C LIBRARY j 
 
 UNIVERSITY OF 
 CALIFORNIA 
 
 SAN DIEGO \
 
 ft
 
 LOGIC; 
 
 t 
 
 THE SCIENCE OF INFERENCE. 
 
 SYSTEMATIC VIEW OF THE PRINCIPLES OF EVIDENCE, AND 
 
 THE METHODS OP INFERENCE IN THE VARIOUS 
 
 DEPARTMENTS OF HUMAN 
 
 KNOWLEDGE. 
 
 JOSEPH DEVEY. 
 
 LONDON: 
 HENRY G. BOHN, YORK STREET, COVENT GARDEN. 
 
 MDCCCLIV.
 
 PREFACE. 
 
 THE following pages comprise an attempt to systematise 
 the various forms of inference engaged, either in the con- 
 struction of science, or in the generation of opinion and 
 belief. Notwithstanding the diversity of the subject, the 
 author has endeavoured to meet its widest requirements; 
 not neglecting, while he has devoted the greater portion of 
 the treatise to the consideration of the laws and methods 
 of inference in their simplest and most complex combina- 
 tions, to include in his design a description of the different 
 subject-matter on which they are ordinarily employed, and 
 the foundations on which their processes ultimately rest. 
 If, to views so discursive, he has been able to impart any- 
 thing like systematic completeness, the merit is due not 
 so much to him as to the excellent treatises which have 
 already elaborated distinct portions of the subject and guided 
 him through much of his labour. 
 
 Logic, owing to the opposite schools of metaphysicians, 
 lias met with various, and even conflicting treatment in 
 nearly every age. It appears to be the only subject of which 
 the difficulties multiply with the spread of knowledge, and 
 which, instead of disentangling itself from the quarrels of the 
 past, periodically carries forward all its old perplexities to be 
 added to the account of the present. The disputes of JEnesi- 
 demus with the ancient stoics is still rife in Germany, and 
 
 b
 
 Tl PBEFA.CE. 
 
 the gauntlet which Bacon threw down to the peripatetics of 
 his age, is as warmly taken up by their successors in the 
 present, as if the Novum Organum had been only yesterday 
 ushered into the world. Hence, in the present vacillating 
 state of the science, with its limits as well as its subject-mat- 
 ter depending on each individual's fancy or caprice, no one 
 knows when he finds the name of Logic on the back of a 
 work what he is to expect. It may be a dish of metaphysics, 
 a dry piece of scholastic wrangling, or an abstract treatise 
 on method ; and should the views of the author be ultra, 
 the reader will not improbably find a great many pages taken 
 up with anathematising every view of logic but that assumed 
 in the text. 
 
 Now, this is not a satisfactory state of that science which 
 concerns the operation of the faculty in which men chiefly 
 glory, not only as the mark which pre-eminently divides them 
 from the brute creation, but also as the primary source of 
 those distinctions of rank and supremacy which obtain in 
 society. Nor has the writer met with anything in logical 
 treatises to necessitate the conflicting diversity of view in 
 which they regard the science. There is nothing in the body 
 of Aristotle's speculative views to hinder them from being 
 engrafted on the practical doctrines of Bacon ; nor anything 
 in the a priori methods of Descartes essentially antagonist 
 even to the inductive methods propounded by Comte and 
 Helvetius. Apart from the metaphysical tenets of these 
 schools, the general body of their logical doctrines may 
 be combined in one system. All have their distinct func- 
 tions in the generation of scientific belief, and by the diver- 
 sity of view which they bring to bear on any object, tend to 
 strengthen and verify the accuracy of each other's processes. 
 The writer has, therefore, avoided the fragmentary treat- 
 ment of logic pursued by his predecessors, and attempted 
 to place the science on its right basis, by grouping around
 
 PREFACE. Vii 
 
 the central idea of Inference the various methods and sys- 
 tems which are connected with its functions in the leading 
 divisions of knowledge. The instruments may be diverse, 
 but they all range themselves as so many subordinate con- 
 ceptions round the leading idea of the science, and may be 
 regarded as so many means of dissipating doubt, detecting 
 error, and placing trath beyond cavil. 
 
 Some persons manifest as much care in adjusting the limits 
 of a science, as if they were laying down the confines of pro- 
 vinces, or the boundaries of empires. The writer has not 
 deemed this exact nicety beneficial to a science which is in 
 a greater measure than any other interwoven with every 
 department of human knowledge. He has therefore intro- 
 duced into his pages everything which had a strong bearing 
 on inference, whether as regards metaphysical discussions 
 on the foundations of evidence, or collateral disputes which 
 have been raised in the present day on the doctrine of quan- 
 tification. He has not, however, adopted any of the innova- 
 tions which Sir W. Hamilton would introduce into the 
 scholastic logic, nor indeed omitted any portion of the 
 Aristotelian system, except the part excluded by the intro- 
 duction of special canons for each figure. With regard to 
 the utility of the peripatetic system and its correlation with 
 the other branches of logic, the views of the writer are in a 
 mean ratio to those of Mill and "Whately. "While he concurs 
 with Bacon in deeming this branch of the subject more 
 directly applicable to the moral sciences 1 , he does not con- 
 sider it entirely useless in physical investigation ; inasmuch 
 as there can be no inference which may not be faulty as to 
 form, and which, therefore, is not open to receive the aid of 
 the syllogistic canons. 
 
 In conclusion, the author expresses his conviction that 
 
 1 Bacon's restriction referred to politics and theology ; but politics 
 in his days was considered an a priori science.
 
 Till PKEFACE. 
 
 there are only two legitimate methods of treating a practical 
 system of logic, viz. : Either by pursuing the method adopted 
 in these pages, of systematising all the processes of infer- 
 ence which are embodied in the various departments of 
 knowledge ; or by selecting some particular province or 
 group of sciences, and pointing out the inferential methods 
 employed in their construction. In the direction of the first, 
 or general system of logic, Mill's is the only attempt that has 
 hitherto been made, and he has excluded the Aristotelian 
 portion of the subject. Of the last, or specific kind, several 
 treatises have appeared, but in most cases carrying down the 
 subject to subdivisions too minute to entitle Logic to the 
 claim of a distinct science 1 . When confined to the investi- 
 gation of a single subject, as in Oersterlen's Medicinische 
 Logik, or in the clever treatise of George Cornewall Lewis, 
 On the Methods of Observation and Reasoning in Politics-, 
 Logic, however valuable the results in other respects, is taken 
 out of its niche in the temple of the arts, and blended with 
 the substance of the other sciences. 
 
 J. D. 
 
 London, 1854. 
 
 1 The most amusing in this way is decidedly that on Parliamentary 
 Logic by " Single- speech" Hamilton. 2 The reader may profitably 
 eonsult another work by this ingenious writer, On the Force of Autho"- 
 rity in Matters of Opinion.
 
 CONTENTS. 
 
 HISTOEICAL INTRODUCTION. 
 ..'. BOOK I. 
 
 OF TERMS. PBOEMIPM. 
 
 CHAPTEE I. Of the Material Relation of Terms. 
 
 PAGE 
 
 1. Conditions of conception, substance, attribute 33 
 
 2. Abstract and concrete connotative and non-connotative terms 34 
 
 3. Relative and absolute, positive and negative terms 35 
 
 CHAPTER II. Of the Formal Relation of Terms. 
 
 1. Generalisation and abstraction .." 37 
 
 2. Genus and species 38 
 
 3. Differentia, property, and accident 39 
 
 4. Extension and intension 42 
 
 5. Nature and rules of logical division 43 
 
 6. Examples of division. The categories and predicables 47 
 
 CHAPTER III. Of Terms with regard to Things. 
 
 1. Formation of distinct conceptions a part of logic 49 
 
 2. What class of terms are liable to indistinctness 51 
 
 3. How conceptions become distinct and confused 53 
 
 4. Double mode of resolving conceptions 54 
 
 5. Tests of accurate conceptions 58 
 
 CHAPTER IV. Of Terms in Relation to Signs. 
 
 jj 1. Use of language in logic 60 
 
 2. Errors to which the formation of general terms are liable 61 
 
 3. Confusion arising from the transitive application of words ... 63 
 
 4. Twofold law of the transformation of names 64 
 
 5. Logical definition 65 
 
 6. Definition how far real 68 
 
 7. Scientific definition 69 
 
 8. Nominal definition , 71
 
 I CONTENTS. 
 
 BOOK II. 
 
 OP PROPOSITIONS. PROEMIUM. 
 
 CHAPTER I. Of Propositions with regard to Matter. PAGE 
 1. Simple complex and incomplex propositions 78 
 
 2. Simple complex propositions 79 
 
 3. Compound expressed propositions 80 
 
 4. Reduction of disjunctive and conditional propositions to cate- 
 
 gorical 83 
 
 5. Tacit, or implied compound propositions 85 
 
 CHAPTER II. Of Propositions with regard to Form. 
 
 1. Quantity of Propositions 87 
 
 ' 2/ Quality of Propositions 89 
 
 3. Distribution of terms in propositions 90 
 
 4. Opposition of propositions 94 
 
 5. Conversion of propositions 97 
 
 BOOK III. 
 
 OP SYLLOGISMS. PROEMItJM. 
 
 CHAPTER I. Of the Properties of Syllogisms. 
 1. Universal canon of mediate inference with the general rules 
 
 of the syllogism 102 
 
 2. Figures of the syllogism 108 
 
 3. Moods of the syllogism 113 
 
 4. Quantification of the predicate (new analytic) considered with 
 
 reference to mood and figure 115 
 
 CHAPTER II. Of the Notation of the Syllogism. 
 
 1. Euler's method 120 
 
 2. Ploucquet's and Lambert's method 123 
 
 3. Sir W. Hamilton's method 124 
 
 4. Use of notation ; equivalent syllogisms ,.. 126 
 
 CHAPTER III. Of the Kinds of Syllogisms. 
 1. Complex syllogisms 127 
 
 2. Conditional syllogisms 132 
 
 3. Disjunctive syllogisms 134 
 
 4. Copulative syllogisms 135 
 
 5. The dilemma 135 
 
 6. The chain syllogism, or sorites 138 
 
 BOOK IV. 
 
 ON THE GENERAL PRINCIPLES OF INFERENCE. PROEMIUM. 
 
 CHAPTER I. Of the Universal Methods of Inference. 
 1. Analysis and synthesis 143
 
 CONTENTS. li 
 
 CHAPTER II. Of the Universal Methods of Inference (continued.) 
 
 PAGE 
 
 1. Induction and deduction meaning of the terms 148 
 
 2. Different kinds of induction, formal and material. Syllogism 
 
 erroneously confounded with deduction 1 50 
 
 3. Theories of reasoning 153 
 
 4. Abstract truths exist independent of experience 1 59 
 
 CHAPTER HI. Of the different Degrees of Evidence. 
 % 1. Various grades of certainty 165 
 
 2. Twofold doctrine of modality 167 
 
 3. The same subject continued. Criteria of evidence. The doctrine 
 
 of sufficient reason 169 
 
 CHAPTER IV. Of the Foundations of Reasoning. 
 1. Number of primitive elements or principles into which all 
 
 knowledge can be resolved. Their relation to each other ... 171 
 
 2. Memory an ultimate source of evidence 173 
 
 3. External sense an ultimate source of evidence 177 
 
 4. Analogy an ultimate source of evidence 185 
 
 5. Reason an ultimate source of evidence 188 
 
 6. Authority an ultimate source of evidence 189 
 
 BOOK V. 
 
 OF THE METHODS OF SCIENTIFIC PROOF AND INVESTIGATION. 
 PROEMIUM. 
 
 CHAPTER I. Of the Methods of the Physical Sciences. 
 1. The nature, grounds, and limits of physical investigation 195 
 
 2. Observation and experiment 209 
 
 3. The methods of experimental inquiry. Discovery of minor 
 
 laws ;' their extension and verification 216 
 
 4. General outline of the inductive method difficulties and 
 
 limits attending the application of its special canons 237 
 
 5. Nature of scientific deduction formation and verification of 
 
 theories 243 
 
 6. Empirical generalisations : theory of probability ; and analo- 
 
 gical evidence '. 252 
 
 CHAPTER IL Of the Methods of the Moral Sciences. 
 1. Nature of the moral sciences: in what respect their methods 
 
 differ from the physical 261 
 
 2. The sciences amenable to the abstract deductive method. 
 
 The functions of the cross-examining elenches and the 
 negative process. Examples ,of scientific praxis 268 
 
 3. The laws which regulate successive states of mind. The 
 
 sociological sciences. The concrete deductive method direct 
 and inverse 277 
 
 4. Probable inference. Example and analogy 295
 
 .ill CONTENTS. 
 
 BOOK VI. 
 
 ON FALLACIES. PROEMIUM. 
 
 CHAPTER I. Of Formal Fallacies, PAGE 
 1. Illicit process and undistributive middle 305 
 
 CHAPTER II. Of Verbal Fallacies. 
 1. Ambiguous middle 307 
 
 CHAPTER III. Of Material Fallacies. 
 1. Non causa pro causa. Fallacy of groundless assumptions ... 313 
 
 2. Incomplete enumeration 320 
 
 3. Fallacy of false analogies 322 
 
 4. Petitio principii 326 
 
 5. Ignoratio elenchi 331 
 
 APPENDIX. 
 Modern schools of logic 337 
 
 APPENDIX TO BOOK I. 
 
 CHAP. II. 1,2. Nominalism and realism 342 
 
 CHAP. II. 6. The categories of Aristotle 347 
 
 CHAP. IV. 1. Use of language in logic 349 
 
 CHAP. IV. 2. Abuse of general terms 351 
 
 CHAP. IV. 3. Transitive application of words 352 
 
 CHAP. IV. 4. Twofold law of the transformation of names 354 
 
 CHAP. IV. Primary and secondary intentions. Analogical use 
 
 of terms 355 
 
 APPENDIX TO BOOK IV. 
 
 CHAP. I. 1. Analysis and synthesis 360 
 
 CHAP. IV. 3. The senses and ultimate sources of evidence 362 
 
 APPENDIX TO BOOK V. 
 
 CHAP. I. 2. Classification and nomenclature 366 
 
 CHAP. I. 3, 4. Formal analysis in physics 371 
 
 CHAP. I. 5. Mathematical reasoning 374 
 
 Division of the sciences 375 
 
 Amperes Tables 380 
 
 Verses Explanatory and Mnemonic 386 
 
 INDEX.., 391
 
 HISTORICAL INTRODUCTION. 
 
 IT does not appear that either the African or Asiatic 
 nations were able, at least before the Grecian era, to distin- 
 guish between the value of rational causes and fabulous 
 traditions, or ever habituated themselves to analysing their 
 thoughts, with a view to elaborate a code of rules for the 
 practical guidance, of the reasoning faculty 1 . The early 
 Greeks were the first people who deemed it requisite, to the 
 acquisition of correct knowledge, to inquire into the real 
 causes of things, but their method of investigation, faltering 
 and uncertain, led to few discoveries, nor gave them sufficient 
 confidence to draw up a code of logical rules for any other 
 purpose than that of verbal dispute. Zeno the Eleatic is 
 the earliest logician to whom antiquity refers 2 , as furnishing 
 the Greeks with a method of wrangling calculated to ensure 
 its possessor a triumph over any opponent who might venture 
 to question his thesis, but without further use or pretence, 
 unless it might be the collateral one of sharpening the 
 mental faculties, and leading to habits of intellectual acute- 
 ness. Though Socrates charges the author of this work with 
 obscurity and confusion, in that part which treats of conse- 
 quences 3 , he did not scruple to adopt the interrogatory 
 method of disputation (epwrrjo-ir) which forms the leading 
 
 1 An account is given in Colebrooke's essays, vol. ii. p. 292, of an 
 Hindu logic, by Gotama, which has, however, so many striking resem- 
 blances to the Aristotelian system, that critics are disposed to rank its 
 publication as posterior to the Organon, and to place its author among 
 the disciples of the Stagyrite. See St. Httaire, Logique d'Aristote, ii. 
 330. * Lived in the LXXX. Olympiad, or about 460 B.C. * Plat. 
 Tarmen. 
 
 :s
 
 2 HISTOKICAL INTEODUCTION. 
 
 feature of the work, and to apply the collection of sophistical 
 questions it contains for the purpose that Zeno pointed out, 
 of leading any person with whom he might happen to dispute, 
 by the concession of some point which seemed unavoidable, 
 into the meshes of absurdity. 
 
 Socrates, however, in furnishing brilliant illustrations of the 
 efficiency of Zeno's dialectics, distinguished three modes of 
 analysis, and laid, the foundation of logic proper, by intro- 
 ducing the terms genus and definition into the Greek 
 language. The first analytical method, which is similar to 
 that employed by geometricians, consists in admitting, by 
 hypothesis, the truth of a proposition until we reject or affirm 
 our judgment, by inferentially linking it with some other 
 recognised truth or absurdity, of which an example may be 
 found in the instruction given by Socrates to Critobulus 1 , re- 
 lative to the means of obtaining true friends, and where he 
 teaches Euthydemus the necessary conditions of true go- 
 vernment. The second of these methods either ascends from 
 particular facts to abstract truths, or detaches general notions 
 from the particular groups which they include, and may be 
 characterised as analogous to the method pursued by natu- 
 ralists, and the inductive system of Bacon 2 . The third 
 separates the notions which are associated with complex 
 ideas, and by distinguishing their properties, tends to dis- 
 pel the confusion which is apt to lurk beneath their indis- 
 criminate assimilation. This method has some resemblance 
 to the resolving process of mechanicians and chemists, and is 
 warmly recommended by Condillac. Perhaps there is nothing 
 on which Socrates bestowed more attention than this case of 
 determining complex ideas by a close examination of the 
 elements into which they are capable of being resolved ; as 
 may be seen in the Memorabilia 3 , where he endeavours to 
 define the idea of wisdom, virtue, goodness, justice, and piety ; 
 and in the second Alcibiades, where he distinguishes the dif- 
 ferent species of ignorance, with their corresponding effects; 
 and in the Crito, where he fixes the true value to be at- 
 
 1 Xenoph. Memor. ii. 13 ; iii. 6. See also Plat. Meno and the 
 first Alcibiades. * See Socrates' Conversation with Aristippus, 
 
 Xenoph. Memor. ii. I ; with Charmides, iii. 9 ; and Euthydemus, 
 iv. 9. Also Plat. Hippias. 3 i. 22, 23; iii. 16; IT. 1518.
 
 DESCABTES, EUCLID, AND PLATO. 3 
 
 tached to the opinion of the people, and the essential cha- 
 racteristics of justice. Occasionally Socrates weaves the 
 three modes of procedure into the same demonstration, alter- 
 nately employing each according as the different parts ad- 
 mitted of their application. 
 
 Previous to the time of Socrates, philosophy had been 
 delivered in language borrowed from the poets, and even as 
 taught by Zeno, it only furnished a species of amusement to 
 the sophists who met beneath the royal portico of Athens 1 , 
 to perplex each other with metaphysical subtleties, and 
 darken thought by words of vague import. Socrates was 
 the first to aim at the creation of a philosophical language, 
 by introducing, and insisting upon, the practice of definition 
 as an essential preliminary to correct inference 2 , and re- 
 solving all the disputes of his day into cases of verbal equivo- 
 cation. He dared to strip philosophy of the meretricious 
 ornaments of rhetoric, and make language a faithful mirror 
 for the reflection of the most delicate rays of thought. 
 
 Of the pupils of Socrates, Euclid and Antisthenes de- 
 veloped the doctrines of Zeno. The former expanded the 
 third part of his treatise which referred to sophistical ques- 
 tions, and is the author of many of the fallacies attributed 
 to the Stoical School. Simon of Athens and Simmias of 
 Thebes were closer followers of Socrates ; but the logical 
 treatises in which they professed to methodise 3 the system 
 of their master have not come down to us. 
 
 Plato wrote no treatise on the science, and what he de- 
 livered must be collected from the body of his writings and 
 his method of treating the subjects of the dialogues. From 
 these sources, it appears that he had an adequate conception 
 of the inverse methods of analysis and synthesis, and wrote a 
 work explanatory of their different properties, which, how- 
 ever, has not come down to us. In his Philebus he prefers 
 the latter method, but in his written or exoteric works 
 he constantly employed the other. Plato only discrimi- 
 nated two modes in which reason can be exercised: viz., 
 that of departing from general principles to arrive, through 
 the medium of perception, at the knowledge of individual 
 facts, and the mounting from these general principles, with- 
 
 i sroia /3u<riXfoj. 2 Arist. Metapby. i. 6. 3 Simon, Art of 
 
 dispute ; Simmias, On truth and reasoning. 
 
 B2
 
 4 HISTOBICAL INTBODUCTION. 
 
 out the aid of perception, to reach a primary principle by 
 which the different branches of knowledge are linked to- 
 gether, and obtain a fixed and immutable character. His 
 a priori doctrine concerning ideas, which he made the key- 
 stone of his system, would not allow him to admit any species 
 of inference to be legitimate, from the particular to the 
 general, and compelled him to place the perfection of reason 
 in resolving notions into all the qualities they bore, and in 
 seeking to educe from abstract propositions all the furniture 
 of the universe. He, however, contributed to keep alive 
 among his countrymen that caution respecting the use of 
 complex notions which Socrates had introduced, by tracing 
 most of our errors to the vagueness and obscurity of 
 this class of ideas ; and by viewing language simply as an 
 instrument of thought, which caprice, as well as nature and 
 analogy, had conspired to form, he impressed upon his fol- 
 lowers, with no less force, the necessity of defining all terms 
 of a compound or abstract character before employing them 
 in reasoning. 
 
 The treatises of Aristotle, which his Greek as well as mo- 
 dern commentators have agreed to consider, under the title of 
 the Organon, as parts of one work, embrace an exposition of 
 every principle which concerns method, truth, the operations 
 of the reasoning faculty, and the foundations of evidence ; 
 subjects which, being widely distinct from pure metaphysics, 
 evidently show that Aristotle had not that limited idea of 
 the domains of the science within which some illustrious 
 modern logicians would fain confine it 1 . Aristotle regarded 
 logic as the code of human reason ; but, since ideas are the 
 materials of the edifice it is called to construct, the Stagy- 
 rite deemed it expedient to commence the work with an in- 
 ventory of the immense number of conceptions with which 
 the mind is furnished, marshalling them in distinct rank and 
 file, that every notion may be found in its proper class, and 
 every class ranged under the head of its appropriate divi- 
 sion. This portion, which comprises the categories, may be 
 regarded as the frontier-ground where psychology is blended 
 with logic where the one science terminates and the other 
 begins. 
 
 J See Whately's Logic, Introd. p. 8, and Sir W. Hamilton's critique 
 on this work in the Edin. Kev. for April, 1833, or in his recently col- 
 lected essays.
 
 ABISTOTLE. 5 
 
 To combine the isolated elements expounded in the cate- 
 gories is the function of judgment, which, verbally expressed, 
 gives rise to propositions 1 . Several propositions connected 
 by certain laws constitute reasoning, and the most simple 
 form of it is that which unites two ideas by declaring 
 their identity with a third, through the medium of three pro- 
 positions, termed the premises and the consequence. Hence 
 the construction of the syllogism a Greek word, signifying 
 this association of verbal judgments, which Aristotle follows 
 out into all its developments, and of whose legitimate forma- 
 tion he clearly enounced the rules. The Book of Interpre- 
 tation, comprising the second portion of the Organon, re- 
 lates to the exactitude of propositions ; the Prior Analytics, 
 which immediately succeeds, expounds the law of the syllo- 
 gism, its figures, and modality. 
 
 The art of combining syllogisms in a compact chain of 
 conclusive demonstrations aud the general principles of evi- 
 dence are taught in the Posterior Analytics. The subjects 
 of syllogistic probability and the laws of dispute, so far as 
 matters of opinion are concerned, are laid down in the 
 topics ; while the concluding section of the Organon is 
 employed about sophistical arguments, or the means of de- 
 tecting error in syllogisms constructed in contravention of 
 the laws of reasoning. 
 
 Of the general doctrines of Aristotle concerning the founda- 
 tions of evidence and the different scientific methods, it may 
 be sufficient to state that he regarded experience as the 
 source from which the materials of each science must be 
 drawn, and pointed to induction as the proper mode of con- 
 structing general propositions out of the facts which it 
 yields ; nevertheless, he rather inconsistently refused to 
 the intermediate axioms so derived any character of cer- 
 tainty, until they had been applied by deduction to demon- 
 strate the existence of the particular facts out of which they 
 had sprung. His nominalism did not even lead him to deny 
 the existence of universal axioms which derived their co- 
 gency from other sources than experience, or hinder him 
 from tracing our knowledge as much to the intrinsic percep- 
 tion of such principles, and the consequences evolved out of 
 them by deduction, as to the recognition of simple facts and 
 ' De Interpret, c. 2, 3, 11, 12.
 
 6 HISTORICAL INTBODUCTION. 
 
 the general laws to which they inductively led 1 . Hence he 
 clearly distinguished the two modes of knowledge mediate 
 and immediate : the former identified with proof, the latter 
 with first principles; which he strongly insisted that no person 
 could attempt to prove without landing himself in the belief 
 of the impossibility of knowledge 2 . He also assigned a limit 
 to definition as well as evidence, and clearly shows that any 
 effort to define simple terms must involve the logician in a 
 vicious circle, since it can only be achieved by words of a 
 more complex character, whose signification already has as- 
 sumed the object of the definition which is sought to be esta- 
 blished 3 . Aristotle also distinguished the definition of names 
 (i. e. that which assigns any arbitrary meaning to a term 
 otherwise indeterminate) from the definition of things, which 
 he instructs the logician to express in terms of the nearest 
 genus and most approximate difference, if he would compare 
 the thing defined with those which have most analogy with 
 it, and discriminate their common properties and several 
 points of difference. To define, however, is not to demon- 
 strate ; the object of definition being rather to serve as a 
 basis of science, by fixing the sense of terms to be employed 
 in eliminating new truths than as a direct inlet to fresh 
 knowledge 4 . 
 
 "We meet also in the same part of the Organon 5 a dis- 
 tinction between absolute and relative principles, the first of 
 which Aristotle places in the nature of things being ex- 
 pressed in universal axioms and propositions, the furthest 
 removed from sense ; he assigns the latter to the judgments 
 we make respecting individual facts, \vhich, as they are 
 mainly derived through sensation, and are most proximate 
 to sense, are the first in the order of knowledge^. To this 
 contrast he refers three others : that of the universal and 
 particular, that of the necessary and contingent, and that of 
 the essence and accident. Absolute knowledge embraces 
 the real essence of things, which Aristotle invested with the 
 attribute of necessity ; relative knowledge comprises what is 
 particular and contingent, and every other property con- 
 nected, in Aristotle's view, with the accident of things. The 
 
 1 Post. Analyt. b. i. c. 1, 2, 8, 18. 2 Ibid. b. i. c. 3. 3 Ibid. 
 
 b. i. c. 1. 4 Ibid. b. ii. c. l, 2, 3, 4, 12, 14. 5 Ibid. b. i. c. 2. 
 
 Ibid.
 
 ABISTOTLE. 7 
 
 first only, admitting of demonstrative proof, deserved the 
 name of science ; the second, as affording scope merely 
 for the inductive method, appertained solely to belief and 
 opinion 1 . 
 
 It is unfortunate that these distinctions should have been 
 mainly founded upon a glaring error in the Aristotelian 
 physics : viz., that of attributing contingency and accident 
 to what were simply isolated instances of general laws modi- 
 fied by peculiar circumstances, as they led the Stagyrite to 
 divest one branch of proof of the certainty which belonged to 
 it, and thereby mainly contributed to disseminate those false 
 ideas concerning induction which kept positive science sta- 
 tionary for nearly two thousand years. If induction could 
 only explore contingent events, and if experience can only be 
 consulted through its method, it is evident that all the facts 
 derived from this source must partake of uncertainty, and that 
 Aristotle resolved all our knowledge into a principle which 
 had no sufficient basis. By what means demonstration con- 
 verted the facts to which it led into a certainty they could 
 not possess even from the most compacted link of induc- 
 tive inference, or how universal, absolute, and necessary pro- 
 positions can be identical with particular and contingent 
 judgments derived from sense, the Stagyrite does not inform 
 us ; and the Organon is consequently transmitted to posterity 
 with doctrines upon the applied part of logic which conflict 
 with each other, and convey, with respect to the most fecund 
 methods of introducing the empiric element into science, the 
 falsest impressions. It is, however, fair to add that the greater 
 portion of Aristotle's logical treatises has been lost, and that 
 those which have come down to us have not escaped the 
 ravages of time and the mutilations of commentators. 
 
 "With the exception of Theophrastus and Eudemus, who 
 extended the boundaries of the Aristotelian logic by the in- 
 vention of the five moods and the important doctrine of hy- 
 potheticals, we meet with no important writers on the 
 science till the early centuries of the Christian era. In the 
 intervening period the writings of Aristotle seem to have 
 been buried, though the logical portion of them was tradi- 
 tionally handed down by his disciples, and contributed to 
 
 1 Prior Analyt. b. L c. 2, 3, 12, 17 ; ii. c. 24. Post. Analyt. b. i. 
 C. 1, 4, 6, 8, 13, 29, 30, 33; ii. C. 3, 4, 7, 12.
 
 8 HISTOEICAL INTRODUCTION. 
 
 guide the speculations of some of the Roman sages. In the 
 second century, however, owing to their discovery by An- 
 dronicus of Ehodes, they met with a considerable revival, 
 and we find them the subject of many learned commenta- 
 ries by Galen, Ammonius, Alexander, and Porphyry. Yet 
 not one of these made any valuable accession to logic, the 
 labours of Galen 1 being confined to the discovery of the 
 fourth figure, and those of Porphyry to his work on the pre- 
 dicables. Their writings, however, though unimportant in 
 themselves, were not unproductive in results. They gave 
 rise to a spirit of philosophic inquiry among the Arabians 
 when the thirst of conquest had subsided, and, by broaching 
 the question of nominalism and realism among the Maho- 
 metan and Christian doctors, led thought out of the stagnant 
 flats in which five centuries of war and rapine had con- 
 fined it. 
 
 From the scholastics logic inherited a great abundance of 
 acute distinctions which helped to disperse much of the con- 
 fusion apt to lurk in terms and propositions of a complex 
 character ; but it is hard to say whether the waste of verbal 
 subtleties with which they encumbered the science, and their 
 
 1 This is the current opinion at Oxford ; but it is fair to state that 
 Galen wrote a treatise on the art of demonstration, which, on the 
 authority of Hipp. Decreta (ii. cap. 30, ix. cap. 1 ), had it reached us, 
 would have placed him in the rank of the most pioneering logicians 
 of the present day. Galen is there represented as placing the radical 
 vice of the ancients in seeking fecund propositions for science in abstract 
 dialectics, and in abusing general notions by substituting them for the 
 light of facts; and is made to define with surprising exactness the na- 
 ture of synthesis and analysis, with their correlative methods, point- 
 ing out the errors of relying on either of these methods to the exclu- 
 sion of the other, and the necessity of combining both as the condition 
 of perfect science (De Hipp, et Plat. Decret. ix. cap. 5). If we may 
 believe these authorities, he makes sense the criterion of simple 
 objects, the understanding those of complex and rational ones, but sub- 
 sequently establishes the mutual dependence of these two channels of 
 knowledge. Observation imparts the signs of things, the understand- 
 ing abstract truths; the first is the origin of discovery, and leads to the 
 decomposition of the principles of the sciences, the second extends dis- 
 covery to new cases by demonstration, and establishes the alliance of 
 the facts so pointed out, with empirical truths, a union which alone 
 constitutes perfect knowledge (De Optim. Sect. c. 2; De cujusque 
 animi prec. cogn. atque Med. c. 3, 6, 8; De optim docendi genere, de 
 Hipp, et Plat. Decret. vii. 8, ix. 1, 8). Galen traces the greater part 
 of our errors to precipitate assimilation.
 
 THE SCHOLASTICS. 9 
 
 constant use of the syllogism in its naked, skeleton-like form, 
 did not counterbalance the advantages which undoubtedly 
 sprung from the exactness of their terminology. Their want 
 of elegance, however, in logical exposition must be traced to 
 the slender resources which Boethius' 1 translation afforded 
 them, to whom they were mainly indebted for their know- 
 lege of the Organon ; while the entire absence of anything 
 like physical science or experimental observation threw their 
 minds upon abstract principles and a priori reasoning, and 
 may form some excuse for their devotion to pursuits in 
 which the most gigantic intellects must have run to seed. 
 Their logical works are multitudinous ; yet all wear the same 
 aspect and teach the same doctrines, unless in the solitary 
 point about universals, on which only they presumed to 
 differ. Diligent bibliographers 2 have been able to catalogue 
 nearly two thousand treatises from this source, all of which 
 may be characterised as the bare formulising of the peripa- 
 tetic logic 3 . It is strange that men should have taken such 
 pains to re-echo what had been so often repeated before 
 them; but there were only two or three subjects upon 
 which the mind could be employed viz., metaphysics, logic, 
 and theology, and the religious uniformity of the age caused 
 the same doctrines on these topics to be continually re- 
 produced. 
 
