 355 
 
 have no place in his system ; and in this opinion, he has 
 been followed by certain extreme empiricists. But it 
 need scarcely be pointed out that to suppose a registra- 
 tion of facts will enable us to dispense with hypotheses, 
 is as though one were to suppose that the invention of 
 the rule and compasses would enable us to dispense 
 with genius in the architect. 
 
 Yet notwithstanding the important role played by 
 hypotheses in discovery, no part of the scientist's task 
 is more important than the rigid testing of suggested 
 hypotheses. The aim of all investigation is the discovery 
 of truth. To this hypotheses are but means and instru- 
 ments. The scientist must not be so captivated by the 
 ingenuity of his hypothesis, and the accuracy with which 
 it appears to explain the phenomena, as to accept it as 
 true before he can say with certainty that his evidence 
 is such as to exclude every other supposition. The 
 greatest discoverers have insisted forcibly on this truth. 
 Pasteur in his address to his colleagues at the inaugura- 
 tion of the Institut Pasteur writes as follows : " For 
 ' the investigator it is the hardest ordeal which he can 
 ' be asked to face, to believe that he has discovered a 
 ' great scientific truth, to be possessed with a feverish 
 ' desire to make it known, and yet to impose silence on 
 ' himself for days, for weeks, sometimes for years, whilst 
 ' seeking to destroy those very conclusions, and only 
 ' permitting himself to proclaim his discovery when all 
 ' the adverse hypotheses have been exhausted." 
 
 Descriptive Hypotheses. Hypotheses are employed in 
 science for another purpose, besides that we have just 
 considered. When a number of facts relating to a 
 certain subject have been gathered together, and the 
 true explanation of the facts is still to seek, it is often 
 useful to group them round some hypothesis, even 
 though it should hardly seem likely that this hypothesis 
 will be found to represent the actual truth. Such a 
 mode of colligating the facts, as it has been termed, enables 
 us to describe them in terms of a coherent system, and 
 
356 PRINCIPLES OF LOGIC 
 
 may afford us a basis for deductions relating to future 
 phenomena of the order in question. A good instance 
 is afforded by the Ptolemaic hypothesis in regard to 
 the heavenly bodies. The ancients were well aware 
 that the system of cycles and epicycles was but an hypo- 
 thesis. St. Thomas expressly calls attention to the fact 
 that at some future time it may be discovered that some 
 other supposition is better able to account for the facts. 1 
 Yet it served a useful purpose, assisting many generations 
 of astronomers in framing their calculations. It may 
 be noted also that Andreas Osiander, in the letter which 
 he wrote by way of preface to the work of Copernicus, 
 reminds the reader that the hypotheses of astronomers 
 are not necessarily asserted to be true by those who 
 propose them, but only to be ways of representing facts. 2 
 Many theories in modern physics are of this character. 
 Such, for instance, is the Atomic theory of Dalton. 
 Such is the Electron theory of matter, which in the last 
 few years has won for itself considerable popularity. 
 
 The view discussed in 3 and 4 of the preceding chapter 
 tends not a little to confuse hypotheses of this kind with 
 established truths of science. Mill justly pointed out 
 that there is no reason why a false hypothesis should 
 not afford deductions agreeing in a surprising way with 
 facts (Logic, III., c. 14, 6). Yet because the deductions 
 from Fresnel's undulatory theory of light are in accord 
 with facts, Jevons tells us that we must needs accept 
 it and all that it involves, as true. "We are asked by 
 ' physical philosophers," he writes, " to give up our pre- 
 ' possessions, and to believe that interstellar space is 
 
 1 St. Thomas, Sutnma Theol. I., Q, 32, Art. i, ad. 2. Ad aliquam rem duplici- 
 ter inducitur ratio. Uno modo ad probandum sufficienter aliquam radicem : 
 . . . Alio modo inducitur ratio non quae sufficienter probet radicem, sed 
 quae radici jam positae ostendat congruere consequentes effectus. Sicut 
 in astrologia ponitur ratio excenticorum et epicyclorum ex hoc quod, hac 
 positione fact a, possunt salvari apparentia sensibilia circa motus coelestes : 
 non tamen ratio haec est sufficienter probans, quia etiam forte alia positione 
 fa eta salvari possunt.' The expression salvare apparentia sensibilia is the 
 Latin equivalent for <r&eiv ra <f>aiv6/jieva. Cf. Ueberweg, 134. 
 
 8 " Neque vero necesse est eas hypotheses esse veras, immo ne verisimiles 
 quidem, sed sufficit hoc unum, si calculum observationibus congruentem 
 exhibeant." Copernicus, De Revolutionibus, p. i. 
 
HYPOTHESIS 357 
 
 ' filled with something immensely more solid and harder 
 ' than steel. . . . We live and move without appreci- 
 ' able resistance through this medium, immensely harder 
 ' and more solid than adamant. ... It is no more 
 ' than the observed phenomena of heat and light force 
 'us to accept" (Principles, p. 515). The observed 
 phenomena of heat and light force us to nothing of the 
 kind. All that can be said, is that they are such as to 
 render this a convenient, though hypothetical, method 
 of representing the facts. 
 
 Newton again and again points out the importance 
 of distinguishing between the established truths of science 
 and mere hypotheses. Hypotheses, he says in a famous 
 passage, have no place among the conclusions he pro- 
 poses for our acceptance hypotheses non fingo. And 
 for this reason, he refuses to hazard any conjecture as 
 to the cause of gravity, and bids us not regard the term 
 ' attraction ' as indicating any theory as to the manner 
 in which bodies are urged one towards another ; for 
 he has not been able to discover from the phenomena, 
 the cause of their gravitation. He employs the word 
 as a mathematician to signify the mechanical law, in 
 accordance with which bodies act. 1 
 
 2. Origin of Hypothesis. The source of an hypo- 
 thesis is to be found either in an induction based on 
 grounds which are recognized as only probable, or in 
 an analogy. This may be illustrated by one or two 
 instances of hypothesis, which we have already had 
 
 1 See the Scholium generate at the end of the Pnncipia, " Rationem vero 
 harum gravitatis proprietatum ex phaenomenis nondum potui deducere, et 
 hypotheses non fingo. Quid enim ex phaenomenis non deducitur, hypothesis 
 vocanda est : et hypotheses, seu metaphysicae, seu physicae, seu qualitatum 
 occultarum, seu mechanicae, in philosophia experimentali locum non habent." 
 With this passage, the following words from Definition VIII. in Part I. of the 
 Principia may be compared. " Voces autem attractionis, impulsusvel pro- 
 pensionis cujuscunque in centrum, indifferenter et pro se mutuo usurpo : 
 has vires non physice sed mafchematice tantum considerando. Unde caveat 
 lector ne per hujusmodi voces cogitet me speciemvel modum actionis cau- 
 samve aut rationem physicam alicubi definire vel centris (quae sunt puncta 
 mathematica) vires vere et physice tribuere : si forte aut centra trahere aut 
 vires centrorum esse dixero." 
 
35& PRINCIPLES OF LOGIC 
 
 occasion to consider. When Sir D. Brewster observed 
 the colours of mother-of-pearl on the bee's-wax, his 
 hypothesis that iridescence is caused by striation, was 
 clearly a rapid induction. The data before him were 
 two objects, both striated and both iridescent. The 
 hypothesis, which presented itself, was that possibly 
 striated objects as such are iridescent, that striation is 
 the cause of the phenomenon. 
 
 Analogical hypotheses are no less frequent. Such 
 in fact was Newton's hypothesis in regard to the 
 moon : 
 
 Bodies near the surface of the earth are under the 
 
 influence of gravity. 
 The moon resembles bodies near the surface of the 
 
 earth, in so far as it tends towards the earth. 
 The moon may be under the influence of gravity. 
 Such too was James Watt's hypothesis as to the motive 
 force of steam : 
 
 Ordinary agencies employed to raise weights do so 
 
 by the exercise of motive power. 
 Steam resembles these agencies in its power to raise 
 
 a kettle-lid. 
 
 Steam may be possessed of motive power. 
 There is no essential difference between the two modes 
 of arriving at hypotheses ; for, as we have seen (Ch. 16, 
 6), the basis of every analogy is a probable induction, 
 by which the two classes S t and S 2 are brought together 
 in some universal concept. 
 
 An analogical hypothesis will prove valueless, unless the 
 character on which it is based is important in relation 
 to the attribute to whose presence we conclude. The 
 power, however, to distinguish between what is import- 
 ant and unimportant in any regard, depends not on a 
 knowledge of rules, but on native intelligence, and on 
 acquaintance with the matter in hand. The same re- 
 mark also applies to hypotheses based on induction. 
 Their value must depend on the perspicacity and in- 
 sight of the investigator, in detecting which attributes 
 are likely to be causally connected. 
 
HYPOTHESIS 359 
 
 3. Conditions of a Legitimate Hypothesis. The re- 
 quisites of a valid hypothesis have been variously formu- 
 lated. The following are the conditions as proposed 
 by Jevons (Princ., p. 511). 
 
 (1) The hypothesis must allow of the application of 
 
 deductive reasoning, and the inference of con- 
 sequences capable of comparison with the results of 
 observation. 
 
 (2) It must not conflict with any laws of nature or 
 
 of mind, which we hold to be true. 
 
 (3) The consequences inferred must agree with the 
 
 facts of observation. 
 
 The first of these conditions needs no comment. The 
 sole object of an hypothesis is to suggest a cause capable 
 of accounting for the facts before us. Hence, unless 
 it is such that we are able to deduce the phenomena 
 from it, it fails to fulfil the very purpose for which it 
 exists. 
 
 The second rule that the hypothesis must not conflict 
 with any known law of nature or of mind, must not be 
 understood to mean that the cause supposed must always 
 act in accordance with laws, with which we are familiar. 
 All that is necessary is that it should not violate a law, 
 of whose existence we have positive evidence. We may 
 be forced sometimes to posit a cause, which acts in a 
 manner to which we have no known parallel. Thus, 
 to take an instance in point, it has seemed to some 
 thinkers that the Atomic theory is beset with so many 
 difficulties, that it would be preferable to adopt the 
 view that matter is continuous, and that though con- 
 tinuous, it is capable of contraction and expansion. 
 Here, the hypothesis proposes for our acceptance a 
 phenomenon subject to a law quite unlike those with 
 which we are familiar. Yet it cannot on that ground, 
 be dismissed as an impossible supposition. Professor 
 Poynting well remarks on this subject : 
 
 " If we believed that a piece of matter is as continuous as it 
 ' seems to the eye, we should have to admit that contraction 
 ' and expansion are simple facts, facts like any others. This 
 
360 PRINCIPLES OF LOGIC 
 
 ' supposition was characterized by Principal Sir A. Riicker in 
 ' his British Association address at Glasgow, as unintelligible 
 ' and absurd, in that it leaves contraction and expansion unex- 
 ' plained. This appears to me to be carrying the passion for 
 ' explanation to excess. To say that any simple fact, any fact 
 ' which so far stands by itself and is unlike others, must have a 
 ' hidden likeness, must be explicable, and that the contrary is 
 ' absurd, is an d priori way of dealing with Nature, which she 
 ' may at any time resent and refute, by bringing our so-called 
 'explanations to nought." 1 
 
 In the same way, the third rule must not be so strictly 
 interpreted as to signify that the consequences inferred 
 from the proposed hypothesis must so agree with all 
 the facts, as to leave no perplexities. It may well be 
 that we are justified in accepting an hypothesis on the 
 ground of its evident reasonableness, even though some 
 facts remain, which prima facie appear to contradict 
 it, and of which no explanation can as yet be suggested. 
 Such was the case in regard to the heliocentric theory, 
 when first proposed by Copernicus. It seemed to demand 
 that the planet Venus, when nearest to the earth, should 
 appear to be of sixteen times the size, which it has when 
 most remote. This, of course, is not the case. Yet 
 this apparently inexplicable difficulty did not prevent 
 the acceptance of the Copernican theory by many of 
 the most cultivated minds. 2 The seeming contradiction 
 was removed, when Galileo through his telescope saw 
 that Venus passes through moon-like phases, and that 
 what we see is not the whole area of 'the planet, but its 
 luminous part only. The portion which is luminous 
 when the planet is near the earth, is less than that which 
 is luminous when the planet is more remote. 
 
 It is evident that an hypothesis acquires more and more pro- 
 bability in proportion to the number of facts which it explains ; 
 and that if it leads to the prediction of facts, which subsequently 
 prove to be true, this tends in an especial manner to confirm it. 
 An hypothesis in regard to natural law, is further greatly com- 
 
 1 ' Physical Law and Life ' in the Hibbert Journal, Vol. I., p. 728 (1903). 
 
 2 Andreas Osiander in the prefatory letter before alluded to, states that 
 this is an insuperable objection to the acceptance of Copernicus's theory 
 regarded as an account of the actual facts. 
 
HYPOTHESIS 361 
 
 mended by its simplicity, since all recognize it is characteristic 
 of the complex processes of Nature, that they are governed by 
 wide and simple laws, simplex veri sigillum. On this point 
 something has already been said in reference to Newton's first 
 Rule of Philosophizing (Ch. 22, 6). If an hypothesis suffices to 
 explain a vast variety of phenomena by a single simple law, that 
 alone affords an argument that we have detected the plan followed 
 by the Supreme Reason to Whom the order of the universe is due. 
 Attention has been called (Ch. 18, 5) to the expression Experi- 
 mentum Crucis, employed when we are able by the test of a 
 decisive experiment, to exclude one of two rival hypotheses, 
 and so to demonstrate the truth of the other. 
 
 4. Various Kinds of Hypotheses. Different terms 
 are employed to designate different kinds of hypotheses. 
 The most important of these are as follows : 
 
 (1) Hypothesis of Cause. This expression is used 
 when the hypothesis relates to the agent, or to what 
 we regard as the agent, producing the phenomenon 
 under consideration. Thus when Pasteur was led to the 
 belief that fermentation was caused by yeast-cells, his 
 supposition was an hypothesis of cause. Such too was 
 Pascal's hypothesis referring the rise of the mercury 
 column to atmospheric pressure. In this category we 
 may also reckon the ancient hypothesis that meteoric 
 stones were due to the activity of terrestrial volcanoes. 
 
 (2) Hypothesis of Law. Often our supposition does 
 not relate to the cause of the phenomenon, but to the 
 law governing its operation, the formula, so to 
 speak, which expresses it. These are termed hypotheses 
 of law. Until Newton established his proofs, the conj ecture 
 that the courses of the planets' orbits were determined 
 by a force varying according to the law of inverse squares, 
 was an hypothesis of law. Such were also the nineteen 
 different hypotheses made by Kepler as to the orbit of 
 Mars, before he was fortunate enough to light on the 
 true explanation. Mendelejeffs famous hypothesis that 
 the properties of the elements would be found to vary peri- 
 odically as their atomic weights, belongs to the same class. 
 
 (3) Working Hypothesis. We have already explained 
 at length the meaning of a Descriptive Hypothesis. The 
 
362 PRINCIPLES OF LOGIC 
 
 expression ' Working Hypothesis ' is used when it is 
 desired to lay special stress on the provisional character 
 of the assumption, and on the conviction of the investi- 
 gator that it will need large modifications, before it 
 will be found satisfactorily to account for all the facts, 
 for which it should provide an explanation. 
 
 Theory : Hypothesis : Fact. In physical science the terms 
 theory and hypothesis are employed in contrast to each other. 
 The term theory is ordinarily understood to signify that the sug- 
 gested explanation is held to have been satisfactorily proved, 
 and to be no longer open to question. Thus we find writers use 
 the expression ' Theory of Gravitation,' not ' Hypothesis of 
 Gravitation.' So too the divergence of opinion between two 
 schools may be marked by the fact that the same doctrine is 
 by the one termed a theory, by the other an hypothesis. Such 
 expressions as ' the theory of Evolution ' and ' the evolutionary 
 hypothesis,' indicate clearly enough the tendency of the work 
 in which they occur. There are however certain scientific writers 
 who do not adhere to this distinction, but assign other significa- 
 tions to the terms in question. 
 
 The term Fact is sometimes restricted to signify the particular 
 concrete facts of experience. Sometimes it is extended to in- 
 clude whatever has been proved to be real, and in this sense can 
 be used of a theory whose truth has been established. 
 
CHAPTER XXIII. 
 
 QUANTITATIVE DETERMINATION I ELIMINATION OF CHANCE. 
 
 i. Measurement. In the ascertainment of many 
 natural laws, precise quantitative determination is 
 required. " Accurate and minute measurement," says 
 Lord Kelvin, " seems to the non-scientific imagination, 
 ' a less lofty and dignified work than the looking for 
 ' something new. But nearly all the grandest dis- 
 ' coveries of science have been the reward of accurate 
 ' measurement, and patient, long-continued labour in 
 ' the minute sifting of numerical results." It is not, 
 of course, the case that all laws are capable of quantita- 
 tive expression. It is, for instance, as much a law of nature 
 that dogs are carnivorous, as that the wave-length of 
 the red line in the spectrum of cadmium is the i, 553,164^1 
 part of a metre. The laws of light demand quantitative 
 expression : those of zoology are purely qualitative. 
 
 It should be noted that in those sciences in which 
 measurement is employed, the stage of accurate quanti- 
 tative determination is always an advance on an earlier 
 period in which investigation was concerned with quality 
 alone. Thus in chemistry the nature of the elements 
 composing a compound is first discovered : the accurate 
 determination of the precise amount of each element is 
 a subsequent stage. Somewhat similarly in the science 
 of astronomy, the qualitative character of the earth's 
 motion as an ellipse round the sun was first established, 
 and then by exact quantitative methods the precise 
 form of that ellipse was ascertained. 
 
 In a treatise which has for its subject the general 
 methods employed in the discovery of physical laws, 
 
364 PRINCIPLES OF LOGIC 
 
 something must be said as to the nature of measurement, 
 and as to the conditions affecting it. 
 
 All measurement is an act of comparison. To take 
 the measure of a magnitude is to determine the relation 
 it bears to some other quantity, which we have adopted 
 as a standard. As regards spatial measurement, the 
 standard quantity for scientific purposes is the metre 
 and its subdivisions, the centimetre, millimetre, etc. 1 
 For temporal measurement the standard is the period 
 constituted by the earth's revolution on its axis, the 
 day : this being subdivided into hours, minutes, seconds. 
 
 The act of comparison is beset by great difficulties. 
 The conditions under which it is carried out, forbid us 
 to hope for perfect accuracy. In the first place it depends 
 in the last resort on sense-perception. The senses are 
 trustworthy to a certain point : but they demand that 
 their object should be proportioned to their powers. 
 When we force them to ascertain something which 
 transcends these limits, they decline the task : and we 
 find that the reports as to an object, given by the same 
 sense on different occasions, are at variance with each 
 other. To ensure accuracy, instruments have been 
 devised, which enable us to determine magnitudes many 
 thousand times finer than the finest sense can perceive. 2 
 But this does but push the difficulty one stage further 
 back. The discrepancies, it is true, relate now, not to 
 millimetres, but to millionths of a millimetre. But they 
 still exist. Moreover, the instruments themselves, though 
 capable of far more accurate measurement than the 
 unaided senses, involve imperfections of their own. 
 
 1 What is the metre ? The standard metre is a piece of metal preserved 
 at Paris, which originally was intended to represent precisely one ten-millionth 
 part of the earth's quadrant. An artificial standard of this kind has however 
 certain inconveniences. We have e.g., no guarantee that it will not change by 
 age through the settling down of its component molecules. Hence the scien- 
 tific world has adopted a natural standard. By a metre is understood a piece 
 of metal whose length at o C. at the epoch A.D. 1906=1,553,164 times 
 the wave-length of the red line in the spectrum of cadmium, when the latter 
 is observed in dry air at the temperature of 15 C. of the normal hydrogen- 
 scale at a pressure of 760 mm. of mercury at o C. 
 
 * Thus Nichol's radiometer can detect the heat received from Vega or 
 Arcturus. 
 
QUANTITATIVE DETERMINATION 365 
 
 Metal contracts and expands with variations in the 
 temperature. It is also impossible so to fit the parts 
 of the mechanism together, as to ensure the perfect 
 working of the instrument. And, as we shall shortly 
 show, these are not the only sources, whence errors in 
 our observation arise. 
 