 As soon, however, as Greek learning had been scattered 
 over Europe from the shrines of Constantinople, a spirit of 
 disaffection at once manifested itself against the Stagyrite's 
 supremacy ; and, as his assailants deemed the Organon the 
 citadel of his empire, they sought, in destroying that, to 
 complete his overthrow. Their efforts do not appear to have 
 ended in anything very decisive, since they attacked the old 
 logic entirely on false grounds, and had nothing to set up in 
 its place, save some crude theories about method and the 
 value of dichotomies. Nizolius flanks his attack 4 on the 
 Organon with the strange assertion that correct reasoning 
 
 1 Published at the commencement of the sixth century. 2 See 
 Blakey's Logical Catalogue. Even he has not mentioned half of them. 
 3 The treatise of St. John of Damascus is the only exception which we 
 encountered in looking over a formidable number at the Cheetham and 
 Bodleian libraries. 4 De Veris Principiis et Vera ratione Philo- 
 sophandi, ii. c. 1.
 
 10 HISTOEICAL nfTEODUCTION. 
 
 consists in a clear and transparent diction, and confounds 
 persuasion with conviction in attributing to the flashes of the 
 rhetorician the effects which can only follow from sound 
 reasoning. Eamus, who endorsed many of the views of 
 Nizolius, affirmed with rather amusing gravity that he had 
 studied the Organon for ten years without becoming a better 
 geographer or a wiser historian; and proceeded to attack 
 that treatise, on the ground that it did not teach men facts 1 . 
 Tet the method of division by dichotomy, which he at- 
 tempted to substitute for the peripatetic logic 2 , was simply 
 an unnatural extension of the disjunctive syllogism, whose 
 functions the Organon had already pointed out ; and which, 
 if practically enforced, would have stunted the growth of 
 reason by reducing the entire sphere of its operations to one 
 of its least significant forms. This substitution, however, 
 does not appear to have been sufficiently absurd to lack 
 supporters in more recent times : its innovating character 
 found strong favour with Milton 3 , while Condillac advocated 
 it in his Calcul, and Bentham in his Chrestomathia. 
 
 The zeal with which Eamus went about the demolition of 
 the Organon was frequently displayed at the sacrifice of 
 consistency; and the charges which he urged against its 
 author, if they had any weight, would often rebound with 
 much more force against himself. He reproaches Aristotle 
 with his exclusive adoption of the analytic method, and 
 gives his preference to synthesis ; while his celebrated divi- 
 sions (dichotomise) are so many glaring instances of analysis. 
 His system received the name of the Causal method, not 
 because it offers any instrument for the investigation of 
 causes, but because it places in causes a means of definition, 
 and one of the characters which determine the conformity of 
 argument with things. 
 
 Patrizzi and Concio likewise became famous about the 
 same era by their audacious attacks upon the Stagyrite ; but 
 beyond a few isolated gleams of light upon method, they do 
 not appear to have been in possession of anything so good 
 
 1 Animadversiones in Dialecticam Aristotelis, i. iv. For its deve- 
 lopment, see Institutiones Dialecticse, ii. Paris, 1543. Scholse Dia- 
 lecti. Bas. 1559. 2 Ramus took his bifurcate division from the 
 Isagoge of Porphyry. 3 Artis Logicae Plenior Institutio, 1672.
 
 ATTACKS OK AEISTOTLE. 11 
 
 as the system they attempted to pull down. Patrizzi, indeed, 
 gave Bacon that magnificent hint about laying the foundations 
 of philosophy entirely anew, and erecting the fabric by the scaf- 
 folding of induction ; but his attempt at the task was converted 
 by the platonic ideas he adopted into a ludicrous travesty of 
 his own principles. Concio's views of method were far more 
 distinct, and they are laid down with a particularity which 
 shows that his conceptions grew out of a practical acquaintance 
 with the modes by which the sciences might be moved out 
 of the ruck in which they had so long been embedded. In 
 his work on the subject 1 he places the problem of logic in 
 determining the relation of the known to the unknown, which 
 may be distributed under different classifications : that of the 
 relation of the general to the particular; of the whole to 
 its parts ; of the compound to the simple ; of the cause to 
 the effect ; or that of the reverse order of these divisions. 
 Each development of these relations led him to distinguish 
 three sorts of analysis, not discriminated up to his time, and 
 subsequently confounded by Condillac viz., that which pro- 
 ceeds from the general to the particular, from the whole to 
 its parts, and from the ends to the means. They are, how- 
 ever, commonly united, though one of them generally pre- 
 dominates in the same investigation. Of the three, Concio 
 gives the preference to that which proceeds from the end to 
 the means, or from the effect to the cause ; and controverts 
 the notion that analysis is the best instrument of discovery, 
 and synthesis the most available for the purposes of exposi- 
 tion. According to Concio, the true method of instruction 
 is to reveal the paths which led the discoverer to the truths 
 we seek to explain 3 . For the rest, in his definitions, nomen- 
 clature, and classifications, he follows Aristotle ; asserts with 
 the Stagyrite the illogical consequences of defining the first 
 and last terms in the ladder of reasoning, and, like him, pro- 
 pounds the general principles, but failed to develope the 
 theory of the combination of rational deductions with experi- 
 mental truths. 
 
 As the discoveries, however, of Galileo gradually revealed 
 the hollow [nature of the Aristotelian physics, the Organon, 
 which had been partly instrumental in their formation, began 
 
 1 De Methodo, 9, p. 29. Ibid. 17, pp. 8490.
 
 12 HISIOEICAL INTRODUCTION. 
 
 to lose ground in proportion, and a voice was heard from 
 England's great chancellor arraigning the author on the 
 charge of having corrupted science by an extravagant per- 
 version of logic 1 . Bacon, however, in descending into the 
 details of the impeachment 2 , did not evince any clear ideas of 
 the points where Aristotle had failed, though he exhibited 
 astounding ingenuity in unmasking the several causes which 
 had impeded the progress of science, and in constructing a 
 system calculated to neutralise their effects in future. The 
 error of the Stagyrite was hardly, as Bacon alleged, in intro- 
 ducing a mode of reasoning compounded of propositions and 
 middle terms which were liable to all the illusions of lan- 
 guage, since no one can demonstrate without the aid of this 
 method ; but in the assumption of metaphysical axioms and 
 definitions untested by experience, in conformity with which 
 he attempted to prejudge every fact that nature presented 3 . 
 Against the errors which arose from the application of such 
 principles, Bacon effectually provided by excluding every 
 generalisation from the domain of philosophy which did not 
 fairly arise out of the rigorous examination of the pheno- 
 mena it included ; and in framing a code of rules by which 
 the mind might be led from particular facts to intermediate 
 axioms, and from these ascend to the universal laws which 
 enchain the universe. "When general propositions were so 
 reached through the medium of a legitimate induction, 
 Bacon allowed the utility of the inverse method of demon- 
 strating the individual facts which these universal state- 
 ments included, and tracing their remotest consequences, 
 by which we are led not only to the particular propositions 
 by whose immediate consideration we rose to their dis- 
 covery, but to others of which we had no previous know- 
 ledge 4 -. 
 
 Hence it will appear that the doctrines of the two Orga- 
 
 1 Novum Organum, b. i. aph. 63. (Bohn's Scientific Library.) 
 * See Introduction to the De Augmentis. 3 Such are the principles 
 that nature abhors a vacuum, the abstract perfection of circular 
 motion, his separation of celestial from terrestrial mechanics, and 
 his definitions of light and heavy, motion and transparency formed 
 without any consideration of the objective realities to which they refer, 
 and sometimes in defiance of them. * Nov. Organuin, i. aph. 18; 
 De Augmentis, i. vi. c. 2.
 
 AEISTOTLE AND BACON. 13 
 
 nons are not so conflicting as is commonly reputed, and that 
 after abating some exaggeration of view on each side, one 
 may be fairly taken as supplementary to the other. Aris- 
 totle insists, as well as Bacon, upon the necessity of blend- 
 ing abstract with experimental truths if we would attain to 
 perfect science 1 ; but both mistook the exact forms in which 
 the combination should be effected, one making induction 
 (the instrument of investigating truth) the chief agent in 
 the j formation of each science ; the other, deduction, which 
 is more properly the means of demonstrating truth when 
 discovered. The error, however, lies only in the extreme 
 length to which they pushed the two mutually corroborative 
 poles of proof, and would have disappeared, had each only 
 taken the pains to reconcile the discrepancies of their own 
 statements on the subject. Bacon refused to take things 
 as principles of evidence upon any other testimony than ex- 
 perience ; he nevertheless frequently admits the cogency of 
 demonstrative laws, which derive their force from abstract 
 truths, to discover facts which have not fallen under our ob- 
 servation. Aristotle, while he resolves all our knowledge into 
 experience, strips induction, the only method by which it 
 can be consulted, of every claim to certainty. It does not 
 appear to have occurred to either that abstract principles 
 can only be combined with experimental truths through the 
 blending of their correlative methods, and that their respec- 
 tive functions must be employed according as each science 
 admits of their influence. To deny the relevancy of demon- 
 stration because the laws of induction have been legitimately 
 propounded, is as absurd as to impugn the utility of the wind- 
 mill because the steam-engine has been invented ; and if 
 Aristotle and Bacon have contributed to this error, they have 
 contradicted themselves as much as each other. 
 
 Though Bacon's method has received no brilliant confir- 
 mations out of the circle of the experimental sciences, he ex- 
 pressly urges its competency 2 to meet all the purposes of 
 scientific inquiry. This statement, however, is only true so far 
 as the introduction of the empiric element is concerned, and 
 the verificatory functions which it is only competent to dis- 
 charge where abstract evidence can be brought to the touch- 
 
 1 Post. Analyt. b. i. c. 1, 2, 8, 18. Introduction to the Instauration 
 le Aug.- i. vi. c. 2. Nov. Org. i. aph. 18. (Bohn'a Scientific Library.) 
 ' Novum Organum, b. i. aph. 127.
 
 14 HISTORICAL rtTTBODTJCTION. 
 
 stone of facts. Out of this sphere its application is unnatural, 
 and the attempt to obtrude it into ethical science has given 
 birth to utilitarian chimeras, as -wild and fanciful in their way 
 as those which arose from the unseasonable application of the 
 counter-method to physics. In general, however, abstracting 
 from the zeal of one or two small philosophical sections, who 
 place each other out of the pale of reason, the functions that 
 the two Organons are destined to fill have been practically as- 
 signed to them, and their spheres kept, perhaps, even more 
 distinct than is advantageous for science. Aristotle still rules 
 over ethics, hermeneutics, and jurisprudence, and as the master 
 of scholastic divinity he yet contrives to mould the minds of 
 those who sway the Christian world ; but it is the distin- 
 guished prerogative of our immortal countryman to preside 
 over the field of nature, and teach man to unveil its secrets 
 and subject its wildest elements to his will. 
 
 Notwithstanding that the claims of the inductive method 
 in all cases of appeal to facts had been urged before Lord 
 Bacon, and by none with more philosophical exactness than 
 his great namesake 1 , he was the first to give them an ex- 
 tensive development, and to announce them witli that spirit- 
 stirring eloquence which, conspiring with the awakening 
 thought of the age, gained them a speedy entrance into the 
 scientific mind of Europe. After the publication of the 
 Novum Organon all logic seemed to be resolved into method, 
 and the success of that great work raised up rivals as well 
 as imitators in that department of the science. Descautes 
 would not admit that diversity of doctrines could be attri- 
 buted to any other cause than the diversity of modes pursued 
 in their establishment; and as he regarded mathematical 
 proof as furnishing the highest gradation of certainty, he 
 endeavoured to raise a theory of method on the geometrical 
 model 2 , and in its execution penetrated into some of the 
 most subtle operations of thought. In conformity with his 
 general principle, he was obliged to avow the homogeneous 
 nature of all knowledge, which he placed in the composition 
 of known things 3 , and by not accepting anything as certain 
 
 1 Roger Bacon, Opus Magus. 2 Discours sur la Methode, i. ii. 
 
 Regies pour la Direction de 1'Esprit, part i. r. 4. Medit. Pref. Prin- 
 cipes de Philosophic, Pref. 3 Regies pour la Direction de 1'Esprit, 
 
 p. ii. r. 13.
 
 DESCABTES. 15 
 
 but what immediate intuition or legitimate deduction reveals, 
 to limit induction to the functions of determining the state 
 of a question, of disengaging it from irrelevant matter, and 
 subdividing it into complete and consecutive categories ; all 
 which operations Descartes viewed with. Aristotle as so 
 many preliminaries to demonstration 1 . Hence he does not 
 establish his series of truths by classes of facts, gradually 
 becoming more general and less complex in the ascent of 
 proof, but by chains of inference which derive their force 
 from the most abstract laws of thought ; and here we meet 
 with the great divergency of the two paths pursued by him 
 and Lord Bacon. 
 
 Evidence, according to Descartes, is the result of the le- 
 gitimate exercise of all the operations of reason in the 
 acquisition of knowledge. Induction and analysis prepare 
 the way ; intuition commences, but deduction completes the 
 work. In the pursuit of the latter branch, we are led from 
 words, or abstract principles, to things ; from the same to 
 the same ; from the whole to its parts, and vice versa, or 
 from the effect to the cause, and inversely 2 . All his rules 
 for the direction of the mind in these operations may be re- 
 duced to the following. To submit our thoughts to the test 
 of a rigid analysis, removing all simple presumptions, doubt- 
 ful opinions, and obscure notions 3 . To examine if the thing 
 to be determined spontaneously presents itself to us, or 
 whether it is known through the medium of another object, 
 and in the latter case to discover the class from which it is 
 to be deduced. For the rest, every scientific question may 
 be reduced to the solution of a mathematical problem ; since 
 it encloses an unknown object which it is necessary to dis- 
 engage and explain, by obtaining the sign and determining 
 the conditions which belong to it 4 . Descartes failed to dis- 
 criminate with sufficient precision the methods of analysis 
 and synthesis, misled by the error that they admitted of the 
 same development in speculative philosophy as in geometry. 
 
 1 Post. Analyt. ii. c. 13. (Bohn's Scientific Library.) s Bugles, 
 &c. p. ii. r. 12. 3 Ragles, &c. p. i. r. 12. Dis. Math. p. i. 
 
 Princip. de Philoa. part i. art. 66. * Kfcgles, &c. p. i. reg. 12; 
 
 p. ii. regs. 13, 1719.
 
 16 HISTORICAL INTRODUCTION. 
 
 He deemed his meditations an instance of analysis, because 
 they established the knowledge of God as a cause, from the 
 effect of his own existence, notwithstanding his proof of the 
 Divine Being is eminently synthetic. In another portion of 
 his works 1 he attempted to establish his metaphysical system 
 upon a synthetic basis. But, on comparing the two modes 
 of procedure, we find only a difference of arrangement in the 
 compilation of the work, and not a reverse order in the de- 
 velopment of the ideas. 
 
 With these principles it will be readily seen that Descartes 
 could admit no other criterion of truth than the logical 
 axiom, " all that which is included in the idea of a thing may 
 be affirmed of it." He considered this principle competent to 
 legitimise all inference, and as he called his celebrated enthy- 
 meme, " I think, therefore, I am," his generative principle, 
 or the corner-stone of the edifice, he deemed his philosophical 
 criterion the regulating line which determined the rectitude 
 of the facts of which the structure was composed. The dis- 
 crepancy, however, of limiting intuitive certainty to one me- 
 taphysical maxim, and of assuming at the same time a logical 
 axiom, having no connexion with it as the test of the exten- 
 sion of that certainty to other truths, he does not endeavour 
 to explain, or to show how a principle purely logical can 
 be rationally applied to any objects out of the sphere of ab- 
 stract and conditional truth. Wishing to impose upon every 
 science the same criterion of evidence, and to unfold their 
 truths by the same method, he applies a maxim which can 
 only regulate the interior combinations of our ideas, to legiti- 
 mise the relation of real things in the objective world. Hence, 
 as far as natural science was concerned, Descartes wrecked 
 his genius on those abstract principles which Bacon had 
 pointed out as the philosophical Charybdis of antiquity. By 
 degrading induction from its legitimate functions, and en- 
 deavouring to reason out natural facts by the a priori method, 
 his theories burst like soap-bubbles, almost as soon as they 
 were formed ; while the system of Bacon, in the hands of the 
 illustrious Newton, gave rise to a philosophy founded on the 
 basis of observation and experience, which will last so long as 
 reason and the nature of things remain as they are. 
 1 Reponse aux Premier Objections, part i. p. 441.
 
 MAEIOTTE AND THE POET EOYALISTS. 17 
 
 "With the exception of a stray treatise or two, like Lord 
 Herbert's De Veritate, Tschirnhausen's Medicina Mentis, 
 and Spinosa's De Emendatione Intellectus, nothing of any 
 importance appeared upon methodology after Descartes ; but 
 logic did not retire to its old limits without making some 
 provision for the new processes of inference that had arisen, 
 and attempting to reconcile the operations of reason in the 
 pursuit of the new sciences with the principles it had ap- 
 plied to the construction of the old. Mariotte 1 was the first 
 to extend the Aristotelian logic by the introduction of ex- 
 perimental principles, and to endeavour to bring all the 
 operations of inference into harmony with each other, by 
 linking the increasing powers of the new calculus, the laws 
 of induction and demonstration, to the same homogeneous 
 axioms and definitions ; thus seeking to make logic stand to 
 the other sciences as algebra to mathematics; a supreme 
 and universal science, offering the key to the unknown in 
 every department of knowledge, and expounding all the 
 methods by which truth can be sought out and demon- 
 strated. 
 
 A work of this kind, though without aiming at so close an 
 assimilation of the different methods of proof, appeared in the 
 Port Royal Logic 2 , written by Arnauld and JSTichole with a 
 view to bring the old Organon in closer alliance with the 
 Cartesian philosophy. The peripatetic logic, however, though 
 not absolutely disparaged, is considered of subordinate im- 
 portance to the rules of their master, and the methods of 
 geometry in the natural and speculative sciences ; and an 
 examination of the sophisms apt to spring from self-love, 
 interest, or passion in points of dispute, is held out as far 
 more likely to lead to the dissemination of truth and the- 
 overthrow of error than attention to the laws of quantifica- 
 tion, or to the legitimacy of syllogistic moods 3 . The eight 
 rules condensed from Descartes, intended by the authors to 
 comprise the different methods to which the sciences owe 
 
 1 Essai sur la Logique, printed at the end of the two volumes of 
 his physical treatises. 2 First appeared in 1662. For a more detailed 
 account of this work we must refer the reader to the introduction to 
 the translation of this work by Spencer Baynes, and to Pcre Buffier's 
 critique at the end of his Logic. 3 Part iv. on Method, which con- 
 tains a posthumous paper of Pascal on the Method of the Geometers. 
 Part iii. ch. 20.
 
 18 HISTOEICAL INTEODTTCTION. 
 
 tlieir development, are not so calculated to guide the mind to 
 the discovery of truth as to fortify it from error ; a failure of 
 design which arose from their absolute neglect of the induc- 
 tive element, and the nonchalance with which they treated 
 judgments of facts. Even this exclusive adherence to de- 
 monstration did not enable them to bring the new methods 
 into harmony with the syllogysm, or to promote anything 
 like consilience of parts in the exposition of their doctrines. 
 They treated the old logic as a thing going out of fashion, 
 yet too respectable to be despised, while their exclusion of 
 the most powerful instrument of discovery left tlieir demon- 
 strative code much in the position of Quixote's system of 
 strategics, which defined with the greatest precision the 
 movements to be observed after the defeat of an enemy, 
 without throwing any light upon the mode by which that 
 defeat was to be accomplished. 
 
 Locke, whose treatise immediately followed, revived the 
 old cry of the absolute worthlessness of the Aristotelian 
 syllogism even in matters of speculative reasoning, where 
 Bacon had confessed its power, and seemed inclined with 
 Eainus to limit the functions of reason to correct definition 
 and methodical analysis. Beyond these preliminaries to 
 demonstration he refused to acknowledge the efficiency of 
 any rules for the guidance of the judgment, and assimi- 
 lated, like Descartes, moral proof to mathematical in- 
 ference, that the consequence might follow from the correct 
 statement of the conditions of the question. In determining 
 the origin of our simple ideas, the growth of their complex 
 forms, the reality of knowledge which he made to consist in 
 the conformity of words with things, the use and abuse of 
 language, and the nature of truth which he placed in the 
 conjunction and separation of signs according as the things 
 they denote agree or differ, Locke found a field better 
 adapted for his keen analytic powers than the regions of 
 pure logic, in which, through his inability to demonstrate, 
 he was peculiarly unfitted to move. But the attempt of the 
 Essay on the Understanding to carry the inductive method 
 into psychology is not without its uses to the logician. It 
 accustoms him to analyse his notions with rigorous precision, 
 to provide against the errors of popular phraseology, and dis- 
 perse the equivocations apt to cluster round certain forms of
 
 LOCKE AND CONDILLAC. 19 
 
 expression. It is wrong, however, to confront it with logic, 
 or include it in the same category. It only takes us to the 
 threshold of the science, and leaves us there. 
 
 Condillac 1 gave a more explicit development to the views 
 of Locke by resolving the elements of all kinds of reasoning 
 into the mathematical principle that the same is the same, 
 thus referring all truth to identity of ideas, and reducing the 
 artifice of reasoning to the mere transformation of signs 
 between propositions brought into relations of equality 2 . 
 Hence, as algebraical forms constituted the only laws to be 
 observed in the process of inference, the functions of logic 
 were restricted to definition, the syllogism was treated as a 
 joke 8 , and the highest results of reasoning in any walk of 
 science deemed of no further utility than the formation of a 
 philosophical language. As Aristotle delighted in contrasts, 
 Condillac was singularly enamoured of unity, and simplified 
 everything. According to him, there was only one criterion 
 of certainty, one method of proof ; only one order of analysis 
 and one source of error. His unique analysis consists 
 merely of a method of division already laid down by Des- 
 cartes, the specific object of which was to make a complete 
 inventory of all the parts which constitute a whole. His 
 sole fount of error is the employment of words without de- 
 termining the ideas they are intended to convey 4 . 
 
 The principal merit of Condillac consists in his clear expo- 
 sition of the principles which lead to the legitimate alliance 
 between abstract truths and judgments of fact 5 ; but this 
 portion of his work stands out in strong antagonism with 
 the rest of his logical theory, which reduces all propositions 
 to abstract and rational judgments, and makes their identity 
 constitute the foundations of science. The consequences of 
 such a principle in psychology demonstrate its illogical 
 nature, and would land Condillac in opinions quite opposite 
 
 1 His Logic does not follow the Essay on the Understanding in the 
 order of time Wolf comes between the one being published in 1 685, 
 the other in 1753; but the authors are too commonly classed together 
 to be separated. 2 Langue de Calcul. Objet de 1'Ouvrage. L'Art 
 de Penser, part i. c. ix. Logique, c. viii. 3 Ibid. Le syllogisme est 
 on amusement de college ; nous ne faisons aucun usage de tout cela. 
 4 Langue de Calcul. Objet de 1'Ouvrage. L'Art de Penser, par. ii. c. 6. 
 * L'Axt de Penser, part i. c. 8 ; ii. c. 7. 
 
 o2
 
 20 HISTOBICAL INTRODUCTION. 
 
 to those which he strove to establish, and which he ia com- 
 monly supposed to represent. If all science is limited to the 
 identity of our ideas compared with each other, irrespective 
 of inductive evidence, we surely can know nothing of the re- 
 lation of our ideas to things. We enclose ourselves in a 
 circle of idealism, and place a gulf between 'our knowledge 
 and the external world, which no logic can bridge over. 
 
 Against the extreme doctrines of Descartes and Locke 
 there had been a strong reaction in Germany, headed by 
 Leibnitz ; but its logical bearings were not formally ex- 
 pounded before Wolf issued his great encyclopaedia of the 
 sciences 1 . The views of this eclectic are similar to those 
 already attributed to Mariotte, being an attempt to combine 
 all that was sound in the old and new Organons and methods, 
 and vindicating for logic its natural position, as a sort of 
 propadeutic to all the sciences, that knowledge might rest on 
 consistent principles, and a termination be put to many irre- 
 levant disputes in philosophy. To this end Wolf sought to 
 shed a new light on the maxims of Descartes, of Locke, and 
 Leibnitz, and to reconcile many of their statements with 
 respect to the character of clear and confused, adequate and 
 inadequate ideas, by introducing a distinction between the 
 formal qualities with which the mind is apt to clothe its con- 
 ceptions, and the material qualities which arise solely from 
 the nature of the objects themselves 3 . This distinction forms 
 the basis of the two branches of his logic ; formal conceptions 
 being connected through abstract principles with demonstra- 
 tive reasoning, while those of a material character are allied 
 with experience, and give rise to the functions of induction. 
 The principle of causality is the guide of the second, the ne- 
 gative process that of the first. He attempts to reconcile the 
 discrepancies of Aristotle between these two orders of truths, 
 by showing how universal propositions are connected with 
 particulars by the scaffolding of inductive inference which 
 Bacon had designed ; though Wolf failed to unite the two 
 methods under one criterion of evidence. The intuitive 
 
 1 Wolf published, in 1710, a small treatise on Logic, under the title 
 
 of Vernunftige Gedanken von den Kraften des Menschlichen Ver- 
 
 , standes ; but his great Latin treatise on the subject, from which our 
 
 references are taken, did not appear till twenty years later. 2 Logica, 
 
 pars. i. 2, c. 1, 2, 77116. Psychologia Empirica, i. 3035.
 
 WOLF AND HIS GERMAN SUCCESSOBS. 21 
 
 judgments which underlie each mode of proof, are distin- 
 guished with sufficient clearness : the several uses of hypo- 
 thesis determined, and the laws of causality traced out with 
 the practised eye of a metaphysician 1 . 
 
 Notwithstanding the completeness, simplicity, and preci- 
 sion of these views, "Wolf has been charged with investing 
 simple truths with all the pomp of demonstration 3 , and with 
 converting the proof of ordinary facts into theorems of geo- 
 metry. But these attempts arose from a desire to bring the 
 complex parts of his treatise into logical symmetry, by con- 
 necting them with rational criteria, and by making the in- 
 ductive and demonstrative methods coalesce and verify each 
 other as much as possible. In furtherance of the same sim- 
 plification, Wolf had asserted the homogeneous character of 
 the speculative and mathematical branches of deduction, sup- 
 posing that as the whole series of geometrical proof could be 
 drawn out in syllogistic array, to which, indeed, he attributed 
 their cogency ; so the whole chain of philosophical inference 
 admitted of the same rigorous precision as those of quantity 3 ; 
 a statement which was subsequently challenged by Eudiger, 
 on the ground that mathematics embraced probability, but 
 philosophy the transition from the possible to the real 4 . 
 
 Among the opponents or followers of Wolf, we meet with 
 few marked contributors to logical science till the time of 
 Lambert. Eudiger introduced the logic of analogy, so much 
 neglected by the moderns, and entirely passed over by the 
 ancients ; and Walch pointed out the extensive application 
 it might receive in the various branches of the moral and 
 natural sciences 5 . Crousaz, who wrote his treatise on the 
 principles of Bacon and Locke, contributed an excellent 
 chapter on probability and on causality 6 , in which he at- 
 tempted to rectify the peripatetic classification by substi- 
 tuting an exact category of all the relations to which the 
 
 Logica, pars. ii. 2, c. i. 2, 662709; c. 3, 727728; Discur. 
 Prelim, c. 4, 126 129. * Galluppi Lezioni di Logica. Wolf cer- 
 tainly attempts to define existence, but he does so against his own rule. 
 ' Discur. Prelim, c. iv. 139. 4 De Sensu Veri et Falsi, i. 4; Halle, 
 1709. See 
 sciences, 
 
 sic, 1747. * Phil. Lex. Einleitung 
 25. Logique, part i. 2, c. 6.
 
 22 HISTORICAL INTRODUCTION. 
 
 word cause may be applied, with their respective distinctions ; 
 putting forth, similar -views of the science to Crousaz, Pere 
 Regnault made a successful attempt to popularise logic, by 
 expounding it in a conversational form 1 . His book, written 
 in a clear and sketchy manner, in imitation of Fontenelle, 
 was issued in a spirit of compromise, being an attempt to 
 reconcile the old notions on logic with the empiric principles 
 that domineered over his age. 
 
 But the most important accession to logic at this epoch 
 was the introduction of a scheme of notation calculated to 
 reduce its method to algebraic simplicity, an improvement 
 which grew out of the ancient constitution of the science, and 
 destined to be prolific in great results. Aristotle had con- 
 ceived that the combinations of abstract ideas in reasoning 
 might be reduced to a certain number of formulas, and that 
 ideas might be distributed into certain classes. Hence 
 sprung his rules for the syllogism, his categories, and com- 
 mon-places. In the middle age, Raymond Tally had founded 
 his combinatorial art on the development and abuse of this 
 great conception. Wilkins, Athanasius Kircher, and Dal- 
 garno flattered themselves they were possessed of the power 
 to represent the entire system of our ideas in a language 
 competent to produce all their analogies. An attempt was 
 now made to apply the same notion to logic, by giving that 
 science the form of mathematical calculation, and investing 
 it with the rigour of its methods. 
 
 "With this view Plouquet introduced, and Lambert per- 
 fected, a system of particular signs directed to express the 
 logical relations of ideas. [Following Locke, Lambert 2 first 
 endeavoured to determine the signs of the relations of simple 
 ideas, and left those of the complex ones to be determined 
 by the combinations of their elements. The identity of pro- 
 
 1 La Logique en forme d'entretien ou Tart de trouver la verite. 
 * Published his views in the Neues Organon and Architectonic (1764) ; 
 the former work embracing the rules to which the form of scientific 
 knowledge can be reduced; the latter fixing the general notions which 
 are to constitute their matter. The first work comprises four divisions, 
 yiz. Dianoiologie, or the art of thinking ; Alethologie, which considers 
 truth in its elements ; Semiotic, which assigns to truth its exterior 
 characters ; and Phenominology, or the distinction between appear- 
 ances and reality. His Architectonic relates to metaphysics, and is 
 consequently out of our plan.
 
 LOGICAL NOTATION. 23 
 
 Positions in his system is represented by the sign of equality, 
 he relations of genus and species by exponents varying in 
 power proportionate to the extension of the distinguishing 
 difference ; and those of opposition, of analogy, of quantity 
 and quality, of the known to the unknown, are expressed by 
 other marks analogous to those of algebra. As there are in 
 logic simple as well as compound relations, this theory has 
 its corresponding proportions and progressions, and assigns 
 to logic its series and limits as well as to the higher algebra 1 . 
 But the greater part of the notation lies open to all the 
 objections urged against investing matters of moral specula- 
 tion with the rigorous precision of quantity, and has, in fact, 
 remained unenforced unless by one or two stray logicians 
 who, like Condillac, made the homogeneity of the two classes 
 of truths the groundwork of their system. The scheme, how- 
 ever, led Euler 2 to devise a system of figures solely re- 
 stricted to represent the logical relations of our conceptions, 
 apart from any assumptions of particular doctrines, and pre- 
 pared the way for Sir William Hamilton's mode of notation, 
 which, by enabling us to render the equivalent and con- 
 vertible syllogisms in the different figures at a glance, accord- 
 ing to extension or intention, has simplified all the relations 
 of pure logic, and would form, were it not narrowed to a 
 particular system, one of the most important features in its 
 progress 3 . 
 
 Since the fall of the "Wolfian system, and ', the inaugura- 
 tion of a popular literature in Germany, logic has gradually 
 subsided in that country into a history of dreams. Even 
 such scientific logicians as Platner and Schulze, who knew 
 
 1 Versuche einer Zeichenkunst, in Lambert's Logische und Philoso- 
 phische Abhandlungen. Berlin, 1787. See also Fragment 4. . 2 Lettres 
 a une Princesse d'Allemagne. s Lambert is the only logician who 
 has attempted to complete the unfinished parts of Bacon's method, as 
 projected in the Novum Organon, b. ii. aph. 21. He is also commonly 
 reported to have substituted the four dicta of the syllogistic figures in 
 the place of the dictum de omne et nullo laid down by Aristotle as the 
 condition of all perfect inference. Prior Anal. i. ch. 5 and 6. See 
 Mills' System of Logic, vol. i. p. 232 ; Buhle's Geschichte, vi. 543 ; and 
 Troxler's Logik, ii. p. 62. But Thompson contradicts these authorities 
 in assigning the invention of the three first dicta -to Keckermann 
 (Logic, iii. ch. 7 9), whose work appeared a century earlier. Thomp- 
 son's Outlines of the Laws of Thought, p. 245.
 
 24 HISTOBICAL INTRODUCTION. 
 
 the importance of maintaining the independence of their art, 
 bound it up to a great extent with empiric psychology ; 
 while more audacious thinkers have confounded its axioms 
 and rules with a mass of metaphysical hypotheses, framed for 
 no other purpose than the invention of argument to contra- 
 dict common sense. Yet, with a view to clearness and pro- 
 priety of thought, it is evidently necessary that every science 
 should be treated strictly on its own grounds, and most 
 scrupulously distinguished from the sciences which lie upon 
 its confines ; while it is no less essential to the progress of 
 knowledge that those mental phenomena which admit of irre- 
 fragable proof, and stand upon a certain foundation, should 
 be separated from a heap of supposititious paradoxes, whose 
 leading object appears to be, to deny what is, and to prove 
 what is not. Kant felt the truth of these views, and in his 
 new philosophy assigned to logic its old limits, but his 1 suc- 
 cessors have found in his doctrines principles which impugn 
 this division, and their final development by Hegel has ter- 
 minated in a position which tears up the old logic by the 
 roots, introducing as the criterion of truth the very tenet that 
 it upheld as the test of falsity 2 . 
 
 In Italy a few excellent treatises have appeared on the 
 science within the last hundred years ; among which the works 
 of Genovesi and Galluppi 3 stand conspicuous for complete- 
 ness, precision, and exactitude. Though they follow "Wolf 
 in applying the mathematical methods to the speculative 
 sciences, they do not invest them with the same degree of 
 certainty; but as evidence admits three classes of truths. 
 