 In most cases, the enquiry into a law of nature has 
 relation to some special purpose ; and when an element 
 of error is very minute, it ceases to be of any importance 
 in regard to the purpose in hand, and may be safely dis- 
 regarded. Thus, to the engineer who is constructing 
 an iron bridge, it is of vital moment to know the laws 
 as to the expansion of metals. It is said that the longitu- 
 dinal expansion in the Forth bridge is such as to amount 
 to a difference of seven feet between the summer and 
 the winter measurement. Unless space is allowed for 
 such expansion, the strain involved would rapidly prove 
 fatal to the most solid structure. But it is sufficient 
 for the bridge-builder to attain a certain degree of accu- 
 racy. To determine the law with greater precision, 
 would for him be but lost labour. For other kinds of 
 work, greater exactitude may be required. The intro- 
 duction of compensations for temperature into a naval 
 chronometer demands a delicacy of adjustment very 
 different from that which is supposed in building a bridge. 
 The law of expansion must be determined far more 
 exactly. Yet even here there is a point, at which the 
 accuracy attained suffices for the needs of the navigating 
 officer ; and that point is far short of absolute perfection. 
 
 For the practical needs of life, nothing is lacking to 
 us. It is when man seeks to satisfy his desire to know, 
 that he discovers how endless is the task of unravelling 
 the secrets of Nature. To enumerate but a few among 
 the sources of error with which he has to reckon, we may 
 mention not only the limitations of sense and the problem 
 presented by changes of temperature, but further, the 
 impossibility of securing perfect rigidity in the instru- 
 ment, and in optical investigations the difficulties which 
 arise through refraction. There may also be some 
 
366 PRINCIPLES OF LOGIC 
 
 unsuspected electrical or magnetic influence exercising 
 a disturbing effect. Finally, there is always the ' personal 
 equation/ by which name we denote the deviations 
 from accuracy caused by anything in the personality 
 of the observer. 
 
 The effect of such disturbing causes is well illustrated 
 by the case, in which after various observations have 
 been taken as to the position of a star, and every effort 
 has been made to ensure absolute exactitude in each, 
 the calculated results are found to be at variance. They 
 may approximate closely, but each places the star in a 
 position slightly different from that indicated by the 
 others. 
 
 This may fairly be said to be the normal case when 
 delicate quantitative determination is in question. What 
 course then is the investigator to adopt ? His first 
 step must be to eliminate by calculation all errors of 
 which he has cognizance. Thus allowance may at once 
 be made for any slight idiosyncrasies of a particular 
 instrument ; and in the case of those observers whose 
 personal equation is constant, this can similarly be cor- 
 rected. When this has been done, reason prescribes 
 that he should take the mean of his observations, and 
 adopt this as a nearer approximation to the truth than 
 any of the separate measurements. By the word ' mean ' 
 we do not here signify simply the ' average ' or ' arith- 
 metic mean.' It is not always practicable to avail our- 
 selves of this. In the next section, we shall discuss 
 the way in which the mean must be determined. But 
 we must now show why the mean of a number of experi- 
 ments is to be regarded as equivalently their combined 
 testimony. 
 
 The reason for this will be seen, if, in illustration, we 
 examine the case of a particular cause of error, namely 
 sense-perception. If we consider the nature of sense- 
 perception in the abstract, it is clear that, viewed as a 
 cause of error in the measurement of a magnitude, it 
 is indifferent as to excess or defect. It tends equally 
 to mistakes on either side. The inaccuracy, which 
 
QUANTITATIVE DETERMINATION 367 
 
 characterizes its testimony, arises not from any special 
 tendency to exaggerate or to diminish, but from the 
 inability of the senses to attain perfect exactitude. 
 Hence it follows that as the number of observations is 
 increased, the mean error will grow less and less, excess 
 and defect at least at the end of an infinite series, 
 tending to a ratio of equality. To suppose otherwise 
 to imagine that the term of the whole process would 
 be inequality is to suppose an effect without a cause. 
 But this involves that when very many observations 
 of a magnitude have been taken, if there is good reason 
 to regard them as equally reliable, the mean of these observa- 
 tions will give us as near an approximation to the true 
 magnitude as it is possible for us to obtain. 
 
 Now we may safely hold that the various sources of 
 error, which we are unable to eliminate independently, 
 are of this character. They are indifferent to excess 
 or defect. The observations taken in a particular state 
 of the temperature may perhaps tend to exaggeration : 
 but there will also be days on which the error will be in 
 the opposite direction. In proportion as the number 
 of competent observers increases, and reliable observa- 
 tions are multiplied, so there should be a corresponding 
 approximation to absolute accuracy. 
 
 It is found in practice that the experimental error of measure- 
 ments, varies inversely as the square root of the number of obser- 
 vations, whose mean is taken. Thus the error contained in the 
 mean of 81 observations will be 3 times less than the error of 9 
 observations. 
 
 In the collation of experiments, investigators at once reject 
 any measurement which differs widely from the testimony of 
 the others. Small discrepancies are explicable. But a wide 
 divergence cannot arise in the manner indicated. Either the 
 observation was carelessly made, or in some way the conditions 
 must have been different. 
 
 * 2. Methods of Approximation. There are two ways in 
 which the mean of a number of observations may be found. 
 These are (i) the method of means, (2) the method of least squares. 
 As the term ' mean ' has by custom been assigned to one of these 
 two methods, it will be more convenient to speak of the two as 
 
368 PRINCIPLES OF LOGIC 
 
 Methods of Approximation rather than as Methods of deter- 
 mining the mean. 
 
 We shall describe these two methods separately. They are 
 distinguished for practical purposes ; but it will appear that 
 the first of the two is really a simple case of the second. 
 
 (i) Method of Means. This method the simple plan of taking 
 the average, is only applicable when we are dealing with a 
 single magnitude, as for instance the length of a line. The sum 
 of the observed measurements is taken, and is divided by the 
 number of the observations. Thus if four observations have 
 been made as to the length of a line P, and these are denoted 
 respectively by P v P 2 , P 3 and P 4 , the mean will be represented 
 
 t P. + P 2 + P 3 + P. 
 by the formula, - 
 
 4- 
 
 The method is susceptible of various modifications. Thus, 
 investigators are accustomed to attribute weight to their obser- 
 vations, in proportion to their assumed value. If, for instance, 
 one observation has been made under especially favourable 
 circumstances, another under less favourable, and a third under 
 somewhat unsatisfactory conditions, they would adopt the plan 
 of attributing to the first of these the weight of three observa- 
 tions, and to the second the weight of two. This would give 
 
 . 3P 1 + 2P 2 + P, 
 
 as a formula - * 1 
 
 6. 
 
 (ii) Method of Least Squares. The Method of Means, as we 
 have said, can only be applied when we are dealing with a single 
 magnitude. Such a case is infrequent. As a rule, greater com- 
 plexity is involved. For instance, we may suppose a case where 
 we are engaged in determining a magnitude P, and our observa- 
 tions consist of two series, one relating to P, and a second relating 
 to a magnitude q, which is some function of P. That our illus- 
 tration may be a simple one, we will suppose q to be the square 
 root of P. The two series may be represented respectively by 
 P v P 2 , P 3 . . . P n and q v q 2 , q 3 . . . q n ; and we have reason 
 to regard each series as of equal reliability. How are we to 
 deal with such a case ? One way undoubtedly would be to take 
 the squares of the values of q, and then find the arithmetic mean 
 of the P and q series in combination. But there is a serious 
 objection to this rough-and-ready way of calculating. There is, 
 according to our supposition, a parity between the errors of the 
 P series and those of the q series. By squaring the values of q, 
 we have greatly increased the relative amount of error in that 
 series, and thus have destroyed the parity between the two sets 
 of values. We have not in this way secured a body of equally 
 reliable values, which justify us in supposing that as the number 
 of our observations increases, so the mean error must constantly 
 decrease. We no longer have the same right to disregard the 
 
ELIMINATION OF CHANCE 369 
 
 residuals, as those quantities are called by which our measure- 
 ments differ from the mean. Hence, wherever calculations 
 demanding great precision are in question, it is advisable to 
 employ another method which is mathematically superior, viz. : 
 the Method of Least Squares. This consists in discovering that 
 value which makes the sum of the squares of the residuals, the least 
 possible. An algebraic process enables us to assign the particu- 
 lar value of P, which stands in that relation to the two series. 
 It will be observed that this characteristic belongs to the arith- 
 metic mean itself. In the average or arithmetic mean of two 
 or more numbers, we have the value which makes the sum of 
 the squares on the residuals the least possible. If we choose any 
 other value than the mean, be it above or below, and take the 
 squares of the quantities by which that value differs from the 
 original numbers, the sum of these squares will be greater than 
 the sum of the squares of the residuals given by the mean. 1 But 
 it is not a property of the arithmetic mean as such. It is a pro- 
 perty of the mean generically ; and even when the arithmetic 
 mean would be of no service, we can adopt this more general 
 method. The Method of Means is rightly termed a special case 
 of the Method of Least Squares. 
 
 3. Chance. Another method sometimes usefully 
 employed in discovering and determining a law of nature, 
 now claims our attention. It is termed the Elimination 
 of Chance. The scope of this method is limited. We 
 cannot by its means establish a relation of cause and 
 effect between two phenomena. It merely serves to 
 show the presence of an Empirical Law. This term 
 ' empirical law/ is used with some variety of meaning. 
 It is sometimes employed to signify any law of nature, 
 which is with good reason believed to be a derivative 
 law, capable of explanation by being brought under 
 some more universal law, though as yet it has not been 
 so explained. But more usually, as in this section, a 
 restricted signification is given to it, and it denotes an 
 observed uniformity between phenomena, which we see 
 to be connected, though how they are connected we 
 
 1 Thus, if we take the three numbers 8, 10, 12, whose mean is 10, the sum 
 of the squares on the residuals (i 2 +2 2 ), is 8. If instead of taking the mean, 
 we select a number either above or below it, we shall find the sum of the 
 squares on the new residuals will exceed 8. Thus if we take the number 9, 
 they will be 3 2 +i 2 =io. 
 
370 PRINCIPLES OF LOGIC 
 
 know not. They are connected for us empirically, that 
 is, in our experience : but they are not connected for 
 us rationally, that is, in our intelligence. We observe 
 that under certain conditions X is followed by Y. But 
 whether X is the cause of Y, or whether they are both 
 effects proceeding from A, or whether X is a necessary 
 condition enabling A to produce Y of all this we are 
 ignorant. Knowledge of these empirical laws, imperfect 
 as it is, is of great importance to us ; for it is not infre- 
 quently the first stage in discovering a true law of nature. 
 
 Before proceeding to the discussion of the method in 
 question, it will be well to state clearly what is meant 
 by Chance. 
 
 The term Chance is accurately defined by Mill. " We 
 ' may say," he writes, " that two or more phenomena 
 ' are conjoined by chance . . . meaning that they are 
 ' in no way related by causation." And again, " Facts 
 'conjoined by chance are separately the effect of causes, 
 ' and therefore of laws : but of different causes, and of 
 ' facts not connected by any law " (Logic, III., c. 17, 2). 
 
 Thus if I visit London, and there unexpectedly meet 
 an old friend, who was as ignorant of my presence in 
 the metropolis, as I of his, I attribute the meeting to 
 chance. In doing so, I do not regard Chance as a positive 
 entity, to whose causality the meeting was due. I 
 simply signify that the event was a coincidence, that it 
 was outside the scope of either of the two causal series 
 needed to bring it about. 
 
 If we consider the causal series in this universe sepa- 
 rately, then many of the events that take place are, in 
 relation to the separate series, casual. They are not 
 such effects as the agent of its own nature tends to pro- 
 duce ; but are, in fact, conjunctures. Hence, chance 
 corresponds to a real element in our experience ; and 
 nothing is gained by saying that since everything has 
 a cause, there can be no such thing as chance. 
 
 It should, however, be borne in mind that what is 
 casual in regard of this or that particular cause, may be 
 a result directly intended by a superior cause, to which 
 
ELIMINATION OF CHANCE 371 
 
 the two causes in question are subordinate. This point 
 has been illustrated by the case of a master, who de- 
 spatches two servants on different errands, each without 
 the knowledge of the other, to the same place. Their 
 meeting is, as far as they are concerned, casual. But 
 to the master, it is the result in view of which the action 
 was planned, and to which its various stages were all 
 directed. This suggests how in our lives coincidences 
 may, if considered in relation to an overruling Provi- 
 dence, be directly intended, and constitute the true 
 term of a chain of causality. Bain, when dealing with 
 this subject, remarks that none but the superstitious 
 could have seen any connexion between the death of 
 Oliver Cromwell and the storm which, when he was 
 expiring, burst over London. ' Each event/ he urges, 
 ' grew out of its own independent series of causes. . . . 
 ' They concurred in time, and that is all that should be 
 ' said concerning them ' (Logic, III., c. 9, i.). The par- 
 ticular instance selected is a matter of indifference, and 
 does not concern us. But the objection involves apetitio 
 principii ; for it implicitly denies the existence of a 
 First Cause, who disposes and orders all finite and 
 subordinate causes. 1 
 
 The meaning we attach to Chance, when we attribute 
 to it, for example, the result of a throw at dice, is but very 
 little removed from the sense, which we have been 
 discussing. In this case, it is true, the result is not due 
 to a coincidence. The physical action of the player 
 may in a true sense be held to be the reason not only 
 that dice fell from the box, but that on coming to rest, 
 they present such and such faces. Yet the player does 
 not attribute this latter effect to himself, because his 
 action in throwing was not designed to produce that 
 particular result. In general, we regard as our own 
 only those effects which we designed our action to produce. 
 Here, the action was solely directed to ejecting the dice 
 from the box ; it bore, and could bear, no relation to 
 any particular face turned up. Hence, we do not attri- 
 
 1 On the subject of Chance, cf. St. Thomas, Summa Theol. I., Q. 116, Art. I- 
 
372 PRINCIPLES OF LOGIC 
 
 bute the good or ill success of the throw to ourselves. 
 We regard it as casual, just as we regard the unlocked 
 for meeting with a friend as casual. 
 
 4. Elimination of Chance. The Elimination of 
 Chance is a method by which we show that the conjunc- 
 tion between two circumstances is not casual, that they 
 must be connected in virtue of some law. It is based 
 on the principle that if two events are connected by 
 chance alone, their connexion will not be stable. The 
 cases in which X is followed by Y, will be balanced by 
 other cases in which it appears without Y. On the 
 other hand, if one event accompanies the other in a way 
 that cannot be attributed to mere chance, then we are 
 justified in supposing that there is valid evidence for 
 the existence of a causal connexion. The principle, it 
 will be seen, is identical with that of the Method of 
 Agreement. But it is peculiar to the Elimination of 
 Chance, that it enables us to allow for a number of cases 
 in which, owing to what are termed counteracting causes, 
 the law is not verified, the antecedent appearing without 
 the consequent. 
 
 The method is well illustrated by the case, in which 
 it is employed for the detection of loaded dice. If a 
 die shows a marked tendency to turn up the number 
 six, the question naturally suggests itself whether the 
 appearance of that face, is after all a purely casual result 
 of the throw. Is it not a direct and natural result of 
 the action, due to the presence of a bias within the die ? 
 We know that if the die is perfectly normal the figure 
 six should appear on the average but once in six throws. 
 If then it turns up, not once in every six throws, but 
 three times in every four, we may justly conclude that 
 there is something amiss. 
 
 In a case like this, the reason which convinces us that 
 the result is not casual, is the same as that on which we 
 relied to shew that we are justified in adopting the mean 
 of a number of measurements as the nearest approach 
 to the true determination of a magnitude. For, since 
 
ELIMINATION OF CHANCE 373 
 
 in the case of a normal die, our action in throwing has no 
 natural tendency to turn up one face more than another, to 
 suppose a great preponderance in favour of a special re- 
 sult, would be to suppose an effect with no adequate cause. 
 
 Yet here we are met with a difficulty. It is only 
 after an infinite series that we can count on attaining a 
 ratio of equality between the number of times that 
 each face has appeared. No impossibility is involved 
 in the supposition that in the first four throws with a 
 perfectly normal die, the six should appear three times, 
 and that after twenty or thirty throws, the proportion 
 of sixes should be greatly above the due average. Now 
 every series of experiments, which we can adduce as 
 evidence, is finite, not infinite. How are we to decide 
 that the excess over the proper average, is such as to 
 postulate a cause ? Must this decision be left to the 
 rough estimates of common-sense, or is it possible to 
 obtain some scientific determination of the question ? 
 
 This problem has been dealt with in the mathematical 
 theory of Probability. To that subject, our next section 
 must be devoted. 
 
 It is evident that the point we have raised has an 
 important bearing on the question of the adoption of 
 the mean measurement. There also we calculate from 
 a limited number of measurements, and not from the 
 infinite series, which would render us certain that excess 
 and defect must have attained equality. Hence, in 
 that case too, the investigator employs the theory of 
 Probability, and determines by the aid of its calculus 
 how far it is in any degree probable that his results may 
 be erroneous. 
 
 5. Probability. Even when a proposition is not 
 certain, there may be valid motives for giving a definite 
 measure of rational credeuce to it. In this case we say 
 that the proposition is more or less probable : and by 
 the probability of the proposition we understand the 
 measure of rational credence due to it. 
 
 In the mathematical theory of probability, numerals 
 
374 PRINCIPLES OF LOGIC 
 
 are employed to denote the measure of credence. Certi- 
 tude as to the truth of a proposition is denoted by unity, 
 certitude as to its falsehood by zero. Where the motives 
 are such as to lead us to give it a probable assent, our 
 credence is denoted by a fraction corresponding to the 
 weight of the motive. 1 The question may indeed suggest 
 itself, whether it is possible thus to measure motives. 
 It is perhaps, for the present best answered by our old 
 illustration of the dice. Here the motives which influ- 
 ence our expectation of the six, are 5 against its appear- 
 ance and but I in favour. Hence the probability of 
 the proposition that the six will appear, is i. 
 
 What has been said will have shown that the meaning 
 of the term probability as here employed, differs somewhat 
 from its customary use. As it is ordinarily used, we 
 only term probable that which happens more often than 
 it does not. What happens but seldom, is designated 
 as possible, not as probable. But in mathematics even 
 that which is barely possible, is reckoned as probable, 
 its probability being expressed by a fraction corresponding 
 to such motives as it can claim. 
 
 What is the proper subject-matter of the theory of 
 Probability ? 
 
 There are certain classes of events, such that, though 
 we are able to affirm with confidence that a particular 
 proposition will be true in regard to a definite proportion 
 of them, yet we cannot affirm this proposition of any 
 member of the class taken separately. Let us suppose 
 that in regard to the population of England at the present 
 epoch, reliable statistics, extending over many years, 
 shew us that from every thousand men of twenty-five 
 years of age, ninety per cent, live to be thirty-five. In 
 such a case, we have no doubts that this will hold good 
 of the population as a whole in the near future ; but 
 we should not venture to assert of any particular indi- 
 vidual who is now twenty-five years old, that he will 
 live another decade. Similarly, I may have good grounds 
 
 1 ' La probabilite est done une fraction toujours inferieure a i.' M. Victor 
 Baudot in the article Probability in the Nouveau Dictionnaire des Sciences^ 
 
ELIMINATION OF CHANCE 375 
 
 for believing that in the coming autumn five days out 
 of every seven will, in the part of England where I live, 
 be wet. But I cannot venture to predict of any special 
 day, whether it will be among the fine or the rainy ones. 
 
 It is where our knowledge regarding events is of this 
 character, that probability has its place. Now it will 
 be noticed, that our knowledge here has two special 
 features. In the first place, it is based on the existence 
 of law. If we were not convinced that the proportion 
 of deaths to survivals between the ages of twenty-five 
 and thirty-five was the result of definite laws, which 
 will continue to produce the same result under similar 
 conditions, we should have no ground for believing that 
 this proportion would be maintained. We cannot argue 
 from past to future, from the known to the unknown, 
 except on the ground of some law. Even when we hold 
 that, in the long run, each face of the die will appear an 
 equal number of times, we do so relying on the principle 
 that no event can take place without a sufficient reason. 
 Secondly, our knowledge is of a very restricted kind. 
 We know that causes exist producing certain results 
 according to a definite law, but these causes are so com- 
 plex as to elude any attempt to track their operation in 
 detail. Our only resource is to take some class, within 
 which they operate, and see what is the proportion of 
 the cases, in which the event occurs, to those in which 
 it does not occur. Thus, we take the class Englishmen 
 between twenty-five and thirty-five, and estimate what 
 is the proportion of cases, in which the causes that are 
 hostile to human life, actually destroy it. The class 
 we select, though it be one within which the cause 
 operates, must, of course, be such that in a certain number 
 of cases the effect is not produced. Otherwise, we 
 should have certainty, not probability. 
 
 Although probability is thus based on definite data, 
 it supposes a certain ignorance as its condition. To an 
 omniscient Being, there can be no probability ; for to 
 such a one the law governing each cause would be known. 
 