 1 Critik, p. 74. See also his Die Wissenschaft der Verstandes 
 regeln Uberhauft. Kant's Logik was a posthumous work, and com- 
 piled at his request from his own papers by Gottlob B. Jahsche. 
 The introduction is longer than the entire work, and contains little 
 worthy of remark beyond some formal distinctions, principally de- 
 signed to separate pure from applied logic. 8 It is idle to attempt 
 to refute a man who assumes the livery of falsehood as the badge of 
 truth, and who asserts that, when you have involved him in a contra- 
 diction, you have only established the truth of his principles. It would 
 appear that Hegel's Wissenschaft der Logik screens itself by such an 
 assumption from any attack on the part of the old, and that there 
 requires a logic absolutely superior to both to decide the controversy. 
 3 Genovesi was contemporary with Condillac and Benedict XIV. Gal- 
 luppi's treatise, Lezioni di Logica e di Metafisica, was issued so re- 
 cently as 1841.
 
 ITALIAN AND ENGLISH LOGICIANS. 25 
 
 viz., mathematical, moral, and sensible, they likewise dis- 
 criminate the same number of certainties, and lay down 
 criteria for their determination. This portion of their system 
 is connected with a rigid analysis of the sources of evidence, 
 which is resolved into intuitive perception, sensation, reason- 
 ing, and testimony 1 a leaf taken from the scholastic logic in 
 use among Catholic universities 3 , and evidently connected 
 with the science, though generally neglected of late years by 
 its popular expositors. Genovesi 3 , whose treatise is more 
 original and concise, but not so profound as Galluppi, has 
 instituted eight simple rules of a more facile and general 
 application than those which appertain to the syllogism, 
 which arise out of his definition of reasoning as that of de- 
 veloping a confused idea, so as to render it distinct in 
 making its clear portion explain that which is confused ; and 
 condenses into a few maxims the principles which control 
 a priori and a posteriori inference. He concludes his logic 
 with a survey of the entire systems of knowledge in a classi- 
 fied form, and with an exposition of the harmony which 
 ought to reign between their several groups, and a precise 
 statement of their peculiar characteristics and fundamental 
 principles. 
 
 As the views of the principal English logicians of the 
 present century are discussed in the body of this work, we 
 need not here go further into detail than to point out their 
 general features, and show the different aspects which the 
 science assumes from their embodiment. At the commence- 
 ment of this era, logic, which had restricted itself to the 
 scholastic garb, was fast declining as a study, not less owing 
 to the sweeping censures of Brown and Dugald Stewart, 
 than to the blighting railleries of our comic dramatists, and 
 the feeble talents of its own expositors. Kett Belsham 
 and Kirwan 4 only repeated what had been said as well, if 
 
 1 Galluppi adds memory and evidence, but subsequently resolves 
 memory into an auxiliary agent of the others. Evidence is plainly no 
 faculty, but simply the result of the legitimate exercise of the mental 
 faculties in reasoning. a The most methodical treatise of this class, 
 and surpassing all others in the completeness of its views, is one by 
 Professor Ubajjhs, of Louvain. 3 For his logical views, see Elementa 
 artis Logics Critic and his Delia Logica. Venice, 1799. 4 Bel- 
 sh sun's Compendium appeared in 1801 ; Kirwan's Elementary Logic in 
 1807.
 
 26 HISTOEICAL INTEODTTCTION. 
 
 not better, before them by Crackenthorpe, Wallis, Saunder- 
 son, and others ; and it appeared that the Aristotelian form 
 of the science was on the point of being restricted to scien- 
 tific theology, had not an advocate of colossal dimensions, 
 Archbishop Whately, stood forward to re-assert its em- 
 pire, and answer the Scotch professors with arguments 
 quite as striking as any which they had urged. The work 
 achieved its object. A host of treatises appeared, more or 
 less embodying its principles ; two or three, of course, in 
 the natural order of things, venturing on a condemnation 1 ; 
 and the science experienced a revival which has, during the 
 interval of a quarter of a century 2 , manifested no signs of 
 abatement. 
 
 The great object of Dr. "Whately is to extricate logic from 
 the false views with which it had been connected, and defend 
 and expound its doctrines according to the limits assigned to 
 it by the scholastic divines. With regard to method in the 
 Cartesian sense, or to the trains of thought which have led 
 philosophers to grasp the highest axioms of science, logic 
 has nothing whatever to do. It simply confines itself to 
 analyse and determine the reasoning process so far as it is a 
 verbal operation 3 . Beyond this Dr. Whately will not admit 
 the possibility of an abstract science of evidence, the field 
 being too large and multifarious to permit the methods pur- 
 sued in each science to be succinctly generalised. Hence, if 
 a reader wish to have any idea of the processes by which the 
 mind is led to attain truth, or to appreciate their relative 
 force, he has no other resource than to attack with Leibnitz 
 the entire group of the sciences, and familiarise himself with 
 the encyclopaedia of knowledge. Of the general theory of 
 inference he can know no more than what Aristotle told him 
 some two thousand years ago, when reason had made but a few 
 ill-digested efforts to explain man's position in this world, 
 
 1 Among the former may be mentioned Hind's "Introduction to 
 Logic," and Hill's " Artis Logicae Kudimenta." Dr. Whately's excel- 
 lent treatise, however, experienced severe strictures in the critical 
 examinations of G. C. Lewis, Bentham's New Outline of Logic, and 
 in one of Sir W. Hamilton's essays. 2 Dr. Whately's Elements 
 appeared in 1825. 3 "Logic is entirely conversant about language." 
 " It is the art of employing language properly for the purposes of rea- 
 soning."
 
 WHATELY AND MILL. 27 
 
 and when its highest results were to be found in the victories 
 of the sophist. It is evident such a statement must be 
 received with caution. Had Dr. Whately confined his re- 
 marks to those who confounded metaphysical discussions, 
 mnemonic aids, and educational suggestions, with the science 
 of inference, his censures would have been as applicable as 
 they are forcible ; but to strike at those who claim for logic 
 the analysis of all the methods of inference which reason 
 employs in the investigation of truth, and limit the science 
 to that part of it which the deductive syllogism involves, is 
 arresting generalisation in logic at a stage when it was mani- 
 festly impossible that it could be otherwise than imperfect. 
 Even the a priori forms of the logical faculty cannot be cor- 
 rectly analysed without a distinct reference to the tangible 
 facts about which they are employed 1 , and when Aristotle 
 wrote, physical science was a blank, and law and theology 
 were unborn. 
 
 An attempt has been made to supply a logic embodying 
 the leading forms of inference pursued in the chief depart- 
 ments of science by John Stewart Mill, whose treatise is, 
 perhaps, the only one which presents an adequate concep- 
 tion of the science 2 . "Were it not for the ultra- nominalist 
 theories of the author, and his disposition to regard material 
 objects as the only things to which real inference can be 
 applied 3 , his work, we doubt not, would have been one of 
 the most perfect expositions that logic, as the science of 
 inference, could have received at the present day. He sees 
 distinctly through his subject, exhibits compact and con- 
 secutive thought in harmonising its various details, and 
 withdraws the mind from too much attention to empty 
 formulas and trifling distinctions, which is the bane of the 
 peripatetic logic, and fixes it on the realities of nature. 
 In expounding the theory of induction, which he makes the 
 
 1 In proof, we refer the reader to Aristotle's Theory of Induction. 
 * We regret, in addition, he should have referred his readers to 
 scholastic logicians for an exposition of the laws of the Syllogism, and 
 taken up much valuable space with frivolous metaphysical disputes 
 with Whewel, in which his arguments only go to prove that he is on 
 the wrong side. 3 Mill will not admit there is such a thing as in- 
 ference in Law and Theology, but only interpretation.
 
 28 HISTORICAL INTRODUCTION. 
 
 basis of inference, ratiocination being, in his view, a de- 
 pendent and subsidiary process, he takes the laws of the 
 material world as a sort of middle term by which the methods 
 pursued in all the sciences may be presented even to the 
 uninitiated in a general and perspicuous form, and considers 
 these laws under every point of view in which they are 
 capable of shedding new light upon the processes of science. 
 The result is a masterly analysis of the logic of the physical 
 sciences in the spirit of Lord Bacon, whose chief merit it 
 was to commence the undertaking. In supplying the very 
 gap which Bacon pointed out, Mr. Mill's treatise has placed 
 logic on its legitimate foundations, and constitutes an era in 
 the science destined to be of paramount influence over future 
 times. 
 
 The newest phase, however, which logic has assumed in 
 the present century is that which arises from a thorough- 
 going quantification of the predicate, which Sir W. Hamilton 
 ventures to think will remove many cumbrous forms that 
 now clog the peripatectic development of the abstract law of 
 reasoning, and both simplify and extend its general results. 
 Though this distinguished metaphysician has not yet com- 
 municated his views to the public, a general outline of them 
 has appeared from the pen of Spencer Baynes, in the shape 
 of a prize essay, which Sir William Hamilton, who proposed 
 the subject to his pupils, has endorsed with his sanction. 
 We are unable, however, to see, from Mr. Baynes's state- 
 ment of his views, that the proposed alterations will effect 
 any improvement in this branch of the science, so far as 
 practical utility is concerned, however serviceable such 
 emendations may be in simplifying the abstract statement of 
 the laws of thought. Our reasons will be found in the parts 
 of the treatise which the complete quantification of the pre- 
 dicate would modify, where Sir W. Hamilton's opinions are 
 noticed in detail. De Morgan's treatise, .which deserves 
 honourable mention for its list of privative judgments 1 , em- 
 bodies, we believe, most of Sir W. Hamilton's views on pure 
 logic, but the mathematical mnemonics which run through 
 
 1 De Morgan's Formal Logic, p. 61. Leibnitz (Op. xx. p. 98. Erd- 
 man's ed.) had started, but did not continue the subject.
 
 THE NEW ANALYTIC. 29 
 
 the whole of it, will ever tend to render it a sealed book to 
 those not over enthusiastic about algebraic symbolism. 
 Mr. Thompson's " Laws of Thought" is avowedly written to 
 introduce the alterations proposed by a complete quantifica- 
 tion of the predicate in a popular treatise on logic. But 
 the author by no means adopts the entire doctrines of the 
 illustrious Edinburgh professor ; he ventures to think that 
 many of the new syllogistic moods in his system are useless 
 and nugatory. To a clear exposition of pure logic, Thomp- 
 son subjoins an analysis of the scientific processes which con- 
 stitute the mixed branch of the science, but in too isolated a 
 manner. The work is lucidly written, and forms an in- 
 valuable accession to the literature of logic 1 . 
 
 Notwithstanding the success of these efforts, the age has 
 not been without impugners of the peripatectic system, who 
 with Brown and Locke would tear it up root and branch, and 
 hardly leave a single vestige of it in the science of inference 2 . 
 Though their objections are strikingly stated, we meet with 
 nothing of a very novel character in their works, nor do we 
 think the reasons adduced at all likely to shake the empire 
 of the Stagyrite, so long as that is confined to its strict 
 domain 3 . 
 
 1 Outlines of the necessary Laws of Thought, by the Kev. William 
 Thompson, first published in 1822, but has since gone through two 
 editions. We would refer the reader to this book for a lucid exposition 
 of the bearings of nominalism and realism. 2 B. H. Smart's Outlines 
 of Sematology, and Mr. Samuel Bailey's Theory of Reasoning. 
 3 In this introduction we have been compelled to omit even the 
 mention of many excellent treatises, such as Moberly's, Professor 
 Newman's Lectures on Logic, and Wesley's clever little compendium, 
 " The Art of the Syllogism," owing to the narrow limits to which our 
 space has necessarily confined us.
 
 LOGIC. 
 
 BOOK I. OF TEEMS.
 
 BOOK I. 
 
 OF TEEMS. PEOBMIUM. 
 
 ALL reasoning is founded upon judgments, and these can 
 only be employed about the mind's conceptions of things, 
 which enunciated in language are called terms. Hence 
 logic, at the outset, concerns itself with the formation of, 
 and verbal expression of, conceptions, so far as these opera- 
 tions concur to the deduction of correct inference. This 
 limit, we conceive, may be as easily drawn as that which 
 marks the boundaries of any other science in the group of 
 those which have language as a subject-matter in common. 
 If it is obvious that grammar has to deal with terms only as 
 they concern correct speaking, and rhetoric only as the em- 
 ployment of them is calculated to excite certain emotions, it 
 is no less obvious that in logic we must restrict ourselves to 
 that view of them which concerns the operations of the mind 
 in correct reasoning, and the part they play in the process. To 
 attain this object two things are manifestly requisite. First, 
 to trace the results of the diiferent processes of thought to 
 which objects must be subjected, before their relations of 
 agreement or disagreement to each other can be adequately 
 ascertained ; the second, to examine the process by which 
 notions and signs become the representatives of these objects, 
 with a view to discover how far, and under what sense, the 
 abstractions and names with which they ax-e clothed may be 
 relied upon as a correct designation of the properties which 
 they imply. These two heads cover the entire ground of the 
 Aristotelian and Baconian analysis of terms, and will, if fully 
 developed, exhaust the subject. The first is intended to ex- 
 plain all that relates to conceptions with regard to their form, 
 while the second will comprise everything which has reference 
 to their matter. The prior member of the division naturally 
 resolves itself into material and formal relation, the first of 
 which will form the opening chapter.
 
 C. I. 1.] MATERIAL DELATION. 33 
 
 CHAPTER I. 
 
 MATEEIAL BELAT1ON OF TEBMS TO EACH OTHER. 
 
 1. Conditions of Conception Substance Attribute. 
 
 IT is clear that the mind can form no distinct conception 
 of an object without ascribing to it some property, or with- 
 out receiving an impression of its existence in some mode or 
 manner. The object which is thus supposed to exist by 
 itself is denominated substance; the property assigned to it is 
 called its attribute. Thus, in the proposition that stone is 
 flinty, we assign the mode or attribute of flintiness to the 
 substance stone ; and not unfrequently condense both into 
 one expression as a flinty stone. 
 
 The names of objects were denominated by the schoolmen 
 substantive or absolute. The names which represent things 
 as modified for example, round, hard, just, prudent as con- 
 notatives, from the Latin word connotare (to mark along 
 with), because, while they point out distinctly the mode, they 
 also denote the subject in which it inheres. This designa- 
 tion is of great use in keeping in view the distinction be- 
 tween the names which simply denote objects, without any 
 reference to their attributes, such as proper names and those 
 which imply along with them, denotation or marking out of 
 the object, the attributes with which it is invested. 
 
 All attributes are either adjectives or substantives, gene- 
 ralised from them, as human or humanity ; corporeal, cor- 
 poreality ; rational, rationality ; and necessarily imply rela- 
 tion to some substance of which they are the mode. This 
 relation may be either essential or accidental that is, con- 
 tingent. An essential attribute enters so far into our idea 
 of the substance to which it refers, that we cannot conceive 
 it to exist without incorporation with it. In this manner 
 rotundity is essential to a circle, rationality to man, and four- 
 sidedness to a square ; since these notions invest them with 
 the properties that constitute their being. A contingent 
 
 D
 
 34 DELATION OF TERMS TO EACH OTHEB. [B. I. 
 
 attribute may, on the other hand, as the term imports, exist 
 apart from the substance to which it implies relation. Be- 
 cause many men are found black, it cannot be inferred that 
 any particular colour enters into our conception of humanity 1 . 
 
 2. Abstract and Concrete Connotative and Non-Conno- 
 tative Terms. 
 
 "When the mind embodies the attribute in a subject, the 
 notion thus definitely limited is called concrete; when it 
 views the attribute in a substantive form, apart from the 
 object, the term is called abstract. Thus, when the property 
 of wisdom is considered with reference to man, we get the 
 concrete " sage ;" but if we generalise the term wise, and 
 view it without reference to the object it denotes, we obtain 
 its abstract " wisdom 2 ." All general names, however, since 
 the time of Locke, have been denominated abstract, and 
 common usage has conventionalised the expression ; but the 
 term was employed by the schoolmen solely to designate 
 that large section of words which substantise attributes, and 
 to that sense it ought to be restricted. Hence, as abstract 
 terms generally refer to one special property, as whiteness, 
 rotundity, or smoothness, they are designated non-connota- 
 tive, since they do not imply any object beyond it. 
 
 Substances may be said to be singular when the mind 
 employs itself about any one definitely, as this tree, that 
 
 1 The distinction between mode and substance is not, as the Port 
 Koyal Logic asserts, that the true mode cannot be conceived apart from 
 its relationship with the substance which it implies, while the substance 
 can; for when that relation is essential, the substance can no more be 
 conceived without it than the attribute. The clear distinction between 
 attribute and substance is fundamental to correct reasoning; but it 
 appears to us to lie in the discrimination of one property from a 
 congeries of properties, the former of which always finds expression 
 in an adjective form, or as a substantive generalised from an adjective. 
 2 Hence abstract words generally are not capable of being pluralised, 
 while all concrete are. A principle which led the Greeks to adopt the 
 very elegant contrivance of using the same word to denote the general 
 idea, while they marked the abstract or concrete character it bore by 
 a simple alteration of the number; the plural of an abstract noun 
 being used for the singular of a concrete. For instance, rf^w; is the 
 abstract term for art; re^vai the concrete designation of the par- 
 ticular exercise of the art. See ^Esch. Agam. 249.
 
 C. I. 3.] MATEEIAL BELATIOH. 35 
 
 house, or when the thing actually existing stands apart by 
 itself, as the city of London, the university of Durham. 
 They are denominated general or common when they are 
 viewed in connexion with the class to which they belong, as 
 tree, city, university, &c. It may be necessary to distinguish 
 general from collective terms. The former can be predi- 
 cated of each individual of a multitude ; a collective name 
 cannot be predicated of each separately, but only of all taken 
 together. Thus, Kellerman's division of infantry could not 
 be predicated of every individual who composed it, but only 
 of the collective body. Such a term is considered as a single 
 collective name ; but if we mention a division of infantry, 
 without reference to any special one, the name must be con- 
 sidered as general and collective. 
 
 All concrete general terms are connotative. The word 
 man, for instance, denotes an indefinite number of indi- 
 viduals, of whom taken as a class it is the name, but it is 
 applied to them because they possess certain attributes : as 
 animal life, corporeity, rationality, and a certain external 
 form which is called human. Every existing being which 
 possessed these attributes would be called a man ; but none 
 could be so denominated that wanted any of these qualities. 
 If a race of animals were discovered like Swift's Houyhnhms, 
 possessing reason equal to human beings, but invested with 
 another corporeal form, some other name than that of man 
 would be required for their denotation. On the other hand, 
 most singular names are non-connotative, since they denote 
 the individual objects to which they are applied, without im- 
 plying any attribute in connexion with them. For example : 
 when we call a boy " Edward," or name a girl " Clotilda," it 
 is simply to enable these individuals to be distinguished from 
 their kind without awakening in the mind any impressions 
 concerning their attributes. 
 
 3. Relative and Absolute, Positive and Negative Terms. 
 
 When the mind considers any object as connected in any 
 way with another, the term in which it is expressed is called 
 relative. Such are father, son, ruler, subject, cause, effect, 
 and those various degrees of comparison by which subjects 
 
 D2
 
 36 EELATION 01? TEEMS TO EACH OTHEE. [B. I. 
 
 are contrasted together : as like, unlike ; longer, shorter, &c. 
 Absolute terms are those which express the object inde- 
 pendent of such relation : as man, house, animal. "When 
 two objects which are pairs are viewed in reference to the 
 relation they hold to each other, the terms in which they 
 are expressed are denominated correlative. Thus : though a 
 king is the ruler of men, king and man are not correlative, 
 but king and subject are. 
 
 When the mind attributes any definite property to a sub- 
 ject, the mode so assigned is termed positive: as, a man 
 reasoning. If the term denote that such a quality might be 
 conceived to exist in the subject, but does not, the attribute is 
 called privative : as dumbness, a man who is silent, a blind 
 child. If the mode is inconsistent with the subject of which 
 it is predicated, it is then called negative : as a dumb picture, 
 a lifeless statue. "We may notice, however, that attributes 
 are often positive in form, while they are negative in reality. 
 Thus: the words idle or sober, though positive in form, 
 merely connote the absence of activity and drunkenness. 
 Some terms, on the other hand, conceal a positive attribute 
 under a negative form : as truthlessness does not express the 
 mere absence of truth, but the positive attribute of lying. 
 
 Notions are said to be contradictory when they completely 
 exhaust all nameable things : as animate and inanimate, cor- 
 poreal and incorporeal, organised and unorganised ; for it is 
 impossible that one or other should not belong to every 
 object; as there is nothing that can be both, so there is 
 nothing that can be neither. On the other hand, contrary 
 notions are those which cannot be predicated of the same 
 subject at the same time, though there are many subjects to 
 which they do not apply at all, and others to which they are 
 applicable at different times. Nothing can be at once dis- 
 creet and imprudent ; but a man may be so at different 
 .epochs of his life, while a tree can never be deemed either.
 
 C. H. 1.] FOBMAL BELATION. 37 
 
 CHAPTER n. 
 
 FORMAL RELATION OF TEEMS TO EACH OTHER. 
 
 1. Generalisation and Abstraction. 
 
 THE principal act by which the mind arrives at the various 
 conceptions we have enumerated, is abstraction. By this 
 faculty we can divide substance into its logical parts, viz., 
 subject and attributes, and restrict our attention to any 
 definite mode, apart from the subject in which it is supposed 
 to inhere. This is clearly evinced by geometricians, who in 
 treating their science do not, as is the vulgar opinion, sup- 
 pose that there are lines without breadth, or surfaces without 
 depth, but simply that they are able to consider length apart 
 from breadth, which is even competent to the peasant when 
 he measures the distance from one town to another. 
 
 It is obvious that by the same faculty we can detach our 
 mind from the accidental properties of a subject, and consider 
 its essential attributes alone. As in the case of a human 
 being, we may withdraw our thoughts from his individual 
 peculiarities, as height, complexion, colour of hair, &c., 
 and attend solely to those qualities which enter into the 
 essentiality of his being, as a particular form of corporeity 
 endued with reason and animal life. In the same manner, 
 when we draw a triangle on paper we are able by an 
 instantaneous process of thought to withdraw our attention 
 from the place where it is, and the other accidents which 
 determine it, and consider the diagram as a figure bounded 
 by three right lines. "We thus obtain a conception which 
 applies to all triangles indiscriminately; as in the former 
 example, we obtained a conception which included under it 
 all members of the human family. By fixing the results of 
 these processes of thought in permanent language, as man, 
 triangle, animal, we obtain the terms we have already de- 
 signated common from being applicable to all the indivi- 
 duals included under them alike, and which are sometimes 
 called predicables, because they can be predicated of each 
 affirmatively.
 
 38 EELATION OF TEEMS TO EACH OTHEE. [B. I. 
 
 2. Genus and Species. 
 
 By this process of generalisation the mind is enabled to 
 dilate or contract its view of objects to an extent only limited 
 by the boundaries of human intelligence. We may, by ab- 
 stracting from or adding to any conception within the range 
 of actual existence, proceed through the varied scale of being 
 till we reach the highest or lowest link it opens out to 
 us. Thus, by observing a particular horse, Bucephalus, 
 grazing with others in the same field, and abstracting the es- 
 sential qualities of the group from those which are merely 
 accidental, as colour, size, age, &c., we get the common 
 notion of horse. If again we contrast the notion of horse 
 with cow, wolf, tigress, we observe that they have one 
 property in common viz., that of suckling their young, 
 and abstracting this from the other qualities in which 
 'they differ, we form the wider conception of mammalia. Car- 
 rying the process still further, we may compare the mam- 
 malia with birds, fishes, insects, and worms, whence per- 
 ceiving that all these, however different, agree in connoting 
 corporeal life and sensation, we arrive at the wider conception 
 animal, which embraces all material living things. In the 
 same manner animal may be considered in relation to inani- 
 mate objects, when the abstraction of life and sensation will 
 leave us the residuum of corporeal substance common to 
 both. Another step will lead us to the most general con- 
 ception the mind is capable of forming viz., that of being 
 as synonymous with substance, i. e. a substratum in which 
 certain properties inhere. The mind, in its view of objects, 
 ranges with equal freedom through the descending and 
 upward series, and by bringing any two notions into the 
 scale can ascertain their definite relation to each other. 
 Thus the notion animal connotes distinct qualities, in which 
 mammalia and insects equally participate ; it can, therefore, 
 be predicated of both; but mammalia and insects, though 
 included in one compact term, designate different attributes 
 in the kinds which they represent, and on that account reci- 
 procally exclude each other. 
 
 When a notion is considered as included in one more 
 general it is called a species, and the containing term in con- 
 nexion with it is denominated genus. Thus body and mind
 
 C. H. 3.] FORMAL EELATION. 39 
 
 are contained in the notion of substance ; as rhinoceros and 
 elephant in that of animal. They are, therefore, species of 
 which substance and animal are the genera. Things which 
 are species to one genus may be respectively genus and 
 species when viewed in relation to each other. Thus man 
 and animal are species with reference to substance; but 
 animal is the genus of .man, who in turn is a species of 
 animal. Species, however, of the same genus which mutually 
 exclude each other are denominated co-ordinate species : as 
 mammalia and insects are the co-ordinate species of animal. 
 In like manner the same notion may be a genus when com- 
 pared with the things to which it extends, and a species 
 when compared to another term which is more general. 
 Thus body, which is a genus in respect of organised and 
 unorganised things, is a species in relation to substance ; and 
 quadrilateral, which is a genus with reference to parallelogram 
 and trapezium, is a species in relation to figure. Such terms 
 as are respectively genus and species, according to the light 
 in which they are viewed, are called subaltern genera or 
 species. There are, however, species which cannot become 
 genera, as circle includes only individual circles which are all 
 of the same species. These are termed infirma species, of 
 which there are many kinds. But there can only be one 
 absolute genus summum genus, which is not a species ; 
 whether we choose to call it being or substance, is a point 
 for metaphysical rather than for logical discrimination. 
 
 3. Differentia, Property, and Accident. 
 
 But, besides genera and species, which being the results 
 of the general ideas that represent their objects to us as 
 things or modes of things denoted by substantives, there 
 are a class of notions formed by the abstracting power of the 
 mind that have reference to objects as things modified, and 
 are generally expressed by adjective or connotative terms : 
 these, when compared with the substances to which they re- 
 late, will fall under the head of difference, property, or acci- 
 dent. 
 
 When we divide a genus into its species, as animal into 
 horse, bird, or man, &c., we have regard to some essential 
 attribute, which not only distinguish them from their com-
 
 40 BELATION OF TEEMS TO EACH OTHEB. [B. I. 
 
 mon genus, but separate them from each other. Without 
 such attribute, it is evident the species would be confounded 
 with the genus, and with each other. Eor example, body 
 and mind are two species of substance ; but we are only led 
 to conceive them such because body, though included in sub- 
 stance, is distinguished from it by an attribute which sub- 
 stance does not connote, viz., that of extension, and mind 
 by that of thought : which attributes in turn serve to 
 separate the species from each other. Now such essential 
 attribute, whatever it be that leads us to discriminate the 
 species from the genus, is called, as the sense implies, its dif- 
 ference hence, the genus with its difference makes up our 
 idea of species. Thus metal-wire, endued with polarity, con- 
 stitutes a magnet, so that the species includes all the attri- 
 butes of the genus, just as the genus includes all the subjects 
 of the species. Or, to take a plainer instance, man is a 
 responsible animal ; the term animal (genus) includes every 
 kind of organised being endowed with sensation, among 
 which man finds a place ; while the term man (species) in- 
 cludes all the qualities of free-will and reason, combined with 
 material agency, in which the attributes of the genus, viz., 
 organised and percipient sensation, necessarily are com- 
 prised 1 . 
 
 The species, however, may be distinguished from the genus 
 by other essential attributes besides that which constitutes 
 the difference, and which, as the difference is generally the 
 leading quality, is often implied in, or dependent upon, it. 
 Thus extension is the differentia of matter, but in examin- 
 ing the nature of extension we find it connotes divisibility. 
 Hence we call this quality a property of matter. Occa- 
 sionaDy, however, a property may be something distinct from 
 the differentia that is not implied in it, as it is an essential 
 quality of a triangle that its three angles be equal to two 
 right angles ; but this property is not implied in the dif- 
 ferentia which distinguishes a triangle from other figures, 
 viz., three straight lines which enclose a space. Hence pro- 
 
 1 Difference does not occupy a distinct place among the predicables 
 of Aristotle, though it may be inferred from his category. See Organ. 
 Top. ch. iv. The division of predicables in the text was first fully 
 drawn out from his Topics, by Porphyry.
 
 C. H. 3.] FOEMAL BELATIOJT. 41 
 
 perty may be taken to be such essential attribute of the 
 species as is not employed for its differentia. 
 
 Since the difference and property of a species must be 
 essential to our conception of any of the individuals included 
 under its class, it is evident that their universality must be 
 co-extensive with it. They are, therefore, creations which 
 depend as much upon the mind's generalising faculty, as 
 genera and species, and are not improperly included with them 
 in the same category. It should, however, be observed, 
 as the mind is generally led to adopt that attribute as 
 the differentia which is most important to the end it has in 
 view, that which may constitute the property of a species 
 with one may form its differentia with another. Thus, in 
 naval science, the polarity of the magnet is the quality which 
 would be viewed as the differentia, while by those who 
 employ magnets for more expeditiously picking up bits of 
 iron, this might be regarded as a property, but the attracting 
 power of the magnet would constitute the differentia. 
 
 Any quality that does not enter into our conception of the 
 essence of a species, but may be absent or present, that 
 species continuing the same, is called an accident of the 
 species. Thus a man may be walking, or he may be a Ma- 
 hommetan. Of these two examples the former is called a 
 separable accident, because it may be separated from the in- 
 dividual; and the latter inseparable, for a contrary reason. 
 Every accident, however, must be separable from the species, 
 otherwise it would be a property. 
 
 It is very important here to observe, that no term can be 
 determined, to belong to any of these five universal predi- 
 cables unless it be specified of what it is to be predicated. 
 For example, the term " red" would be considered a species 
 with regard to colour ; a genus, in relation to the terms 
 " pink," " scarlet," &c. It might be regarded as the dif- 
 ferentia of " red rose," as a property of " blood," and as an 
 accident of " a house." Thus the power of resisting oxidi- 
 sation is an accident in reference to the term metal, but it is 
 a property of gold and several other metals ; and hence we 
 may infer that, in all cases, the differences or properties of 
 any lower species will be accidents in reference to the higher 
 class in which they are comprised.
 
 42 BELAT10N OF TEEMS TO EACH OTHEE. [B. I. 
 
 4. Extension and Intension. 
 
 By examining the relations which genus and species bear to 
 each other, and the different natures of the wholes by which 
 one is said to be included in the other, we shall distinguish 
 a very important law of abstraction. It is evident we 
 cannot detach any properties from a notion without extend- 
 ing the list of objects to which it is applied. Thus, if we 
 abstract from a rose those peculiar properties which consti- 
 tute its essence, and attend solely to those which it connotes 
 as a plant, we extend its application, before limited to 
 flowers with red petals, to the oak, fir, lichen, geranium, and 
 a countless variety of others. This view of a conception, re- 
 stricted solely to the number of objects it denotes, is called 
 its extension. But, in proportion as we extend the applica- 
 tion of a notion to denote -a greater number of objects, the 
 notion must necessarily comprehend fewer properties ; as in. 
 extending rose to plant we dropped petals, leaves, stamina, 
 and pistals, for vegetable growth, the only property we can 
 assign to plant. But as we narrow the sphere of a notion 
 the qualities which it comprehends proportionably increase. 
 As in restricting the term body to animal, we are obliged to 
 endue it with the qualities of life and sensation ; and if we 
 still further narrow it to man, we must comprehend reason 
 in the list. This view of a conception in relation to the 
 properties it connotes is called its comprehension. 
 
 Hence the comprehension of a notion is always in the in- 
 verse ratio of its extension ; the maximum of the one being 
 necessarily the minimum of the other. This arises from the 
 different nature of the counter wholes which these quantities 
 represent, the one comprising an assemblage of attributes, 
 the other of objects ; the one a concrete, the other an abstract 
 whole. Thus in the individual when the greatest number of 
 attributes is united, comprehension is at its maximum, and 
 extension at its minimum ; while in the most abstract notion 
 the mind can form, viz., that of being, extension is at its 
 maximum, and comprehension necessarily at its minimum, 
 since it only connotes the single attribute of existence 1 . 
 
 1 Bayne's translation of the Port Royal Logic, 2nd ed. note 17.
 
 C. H. 5.] FOBMAL BELATION. 43 
 
 5. Nature and Rules of Logical Division. 
 
 "When we enumerate all the co-ordinate species included 
 in a general term, or, in other words, when we state in full 
 all the objects which such term denotes, we are said to sub- 
 ject it to a logical division. Such a process is, in fact, identi- 
 cal with the statement of a conception in terms of its exten- 
 sion 1 . 
 
 Dr. Whately, with all deference to such high authority, 
 confounds, as it seems to us, the operation of narrowing a 
 term to certain attributes, with the statement of the objects 
 which are included under it, in calling the process by which 
 we obtain a logical division the reverse of generalisation 2 . 
 This can hardly be correct in the majority of cases; for 
 in that process we abstract not objects, but attributes of 
 objects. So that the inverted operation would lie in the 
 annexation of the abstracted attributes ; that is in the 
 narrowing a term to a smaller circle of objects, by in- 
 creasing its definitive properties. "We need hardly say that 
 such an operation is widely distinct from enumerating the 
 several kinds of objects denoted by a common term, which is 
 the main branch of logical division. Thus, body may be di- 
 vided into stone, plant, brute, man, and other things, which 
 form its co-ordinate species. In the same manner organised 
 substance may be divided into plant, brute, and man, which 
 are contained under its extension as subject parts. 
 