 It will be observed that the probability of an event 
 
376 PRINCIPLES OF LOGIC 
 
 to one person, is often not the same as its probability 
 to another. Thus, of a man concerning whom I only 
 know that he is an Englishman twenty-five years of age, 
 I may say that the chances of his living to be thirty- 
 five, are 9 to i. Some one who is better informed, and 
 knows that he is a worker in a factory, where the pro- 
 portion of those who survive to be thirty-five, is only 
 80 per cent., may say that his chances are but 4 to i. 
 The reason of this divergence lies simply in the fact that 
 the data are gathered in relation to different classes. 
 The former case deals with the chances of the man, in 
 so far as he is an Englishman ; the latter with his chances, 
 in so far as he is a worker at such and such a trade. 
 
 It may perhaps be asked, in what sense we regard 
 the probability of an event as the chances of that event. 
 This question will be answered if we consider what is 
 involved in the expression of probability as a fraction. 
 When, for instance, we say that the probability an English- 
 man of twenty-five will survive to be thirty-five, is T 9 Q, 
 we mean that we view the class in question as divided 
 into ten parts, nine of which belong to the survivors, 
 and one to those who die. We consider these ten parts 
 as representing ten alternatives of equal likelihood, just 
 as when the die is thrown, we regard it as equally likely 
 that any one of the faces may appear. But as nine of 
 the alternatives are the same, the chance in favour of 
 that event is -f^. In considering the alternatives as 
 equally likely, we in no sense deny that in every case 
 the event is determined by its own causes. But in rela- 
 tion to our principle of enumeration, there is an equal 
 likelihood of each alternative. As regards the fact that 
 a person is an Englishman of five and twenty, his survival 
 to the age of thirty-five or his death previous to it, is a 
 casual result. 
 
 We have now explained in outline the meaning of 
 probability, and shewn what are the cases in which we 
 can discover by a mathematical calculus, the measure 
 of credence which a proposition claims. It remains to 
 
ELIMINATION OF CHANCE 377 
 
 point out how this calculus can assist us to determine 
 with accuracy the point at which the repeated conjunction 
 of two events affords conclusive evidence of causal 
 connexion. 
 
 Let us take a case, in which we have to draw a ball 
 from a bag containing three white balls and two black, 
 replacing after each trial the ball chosen. The chances 
 of drawing a white ball are f- ; and if a large number 
 N trials be made, it is probable that the white ball will 
 
 iN 
 appear - - times. Yet it must be owned that though 
 
 o 
 
 this number is more probable than any other, the prob- 
 ability that it will be exactly realized is but remote. The 
 famous mathematician James Bernouilli (1654-1705) 
 proposed to himself to determine within what limits 
 in a large number of trials, the result actually obtained 
 will approximate to the ideally most probable result. 
 This difficult problem occupied his thoughts during 
 twenty years, and his solution of it is known as Bernouilli' s 
 theorem. In a case such as the above, where the prob- 
 ability of the event in each trial is f , he showed that the 
 odds are 1,000 to i that in 25,500 trials, the event shall 
 occur not more than 15,841 times, and not less than 
 14,819, that is that the deviation from 15,300, the 
 ideally probable number, shall not exceed -$ of the 
 number of trials. 1 
 
 It need hardly be said that such a probability amounts 
 to a moral certainty. 
 
 Further, as the number of trials is multiplied, the ratio 
 of the number of deviations to the number of occasions 
 on which the occurrence agrees with the laws of prob- 
 ability, will grow less and less. 2 
 
 1 Vide article on Probability in EncycL Britan. (gth edit. vol. 19, p. 769) 
 by Prof. Croft on. 
 
 2 The following is the account of Bernouilli's theorem in M. Victor Baudot's 
 article Probabilite in the Nouveau Dictionnaire des Sciences. 
 
 " Theoreme de Jacques Bernouilli.- Definissons d'abord ce qu'on nomme 
 'ecart : supposons que la probabilite d'un evenement soit p et qu'on fasse ^ 
 epreuves successives, pendant lesquelles 1'eve'nement se produit m fois : 1' ecart 
 ' est la difference positive ou negative /*/> m. Ainsi, on lance 4040 fois une 
 ' piece en 1'air, fj. =4040 ; la probability p qu'on ait face est J, done v-p 
 
378 PRINCIPLES OF LOGIC 
 
 The bearing of this upon the elimination of chance 
 is evident. If we are able to say that in a definite number 
 of trials, certain limits will not be overstepped, and if 
 it is discovered that the result is totally at variance 
 with our mathematical estimate, then it becomes clear 
 that we were mistaken in our view as to the nature of 
 the case. We are manifestly not dealing with events 
 conjoined only by chance, the relative number of whose 
 conjunctures is determinable on mathematical principles, 
 but there is a law of connexion (or of repugnance) at 
 work. A loaded die gives, it is true, very irregular results. 
 Were it not so, it would be detected at once, and so 
 defeat its own purpose. But there comes a point at 
 which after a certain number of trials, the mathematician 
 is able to say that the appearances of the six exceed the 
 limits of mere chance, and that the very act of throwing 
 must tend to turn that face uppermost. 
 
 Philosophical Probability. We have been dealing in 
 this chapter with Mathematical Probability alone. It 
 remains to add a few words, in order to distinguish it 
 clearly from Philosophical Probability the probability 
 with which we are concerned when judging as to the 
 value of various hypotheses (Ch. 22, 3). Where this 
 is in question we estimate the relative degree of rational 
 credence to be attached to two suggested explanations. 
 But we cannot apply mathematical methods to deter- 
 mine the quantitative measure that expresses that rela- 
 tion. The comparison is qualitative, not quantitative, 
 
 ' si face se montre 2,048 fois, on dira que 1'ecart est - 28 ; si elle se montrait 
 ' 2,000 fois, 1'ecart serait 20. Le theoreme de Bernouilli revient a ceci : ' Si 
 
 on fait un nombre ind6finiment croissant d'epreuves 1'ecart est infiniment 
 
 petit par rapport au nombre des epreuves.' II faut bien remarquer que c'est 
 1'ecart relatif qui tend vers zero, 1'ecart absolu devient au contraire de plus 
 
 en grand. Cette derniere remarque fait comprendre certains resultats qui 
 ' peuvent paraitre, au premier abord, contraires a 1'evidence : Pierre et Paul 
 ' jouent, sans jamais se lasser, a pile ou face, 1'enjeu est chaque fois de i franc ; 
 ' il arrivera un moment ou Tun des deux adversaires sera ruine ; il est vrai 
 'que le rapport du nombre des parties gagnees par chaque joueur au nombre 
 ' des parties perdues par le meme tend vers i quand on joue indefiniment, 
 c mais la difference de ces deux nombres, et c'est la ce qui ruine Tun des joueurs, 
 ' grandit aussi de plus en plus." 
 
ELIMINATION OF CHANCE 379 
 
 and it is only where quantity is concerned that numerical 
 calculation is possible. 
 
 Philosophical probability resembles mathematical prob- 
 ability in that it rests on the principle that similar con- 
 junctions of events demand a cause or law governing 
 them and accounting for them. To suppose a series 
 of independent causes, when the resemblance of the 
 events is real and not imaginary, is as much out of the 
 question in the one case as in the other. But it differs 
 from mathematical probability in that its degree is 
 estimated by the character of the explanation suggested : 
 and this is judged by the ability of the hypothesis to 
 account for the facts, by the analogy it bears to other 
 known causes, by its intrinsic reasonableness. We have 
 indeed no means of measuring values such as these 
 numerically. We cannot determine the number of 
 possible laws which might account for the facts, nor 
 range them in a quantitative scale according to the 
 degree of reason and harmony they manifest. 1 But 
 although numerical calculation is impossible, the scientist 
 can affirm without hesitation that of two alternative 
 explanations the one is more probable than the other. 
 
 1 " Mais d'autre part, la probabilite philosophique differe essentiellement de 
 la probabilite mathematique, en ce qu'elle n'est pas re*ductible en nombres : 
 *non point a cause de 1'imperf ection actuelle de nos connaissances dans la science 
 ' de nombres, mais en soi et par sa nature propre. II n'y a lieu ni de nombrer 
 les lois possibles, ni de les Schelonner comme des grandeurs, par rapport a 
 4 cette proprie 1 te de forme qui constitue leur degr6 de simplicit6, et qui donne, 
 ' dans les degr6s divers, a la conception theorique des phenomenes, la symmetric, 
 ' 1'elcgance et labeaute." A. Cournot in Franck's Dictionnaire des Sciences 
 Philosophiques. 
 
CHAPTER XXIV. 
 
 CLASSIFICATION. 
 
 i. Classification. We have already (Ch. 19, i) 
 distinguished the natural sciences into two groups 
 those which deal primarily with the static forms of 
 Nature, and those which deal with her dynamic activities. 
 To the first group belong, for instance, Systematic 
 Botany and Systematic Zoology, the portion, that is, of 
 the sciences of Botany and Zoology, which deals with 
 the distribution of animals and plants into their genera 
 and species. Here, just as in the physical sciences, the 
 object which the investigator sets before himself is the 
 knowledge of natural laws. He seeks to establish neces- 
 sary and invariable connexions between attribute and 
 attribute. Thus it is the science of Systematic Zoology 
 which teaches us that each of the general types, mammals, 
 birds, reptiles, amphibians and fishes is characterized 
 by certain definite properties peculiar to the class in 
 question, and found in each and every member of the 
 class without exception. The methods, however, em- 
 ployed in this group of sciences, differ in some measure 
 from those we make use of in physical science. The 
 relative importance of Observation and Experiment in 
 the one group, is almost the direct converse of what it 
 is in the other. In the physical sciences, Observation 
 unaided by Experiment can do comparatively little. 
 The successful investigator is he who can best devise 
 and best conduct his experiments. In the sciences deal- 
 ing with Nature's stable forms, Experiment, hitherto 
 at least, has played a smaller part. 1 It is on Observa- 
 
 1 The discoveries of Abbot Gregor Mendel, and the application of the 
 principles called after him ' MendeUsm,' seem to point to a far greater em- 
 ployment of Experimental Methods in these sciences in the future. 
 
 3FO 
 
CLASSIFICATION 381 
 
 tion, that investigators have had principally to rely. 
 Further, the method of Classification, with which we 
 are concerned in this chapter, is altogether proper to 
 those sciences. Thus they are not infrequently simply 
 termed the Classificatory Sciences. 
 
 The work of Classification is to group individuals 
 according to their natural species, and to group the 
 species according to their natural co-ordination and sub- 
 ordination. Hence the object which we propose to 
 ourselves in this Scientific or as it is usually termed, 
 Natural Classification, is the knowledge of the order 
 which Nature offers to our contemplation. In the 
 natural grouping of the classes, the mind contemplates 
 the unity, the harmony, the reason, which pervades 
 the whole creation. It recognizes that there is working 
 in Nature an intelligence, to which its own is akin. Classi- 
 fication is far from being, as some describe it, merely 
 an aid to the attainment of practical ends. It is a 
 method subservient to speculative science. 1 
 
 By many writers, as we have already noticed, Classifi- 
 cation has been confused with Logical Division. They 
 are correlative, the one to the other : they are not 
 identical. In Classification, we deal with the real order : 
 it is the concrete individuals whom we classify. To 
 this classification of the individuals, there corresponds 
 in the conceptual order a logical division. The concept 
 of the genus the logical whole is divided by the addi- 
 tion of differentiae into its species, and these again into 
 subordinate species, until the logical unit, the ultima 
 species, is reached. 
 
 The term Classification is, however, not confined to 
 the Natural Classifications of which we have spoken. 
 The exigencies of practical life often demand that we 
 should form Artificial Classifications. Whenever we 
 
 1 Cf. Franck, Dictionnaire des Sciences Philosophiques, Art. Classification. 
 1 Les classifications dites naturelles ne nous laissent pas le choix entre plusieurs 
 points de vue ; il n'y en a qu'un seul qui soit vrai, et pour le d^couvrir, il 
 faut prealablement evaluer, avec le concours de 1'experience et du raisonne- 
 ment, 1'importance relative des diverses parties des objets. Tel est le principe 
 de la subordination des caracteres, que M. de Jussieu a le premier degage, 
 et qui generalise par M. Cuvier a renouvele la face des sciences naturelles.' 
 
382 PRINCIPLES OF LOGIC 
 
 have to deal with a great number of individual objects, 
 if we are to avoid complete bewilderment, we must 
 find some means of classifying them. The arrangement 
 may be wholly arbitrary, as for instance, that of a bio- 
 graphical dictionary, in which men of different races 
 and colours, some of them famous for their virtue, and 
 some for their crimes, are distributed into twenty-six 
 groups according to the place which the first letter of 
 their name holds in the alphabet. A more artificial 
 system could hardly have been selected. Yet it is well 
 adapted to its purpose ; for our aim is not speculative, 
 but purely practical. It is that we may without diffi- 
 culty be able to find any particular biographical notice, 
 which we desire to consult. 
 
 Before dealing with Natural Classifications, it will be 
 well to consider shortly these Artificial Classifications, 
 noting how completely they differ from those which 
 form the proper subject of this chapter. 
 
 2. Artificial Classification. Any attribute whatever 
 may be chosen to serve as the basis of an Artificial Classifi- 
 cation, provided that it fulfil two conditions. It must 
 be common to the whole group of objects to be classified, 
 and its different modifications must be sufficiently dis- 
 tinct to enable us to assign each individual to one and 
 one only of the subordinate classes. Hence, according 
 to the purpose which a man has in hand, he will select 
 a different attribute as the ground of his classification ; 
 and the same group of objects will be found variously 
 classified by different men. Thus the same collection 
 of engravings might be classified by an historian according 
 to the events represented, by an artist according to the 
 various schools of art or according to the individual 
 artists whose work was found in the collection, by a 
 print-dealer according to market value. 
 
 The cases, in which we employ Artificial Classifications, 
 are of two kinds, which need to be carefully distinguished. 
 
 We may be concerned (i) with a limited number of 
 individuals. The classification of the words in a par- 
 
CLASSIFICATION 383 
 
 ticular language, of the pictures in a gallery, of the auto- 
 mobiles in a given region, will serve as instances. Or 
 (2) the number of individuals to be classified may be 
 unlimited. This occurs, when we are dealing with all 
 the members of some natural class. 
 
 In the first of these cases, we often find it convenient 
 not to select a characteristic which the objects already 
 possess, as the basis of classification, but ourselves to 
 confer a characteristic for this very purpose. We affix 
 an artificial mark to each member of the class, and then 
 wherever we may chance to come across any individual, 
 we recognize its place in our classification. The method 
 is familiar to us in its application to the army, police 
 force, automobiles, etc. 
 
 In the second case of which we have spoken, we must 
 perforce rely on some natural characteristic. The 
 famous Linnaean system of botany affords us the classical 
 instance of such classification. In this system, the 
 various species of plants are arranged in genera accord- 
 ing to the number of stamens and pistils they possess, 
 and irrespective of any other similarity or dissimilarity 
 than is afforded by this single characteristic. Such a 
 distribution is rightly termed artificial, even though it 
 is based, as we have stated, on a natural characteristic. 
 It brings together into a common genus, species which 
 are connected by the sole fact that they have the same 
 number of stamens and pistils, but which in all else are 
 remote from each other : and it relegates to widely 
 divergent classes, species which in the natural order 
 are closely allied. 
 
 Investigators have had recourse to these classifications, 
 when the perplexities of the natural system have been 
 such as to baffle their efforts to arrange the classes. 
 In such cases, they have judged an artificial system 
 better than chaos. It at least enables us to assign a 
 definite place to each member of the group in virtue of 
 distinctive and easily recognizable marks. Yet such 
 a classification is only of temporary value. Even for 
 the practical end in question, the natural classification 
 
384 PRINCIPLES OF LOGIC 
 
 is far the most convenient, and in the long run the arti- 
 ficial system is discarded in its favour. What artificial 
 arrangement, for instance, could assign such distinctive 
 class-marks as are afforded by the classification of 
 phanerogamous plants into dicotyledons, monocotyledons, 
 conifers and cycads, or of vertebrates into mammals, 
 birds, reptiles, amphibians, fishes ? It is true that the 
 riddles of natural classification are many. To these 
 we shall advert in a subsequent section. But it is never- 
 theless the case that natural classes display conspicuous 
 and characteristic features, by which, better than by 
 any other attribute we might select, we may assign to 
 each object a determinate place in the group to which 
 it belongs. 
 
 3. The Doctrine of Natural Species. The aim of 
 
 Scientific Classification is, as we have already noted, to 
 group individuals according to their natural species, 
 and to group the species according to their natural 
 co-ordination and subordination. 
 
 It is evident that Classification, thus understood, 
 depends entirely on the existence of species. Yet it is 
 a fundamental tenet with many men of science that the 
 doctrine of natural species is destitute of all solid 
 foundation. We propose to consider this question in the 
 present section. It would be idle to discuss how species 
 should be classified, were it dubious whether they exist 
 or not. 
 
 It is a manifest fact of experience, that a vast number 
 of the members of the animal and vegetable kingdoms 
 are, at the present epoch of the world's history, distributed 
 in types. They are not a mere assemblage of individuals, 
 all of them so different the one from the other, that it 
 is impossible to affirm a universal proposition about any 
 determinate group. On the contrary, the types in 
 question involve, not only certain broad notes of resem- 
 blance, but a multitude of the most detailed character- 
 istics, common to every member of the class. The 
 minuteness of these resemblances is often extraordinary. 
 
CLASSIFICATION 385 
 
 This point is well brought out in the following passage : 
 "Not so mysterious as the similarity of character, 
 ' but equally wonderful, is that of the outward form. 
 ' .... I will take a bird which every one must know 
 ' the Chaffinch. Every cock Chaffinch has a black 
 ' forehead, and a bluish grey head and nape, with a 
 ' narrow half-collar of oil-green between this and the 
 ' chestnut of his back : the quill feathers of his wing 
 ' have each a narrow edging of greyish-white : of the 
 ' wing coverts, some are always black, and some white, 
 ' and one row is black at the base with a white tip to 
 ' each feather : the inner primaries have each a white 
 ' patch at the base of the outer web, while the pair of 
 ' tail feathers next to the outer ones, have each a narrow 
 ' white outer margin and a triangular patch on the inner 
 ' web. . . . Never assuredly did human skill more 
 ' accurately reproduce the simplest of designs. It makes 
 ' the matter not less but more astonishing that the bird 
 ' exhibits unmistakeable tendencies to vary. . . . What 
 ' is it that holds such tendencies in check ? " x 
 
 The similarities are not merely external. In every 
 type they manifest themselves through the whole of 
 the organism. The conclusion seems forced upon us 
 that the complicated system of characteristics, of which 
 the type consists, constitutes in each case a morphological 
 unity. The type is not merely an average standard, to 
 which the members of the class approximate more or 
 less roughly, some of them lacking some of the character- 
 istics, and some lacking others. These characteristics 
 unite to form a whole, and each such whole is a closed 
 system in itself. 
 
 Moreover, not merely is it the case that morphological 
 structure is identical in all the members of the class ; 
 but the process of development, of metamorphosis when 
 such occurs, and of reproduction, are the same in each 
 individual, and as far as our experience reaches, are 
 repeated generation after generation without change. 
 
 1 J. Gerard, S.J., Science and Scientists, p. 70. 
 
 CC 
 
386 PRINCIPLES OF LOGIC 
 
 Biologically as well as morphologically the type is a 
 unity. 
 
 Notwithstanding the weight of these facts, the exist- 
 ence of separate species is denied, as a view now entirely 
 superseded by the doctrine of Evolution as enunciated 
 by Darwin and so widely accepted since his day. At 
 the present time, the theory of Evolution has been deve- 
 loped along several different lines. Hence it is impos- 
 sible to give an account of it which shall be both brief, 
 and at the same time complete. According to the teach- 
 ing of the founder of the school, the manifold forms of 
 animal and plant life now existing owe their origin to 
 the principle of Natural Selection. Animal and plant 
 life is susceptible of indefinite variation, and in the 
 struggle for existence, the weaker and less efficient forms 
 have been extirpated, the stronger and better-equipped 
 alone have survived. The characteristics which mark 
 the different birds and beasts, are not, as had been 
 thought, due to the impress of different types. They 
 are merely the record of this long battle. There is no 
 such thing as type. Class merges into class ; and there 
 are no abrupt transitions in the scale of living beings. 
 
 The more recent followers of Darwin admit that 
 Natural Selection alone is insufficient to account for 
 the phenomena. Each of the more eminent among them 
 has a different theory as to the true explanation of our 
 present classes. On one point, however, they are agreed : 
 they are unanimous in holding that what seem to us to 
 be distinct types, have all arisen from a common stem, 
 through an accumulation of small changes : that there 
 are no breaks in Nature's chain : that species are a 
 figment of the imagination. Professor Ray Lankester 
 thus describes the effect as he conceives it, produced 
 by Darwin's Origin of Species : 
 
 " Universal opinion has been brought to the position 
 ' that species as well as genera, orders and classes, are 
 ' the subjective expressions of a vast ramifying pedigree, 
 ' in which the only existences are individuals, the apparent 
 ' species being marked out, not by any distributive 
 
CLASSIFICATION 387 
 
 ' law, but by the purely non-significant operation of 
 ' human experience." 1 
 
 Now those who maintain the existence of distinct 
 species, are in no way concerned with the question as 
 to the manner in which they originated. The point at 
 issue is a different one, namely whether at the present 
 time there do not exist types, each of which is a morpho- 
 logical and biological unity in the sense explained : 
 whether there is not a real objective principle present 
 in each member of the type, in virtue of which it possesses 
 certain characteristics common to every individual of 
 that species. Notwithstanding the popularity which 
 the Darwinian hypothesis still enjoys in certain schools 
 of thought, it may be said without hesitation that the 
 weight of evidence is overwhelmingly in favour of the 
 existence of such types. To this effect we may cite 
 some words of Fr. Wasmann, one of the most competent 
 German authorities : 
 
 " The world of organic life, at the present day as also 
 ' in the past, certainly does not consist as the Dar- 
 ' winian form of the theory of evolution would have us 
 ' believe ... of a chaos of minute variations. . . . 
 ' It constitutes on the contrary a well ordered system 
 ' of species, genera, families, orders, classes, phyla." 2 
 
 Fr. Wasmann's conclusion is the more interesting 
 inasmuch as he adheres to the view that our present 
 species originated by evolution, though not in the manner 
 suggested by Darwin. 
 
 Another investigator of the first rank, the Dutch 
 botanist H. de Vries, has recently shown that such 
 experience as we possess regarding the origin of classes 
 by descent, tends to prove that the transition need not 
 take place by the accumulation of numberless small 
 differences, but may be sudden and abrupt, involving 
 the production of a new type in the full sense of the 
 word. 3 He himself discovered among some ' escape ' 
 
 1 Encycl. Brit, (gih ed.), Art. Zoology, vol. 24, p. 805. 
 
 2 Die moderne Biologic und die Entwicklungstheorie (3rd ed.), p. 316. 
 8 Die Mutationstheorie, 1903. 
 
$88 PRINCIPLES OF LOGIC 
 
 specimens of Oenothera Lamarckiana (the large-flowered 
 evening primrose) several novel forms which displayed 
 that persistency in their characteristics, which is the 
 mark of the true species as distinguished from the mere 
 variety. 
 
 It is urged as a conclusive objection to the doctrine 
 we are now defending, that in some genera there is found 
 a series of transitional forms so complex and various that 
 the number of species into which they are divided in 
 any system, depends on the personal predilection of the 
 systematist. As instances in point, our attention is 
 called to the fact that the number of German species 
 of hieracium (hawk-weed) has been fixed by one author 
 at 300, by another at 106, by a third at 52, while a fourth 
 is content with only 20. The willows, brambles, and 
 calcareous sponges, are said to afford examples of the 
 same state of things. 
 
 The difficulty indicated has been met in more than 
 one way. Wasmann contends that in the animal and 
 plant world there are classes in which the formation of 
 new species is not yet at an end. This he believes is 
 fairly clear in the case of many plants such as hieracium 
 and rubus : and he claims that his own investigations 
 regarding the dinarda show that it is true of some at 
 least among the lower animals. He considers moreover 
 that in certain cases, the development of new types pro- 
 duces a greater variety of transitional forms, than appear 
 in the instances observed by de Vries. 
 
 Others meet the objection in a different manner, and 
 reply that it proves no more than that hitherto the 
 species constituting the genera in question, have not 
 yet been distinguished. When the species of any genus 
 are closely allied, and there is moreover considerable 
 variability within the limits of the different species, 
 their separation is necessarily attended with great diffi- 
 culty. In such cases, it must be a matter of prolonged 
 labour to distinguish the types, and determine the defini- 
 tion of each. It has yet to be shewn that in the genera 
 in question this task is impossible, and that we may 
 
CLASSIFICATION 389 
 
 not eventually succeed in determining a precise and 
 definite boundary between species and species. 
 
 The solution of this problem may be left to scientists. 
 We are not concerned with the question whether natural 
 species are universal. It is enough for our purpose, if 
 it be admitted that they exist even within a limited 
 range, and that we have thus a ground for classifications 
 based not on the ' non-significant operations of human 
 experience/ but on Nature's own ' well-ordered system 
 of species and genera.' 
 
 4. Natural Classification. The systematic ordering 
 of species according to their natural relationships is 
 rendered possible by the fact that the numerous char- 
 acteristics which constitute the type, have a hierarchical 
 order among themselves. If for instance, we enumerate 
 the characteristics present in a bos taurus one of our 
 ordinary domestic cattle, it is patent that some are 
 proper to the species taurus ; they are not found in the 
 other bovinae but in the bos taurus alone. Others belong 
 to all the bovinae : others again are qualities of every 
 ruminant. There are some, which are distinctive of 
 the mammal as such ; and some which are common to 
 all vertebrates. 
 
 The series of properties which distinguish every such 
 grade are connected one with the other in such wise, 
 that from one of these properties we may argue to the 
 presence of the others. " Hoofs on the feet," says 
 Cuvier, " indicate molar teeth with flat crowns, a very 
 ' long alimentary canal, a large or multipled stomach, 
 * and a great number of relations of the same kind." l 
 Similarly, just as the characteristics of the ungulata 
 are thus determined by their mutual relation, the general 
 features of the carnivora and other orders are no less 
 rigidly connected. 
 
 It is not, of course, the case that an animal is a mere 
 agglutination of notes ; that, e.g. all ruminants are 
 identically the same up to a certain point, but that while 
 
 1 Cuvier, Lepons d'Anatomie comparee, t. i, ire Lepon, Art. iv, 
 
390 PRINCIPLES OF LOGIC 
 
 the oves have a few additional notes of one description, 
 the bovinae possess corresponding peculiarities of another 
 kind. All ruminants are doubtless distinguished by 
 characters that are generically alike. But though the 
 general type of an ox and a sheep, in so far as they are 
 ruminants, is the same, the actualization of that general 
 type is different in every detail. The stomach of a 
 sheep is not like the stomach of an ox. Yet both are 
 expressed in the common concept of ruminant ; for 
 the concept admits of, and demands, ulterior determina- 
 tion. It is generic, and does not inform us in what 
 specific form the general type is realized. 
 
 The hierarchical order described, is one of subordina- 
 tion between the grades. If, for example, the investi- 
 gator, who is examining some fossil, can detect a feature 
 proper to the mammalia as such, he knows that the 
 digestive system of the animal must have been realized 
 in one out of a few clearly distinct modes. The general 
 character of mammal is compatible with any of these 
 modes. They, on the other hand, are incompatible 
 with any other animal form than that of the mammalia. 
 Each of them is found only among the mammals, but 
 none of them embraces the whole of that class. Hence, 
 the characteristics of the mammal are more fundamental 
 in the structure of the animal, than those which belong 
 to it as ruminant : those which mark it as a ruminant, 
 are more fundamental than those which it possesses as 
 a bos. The properties which distinguish the lower grades 
 are subordinate to those which mark the higher. This 
 will explain what is meant by the term important as 
 applied to some characteristic. It is often said that 
 our classifications must be based on the relative import- 
 ance of properties. The importance of a property 
 depends on the position it holds among the characteristics, 
 considered in their natural subordination. Those pro- 
 perties are the most important, which are the most 
 fundamental in the structure of the animal, and which 
 thus exercise a determining influence on the greatest 
 number of characteristics. 
 
CLASSIFICATION 391 
 
 The different grades of properties will enable us to 
 frame the definitions, on which the attainment of the 
 classification depends. When we have, by a careful 
 process of observation, and so far as experiment is possible, 
 by experiment, secured the true definitions, the classi- 
 fication is achieved : we know how Nature has distributed 
 the real order into its classes. 
 
 In regard to natural classes, we must, as we have 
 already noticed (Ch. 10, 2) define by properties. Our 
 definitions are Distinctive Definitions. Both genus and 
 differentia contain an indefinitely large series of notes ; 
 nor have we any means of knowing when we have 
 exhausted the properties of any class. 
 
 The preceding considerations will justify the following 
 rules, which are those usually given for the work of 
 natural classification. 
 
 (1) All groups should be so constituted as to differ 
 
 from each other by a multitude of attributes. 
 
 (2) The higher the group, the more important should 
 
 be the attributes by which it is constituted. 
 
 (3) The Classification should be graduated, so that 
 
 the groups with most affinity should be nearest 
 together, and so that the distance of one group from 
 another may be an indication of the amount of 
 their dissimilarity. 1 
 
 It must not be supposed that the classification of the 
 natural orders is a simple matter. While certain main 
 outlines are easily recognizable, there is much that is 
 profoundly obscure, and which seems destined to baffle 
 the most earnest seekers after truth. This is especially 
 the case at both extremities of the great scale. The 
 classification of the lower animals presents manifold 
 riddles. And the great principle which determines the 
 whole hierarchical subordination, is still in dispute. The 
 school of Linnaeus sought it in an ascending scale of 
 greater complexity of organization : de Jussieu and 
 
 1 Cf. Welton, Manual, 01. 
 
392 PRINCIPLES OF LOGIC 
 
 Cuvier believed it to lie in the different types of ana- 
 tomical structure, which characterize certain great 
 divisions of the animal kingdom : Darwin, in the laws 
 of descent. 
 
 Moreover, even where most progress has been made, 
 Nature refuses to be bound by our hard and fast lines. 
 The natural order is too complex and too various to fit 
 into our schemata. Our system may be admirably 
 suited for a large part of the animal or vegetable world ; 
 but there will always be some classes, which seem to 
 demand a totally different arrangement. It may be 
 well, to indicate one or two of the difficulties, which foil 
 the systematizer. 1 
 
 (1) In co-ordinate classes, the same organ is often 
 found to possess very different values. Thus, in mam- 
 mals, the dental formula is an important pioperty, 
 determining the character of many other attributes. In 
 the parallel class of fishes, it is relatively of no value, 
 while the nature of the integument is of high importance 
 among fishes, but of little or none among mammals. 
 
 (2) The same property is of different value at different 
 stages of the animal's life-history. Sometimes, organs 
 which are indispensable during the embryonic stage, 
 lose their value when it attains maturity. Further, 
 some animals, if judged by their embryonic characters, 
 have a claim to be ranked in a class from which in their 
 maturity they would be far distant. On grounds such 
 as these, the Ascidians or Sea-squirts are now frequently 
 assimilated to the Vertebrates under the common 
 denomination of Cordata. 
 
 (3) The same animal may possess organs, which are 
 characteristic of different species. Thus, the Sloth has 
 a dental formula, which would place it among the lowest 
 mammals, while many of its properties would entitle it 
 to a place among the Primates. 
 
 1 ' On ne peut pas demander a la science de nous montrer dans la plan de 
 la JNature une nettete de divisions, une inflexibilite de lignes, dont nous nous 
 accomoderions fort sans doute, mais dont la Nature, qui a mieux a faire ap- 
 parement, ne s'accomode pas.' Rabier, p. 211. The examples which follow 
 are drawn from M. Rabier's work. 
 
CLASSIFICATION 393 
 
 This inability of ours to make a final scheme coinciding exactly 
 with Nature's plan, led Whewell to advance his theory of Classi- 
 fication by Type. The term ' type/ as will be seen, is here used 
 in a different sense from that in which we have been employing 
 it. We cannot, he urges, classify by definition ; for there will 
 always be classes which fall outside our definition of the genus, 
 and yet must be reckoned as belonging to it. We must classif)' 
 by type. " A type is an example of any class, for instance a 
 ' species of a genus, which is considered as eminently possessing 
 ' the character of that class. All the species which have a greater 
 ' affinity with this type-species than with any other, form the 
 ' genus, and are arranged about it, deviating from it in various 
 ' directions, and in various degrees. Thus a genus may consist 
 ' of several species which approach very near the type, and of 
 ' which the claim to a place with it is obvious : while there may 
 ' be other species which straggle further from this central knot, 
 ' and which are yet more closely connected with it than any 
 'other" (see Mill, IV., c. 7, 3). 
 
 To this theory Mill objects that if classifications were framed 
 not by definitions but by these exemplar-types, no general pro- 
 position of any kind could be asserted about the class : whereas 
 classifications are chiefly valuable in so far as in them we attain 
 to general truths and laws of Nature. " The truth is," he says, 
 " that every genus or family is framed wi>h distinct reference 
 ' to certain characters, and is composed first and principally, of 
 ' species which agree in possessing all these characters." It is 
 these characters, as he rightly holds, which give us the definition 
 of the class. " To these [species] are added as a sort of appendix, 
 ' such other species, generally in small number, as possess nearly 
 ' all the properties selected : . . . and which, while they agree 
 ' with the rest almost as much as they agree with one another, do 
 ' not resemble in an equal degree any other group " (IV., c. 7, 4) . 
 
 * 5. Classification by Series. Mill devotes a chapter to what 
 he entitles Classification by Series : he holds that the Natural 
 Classifications of the animal and vegetable kingdoms should 
 conform to this type. This Classification by Series is, however, 
 something quite distinct from Natural Classification, as we have 
 understood it. We have regarded the attainment of a Natural 
 Classification as an end desirable in itself ; since in such a classi- 
 fication we possess speculative knowledge of the real order. To 
 Mill, classification is merely a means : it is an operation sub- 
 sidiary to induction, which provides, "that things shall be 
 ' thought of in such groups ... as will best conduce to the 
 ' remembrance and ascertainment of their laws " (IV., c. 7, i). 1 
 
 1 This view of Classification finds expression in the terms Classifications for 
 General Purposes and Classifications for Special Purposes, by which Mill desig- 
 
394 PRINCIPLES OF LOGIC 
 
 Thus, the object of a systematic classification of animals, is to 
 assist us in discovering the laws of animal life. The two re- 
 quisites of a classification, intended to aid in the study of any 
 phenomenon, are, he tells us, (i) that it should embrace every 
 class of things in which that phenomenon is found, and (2) that 
 it ;. hould " arrange those kinds in a series, according to the 
 ' degree in which they exhibit it, beginning with those that 
 ' exhibit most of it, and terminating with those that exhibit 
 ' least " (IV., c. 8, i). This method of arrangement is required, 
 because it is in this way that we are enabled to apply tholMethod 
 of Concomitant Variations, and observe what phenomena vary 
 in the same ratio as the one under consideration. It follows 
 that a Natural Classification of animals will place man as the 
 example of life in its highest degree, and will arrange the other 
 species in a descending scale. It should not however be thought 
 such a classification involves that all the species are to be drawn 
 up in a linear progression. Many of the subordinate classes 
 would probably be equidistant from the leading type, so that 
 the arrangement would be best compared to the disposition of 
 objects at various distances from one centre. 
 
 Mill attributes this portion of his theory to Comte, and regards 
 it as of considerable importance. But it may be doubted whether 
 it possesses the value he attaches to it. 
 
 nates Natural and Artificial Classifications respectively. These terms are 
 preferred by many logicians who, on the ground that there are no fixed species, 
 deny that any classification is, properly speaking, Natural. 
 
CHAPTER XXV. 
 
 METHOD. 
 
 i. Scientific Method. Some treatment of Method 
 forms part of most works on Logic. Two separate 
 subjects are, however, included under the common 
 designation of Method : (i) the different ways in which 
 scientific knowledge can be attained and presented to 
 the mind, and (2) the general rules which should guide 
 us in the arrangement of our arguments. 
 
 In the present section we are concerned solely with 
 the first of these. It is a question, which, strictly speak- 
 ing, belongs to the first part of this work ; and some 
 portion of the matter proper to the section, has been 
 anticipated. Yet we have reserved the more formal 
 consideration for the present chapter. 
 
 There are two ways in which the mind can acquire 
 scientific knowledge. It may attain it by passing from 
 the cause to the effect, from the law to the fact exempli- 
 fying the law, from the essence to the property ; or on 
 the other hand, it may pass from the property to the 
 essence, from particular events to universal laws. One 
 of these ways, it must needs use. For it is characteristic 
 of science, that in it we know not merely the fact, but 
 the reason of the fact. We view the fact as the expres- 
 sion of a law, the effect of a cause. In order to possess 
 knowledge of this kind, we must either have passed from 
 the antecedent to its consequent, or from consequenl 
 to antecedent. 
 
 These two ways are known respectively as Synthesis 
 and Analysis. 1 The reader will see that the distinction 
 
 1 The Scholastic logicians employ the synonymous terms methodus com- 
 positionis and methodus resolutionis. Vide St. Thomas, Opusc. 63 in Boeth> 
 Q. 6, Art. i, ad. 3. 
 
39^ PRINCIPLES OF LOGIC 
 
 between them is based on the same principle as that 
 between Progressive and Regressive Reasoning (Ch. 12, 4, 
 Ch. 21, 2). The scope of Synthesis and Analysis is how- 
 ever somewhat wider than that between the two forms 
 of deductive argument. Analysis embraces not merely 
 Regressive Deduction but further, Induction : for by 
 Induction we argue from facts to laws : from particular 
 events to the universal principle. Every act of Natural 
 Classification is thus an analytic process. For in classi- 
 fying, we bring to light a law : we pass from the complex 
 individuals to the simple universal type. 
 
 There is, it is true, a perfection in the method of Syn- 
 thesis, which is lacking in that of Analysis. Knowledge 
 finds its ideal, when the mind grasps first the truth of 
 principles, and from them reasons to their results. In 
 such reasoning, we trace the same path as Nature. The 
 logical process is in full harmony with the ontological, 
 the conceptual order with the real. 
 
 But human science inevitably depends more on Ana- 
 lysis than on Synthesis. For our knowledge begins 
 from the concrete particular. It is from singular objects 
 perceived by sense, that we must discover universal 
 laws : from effects, we must pass to their causes. Even 
 when we employ the synthetic method in exposition, 
 this is not because we have grasped the truth of the 
 principle first : we are merely retracing the steps 
 we have previously travelled along the via resolutions 
 (Ch. 21, 2). 
 
 This will explain the well-known Scholastic distinction 
 between things which are better known to us (notiora quoad 
 nos) and things which are better known naturally (notiora 
 secundum naturam, notiora simpliciter). 1 To us concrete 
 particulars the object of sense-perception are better 
 known than universals ; while the universals which are 
 
 1 The distinction is Aristotle's. An. Post. I., c. 2, 4. Elsewhere (Met. 
 II. c. i, 2) he compares man's intellect to the eye of a bat, which sees in the 
 dark, but is dazzled and blinded by the light of day. For our faculties find 
 their connatural object in the particular ; yet, if considered not in relation to 
 our faculties but in its own nature, the more universal is any principle and 
 the wider its range of application, the ampler must be the knowledge which 
 it really affords. 
 
METHOD 397 
 
 intelligible to reason, are ' better known naturally/ 
 Analysis is the method, in which starting from things 
 which are nobis notiora, we reach the principles which are 
 notiora secunduam naturam. In Synthesis, as we have 
 already said, we follow the path of Nature herself. 
 
 There is one science, and one alone, viz., Mathematics, 
 in which Synthesis is the native process of the mind. 
 Our faculties give us an insight into the nature of spatial 
 extension and figure, such that in this case it is connatural 
 to the intellect to reason from principles to their necessary 
 consequences. Here, what is better known to Nature, 
 is at the same time also better known to us. 1 Hence, 
 just in the measure that we can apply Mathematics to 
 the solution of problems in the other sciences, those 
 sciences can be treated synthetically. 
 
 In some measure indeed, Mathematics employs the 
 analytical method ; and the other sciences make use of 
 synthesis. Geometrical problems are not infrequently 
 dealt with by analytic reasoning. The problem is sup- 
 posed solved, and we trace step by step what principles 
 are involved in its successful solution. If this process 
 leads us at last to principles known to be true, we are 
 able to reverse the reasoning, and deduce the solution 
 from these principles. This regressive method in Mathe- 
 matics is the original sense of the word Analysis. It 
 was employed by the Greek mathematicians with this 
 signification. 
 
 We make use of Synthesis in the natural sciences in 
 certain cases, where the composition of causes is involved. 
 Jevons supplies a good example in regard to the nature 
 of storms. Here the complexity of the operative con- 
 ditions is such as to render analytic reasoning almost 
 out of the question. We can however employ the con- 
 verse method, and argue from experiments of the labo- 
 
 1 Cf. St. Thomas in An J Post. I., lect. 4. " Non enim aliquid potest fieri 
 nobis notum nisi per id quod est magis notum nobis. Quandoque autem id 
 qnod est magis notum quoad nos, est etiam magis notum simpliciter et secun- 
 dum naturam : sicut accidit in mathematicis. . . . Item quandoque id 
 quod est notius quoad nos, non est notius simpliciter, sicut accidit in naturali- 
 bus." 
 