 This mode of division is regulated by rules. The first is, 
 that it be complete ; or in other words, that all the parts, or 
 members, must be exactly equal to the thing divided ; as even 
 and odd comprehend the whole extent of the term number, 
 there being no number which is not included under one of 
 these branches. It is a common error with the schoolmen to 
 assume an incomplete for a complete division ; and having 
 limited the subject to their own category, to argue as if the 
 thing discussed had no existence beyond it. The mistakes in 
 
 1 A conception, however, is capable of being divided into the quali- 
 ties which distinguish its co-ordinate species from each other. As 
 every animal is rational or irrational, every line is straight or curved, 
 every substance is organised or unorganised, material or immaterial, 
 &c. * Logic, p. 151, 7th ed.
 
 44 BELATION OF TEEMS TO EACH OTHEE. [B. I. 
 
 these cases appear to have arisen from taking terms in a contra- 
 dictory sense, which were only contrary ; and also from dealing 
 with subjects so vague and abstract as to defy human intelli- 
 gence to fix them by any exhaustive denotation. Thus, if 
 one divided spirit (in its rational sense) into human, angelic, 
 and divine, and discussed its properties as if restricted to the 
 beings whom those terms denote, his inferences concerning 
 them would be open to grave doubt in a philosophical point 
 of view, since we have no scientific data to confine the exist- 
 ence of such a principle to such tripartite sphere. Again, did 
 a philosopher divide men into ignorant and learned, or a theo- 
 logian into virtuous and vicious, a physician into diseased 
 and healthy, the least discerning would immediately perceive 
 that, if they dealt with these branches of their subject as in- 
 cluding the entire of the human family, a serious error would 
 be committed. For there is a certain medium of knowledge 
 which removes a man from the rank of the ignorant, though 
 it does not place him among the learned ; between virtuous 
 and vicious there is a medium state, to which we may apply 
 what Tacitus said of Gralba, " Magis extra vitia qiiam cum vir- 
 tutibits 1 ." For there are many who are excluded from vice 
 by the same inactivity which prevents them from doing good. 
 Between diseased and healthy there is the state of conva- 
 lescence and of the man ailing, and so with numerous others. 
 Ramus, to ensure obedience to this rule, reduced all division 
 to a twofold form, which should exhaust the subject at every 
 stage of the process. This form did not, as is expressly as- 
 serted by Reid and others 2 , originate with Eamus, but was 
 frequently employed by Aristotle 3 and the scholastics, when- 
 ever the subject seemed to invite its application. This divi- 
 sion proceeds upon the principle, that a term, along with 
 its contradictory, comprehends everything. Thus substance 
 may be divided into material and immaterial ; material into 
 organic and inorganic ; organic into percipient and non- 
 percipient ; and the repetition of the process, so as to carry- 
 on the subdivision to the required length, is called by phi- 
 
 1 Hist. i. 49. - See Keid's Analysis of Aristotle, art. Categories. 
 It is curious to observe a divine analysing an author whom he seems 
 never to have read. 3 The Stagyrite, however, condemns the proce- 
 dure as useless for scientific discovery. Anal. Post. ii. ch. 5 ; An. Prior, 
 i. ch.31.
 
 C. II. 5.] FORMAL EELATIOK. 45 
 
 losophers abscissio infiniti. Though this bifurcate division is 
 cumbersome, from the vast quantity of subdivisions to which 
 it leads, and also obscure, since it leaves us entirely in the 
 dark with regard to the properties of the most extensive 
 member of division, there are many cases in which it can be 
 turned to account in scientific discovery 1 . 
 
 The second rule which a logical division ought to observe 
 is, that the constituent members must exclude one another, 
 on the principle of the division which formed the logician's 
 point of departure. Thus, if a naturalist were to throw 
 light on the horse tribe by dividing them into Arabic, 
 French, English horses, racing horses, waggon horses, 
 grey horses, chestnut horses, cab horses, &c., no one would 
 give him credit for any distinct knowledge of his sub- 
 ject. Yet, ludicrous as this division may appear, there 
 are not wanting instances in which the greatest philosophers, 
 through losing sight of the mutual exclusion of the dividing 
 member on the ground of one unique principle of division, 
 have committed follies quite as absurd in the higher walks 
 of science. Thus Bacon, without any distinct point of de- 
 parture, divides motion into every conceivable kind that can 
 be presented to the eye 2 , or even entertained by the mind, 
 without any distinct idea of what he is aiming at, save a 
 loose cataloguing of every sort of motion on which a distinct 
 name could be fixed. In this way he enters into an elaborate 
 detail of motions of pressure, motions of coercion, motions of 
 liberty, motions of art, motions of union, motions of strife, 
 and a dozen other kinds of motions, equally homogeneous, 
 which, like the above ludicrous division of the horse tribe, 
 present no real difference in kind, and are capable of being 
 affirmed of the same subject. Some of Aristotle's divisions 
 are equally trifling and absurd 3 . 
 
 As any subject may be considered in a variety of ways, it is 
 
 1 As to what respect, see History of Logic, Ramus, p. 10. 2 Novum 
 Organ, book ii. app. 48. His division of methods, in the 6th book of the 
 De Augmentis, not much better. Bacon was endowed with a spirit 
 eminently nomenclative, which led him to throw every thing he treated 
 into tables; but though he continually reproaches the scholastics with 
 confounding the essential differences of things, he never ceases to 
 commit the same fault himself. 3 An instance of illogical divi-
 
 46 BELATION OF TEEMS TO EACH OTHER. [B. I. 
 
 necessary to understand the object we have in view in subject- 
 ing it to a division, and allow that to be our guide throughout. 
 Thus horses would be divided by an agriculturist according 
 to their uses ; by a naturalist, with reference to their tribes ; 
 but these two principles could not be introduced in the 
 same division without giving rise to confusion, by running 
 the dividing members into one another, and defeating the 
 object of logical division altogether. In like manner the 
 division of a library could not be undertaken without some 
 precise notion of the principle of the arrangement. If 
 books are to be divided according to their sizes, we under- 
 stand that folios will comprise one section of the subject, 
 and quartos and duodecimos two others. If the matter of 
 which they treat is to form the basis of the arrangement, all 
 know that history, fiction, theology, and the leading branches 
 of science, will form the prominent members of the division. 
 But should the language in which they are written be the 
 ground of the division, the dividing members are still more 
 obvious. 
 
 It is not necessary that the dividing members absolutely 
 exclude each other, but only in the point of view upon which 
 the division is framed. Thus writers of fiction may be divided 
 into poets, dramatists, and novelists; but the members of 
 such division, though mutually exclusive, as far as the kinds 
 
 sion quite as flagrant as either of those just given was furnished 
 by Watt, in that very part of his Logic written to guard his readers 
 against it: " Furnish yourself," said he, " with a rich variety of ideas ; 
 acquaint yourselves with things ancient and modern; things natural, 
 civil, and religious; things domestic and national; things of your native 
 land and foreign countries ; things present, past, and future; and above 
 all, be well acquainted with God and yourselves; learn animal nature 
 and the workings of your own spirits." To which he adjoins the very 
 sapient remark, that so complete an acquaintance with things in 
 general will be of very great advantage. To the success of Watt's 
 Logic, which is one of the most widely circulated books on the science 
 in the English language, may be ascribed much of the prevalent con- 
 fusion about logic. It is a bad compound of the worst parts of Locke 
 with the worst parts of Arnauld. Watt seems to have taken the chap- 
 ters on the Human Understanding and the Port Royal Logic as they 
 came to hand, and stitched them together, without caring how the 
 apocryphal d priori principles consorted with the crude experimental 
 notions, so as he made a book out of them. The elder Degerando sets 
 down this work as the text-book at Oxford.
 
 c. ii. 6.] 
 
 FOEHAL BELATION. 
 
 of imaginative writing are concerned, which is the principle 
 of the division, doea not imply that some poets may not be 
 novelists, or some dramatists writers of romances. 
 
 The reader will observe that division, in a logical sense, 
 has a far different signification to the separation of the com- 
 ponent parts of a thing which is its natural meaning. We 
 divide a flower into leaves, stamens, and petals, each of which 
 is much less than the whole ; but in the metaphorical sense 
 of the word which logic implies, each member of the division 
 is in reality greater than the whole, for we cannot assign to 
 the genus flower its constituent species rose, geranium, 
 tulip, &c., without expressing, in addition to the general 
 notion of the term, the peculiar differences which separates 
 one species from the other. 
 
 6. Examples of Division. The Categories and Predicdbles. 
 
 The most complete examples of logical division are fur- 
 nished by Aristotle, in his enumeration of everything that 
 can be made the subject or the predicate of a proposition, 
 and of all the possible relations which the subject and pre- 
 dicate can have to each other. The former class are de- 
 nominated categories or predicaments, and muster every 
 object of human apprehension under ten heads ; so that, as 
 every soldier belongs to some company, and every company 
 to some regiment, in like manner all the notions that enter 
 into the human mind have their place in one or other of 
 these categories, and by proper subdivision may be drawn up 
 in rank and file, and passed under review 1 . 
 
 Being. 
 
 Substance ( 
 
 Mode of sub- 
 stance. 
 
 Absolute. 
 Relative (4). 
 
 5 Matter i. e. quantity (2). 
 Form i. e. quality (3). 
 
 'Action (5). 
 Suffering (6). 
 Where (7). 
 When (8). 
 Posture (9). 
 , Habit (10). 
 
 We have given Sir W. Hamilton's distributions of the predica- 
 ments, as the most perfect that can be selected. See his edition of 
 Reid's Works, p. 687. A humorous illustration of the categories is 
 given by Cornelius to his pupil, Martinus Scriblerus. Cornelius was 
 forced to give Martin sensible images: thus calling up the coachman.
 
 48 DELATION OF TEEMS TO EACH OTHEB. [B. I. 
 
 This division, commonly known by the name of the five 
 predicables, expresses every conceivable relation of subor- 
 dination or co-ordination to which the forms of inference 
 necessarily subject these classes of predicaments. So far 
 our treatise on terms has hardly consisted of anything else 
 than an explication of them, as the following summary will 
 
 show: 
 
 Every predicable expresses either 
 
 The whole essence of the 
 subject i. e. species. 
 
 Or part of its 
 essence. 
 1 
 
 Or somethi 
 its es 
 
 Qg joined to 
 sence. 
 
 Genus difference. 
 
 Property. 
 
 Acci 
 
 dent. 
 
 Universal, but Peculiar, but Universal and Separable in- 
 not peculiar. not universal. peculiar. separable. 
 
 If, then, the predicaments present us with every intelligible no- 
 tion, the predicables reveal all the conceivable modes in which 
 these notions can be compared together. The categories deli- 
 neate the boundaries which intersect the vast region of human 
 knowledge ; the predicables state the result of those laws of 
 thought which lead to their discrimination. The one pre- 
 sents us with all the objects cognisable to human intelligence ; 
 the other, with all the forms which characterise the operations 
 of that intelligence in dealing with them. The one reveals 
 the compartments under which the phenomena presented by 
 nature may be arranged ; the other, the results of the appli- 
 cation of rational principles to the objects they represent. 
 By the union of both, the whole furniture of the human mind 
 is presented to us at one view, and the registry of all nameable 
 things in the universe and of the world-embracing mechanism 
 of thought brought within the compass of a nutshell. 
 
 he asked him what he had seen at the bear-garden? The man 
 answered he had seen two men fight for a prize: one was a fair man, a 
 sergeant in the guards; the other black, a butcher; the sergeant had 
 red breeches, the butcher blue ; they fought upon a stage about four 
 o'clock, and the sergeant wounded the butcher in the leg. Mark (quoth 
 Cornelius) how the fellow runs through the predicaments men (sub- 
 stantia), two (quantitas), fair and black (qualitas), sergeant and 
 butcher (relatio), wounded the other (actio et passio), fighting (situs), 
 stage (ubi), two o'clock (quando), blue and red breeches (habitus).
 
 C. III. 1.] TEEMS WITH EEGAED TO THINGS. 49 
 
 CHAPTER III. 
 
 TEEMS WITH EEGAED TO THINGS. 
 
 1. Formation of Distinct Conceptions a Part of Logic. 
 
 THUS far our design has been simply to register the dif- 
 ferent relations which any two terms assume when their 
 agreement or disagreement is to be ascertained ; but for the 
 comparison to terminate in a correct result, it is evident that 
 the terms themselves must be accurate exponents of the 
 properties for which they stand, and not as Bacon says, be 
 rashly abstracted from things. For instance, suppose it 
 required to be known if the quality spontaneous may be 
 affirmed of the motion by which air rises out of water, it is 
 necessary that the word spontaneous should imply some 
 distinct property, and that the phenomenon denoted by the 
 aqueous motion of air should be completely understood 1 . 
 This part of the subject, viz., the obtaining clear concep- 
 tions of the terms which are brought into contrast, is obvi- 
 ously the first step, and the one most decisive in the investi- 
 gation of truth. Without it the most perfect accuracy in 
 the subsequent processes will but propagate error, so that 
 we can only expect to be right by accident 2 . Tet writers 
 on the scholastic logic relegate this branch of the subject 
 from the science as something extraneous to its object, as if 
 the operation of abstracting notions from things was not as 
 necessary to the establishment of correct conclusions, as a 
 knowledge of the relations which such notions can bear to 
 each other, and the laws of inference to which they lead. 
 The warmth with which this view of the science has been 
 maintained, has driven Bacon and his followers into the 
 opposite error of depreciating the scholastic rules and nar- 
 rowing the entire scope of the science to the formation of 
 
 1 However obvious the remark may appear, the neglect of it in the 
 illustration alluded to, led Aristotle to lose sight of the fact that air 
 was forced to the surface by the pressure of the water beneath, and to 
 assert that the motion was the effect of the air seeking to join its own 
 element. 2 See Bacon's distribution of the great instauration, and 
 the preface to the Novum Organum, with note upon the context. 
 (Bohn's Scientific Library.) 
 
 B
 
 50 TEEMS WITH REGABD TO THINGS. [B. I. 
 
 correct and appropriate conceptions, and the inductive gene- 
 ralisations built upon them. We, however, instead of per- 
 ceiving any antagonism between the two systems, think 
 that they so far coalesce as to form correlative branches of 
 the same science. What opposition can there be between 
 the operation which abstracts notions from things, and that 
 which establishes the different modes in which such notions 
 are contrasted together? The same mental faculty is 
 evidently at work in both cases, and though on different 
 objects, with the same view, viz., the eliciting truth out of 
 the material presented to the judgment. In the first case, 
 the mind is employed in fitting notions to objects ; in the 
 second, in fitting notions to each other. With much more 
 reason might the craft of the stonemason, which is the 
 preparation of stones for building, be viewed as something 
 directly obstructive to the process of laying stones on each 
 other, to which it is a necessary preliminary. In fact, 
 the very subject-matter which each party claims as the 
 peculiar province of their own view of the science, show 
 that the ground is common between them. For what is the 
 purport of a real definition in the scholastic sense but the 
 adaptation of notions to convey the correct properties of 
 things? And what principles does the physicist put into 
 requisition in seeking the same object, but those involved 
 in the rules of scholastic definition. 
 
 Though the distinct conceptions is undoubtedly a part, 
 and no small part, of logic, it has its boundaries, which it 
 will be well not to go beyond. In the first place, it is not 
 our province to treat of the mechanism of the formation, viz., 
 whether objects are directly perceived by the mind, or whe- 
 ther they convey impressions thereto by sensible or spiritual 
 images, or whether such impressions are only modifications 
 of the percipient mind ; nor is it our business to enter into 
 the origin of abstract ideas, and consider how far they are 
 conceptions of general properties, or generalisations from 
 individual groups, or in what light their existence may be 
 considered as restricted to the human mind, or as existing 
 in that of the divine artificer ; for all these questions involve 
 metaphysical theories, concerning which the greatest minds 
 have differed, and are quite extraneous to logic, which deals 
 with principles about whose cogency there cannot be the
 
 C. III. 2] WHAT TEEMS ABE INDISTINCT. 51 
 
 slightest doubt. With that branch of the formation of con- 
 ceptions we have to do, not which treats of the mechanism 
 of our conceptions, but of the principles and rules by which 
 their trustworthiness may be ascertained, as exponents of 
 clear and definable objects. But since this view is so ex- 
 tensive as to embrace, in some measure, the entire scope 
 of logic 1 , it will be necessary to limit it at this stage to 
 that part of the process which concerns the mere obtaining 
 materials for inference. We shall therefore, at present, con- 
 fine ourselves to pointing out the characteristics of distinct 
 and indistinct conceptions ; the leading sources, including 
 language, from which such marks arise, and how far defini- 
 tion confirms those which are clear, while it disperses un- 
 settled or indistinct connotation. 
 
 2. What Class of Terms are liable to Indistinctness. 
 
 And here it is necessary to refer to our distinction between 
 the denotation and connotation of names as fundamental 
 to the subject. It is evident when we point out any special 
 object, as this book, that table, we imply i. e. connote, 
 no peculiar properties proposed by that object, but merely 
 point out i. e. denote, the thing itself. Hence all singular 
 names, with few exceptions 2 , or general names used in a 
 singular sense, being employed not to convey information 
 concerning the objects they denote, but simply to point them 
 out as things towards which the attention is directed, never 
 
 1 Genovesi correctly remarks that all reasoning is nothing else than 
 the dispersion of what is confused and indistinct in a term by that 
 portion of it which is defined and clear. Hence, if some limit was not 
 introduced in the exposition of terms, it would absorb the entire field 
 of logic. The boundary drawn in the text is taken from Whately 
 (book ii. ch. i. note). But Reid (see his Hist. Arist. Organ, p. 686, in 
 the recent edition of his works by Sir W. Hamilton) is disposed to 
 allow no place to terms in logic at all, only with a view to, and so far 
 as is necessary, to the explanation of propositions, and these latter 
 again only so far as is indispensable to the knowledge of the syllogism. 
 But this distinction, however consonant to a system of formal logic, is 
 too wire-drawn for the purposes of practical utility. 3 The conno- 
 tative individual names alluded to are sun, God, or such as from the 
 form of expression lead to the implication of some attribute ; as the 
 first King of France, or the present Chancellor of the Exchequer; 
 yet the latter names are used generally in a strictly denotative 
 sense. 
 
 2 

 
 52 TEEMS 'WITH EEGAED TO THINGS. [B. I. 
 
 fail to attain their object, and can be in no instance the cause 
 of confusion in our judgments. They involve no abstraction 
 of words from things, no wrapping up of multiform pro- 
 perties in one expression, like individual complex or concrete 
 general terms, and, therefore, do not require any elucidation 
 at the hands of the logician. There is another class of terms 
 equally exempt from notice in this place ; viz., those which 
 are abstracted from one branch of the concrete general 
 terms we have mentioned, as rationality from rational, 
 corporeity from corporeal, whiteness from white, because 
 they do not generally connote any attribute distinct from 
 the abstract name they denote ; or, if they do in some in- 
 stances, it is only as names restricted to an individual sense 
 simply by virtue of the process by which the general concrete 
 term is formed. It is, therefore, on individual complex and 
 general concrete terms alone that the attention of the 
 logician must be concentrated, as the central points of con- 
 fusion in erroneous judgments, since connoting several pro- 
 perties, they are liable to be imperfectly known, and not 
 only seen in partial lights, but connected with objects with 
 which they can have no relation. Thus iron, one of the 
 simplest of this class, conveys a widely diflerent notion of its 
 properties to one who has heard of magnetism than to 
 another in a contrary predicament. The vulgar who regard 
 this metal as incombustible, and the chemist who sees it 
 burn with the utmost fury, and who has other reasons for 
 regarding it as one of the most combustible bodies in 
 nature ; the poet who uses it as an emblem of rigidity, 
 and the smith and engineer in whose hands it is plastic 
 and moulded like wax into every form ; the jailor who 
 prizes it as an obstruction, and the electrician who sees 
 in it only a channel of open communication, by which that 
 most impassable of all objects, the air, may be traversed by 
 his imprisoned fluid, have all imperfect and some conflicting 
 notions of the word 1 . And so it is with other complex 
 terms ; some are indefinite, as hard or soft, light or heavy, 
 and others so intricate, as life, matter, instinct as to mock 
 every attempt of science to unfold their entire connotation. 
 
 1 Sir John Herschel, Discourse on the Study of Nat. Phil. p. 20.
 
 C. III. 3.] HOW CONCEPTIONS BECOME DISTINCT. 53 
 
 3. How Conceptions become Distinct and Confused. 
 
 Though this class of terms are, in the generality of in- 
 stances, formed for us, and in no case do we create them 
 except in discovering or combining new truths, it is hardly 
 possible for us to attain any clear insight into the causes of 
 their distinctness or ambiguity but by analysing their com- 
 position, and closely watching their growth in the mind. To 
 commence with some of the simplest examples, it is evident 
 that the word man implies an assemblage of properties, which 
 the mind, through the faculty of abstraction, has first de- 
 tached from the accidental qualities of the individual, and 
 then bound up into a conception which equally represents 
 any member of the human family. Each of the properties 
 which form the aggregate of the conception are known, and 
 possess marks which not only discriminate it from others, 
 but lay open its own nature and constitution. The notion 
 man is, therefore, called clear and distinct, since we know all 
 its properties, viz., rationality, corporeity in a certain shape, 
 animal life, &c., and can, upon a minute survey, adduce the 
 marks by which these properties are so constituted. Take 
 another instance, that of matter. This term also implies a 
 congeries of properties, some of which are as distinctly ascer- 
 tainable as those included in the last example. It is evi- 
 dently an extended substance, composed of divisible particles, 
 which are constantly undergoing change according to regular 
 laws ; but we can scarcely predicate further concerning it 
 with safety. It has its accidental as well as its essential 
 qualities, and, to a certain extent, these can be pointed out. 
 For example, it must be extended, though this may occur in 
 any diversity of form. Colour and shape are alike indifferent 
 to it. It may be animal, vegetable, or mineral ; but it would 
 be hazardous to range its gravitating property in the same 
 category to call it essentially inert, or deny its incompetency 
 to be invested with the attribute of thought. Hence our 
 notion concerning its leading properties are incomplete, and 
 to predicate anything of them with dogmatic certainty would 
 only expose us to error. We know, however, sufficient of its 
 properties to distinguish it generically from mind, and to divide 
 it into many subordinate species. The notion is clear since
 
 54 TEEMS WITH EEGAED TO THINGS. [B. I. 
 
 it communicates a distinct conception of its object, but im- 
 perfect or inadequate to realise everything that it contains. 
 
 It is evident that such examples could be enlarged until 
 they embraced the entire gradations of clearness and indis- 
 tinctness in ideas ; and though the boundaries fade by im- 
 perceptible degrees into each other, philosophers have deter- 
 mined the classes, which they divide with sufficient precision 
 to assign to them the marks by which they may be distin- 
 guished. On examining, however, any of their tables, we 
 find only one generating principle of the degrees of clearness 
 or indistinctness they contain viz., the capability of resolv- 
 ing any subject that may present itself into its constituent 
 elements, and decomposing these until the elements of their 
 elements can also be resolved, and we arrive at the simplest 
 analysis. Thus, the classification of Leibnitz 1 , which is the 
 most popular, will tell us that those notions are most ob- 
 scure whose qualities are so impalpable that we cannot dis- 
 tinguish them from others ; that confused notions, though 
 they admit of such clear discrimination, are perfectly inso- 
 luble with respect to their own nature, while those ideas can 
 only claim the privilege of being distinct and adequate whose 
 properties can be resolved into others whose natures are 
 known 2 . Now this is only a more particular way of stating 
 the general proposition that notions are clear and appro- 
 priate to the objects which they represent in proportion as 
 they unfold their specific properties. 
 
 4. Double Mode of Resolving Conceptions. 
 The general principles which preside over the process is 
 ordinarily pointed out by the source from which bur con- 
 ceptions arise, there being a wide difference between the 
 determination of ideas which refer to sensible objects and 
 those which represent spiritual and abstract ones. It is evi- 
 
 1 Opera Philosophica. Erdman, p. 79. Opera Omnia Dateus, ii. 
 p. i. p. 14. First published in the Acta Eruditorum, 1681. 2 If 
 the elements into which an idea can be resolved are unknown, Leibnitz 
 terms it inadequate. His classification will consequently stand as 
 follows: 
 
 Notion, 
 
 Distinct. Adequate, 
 
 Inadequate.
 
 C. HI. 4.] DOUBLE MODE OF BESOLYING CONCEPTIONS. 55 
 
 dent that, with regard to objects of sense, the accuracy of 
 our notions will depend much upon the results of experience ; 
 while the nature of those which refer to subjects purely ab- 
 stract and spiritual, must be sought from inferences struck 
 out of the primordial elements of the mind. The sources of 
 the first are simple facts derived from objects alien to the in- 
 tellect, through the channel of sensation ; those of the second 
 are pure cognitions, either intuitive or obtained by formal 
 inference, from principles bound up with the nature of the 
 mind itself, and forming part of its constitution. Now, the 
 method of obtaining accurate conceptions of material phe- 
 nomena is either by analysing or dissecting the facts to 
 which they refer, and seeking to educe out of the points of 
 resemblance and difference some determinate notion of their 
 elementary properties ; or by forming such hypothesis as 
 appear to suit the circumstances of the case, and then test- 
 ing its legitimacy by using such verifications as the nature of 
 the phenomena admit. The mode of gaining an adequate 
 knowledge of the second is, by tracing their growth in the 
 mind and fixing their accordance with the intuitive prin- 
 ciples out of which they spring. 
 
 If we confound the principles according to which each of 
 these two classes of ideas are invested with distinct appro- 
 priate connotative powers, our subsequent judgments are 
 certain to be false in the precise proportion of their accu- 
 racy ; or, in other words, we can only expect to escape from 
 the consequences of the wrong conceptions we have formed 
 by a counter error in contradicting or affirming them of each 
 other. Thus, when Aristotle, induced by the abstract per- 
 fection of circular motion was led to assert that all the 
 planets moved in perfect circles, he falsely applied, without 
 looking at his facts, an ideal conception to account for a cer- 
 tain mode of their existence, and could only escape from the 
 consequences of this misconception by mistakes in his subse- 
 quent deductions ; or when Bacon restricted the summum 
 bonum to the subjection of the individual will to that of the 
 community 1 , he applied a principle founded upon experience, 
 to explain an idea which, being purely native to the mind, 
 no facts can reveal to us, and thus gave rise to a false sys- 
 tem of ethics 2 . 
 
 1 De Augmentis, b. vii. ch. 2. The utilitarian philosophy.
 
 56 TEEMS WITH. EEGABD TO THINGS. [fi. I. 
 
 The application of abstract principles, whether real or 
 supposititious, which cannot be brought to the touchstone of 
 facts, to explain the properties of natural objects, has been 
 one of the great sources of all the errors which have hitherto 
 obstructed the progress of physical science. While the 
 phlogistic doctrines of Becher and Stahl were assumed to 
 account for all the phenomena of chemistry, no attempt was 
 made to bring the objects of that science to the test of ex- 
 perience, and connect them with number, weight, and 
 measure. While the notion that nature abhors a vacuum 
 was accepted as a perfect explanation of the rise of water by 
 suction, no essay was tried to determine the properties of the 
 air ; and while the geometrical conceptions falsely attributed 
 to the circle were deemed sufficient to determine the relation 
 of forces in the lever, the principles of mechanics could not 
 assume a rational basis. 
 
 Though the contrary error of introducing empirical prin- 
 ciples into moral subjects, and of seeking to resolve happi- 
 ness, integrity, and similar ideas into the results of mere 
 outward experience, is less palpable, it has been at the 
 bottom of all the errors connected with false systems of 
 ethics, politics, and theology. Hobbes, for instance, when he 
 resolved the idea of natural right into brute force, was neces- 
 sarily led to frame a system of government which, if practi- 
 cally carried out, would have transformed a subject into a 
 slave, and a king into a despot. When Hume, in like manner 
 traced all our notions of virtue and vice to the experience of 
 the effects which society feels from their influence, he founded 
 a system of ethics on an empirical principle, which completely 
 subverted the moral nature of actions, and made adultery in- 
 trinsically as innocent as going to church. Machiavelli 
 could not restrict himself exclusively to the past in drawing 
 out fundamental maxims of political wisdom, without im- 
 pugning some of the plainest instincts of justice ; nor could 
 Mahomet, or any of the Grecian seers, frame a system of 
 religion to flatter the results of man's sensible experience, 
 without introducing depravity into Olympus, and making its 
 denizens the mere roues of pleasure 1 . It is obvious that 
 
 1 Thus Plato's doctrine of ideas, as an Oxford logician (Mr. Karslake) 
 correctly remarks, is perfectly true on the side of moral truth, but he 
 unhappily extended his doctrine to truth at large, and hence all the
 
 C. HI. 4.] CONSEQUENCE OF EBBOKEOUS METHODS. 57 
 
 the greater part of the conceptions to which these subjects 
 relate being written on the heart of man, cannot possibly be 
 ultimately based on experience, and to attempt exclusively to 
 extract them from the latter source while we leave their true 
 fountain unsealed, tends to disenchant man of his high con- 
 ceptions, and, even when not practically carried out, to lower 
 art, and in a proportionate degree to degrade his being 1 . 
 
 Conceptions, when so applied to unfold the properties of 
 objects which exist in an entirely different sphere, may be 
 properly denominated false ; but there is a class which, 
 though as fruitful in erroneous judgments as the ones to 
 which we have adverted, arises from a superficial examination 
 of the properties they would connote. Thus Aristotle, when 
 examining the subject of motion, for once drew his attention 
 from abstract principles to concentrate it on the facts he 
 sought to explain ; and perceiving that bodies fell to the 
 ground as it were spontaneously, and that flame appeared to 
 ascend, and bubbles of air to arise in water by the same 
 means, he called such motions natural, as they all seemed to 
 arise from a spontaneous movement of each body towards its 
 own place, in order to mingle with their kindred element : 
 while other motions never occurred without the impress of 
 an external force, and when reluctantly set in action always 
 manifested a disposition to cease. On comparing these motions 
 with each other, he found they also agreed in one property 
 quite opposite to the former viz., that of motion from their 
 own place ; and denominating the latter violent in contradis- 
 tinction to the former, he flattered himself he had rendered 
 a complete and satisfactory account of the matter. Now had 
 Aristotle only extended his list of motions apparently spon- 
 taneous, to include that of the earth and the planets ; or to 
 that of a fog rising from a lake when the motion takes place 
 
 empiricists were ui arms against him ; while Aristotle's doctrine of 
 the experiential origin of every idea was perfectly true of the physical 
 sphere ; since there is no idea of man in our mind beyond what is ob- 
 tained by abstraction and generalisation from external nature. But 
 he extended his doctrine to universal truth, and denied that goodness or 
 virtue was an idea in any other sense than a generalisation from past 
 experience, and hence the outcry against him of all who were anxious 
 for the immutability of moral truth. > The general methods and 
 
 rules for developing these two classes of conceptions will be given in 
 the fourth book. See Analysis and Synthesis.
 
 58 TERMS WITH REGARD TO THINGS. [B. I. 
 
 in a contrary direction to what his theory would indicate; 
 and had he submitted his instances of spontaneous motion to 
 minuter examinations, and discovered that many like the 
 bubbles of air, for instance did not rise of their own accord, 
 but impelled by the force of the stronger element with which 
 they were in contact ; he would also have discovered that his 
 terms natural and violent only connoted a superficial sem- 
 blance of agreement, and must therefore be deemed inac- 
 curate. 
 
 5. Tests of Accurate Conceptions. 
 
 Even in the rigid analysis of phenomena with a view to 
 the formation of distinct and adequate conceptions, we may 
 fail to attain our object by relying too exclusively either 
 upon sensation or the spontaneous processes of reason. In 
 the latter case we must cross-examine our consciousness, 
 view the objects which it presents us with in every light, 
 connect them in gradual sequence with higher truths, test 
 their accuracy by multiplied and diverging threads of argu- 
 ment, and, in all cases where such a procedure is possible, 
 verify them by a direct appeal to facts. We must appeal, 
 in the former, from sensation in its causes, set one sense 
 against the other, and bring their testimony, in all cases 
 where it is feasible, to the test of accurate measurements 
 and quantitative laws. If we referred, like Lord Bacon 1 , 
 only to sensation as an indication of the presence of heat, 
 we should be greatly deceived, since many of those things 
 which excite in our organs, and especially of those of taste, 
 a sensation of heat, owe this property to chemical stimu- 
 lants, and not at all to their being hot. Again, there are a 
 number of sensations, which, by a wise arrangement of Pro- 
 vidence, are made to refer their seat of action from the mind 
 to the parts of the body where they first occur, though the 
 contrary is the fact. Thus, for instance, the painful sen- 
 sation we experience in the hand or the foot, when fire or 
 steel lacerates them, is nothing else than a feeling of aversion 
 which the mind conceives at some movement in those parts, 
 contrary to the natural constitution of the body. The con- 
 
 1 NOT. Org. b. ii. table 2 (29, 30), &c.
 
 C. III. 5.] OBSERVATION AND EXPERIMENT. 59 
 
 ception of colour, as something inherent in an object, like its 
 weight, hardness, &c., so that it would be impossible to see 
 the object apart from its colour when nothing intervenes 
 between the eyes, and it seems perfectly rational and obvious 
 by the evidence of vision ; yet we need only expose the 
 object in a dark room to the different coloured prismatic 
 rays, to invest it with any particular colour we please, and 
 thus convict sight on its own evidence. 
 