3Q8 PRINCIPLES OF LOGIC 
 
 ratory to what takes place on a larger scale in the atmo- 
 sphere. " Putting together synthetically from the sciences 
 ' of chemistry, mechanics and electricity, all that we 
 ' know of air, wind, cloud and lightning, we are able 
 ' to explain what takes place in a thunderstorm far more 
 ' completely than we could do by merely observing 
 ' what takes pilace in a storm " (Elem. Lessons, p. 207). 
 
 The student will be careful not to confuse the logical analysis, 
 of which we have been treating, with analysis as practised e.g. 
 in chemistry. We have been dealing with the mental process, 
 by which we pass from a result to its principles. Chemical 
 analysis deals with the real order. 
 
 Though the concrete particular is better known to us than is 
 the abstract universal, yet in our knowledge of the concrete 
 particular itself, there is first a transition from the more general 
 to the less general. Thus we see an object at a distance, and 
 recognize it first as substance, then as animal, then man, lastly 
 as such and such an individual. 1 
 
 2. The Methodic Pursuit of Truth. Method has 
 been defined as a systematic manner of carrying on the 
 search for truth. Such a definition might indeed be 
 applied to Method as explained in the last section : it 
 might signify the two systems of Analysis and Synthesis. 2 
 But it may also be taken to signify the general rules, 
 which should guide us in the arrangement of our reason- 
 ings ; and in more recent times the term has often been 
 understood in that sense. Various lists of such rules 
 have been drawn up by different authors. 
 
 Jevons has well remarked that it is quite impossible 
 to frame prescriptions of this kind. No general direc- 
 tions can possibly be given for the arrangement of things 
 
 1 This point is treated fully by Albertus Magnus, Phys. I., Tr. I. c. 6. If ' Ex 
 istis est advertendum.' Cf. also St. Thomas, An. Post. I., lect. 4. 'In omni 
 enim generatione, quod est in potentia est prius tempore. . . . Cognitio 
 autem generis est quasi potentialis in comparatione ad cognitionem speciei. . . . 
 Unde in generatione nostrae scientiae prius est cognoscere magis commune 
 quam minus commune.' 
 
 8 ' Modus ordinatus procedendi in veritatis inquisitione.' Goudin, I.e. 
 He however understands Method as signifying solely Analysis and Synthesis. 
 The Port Royal definition is as follows : The art of disposing well a series of 
 many thoughts, either for the discovering of truth when we are ignorant of it, or 
 for proving it to others when it is already known (Part IV. c 2, Baynes's trans.) 
 
METHOD 399 
 
 which require an infinite variety of arrangement. No 
 useful purpose, as he rightly urges, can be served by 
 such rules as we find in Aldrich's Logic, where we are 
 told that in every argument we propound : 
 
 1. Nothing should be wanting or redundant. 
 
 2. The separate parts should agree with each other. 
 
 3. Nothing should be treated save what is suitable 
 to the subject or purpose. 
 
 4. The separate parts should be connected by suitable 
 transitions. In brief, completeness, harmony, relevancy, 
 and continuity must be observed. 
 
 The student will observe that these so-called rules 
 of Method are merely what common-sense prescribes in 
 the case of any end which must be attained by the employ- 
 ment of various means. They would be as appropriate 
 in the case of a watch-maker as they are to the logician. 
 What we need, if it were possible to obtain it, is guidance 
 to distinguish what is wanting and what is redundant : 
 and this would depend on the particular matter in hand, 
 of which it supposes expert knowledge. The Cartesians 
 brought it as a reproach against the Scholastics, that 
 they had omitted this part of Logic. In fact, nothing 
 was to be gained by attempting to treat it. 
 
 Since Mill included the general theory of scientific 
 research in Logic, Method has ceased to signify simply 
 the general rules of argument. It has been taken to 
 mean the method of successful scientific research. As 
 an example of the" treatment accorded to the subject 
 from this point of view, we may notice the article on 
 Scientific Method in Baldwin's Dictionary of Philosophy 
 and Psychology. The author of the article Prof. C. S. 
 Peirce in regard to those sciences which have reached the 
 nomological stage in which universal laws are known, dis- 
 tinguishes five steps in the work of scientific research. 
 These steps are, in brief, as follows : 
 
 (i) To form a perfectly definite and consistent idea of what 
 the problem really is : then to develop the Mathematics of the 
 subject in hand as far as possible : and to establish a mathe- 
 
400 PRINCIPLES OF LOGIC 
 
 matical method appropriate to the particular problem, if it be 
 one which admits of exact treatment. 
 
 (2) To consider the methodeutic of the research in hand, and 
 the manner in which analogous subjects have been treated. 
 
 (3) In the third place, if the subject be a broad one, the stu- 
 dent should reform his metaphysics. 
 
 (4) The enquiry into the laws of the phenomena constitutes 
 the fourth stage. This is commenced by a careful observation 
 of the phenomena themselves. Observation is followed by the 
 framing of an hypothesis, the deduction of the results which 
 would follow from the hypothesis suggested, and a verification 
 of the hypothesis by a comparison of its results with the facts. 
 
 (5) Finally the law of the phenomena once made out, it re- 
 mains to measure with precision the values of the coefficients 
 in the equation, which expresses it. 
 
 The steps here prescribed cannot, we think, be regarded 
 as satisfactory. Metaphysics are, without doubt, of 
 essential importance in all scientific questions. But a 
 student, who has embarked on a scientific problem, and 
 equipped himself for the task by the requisite knowledge 
 of the question, can hardly be advised at that stage to 
 embark on the somewhat vague task of ' reforming his 
 Metaphysics.' Logically Metaphysics must take the 
 first place, as the basis of all science. Then follows 
 Mathematics as a requisite for every science in which 
 quantity is concerned. But these, together with the 
 particular branch of Mathematics applicable to the 
 subject in hand, should be supposed known. They are 
 an essential preliminary to the methodic enquiry into 
 the phenomenon under investigation. As regards this 
 essential part, it will be noticed that Prof. Peirce's 
 method is none other than that explanation by hypo- 
 thetical deduction, which we have considered in Ch. 
 21, 3- 
 
 3. Philosophic Terminology. Although it is impos- 
 sible to prescribe precisely for the systematic ordering 
 of our thoughts in the attainment of truth, yet some 
 such general rules may be given for the use of language, 
 the instrument and the support of thought. On the 
 correct use of terms, the attainment of truth is largely 
 
METHOD 401 
 
 dependent. This is, above all, the case in philosophy. 
 If, in speaking of some object that is cognizable by sense, 
 I employ a term properly applicable to something else, 
 I may confuse my hearers : but the thing in question 
 is present to my imagination, and I can hardly mislead 
 myself. But in philosophy, we deal with abstractions 
 remote from sense. The employment of an inappro- 
 priate term, may introduce a wrong idea into the mind, 
 without our being aware of the error ; and the result 
 may in the long run be complete intellectual confusion. 
 To take an example from the history of philosophy, it 
 is impossible to overestimate the harm caused by Kant's 
 restriction of the term ' Analytic proposition ' to those 
 judgments alone, in which the predicate is part of the 
 intension of the subject. This terminology, involved 
 as its consequence, that judgments in which the pre- 
 dicate is a property of the subject, and judgments 
 depending on the experience of sense, were thrown into 
 the common class of ' Synthetic propositions/ 
 
 It need scarcely be pointed out that similar ill effects 
 will ensue, if we employ terms insufficiently defined, 
 and the intension of which we conceive but vaguely. 
 
 The foregoing considerations may be summed up in 
 three rules, of considerable importance for the student : 
 
 (1) To employ the most commonly accepted terms in 
 their most commonly accepted meanings. 
 
 (2) Where any doubt as to the meaning of a term can 
 arise, to define carefully : and in points of great import- 
 ance to make use of technical terms. 
 
 (3) Never to employ a term to which he cannot assign 
 a precise and clearly-defined meaning. 
 
 The completeness of the Scholastic terminology, and 
 its philosophic precision in regard to the definition of 
 each term, were a signal merit of the mediaeval schools, 
 and lightened the labour of the student in no small 
 degree. In these days, on the contrary, we are face to 
 face with a score of different systems ; and the termin- 
 ology of each is different. Nor is this a mere matter 
 of words. In almost every case, a change of terminology 
 
 D D 
 
402 PRINCIPLES OF LOGIC 
 
 betokens a real difference in regard to some philosophic 
 tenet, which is frequently of far-reaching importance. 
 What at first sight appears a mere verbal technicality, 
 not meriting serious attention, is found, on a closer view, 
 to involve a fundamental cleavage of doctrine. 
 
 It will be well for the student to remember that few 
 things contribute more to confusion of thought than 
 a careless employment of the terminology belonging to 
 different schools. The terms of a particular school 
 embody its thought. By such a selection, he may 
 commit himself to inconsistent views, and render clear 
 thinking an impossibility to himself. He may, more- 
 over, unconsciously mould his opinions in a fashion he 
 little contemplates. For, just as the popular beliefs 
 of a nation are largely determined by words and phrases 
 that are in vogue, so too the terminology we employ, 
 does much to fix our views. " Words," says Sir W. 
 Hamilton, " are the fortresses of thought. They enable 
 ' us to realise our dominion over what we have already 
 ' overrun in thought." By employing the terminology 
 of a particular school, we may find ourselves committed 
 to the defence of the fortresses that school has erected. 
 
 * 4. Descartes' Rules of Method. Descartes, in his Discourse 
 on Method (Part 2), gives four general rules of method, by which, 
 as he tells us, he believed it would be possible ' to arrive at the 
 knowledge of whatever lay within the compass of his powers.' 
 These were embodied in the Port Royal Logic, and since then 
 have been cited by so many writers, that it seems advisable to 
 make some mention of them. They run as follows : 
 
 I. Never to accept anything for true which I do not know to 
 be such : that is, to comprise nothing more in my judgment, 
 than what is presented to my mind so clearly and distinctly as 
 to exclude all grounds of doubt. 
 
 II. To divide each of the difficulties under examination into 
 as many parts as possible, and as may be necessary for its 
 adequate solution. 
 
 III. To conduct my thoughts in such order, that by com- 
 mencing with objects the simplest and easiest to know, I may 
 asc nd by little and little, and as it were, step by step, to the 
 knowledge of the more complex : assigning in thought a certain 
 order even to those objects, which in their own nature do not 
 stand in a relation of antecedence and sequence. 
 
METHOD 
 
 403 
 
 IV. In every case to make enumerations so complete, and 
 reviews so general, that I may be assured that nothing is omitted. 
 
 It is remarkable that those logicians, who have cited these 
 rules with approval, appear to assume they were intended to be 
 simply common-sense prescriptions as to the conduct of reason- 
 ing. As a matter of fact, they embody a particular method of 
 scientific research, which is perhaps the most characteristic 
 feature of the Cartesian philosophy, and which none now would 
 care to defend. 
 
 The objects, which the human intellect can know, were dis- 
 tinguished by Descartes into ' absolute ' and ' relative.' The 
 ' relative ' can be known only by resolution into the ' absolute.' 
 The ' absolute ' are incapable of further resolution : every such 
 object is a simple nature, and is of its own essence, knowable. 
 For instance, of the three pairs of correlatives cause and 
 effect, equal and unequal, unity and multiplicity, the first 
 in each case is 'absolute'; the second, 'relative.' Further, 
 axiomatic truths, such as that the whole is greater than its part, 
 are also ' absolute ' objects of knowledge. These ' absolute ' 
 truths are known by intellectual intuition. Once presented to 
 the mind, they are immediately recognized as true ; for they 
 possess the infallible criterium of truth clearness and distinct- 
 ness. No induction is needed to establish these truths. More- 
 over, it is on them that all science must be based. Nothing 
 may be admitted save what is derived from them, and thus 
 shares in their clearness and distinctness (Rule i). 
 
 When we undertake the examination of some phenomenon 
 with a view to its explanation, we must analyse its circumstances, 
 till we discover the ' simple nature ' on which it depends. There 
 our division stops. For ' simple natures ' are irresolvable. 
 Thus, if e.g. the object proposed is the refraction of light, an 
 examination of the circumstances will convince us that the 
 ' simple nature ' concerned, is light itself. A scrutiny of our 
 conception of light, will show us that we possess an intuitive 
 knowledge of its nature (Rule 2). 
 
 The next step will be to proceed from the simple to the com- 
 plex : to deduce, by a synthetic process, in which proposition 
 follows proposition in logical sequence, the phenomena of nature 
 from our intuitive knowledge of these primary truths. The 
 separate sciences, however, do not stand in a relation of antece- 
 dence and sequence. Hence, it is not to be imagined that the 
 whole of knowledge can be connected in one great concatenation. 
 But even where truths do not admit of being arranged in con- 
 nected sequence, a fixed order should be assigned them in the 
 mind (Rule 3). 
 
 From time to time, our analysis or our synthesis will tail us. 
 We shall come to a point, where there is a break in the chain 
 
404 PRINCIPLES OF LOGIC 
 
 between the simple nature and the phenomenon under considera- 
 tion. Then, we must have recourse to the process called by 
 Descartes Enumeration or Induction. It is, however, more allied 
 to Analogy than to what we term Induction. All the known 
 phenomena of a similar kind must be enumerated, and by a 
 consideration of them, we shall be able to determine the point 
 at issue. Thus, for instance, when Descartes is discussing the 
 phenomena of the rainbow, he solves the question by an appeal 
 to what takes place when the sun's rays strike a glass ball (Rule 4). 
 This was the method by which Descartes hoped to establish 
 the whole of science on a mathematical basis, and by which he 
 believed he had solved the principal problems of natural philo- 
 sophy. " I have essayed," he writes, " to find in general the 
 ' principles or first causes of all that is or can be in the world, 
 ' without taking into consideration for this end anything but 
 ' God himself, who has created it, and without educing them from 
 ' any other source than from certain germs of truths naturally existing 
 ' in our minds. In the second place, I examined what were the 
 ' first and most ordinary effects that could be deduced from these 
 ' causes : and it appears to me that in this way I have found 
 ' heavens, stars and earth, and even on the earth, water, air, fire, 
 1 minerals and some other things of the kind." * 
 
 * 5. Leibniz's Views on Method. It was probably due to 
 the influence of Descartes' writings on Method, that Leibniz, at 
 a slightly later date, turned his attention to this subject. To 
 his mind the systematization of knowledge was of the first im- 
 portance. The knowledge possessed by the human race, is, he 
 urges, vast and various : but it is unorganized and dispersed in 
 the works of many authors. System must be brought into the 
 sciences. The ideal before us should be nothing less than a vast 
 Encyclopedia of knowledge, in which every science is repre- 
 sented, and all the truths constituting it are deductively proved 
 from certain first principles. To this ideal, we cannot indeed 
 hope perfectly to attain. We shall often be compelled to rely 
 on some principle which is not self-evident, but which we have 
 good reason to suppose true. No harm will be done by this, if 
 it be frankly stated that the principle is a supposition, and though 
 apparently correct, has not been demonstrated from the primary 
 truths on which the science is based. There are, he holds, such 
 suppositions even in mathematics. Such is Euclid's assumption 
 that two straight lines cannot have a common segment. Not 
 improbably a way will afterwards be found of proving these 
 suppositions, and then all the conclusions we have deduced from 
 them will possess demonstrative value. Nevertheless, our aim 
 should be to achieve a complete deductive proof from a series 
 
 1 Discourse on Method, Pt. 6. 
 
METHOD 405 
 
 of definitions, whose truth is established by identical principles. 1 
 If possible, proofs resting on identical principles should be dis- 
 covered even for axioms. Descartes, he considers, erred in 
 holding that whatever he saw clearly, was true. To postulate 
 such a criterion, is to beg the question. The ultimate criterion 
 must be identical principles. 2 
 
 This method must, of course, be applicable in different degrees 
 to different sciences. In Physics it can hardly be applied ; for, 
 since we are ignorant regarding the essential natures of material 
 substances, we cannot hope to demonstrate their properties 
 deductively. Yet even here, one who is versed in the matter in 
 hand, will probably be able to judge with some accuracy as to 
 the properties likely to belong to a substance. But although 
 the application of this method to the physical sciences presents 
 special difficulties, it is suited in the highest degree to moral 
 science, the noblest object of our faculties. 
 
 Moreover, were the sciences thus systematized, it would be 
 possible to indicate the way to develop the conclusions deducible 
 from first principles and from established facts. This method 
 of discovery would be as simple as are the processes of Arith- 
 metic or Algebra. It was, he assures us, his intention to demon- 
 strate the feasibility of this method, as soon as he should have 
 secured sufficient examples to make its value evident. In a 
 calculus of this kind lies the ultimate perfection of Art of Dis- 
 covery (l'art d'inventer). This art already exists, though it be 
 little cultivated. a 
 
 1 Leibniz (Monadoiogy, 35) defines ' identical propositions ' as " those 
 ' primary principles which cannot be proved, and indeed have no need of 
 ' proof . . . whose opposite involves an express contradiction." 
 
 2 Cf. De Synthesi et Analyst Universal* (ed. Gerhardt, vol. 7, p. 295), ' Itaque 
 cujuscunque veritatis reddi potest ratio, connexio enim praedicati cum sub- 
 jecto aut per se patet, ut in identicis, aut explicanda est, quod fit resolutione 
 terminorum. Atque hoc unicum summumque est veritatis criterium, in 
 abstractis scilicet neque ab experimento pendentibus, ut sit vel identica, vel 
 ad identicas revocabilis.' 
 
 3 See Preceptes pour avancer les sciences, ed. Erdmann, p. 165. Nouveaux 
 Essais, IV., cc. 12, 21. 
 
QUESTIONS ON LOGIC 
 
 THESE questions for the most part are taken from papers set at 
 one or other of the universities of Great Britain or Ireland, or in 
 the examinations for H. M. Indian Civil Service. The source is 
 indicated in each case by an initial letter : O=Oxford, C=Cam- 
 bridge, L=London, G=Glasgow, T.C.D.=Dublin, R.U.I. =Royal 
 University of Ireland, I. C.S.= Indian Civil Service. For the per- 
 mission to print them here, courteously accorded to me by the 
 responsible authorities, my thanks are due. 1 
 
 The numbering of the exercises corresponds to that of the 
 chapters. 
 
 EXERCISE I. 
 
 1 . What are the three parts of logical doctrine ? How may they 
 be named (a) with reference to language, (b) with reference to 
 thought ? (C. Prev. 1902.) 
 
 2. To what extent is Logic concerned with language ? What are 
 the respective provinces of (i) Logic, (2) Grammar, (3) Psych- 
 ology ? 
 
 3. Examine the following statements as to the province or 
 function of Logic : 
 
 (a) The science not of Truth but of Consistency. 
 
 (b) The science of the operations of the understanding which 
 
 are subservient to the estimation of evidence. 
 
 (c) A machine for combating fallacy. (L. Inter. A rts, 1 905 . ) 
 
 4. Distinguish between (a) the conceptualist and nominalist 
 methods of treating Logic, (b) Logical and psychological laws of 
 thought. (T.C.D. 2nd year Hon. 1904.) 
 
 5. Discuss the various attempted definitions (not descriptions) 
 of Logic, with which you are acquainted. (O. Mods. 1907.) 
 
 6. Discuss the validity of the distinction between Formal and 
 Material Logic, and comment upon other ways of expressing the 
 same or a related distinction. (L. Inter. Arts, 1903.) 
 
 EXERCISE II. 
 
 i. Explain the nature of Abstraction. Of what importance is 
 this operation in the formation of the Logical Concept ? 
 
 1 For leave to print questions drawn from Indian Civil Service papers T am 
 indebted to the Controller of H.M. Stationery Office. 
 
 407 
 
408 PRINCIPLES OF LOGIC 
 
 What do you understand by a Phantasm ? How does a Phan- 
 tasm differ from a Concept ? 
 
 2. Define Term, Concept : and illustrate from a logical point of 
 view the process of forming a concept. 
 
 Is every General term the name of a class ? Give your reasons. 
 
 (L. Inter. Arts, 1906.) 
 
 3. Explain concisely the distinction (a) between General and 
 Singular Terms ; (b) between Concrete and Abstract Terms ; 
 illustrating your explanation by a discussion of the logical charac- 
 teristics of the following terms : The University of London, 
 Logic, Iron, Sound, Fallacy. (L. B.Sc. 1906.) 
 
 4. Discuss the distinctions (a) between Collective and Distribu- 
 tive ; (b) between Positive and Negative Terms. Illustrate your 
 discussion by examining the following statements : 
 
 ' All the plays of Shakespeare cannot be read in a day.' 
 ' Any one who is not industrious must be accounted idle.' 
 
 (C. Prev. 1904.) 
 
 5. ' The Connotation of a name consists of the qualities on ac- 
 count of which the name was given.' 
 
 ' The Connotation of a name consists of the qualities implied in 
 actual discourse.' 
 
 Consider the distinction of Connotative and Non-Connotative 
 names in the light of these propositions. (O. Mods. 1906.) 
 
 6. (a) What do you understand by a Non-Connotative term ? 
 Is " the longest river in the world " Connotative or Non-Connota- 
 tive ? 
 
 (b) Examine the following : ' Popocatapetl is a Non-Connota- 
 tive term to us, only so long as we do not know what the Mexicans 
 mean by the word.' (L. Matr. 1905.) 
 
 7. Explain and criticise the view that Extension and Intension 
 vary inversely. (O. Mods. 1904.) 
 
 8. What is meant by Infinite terms ? The notion of such terms 
 has been denied. How can it be defended ? 
 
 9. Consider carefully the distinction between Concrete and 
 Abstract terms. Under which head (if under either) would you 
 class Adjectives ? (O. Mods. 1907.) 
 
 10. Explain the division of terms into (a) Univocal, Equivocal, 
 Analogous : (b) Terms of First Intention, Terms of Second In- 
 tention. 
 
 EXERCISE III. 
 
 1. ' Judgment is a synthesis of two concepts.' 
 
 ' Judgment is an act of division rather than an act of synthesis. 
 Comment on these statements. 
 
 2. Explain the significance of the logical copula. 
 
 3. " Judgment consists in comparing together two notions 
 or ideas of objects derived from simple apprehension, so as to 
 ascertain whether they agree or differ." 
 
QUESTIONS ON LOGIC 409 
 
 Critically examine this view, and indicate carefully the relation 
 you take to hold between notions, judgments and inferences. 
 
 (L. Inter. Arts, 1905.) 
 
 4. Discuss the significance for logical purposes of the distinction 
 between Analytic and Synthetic Judgments. 
 
 (L. Inter. Arts, 1903.) 
 
 5. What is the exact meaning of " some " in a logical judg- 
 ment ? 
 
 Express the following sentences in logical form : 
 
 (i) When a man aims blindly, he sometimes hits the mark. 
 
 (ii) Few men get all they want. 
 
 (iii) No Scotsmen need apply. 
 
 (iv) Many a flower is born to blush unseen. 
 
 (v) A few sailors were saved. 
 
 (vi) Men alone can be members of Parliament. 
 
 (G.M.A. 1907.) 
 
 6. Explain the distinction between Complex and Compound 
 Propositions, and show its importance. 
 
 (T.C.D. 2nd year Hon. 1904.) 
 
 7. Give the sense of each of the following sentences in such a 
 way as to show its logical quantity and quality : 
 
 (1) No news is good news. 
 
 (2) Set a thief to catch a thief. 
 
 (3) One of the commonest of stupid misstatements is that 
 
 all our public monuments are bad. (C. Prev. 1902.) 
 
 8. Define Exclusive and Exceptive propositions. What is the 
 logical relation, if any, between them ? Express the following 
 propositions in logical form : 
 
 (a) The only man in the house was the landlord. 
 (6) Any one but an idiot would believe it. 
 
 (c) No admittance except on business. 
 
 (d) Members alone can vote. (L. Inter. Arts, 1906.) 
 
 9. Reduce to logical form : 
 
 (a) The older we are the more experienced we become. 
 
 (b) Few men really know their own mind. 
 (c} Children alone are admitted. 
 
 (d) Any answer is not good enough. (L. Matr. 1905.) 
 
 10. Give a brief account of Modal propositions as understood 
 in the traditional Logic. Contrast this system with that intro- 
 duced by Kant. 
 
 11. In what sense if any are Universal Categorical judgments 
 hypothetical ? (I.C.S. 1901.) 
 
 EXERCISE IV. 
 
 i. Define a Law of Thought : and explain how it is possible for 
 a law of thought to be violated. (C. Prev. 1904.) 
 
410 PRINCIPLES OF LOGIC 
 
 2. Discuss the logical significance of the laws of Identity, Con- 
 tradiction, and Excluded Middle. (L. Inter. Arts, 1903.) 
 
 3. Enunciate in the form that seems to you most appropriate 
 to the Science of Logic, the laws of Identity, Contradiction and 
 Excluded Middle. Give reasons for \ preferring the form you 
 select. 
 
 4. Discuss the claim of the Law of Identity to be a Law of 
 Thought independent of the Principle of Contradiction. 
 
 5. Are the principles of Contradiction and Excluded Middle as 
 stated by Aristotle, true without exception ? (I.C.S. 1901.) 
 
 * 6. Mill rejects two common theories as to the Law of Contra- 
 diction and substitutes his own. Discuss. 
 
 (T.C.D. 2nd year Hon. 1904.) 
 
 * 7. What do you take to be the ground of validity of the laws 
 of Contradiction and Excluded Middle ? Notice briefly any other 
 theories regarding this subject with which you may be acquainted. 
 
 EXERCISE V. 
 
 1. Is the use of circles in Logic legitimate ? (O. Mods. 1908.) 
 
 2. What are the desiderata in a perfect system of diagrammatic 
 representation ? How far does Euler's system fail to realize these 
 requirements ? Is the task of finding an ideally perfect scheme 
 capable of fulfilment ? 
 
 3. (a) Contradiction is the most perfect form of logical opposi- 
 tion. Explain this. 
 
 (b) Show that the principle of Contradiction does not apply 
 to sub-contraries. (R.U.I. 2nd Arts, Hon. 1906.) 
 
 4. State, giving examples with S and P used for terms, what 
 can be asserted as to the truth of a proposition from : 
 
 (a) the falsity of its contrary. 
 
 (b) the truth of its sub-contrary. 
 
 (c) the falsity of its subalternate. (L. Inter. Arts, 1905.) 
 
 5. Discuss the character of the following oppositions : 
 
 (a) Men are mortal : Men are not mortal. 
 
 (b) All swans are white : Some swans are black. 
 
 (c) All swans are white : No swans are white. 
 
 (L. Matr. 1904.) 
 
 6. It has been asserted that the rule, ' Subcontrary propositions 
 cannot both be false/ is erroneous. The two propositions, ' Some 
 men (i.e. Europeans) are black/ ' Some men (i.e. Ethiopians) are 
 not black/ are, it is urged, particular propositions of opposite 
 quality, yet both are false. Examine the argument. 
 
 7. Assign contradictory and (where possible) contrary forms 
 for the following propositions : ' Dead men alone tell no tales/ 
 ' Caius said that it was all up with the army/ ' All except the idle 
 have a right to the means of life/ ' Half the flock perished of the 
 pest.' 
 
QUESTIONS ON LOGIC 411 
 
 EXERCISE VI. 
 
 1. Define Immediate Inference : and give an example of each 
 of the following : Inference by Subalternation ; Conversion ; 
 Contraposition ; Added Determinants ; Converse Relation ; giv- 
 ing in each case a brief justification of the process. 
 
 (L. B.Sc. 1903.) 
 
 2. (a) Express the following in strict logical form, and if pos- 
 sible give in each case the converse of the contrapositive : 
 
 (1) Only ants are really industrious. 
 
 (2) Some insects only are industrious. 
 
 (3) No leaves are other than white. 
 
 (b) Examine the following inference : A tortoise is an animal. 
 Therefore an unusually swift tortoise is an unusually swift animal. 
 
 (L. Matr. 1904.) 
 
 3. Enumerate and illustrate the several forms of Immediate 
 Inference, and consider to what extent they give us new truth. 
 
 (O. Mods. 1906.) 
 
 4. Define Conversion and Obversion. Find the obverse of the 
 converse of (a) None but the brave deserve the fair ; (b) Some 
 who are well educated are credulous : and the converse of the 
 obverse of (c) Where there is smoke there is fire ; (d) Not all is gold 
 that glitters. (C. Prev. 1904.) 
 
 5. Investigate the formal relations between : 
 
 (a) All 5 is P, and All not-5 is P. 
 
 (b) All not-5 is P, and All not-P is 5. 
 
 (c) All not-5 is P, and All 5 is not-P. 
 
 (R.U.I. 2^^/5,1896.) 
 
 6. Mention all the Immediate Inferences which may be drawn 
 from the proposition, ' None but the brave deserve the fair.' In- 
 dicate very briefly the peculiarities of each inference you draw. 
 
 (R.U.I. 2nd Arts, 1896.) 
 
 7. ' What is inferred in Conversion is not properly something 
 else than the convertend, but the same thing.' Is this so ? 
 
 Explain what is meant by Immediate Inference, and state how 
 many valid kinds might be included within the range of Formal 
 Logic. (R.U.I. 2nd Arts, Hon. 1901.) 
 
 8. (a) Define Obversion and point out the principle on which 
 this form of inference is based. 
 
 (b) State the logical relation, if any, that holds between the 
 first of the following propositions and each of the others. If any 
 proposition cannot be inferred from the first, say whether it is 
 consistent with it or not. 
 
 (i) Good men alone are wise, 
 (ii) He who is good is not unwise, 
 (iii) Any one who is not good is unwise, 
 (iv) No unwise men are good.- 
 
412 PRINCIPLES OF LOGIC 
 
 (v) Not all good men are wise, 
 (vi) It is false that all unwise men are good. 
 
 (G. M.A. 1906.) * 
 
 9. How would you show that the denial of a denial amounts 
 to an affirmation ? (I.C.S. 1895.) 
 
 10. Show how a statement may be expressed formally as an 
 A or an E or an I or an O proposition. Does this change of form 
 involve any material change of meaning, and is its application of 
 any practical value in Logic ? (R.U.I. 2nd Arts, 1902.) 
 
 EXERCISE VII. 
 
 1. What is meant by the import of Propositions ? State various 
 views which logicians have held on this subject. Which view 
 seems to you preferable, and why ? (L. Inter. Arts, 1903.) 
 
 2. " General Propositions assert a relation between classes." 
 Discuss this statement. (O. Mods. 1907.) 
 
 * 3. State and discuss the doctrine of the quantification of the 
 predicate. (G. M.A. 1906.) 
 
 4. Discuss the various interpretations of the logical proposition 
 implied by the following modes of expressing the judgment ' All 
 men are mortal ' : 
 
 (a) Men=men mortals. 
 
 (b) Every man possesses the attribute of mortality. 
 
 (c) The attribute of mortality constantly accompanies the 
 
 attribute of humanity. 
 
 5. " Many propositions which in reference to the universe of 
 sensible experience would be meaningless, when referred to the 
 real universe of discourse are seen to be significant and true." 
 Discuss this statement. 
 
 * 6. 'To say that all A is B, is in fact merely to assert that 
 the real world contains no objects that are A's, but that fail to be 
 of the class B.' Discuss, explaining what kind of propositions 
 appears to you to be most truly ' existential.' (I.C.S. 1902.) 
 
 * 7. Critically examine the view that particular propositions 
 do, and that universal propositions do not imply the existence of 
 their subjects. 
 
 * 8. Explain what is meant by the assertion that the ultimate 
 subject in judgment is Reality as a whole. (G. M.A . 1905.) 
 
 EXERCISE VIII. 
 
 1. What are the Predicables ? Exemplify by reference to the 
 word ' triangle.' (G. M.A. 1907.) 
 
 2. Set down with explanation the heads of predicables. 
 
 (C. Prev. 1902.) 
 
 3. How must the belief or disbelief in the existence of real kinds 
 in nature, affect the doctrine of the Predicables ? 
 
 (O. Mods. 1906.) 
 
QUESTIONS ON LOGIC 413 
 
 4. ' The individual substance is the ultimate subject of all 
 predication.' What bearing has this principle on the Porphyrian 
 doctrine of the Predicables ? Is the principle defensible in the 
 light of such a proposition as, ' The person approaching is Callias ' ? 
 
 5. Give an account of Property and Accident. How far are 
 they distinguishable ? (O. Mods. 1907.) 
 
 6. Explain and comment on the distinction of Accidents into 
 separable and inseparable. (O. Mods. 1908.) 
 
 7. Can Porphyry's fivefold division of the Predicables be shewn 
 to be exhaustive ? 
 
 * 8. What do you understand by Moderate Realism ? Distin- 
 guish it carefully from Platonic Realism on the one hand and 
 Conceptualism on the other. 
 
 * 9. Explain the nature of the Controversy between Nominal- 
 ism and Realism. Upon what questions in Logic does the con- 
 troversy bear, and how ? (O. Mods. 1908.) 
 
 * 10. ' Universalia ante rem,' ' Universalia post rem.' Explain 
 and discuss. (O. Mods. 1905.) 
 
 EXERCISE IX. 
 
 1. Give some account of the Categories, and of their place in 
 Logic. (O. Mods. 1906.) 
 
 2. Enumerate the ten Categories, and distinguish them care- 
 fully with examples. What do you suppose to have been the 
 origin and purpose of the list ? (O. Mods. 1907.) 
 
 3. Distinguish carefully between the Categories as a part of 
 logical and as a part of metaphysical doctrine. 
 
 4. What do you understand by Predicamental lines ? Discuss 
 their connexion with the logical analysis of science. 
 
 5. Explain briefly how the doctrine of the Categories throws 
 light on the question of the Import of Propositions. 
 
 * 6. Contrast the Aristotelian Categories with any other system 
 with which you may be acquainted. Shew why as a part of logical 
 doctrine the Aristotelian system is to be preferred. 
 
 EXERCISE X. 
 
 1. Discuss the question whether things, concepts, or names are 
 the object of Definition. 
 
 2. Indicate and exemplify the methods by which we form 
 definitions. State the most important rules of definition. 
 
 (R.U.I. 2nd Arts, 1906.) 
 
 3. State the meaning of Definition, and carefully explain any 
 technical terms that you use in your statement. 
 
 Comment critically with examples on (a) the distinction between 
 nominal and real definition, (b) the distinction between the defin- 
 able and the undefinable. (L. Inter. Arts, 1906.) 
 
 4. " The distinction between nominal and real definitions cannot 
 
414 PRINCIPLES OF LOGIC 
 
 be maintained. No definition is ever intended to explain the 
 nature of a thing." Can this position be sustained ? 
 
 (O. Mods. 1904.) 
 
 5. In an examination into the nature of definition, must we 
 distinguish between ordinary definition and scientific definition ? 
 Are Genetic definitions properly called definitions ? 
 
 (R.U.I. 2nd Arts, Hon. 1905.) 
 
 6. (a) Discuss the connexion between the theory of definition 
 and the theory of the predicables. 
 
 (b) Consider carefully the following definitions : 
 
 (1) Light is a mode of motion. 
 
 (2) A contrapositive is the converse of the obverse. 
 
 (3) A woman is a creature who cannot reason and who pokes 
 the fire from the top. (L. Matr. 1905.) 
 
 7. Give examples showing the importance of defining the tech- 
 nical terms of a science. Why is it in defining a species, the 
 proximate genus and differentia should be given but no proprium 
 or accidens ? (C. Prev. 1904.) 
 
 8. Explain the nature of Logical Division, and indicate care- 
 fully the relations between logical part and logical whole. 
 
 9. To what chief defects is Logical Division liable ? Can they 
 be obviated by the process of Dichotomy ? (O. Mods. 1905.) 
 
 10. Distinguish Logical Division from division of other kinds. 
 Comment on the division of man into ' rational ' and ' animal ' ; 
 of a house into stone, timber and mortar ; of Socrates into body 
 and soul ; of the soul into intellect and will. 
 
 11. Explain the expressions : fundamentum divisionis, cross- 
 division, division by dichotomy, division per se, division per 
 accidens. 
 
 12. Explain carefully what the Scholastic philosophers meant 
 when they said that all men are such in virtue of a common 
 ' humanity.' 
 
 EXERCISE XI. 
 
 1. Explain the meaning of the expression ' middle-term.' 
 Does the middle-term of a syllogism always hold that relation to 
 its extremes which the name implies ? Is the expression under- 
 stood in the same sense by all logicians ? 
 
 2. Distinguish the necessity of the consequence from the neces- 
 sity of the consequent. Does Logic in any department attempt 
 to secure both ? (R.U.I. 2nd Arts, Hon. 1905.) 
 
 3. Give the rules of quality and of distribution, which are 
 necessary and sufficient for securing the validity of a syllogistic 
 argument. Give an illustration in which one and only one of the 
 rules is violated. (L. B.Sc. 1903.) 
 
 4. (a) How is it that EIO is always valid, and IEO is never 
 
QUESTIONS ON LOGIC 415 
 
 valid, if the difference between them is one of mere order of 
 premisses ? 
 
 (b) Determine the rules of the third figure, and enumerate fully 
 the characteristics of that figure. (R.U.I. 2nd Arts, 1901.) 
 
 5. (a) Why does p never occur in the first syllable of any named 
 mood ? Has it the same meaning in Darapti and in Bramantip ? 
 
 (b) Why is it that in all figures " the conclusion must be nega- 
 tive if the minor premiss be negative " ; and " the conclusion 
 is not A if the major term be subject ? " 
 
 (R.U.I. 2nd Arts, Hon. 1902.) 
 
 6. What is the special use of the second figure of the syllogism ? 
 Construct an example of a real argument (not in letters) in one 
 of the moods of this figure. Reduce Baroco both directly and 
 indirectly. (R.U.I. 2nd Arts, 1902). 
 
 7. Assuming the general rules of the syllogism, deduce that OAO 
 is only possible in Fig. 3. (L. Matr. 1905.) 
 
 8. Prove that nothing can logically be inferred from two parti- 
 cular premisses. (L. Matr. 1904.) 
 
 9. Prove that if the middle-term of a syllogism be twice distri- 
 buted, the conclusion must be particular. (L. Inter. Arts, 1905.) 
 
 10. Define ' illicit process,' and explain with illustrations the 
 reasons which make it illicit. 
 
 Why can an O proposition occur as a major premiss only in Fig. 
 3, and as a minor only in Fig. 2 ? (R.U.I. 2nd Arts, 1905.) 
 
 * 1 1 . Show that all the moods of the first figure can be directly 
 or indirectly reduced to Barbara. (R.U.I. 2nd Arts, Hon. 1901.) 
 
 12. Resolve some short example of a geometrical demonstration 
 [e.g. Euclid I. 6] into its constituent syllogisms, indicating major 
 and minor premiss; in each case, and showing what axioms or 
 previous propositions are introduced and how. (L. B.Sc. 1903.) 
 
 EXERCISE XII. 
 
 1. State the dictum de omni et nullo, and prove from it the 
 ' special rules of the first figure.' (L. Inter. Arts, 1906.) 
 
 2. What is the object of Reduction, and how far does it alter 
 the character of an argument ? Illustrate your answer by con- 
 structing and reducing syllogisms in Cesare and Disamis. 
 
 (O. Mods. 1906.) 
 
 3. Critically consider various ways in which the ultimate 
 principle of syllogistic inference has been formulated. 
 
 "In no case can a syllogism with two singular premisses be 
 viewed as a genuine syllogistic or deductive inference." Examine 
 this. (L. B.Sc. Hon. 1905.) 
 
 4. Reduce the following, or the arguments involved in them to 
 syllogistic form, stating figure and mood if valid : and fallacy if 
 invalid : 
 
 (a) All living things are interesting, and some interesting 
 
4i 6 PRINCIPLES OF LOGIC 
 
 things are beautiful. Therefore some living things are 
 beautiful. 
 
 (b) No guest is unwelcome. Hence since some guests have 
 not been introduced, it follows that the welcome have not 
 in all cases been introduced. (L. Maty. 1904.) 
 
 5. Express the following arguments in syllogistic form, and 
 examine their validity from a logical point of view : 
 
 (a) ' Freedom means power to do or to forbear from doing 
 
 any particular act, upon preference : and since the will 
 is merely the power of preference, the question whether 
 the will is free is an unmeaning one : therefore the 
 only proper question is whether a man (not his will) 
 is free.' 
 
 (b) ' Now for the poet, he affirmeth nothing, and there- 
 fore never lieth. For as I take it, to he is to affirm 
 that to be true which is false : but the poet never 
 affirmeth : therefore though he recount things not true, 
 yet because he telleth them not for true, he lieth not.' 
 
 (R.U.I. 2nd Arts, Hon. 1901.) 
 
 6. ' All reasoning is from universals to particulars.' 
 ' All reasoning is from particulars to particulars.' 
 
 What is the bearing of these two theories on the doctrine of the 
 syllogism ? (O. Mods. 1906.) 
 
 7. State in general and criticise Mill's theory of the syllogism. 
 
 (T.C.D. 2nd year Hon. 1904.) 
 