 It was mainly to the want of a knowledge of experiment 
 as an assistant to the analysis of natural phenomena that the 
 ancients failed to obtain that command of clear and appro- 
 priate conceptions which have led to the formation of the 
 physical sciences, and marked the successive stages of their 
 growth. They failed to discover the laws of mechanics, 
 because they had no clear ideas of pressure, resistance, 
 momentum, and uniform and accelerating force ; but the 
 absence of such conceptions must be attributed to their 
 slight of experiment, or their neglect to trace the principles 
 of equilibrium and motion, by producing those phenomena 
 under circumstances of sufficient variety to reveal their laws. 
 In like manner the tardy development of optics, electricity, 
 magnetism, mineralogy, and the higher generalisations of 
 chemistry, may be ascribed to the absence of any concep- 
 tion of polarity, men contenting themselves with expressing 
 wonder at what they deemed capricious freaks of Nature's 
 workmanship, instead of ransacking her laboratory with a 
 view to discover kindred phenomena, and to bind them up 
 in one conception, which should connote their peculiar pro- 
 perties, and serve as a new kind of intellectual sense in 
 leading to more wonderful discoveries. 
 
 It may, however, be observed, that it is not essential to 
 the clearness of a conception that we should know all the 
 properties of the things we class together. That would be, 
 as Stuart Mill correctly observes, to have our conceptions of 
 the class complete as well as clear. It is sufficient if we 
 never use a conception without having ascertained what 
 attributes it is intended to connote, and in virtue of what 
 properties its component parts are bound together. For 
 the rest, if we never strain a conception to mean more than 
 our knowledge of the properties which it connotes implies, 
 OP introduce it into a sphere foreign to its application ; if we
 
 60 TEEMS IN RELATION TO SIGNS. [B. I. 
 
 reject all those which are too vague and indefinite to admit 
 of determinate extension and intension, and endeavour by a 
 strict analysis, pursued in the spirit we have pointed out, to 
 invest those which only are distinct enough to bear a logical 
 determination with a distinct connotative character 1 , our 
 progress may be slow, but the ends of logic will be gained, 
 in securing the preliminary operations of reasoning from 
 error. 
 
 CHAPTEE IV. 
 
 CONCEPTIONS IN EELATION TO SIGNS. 
 
 1. Use of Language in Logic. 
 
 THOUGH our ideas are mainly acquired though the medium 
 of sensation and reflection, we should find ourselves at a loss 
 to preserve the more general and complex ones in a perma- 
 nent form, or to convey them to others, without assigning^to 
 each a peculiar mark or name by which it might be distin- 
 guished. With regard, indeed, to individual objects which 
 have no connotative meaning, or those whose properties are 
 bound up with sensible objects, and depend on no abstract- 
 ing faculty for their formation, verbal signs would be hardly 
 necessary to this end, inasmuch as the appearance of the 
 objects themselves would awaken their respective ideas in 
 the mind; yet even in these instances, which comprise a 
 very small class of the conceptions employed in ordinary 
 language, a sign is imperatively necessary to recal the idea, 
 in the absence of its object to the mind of others, and to 
 reason about it in conjunction with those of purely abstract 
 formation in our own. 
 
 1 The words in the text have reference to the double capacity of 
 conceptions, which have been called by Sir W. Hamilton the cardinal 
 point of logic. They may be expressed as follows : 
 
 A conception viewed as a 
 
 logical whole, metaphysical whole, 
 
 has has 
 
 extension, intension or comprehension, 
 
 breadth, depth, 
 
 sphere, matter, 
 
 objects, marks, 
 
 power to denote. power to connote.
 
 C. IV. 2.] FUNCTIONS OF LANGUAGE. 61 
 
 The importance of language, however, as an instrument 
 of thought, rises in proportion to the degree of abstracting 
 power with which each individual is invested ; savage tribes 
 and semi-civilised people requiring it very little, while nations 
 of any pretension to refinement find its application on an 
 extensive scale essential at every step, not only as a means 
 of intellectual progress, but to maintain them in their actual 
 position. Barbarous tribes, and even a large mass of the un- 
 educated people of civilised communities, seldom lift them- 
 selves above individual objects, and in their inferences com- 
 monly creep along the ground of particulars. Hence, in 
 their reasoning, nothing is required unless association to 
 suggest ideas and sense to perceive their congruity or dis- 
 agreement ; a mode of inference of which brutes are capable, 
 though in a less degree. But with men who deal in large 
 generalisations, language is peremptorily required to fix the 
 complex ideas to which their minds have attained in com- 
 paring classes of particular truths, and to enable them, by 
 combining a wide range of properties in one expression, to 
 start anew from groups of comprehensive details, as if they 
 were so many particular facts, in order to reach still more 
 extensive generalisations. 
 
 2. Errors to which the Formation of General Terms are 
 liable. 
 
 But if language is thus essential to scientific reasoning, 
 in clenching the results of the mind's abstracting power, it 
 must be said to accomplish this at no ordinary sacrifice, since 
 it introduces into the sphere of its operations all the confu- 
 sion to which vulgar conceptions, the caprices of custom, and 
 the revolutions of the outer world, give rise. Unless in 
 matters of physical science, where the formation of general 
 terms is exclusively in the hands of professional guides, such 
 names generally owe their origin to the vulgar, who, struck 
 with a confused feeling of resemblance between several 
 objects, combine them in one expression, without exactly 
 knowing the common properties which their appellation is 
 designed to connote. Take the word civilised, for instance. 
 Having observed that men who live in cities agree in the 
 possession of certain marks of refinement which the denizens
 
 62 TEBM8 IN BELATION TO SIGNS. [fi. I. 
 
 of forests do not manifest, they call the former civilised, 
 though without knowing exactly in what the essential mean- 
 ing of the word consists, or the number of properties which 
 is required to justify its application. Hence no two persons, 
 even among the most educated, would be found to agree in 
 determining the limits of this word, or its abstract civilisa- 
 tion, and when it is predicated of anything no other person 
 knows, and even the speaker himself is ignorant of the pre- 
 cise objects he means to assert. Every person need only 
 examine the vocabulary of general names he is in the habit 
 of using, as beauty, greatness, honour, and gentleman, to 
 discover a host of others which exemplify this uncertainty in 
 a still more striking manner. 
 
 Even with names whose connotation is less exposed to 
 cavil, being determined with precision by men of accurate 
 habits of thought, or marked out by our common instincts, 
 much confusion may originate by the fluctuations of belief 
 and opinion, which fling the mind upon new modes of thought, 
 and unfix its old creations. The word piety was doubtless 
 applied by the ancients to denote that class of actions which 
 took place in conformity with the moral law, and the pre- 
 scribed usages of their religion. With Christians, a stigma 
 would be fixed on the majority of cases to which they applied 
 the name. The same term in the writings of a Pagan phi- 
 losopher we could hardly take upon ourselves to determine 
 until we knew the school to which he belonged ; while the 
 sense which the modern divine attaches to it agrees with 
 none of those schools, and the meaning this word bore in the 
 mouth of French society at the close of the eighteenth 
 century conflicts with all. 
 
 "When such names become connected with philosophical 
 doctrines or habits of belief which men choose to uphold as 
 the fundaments of truth or the arbiters of their destinies, the 
 contests to which they either give rise or serve to aggravate 
 are innumerable, and become too much interwoven with the 
 feelings to be settled by the rules of the mere logician. What 
 acrimonious disputes have arisen among modern polemics 
 about the respective merits of faith and works, which, had 
 they only reflected that the scholastic theology employed the 
 former term only to express a simple act of belief, would 
 never have taken place. Some controversialists, seeking to 
 resolve such disputes by having recourse to the derivation of
 
 C. IT. 3.] TEANSFOBMATIOK OF TEEMS. 63 
 
 the word, regard a bishop as a sort of moral inspector, be- 
 cause the original Greek word fnia-Ko\os signifies to over- 
 look. They might as well call a policeman an apostle, because 
 he is sent forth (aTroo-reAAeti'), or the church an assembly of 
 democrats, because exXijo-ta was used by the Greeks to de- 
 signate a popular meeting. 
 
 3. Confusion arising from the Transitive Application of 
 Words. 
 
 It is one great law of association of ideas that leads man- 
 kind to fix the same term to a congeries of objects, some of 
 which have nothing in common, though they may be con- 
 nected by a confused feeling of resemblance in the interme- 
 diate links which led to the adoption of a common term. 
 Thus, as Dugald Stewart observes, if we allow A, B, C, D, E, 
 to denote a group of objects, in which A possesses some 
 quality in common with B, and B a quality in common with 
 C, and C with D, &c., while no quality can be found in com- 
 mon with any three objects in the series ; the affinity between 
 A and B may produce a transfer of the name of the first to 
 the second ; and that in consequence of the other affinities 
 which connect the remaining objects together, the same name 
 may pass in succession, though the intermediate links from 
 A to E, and a common appellation be affixed to both of those 
 objects, though they may widely differ in their nature and 
 have not one property in common. When the association is 
 slight and casual the several meanings will remain distinct 
 from each other, and assume, in process of time, the appear- 
 ance of capricious varieties in the use of the same arbitrary 
 sign ; but where the association is so natural as to become 
 virtually indissoluble, these transitive meanings will coalesce 
 in one complex conception, and every new transition will be- 
 come a more comprehensive generalisation of the term in 
 question 1 . 
 
 This law, in its last result, has been the source of infinite 
 confusion in reasoning, since it generally gave rise to the be- 
 lief that the general name thus established connoted a com- 
 mon property among the objects it designated, and led grave 
 philosophers into the chimerical search of finding it out. The 
 endeavours of Plato to abstract the essential properties of the 
 
 1 Philosophical Essays, 226, 27.
 
 64 TEEMS IN EELATION TO SIGNS. [B. I. 
 
 good, the fit, the becoming, from a crowd of dissimilar objects, 
 though furnishing perfect examples of the preliminary pro- 
 cess to induction, was really so much heating of the air, since 
 the phenomena whose common properties he attempted to 
 discover had really no common properties at all ; and Aris- 
 totle's attempt to trace the common idea, which in the case 
 of any effect belongs to the efficient, to the matter, to the 
 form and to the end, with Bacon's inquisition into the nature 
 of heat, must be placed in the same category. In each of 
 these cases the above philosophers, led astray by the confused 
 generalisations of the vulgar, which they unsuspectingly ac- 
 cepted as something real, wasted an infinity of sober calcu- 
 lation to reach a definition which should serve for several 
 distinct meanings at once, and classify objects which had no 
 property in common. 
 
 4. Twofold Law of the Transformation of Names. 
 
 But in a greater degree than mental law, custom is a great 
 arbiter of language, and tends to confuse the ideas they de- 
 note, either by completely changing the signification of 
 words, or widening and contracting their logical or meta- 
 physical sphere. The first case may be exemplified in the 
 word Pagan, originally equivalent to a villager*, but which,, 
 from having been used in the fourth century of the Christian 
 era to denote the country-people among whom the old my- 
 thology still lingered, came gradually to suggest the idea of 
 a worshipper of the old divinities, until the additional pecu- 
 liarity of their residence being also wiped out, the term sug- 
 gested nothing else. In the same manner villain, which in 
 the middle ages signified a serf of the soil, came to imply, 
 after serfdom had been abolished, all the hateful qualities of 
 crime and guilt by which many of that class had been distin- 
 guished. 
 
 These cases, however, are extreme instances of a move- 
 ment of generalisation continually going on in language, and 
 are not likely, when the new meaning is completely evolved, 
 to generate confusion ; it is only in the transition state, 
 when two or three distinct conceptions are floating about 
 a name, or when words are extended to fresh classes of objects 
 
 1 From the word pagus, a village.
 
 C. IV. 5.] LOGICAL DEFINITION. 65 
 
 without sufficient discrimination between the old connota- 
 tion and the new cases to which they begin to apply, that 
 any error is to be dreaded. The phrase landed proprietor, 
 for instance, with the first English conquerors of our East 
 Indian settlement, would have led to no error had it recast 
 its connotation at the same time that it extended its sphere. 
 It was the application of the term in its old signification to 
 fresh cases, which the framers of that signification had never 
 contemplated, that led the conquerors of Bengal, by con- 
 founding limited with absolute rights, to drive whole classes 
 of men to ruin and despair, to fill the country with banditti, 
 and to produce, with the very best intentions, the disorgani- 
 sation of the country. 
 
 A counter movement to the generalisation which custom 
 produces in language, may be witnessed in such terms as 
 loyalty, when the original meaning becomes specialised. 
 That word was accustomed to signify fair, open dealing, as it 
 indeed still means in French, whence it was imported ; 
 whereas it is now restricted to the single case of fidelity to 
 the throne. This tendency to use general words in a re- 
 stricted sense is much increased as civilisation advances, 
 owing principally to the growing habit the refined manifest 
 to keep the disagreeable aspect of things as much out of sight 
 as possible, and to speak of objects which give rise to any 
 unseemly ideas, so as to convey the faintest suggestion of 
 their characteristic qualities. The effect, however, of this 
 law is not so much to unfit a language for the purposes of 
 accurate discrimination, as to render its general terms un- 
 steady exponents of their old meanings, and to leave the par- 
 ticular ones whose places they have invaded to fall into 
 desuetude and decay. 
 
 5. Logical Definition. 
 
 To remedy the errors to which the mind is exposed from 
 the fluctuations of language, as also more distinctly to realise 
 and determine the nature of its conceptions, recourse is had 
 to definition that is, a mode of laying down their exact 
 boundaries, and marking each by so essential a feature of its 
 nature as shall imply all the properties it connotes. The 
 logical rule for this purpose is to express the object whose
 
 66 TEEMS IN RELATION TO SIGNS. [B. I. 
 
 definition is sought in terms of its proximate genus and 
 difference. Every conception capable of entering the mind 
 Aristotle 1 , as we hare seen, ranged under the head of one of 
 his ten categories, and when he wished to hunt out, as 
 he called it, the essential nature, or, according to Albertus 
 Magnus, the quiditas of a thing, the enunciation of whose 
 nature constituted its definition, he divided the head of the 
 category in which it was included into its subaltern genera 
 until he reached the one under which the object before him 
 was contained, and this last genus, along with the specific 
 difference by which it was divided, constituted its logical 
 definition. Thus the definition of triangle is obtained by 
 the subdivision of quality into its four kinds, including 
 figure, and figure into its various kinds, including plane recti- 
 lineal, the last of which is the proximate genus, as the 
 triangle constitutes one of its species, with the distin- 
 guishing difference of three sides. "We need not, however, 
 follow so circuitous a route, as a very slight knowledge of 
 the subject, with moderate habits of generalisation, will be 
 sufficient to suggest the proximate genus without the inter- 
 vention of a category. 
 
 It happens, in the majority of cases, that the distin- 
 guishing difference may be selected from a variety of 
 properties, each equally essential to a proper conception of 
 the object ; as in the triangle, the attribute of its three 
 angles being equal to two right angles is of no less im- 
 portance than its possession of three sides ; yet there is one 
 of these properties generally which strikes us as more pro- 
 minent than the rest, or which is more important in re- 
 ference to the end we have in view, and this, consequently, 
 ought to constitute the differentia in our definition. It is 
 always essential, however, to the greater accuracy of our 
 conception that we steadily keep the distinction between pro- 
 perty and differentia in view, and do not employ an attribute 
 which is virtually implied i. e. easily deducible from others 
 of superior importance. That property ought to be selected 
 as the differentia out of which all the others can be the most 
 easily evolved. Another caution to be observed is that 
 the genus do not enter into i. e. constitute a part of the 
 
 1 Anal. Post. ch. 13. Pacian's division.
 
 C. IV. 5.] LOGICAL DEFINITION. 67 
 
 difference 1 . In some cases, however, this blending is un- 
 avoidable ; as in the definition of curved and right lines, the 
 idea of rectitude and crookedness which form their specific 
 difference cannot be viewed apart from length, which consti- 
 tutes their genus. 
 
 The great end of logical definition appears to be to unfold 
 the nature of a thing in as few words as possible, that the 
 notion may be clearly seized by the mind, and no entrance 
 given to words which admit of doubt or cavil. If properties 
 which are virtually implied in the specific difference were 
 expressly associated with it in the definition, it is clear this 
 object would not be gained, the mind being liable to view 
 the two properties as separable 2 . Thus, to define a parallelo- 
 gram, as a four-sided figure whose opposite sides are parallel 
 and equal, might lead the mind to suppose that there may 
 be a four-sided figure whose opposite sides are parallel, but 
 not equal. For the mention of any circumstance introduced 
 into the statement of a definition or of a precept, is to be 
 presumed so necessary to be inserted that the definition or 
 precept would not attach if this were absent. If we were 
 told that some celestial phenomena could not be seen by 
 the naked eye, it would be inferred that it might be visible 
 through a telescope, just as it has been concluded from 
 St. Paul's injunction, " Let a bishop be a man of one wife," 
 that the laity might have two. 
 
 The proximate genus is laid down as an essential part of 
 this kind of definition, since, if a genu& more remote was 
 taken, the definition would be too extensive i. e. include 
 more than its object. Thus, to define fish as an animal 
 which lives in water, would include under that name all the 
 insects who live in the same element. In like manner, the 
 definition would be inadequate, if an accidental property was 
 taken for the specific difference. For instance, if we were 
 to define fish as an animal which has an air-bladder, the 
 definition would be too narrow, since there are many fish 
 without any. 
 
 1 Galluppi's Lczioni di Logica, 22, p. 168. 2 Wolf has very 
 
 property said, "In definitione ermraerare debent notae nee plures, nee 
 pauciores quam quae ad rem clefinitem agnoscendam et ab aliis dis- 
 tingueudam sufficiunt." 15. 
 
 F 2
 
 68 TEEMS IN RELATION TO SIGNS. [B. I. 
 
 It is clear that individual terms are not capable of strict 
 logical definition, though they may be distinguished with 
 sufficient accuracy from others by an analogous process. 
 Thus to describe a rosadendron, we take the peculiar pro- 
 perties of its petals as its specific difference, while we assume 
 the species flower as its genus. There are also a large class 
 of simple terras, merely used in a denotative character: to 
 define these in terms clearer than their own would be im- 
 possible, and hence they are accepted by all as perfect ex- 
 ponents of their own meaning 1 . This is according to the 
 nature of the case ; for if we attempted to define every 
 word, it is clear that, in many instances, the thing defined must 
 enter into the definition, since it would be impossible to 
 commence the task without assuming some words in our 
 first definitions as already sufficiently clear ; nor could we 
 close it without defining the words so assumed in terms 
 of the definitions which they had contributed to establish. 
 In every instance, however, in which this occurred, our 
 definition would be a nullity. To say a circle is a circular 
 figure, is really to say nothing. Hence Locke cautions us 
 against using words in our definitions which are synonymous 
 with the thing defined 2 . Wolf calls this the vicious circle 
 of definitions, and cites as an instance of it the definition of 
 a day as a part of time made up of twenty-four hours. 
 
 6. Definition how far Real. 
 
 If we consider with Locke 3 the real essence of a thing 
 that by which it is constituted what it is ; or that one 
 quality if there be such upon which all its other qualities 
 depend, it is evident no definition that we can frame of any- 
 thing existing external to us can be accepted as unfolding 
 the real essence of its subject, but only what is commonlv 
 termed the nominal essence, viz., that by which the miud 
 conceives it to be what it is. But as the ideal nature of 
 a thing is identical with its real nature in all conceptions 
 
 1 Descartes' Principes de Philos. 4, x. Wolf, however, together with 
 Baumerster, attempted to define existence, but only succeeded in 
 darkening the meaning of the word. - B. 3, c. 4, 6. 3 B. 3, 
 
 c. 3, 15. Yet in b. 3, c. v. he restricts his meaning to the essence of 
 simple ideas and those of substances, and allowed the names of mixed 
 modes and artificial things to signify the real essences of their species.
 
 C. IT. 7.] DEAL AND NOMINAL ESSENCES. 69 
 
 which are purely of the mind's creation ; to define these in 
 terms of their real essence, we need only assign to them 
 those attributes which led the mind to erect them into 
 distinct conceptions. In mathematics for instance, every 
 definition will imply all the properties that belong to the 
 thing defined, since they entered into the mind's conception 
 of it ; and in morals, where any partial ideas are bound up 
 into a complex one, as in parricide, incest, sacrilege, &c., the 
 mind will at once recal the ideal attributes which led to its 
 formation as constituting its real definition, little solicitous 
 whether such entities have existed or are ever destined to 
 exist in nature. 
 
 It is very important, however, to observe, that this ques- 
 tion cannot be so summarily disposed of as Locke ima- 
 gined, since that can hardly be called an ideal definition 
 which has its roots in the nature of objective realities, and 
 is determined by their complexion. If it does not unfold the 
 entire nature of the thing, or in other words, leaves out even 
 of its implied statement many properties which are involved 
 in its existence, it at all events suggests a portion of such 
 nature, and, pro tanto, is real. The condition that the defini- 
 tion express that quality of the object on which all its other 
 properties depend in order to be real, is wholly hypothetical, 
 since no person can undertake to say whether such property 
 exist: and to postulate an imaginary essence as essential 
 to unfolding the real nature of a thing, is very much like 
 proving what is by something which is not. In many cases 
 the absence of such all-embracing quality can be fully shown 
 without affecting the real nature of the definition, as in those 
 instances which refer to the actions of things rather than 
 to their constitutive properties. For example, when examin- 
 ing the nature of motions produced by gravity it was found 
 that their uniformity was the result of the ratio of the velo- 
 city to the time elapsed, these co-ordinate attributes were 
 allowed to constitute the real definition of uniform motion, 
 though they fail to express its entire nature, and lead to no 
 derivative properties. 
 
 7. Scientific Definition. 
 
 Clear definitions of the last kind are of immense scientific 
 importance, inasmuch as the quick progress of physical 
 knowledge in modern times may be ascribed to the results to
 
 70 TEEMS IN DELATION TO SIGNS. [B. I. 
 
 which they have conducted, and is involved in the process 
 of their formation. Hence, the establishment of scientific 
 definition is the reverse of that laid down by Aristotle, 
 beginning with the most scrupulous examination of the ele- 
 ments of the objects to be defined, and endeavouring to 
 arrive at their exact nature by subjecting it to every combi- 
 nation that experiment can devise. The phenomena, among 
 which the elements of the object is to be sought, will of 
 course be pointed out by the nature of the question in- 
 volved, as Aristotle's genus and differentia were hunted out 
 from their corresponding category ; but these elements, de- 
 pending on the laws of physical substances, can only be 
 selected through the medium of observation and comparison, 
 For example, the inquiry concerning the law of falling bodies 
 led to the question, whether the proper definition of a uni- 
 form force is proportional to the space from rest, or to the 
 time. Taking it for granted, what indeed had been fully 
 proved, that gravity was a uniform force, the results of ob- 
 servation collected from a series of experiments, being sub- 
 jected to the test of calculation, showed that the ratio of the 
 velocity was to the time elapsed. In like manner, when it 
 was observed, in the case of two bodies infringing upon each 
 other, that the momentum lost by the one is equal to that 
 gained by the other, the question naturally arose what is that 
 of which a body when it sets another body in motion loses 
 exactly as much as it communicates ? And when experiment 
 had shown that this something was the product of the 
 velocity of the body by its mass, or its quantity of matter, 
 this became the definition of momentum. 
 
 The establishment of scientific definition, therefore, is part 
 of the business of discovery, and requires for its accomplish- 
 ment no small portion of that sagacity by which truth is de- 
 tected ; whereas logical definition in all cases, where it is not 
 hypothetical, has really no other aim than to demonstrate 
 truth when discovered, in placing the essential nature of one 
 of the terms out of which it is to be evolved clearly before the 
 eye. In moral speculations, indeed, when we arrive at 
 truths unknown before, by grave deduction from principles 
 independent of experience, it is quite possible, and in most 
 cases expedient, to establish our definitions according to the 
 Aristotelian rule ; but where the laws of physical nature are
 
 C. IT. 8.] WHAT DEFINITIONS PEOYISIONAI. 71 
 
 concerned, it is clearly absurd to attempt to frame our ideas 
 of the objects they involve by any other method than that of 
 registering their principal properties as observation and com- 
 parison point them out. In this way many of our defi- 
 nitions will be necessarily progressive and provisional ; ex- 
 tending their connotation as the progress of discovery throws 
 additional light upon the intrinsic nature of the object they 
 design to unfold ; they will nevertheless be clear and explicit 
 in drawing a boundary between the light and dark side of a 
 subject, and excite inquiry by placing the mind directly in 
 front of the unknown 1 . 
 
 8. Nominal Definition. 
 
 Up to this point, all our remarks refer to those defi- 
 nitions which concern things. There are, however, a dif- 
 ferent class, which arise from giving a settled meaning 
 to names otherwise vague and uncertain in their conno- 
 tation, with a view to exclude any ambiguity from phrases 
 in which they may happen to be employed. Such definitions 
 are called nominal, or definitions of names 2 . For instance, 
 the word spirit occurs in dispute, and introduces the usual 
 half-a-dozen meanings that commonly cluster round it. "We 
 ought in that case, with a view to avoid anything like 
 equivocation, to restrict the word to some one of these signi- 
 fications, or if none of the attributes formerly assigned to 
 it convey our sense, to invest it with a new signification. 
 
 1 Aristotle being entirely unacquainted with the modern method of 
 discovery, had no distinct conception of the kind of definition it em- 
 ployed. Whenever he departs from his own method, it is only to en- 
 tangle himself in vague metaphysical distinctions and imaginary 
 assumptions ; as an instance of which, we may take his definition of 
 motion the act of a being in power, inasmuch as it is in power ; and 
 of light the act or energy of a transparent body, inasmuch as it is 
 transparent. In these cases, he first assumed the motion of body or 
 being, then that of act and potentiality, and refused to consider nature 
 unless under these two arbitrary assumptions. 2 Archbishop 
 
 Whately seems to confound them with the etymological explana- 
 tion of a word which may be found in a dictionary. Logic, b. ii. 
 C. v. 6. But there is a wide difference between nominal defini- 
 tions and the meaning arising from the conventionalities of a lan- 
 guage. _In the first case we define a word arbitrarily, in order that 
 our conceptions may be clearly communicated to others ; in the latter 
 we adhere to that signification which is attached to it by the common 
 usage of society.
 
 72 TEEMS IN BELATION TO SIGNS. [B. I. 
 
 The meaning thence arising in either of these cases would 
 constitute the nominal definition of spirit. 
 
 Such definitions are clearly distinguishable in many re- 
 spects from the definitions of things, though each come 
 under the common classification, and are subject to the same 
 rules and exposition. For a word being a sound to which 
 we may attach any signification we please, provided we ap- 
 prise others of our intention, a nominal definition cannot be 
 contested, but must be taken as a principle ; but definitions 
 of things may be contested by those who deem them false, 
 and cannot be assumed as principles until they are fully 
 demonstrated unless, indeed, they are evident of themselves 
 as axioms. We are not, however, to infer anything more 
 from a nominal definition than the idea which we have at- 
 tached to the name ; or believe that, because we have given 
 the name a definite meaning, that it must signify something 
 real. For example, if any one call heaviness the inward 
 principle which makes a stone fall without being impelled by 
 anything, though we cannot contest the definition, since it 
 merely enables us to understand what he wishes to say, we 
 ought not to admit that to be anything real which he means 
 by the word heaviness, because there is no such principle in 
 stones. 
 
 As a further instance of nominal definition, may be ad- 
 duced the apparent discrepancy between the meaning of the 
 term idea as taken in the Peripatetic, Cartesian, and Lockian 
 schools. The first maintained that all ideas were false ; the 
 second that all ideas were true ; and the third, that ideas 
 were neither true or false. Which opinions, though their ap- 
 parent antagonism is apt to set precipitate people by the ears, 
 are really all correct, since the relation of ideas to outward 
 realities are assumed by each in opposite senses. For Aris- 
 totle, taking the word idea as synonymous with the sensible 
 image which the exterior object, through the medium of the 
 senses, conveys to the mind, maintained that such idea was 
 false because it did not represent the object as it really 
 existed in nature. Thus the visual impression we receive of 
 the stars is that of " small patens of bright gold," and not 
 suns or worlds, as science demonstrates them to be. But Des- 
 cartes applied the term ideas to the reflection of the sensible 
 image in the mind ; and, consequently, asserted their truth,
 
 ' C. IT. 8.] NOMINAL DEFINITIONS. 73 
 
 on the ground that they correctly represented things as they 
 appeared to us a doctrine of course which no peripatetic 
 could dispute. "While Locke, using the term idea to denote 
 the mere presence of an object in the mind, asserted it could 
 not be either true or false until we expressed some judgment 
 concerning it ; and then the truth or falsity would not enter 
 into the idea, but into the nature of the inference of which 
 we had made it the subject an opinion which we opine 
 neither Aristotle or Descartes would be inclined to quarrel 
 with. 
 
 The neglect of nominal definition, when names are liable to be 
 taken in a variety of senses, occasions interminable disputes, 
 and leads men, by confounding what is clear and true in con- 
 fused ideas with- what is false and obscure, into very decep- 
 tive errors. Thus philosophers formerly associating the word 
 fire with heat, and stone with heaviness, believed that nothing 
 could be clearer than that the former was hot and the latter 
 heavy, without in the least imagining that these two judg- 
 ments might be false in one sense and true in another. If 
 they signified by heat simply that which really produces the 
 sensation of heat in us, and by heavy that which falls to the 
 ground when nothing upholds it, the assertion evidently 
 would be accurate; but if they understood by heat that 
 which is the cause of that sensation, whatever it be, within 
 us, and by weight that which has in itself a principle which 
 makes it fall towards the centre of the earth without being 
 impelled by anything, it is evident that neither proposition 
 would agree with facts. 
 
 It is also a very common practice, and perhaps by none 
 more assiduously followed than by Aristotle and the scho- 
 lastics, to confound the definition of things with the de- 
 finition of names, and to invest the former with that un- 
 contested character which can only belong to the latter. 
 For example, when the peripatetics defined that quality in a 
 concave mirror which burns wood, when applied to the sun- 
 beam, to be an ustorious principle arising from its substantial 
 form ; and insisted upon the acceptance of this definition as 
 a satisfactory explanation of the phenomenon in question ; 
 or when they referred the hardness, colour, heat, and other 
 properties of bodies to certain occult qualities, in virtue of 
 which they are as they are, and beyond which it is useless to
 
 74 PBOPOSITIONS. [B. n. 
 
 inquire further, they palmed bad nominal definitions, con- 
 veying no meaning of a positive character, upon their age 
 as correct exponents of natural facts ; and succeeded, ridi- 
 culous as it may appear, in passing on these deceptions 
 through numerous generations, by assuming the tone of 
 men who had nothing to learn, and pretending to treat 
 those who denied such principles as men who were not 
 worth disputing with 1 . 
 
 BOOK II. 
 
 PROPOSITIONS. PBOEMTU1L 
 
 CONCEPTIONS of themselves imply nothing, beyond the 
 fact of consciousness. It is only by comparing them toge- 
 ther, with a view to their mutual agreement or exclusion, 
 that we obtain knowledge ; and the sentence by which this 
 act of the mind is enounced, is called a proposition. Hence a 
 proposition may be defined to be an indicative sentence, that is, 
 a sentence affirming or denying, the adjective being accessory, 
 as differentia, to exclude questions and commands, which are 
 also sentences, but unaccompanied by any act of judgment. 
 In whatever order the two terms which constitute the matter 
 of a proposition stand, that which we afiirm is called the 
 attribute or predicate, and that of which we affirm, the sub- 
 ject 2 . The verb which connects them is called the copula. 
 
 It is hardly for us to inquire into the nature of the 
 
 1 Definitions are commonly divided by logicians into other classes, 
 such as accidental, which denotes one in which the differentia is an 
 accident, not an essential property of the subject, as a man is an 
 animal who sows wheat and plants vines : and physical, in which 
 the object is simply divided into its natural parts as, Britons 
 are those who dwell in England, Scotland, or Wales. But we 
 need not trouble the student with a host of distinctions, which owe 
 their rise to scholastic trifling. 2 If the student will remember 
 
 that what we affirm is the attribute of every proposition, and that 
 of which we affirm, the subject, he can never be at a loss to dis- 
 tinguish these two terms in any proposition, no matter however 
 complex, or in whatever order its members may be found. For 
 example, in the proposition, "It is disgraceful to obey one's pas- 
 sions ;" it is clear from the sense that to obey one's passions is 
 the subject, since we affirm of it the term disgraceful. Of a simi- 
 lar kind are such propositions: It is foolish to listen to flatterers. 
 It is hail which falls. Propositions, however, may be blended with
 
 B. II.] SUBJECT A1TD ATTBIBTTTE. 75 
 
 mental phenomena which constitute judgment ; whether it 
 consists, as the conceptualists say, in the expression of a 
 relation between two ideas, or according to the doctrine of 
 the nominalists, in the simple expression of agreement or 
 disagreement between names. Such a discussion is rather 
 of metaphysical than logical concernment. Though it is 
 essential, as the principal at stake deeply concerns the 
 theory of reasoning, that the logician should have made up 
 his mind on the subject, and shape his views of the science 
 in accordance with the conclusions to which he has arrived, 
 that the structure may arise in harmonious consistency with 
 its metaphysical foundations. 
 