 8. ' The problem of inference is something of a paradox : for 
 we have not got inference unless the conclusion is (a) in the pre- 
 misses, (b) outside the premisses.' Examine this statement. 
 
 (R.U.I. B.A. Hon. 1901.) 
 
 9. Critically examine the opinion that there are other forms of 
 inference besides syllogistic reasoning. Notice any views on this 
 point defended by recent writers. 
 
 10. On what grounds and with what justice has superiority 
 been attributed to the first figure of the syllogism ? Should a 
 fourth figure be recognized ? (O. Mods. 1904.) 
 
 EXERCISE XIII. 
 
 1. Give the chief forms of argument involving hypothetical or 
 disjunctive propositions : and examine whether they are governed 
 by the same principles as the categorical syllogism. 
 
 (L. Inter. Arts, Hon. 1903.) 
 
 2. Discuss the question whether the reasoning of the hypothe- 
 tico-categorical syllogism is mediate or immediate. 
 
 (T.C.D. 2nd year Hon. 1904.) 
 
 3. ' The theory that a hypothetical proposition cannot be 
 satisfactorily reduced to categorical form, does not apply to the 
 hypothetical syllogism. The latter may be expressed without 
 
QUESTIONS ON LOGIC 417 
 
 material alteration, modus ponens in Fig. i, modus tollens in 
 Fig. 2. Discuss and illustrate these statements. 
 
 (R.U.L ^nd Arts, Hon. 1905.) 
 
 4. What proof would you offer of the rules of the hypothetical 
 syllogism ? Give concrete examples in illustration of the rules. 
 
 (L. Inter. Arts, 1906.) 
 
 5. Explain and discuss the following assertion : ' In a dis- 
 junctive proposition the positing of one assertion does not warrant 
 the sublating of the other, though the sublating of one posits the 
 other.' (R.U.I. 2nd Arts, 1902.) 
 
 6. Given that " If a student is a man, he gains his degree either 
 through satisfying the examiners or through payment of a fee," 
 what conclusions can be drawn from the following : 
 
 (a) X has neither satisfied the examiners nor paid his fees. 
 
 (b) X has both satisfied the examiners and paid his fees ? 
 
 (L. Matr. 1904.) 
 
 7. Explain : "A dilemma is a complex hypothetical argument 
 which is often used fallaciously, because we often overlook one of 
 the possible alternatives." Give a concrete example of the dilem- 
 ma to illustrate your remarks. (R.U.I. 2nd Arts, 1906.) 
 
 8. Discuss the logical value (a) of constructing, (b) of rebutting a 
 dilemma. (O. Mods. 1905.) 
 
 9. What are the essential characteristics of the Dilemma ? How 
 many different kinds of Dilemma are recognized ? Give an example 
 (in symbols) of each. 
 
 Indicate the most common sources of fallacy in dilemmatic 
 arguments, with illustrations. (L. Inter. Arts, 1906.) 
 
 EXERCISE XIV. 
 
 1. Analyse the conception of Cause, as it is used in inductive 
 investigation. (G. M.A. 1906.) 
 
 2 . Define precisely what Science understands by the Cause of an 
 event, and illustrate your definition, by a typical example of causa- 
 tion as determined by experiment. 
 
 What is the relation of the scientific conception of Cause to the 
 conception of Cause as the sum-total of the conditions on the 
 occurrence of which the event depends ? 
 
 Can you account for the divergence between the scientific and 
 the popular views as to the Cause ? (L. Inter. Arts, 1905.) 
 
 3. Describe carefully the inductive process, by which from 
 particular facts we pass to the knowledge of a universal law. Con- 
 sider to what extent and for what reasons the multiplication of 
 instances is necessary to the formation of a valid induction. 
 
 4. Explain and illustrate the nature of Induction and its relation 
 to Deduction. Illustrate the importance of both processes in 
 science by examples taken from any of the Natural Sciences. 
 
 (O. Mods. 1907.) 
 E E 
 
4 i 8 PRINCIPLES OF LOGIC 
 
 5. State and examine the grounds on which the following state- 
 ment has been made : ' No inference is possible unless a general 
 proposition be somewhere in the background.' (G. M.A. 1905.) 
 
 6. Describe the Inductive Syllogism of Aristotle. Estimate 
 the logical value and the practical utility of the argument : and 
 state whether in your opinion it is rightly termed an ' inductive * 
 argument. 
 
 7. Examine the claims of a ' Perfect Induction ' to be regarded 
 as an inductive process. (O. Mods. 1905.) 
 
 EXERCISE XV. 
 
 1. Consider carefully the relation of the principle of the Uni- 
 formity of Nature to the inductive process. Is there a parity 
 between the function of the dictum de omni in deduction, and the 
 principle of Uniformity in Induction ? 
 
 2. State precisely what you understand by " the uniformity of 
 nature." Is it capable of proof, and if so, of what kind ? 
 
 (G. M.A 1906.) 
 
 3. Comment on the following : " The contrary of every matter 
 of fact is still possible, because it can never imply a contradiction. 
 That the sun will not rise to-morrow is no less intelligible a pro- 
 position and implies no more contradiction, than the affirmation 
 that it will rise " (Hume}. (L. Inter. Arts, 1906.) 
 
 4. Is a plurality of causes possible ? (G. M.A. 1908.) 
 
 5. " Cessante causa, cessat effectus." Explain. 
 
 6. Discuss Mill's view that the principle of the uniformity of 
 Nature is arrived at by Induction. (O. Mods. 1906.) 
 
 7. Define the conception of Cause as used in Science. How far 
 is the conception consistent with the admission (a) of plurality of 
 causes, (b) of plurality of effects ? (L. B.Sc. Hon. 1903.) 
 
 * 8. What is meant by the assertion of certain logicians that 
 " the Unity of Nature " is a more correct term than " the Uni- 
 formity of Nature " ? Critically examine the doctrine presup- 
 posed by the former of these expressions. 
 
 EXERCISE XVI. 
 
 * i. Explain with examples the Aristotelian Enthymeme. 
 
 2. Define : polysyllogism, epichirema, sorites ; and give a 
 symbolical example of each. (T.C.D. znd year Hon. 1904.) 
 
 3. State the rules of the Sorites, and prove them briefly. Ex- 
 amine the following : ' The final good of man is to be realized 
 only in virtuous action. But action will not be right and virtuous, 
 unless the will be also right : and the Tightness of will depends on 
 ordered habits of the soul, and that again springs from right 
 general principles.' (R.U.I. 2nd Arts, 1905-) 
 
 4. Explain and illustrate the nature of analogical reasoning. 
 What are its dangers ? (G. M.A . 1907.) 
 
QUESTIONS ON LOGIC 419 
 
 5. Distinguish between Induction and Analogy. Is the analo- 
 gical argument syllogistic ? (R.U.I. 2nd Arts, 1906.) 
 
 6. "In Analogy we must weigh the points of agreement, and 
 not merely count them." How far does Mill recognize this ? 
 How is the precept to be carried out ? (O. Mods. 1906.) 
 
 EXERCISE XVII. 
 
 1. Explain and illustrate the following fallacies : Petitio prin- 
 cipii, Ignoratio Elenchi, A dicto secundum quid ad dictum simpliciter 
 (and the converse), Composition, Division. (L. Inter. Arts, 1906.) 
 
 2. Illustrate from current controversies any of the commonly 
 recognized fallacies. (O. Mods. 1904.) 
 
 3. Classify the fallacies which are incident to Formal Reasoning, 
 and give one example under each of your divisions. 
 
 (R.U.I. 2nd Arts, 1902.) 
 
 4. Examine and name three of the following inferences : 
 
 (a) Slang is metaphor : metaphor is poetry : therefore slang 
 
 is poetry. 
 
 (b) Cleon is not Socrates : Socrates is a man : therefore 
 
 Cleon is not a man. 
 
 (c) Aristotle is a word of four syllables : Aristotle is acute : 
 
 therefore acute is a word of four syllables. 
 
 (d) No one is born a slave, because every one is born with all 
 
 his original rights. 
 
 (e) No one can become a slave, because no one from being a 
 
 person can become a thing. (R.U.I. 2nd Arts, 1901.) 
 
 5. Under what conditions can we infer causal connexion be- 
 tween two phenomena on the ground of the observed frequency 
 of their concurrence ? Illustrate the fallacies incident to such 
 inference. (L. B.Sc. 1903.) 
 
 6. Consider the following : 
 
 Counsel : There was no written agreement for the sale of this 
 carpet. 
 
 Plaintiff : Well, you don't have a written agreement when you 
 buy a loaf. 
 
 Counsel : You don't cover a floor with a loaf. 
 
 Plaintiff : Neither do you eat a carpet. (O. Mods. 1906.) 
 
 7. Explain the distinction between logical and material fallacies, 
 illustrating by some of the most conspicuous examples of each 
 kind. (O. Mods. 1905.) 
 
 8. Define the term Fallacy as employed in Logic, and distinguish 
 a fallacy from a false belief. 
 
 Test the following arguments, and name any fallacies they may 
 contain : 
 
 (a) Hi-managed business is unprofitable. Railways are never 
 ill-managed. Therefore all railways are profitable. 
 
420 PRINCIPLES OF LOGIC 
 
 (b) A vacuum is impossible : for if there is nothing between 
 
 objects, they must touch. 
 
 (c) The governor of a country ought not to be blamed for 
 
 using his influence to further his religious views, for 
 every man has a right to inculcate his opinions. 
 
 (L. Inter. Arts, 1905.) 
 
 9. Write out the principal heads of one or more celebrated 
 classifications of Fallacies, explaining the terms employed. 
 
 (R.U.I. 2nd Arts, 1896.) 
 
 10. Logic has been described as " a machine for combating fal- 
 lacy." How far does this description seem to you appropriate ? 
 
 (G. M.A. 1905.) 
 
 EXERCISE XVIII. 
 
 1. Consider critically the Aristotelian division of Philosophy 
 into Metaphysics, Mathematics, Physics. 
 
 2. Discuss the relation between Logic and Metaphysics, giving 
 historical references. (I.C.S. 1901.) 
 
 3. Discuss the position of Logic among the Sciences. What 
 special view on this subject is implied by the use of the word 
 Organon as a name for Aristotle's logical treatises ? 
 
 4. " Arithmetic and its fundamental principles are independent 
 of our experiences and the order of the world ." Discuss this state- 
 ment. (L. B.A. Hon. 1905.) 
 
 5. " Logic aims at being not the Physics but the Ethics of 
 Thought " (Sigwart). Discuss this statement. 
 
 6. ' Quidquid existit est singular e.' ' Scientia est de univer- 
 salibus.' Discuss these two Scholastic principles. How far have 
 they a claim to absolute validity ? Notice any systems which seem 
 to you to have violated one or other of them. 
 
 7. What important features of Logic as it is at present taught, 
 do we owe to the influence of Bacon ? How far is the novel element 
 a legitimate development of the principles of the science ? 
 
 EXERCISE XIX. 
 
 1. When has Observation more advantages than Experiment ? 
 and why is Experiment usually more advantageous than Observ- 
 ation ? (R.U.I. 2nd Arts, Hon. 1902.) 
 
 2. " Observation and Experiment (supposing no aid from 
 deduction) can ascertain sequences and coexistences, but cannot 
 prove causation." Examine. (O. Mods. 1904.) 
 
 3. What do you hold to be the essentials of a truly scientific 
 experiment ? (L. Matr. 1904.) 
 
 4. How far does Experiment differ from Observation,^ Is the 
 difference fundamental ? Show the dependence of Observation 
 
QUESTIONS ON LOGIC 421 
 
 on previous knowledge, and in what sense it always involves 
 inference. (L. Inter. Arts, 1906.) 
 
 5. What is the logical character of the appeal to the testimony 
 of the senses ? Does this testimony really bear witness to the 
 motion of the sun relatively to the earth ? (L. Inter. Arts, 1905.) 
 
 EXERCISE XX. 
 
 1. Show exactly how Mill's Method of Agreement differs from 
 Simple Enumeration. 
 
 On what presuppositions is the former method applicable ? 
 What are its defects and its utility in scientific discovery ? 
 
 (L. Inter. Arts, 1906.) 
 
 2. Explain the Method of Concomitant Variations. Give 
 examples of cases where its application is extremely profitable, 
 and point out the limitations attending its use. 
 
 (L. Inter. Arts, 1906.) 
 
 3. Analyse and describe in logical terms the method by which 
 any important discovery of recent years was made. 
 
 (O. Mods. 1906.) 
 
 4. Distinguish carefully between the Method of Difference and 
 the Method of Residues. (O. Mods. 1905.) 
 
 5. How far does the validity of any of the Inductive Methods 
 depend on the possibility of expressing Cause and Effect qu an ti- 
 tively ? (O. Mods. 1906.) 
 
 6. Examine and explain Mill's view that Plurality of Causes 
 renders the Method of Agreement uncertain. (O. Mods. 1904.) 
 
 7. Explain why the Method of Agreement requires many 
 instances, while the Method of Difference is satisfied with one 
 precise experiment. Why is the Method of Agreement of little 
 value, as compared with the Method of Difference ? 
 
 (R.U.I. 2nd Arts, 1905.) 
 
 8. How would Inductive Logic proceed to investigate the 
 influence upon character of any one of the following : (a) climate, 
 (b) athletics, (c) an artistic profession ? (O. Mods. 1905.) 
 
 9. Can the Method of Residues be fairly considered inductive 
 in character ? (O. Mods. 1904.) 
 
 10. Explain the Joint Method of Agreement and Difference, and 
 give a concrete example. (R.U.I. 2nd Arts, 1906.) 
 
 11. " The Plurality of Causes must be considered as something 
 which actually occurs in Nature, and which as often as it occurs, 
 ought to be capable of being discovered by the methods of in- 
 duction." 
 
 Explain and discuss this statement. (O. Mods. 1908.) 
 
 12. What does Mill mean by Cause ? How far are his methods 
 adequate for the discovery of causes in his own sense of the word ? 
 
 (O. Mods. 1907.) 
 
422 PRINCIPLES OF LOGIC 
 
 EXERCISE XXI. 
 
 1. What is the object of Explanation ? Describe and illustrate 
 its principal forms. (O. Mods. 1907.) 
 
 2. " The object of Science is explanation" 
 
 " Science never explains : she only reduces complex events to 
 simple ones of the same kind, as when she deals with certain phe- 
 nomena of magnetism by supposing every ultimate unit of the 
 substance to act as if it were a magnet." 
 
 Consider these statements. (L. Inter. Arts, 1905.) 
 
 3. Indicate carefully the meaning of the term ' law ' as em- 
 ployed in natural science. Distinguish between empirical laws, 
 laws of nature, and ultimate laws. 
 
 ' A truly universal law is not a demonstrable truth.' Discuss 
 this. (L. Inter. Arts, 1906.) 
 
 4. Distinguish the different processes included in or subservient 
 to Induction, and discuss the relations of Induction to Description, 
 Hypothesis, and Explanation. (C. Mor. Sc. tripos. 1905.) 
 
 5. Bring out the full meaning of the dictum that ' Induction is 
 the Inverse of Deduction.' 
 
 Comment on the following : ' All knowledge is founded ulti- 
 mately on Induction, all reasoning on Deduction.' 
 
 (L. B.Sc. 1903.) 
 
 6. ' The secondary application of the Deductive Method is not 
 to prove laws of phenomena, but to explain them.' Enumerate 
 the different kinds of explanation recognized by Mill, and show 
 in what way each is deductive. (O. Mods. 1906.) 
 
 7. Comment on the phrase Hypotheses non fingo as employed by 
 Newton : and explain the expression vera causa. 
 
 EXERCISE XXII. 
 
 1. What is an hypothesis ? How is an hypothesis verified ? 
 Which of the empirical methods is fruitful in hypotheses ? Which 
 might be fruitfully used for verification of an hypothesis ? 
 
 (R.U.I. 2nd Arts, 1901.) 
 
 2. Illustrate the use of hypothesis in scientific explanation. 
 
 (C. Prev. 1904.) 
 
 3. Examine and illustrate the characteristics of Hypothesis as 
 a conscious process of scientific investigation. Show that a 
 rejected hypothesis need not necessarily have been fruitless. 
 
 (L. Inter. Arts, 1906.) 
 
 4. Explain and comment on the expressions : Working hypo- 
 thesis, Hypothesis of Cause, Hypothesis of Law. 
 
 5. " Men are now cured of their passion for Hypotheses " 
 (Hume}. "Hypothesis is induction looked at from the inside." 
 What different views of the nature and function of hypothesis 
 are represented by these statements ? (I.C.S. 1903.) 
 
QUESTIONS ON LOGIC 423 
 
 EXERCISE XXIII. 
 
 1. Explain the importance of Measurement in inductive investi- 
 gation. Notice the circumstances which principally contribute 
 to render Measurement a task of difficulty. 
 
 2. Carefully consider the statement that accurate quantitative 
 determination is the ultimate stage in the establishment of every 
 scientific theory. 
 
 3. " There is no such thing as Chance. To attribute an event 
 to Chance is merely a way of saying that we are ignorant of its 
 cause." 
 
 " There is no such thing as Chance. What we attribute to 
 Chance, we should rightly attribute to Providence." 
 
 Discuss these statements. Does either of them contain an 
 adequate account of Chance ? 
 
 4. Determine the province of the theory of Probability in in- 
 duction. If it be admitted that no result of inductive reasoning is 
 absolutely free from doubt, does it follow that induction should 
 be based on the theory of Probability ? (L. Inter. Arts, 1905.) 
 
 5. Explain what is meant by the doctrine of philosophical 
 probability. Illustrate by examples. 
 
 EXERCISE XXIV. 
 
 1. Discuss the value of Natural Classification as a scientific 
 method. 
 
 2. Give the rules of Classification : and notice the chief diffi- 
 culties which attend the task of establishing a valid Classification. 
 
 3. What do you hold to be the relation between Logical Division 
 and Classification ? 
 
 4. Explain and illustrate the distinction between Natural and 
 Artificial Classifications, noticing the purpose and characteristics 
 of each. What objections have been felt by some in admitting 
 this distinction ? 
 
 * 5. What is meant by Classification by Type, and Classification 
 by Series ? 
 
 EXERCISE XXV. 
 
 1. Explain the expressions : Method of Discovery, Method of 
 Instruction. Illustrate by examples the practical importance of 
 this distinction. 
 
 2. In what senses have the terms Analysis and Synthesis been 
 employed by writers on Logic ? Is there anything common to 
 these senses on one hand, and the signification which the words 
 possess in the physical sciences on the other ? 
 
 3. " The human intellect was well compared by the Schoolmen 
 to the eye of the owl, which in the dusk can see, but is blinded 
 by the brighter light of day. Not without reason did they 
 
424 PRINCIPLES OF LOGIC 
 
 distinguish between those things which are better known to 
 Nature, and those which are better known to us." Discuss. 
 
 4. To what extent is it possible to prescribe rules for the meth- 
 odic conduct of our thought in the pursuit of truth ? Examine 
 critically any such scheme of rules with which you may be 
 familiar. 
 
 5. How far can it be said that the attainment of truth in philo- 
 sophy, depends on the employment of an accurate philosophic 
 terminology ? 
 
 *6. Give Descartes' Rules of Method. Show that they no longer 
 can be regarded as possessing any philosophical value. 
 
 *7. Briefly explain Leibniz's theory of Method. What is to be 
 thought regarding his views on Identical propositions ? 
 