 According to the opinions to which such speculations lead, 
 propositions are denominated real and verbal, identical, or 
 essential and accidental, as the different relations in which 
 their terms stand to each other and to their subject-matter 
 determine. If the predicate assign to the subject a deter- 
 minate attribute whose agreement has been ascertained from 
 experience, or withhold such attribute on the same evidence, 
 as : man is mortal ; a charlatan is not worthy of esteem 
 all would concur in denominating such propositions real, 
 
 matter extraneous to the mere attribution or denial of a quality with 
 respect to the subject, as in the instance of active verbs, accompa- 
 nied with two or more cases. Thus : God commands us to honour our 
 parents. The law bids us to respect the queen : where, without 
 changing the active verb into its passive, we may find it difficult to dis- 
 tinguish either subject or attribute. As soon as this is done, however, 
 the terms of both propositions, by the application of the test, be- 
 come easily apparent, as: Our parents are to be honoured (by the 
 command of God). The queen is to be respected (according to the 
 injunction of the law). 
 
 It occasionally happens that the attribute is one simple word, while 
 the subject is composed of many propositions, as hi the stanza of 
 Horace: 
 
 Beatus ille, qui procul negotiis, 
 Ut prisca gens mortalium ; 
 
 Paterna rura bobus exercet suis, 
 
 Solutus omni faenore; 
 
 where beatus is the attribute, and all the rest the subject. We also 
 sometimes meet with sentences hi which the determination of the 
 predicate will depend upon the emphasis which the speaker chooses 
 to lay upon a particular word. Thus: The Organon of Bacon was 
 not intended to supersede the Organon of Aristotle, where at least 
 six of the principal words may separately be taken as the predicate, 
 according as the stress is laid upon each in the enunciation of the 
 proposition.
 
 76 PEOPOSITIONS. [B. 11. 
 
 though some might deny their existence 1 ; but should the 
 terms simply relate to the meaning and extent of the 
 words employed, and not to the things signified by them, 
 as : proper names are not connotative, the resulting proposi- 
 tion is verbal. In like manner, propositions may be called 
 accidental, essential, or identical, according as the property 
 represented by the attribute is merely an accessory of, or 
 inherent in, or equivalent to, the subject 2 . 
 
 Regarding the two terms of a proposition as expressive of 
 its matter, and the act by which they are confirmed or sepa- 
 rated as relating to its form, all that the logician has to advance 
 upon this portion of the science may be treated under these 
 two heads. The material aspect of propositions subdivides 
 itself into simple and compound ; the former section branch- 
 ing out into complex and incomplex, the latter into ex- 
 pressed and tacit propositions. Simple complex proposi- 
 tions may be subdivided into determinative and explicative ; 
 
 1 As Hobbes, and the extreme section of the nominalists. 2 Mill 
 gives a different account. According to his theory of reasoning, 
 when we attribute to a subject any property which attaches to it as 
 a class, we form an identical judgment ; or, in other words, we sim- 
 ply affirm what is as, man is an animal ; a tree is a substance ; 
 since all the properties which constitute the class make up our idea of 
 each individual included, and to predicate the one of the other is 
 simply tautological. To such propositions he applies the three names, 
 essential, identical, and verbal, denominating those accidental and real 
 which register the results of our experience. We, however, cannot see 
 any ground for the distinction taken between the attribution of pro- 
 perties which constitute a class, to one of the individuals included 
 under it, and of those derived from experience, to a subject with whose 
 nature they have never been associated. For how are classes formed 
 even according to Mr. Mill's own showing if the first category of 
 properties do not grow out of the second ? But surely there is nothing 
 beyond a distinction of time between the attribution of a property to 
 an object that has been discovered by induction, and that of a property 
 which has already entered into our conception of it through the 
 habit of association. Both marks may be equally essential to its 
 constitution, though the former may be less prominent, and require 
 something more than a superficial glance to distinguish it. The 
 name identical, which Mr. Mill gives to what he calls verbal defi- 
 nition, appears equally unfortunate. When a horse is said to be an 
 organised being, endued with sensation, we do no infer that the predi- 
 cate is coextensive with the subject, which, however, is the mark of 
 identity in a proposition. Locke more correctly affirms, that all identical 
 propositions are tautologous, and cites as examples those in which 
 the subject and predicate are exactly equivalent to each other. 
 Hum. Under, iv. viii. 4.
 
 JJ. II.] 
 
 DIVISION OF PEOPOSITIONS. 
 
 77 
 
 expressed compounds into copulative, disjunctive, conditional, 
 and causal ; and tacit compounds into exclusive, exceptional, 
 and comparative. The relation of these sections will be 
 sufficiently clear from the following scheme : 
 Propositions with regard to their matter. 
 
 Simple and compound 
 
 Complex, incomplex 
 
 Determinative, explicative. 
 
 Expressed 
 
 Tacit 
 
 Copulative, disjunctive, 
 conditional, and 
 causal 
 
 Exclusive, 
 
 exceptional, and 
 
 comparative. 
 
 As regards their form, propositions are usually divided 
 into affirmative and negative, and these, accompanied with 
 two other properties of propositions, give rise to the process 
 of opposition and conversion, which, as they mainly depend 
 upon the form, may be treated under that head 1 . 
 
 1 Kant's division of propositions is according to the four necessary 
 forms with which a judgment must be invested, viz., quantity, quality, 
 relation, and modality. With a little alteration, the scheme in the 
 text might be blended with it, which would enable the student to recal 
 at a glance everything important to recollect in connexion with this 
 branch of logic. Thus 
 
 'with regard to^ simple } complex 5 determinative 
 relation ( explicative 
 
 ) incomplex 
 
 compound 
 
 expressed C categorical 
 3 disjunctive 
 (. conditional 
 
 tacit 
 
 Propositions \ with regard to } probable 
 modality > contingent 
 ) necessary 
 
 with regard to ") universal ^ opposition 
 
 f exclusive 
 \ exceptional 
 (.comparative 
 
 quantity > particular 
 j singular 
 
 with regard to } affirmative 
 
 quality > negative 
 . j limited 
 
 and 
 conversion
 
 78 PEOPOSITIONS WITH EEGAED TO MATTER. [-B. II. 
 
 CHAPTEE I. 
 
 PEOPOSITIONS WITH BEGAED TO MATTEE. 
 
 1. Simple Complex and Incomplex Propositions. 
 
 a proposition has only one subject and one attri- 
 bute, it is called simple as, Mirandola was a platonist ; 
 should either or both of these terms comprise more than one 
 subject, or predicate, it is denominated compound as, Plato 
 and Pericles were cotemporaries ; or, Sir Thomas More was 
 both a judge and philosopher; Charlemagne and Alcuin 
 founded schools and erected churches. There are, however, 
 many propositions which embrace in reality only one subject 
 and attribute, but which nevertheless appear compound, on 
 account of certain incidental propositions being connected 
 with one or both of the terms by who or which, whose func- 
 tion is in these cases to constitute one proposition out of 
 many. Thus: Alexander, who was the most generous of 
 kings, conquered Darius ; or, expressing the incidental pro- 
 position, as a Latin substantive in apposition Alexander, the 
 most generous of kings, conquered Darius ; or, Boethius, the 
 most learned man of his time, translated Aristotle. Such pro- 
 positions are termed simple complex, for though the attribute, 
 or subject, may embrace several propositions, they do not on 
 that account lose their unity. By destroying that unity, 
 however, they become compound propositions : as, Alexander 
 was the most generous of kings, and the conqueror of Darius ; 
 Boethius was the most learned man of his time, and the 
 translator of Aristotle. 
 
 The complexity of a proposition may fall on the subject, on 
 the attribute, or on both. Thus: Every man who fears 
 nothing is a king is an example of the first: Piety is a 
 good which renders man happy in the greatest adversity 
 is a case of the second : and The great who oppress the 
 poor will be punished by Providence, who is the protector of 
 the oppressed is an instance of the third. As it is a pecu- 
 liarity of such propositions that they may be contradicted in 
 two ways, viz., either by denying the attribute or the inci- 
 dental proposition of the subject, it follows that all proposi-
 
 C. I. 2.] SIMPLE PBOPOSITIOKS. 79 
 
 tions compounded of active verbs and their objects must be 
 reckoned complex, since they admit of double contradiction, 
 and thus imply two propositions. For example, the statement 
 Brutus killed a tyrant : may be expressed, Brutus killed 
 one who was a tyrant, and may be consequently contradicted 
 either by denying that Brutus killed any one, or that the 
 person whom he killed was a tyrant. 
 
 2. Simple Complex Propositions. 
 
 Incidental propositions may be annexed to a subject, either 
 with a view to unfold some of its essential properties, or to 
 restrict its signification. In the former case they are denomi- 
 nated explicative, in the latter determinative. Thus : " Men 
 who are endowed with reason are responsible beings," is a pro- 
 position in which the incidental term is explicative, the feature 
 of rationality being an essential part of man ; the attribute 
 consequently may be considered, apart from, the incidental 
 proposition, as solely referable to the subject, as, " men are 
 responsible beings." But when the incidental proposition 
 simply restricts the meaning of the subject, in annexing to it 
 a property which is not coextensive with it, as Men who 
 are pious are charitable, such incidental proposition is called 
 determinative, and the attribute can no longer be considered 
 as affirmed of the subject alone, but must be applied to it as 
 restricted by the incidental proposition. !Por it would be 
 evidently wrong to say, " men are charitable," since we know 
 that a great many of them are malevolent. Hence inci- 
 dental propositions which are explicative are readily dis- 
 tinguished from such as are denominative, by omitting the 
 part qualifying the subject. In which case, the explicative 
 proposition will lose nothing of its truth ; while the deter- 
 minative will imply an absurdity. 
 
 Error is only liable to steal into incidental explicative 
 propositions, since they alone affirm an attribute of the 
 subject to which the relative pronoun appertains. For ex- 
 ample : the proposition, " Horace "Walpole, who was the son 
 of the Earl of Orford," affirms, though incidentally, that 
 Horace was the son of that nobleman, and consequently, 
 if it be not so, as some suspect, it states a falsehood. 
 Should error, however, lurk in the incidental proposition, 
 it cannot affect the truth of the principle. Thus : " Horace
 
 80 PBOPOSITIONS WITH BEGAHD TO MATTEE. [u. II. 
 
 "VValpole, who was the son of the Earl of Orford, wrote the 
 most delightful letters in the English language," would not 
 be considered the less true if Horace was the son of another 
 man. Incidental determinative propositions cannot be false, 
 since they are simply applied to restrict the signification of 
 the object without affirming or denying anything concerning 
 it, beyond the mere assumption of their possibility. For 
 example : when we say, " senators who never say or do any- 
 thing by favour or party feeling," we do not say that there 
 are senators who so comport themselves, though we virtually 
 imply the possibility of their existence; and so far such 
 propositions may be false. 
 
 3. Compound Expressed Propositions. 
 
 We have seen that compound propositions are distin- 
 guished from simple by the plurality of one or both of their 
 terms. Now, according as the composition is denoted ver- 
 bally or implied, these may be denominated, expressed or 
 tacit. The prior member of the division embraces copu- 
 lative, causal, disjunctive, and conditional compounds. Of 
 these, copulative and causal may be united under the head of 
 categorical. 
 
 As all propositions are termed categorical which affirm or 
 deny anything directly of another, every simple proposition 
 may rank under that head ; but the term is taken here to 
 distinguish that class of compounds connected by the copu- 
 lative conjunctions and and because from those which are 
 hypothetical and disjunctive, with a view to trace their 
 peculiar laws, and define the respective relations of each of 
 these classes to one another 1 . 
 
 Copulative compounds may comprise a plurality of sub- 
 
 1 Dr. Whately takes categorical as opposed to compound, which he 
 calls identical with hypothetical syllogisms, including under the latter 
 term, conditional and disjunctive syllogisms (Logic, b. ii. c. iv. $2). 
 But this is surely wrong ; for compound propositions, besides all 
 simple propositions, include many which are categorical, while the 
 term hypothetical is synonymous with conditional, and to substitute 
 it for compound is to confound a genus with its species. Boethius, the 
 first among the Latins who elaborated this part of logic, employs in- 
 differently the terms hypotheticus conditionalis non simplex for the 
 genus, as opposed to categoricus. See Edinburgh Review, April, 1833. 
 The division of categorical into pure and modal (Logic, b. ii. c. ii. 1), 
 in which the archbishop, as usual, follows Aldrich, is equally unfortu-
 
 C. I. 3.] COMPOUND PROPOSITIONS. 81 
 
 jects, of attributes, or of both, and accordingly give rise to 
 three corresponding kinds of propositions. Thus, the pro- 
 position, death and life are in the power of the tongue, con- 
 tains a plurality of subjects ; while the dicta of Horace, that 
 " a well-regulated mind hopes for prosperity in adversity, and 
 fears adversity in prosperity 1 ," and "neither houses, nor 
 lands, nor heaps of gold and silver, can chase away fevers 
 from the body, or cares from the minds of their possessors 2 ," 
 comprise a plurality of attributes and a plurality of subjects 
 and attributes respectively. The truth of these propositions 
 depends on the truth of each of their parts ; the falsity of 
 any one of which invalidates the whole. 
 
 Copulative propositions are only considered negative when 
 the negation falls on the conjunction, which may, however, 
 happen in various ways, sometimes at the head of a sen- 
 tence, as, " we cannot be in love and be wise 3 ;" occasionally 
 in the centre, " as love and majesty do not agree together 4 ". 
 
 Causal propositions are those which express the cause and 
 effect of a thing together. For example : a stone unsus- 
 tained falls, because it is heavy: such a prince was un- 
 fortunate because he was born under a certain constellation. 
 To be true, such propositions require the proof of three 
 tilings, viz., the reality of the existence of both cause and 
 effect disjointly, and then the establishment of the fact that 
 the effect really follows from the cause which has been 
 assigned to it. The neglect of the former of these con- 
 ditions gave rise to the absurd attempt of the Royal Society 
 to solve the celebrated problem of Charles II. Why does 
 a fish lose its weight by being immersed in water ? Had 
 the members set out with ascertaining the reality of the 
 
 nate, since it leads the student to infer that there are pure propositions 
 which are not modal, and restricts the term modality to a meaning 
 which in its strict sense that word does not bear. 
 Sperat infestis, metuit secundis 
 Alteram sortem, bene praeparatum 
 Pectus. Hor. Car. ii. 10. 
 Non domus et fundus, non seris acervus et auri, 
 ^Egroto domini deduxit corpore febres 
 Non animo curas. Hor. EpisL i. 2. 
 Amare et sapere vix deis conceditur. P. Syrus, Sent. 20. 
 Non bene conveniunt, nee in una sede morantur 
 Majestas et amor. Ovid, Metam. ii. 846. 
 O
 
 82 PBOPOSITIONS WITH BEGAED TO MATTER. [B. n. 
 
 fact which Ms majesty called upon them to solve, they 
 might have escaped from the absurdity of applying their 
 grave powers to account for a nonentity. The falsity of a 
 causal proposition may be shown by impugning either the 
 reality of the effect, or its sequence from the cause. Thus, 
 the statement that the change in the general climate of the 
 globe is owing to the earth having cooled from a state of 
 absolute fusion) may be contradicted, by proving that such 
 absolute fusion could never have occurred, or was insuf- 
 ficient to account for the phenomena in question. If the 
 existence of the subject only be disproved, the proposition 
 is simply put out of court as an assertion about nothing. 
 
 Disjunctive propositions consist of two or more simple 
 propositions, into which the disjunctive conjunctions either, 
 neither, and their correlatives enter, and the force of which 
 is to state an alternative. For example : " A man is either a 
 fool or physician at forty ;" " women either love or hate, they 
 are never indifferent 1 ;" every deliberate action is either 
 good or evil. The truth of these propositions depends upon 
 the necessary opposition of the parts which ought to exhaust 
 the subject and admit of no medium. But as such absolute 
 exhaustion is not attainable in all subjects, those disjunctives 
 may be considered morally true which approximate to it. 
 For instance, though the proposition, men act either from 
 interest or fear, is not absolutely true, since there are some 
 who act from neither of these passions, but from a consider- 
 ation of their duty ; yet it may be accepted as morally cer- 
 tain, because it embraces the two motives which influence 
 the majority of mankind. The proposition, however, that 
 every man who disobeys the law, is either ignorant of its 
 existence or misconceives its import, is neither morally nor 
 absolutely true, since the greater portion of defaulters in- 
 fringe it through defect of will. Though the truth of one and 
 only one of the members is generally implied in these propo- 
 sitions, and the division is consequently reckoned exclusive, 
 this, as in the instance of the proposition just cited, is by no 
 means universally the case. For all men are generally im- 
 pelled by interest, fear, and duty, at some time or other in 
 their lives, and occasionally are influenced by the three 
 motives conjointly ; so that from the affirmation of one, we 
 
 1 Aut amat aut odit, mulier; nihil est tertium. P. Syrus, Sent. 26. 

 
 C. I. 4.] SEDUCTION OE PROPOSITIONS. 83 
 
 are not led, as in alternatives properly exclusive, to reject 
 the other. 
 
 Conditional propositions are those which assert the neces- 
 sary dependence of one proposition on another ; for example : 
 if the soul is spiritual it is indivisible. The clause which 
 conveys the condition is called the antecedent, the other the 
 consequent. These propositions may be true with regard to 
 the necessary connexion of their parts, but false with regard 
 to their matter. As : if the will of the creature is capable 
 of frustrating the absolute will of God, God is not almighty. 
 If the earth was not made by a wise artificer, it was either 
 produced by a fortuitous concourse of atoms, or must have 
 existed from eternity. Hence, in relation to the truth of this 
 class of propositions, we need only examine the connexion, 
 since if that be true, the sentence, so far as it is conditional, 
 holds good. Though in every instance, where the depen- 
 dence is established, the consequent follows from the ad- 
 mission of the antecedent, the antecedent could not be 
 inferred from the truth of the consequent. Thus, though 
 we may say : If he be & man he is a two-footed animal, we 
 cannot infer from his being a two-footed animal that he is a 
 man. For the same consequent may follow from other ante- 
 cedents. 
 
 4. Seduction of Disjunctive and Conditional Propositions 
 to. Categorical. 
 
 Though the validity of these kinds of compounds can be 
 sufficiently tested by the rules already given, it is sometimes 
 necessary, to avoid all ambiguity in the higher processes of 
 inference, to reduce them to the simpler form of categorical 
 propositions. For this purpose we must consider every 
 conditional proposition as a simple affirmative with the 
 antecedent for its subject, and the consequent for its pre- 
 dicate ; for example, " if its inhabitants are industrious 
 a country is likely to prosper," is equivalent to saying that 
 the case of its inhabitants being industrious is a case of a 
 country being likely to prosper. No hypothetical proposi- 
 tion is valid which cannot be reduced to such a form. 
 
 This law of reduction springs from the identity of the 
 logical function of categorical and conditional propositions, 
 
 02
 
 84 PROPOSITIONS WITH EEGAED TO MATTEB. [B. II. 
 
 which simply consists in affirming the invariable connexion 
 between their two terms, the only difference being that in 
 categoricals the terms which are generally simple declare 
 that a thing or class of things has some property, while in 
 conditionals, the terms which always consist of propositions 
 affirm either the causal coincidence of two facts or the de- 
 pendence of two truths. "When it is affirmed that all the 
 tissues of the body continually decay and are reproduced, 
 it is signified that wherever one of the tissues of the human 
 body exist, decay and reproduction are going on ; and in like 
 manner, when we assert, if the moon comes between the sun 
 and the earth, the sun will be eclipsed, we mean that when 
 the moon is found in that position a solar eclipse will accom- 
 pany it. In both instances one thing is affirmed to be a 
 concomitant of the other. In the categorical a thing has 
 the mark expressed by the predicate, while in the conditional 
 a fact has another fact for its mark. The formula therefore 
 represented by the case, fact, or notion of this existing is a 
 case, fact, or notion, of that existing is sufficient for the re- 
 duction of any conditional to a categorical proposition 1 . 
 
 Disjunctive propositions may be reduced to conditionals 
 by assuming as an antecedent, the contradictory of one or 
 more of its members, " thus either the earth is eternal, or 
 the work of chance, or the work of an intelligent being," is 
 equivalent to " if the earth be not eternal it is either the 
 work of chance or the work of an intelligent being," the 
 proposition in that case will nevertheless remain partly dis- 
 junctive. It may, however, be divested of its hybrid cha- 
 racter, and transformed into a compound categorical by 
 adhering to the formula above laid down. For example : 
 " The possible cases in this matter are that the earth is 
 eternal, that it is the work of chance, and that it is the 
 work of an intelligent being." And again, either Horace 
 "Walpole is right in his historic doubts, or Richard III. was a 
 monster; which proposition, categorically expressed, is, "the 
 possible cases in this matter is that Horace Walpole is right 
 in denying the existence of Richard III., and that of the 
 monarch being a monster." 
 
 1 Thompson's Laws of Thought, p. 169, 2nded.
 
 C. I. 5.] TACIT PEOPOSITIONS HOW CONTBADICTED. 85 
 
 5. Tacit, or Implied Compound Propositions. 
 These may be discussed under the head of exclusives, 
 exceptional, and comparatives. Those are termed exclusives 
 which indicate that the attribute agrees with one subject, 
 and that it agrees with nothing else. They consequently 
 contain two judgments, and are for that reason called com- 
 pound. For example, the conclusion of one of Martial's 
 epigrams : " The only riches which will always remain with 
 you are those which you have freely given away 1 ;" and the 
 apothegm, " virtue is the only true nobility 2 ." The truth of 
 these propositions depends upon the agreement of the attri- 
 bute with the subject, and with nothing else. Hence they 
 can be contradicted in three ways, viz., either by denying the 
 agreement of the attribute with the subject, or by affirming 
 that it agrees with something else, or by pursuing both of 
 these courses. For instance, against the expression of Mar- 
 tial, it may be urged, that riches which we give away do not 
 remain with us: that the riches which we keep remain 
 with us as well as those which we give away: that the 
 riches which we keep remain with us, and not those which 
 we give away. In like manner the celebrated maxim of 
 the academics, " that it is certain that there is nothing 
 certain," which affords another instance of an exclusive 
 proposition, was differently contradicted according to the 
 opinions of the sects who opposed it. For the Dogma- 
 tists maintained that it was doubly false, since in the first 
 place if it could be affirmed that nothing was certain, at 
 least the act of the mind by which that judgment was pro- 
 nounced was certain ; and in the second place they main- 
 tained that many other things could be known with the ut- 
 most certainty. The Pyrrhonists said the proposition was 
 false for a contrary reason, viz., that everything was so 
 uncertain that it was even doubtful whether there tras 
 nothing certain 8 . 
 
 Exceptives are only another kind of exclusives, in which, in- 
 stead of affirming the attribute of the subject alone, we deny 
 
 Ep. B. v. Ep. 43 
 
 1 Quaa dederis solas semper habebis opes. Ep. B. v. Ep. 
 * Nobilitas sola est atque unica virtus. Juvenal, Sat. vii 
 3 Or according to the inimitable author of " Don Juan," 
 " Who doubt that even doubt itself is doubting." 
 
 viii. 20.
 
 86 PROPOSITIONS WITH BEGABD TO MATTEE. [B. II. 
 
 it of everything else, and express the subject as an excep- 
 tional case. Thus: "The Platonists alone, of the ancient 
 philosophers, recognised the spirituality of God," becomes 
 exceptive when we affirm that " none of the ancient philo- 
 sophers except the Platonists recognised the spirituality of 
 God 1 ." This proposition evidently involves two judgments : 
 first, that the ancient philosophers believed God corporeal ; 
 and the second, that the Platonists believed the contrary. 
 Many of the terse sayings of P. Syrus and Seneca are of 
 this character. As : " The miser does no good except by 
 dying 3 ." " No one thinks himself miserable except by com- 
 paring himself with those who are more happy 3 ." 
 
 The truth of these propositions depends upon the truth of 
 the whole and the truth of the exception, and hence they may 
 be contradicted in the same way as the exclusives. For 
 example, the assertion of the stoics, that " Except the wise 
 man (formed after their model of wisdom) all men are fools," 
 may be met by maintaining 1st. That the wise man of the 
 stoics was as great a fool as other men ; 2ndly. That there 
 were others besides their wise man who were not fools ; and 
 3rdly. That their wise man was really a fool, and many 
 others were not. 
 
 Propositions which consist of comparisons involve two 
 judgments : first, the existence of the thing in a peculiar 
 mode ; and secondly, the degree which it holds in that mode. 
 Thus the sentence of Syrus : The greatest of all losses is 
 the loss of a friend 4 , implies both that the death or estrange- 
 ment of a friend is a loss, and the greatest of all losses. Also 
 the remark of Horace : " More impression, even in important 
 matters, is produced by a little agreeable raillery, than by the 
 best arguments 5 ," implies, in addition to the degrees of the 
 impression, the reality of its existence. 
 
 1 In like manner the exceptive proposition of Terence, 
 
 " Imperitus, nisi quod ipse facit, nihil rectum putat," 
 has been transformed by Cornelius Gallus into this exclusive: 
 " Hoc tantum rectum quod facit ipse putat." 
 
 2 Avarus nisi cum moritur, nihil recte facit. P. Syrus, Sent. 62. 
 
 3 Est miser nemo nisi comparatus. Seneca, Troas, 1021. 
 
 4 Amicum perdere, est damnorum maximum. P. Syrus, Sent. 34. 
 * Bidiculum acri 
 
 Fortius ac melius magnas plerumque secat res. 
 
 Hor. Sat. i. 10.
 
 C. H. 1.] QUANTITY OF PEOPOSITIONS. 87 
 
 Hence the truth of comparatives" depends upon the truth of 
 the two senses they bear, and may be contradicted by denying 
 either of them ; as the maxim of Epicurus, " That pain is 
 the greatest evil," was impugned by the stoics, on the ground 
 that pain was not an evil at all ; while the peripatetics, 
 though allowing pain to rank in the category of evils, main- 
 tained that vices and other irregularities of the mind were 
 much greater evils. 
 
 CHAPTEE H. 
 
 PBOPOSITIONS WITH EEGAED TO POEM. 
 
 1, Quantity of Propositions. 
 
 ALL propositions are divided into universal, particular, and 
 singular, according to the extent (i. e. quantity) to which the 
 predicate is affirmed of the subject. If the predicate is affirmed 
 of the whole of the subject, the proposition is universal ; if 
 of a part of it only, the proposition is particular. For exam- 
 ple : " All vicious men are miserable ;" " No miser is rich ;" 
 are universal, and their subject being applied to the attribute in 
 its broadest sense, is said to be distributed. But " Some poor 
 men are not unhappy;" "All despots are not cruel," are 
 particular. Their subjects are consequently said to be not 
 distributed, being only connected with the attribute accord- 
 ing to a certain indeterminate part of their extension. 
 
 When the subject of a proposition is a singular term, it is 
 also called singular, as " Colbert first introduced the funding 
 system into France ;" "Victoria is worthy of the homage of 
 her subjects :" but as such propositions resemble the uni- 
 versal in having the predicate affirmed of the subject accord- 
 ing to the whole of its extension, they are ranked under that 
 head. For it is only essential to the universality of a propo- 
 sition that its subject be taken in the whole of its sphere ; 
 whether that sphere be great or small does not in the least 
 concern it. Single propositions, however, may be fairly 
 reckoned particular when accompanied with a qualifying 
 word, which restricts the attribute to a portion of the sub- 
 ject, as Non omnis moriar: I shall not altogether die;
 
 88 PEOPOSITIONS WITH EEGAED TO FOBM. [fi. II. 
 
 Caesar was not wholly a tyrant. But, strictly speaking, such 
 propositions, admitting of a variation in quantity, are not 
 properly considered singular, the subject being not Caesar, but 
 the parts of his character 1 . 
 
 When the subject of the proposition is a common term, 
 the universal signs, "every, all, no, each," are used to signify 
 it is distributed, and the particular signs, "some, there are," 
 &c., to indicate the contrary. Should the common term, 
 however, be without any sign, the quantity of the proposition, 
 which in that case is termed indefinite, is ascertained by the 
 matter of the judgment, or in other words, the nature of the 
 connexion between the two terms. Where the mind conceives 
 such connexion necessary, either through its inability to con- 
 ceive the two terms apart, or from its knowledge of their 
 essential association, the proposition which they constitute is 
 deemed universal, as " Birds are not quadrupeds ;" " Circles 
 have their radii equal;" "The planets move in ellipses;" 
 " The elementary atoms of matter combine in definite propor- 
 tions 2 ." Where the connexion is only casual or accidental 3 , 
 the proposition will be particular, as " Birds sing ;" " Sena- 
 tors are eloquent;" "Food is necessary to life ;" where the 
 matter implies that the predicate cannot be said of the en- 
 tire class of objects for which the subject of the proposition 
 stands 4 . Should the nature of the connexion, however, be 
 
 1 Whately's Logic, b. ii. ch. ii. 2. 2 Though the matter of 
 
 these propositions, i. e. the connexion between their terms, is not 
 equally necessary, since the negation of the two first examples would 
 be inconceivable, while the denial of the two last would suppose no 
 absurdity; yet, since the necessity of the connexion of the terms of the 
 latter depends upon the laws of nature, its competency to imply a 
 universal may be presumed equal to the former. 3 Archbishop 
 
 Whately, after Aldrich, calls this kind of connexion contingent. But 
 that phrase is applied by the scholastics, and their modern successors, 
 as also by Kant, to denote that class of facts which depend upon 
 natural laws as contradistinguished from absolute truths which can- 
 not be conceived otherwise than they are. In that sense, the word 
 would exclude many instances of necessary connexion, and is there- 
 fore likely to mislead. * The Port Royal logicians cavil with 
 the idea of the distinction between necessary and accidental matter 
 as affording a clue to the quantity of indefinites, and would sub- 
 stitute doctrine and circumstances of fact in their place. Logique, 
 part ii. ch. xiii. Thus : Angels have no body being a matter of doc-
 
 C. II. 2.] QUALITY OF PBOPOSITIONS. 89 
 
 doubtful, it is evident, since we can only affirm or deny tlie 
 predicate of those cases in which we have tested the certainty 
 of our judgment, that the proposition must be particular. 
 Hence indefinite propositions have no place in the logical 
 system, and are only mentioned here to put the reader on 
 his guard against them 1 . 
 
 2. Quality of Propositions. 
 
 The division of propositions into affirmative and negative 
 gives rise to their quality ; an affirmate proposition, of course, 
 being that whose copula is affirmative, as " fish breathe ;" and 
 a negative one whose copula is negative, as " misers are not 
 happy." 
 
 Some logicians, however, hold 3 that there is in reality no 
 negative in thought, but only in the form of expression. To 
 say " Adeline" is not tall, is to say that she is short. This is 
 correct in those cases where the negative is not referred to 
 the verb, but to one of the terms. For then we regard the 
 predicate, or subject, as a thing limited that is, as a positive 
 thing deprived of some property. For example: Human 
 knowledge is not perfect, is equivalent to human knowledge 
 is imperfect ; and some graduates are not learned, is equal 
 to some graduates are unlearned ; but when the negative 
 is referred to the verb, the proposition must be considered 
 negative as respects the form, otherwise we might argue 
 that no proposition could be considered affirmative, as every 
 judgment is capable of assuming a negative form. 
 
 The quality or form of a proposition may be either simple 
 (pure) or complex, as well as its matter. Thus " Caesar 
 loved Cleopatra," is an instance of the simple kind of affirma- 
 tion. " Copernicus proved demonstratively that the Helio- 
 centric theory was true," is an example of the second ; for 
 
 trine, is universal; while: Soldiers were engaged in review being 
 one of fact, is particular. But this, in reality, is only expressing the 
 same distinction in theological language. * Logicians, however, 
 
 distinguish a species of moral universality, which, though not without 
 exception as in the case of absolute or metaphysical universality, yet 
 are sufficiently approximate to enable us to found an argument upon 
 them, as Women are talkative ; Old men are prudent. Professor 
 de Morgan calls attention to these under the head of plurative judg- 
 ments (Formal Logic, p. 325). a De Stutt Tracy, Grammaire, 
 part i. c. 4.
 
 90 PROPOSITIONS WITH EEGAED TO FORM. [B. II. 
 
 the terms " Copernicus proved demonstratively" is only 
 alleged in support of the affirmation that the Heliocentric 
 theory is true, and consequently does not fall upon the 
 matter but upon the form. 
 
 Cases, however, sometimes occur where the complexity 
 may be applied to both, and, according as it is so taken, com- 
 pletely change the meaning of the sentence ; as " Locke 
 asserts that all our ideas have their origin in sensation and 
 reflection," may imply a wish on the part of him who utters 
 it to uphold that doctrine ; in which case the first part of 
 the sentence, " Locke asserts it," must be regarded as an 
 incidental proposition adduced in support of the affirmation 
 in the latter : or it may denote an intention to express this 
 doctrine as the opinion of philosophers without affirming any- 
 thing about its truth ; in which case the first part, viz., "Locke 
 asserts," would become the principal proposition, and the last 
 would only form a portion of the attribute. The complexity 
 then would fall upon the matter, but the signification would 
 be entirely changed. In such ambiguous phrases, however, 
 the nature of the incidental proposition may easily be col- 
 lected from the intention of the speaker or writer. 
 
 Many logicians in this place consider the morality of 
 propositions that is, the degree of certainty with which the 
 mind affirms or denies the connexion between the terms of 
 any proposition it may entertain. Of these there are many 
 gradations, as each person may ascertain by consulting his 
 own consciousness ; but as their explication would involve 
 the question of the foundations of evidence, we join the 
 modern schoolmen in relegating them from this part of 
 logic. 
 