INDEX OF SUBJECTS 
 
 A dicto simpliciter ad dictum Canon of syllogism, 187 
 
 secundum quid, 275 
 Absolute terms, 32 
 Absolute and qualified statement, 
 
 Fallacy of, 275 
 Abstract terms, 23 
 Abstraction, 16 
 Accent, Fallacy of, 272 
 Accident, Fallacy of, 274 
 Accidents, Logical, 127 
 Accidents, Real, 24, 30 
 Action, Category of, 138 
 Added Determinants, 102 
 Adequate Concepts, 18, 123 
 Adversative propositions, 56 
 /Esthetics, 6 
 
 Affirmative propositions, 46 
 Agreement, Method of, 321 
 Agreement and difference, Joint 
 
 method of, 322 
 Amphibology, 269 
 Analogous terms, 35 
 Analogy, 259, 358 ; false analogy, 
 
 286 
 
 Analysis, 352, 395 
 Analytic propositions, 51 
 Analytically-formed definitions, 
 
 157 
 
 Antecedent, 64 
 Apodictic propositions, 60 
 Apprehension, Simple, 3 
 Approximation, Methods of, 367 
 Argumentum ad hominem, etc., 277 
 Argumentum a silentio, 279 
 Arithmetical quantity, 296 
 Artificial Classification, 382 
 Artificial Division, 162 
 Assertoric propositions, 60 
 Attribute, 3 
 Attributive view, 109 
 Axioms, 53n 
 
 Being, Concept of, 70,139, 149 
 Bernoulli's theorem, 377 
 
 Capacity and incapacity, 138 
 
 Categorematic words, 19 
 
 Categorical proposition, 39 
 
 Categories, their metaphysical 
 aspect, 137 ; their logical aspect, 
 142 ; their relation to science, 
 144 ; as a classification of 
 predicates, 145 ; Mill's cate- 
 gories, 147 ; Kant's categories 
 148 
 
 Causal definitions, 156 
 
 Causes, doctrine of the four, 157 ; 
 definition of cause, 220 ; deter- 
 mining cause, 222 ; composi- 
 tion of causes, 246 ; combina- 
 tion of causes, 246 ; plurality 
 of causes, 243 ; cause in esse 
 and cause in fieri, 247 
 
 Cessante causa, cessat effectus, 246 
 
 Chains of reasoning, 255 
 
 Chance, 369 ; elimination of 
 chance, 372 
 
 Class-inclusion view, 106 
 
 Classification, 380 ; artificial clas- 
 sification, 382 ; natural classi- 
 fication, 389 ; rules of classifi- 
 cation, 391 ; classification by 
 type, 393 ; by series, 393 ; 
 difficulties incident to classifi- 
 cation, 392 
 
 Clear Concepts, 18, 123 
 
 Co-division, 165 
 
 Collective terms, 23 
 
 Collective use of term, 38 
 
 Compartmental view, 116 
 
 Complex conception, 103 
 
 Complex propositions, 55 
 
 Composition and division, 270 
 
 Compound effects, 246 
 
 Compound propositions, 56 
 
 Comprehension, 22 
 
 Concept, 3, 15 
 
 Conceptualist view of Logic, 8 
 
 425 
 
426 
 
 INDEX OF SUBJECTS 
 
 Conceptualism, 132 
 
 Conclusion, 3, 170 
 
 Concomitant variations, Method 
 of, 324 
 
 Concrete terms, 23 
 
 Condition, 221 ; positive and 
 negative conditions, 242 
 
 Conditional propositions, 64, 66 
 
 Confusion, Fallacies of, 284 
 
 Conjunctive propositions, 66 
 
 Connotation, 26 
 
 Connotative terms, 24 
 
 Consequence, 171 ; modal con- 
 sequence, 104 
 
 Consequent, 64, 170 
 
 Consequent, Fallacy of, 279 
 
 Contradiction, Principle of, 69 
 
 Contradictory Opposition, 86, 89 
 
 Contradictory terms, 37 
 
 Contraposition, 100 
 
 Contrary Opposition, 86, 90 
 
 Contrary terms, 37 
 
 Conversion, 93 ; Aristotle's proof 
 of, 97 
 
 Converse relation, 103 
 
 Copula, 5, 40, 146 
 
 Copulative propositions, 56 
 
 Correlatives, 33 
 
 Crucial instance, 306 
 
 Deduction, 169 
 
 Deductive Method, Mill's, 342 
 
 Definition, 1 50 ; various kinds 
 of definition, 152 ; limits of 
 definition, 159; rules of defi- 
 nition, 159 
 
 Denominatives, 30 
 
 Denotation, 26 
 
 Desitive propositions, 57 
 
 Determining cause, 222 
 
 Diagrammatic represenbation, 77 
 
 Dichotomy, 166 
 
 Dictum de omni et nullo, 187 
 
 Dictum de diverse, 190 ; de 
 excepto, 190; de exemplo, 190; 
 de reciproco, 191 
 
 Difference, Method of, 322 
 
 Differentia, 123 
 
 Dilemma, 209 
 
 Discretive propositions, 56 
 
 Disjunctive propositions, 65 ; dis 
 
 junctive syllogisms, 207 
 Disposition, 138 
 Distinctive definitions, 154 
 Distribution of terms, 81 
 Distributive use of term, 38 
 Division, 161 ; rules of division, 
 
 165 ; division by dichotomy, 
 
 1 66 ; various kinds of division, 
 168 
 
 Eduction, 93 
 
 Enthymeme, 252 ; Aristotelian 
 enthymeme, 253 
 
 Enumerative judgments, 188, 195 
 
 Epichirema, 256 
 
 Episyllogism, 255 
 
 Equational view, 109, 146 
 
 Equipollence, 98 
 
 Equivocal terms, 35 
 
 Equivocation, Fallacy of, 268 
 
 Essence, 123 
 
 Essential definitions, 57, 155 
 
 Ethics, 5, 293 
 
 Euler's circles, 78 
 
 Exceptive propositions, 57 
 
 Excluded Middle, Principle of, 73 
 
 Exclusive propositions, 57 
 
 Existence, Implication of, no, 113 
 
 Experientia, 233 
 
 Experiment, 310, 315 ; negative 
 experiment, 316 ; natural ex- 
 periment, 317 
 
 Experimental methods, 320 
 
 Explanation, 337 ; by regressive 
 reasoning, 339 ; by hypothe- 
 tical deduction, 341 ; Newtonian 
 explanation, 344 
 
 Exponible propositions, 57 
 
 Extension, 22 
 
 Extremes, 171 
 
 Fallacy, 264 ; definition of, 267 ; 
 
 Aristotle's list of, 267 ; Mill's 
 
 list of, 282 
 False Cause, 280 
 Fact, 362 
 Figure, 138 
 Figures of syllogism, 177; rules 
 
 of the figures, 1 79 ; superiority 
 
 of fig. i, 1 86 ; fourth figure, 191 
 
INDEX OF SUBJECTS 
 
 427 
 
 Figure of Speech, 273 
 First Intention, 34 
 Forma totius, i58 
 Fundamental syllogisms, 182 
 
 General terms, 21 
 Generalization, 338 
 Generalization, Fallacies of, 284 
 Generic propositions, 49 
 Genetic definitions, 155 
 Genus, 124 
 Grammar, 4 
 Ground, 119 
 
 Habit, Category of, 138; quali- 
 tative habit, 138 
 Hamilton's postulate, 40 
 Heteropathic effects, 246 
 Hypothetical deduction, 341 
 Hypothetical propositions, 63 ; 
 import of hypoth. prop., 119; 
 truth of hypoth. prop., 120 
 Hypothetical Syllogisms, 203 
 Hypothesis, 354 ; descriptive hy- 
 pothesis, 355 ; origin of hypo- 
 thesis, 357 ; conditions of valid 
 hypothesis, 359 ; various kinds 
 of hypothesis, 361 
 
 Identity, Principle of, 71 
 
 Ignoratio Elenchi, 275 
 
 Implication of existence, no, 113 
 
 Important characters, 390 
 
 Inceptive propositions, 57 
 
 Indesignate propositions, 49 
 
 Induction, 215 ; perfect and im- 
 perfect induction, 231 
 
 Inductive methods, Mill's, 321 
 
 Inductive syllogism, 228 
 
 Inference, 3 ; immediate infer- 
 ence, 92 ; inferences other 
 than syllogistic, 200 
 
 Infinite terms, 32 
 
 Intension, 22 
 
 Intention, First and Second, 34 
 
 Intermixture of effects, 246 
 
 Inverse method, 343 
 
 Inversion, 101 
 
 Judgment, 3 ; analysis of judg- 
 ment, 41 
 
 Law, various senses of the term, 
 68 ; laws of thought, 67 ; 
 empirical law, 369 ; ultimate 
 laws, 338 ; derivative laws, 369 
 Least squares, method of, 368 
 Logic, definitions of, i, 2 ; divi- 
 sions of, 3 ; a science or an art, 
 5 ; scope of Logic, 7 ; history 
 of Logic, 8 ; Scholastic Logic, 
 ii ; Formal Logic, 12; Sym- 
 bolic Logic, 12, 308 ; Inductive 
 Logic, 12 ; Transcendental Lo- 
 gic, 1 3 ; Hegelian Logic, 1 3 ; 
 Modern Logic, 14; Logic and 
 Metaphysics, 298 
 Logical use of terms, 38 
 Logical Whole and Part, 163 
 
 Major, Illicit process of, 175 
 
 Mai-observation, 285 
 
 Many questions, Fallacy of, 28 1 
 
 Many-worded terms, 20 
 
 Material use of term, 38 
 
 Mathematical reasoning, 199 
 
 Mathematical truths, their neces- 
 sity, 238 ; their nature, 29511 
 
 Measurement, 363 
 
 Means, Method of, 368 
 
 Metaphysics, 6, 296 
 
 Metaphysical necessity, 238 
 
 Method, 395 ; Descartes' rules 
 of method, 402 ; Leibniz on 
 method, 404 
 
 Methodic conduct of thought, 398 
 
 Methodology, 310 
 
 Metre, 364 
 
 Middle term, 170 ; ambiguous 
 middle, 173 ; undistributed 
 middle, 174 
 
 Minor, Illicit process of, 175 
 
 Mnemonic lines, 181 
 
 Modal consequence ; 104 
 
 Modal propositions, 58 
 
 Moods of syllogism, 178 ; subal- 
 tern moods, 182 
 
 Name, 3, 19 
 
 Natural classification, 389 
 
 Natural division, 162 
 
 Natural selection, Doctrine of, 386 
 
 Negative terms, 31 
 
428 
 
 INDEX OF SUBJECTS 
 
 Negative propositions, 46 
 Newton's Rules of Philosophizing, 
 
 349 
 
 Nominal definition, 152 
 Nominalism, 133 
 Nominalist view of Logic, 8 
 Non-connotative terms, 24 
 Non-observation, 285 
 
 Obscure Concepts, 18 
 
 Observation, 310 
 
 Observation, Fallacies of, 284 
 
 Ob version, 98 
 
 Omitted determinants, 102 
 
 Ontology, 6, 296 
 
 Opposition, Square of, 85 ; as a 
 
 means of inference, 88 
 Opposition of terms, 36 
 
 Paradox, 267 
 
 Paralogism, 267 
 
 Part, Logical, 163 ; subjective 
 
 part, 165 
 
 Particular proposition, 47 
 Passion, Category of, 138 
 Petitio principii. 278 
 Phantasm, 15 
 Philosophy, 290 
 Physical necessity, 235 
 Physics, 293 
 Place, Category of, 138 
 Polysyllogisms, 255 
 Porphyry, Tree of, 129 
 Positive terms, 31 
 Posture, Category of, 138 
 Predicables of Porphyry, 121 ; 
 
 Aristotle's Predicables, 131 
 Predicate, 5 ; Quantification of, 108 
 Predicative View, 105 
 Premisses, 3, 170 ; relation of 
 
 premisses to conclusion, 189 
 Privative terms, 31 
 Probability, Mathematical, 373 ; 
 
 philosophical probability, 378 
 Problematic propositions, 60 
 Progressive reasoning, 256 
 Progressive syllogisms, 194 
 Proper names, 21 
 Property, 126 
 Proposition, 3, 39 ; fourfold 
 
 scheme of propositions, 50 ; 
 
 reduction to logical form, 61 
 
 Prosyllogism, 255 
 Psychology, 6 
 
 Quality of propositions, 46 
 Quality, Category of, 137 
 Quality, Passive, 138 
 Quantification of predicate, 108 
 Quantitative determination, 363 
 Quantity of propositions, 46 
 Quantity, Category of, 137 
 Question, 278 
 Quiddity, 123 
 
 Ratiocination, Fallacies of, 284 
 Real definition, 152 
 Real use of term, 38 
 Realism, Moderate, 133 ; Exagger- 
 ated realism, 135 
 Realist view of Logic, 8 
 Reasoning, 3 
 
 Reduction, 182 ; indirect reduc- 
 tion, 184 ; ostensive reduction, 
 184 ; reduction of hypothetical 
 propositions, 206 
 Regressive reasoning, 256 
 Regressive syllogisms, 194 
 Relation, Category of, 138 
 Relative terms, 32 
 Remotive propositions, 56 
 Repugnant Concepts, 18 
 Residues, Method of, 324 
 Rules of Philosophizing, Newton's, 
 349 
 
 Science, definition of, 290 ; specu- 
 lative and regulative sciences, 
 5. 2 93 practical sciences, 297 ; 
 logical analysis of the sciences, 
 144 
 
 Second Intentions, 34 
 
 Simple inspection, Fallacies of, 
 284 
 
 Single-worded terms, 20 
 
 Singular terms, 21 ; singular 
 propositions, 49 
 
 Sophism, 267 
 
 Sorites, Aristotelian, 257 ; Gocle- 
 nian sorites, 259 
 
 Species, 122 ; doctrine of natural 
 species, 384 
 
INDEX JF SUBJECTS 
 
 429 
 
 Strengthened syllogisms, 182 
 
 Subaltern opposition, 88 
 
 Subaltern moods, 182 
 
 Subalternant, 85 
 
 Subalternate, 85 
 
 Subcontrary opposition, 87 
 
 Subdivision, 164 
 
 Subject of predication, 3, 5, 23^ ; 
 subject of inhesion, 23^ 
 
 Subjective part, 165 
 
 Substance, 24, 30 ; category of 
 substance, 137; primary and 
 secondary substances, 122 
 
 Substantial terms, 23 
 
 Suppositio, 37 
 
 Syllogism, 3, 169 ; rules of 
 syllogism, 172 ; validity of 
 syllogism, 195 ; inductive syl- 
 logism, 228 ; hypothetical syl- 
 logism, 203 ; disjunctive syllo- 
 gism, 207 ; syllogismus expo- 
 sitorius, I9ow 
 
 Syncategorematic words, 19 
 
 Synthesis, 395 
 
 Synthetic propositions, 51 
 
 Synthetically-formed definitions, 
 157 
 
 Terms, 3, 18 ; divisions of terms, 
 
 20 
 
 Terminology, 401 
 Tetralemma, 209 
 Theory, 362 
 Time, Category of, 138 
 Trilemma, 209 
 Truth, i 
 
 Uniformity of Nature, 218, 235 
 
 Unity of Nature, 248 
 
 Universal concepts, 16 ; direct 
 
 and reflex universals, 134 ; 
 
 controversy on universals, 132 
 Universal terms, 21 ; universal 
 
 propositions, 46 
 Universe of discourse, in 
 Univocal terms, 35 
 Vicious circle, 279 
 Via compositionis and via reso- 
 
 lutionis, 340, 352, 396 
 Via doctrinae and via inventionis, 
 Whole, Logical, 163 [340 
 
INDEX OF NAMES 
 
 OF AUTHORS CITED AND REFERRED TO IN THE 
 
 WORK. 1 
 
 Albertus Magnus, 233, 302, 324, 
 
 398** 
 
 Aldrich, 399 
 
 Alexander of Aphrodisias, 176** 
 Ammonius Hermiae, 297** 
 Antonius Andreas, O.S.F., 73 
 Augustine, St., gn, 298*1 
 Averroes, 10, 135 
 Avicenna, 10, 135 
 
 Bacon, Francis, 304 
 Bailie, Louis, S. J., 293** 
 Bain, gSn, 205, 245, 308 
 Baudot, Victor, 374, 377 
 Baynes, Prof., 108, 398n 
 Berkeley, 277 
 Bernouilli, 377 
 Boethius, 9, 35, 66, IOOM, i62w, 
 
 1 68, 176% 
 Bosanquet, 14, 61, 74*1, 76, 135, 
 
 201, 339, 344 
 Bradley, 13, 53", 61, 9 2 > 1031*, 
 
 inw, 117, 120, 135. J 76, 200, 
 
 201, 271 
 B^entano, 117 
 
 Cajetan, Cardinal, 45 
 
 Case, Prof., xi, 54, 55,65, 222, 340 
 
 Champeaux, William of, 135*1 
 
 Condillac, 7 
 
 Cournot, A., 379 
 
 Cuvier, 389 
 
 de Morgan, inw, 266, 268, 272** 
 de Regnon, S. J., 222, 234 
 de Verges, Cte, 142 
 de Wulf, ix, xi 
 Descartes, viii, 402 
 Diderot, vii 
 
 Galen, 192, 230% 
 
 Gerard, J., S. J., 385 
 
 Goudin, Antoine, O. P., 35, 398*1 
 
 Green, T. H., 248 
 
 Grotius, vii 
 
 Hamilton, Sir W., 7, 8, 34*1, 58, 
 66, 69, 98, 108, 132*1, i63n, 
 205, 258 
 
 Hegel, 13, 74, 132** 
 
 Herbart, in 
 
 Hobbes, 19, 54, 133** 
 
 Huxley, vii, 245 
 
 Janet, Paul, 224*1 
 
 Jevons, io6w, 109, 175, 314, 321, 
 
 343, 356 
 Joannes a Sto Thoma, 142**, 147*1, 
 
 152*1, 187*1 
 Joseph, Mr., 143**, 164*?, 187*1, 
 
 192*1, 
 
 Kant, 13, 46, 53, 58, 60, 75, 132**, 
 
 148, 167, 191*?, 205 
 Keynes, Mr., 12, 31,63**, HIM, 115 
 
 Lambert, 82 
 
 Leibniz, vii, 54, 71, 72, 73, 232*1, 
 
 278, 404 
 Locke, 71 
 Lotze, 14 
 
 Maher, M., S.J., 240** 
 
 Mansel, 7, 12, 76, 88, 98*1, 132*1, 
 
 167 
 
 Maurus, Silvester, S.J., loow 
 Mellone, Dr., 333 
 
 l The names of Aristotle, St. Thomas Aquinas and J. S. Mill are not contained in 
 this list. The references to them in the work are so frequent, that no useful pur- 
 pose would have been served by including them. 
 
INDEX OF NAMES 
 
 43 J 
 
 Mercier, Cardinal, 12, 41, 
 Monboddo, Lord, 191** 
 
 Newton, 344~353. 357 
 
 Ockham, William of, 132** 
 Osiander, Andreas, 356 
 
 Parmenides, 72 
 Pascal, viii 
 
 Peirce, Prof. C. S., 399 
 Pesch, T., S. J., 72, 144** 
 Petrus Hispanus, i8iw, 192** 
 Picavet, M., xii 
 Plato, 135**, 1 66, 294 
 Porphyry, 9, 121 
 Poynting, Prof., 360 
 Pringle-Pattison, Prof., 292*1 
 Pythagoras, i6iw 
 
 Rabier, M., 151**, 315*1, 
 Ray-Lankester, Prof., 386 
 Read, Prof. Carveth, 307 
 Rickaby, J., S.J., 61 
 Rodier, M., 17, 41 
 Sanderson, John, 114*1 
 Schiller, F. C., 295*1 
 Scotus, 35, 73, 187**, 234 
 
 Shyreswood, William, i8iw 
 Sidgwick, A., I46w 
 Sidgwick, H., 290*1, 291 
 Sigwart, 14, 344 
 Spencer, H., 13 
 Suarez, 73 
 
 Themistius, 17, 41 
 Theophrastus, 178, 192 
 Thomson, Archbp., 108, 220 
 Trendelenburg, 260, 298 
 
 Ueberweg, in. 122*1, 157*1, 192**, 
 217, 
 
 Valla, Laurentius, 258 
 Venn, Dr., 12, 83, 103*1, HIM, 116 
 Versorius Parisiensis, i88 
 von Hartmann, vii 
 
 Wallace, Prof., 140 
 Wasmann, S. J., 387 
 Watts, Dr., 258** 
 Welton, Mr., 278**, 323*1, 344 
 Whetham, Prof., 309 
 Whewell, 341, 344 
 Wundt, 230** 
 
 Zeno the Stoic, 9 
 
THIS BOOK IS DUE ON THE LAST DATE 
 STAMPED BELOW 
 
 
 AN INITIAL FINE OF 25 CENTS 
 
 WILL BE ASSESSED FOR FAILURE TO RETURN 
 THIS BOOK ON THE DATE DUE. THE PENALTY 
 WCILL INCREASE TO SO CENTS ON THE FOURTH 
 DAY AND TO $1.OO ON THE SEVENTH DAY 
 OVERDUE. 
 
 
 IjOT rt r <fOAn 
 
 SB, .23 jaw 
 
 P Jl ,>i -, .UU(J 
 U \J .J%33 
 
 btr iEHsS* 4 
 
 
 
 
 18 tS35 
 
 
 StF - 
 
 
 MAR 12 1336 
 
 
 
 
 FES 26 lam 
 
 
 ! -J i(j 
 
 
 JUN28 1845 
 
 
 
 
 . 
 
 
 -. > 
 
 
 
 
 :, : 
 
 
 VU7 , 
 
 
 
 
 M^^-' 
 
 
 APF 
 
 LD 21-100m-7,'33 
 
A 
 
 
 UNIVERSITY OF CALIFORNIA WBRARY 
 
 '