 3. Distribution of Terms in Propositions. 
 
 "We have said the subject of a universal proposition is dis- 
 tributed, since it is taken in the whole extent of its signi- 
 fication ; and the subject of a particular proposition undistri- 
 buted, because only some of its parts are applied to or excluded 
 from the predicate. Hence it follows, that the distribution 
 of the subject depends upon the quantity of a proposition, 
 and is distributed in universals, and in universals alone. 
 
 The distribution of the predicate, on the other hand, de- 
 pends on the quality of a proposition. For it is sufficient
 
 C. II. 3.] DISTRIBUTION OP TERMS. 91 
 
 to admit the predicate to be affirmed with truth of the 
 subject, that some part of it should agree with the subject ; 
 we consequently cannot infer that it is taken in its whole 
 extent from the bare act of affirmation. But for a negative 
 to be true, it is necessary that the entire predicate should 
 be excluded from the subject. To fulfil this condition, there- 
 fore, in every negative proposition the predicate must be 
 distributed. Hence the two practical rules generally given 
 for distribution are, that none but universals distribute the 
 subject, and none but negatives distribute the predicate. 
 
 But the last rule is not to be taken absolutely, since 
 affirmative propositions occasionally distribute the predi- 
 cate ; as in those cases where the proposition assumes the 
 form of a definition, as common salt is chloride of sodium ; 
 some animals are all men ; and we may even conceive cases 
 in whicli the rule is entirely overridden, as, " some trees are 
 not some plants ;" " no sinners are some men," where the pre- 
 dicate is quantified in common with the subject. But such 
 propositions are evidently unnatural in their present form, 
 and, if not entirely nugatory when transformed to their 
 conventional shape, may be brought under the two rules 
 already given. Thus, "some animals are all men" is equi- 
 valent, according to the first rule, to "all men are ani- 
 mals," and in ordinary parlance, never appears in any 
 other form. Again, the negative proposition that " no 
 publicans are some men," does not preclude our constructing 
 an affirmative judgment out of the same terms, as " all pub- 
 licans are men." Not having, therefore, the force of a 
 negative, it never occurs in speech, and is consequently 
 useless. But a negative proposition which contains two 
 particular terms, as " some lichens are not some plants," is 
 still more nugatory, as it might be affirmed of everything 
 not only existing, but even identical. For if we define 
 common salt to be chloride of sodium, we may, nevertheless, 
 affirm that some common salt is not some chloride of sodium, 
 meaning, of course, that the common salt in this salt-cellar 
 is not the chloride of sodium in that 1 . 
 
 It is not essential to clearness of thought that the pre- 
 dicate be quantified i. e. have a determinate quantity 
 either in judgment or expression. In affirming the agree- 
 
 1 Thompson's Laws of Thought, p. 188, 2nd ed.
 
 92 PEOPOSITIONS "WITH BEGAED TO POEM. [B. II. 
 
 ment or disagreement of two ideas, the mind concentrates 
 its attention upon the double sphere of the subject, and 
 never looks further into the nature of the predicate than is 
 sufficient to enable it to affirm or deny it of the subject. 
 To this end it is by no means necessary that the logical 
 sphere of the predicate be known, at least in affirmative 
 cases, but only such parts of its connotation as are either 
 identical with the subject, or so distinct from it as to imply 
 the non-agreement of the rest of its properties. Thus, when 
 we say "all men are sinners," we pay no attention to the 
 extent to which " sinners" may be affirmed of other objects 
 besides men, it being a law of the mind never to examine 
 further into the nature of the terms upon which it has to 
 decide than the correctness of the judgment warrants. For 
 this purpose it is evidently sufficient to know that each man 
 is peccable without inquiring what other things are so. So 
 much, indeed, is this the case, that in affirming " all men 
 are sinners," very few, unless theologians, upon whom the 
 question has been forced by abstract study, have ever dreamt 
 of asking themselves whether " all men are all sinners," or 
 whether "all men are some sinners," that is, whether the 
 term can be applied to angels and devils also, and even if 
 some brutes are not included under it 1 . Again, it is so 
 far from being essential to the clearness of the proposition, 
 " some men are not rational," to know whether rational is 
 taken in its universal or particular sense, that the very sug- 
 gestion of its quantification is apt to confuse the judgment 
 in pronouncing it. 
 
 Indeed, so foreign is the effort of realising "the new 
 analytic" to the mind, that the thing would never have been 
 dreamt of had not Sir "W. Hamilton been led to it by the 
 development of the general idea of predicate quantification ; 
 
 1 We have gone into this case at some length, as the contrary 
 opinion has been distinctly put forth in favour of a thorough-going 
 quantification of the predicate, on the ground of its absolute necessity 
 to the formation of clear judgments, by Spencer Baynes a writer of 
 some promise in his " New Analytic of Logical Forms," which is 
 simply intended to state the views of Sir W. Hamilton as to the ex- 
 tensive and beneficial nature of the changes which such quantification 
 is calculated to introduce into logic. Mr. Baynes in that work 
 hazards the assertion that " the quantity of the predicate is always 
 contained in thought," a statement which appears to us, as in the ex- 
 ample cited in the text, to be almost exactly the reverse of the truth.
 
 MODES OF PREDICATION. 
 
 93 
 
 c. ii. 3.] 
 
 yet no one, surely, 'would be bold enough to assert that 
 every judgment formed up to this time was less clear, from 
 the fact that mankind had never attended to its twofold 
 quantification. The obliviousness in which the particular 
 details of the general doctrine lay buried 1 , is the very proof 
 required to show that the mind does not need them, and, in 
 fact, never adverts to them in the formation of its judgments, 
 since the agreement or disagreement which such acts pro- 
 nounce can be ascertained with certainty without further 
 knowledge than the double sphere of the subject and the 
 connotation (metaphysical sphere) of the predicate afford. 
 
 The propositions which we have examined in connexion 
 with a quantified predicate, if combined with those which 
 arise out of a quantified subject, will, it is evident, embrace 
 every conceivable mode of affirmative predication ; and we 
 need only negative each proposition it contains to get every 
 conceivable mode of negative proposition, and thus complete 
 the list of simple categorical propositions real as well as 
 possible. Annexing corresponding signs to each of these for 
 the sake of brevity, they stand thus : 
 
 Predicate distributed in conformity 
 with rule. 
 
 Quantity. 
 
 Quality. 
 
 Signs. 
 
 All planets move in ellipses . 
 
 Universal 
 
 Affirmative 
 
 a 
 
 No unjust action is expedient 
 
 Universal 
 
 Negative 
 
 e 
 
 Some muscles act without our 
 
 
 
 
 volition 
 
 Particular 
 
 Affirmative 
 
 i 
 
 Some rocks are not granite . 
 
 Particular 
 
 Negative 
 
 
 
 Predicate distributed against rule. 
 
 
 
 
 Common salt is chloride of 
 
 
 
 
 sodium 
 
 Universal 
 
 Affirmative 
 
 X 
 
 Some plants are all lichens . 
 
 Particular 
 
 Affirmative 
 
 y 
 
 No rational animals are some 
 
 
 
 
 men 
 
 Universal 
 
 Negative 
 
 v 
 
 Some flowers are not some 
 
 
 
 
 rosadendrons 
 
 Particular 
 
 Negative 
 
 z 
 
 1 Mr. Baynes seems hardly to have been aware that in advancing 
 his master's (Sir W. Hamilton) claims to originality in the develop- 
 ment of the doctrine, he was only proving its absolute inutility for all 
 the practical purposes of logic. He first writes a treatise to show that
 
 94 PEOPOSITIONS WITH BEGAB.D TO TOEM. [B. n. 
 
 An examination of the above table will lead to tlie conclusion 
 already pointed out, that all the propositions, the predicate 
 of which is distributed or quantified against the rule, save oc, 
 are unnatural, and, as such, never used ; and that with regard 
 to x the predicate is not strictly, but merely casually, de- 
 finitive, not being implied in the form of the expression. It 
 will be, moreover, seen that the import of y, u, and z, find 
 their correct expression in a natural form only when their 
 terms are arranged to bring them under a, e, i, a ; we con- 
 sequently are led to reject the four other forms of judg- 
 ments as worthless, so far as practical logic is concerned, and 
 rest satisfied with the rule already given as sufficiently in- 
 dicative of the logical sphere of the predicate 1 ; viz., that all 
 universals and no particulars distribute the subject ; all 
 negatives and no affirmatives distribute the predicate : and 
 thus we have a distributing its subject, e both its terms, 
 i neither, and o its predicate. 
 
 4. Opposition of Propositions. 
 
 Opposition of propositions is simply the relation of the 
 agreement or disagreement of propositions which have the 
 same subject and predicate, (matter), but a different quantity 
 
 the quantification of the predicate is essentially necessary to the forma- 
 tion of accurate judgments ; in fact, invariably accompanies such 
 mental acts, and then proves, by way of appendix, that no person ever 
 had such quantification in mind but Sir W. Hamilton. Is not the 
 effect of this procedure clearly to intimate that clear conceptions have 
 been hitherto unknown, or to land Mr. Baynes in aflat contradiction? 
 The dilemma is inevitable, and. Mr. Baynes must choose his horn. 
 1 In rejecting the express quantification of the predicate we find 
 ourselves in respectable company. Aristotle (De Enunciandi Katione, 
 c. vii., and in Anal. Prior, i. c. 27, 9) also rejects it on the ground of 
 its futility; and is followed by nearly all his commentators, including 
 Boethius (Opera Omnia, Basil, p. 348) ; Averroes (Opera Omnia, 
 Venit. b. i. fol. 45) ; and Palius, in Arist. de Interp. c. vii., and Anat. 
 Prior, c. 27, 9, fol. 46. Ambrosius Leo appears the most inclined to 
 treat it with favour; but this arose from his antagonism to Averroes, 
 every one of whose opinions he made it a point to dispute (Castig. Ad. 
 Aver, in Lib. de Interpret.) Isenach, one of Luther's tutors, also 
 coquetted with the doctrine, in his Breviarum Dialectica, a divine 
 attached to the old opinions, whom, Luther says, he killed by expressing 
 before him his withering contempt for scholasticism. For a develop- 
 ment of Isenach's views on the quantification of the predicate, see 
 Mr. Baynes's Appendix to his New Analytic.
 
 C. II. 4.] OPPOSITION OF PEOPOSITI05TS. 95 
 
 and quality, or both, (form). As we can run any given 
 subject, and predicate through the four simple categorical 
 propositions a, e, i, o, forming a distinct judgment in each, 
 any two of which may be said to be opposed, it follows there 
 are four different kinds of opposition viz., Istly, the two uni- 
 versals (a and <?), which are called contraries to each other, as 
 " every man is a responsible agent," " no man is a responsible 
 agent*;" 2ndly, the two particulars (* and 0), which are called 
 subcontraries, as "some man is a responsible agent," " some 
 man is not a responsible agent ;" these two cases differ only 
 in quality, but agree in quantity ; 3rdly, a and i, or e and o, 
 which differ in quantity, but agree in quality, as " every 
 angel is a rational creature," " some angel is a rational crea- 
 ture ;" " no metal is incapable of being magnetised," " some 
 metal is not incapable of being magnetised;" which kind of 
 propositions are called subalternans : 4thly, a and o, e and i, 
 which differing both in quality and quantity, are called con- 
 tradictories, as "all muscat is fruit," "some muscat is not 
 fruit;" "no forms of government are exempt from change," 
 " some form of governments are exempt from change." 
 
 In considering these propositions it will be observed 
 that contraries can never be both true, though they may 
 be both false. For, if it be true that every man is ac- 
 countable for his actions, it is false that some man is not 
 accountable for his actions, which is the contradictory ; and 
 still more false, that no " man is accountable for his actions," 
 which is the contrary. But the falsehood of the one does 
 not imply the truth of the other. Eor example, if it should 
 be false that all men have a right to freedom, it would not 
 follow that, therefore, no men have. 
 
 Subcontraries may be both true, but cannot be both false, 
 as " some men are rich," " some men are not rich," may be 
 both true if we do not consider the negation to regard the same 
 subject as the affirmation ; but it is evident they cannot be 
 both false, unless we are prepared to assert a man can be 
 rich and not rich at the same time. It may, however, be 
 observed, that there is no real contrariety where the subject 
 of the propositions are not identical, and that consequently 
 the term subcbntrary is entirely arbitrary and unmeaning. 
 
 There is also no true opposition in the case of subalternans, 
 since the particulars are consequences of the general, so that
 
 96 PROPOSITIONS WITH BEGABD TO FOBM. [B. II. 
 
 the relation between them is one of partial agreement. For 
 if " all geraniums are flowers," " some geranium is a flower," 
 and if "no man is faultless," "some man is not faultless." 
 But it will be at once seen that the truth of the particulars 
 does not imply the truth of the universals, though their 
 falsity does ; and that the falsity of the universals does not 
 imply that of the particulars. Hence it is evident that there 
 are many cases in which these subalternate propositions are 
 both true, and others in which they are both false. 
 
 The opposition of contradictories is more perfect than any 
 of the others, as they are never both either true or false to- 
 gether ; and hence, if any proposition is known to be true, 
 we infer that its contradictory is false ; if false, that its con- 
 tradictory is true. For example, if every man is a dependent 
 creature, it cannot be true that some man is not a dependent 
 creature, and if, contrariwise, it be true that some man is not 
 a dependent creature, it is consequently untrue that every 
 man is a dependent creature. 
 
 It is important to observe, as the truth or falsity of any 
 proposition must depend upon the nature of the connexion 
 between the two terms, that in necessary matter all affirma- 
 tives are true, and negatives false : thus, all the radii of a 
 circle are equal, is an instance of the first ; no radii of a circle 
 are equal, or some radii of a circle are not equal, is a case 
 of the second : that in accidental matter all universals are 
 false, and particulars true ; as, all islands are fertile, no 
 islands are fertile, are both false, but become true by sub- 
 stituting "some" for "all" and "no:" that in impossible 
 matter all affirmatives are false, and negatives true, as is 
 evident from the nature of the case. By this means, from the 
 nature of the matter, we shall at once be enabled to decide 
 upon the truth or falsity of the judgments in every scale of 
 opposition ; as, e. g. in accidental matter, contraries will be 
 both false, but never both true ; sub-contraries both true, 
 but never both false ; and contradictories always one true 
 and the other false. 
 
 Denoting the four propositions by their symbols, and the 
 truth or falsity of each proposition in each matter by the 
 letter V. for (verum) true, and F. for (falsum) false, the 
 entire doctrine of opposition, and everything which pertains 
 to it, may be elicited from the adjoining scheme.
 
 C. II. 5.] CONYEBSIOH" OF PEOPOSITIONS. 
 
 97 
 
 n-v- -f ,n- 
 
 +f. 
 
 
 V I- 
 
 ^a- 
 
 a CONTRARIES t 
 
 
 1 %, ^ S 
 ^^^ ^ g 
 
 v^'/ 2 
 
 
 i -f 
 a-i;- 
 
 i suBcotnanRiEs o 
 
 / n- 
 
 v i 
 v a- 
 
 
 For practical purposes opposition is important, as showing 
 the force of any assertion, exhibiting the power which it has 
 of resisting any argument brought against it, or against 
 which it is brought. 
 
 5. Conversion of Propositions. 
 
 The conversion of propositions consists in the transposition 
 of their terms, that is, in making the subject the predicate, and 
 the predicate the subject, without affecting the truth of the 
 original proposition. To ensure this it is evident that the 
 quality of the judgment must be preserved, and no term dis- 
 tributed in the converse that was not distributed in the con- 
 vertend. For example, because " all salts are fusible," we can- 
 not infer that all fusible things are salts ; for in that case we 
 would employ the predicate universally in the converse, which 
 was only taken particularly in the convertend. 
 
 "When the distribution of the terms, however, is not 
 affected by the simple transformation of the subject and pre- 
 dicate, the conversion is legitimate, the truth of the converse 
 being expressly implied in that of the convertend, as 
 
 No charlatan is a patriot ; therefore 
 
 No patriot is a charlatan. 
 
 Some boasters are cowards ; therefore 
 
 Some cowards are boasters. 
 
 But this species of conversion, which is called simple, only 
 occurs with e and *, the first of which distributes both its 
 terms, and the last neither. 
 
 But in those propositions which distribute only one of
 
 98 PROPOSITIONS WITH KEGA.RD TO FORM. [fi. II. 
 
 their terms, simple conversion would not be legitimate, as in 
 a ; and to render the terms in the converse equivalent to 
 those in the convertend, we must affix the word some to the 
 predicate. Thus, though we cannot infer from 
 
 All birds are animals, that 
 All animals are birds, 
 
 we can, by limiting the predicate in the converse to the 
 exact extension it holds in the convertend, effect a legitimate 
 conversion, as 
 
 All birds are animals, 
 
 Some animals are birds. 
 
 This species of conversion is consequently known by the 
 name conversion by limitation : e may thus be converted, but 
 a is generally so. 
 
 The proposition o, however, is inconvertible by either of 
 these methods, since, whether the quantity be changed or 
 not, the predicate of the converse will remain undistributed, 
 which was not so in the convertend. We are, consequently, 
 obliged, in order to effect its conversion, to reduce the pro- 
 position to i, by considering not as prefixed to the predi- 
 cate, instead of to the copula. It may then of course be 
 converted simply, that is, by the mere transformation of its 
 terms, the subject assuming the form of an incidental propo- 
 sition. Thus, " some members of the university are not 
 learned" is equivalent to some members of the university are 
 not-learned, or some who are not learned are members of 
 the university. This may be termed conversion by negation, 
 or, as it is commonly called, by contraposition. Not alone o, 
 but every proposition may be converted in this way 1 . Hence 
 we may conclude, that in one of these three modes every pro- 
 position may be legitimately converted ; e and i simply, a e 
 by limitation, and o, a, e, and i by negation 2 . 
 
 An attempt has been made to get rid of the doctrine of 
 conversion thus propounded by introducing the quantification 
 
 1 Archbishop "Whately says only a, but if the student chooses to try, 
 he will find the conversion applicable to each of the four categorical 
 propositions. 2 It may appear that a is capable of simple con- 
 
 version, as in definitions where the predicate is identical with the 
 subject, but as its truth does not follow from the original proposition, 
 there is no conversion in the case, the resulting converse being a 
 different judgment, and not the same judgment in another form.
 
 C. II. 5.] CONVERSION OF PROPOSITIONS. 99 
 
 of the predicate, which would reduce the whole affair to a 
 mere transformation of terms 1 . The simplification, however, 
 if at all practicable, would be purchased at the expense of 
 utility. Take the most complex form which the old doctrine 
 assumes, that of conversion by negation, and transform the 
 terms of a proposition in o, after having quantified the pre- 
 dicate. By this process, the proposition " some metals are 
 not all conductors" would become " all conductors are not 
 some metals," or " no conductors are some metals." Of 
 what conceivable use can the latter judgment be, which the 
 first is not able more properly to effect? Conversion in 
 such cases would frustrate every purpose it is instituted to 
 effect by reducing a proposition from a form in which it is 
 of some use, as conveying substantial information, to another 
 in which it is deprived of a determinate meaning; for it 
 cannot concern us to know that no metals are some con- 
 ductors, since there may be other conductors which are some 
 metals. Yet only in the conversion of o could the quantifi- 
 cation of the predicate effect any direct simplification. For 
 the conversion of a, the sole case where its application is 
 admissible, cannot be more simply provided for than by the 
 old rule ; while that of e, by limitation, if effected in accord- 
 ance with the quantification of the predicate, would lead to 
 the inference of a particular proposition where a universal 
 might be drawn, and consequently be so far nugatory. 
 
 It appears to us that the advocates of a complete quantifi- 
 cation of the predicate are so absorbed in the means which 
 logic employs, as to lose sight of the ends they are intended 
 to effect. The object of conversion is to enable us to throw 
 a proposition either into a clearer form or into one more 
 fitted to sustain the argument which we may be endeavour- 
 ing to establish. But either of these purposes must be 
 defeated by crowding the brain with a series of unnatural 
 propositions, such as the quantification of the predicate would 
 generate, which are never used in ordinary discourse, simply 
 because the mind never considers them adequate either to 
 express the clearness or the force of its conceptions. Even 
 in the supposition of their competency, they could not be 
 substituted for those forms of conversion which logic already 
 employs, each of which has its peculiar functions to fulfil in 
 
 1 Mr. Baynes's New Analytic, which expresses Sir W. Hamilton's 
 views, and bears his imprimatur. 
 
 n2
 
 100 SYLLOGISMS. [B. III. 
 
 the hands of the dialectician. To take the conversion by 
 contraposition, which is the one against which there is the 
 most complaint, its striking importance is manifest in en- 
 abling us to throw a proposition into the negative form, 
 when that form will more easily lead to the establishment of 
 our position than any other ; as is done by Paley in proving 
 the main proposition of his Evidences. The means may be 
 cumbrous ; but a complex arrangement is often required to 
 gain the end in view, where a more simple instrument would 
 fail. No doubt the Cuirassiers at Waterloo felt their armour 
 an encumbrance; but had they exchanged their plates of 
 mail for woollen coats, would they have done their work so 
 well, or, rather, would they have been allowed to do their 
 work at all ? 
 
 BOOK III. 
 
 SYLLOGISMS. PEOEMIUM. 
 
 As the combination of two or more terms leads to the 
 expression of a 'judgment concerning their agreement or 
 difference, so the union of two or more propositions is essen- 
 tial to the formation of inference ; or, in other words, we 
 reason from a comparison of propositions, as we may be said 
 to judge from a comparison of terms. But in order that 
 two propositions may unite to form a distinct judgment, it is 
 necessary they should express something concerning the 
 same object ; or, in other words, that they have one term in 
 common: the agreement or disagreement of the common 
 term with the other terms involved, will then lead to the 
 enunciation of a new judgment, declaratory of the relation in 
 which the dissimilar terms stand to each other. The evolu- 
 tion of such a judgment from two antecedent propositions 
 asserting something concerning a common term, is an in- 
 stance of one of the simplest forms of reasoning ; and the 
 formal statement of the propositions concerned, in their 
 sequential order, is called a syllogism. Thus : 
 
 All planets move in ellipses ; 
 
 But Mercury, Mars, and Venus, are planets, 
 
 Therefore they move in ellipses.
 
 B. III.] TWO KINDS OF INFERENCE. 101 
 
 Though every illative process implies three judgments, in 
 two of which one term is compared with two others, in order 
 that the relation between these last may be accurately deter- 
 mined in a conclusive proposition; yet this number of judg- 
 ments is by no means necessary for every sort of inference. As 
 we have already seen in the opposition and conversion of pro- 
 positions, we can make a series of inferences from two terms ; 
 as from the fact of man being mortal, it is competent to any 
 one to infer that some mortal beings are men, or that no 
 man can be immortal ; that immortal beings are not men, 
 and that he who honours a man honours a mortal ; but such 
 inferences do not embrace any illative process that is, the 
 evolution of any new judgment different from the one already 
 expressed, but only the same judgment in a different form ; 
 and, therefore, are properly excluded from the domain of 
 strict reasoning, which is only employed in eliciting new 
 truths, or in presenting those already discovered in a de- 
 monstrative form to others 1 . Each inference in the case of 
 strict reasoning, when completely analysed, will be found to 
 depend upon three or more such propositions, as we have 
 
 1 The reader must have his eye on this distinction, as it appears to 
 us that the losing sight of it has betrayed some distinguished writers 
 into an erroneous conception of the nature of reasoning. Thus Dugald 
 Stewart resolves the whole process into intuition and memory, and 
 presents us with a case of immediate inference, which the first kind is 
 generally called, as an instance of reasoning in which three judgments 
 are irrelevant, and then proceeds to reject the Aristotelic theory on 
 account of its non-applicability to a case in which there is really no 
 reasoning at all!! (Phil. Hum. Mind, b. iii. c. ii. 1.) Mr. Samuel 
 Bailey, in his recent able Essay on the Theory of Reasoning, seems to 
 fall into the same error, in citing similar cases of reasoning ( ?) as un- 
 recognised by, and foreign to, the Aristotelic syllogism (p. 83), as "all 
 men are fallible," " this man is fallible." Locke (Hum. Und. b. iv. 
 15), who, in this and other places, seems above his disciples, re- 
 stricts reasoning to the sense in which we have taken it, and insists 
 upon the distinction above laid down between the two kinds of in- 
 ference, one of which he calls immediate, the other mediate. All the 
 writers who adopt Stewart's views confound the relation between the 
 formal identity of a syllogism viz., the necessity of the conclusion, if 
 the premises be true, with its material identity viz., the identical 
 truth of each of the three judgments. Though we see the former in- 
 tuitively, we do not see the latter. A middle term is necessary to dis- 
 tinguish it. Truth, like life, is propagated by union: two verities must 
 unite to produce a third.
 
 102 PEOPEBTIES OF SYLLOGISMS. [B. HI. 
 
 described ; and the properties which attach to them in their 
 syllogistic union, and the multiform modes in which they 
 may be combined, will form the subject of the present book. 
 Under the former head we shall treat of the one great 
 canon of mediate inference, and the general rules which are 
 to be observed in its application ; the moods and figures will 
 follow with their special canons and rules, and the number 
 of valid cases of inferences to which these lead will be con- 
 trasted with the more enlarged series which a complete 
 quantification of the predicate is said to establish. The second 
 portion will comprise the different kinds of syllogisms with 
 the laws of the reduction of the more complex to a sim- 
 ple categorical form, to which the syllogistic rules and 
 canons are more applicable. In this book, therefore, we 
 restrict ourselves to the naked syllogism as the inferential 
 link out of which the chain of proof is constructed. How 
 these links are bound together in the evolution of new truths, 
 or in conclusive lines of demonstration; the inductive and 
 deductive forms they usually assume with the laws of their 
 combinations ; the grounds on which all proof rests, and the 
 various axioms which legitimise and discriminate its dif- 
 ferent degrees of certainty ; are evidently matters which re- 
 gard a higher step in the treatise than simple inference, and 
 may be regarded, in Lord Bacon's manner, as certain pro- 
 dromi, or anticipations which prepare the way for the con- 
 sideration of the consecutive forms of reasoning which 
 are to engage our attention in the different sciences. As 
 such we shall consider them apart in the next two books. 
 
 CHAPTER I. 
 
 PEOPEBTIES OF SYLLOGISMS. 
 
 1. Universal Canon of Mediate Inference with the General 
 Rules of the Syllogism. 
 
 As all reasoning may be virtually resolved into a com- 
 parison of two terms with a common third term, with a view 
 to ascertain their respective relations to each other, the 
 geometrical axiom viz., two things which are equal to a
 
 C. I. 1.] TTNIVEBSAL CA^Otf. 103 
 
 third thing are equal to each other which underlies all ma- 
 thematical inference, may be said to be fundamental to every 
 kind of valid inference on whatever matter employed 1 ; but 
 to transform this axiom into the universal canon of in- 
 ference, in such a manner that it shall prospectively embrace 
 all the general rules, requires a preliminary remark respect- 
 ing the sense of the word relation. 
 
 Two terms are said to be related when they stand to each 
 other in the position of subject and attribute ; but this re- 
 lation varies in degree according to the different quantity 
 and quality of the proposition in which it is expressed. 
 Thus, if a subject stand to an attribute in the relation of a 
 universal to a particular, the relation of the attribute to the 
 subject is said to be inferior to that of the subject with the 
 attribute, because the latter embraces fewer objects ; and, 
 in like manner, if a common term be affirmed of one object, 
 and denied or excluded from another, the relation in which 
 such term stands to the latter is called inferior to that of 
 affirmation, since it is much more definitive to affirm than to 
 deny. Hence when two terms, taken in the same extension, 
 are contrasted affirmatively with a common third term, no 
 difference of relation occurs between them in other words, 
 the relation is termed equal ; but when one is applied either 
 particularly or negatively to a common term, while the other 
 is taken universally and affirmatively, the relation of the 
 former is said to be inferior to that of the latter. "With 
 this proviso, we may take the universal canon of reasoning 
 to be : What equal or inferior relation subsists between either 
 of two terms and a common third term, with which loth are 
 related, and one at least positively so, that relation subsists 
 between the two terms themselves 2 . Observing this canon, no 
 syllogism can be formally invalid, and we shall see the reason 
 of this by tracing the manner in which it folds up within 
 itself the general rules of the syllogism. 
 
 1st. Every syllogism must contain no more than three 
 terms. Of these, the two whose relation is to be proved 
 
 1 See Bacon's Primary Philosophy, De Aug. b. iii. c. 2 : " QUCE in 
 eodem tertio conveniunt inter se conveniunt," regula est itidem ex mathe- 
 maticis ; verum simul tarn potens in logica ut syllogismi sit fundam.cn- 
 tum. 3 This canon, with a little alteration, we have taken from 
 Sir W. Hamilton. See Mr. Baynes's New Analytic.
 
 104 PROPERTIES OF SYLLOGISMS. [B. III. 
 
 are called the extremes of the conclusion, or question ; and 
 the term, by which their relation is proved, is called the 
 middle. Of the extremes, again, the subject of the conclu- 
 sion is called the minor term, and that which stands as 
 predicate the major term 1 . 
 
 The term major has been applied to the attribute of the 
 conclusion, and minor to the subject, because in the most 
 natural form of inference 3 , the major was by its position 
 the most extensive, and the minor least. Thus, in the 
 syllogism: All wise men are circumspect; but Solon was 
 a wise man ; therefore, Solon was circumspect ; circum- 
 spect, the major term, is more extensive than Solon, the 
 minor, for we include Solon and all other wise men in 
 circumspect. When the conclusion, however, is either par- 
 ticular or negative, it is impossible to ascertain the relative 
 magnitude between the two terms. There is nothing to 
 prevent in such cases the so-called major term from being 
 much less than the minor, though there is always a pre- 
 sumption in favour of the contrary case, arising from the 
 mental habit of restricting the subject and leaving the 
 predicate unquantified. 
 
 The fulfilment of this rule is secured by that part of the 
 canon which enjoins the relation of two terms with a com- 
 mon third term by way of subject and predicate : but this 
 does not prevent one of the propositions from being con- 
 junctive, that is, from including several distinct terms under 
 it ; for so long as one predicate is affirmed of them, such 
 plural subjects are logically considered as one term. The 
 rule is directly aimed against the assumption of two middle 
 terms, since, in that case, . the extremes, or terms of the 
 conclusion, not being both compared to the same term, 
 could not be conclusively compared to each other. 
 
 2nd. Every syllogism can embrace only three judgments, 
 viz., those commonly called the premises, in which the 
 extremes are respectively compared to the middle, and the 
 
 1 In Greek, major = TO axpov 
 
 minor = TO erepov 
 middle = TO peaov 
 
 2 The first mood of the first figure. See next section.
 
 C. I. 1.] EULES OF THE SYLLOGISM. 105 
 
 conclusion in which the relation of the two extremes is 
 expressed. Of the premises, that in which the middle term 
 is compared with the major or attribute of the conclusion, is 
 styled the major premiss, and that in which the middle is 
 compared with the minor, or subject of the conclusion, is 
 termed the minor premiss. 
 
 There may be some combinations of more than three 
 propositions, which seem to present simple cases of infer- 
 ence ; but if all such are carefully analysed, they will be 
 found to resolve themselves into plural inferences, each of 
 which, when fully expressed, expands into a distinct syllo- 
 gism, with a triplex judgment. The rule, therefore, strictly 
 holds under every circumstance, and, indeed, may be con- 
 sidered as a necessary corollary of that part of the canon 
 which ensures the first rule. For if there be only three 
 terms, each of which is to be compared once only with 
 the two others, it is evident there can be only three judg- 
 ments, viz., those which express the three acts of comparison, 
 since three terms cannot be incorporated in more than three 
 propositions without repetition 1 . 
 
 3rd. The middle term must be distributed once at least 
 in the premises, which is ensured by making it either the 
 subject of a universal, or the predicate of a negative ; for if 
 it be taken particularly in both of the premises, one of the 
 extremes may happen to be compared with one part of its 
 extension, and the other with the other part, as : 
 
 The wise are good ; 
 
 Some ignorant people are good ; 
 
 Therefore, some ignorant people are wise. 
 Here the term good being undistributed, is applied to two 
 different classes of people, and in that double sense predi- 
 cated of ignorant and wise. These extremes are conse- 
 quently compared with two different parts of the term 
 good, so that in lieu of one middle term we have two, 
 against the express sanction of the canon. The same 
 illusion equally obtains where the middle term is ambiguous 
 or equivocal, for in such instances two different senses may 
 be struck out of the word, and the same error committed as 
 
 1 Thompson's Laws of Thought, p. 231, 2nd ed.
 
 106 PBOPEBTIES OF SYLLOGISMS. [B. III. 
 
 if the term had remained undistributed. To cite a glaring 
 instance : 
 
 Light is contrary to darkness, 
 Feathers are light ; 
 
 Therefore, feathers are contrary to darkness 1 . 
 As the purport of the rule, however, is to secure the 
 comparison of each of the extremes with the whole or the 
 same part of the middle, this, it has been argued, may be 
 obtained 3 without an express distribution of the middle ; as 
 when, instead of introducing every part of a third term, we 
 specify what part of it, is intended to be taken in botli 
 premises ; but we cannot so specify the part of the middle 
 without rendering it a singular term, and such we have 
 seen are universal, and consequently distributive. Thus, from 
 the premises : 
 
 Three-fourths of the army were Eussians, 
 Three-fourths of the army were slaughtered ; 
 we may fairly infer that 
 
 Some who were slaughtered were Eussians. 
 For, even supposing the whole of the remaining fourth that 
 were slaughtered were Turks, there would still remain two- 
 fourths in the second premiss to be put to the account of 
 the Eussians, as the following lines will show : 
 Eussians ' [ 
 
 Army I I I I I 
 
 Men slaughtered l_ 
 
 But it is evident that in this case the middle term is of a sin- 
 gular character, and consequently universal, and as such dis- 
 tributed in both premises. 
 
 4th. No term must be distributed in the conclusion which 
 was not distributed in one of the premises, since that would 
 be to employ the whole of a term in the conclusion, when 
 only a part of it had been employed in the premises, which 
 is in reality equivalent to the introduction of a fourth term. 
 Thus: 
 
 Edward is melancholy, 
 
 Edward is wise ; 
 
 Therefore all wise men are melancholy. 
 
 i Archbishop Whately's Logic, b. ii. c. iii. 2. 2 Thompson's 
 
 Laws of Thought, p. 237.
 
 C. I. 1.] EULES OF THE SYLLOGISM. 107 
 
 Again : 
 
 All quadrupeds are animals, 
 
 A bird is not a quadruped ; 
 
 Therefore it is not an animal. 
 
 In the first example, the minor term is taken more exten- 
 sively in the conclusion than in the premises an act which 
 is called illicit process of the minor ; in the second example, 
 the major term is in the same position, and is similarly 
 termed an illicit process of the minor. Between the two in- 
 stances there is, however, this difference, that the illicit pro- 
 cess of the major is far the worse fault, as in that case we are 
 not entitled to draw any conclusion at all ; but in the other 
 we only draw a universal in place of a particular. This rule 
 is expressly provided for by that part of the canon which 
 directs that the terms be expressed in the conclusion accord- 
 ing to the inferior relation which they hold in the premises. 
 5th. From negative premises we can infer nothing ; con- 
 sequently one must be affirmative. For if both extremes are 
 said to disagree with the middle term, they cannot be com- 
 pared together. Thus, from 
 
 Every wise man is not amiable, 
 
 Wo miser is wise, 
 
 we can infer nothing. This rule is expressed in the canon 
 by the clause enjoining that one of the extremes shall be 
 connected with the common third term positively. 
 
 6th. If one premiss be negative, the conclusion must be 
 negative. For in that premiss the middle term is pro- 
 nounced to disagree with one of the extremes, and in the 
 other premiss, which must by the preceding rule be affirma- 
 tive, to agree with the other extreme ; but extremes which 
 disagree with each other can only lead to a negative conclu- 
 sion. This rule is also secured by that part of the canon 
 already quoted as involving the fourth rule ; viz., that the 
 conclusion must follow the inferior relation of the extremes 
 in the premises. 
 
 These rules in the common school logics are extended to 
 eight, and are thus expressed in hexameters : 
 
 Terminus esto triplex medius majorque minorque : 
 Latius hos quam praemissae conclusio non vult : 
 Nequaquem medium capiat conclusio oportet : 
 Aut semel aut iterum medium generaliter esto :
 
 108 PEOPEETIES OF SYLLOGISMS. [B. III. 
 
 Utraque si prsemissa neget, nihil inde sequitur : 
 Ambse affirmantes nequeuut generare negentem : 
 Nil sequitur geminis ex particularibus unquam : 
 Pejorem sequitur semper conclusio partem. 
 
 But if these are examined, the remaining two will be found 
 to be included in the ones we have already particularised. 
 For example, the third and fourth rule preclude all inference 
 from two particular premises, because the resulting syllo- 
 gism would involve either an undistributed middle or an 
 illicit process. As : 
 
 Some minerals are crystals, 
 
 Some stones are not crystals ; 
 
 Therefore some stones are not minerals. 
 The fourth rule, also, collaterally implies, that if one of the 
 premises be particular, the conclusion must be particular, in 
 accordance with the canon, that the terms in the conclusion 
 must follow the inferior relation, if such exist, which obtained 
 in the premises. For, the inferring a universal conclusion 
 in that case would lead to the illicit process of the minor. 
 Thus, from 
 
 All who live virtuously deserve esteem, 
 Some Pagans lived virtuously, 
 we can only infer that 
 
 Some Pagans deserve esteem. 
 
 It may also be remarked, that several of the rules assign the 
 conditions for the existence of a syllogism rather than afford 
 any direct test of its validity. It is likewise important to 
 remember that all the general rules already given are not to 
 be regarded as something distinct from the canon, but as a 
 detailed exposition of its principles, intended to secure in all 
 cases every illative process from error. 
 
 2. Figures of the Syllogism. 
 
 The figure of a syllogism is determined by the situation of 
 the middle term when compared with the extremes of the 
 conclusion in the premises. This may obviously vary in four 
 different ways. For the middle term can either be the sub- 
 ject of the major premiss, and the predicate of the minor, 
 which is the first figure ; or the predicate of the major premiss, 
 and the subject of the minor, which is the fourth figure ; or the
 
 c. i. 2.] riGURES or THE SYLLOGISM. 109 
 
 predicate of both premises, which forms the second figure ; or 
 the subject of both, which constitutes the third figure. Using 
 the initial letters of the different terms, in lieu of concrete 
 exemplifications, the scheme may be thus expressed : 
 1st fig. 2nd fig. 3rd fig. 4th fig. 
 
 M, P, P, M, M, P, P, M, 
 0,M, I, M, M, S, M, S, 
 /. S, P, /. S, P, .-. S, P, .-. S, P. 
 
 Each of these figures have their respective rules, which, how- 
 ever, are involved in the universal canon and the rules already 
 given; and only lead to a separate statement, by way of 
 caution, that none of the figures may violate the principles 
 of the rules already given. Though the reader might easily 
 evolve these special rules, from an examination of each figure 
 in connexion with the main canon, we will state them at 
 length, together with the laws or principles which the four 
 figures exemplify. 
 
 The construction of the first figure requires the major 
 premiss to be universal, and the minor affirmative ; as in the 
 celebrated argument of Aristotle 1 , to prove the inseparable 
 union of the virtues : 
 
 He who possesses prudence possesses all virtue, 
 
 He who possesses one virtue must possess prudence ; 
 
 Therefore he who possesses one virtue possesses all. 
 Por if the minor were negative, the major must be affirma- 
 tive by the fifth general rule, and the conclusion negative by 
 the sixth ; the greater term, which is taken only particularly 
 in the major premiss, would then be taken universally in the 
 conclusion, in contravention of the fourth rule. Now, if the 
 minor must be affirmative, the major premiss must be uni- 
 versal, otherwise the middle term, being the subject of the 
 latter, and the predicate of the former, would be taken twice 
 particularly, against the third rule. 
 
 The principle or law which the first figure exemplifies, is 
 the celebrated dictum de omni et nullo, which Aristotle sup- 
 posed to be inclusive of all reasoning. It may be thus ex- 
 pressed : " Whatever is affirmed or denied of a class may be 
 affirmed or denied of any part of that class 3 ." So that if 
 
 1 Eth. b. Ti. passim. * Arist. Cat. ch. v., and Pri. An. i. ch, v. and 
 vi. See Bohn s Scientific Library.
 
 110 PBOPEBTIES OF SYLLOGISMS. [B. III. 
 
 one attributes to men free agency, we may also affirm it of 
 Ethiopians as part of the class men ; or if it is denied that 
 brutes are thinking beings, we may also aver the same of 
 apes, which are included in the same category. Whatever be 
 the subject-matter, this figure invariably illustrates the same 
 principle ; since in it the greater term is affirmed or denied 
 of the middle, taken universally, and this same middle is again 
 affirmed of the lesser term, in a particular sense, which makes 
 the subject of the conclusion stand in the same relation to 
 the subject of the major premiss as part to a whole, and con- 
 sequently produces a subordination of classes. 
 
 The first figure is generally deemed the most perfect, be- 
 cause all the propositions, a, e, i, o, can be proved by it, 
 and a universal affirmative by it alone 1 . The reason of the 
 latter is, that with a view to make the conclusion a universal 
 affirmative, the lesser term must be taken generally in the 
 minor, and consequently form its subject ; but the middle term 
 being the predicate of the minor, is particular, whence arises 
 the necessity of taking it universally in the major where it is 
 the subject. But this can only occur in the first figure. 
 
 Since the second figure is that in which the middle term is 
 taken twice as attribute, it requires two cautions, with a view 
 to secure its adherence to the general rules of the universal 
 canon. The first is, that one of the premises, and conse- 
 quently the conclusion must be negative ; and secondly, that 
 the major proposition must be universal ; as in Cicero's argu- 
 ment against the Epicureans 2 . 
 
 All true philosophers regard virtue as a good in itself, 
 But the Epicureans do not reckon virtue a good in itself; 
 Therefore the Epicureans are not true philosophers. 
 
 For if both propositions in this syllogism were affirmative, the 
 middle, which in this figure is always the attribute, would 
 be taken twice particularly, against the third rule ; and since 
 the greater term is universally taken in the conclusion, it 
 cannot be taken particularly in the major premiss, where it 
 is the subject without an illicit process, which the fourth rule 
 directly forbids. 
 
 1 Not as Mr. Thompson states (Laws of Thought, p. 242), because 
 it more directly exemplifies the dictum de omni et nullo. 2 De 
 Officiis, b. i. and ii.
 
 C. I. 2.] FIGFEES OF THE SYLLOGISM. Ill 
 
 The second figure illustrates the dictum de diverso, being 
 founded on the axiom, " If one term is contained in, and 
 another excluded from a third term, they are mutually ex- 
 cluded," and is obviously useful for showing the differences 
 of things, and remedying the confusion arising from indistinct 
 conceptions. For instance, when we have to disprove some- 
 thing that has been maintained, or is likely to be believed, we 
 show that the thing we are speaking of cannot belong to 
 such a class, either because it wants what belongs to the 
 whole of that class, or because it has something of which that 
 class is destitute ; in either case the inference will fall into 
 the second figure. 
 
 As the middle term in the third figure is twice taken as 
 subject, it follows, with a view to the observance of the canon, 
 that the minor proposition must be affirmative, and the con 
 elusion particular; as in Adam Smith's reasoning on the 
 moral sentiments 1 , 
 
 Prudence has for its object the benefit of individuals ; 
 
 But prudence is a virtue ; therefore 
 
 Some virtue has for its object the benefit of the individual. 
 For if the minor were negative, the same consequences would 
 follow which have been already pointed out in the case of 
 a minor negative in the first figure. While a general con- 
 clusion would lead to an illicit process ; as the subject, which 
 is only taken particularly in the minor premiss, would then 
 be universal against the fourth rule. 
 
 The principle which the third figure exemplifies may be 
 called the dictum de exemplo, that is, " Two terms which con- 
 tain a common part partly agree, or if the one contain a part 
 which the other does not they partly differ ;" and is generally 
 employed to establish an objection to an opponent's premiss 
 where his argument is such as to require that premiss to be 
 universal. Thus, if any one contended that this or that 
 doctrine ought not to be admitted, because it cannot be 
 explained or comprehended, his suppressed major premiss 
 might be refuted by the argument, that gravitation, as an 
 occult quality, cannot be explained or comprehended : a great 
 part of Butler's analogy might be exhibited in this form 2 . 
 
 The fourth figure is only employed by an accidental awk- 
 
 1 Against Hutcheson and others, who placed all virtue in benevolence. 
 * Whately's Logic, b. ii. ch. iii. 5.
 
 112 PBOPEKTIES OF SYLLOGISMS. [B. III. 
 
 \rardness of expression ; and as the conclusion which the 
 mind would naturally draw from premises in which the 
 middle term appears as the predicate of the first proposition, 
 and the subject of the second, would change it into the first 
 figure, this course is ordinarily taken by simple conversion. 
 Thus, in Cicero's argument 1 : 
 Whatever is expedient is conformable to nature, 
 Whatever is conformable to nature is not hurtful to society ; 
 Therefore what is hurtful to society is never expedient. 
 Here the mind is naturally led to expect the converse of the 
 conclusion to be drawn as the proper consequence, viz., 
 ' : what is expedient is not hurtful to society," which would 
 transform it into a syllogism in the first figure. It would, 
 therefore, be only sanctioning a blunder to invest the fourth 
 figure with axiom and rules 2 , and we mention it, indeed, in 
 this place only to caution the reader against it. 
 
 Some logicians 3 , it may be observed, taking that proposi- 
 tion which is placed first for the major premiss ; and for the 
 minor, that which stands second, apply to the fourth figure 
 the reasonings of the first, and condemn Aristotle for not re- 
 cognising it. If, however, the major and minor premises 
 were to be determined by their situation in the syllogism, it is 
 obvious that the conclusion would be frequently confounded 
 with them, since, in ordinary reasoning, it is as customary to 
 mention the fact and then proceed to the proof, as it is to 
 begin with the proof and then mention the fact ; while in that 
 class of reasonings which take the shape of questions and pro- 
 blems, it is invariably the practice to commence with a state- 
 
 1 De Officiis, b. iii. 9 It was, notwithstanding, done by Lambert 
 and the Port Royal logicians, though Arnauld treated the subject of 
 his labour with some degree of contempt. See 1'Art de Penser, part iii. 
 ch. viii. Aristotle never alludes to the fourth figure; and some logi- 
 cians, on the authority of Averroes (in 1 Pri. An. ch. viii. vol. i. 
 p. 63), have attributed it, as an actual discovery, to Galen; which is 
 much about the same as to attribute phlogiston to Beecher as a chemi- 
 cal discovery, because no one had stumbled upon that error before. 
 Mr. Thompson is of opinion that Galen did not adopt the fourth figure, 
 from the inspection of a Greek copy of Galen's Dialectia, recently 
 published in Paris, from a MS. of the eleventh century. To prove, 
 however, that nothing can be so absurd that will not admit even of 
 elaborate apology, Zaberella has written a book in defence of the 
 fourth figure. 3 Gassendi, Institutio Logica, pars tertia, canon i., 
 
 and Zaberella.
 
 C. I. 3.] ABRIDGEMENT OF PREMISES. 113 
 
 ment of the conclusion 1 . Of the latter instance, we of course 
 find many examples in mathematics ; of the former, any writer 
 will afford us frequent examples. Thus, Horace : 
 Qui melior servo, qui liberior sit avarus ; 
 In triviis fixum, cum se demittit ob assem 
 Non video : nam qui cupiet, metuet quoque : porro 
 Qui metuens vivit, liber inihi non erit unquam 2 , 
 
 which, is reducible to, 
 
 He who is in continual fear is not free, 
 Every miser is in continual fear ; 
 Therefore no miser is free. 
 
 The local arrangement of the propositions, therefore, which 
 affect no change in the argument, are not to be taken as 
 an index of the major or minor premiss, but that proposi- 
 tion must be considered as major, one of whose terms is the 
 attribute of the conclusion, and that the minor, in which the 
 subject of the conclusion is found. 
 
 3. Moods of the Syllogism. 
 
 The designation of the three propositions of a syllogism, 
 in their logical order, according to their respective quantity 
 and quality, constitutes its mood. Thus the syllogism last 
 given, " He who is in continual fear is not free," is in the 
 mood e, a, e. Since there are four kinds of propositions (a, 
 e, i, o), and three propositions in each syllogism, all the pos- 
 sible ways in which these can be 'combined in a syllogism 
 are sixty-four. For any one of these four may be the major 
 premiss, while each of these four majors may have four dif- 
 ferent minors ; and of these sixteen pair of premises each may 
 have four different conclusions. But by bringing each mood 
 to the test of the canon, twenty-eight will be found excluded 
 on account of negative and particular premises ; eighteen by 
 the condition that the conclusion follow the inferior part ; 
 
 1 Sir W. Hamilton asserts, that the Greeks (Pagan and Christian, 
 Peripatetic, Academic, Stoic, Epicurean, and Sceptic, down to the 
 taking of Constantinople) placed first in syllogistic order the minor 
 proposition, and that the Latins, up to the sixth century, were of accord 
 with the Greek, when the example of Boethius caused succeeding 
 scholars to follow the present practice, which assigns the first place to 
 the major premiss. 3 Epist. i. 16. 
 
 I
 
 114 PEOPEETIES OF SYLLOGISMS. [B. III. 
 
 six for the reason that a negative conclusion cannot follow 
 from particular premises ; and one, *, e, o, because the major 
 proposition of a negative conclusion can never be a particular 
 affirmative by the fourth rule. When these fifty-three in- 
 valid moods are subtracted from the list, there only remain 
 eleven, viz. : 
 
 Four Affirmatives and Seven Negatives. 
 
 a, a, a, e, a, e, 
 
 a, i, i, a, e. e, 
 
 a, a, i, e, a, o, 
 
 i, a, i. a, o, o, 
 
 o, a, o, 
 
 e, i, o, 
 
 a, e, o. 
 
 Each, however, of the valid moods are not admissible into 
 every figure, since some may violate the general canon in 
 one figure though not in another. Thus, i, a, iis a valid 
 mood in the third figure, but in the first it would be attended 
 with a distributed middle. So a, e, e would involve in the first 
 figure an illicit process of the major, but is legitimate in the 
 second ; and a, a, a, which is admissible in the first figure, 
 would in the third involve an illicit process of the minor. By 
 a 'similar application of the moods to the figures in detail, it 
 will be found that each will admit only six valid moods ; and 
 of these several, though valid, are useless, as leading to a 
 particular conclusion when a universal might be drawn. As, 
 for instance, a, e, o, in any of the four figures, or a, a, i, in 
 the first figure : Thus, 
 
 All human creatures are entitled to liberty, 
 
 All slaves are human creatures ; 
 
 Therefore some slaves are entitled to liberty. 
 For this reason, five out of the twenty-four moods arising 
 out of the union of six valid moods in each figure are re- 
 jected; so that nineteen remain as the only valid forms in 
 which inference can lead to a useful result ; and even of these, 
 five may be very well neglected as belonging to the fourth 
 figure. As one mood may occur in two figures, it is neces- 
 sary to distinguish both the mood itself and the figure in 
 which it is to be found, and to effect this purpose logicians 
 have devised names, with vowels, corresponding to the several
 
 C. I. 4.] MOODS OF THE SYLLOGISM. 115 
 
 inoods, and arranged them in verses, each line of which 
 answers to the respective figure in which the moods occur. 
 Thus: 
 
 FIG. 1. Barbara 1 , celarent, dam, fm'oque prioris. 
 
 PIG. 2. Cesare, cames-tres, festino, baroko secundae. 
 
 FIG. 3. Tertia, doroptt, disarms, datisi, fielopton 
 
 Borordo, feriso, habet. Quarta insuper addit 
 
 FIG. 4. Bromontt'p, camenes, dimaris, fesapo, fresison. 
 
 The five moods of the fourth figure are sometimes ex- 
 pressed as 
 
 Boralzpton, celantes, dabitis, fopesmo, 
 Frzsesomorum, 
 
 which transform the minor into the major premiss : For it 
 was maintained, as Aristotle had not made a separate figure 
 for these moods, that they were only indirect moods of the 
 first figure with the conclusion reversed, and that, conse- 
 quently, the attribute of the latter was the true subject. But 
 as the conclusion is invariably supposed to be the thing which 
 requires proof, it is certainly preferable to take always as the 
 major the proposition into which the attribute of the conclu- 
 sion enters, and bring them under the first figure by simple 
 conversion. 
 
 4. The Quantification of ike Predicate (new analytic) 
 considered with reference to Mood and Figure. 
 
 The list of valid moods has been enlarged by introducing 
 into the combination the four additional propositions which 
 emerge out of the express qxiantification of the predicate : 
 but as we endeavoured to show that judgments with a 
 quantified predicate were never practically subject to the 
 mind's attention, and that if it needed to express the rela- 
 tions about which they are employed, it would fling them 
 
 1 These verses commence (barbara) ominously enough, and hare 
 been the subject of some wit and banter. It must, however, be con- 
 fessed, considering the age in which they were produced (thirteenth 
 century), and the man in whose works they were first found (Peter 
 Hispanus), that they display an ingenuity which might have excited 
 the envy of the Stagyrite himself. In addition to the distinction 
 of mood and figure, the consonants, combined with the vowels, were 
 intended to serve a distinct purpose in reduction, which, however, the 
 discovery of dicta quite as potent as the axiom de omni et nullo for each 
 of the figures, has rendered nugatory. 
 
 I 2
 
 116 PItOPEBTIES OF SYLLOGISMS. [B. III. 
 
 into one of the forms included in the four judgments, a, i, 
 e, o, to which we have restricted the consideration of logical 
 quantity and quality, we might rest the matter here : since 
 if that position be sound, the extension of valid moods can 
 only be gained by the interpolation of. useless propositions, 
 leading to conclusions or inferences that no one ever seeks 
 to establish. It may, however, be important, considering the 
 high quarter 1 from which the doctrine of the complete quan- 
 tification of the predicate emanates, to give it an ampler con- 
 sideration here, where it is designed to replace the old cate- 
 gory of syllogisms, and which, consequently, is alleged to be 
 the true sphere of its utility. 
 
 The two great ends which the new quantification is designed 
 to accomplish, are the amplification of the valid forms of rea- 
 soning, and through it, the abolition or simplification of all 
 that is cumbrous in the old system of logic. The first of 
 these is certainly effected by the introduction of the four 
 additional propositions, v, y, x, z, already given 2 ; as these 
 would increase the list of judgments to eight ; and the dif- 
 ferent modes of combining eight propositions by three (the 
 number which constitute the syllogism) would be 8 X 8 
 (=64) x 8 =512. After the invalid syllogisms have been 
 excluded from this large category, there remain thirty-six 
 legitimate syllogisms twelve negative and twenty-four affir- 
 mative for each figure, so that if we even restrict ourselves 
 to the three first figures we shall get 108 forms of valid 
 inference in lieu of the twenty-four obtained in the old table, 
 On examining the new forms of judgment, however, the 
 majority of the inferences will be found so weak and indefi- 
 nite as to be of no practicable utility ; while there is hardly 
 one of those which may be said to add something to our 
 knowledge of the subject, which the mind would not throw 
 into one of the first four propositions as a more natural 
 expression of the relation between the subject and the pre- 
 dicate than the constrained forms sought to be introduced. 
 Thus, to take the first case, of what earthly use is it to infer 
 by the mood o, i, z (of the second figure), the following : 
 
 Some minerals are non-conductors, 
 
 Some metals are conductors ; 
 
 Therefore some minerals are not some metals ; 
 1 We need hardly say the distinguished professor of logic and 
 metaphysics in the University of Edinburgh, Sir \V. Hamilton. 
 2 Ante, p. 93.
 
 C. I. 4.] THE NEW ANALYTIC TESTED. 117 
 
 notwithstanding every mood in which x, z occur, that is forty- 
 five out of the 108, end in some intimation of an equally 
 startling character. 
 
 Though the syllogisms in which y occurs alone, or in com- 
 bination \vith any of the four propositions o, e, i, o, are com- 
 petent to communicate information which might fairly form 
 the subject of inference ; yet this is done in so unnatural a 
 manner that the mind, even in its most confused state, never 
 stumbles upon them by the remotest accident. Thus, who 
 could ever be led to infer y, y, y, in the first figure ? 
 Some beasts are all cloven-footed, 
 But some animals are all beasts, 
 Therefore some animals are all cloven-footed. 
 
 Yet this is an average specimen of the class of syllogisms 
 the reader would get from introducing y into the series of 
 propositions. It is obvious, as we have before remarked, 
 that if the mind had to express such a relation it would 
 transfer the terms thus : 
 
 All cloven-footed creatures are beasts, 
 
 But all beasts are animals, 
 
 Therefore all cloven-footed creatures are animals, 
 which would bring the syllogism into the mood a, a, a. On 
 account, therefore, of that mental law which leads us in- 
 variably to affirm the particular of the universal, and con- 
 sequently to assign to the latter the first place, or, in other 
 words, to make it the subject of the judgment, the propo- 
 sition y may be regarded as deformed and useless in logic : 
 its place is always naturally supplied by a. 
 
 The moods in which u occurs, though not so faulty in ex- 
 pression, may be put out of court for the same reasons as 
 y, its functions being so completely discharged by a, that no 
 instance can be adduced of a practicable nature which would 
 call for its interposition. Thus, to take a casual instance, in 
 v, a, a, of the second figure : 
 
 All responsible agents are all men, 
 
 But all Ethiopians are men, 
 
 Therefore all Ethiopians are responsible agents ; 
 
 we do not require the attribute of the major to be taken 
 universally to get the conclusion, which would be equally 
 evident were the more natural judgment (a), viz., "Ail
 
 118 PEOPERTIES OF SYLLOGISMS. [B. III. 
 
 responsible agents are men" substituted in its place. The 
 mind, indeed, never adverts to the extension of the predicate 
 further than is required to ascertain whether it can be 
 affirmed or denied of the subject ; the consideration how far 
 it may overlap it, or to what other things it may be applied, 
 would be quite extraneous to the judgment before it, and is 
 therefore never dwelt upon. Admitting, therefore, the ex- 
 tension of the valid forms of reasoning at which the doctrine 
 of quantification aims, a close inspection of the new judg- 
 ments which arise from its application compels us to reject 
 it as useless ; for where the inference to which they lead is 
 not equivocal or ambiguous, it is too awkward to be ever 
 used ; and, in the latter case, the relations of the judgment, 
 and the subsequent inference, find their natural expression 
 in the nineteen moods already given. 
 
 Nor is the plea of utility unadmitted by the advocates of 
 the new system, who advocate many changes on that ground, 
 although they involve themselves in not a little inconsistency 
 by challenging at the same time for logic the evolution of all 
 the conceivable modes of thought. That the two principles 
 are often in antagonism, no one can deny, since many modes 
 of inference are conceivable which have no practicable utility ; 
 and least of all the proposers of the new quantification, who 
 reject the fourth figure on the very ground that we extrude 
 the new analytic from a practical system of logic 1 , viz., that 
 of its utility ; but as they have admitted the competency of 
 that test to sweep away a figure along with its five moods, 
 they cannot shield themselves from its application to the new 
 table of judgments, which it will be found to explode quite as 
 effectually as the fourth figure. But we are disposed to carry 
 the test of utility to higher ground, and apply it to the very 
 extension of reasoning forms, which it is the professed mis- 
 sion of the new analytic to establish. Is it really conducive 
 to those functions which logic was created to discharge, that 
 the forms of valid reasonings should be multiplied ? We 
 think otherwise. The aim of logical science is simply to 
 teach men to reason legitimately, and to place in their hands 
 a body of rules by which sophisms may be detected ; and the 
 fewer the forms to which all correct and habitual inference 
 may be reduced, the more compact the moods in which all 
 legitimate reasoning can be represented, the better and sooner 
 1 See Mr. Baynes'sNew Analytic.
 
 C. I. 4.] THE NEW ANALYTIC TESTED. 119 
 
 will this object be effected. To scatter the nineteen legiti- 
 mate forms of inference over 108 distinct moods, comprising 
 the conceivable as well as the actual forms of reasoning, is 
 only breaking down the fence which enables us to hunt a 
 sophism into a corner, and by multiplying the valid tests to 
 which any argument can be brought to multiply, besides 
 the additional labour, our chance of error in the application 
 of them. The aim of the new analytic, therefore, in enlarging 
 the field of inference, is hardly fortunate ; in a practical sense 
 it does not succeed, and even if it accomplished its object 
 success would be worse than defeat ; for it would be accom- 
 panied by the destruction of the very simplification which 
 render the doctrine of the syllogism really serviceable to the 
 reasoner. 
 
 It is, notwithstanding, one of the professed aims of the new 
 analytic to simplify logic, and that through the very means by 
 which its lists of valid judgments would be rendered more com- 
 plex ; and it is supposed to effect this object in three ways : 
 viz., by reducing the general rules to one complete canon ; 
 by the abolition of the special rules of the figures ; and by 
 the removal of the erroneous doctrine of conversion of pro- 
 positions and reduction of syllogisms 1 . The first and second 
 notion we need hardly say are simply absurd, inasmuch as 
 the general rules, and even the special rules of the figures, 
 are in nowise distinct from the canon, but only act as so 
 many cautions, which it is advisable for the reasoner to have 
 before him, in order that he may not violate any of its prin- 
 ciples. They might, therefore, be omitted from the old logic 
 with as much propriety as from the system sought to be 
 established, and with more security against error, since its 
 code of valid syllogisms are much fewer than those arising 
 out of the quantification of the predicate, and consequently 
 afford less ground for the violation of the canon. But in 
 reality they can be spared in neither system, as it is obvi- 
 ously necessary, to secure the understanding from error, that 
 every mode by which a deviation can occur from the princi- 
 ples of right reason should be drawn out distinctly before it. 
 The Ten Commandments are reduced by theologians to two ; 
 but it would hardly conduce to the fulfilment of the natural 
 law to insist on that account upon their abolition. 
 
 With regard to the cranky doctrine of reduction, it does 
 1 Mr. Baynes's New Analytic.
 
 120 NOTATION OP THE SYLLOGISM. [is. HI. 
 
 not require the introduction of the new analytic to escape 
 from its intricacies, as the legitimation of each figure by its 
 own axiom renders that doctrine not only nugatory, but 
 absurd. It has been, consequently, avoided by many logi- 
 cians, from the days of Wolf downwards, who never dreamt 
 of quantification ; and we have omitted it in this logic on 
 similar grounds. As respects conversion, we in the last 
 book have shown the object which it is intended to effect is 
 indispensable to many forms of solid argument, and pre- 
 sents a lever of proof which could not be supplied by the 
 quantification of the predicate; its abrogation, therefore, 
 would only weaken the science by depriving it of one of 
 the means of producing conviction. 
 
 The introduction of the new analytic, therefore, can 
 serve no purpose of simplification beyond that already 
 attained, while it would materially enhance the danger of 
 error by enlarging the list of valid moods in each figure, to 
 which the rules would have to be applied, and in some mea- 
 sure introduce the complexity into logic it was designed to 
 abolish. "We consequently reject it on three distinct counts ; 
 because a part of the object at which it aims is chimerical ; 
 because it fails to accomplish the remaining part ; and 
 thirdly, because that portion of the object, even if achieved, 
 would be destructive of the very simplification it is instituted 
 to realise 1 . 
 
 CHAPTEE II. 
 
 NOTATION OF THE SYLLOGISM. 
 
 1. Euler's Method. 
 
 THE relations which mentally subsist between conceptions 
 have been attempted to be represented to the eye by dia- 
 grams, and though some mathematical logicians have carried 
 
 1 It would exceed our limits to answer the particular charges which 
 Sir W. Hamilton, through the medium of his pupil's essay, brings 
 against the old doctrine of mood and figure; such as that of inconsis- 
 tency in the discrimination of mood where there is no difference of 
 quantity and quality, but a mere transposition of terms; and that of 
 mere accidents of expression prevailing over essential forms of thought, 
 in rendering moods valid in one figure, invalid in another. Every one 
 of these allegations admit of a satisfactory reply, which we reserve, 
 however, for another place.
 
 c. ii. 1.] ETTLER'S METHOD. 121 
 
 this species of notation too far 1 , it must be allowed, if kept 
 within moderate bounds, to facilitate logical analysis. 
 
 The most celebrated scheme, and at the same time the 
 simplest, is that of Euler 2 , which represents the sphere of a 
 conception by a circle ; an affirmative judgment by one 
 circle, wholly or partly contained in another ; and a negative 
 by two separate circles. Thus, since the proposition "all 
 plants are organised beings," includes under organised beings 
 many species of plant, the former term is represented by a 
 large circle, and the latter by a small one enclosed within it. 
 If we, consequently, include "avaleas" in the class "plant," 
 this term will fall into a smaller circle than plant, and be 
 enclosed by it in return. We shall thus get the diagram : 
 
 as illustrative of the mood a, a, a, of course in the first 
 figure, in which it can only occur. 
 
 Again, were we to infer that " some stones have deter- 
 mined figures," from the fact that " all crystals have deter- 
 minate figures," and some stones are crystals, the scheme 
 may obviously be represented by making the circle which 
 denotes crystals cut the circles denoting stones and deter- 
 minate figures. Thus : 
 
 This constitutes a, i, i, of the first figure. The mood e, t, o 
 of the same figure is represented in a simpler form. Thus, 
 supposing it required to prove some men are not respon- 
 sible agents, our argument would naturally be : 
 
 ' * Ploucquet, one of the first to introduce it, appears to labour under 
 this error with Condillac. Prof, de Morgan, in his excellent trea- 
 tise on Formal Logic, may be said, to use a phrase of Bacon's, " to 
 corrupt logic by mathematics." What end can it serve to invest logical 
 relations with the forms of the calculus, and to be constantly carrying 
 analogies below zero, and considering them under some relation of in- 
 finitude ? * Lettres a une Princesse d'Allemagne, vol. ii. p. 110, 
 and continuation.
 
 122 NOTATION OF THE SYLLOGISM. [B. III. 
 
 None who have lost their reason are responsible ; 
 But some men (lunatics) have lost their reason ; 
 Therefore, some men are not responsible. 
 
 Assuming A for the middle term, B for the attribute of the 
 conclusion, and C for the subject, we get either of the two 
 figures, 
 
 For it is not necessary to know how far C may be included 
 in B to infer the conclusion ; it may, in fact, either be iden- 
 tical with it, or wholly included in it, or only in part. 
 
 In addition to the transparent clearness with which 
 this notation serves to bring out the relative extension of 
 the terms of a syllogism, it occasionally is useful in show- 
 ing the falsity of an argument, hardly perceptible when 
 conveyed in ordinary language, as, 
 
 Some learned men are misers, 
 
 No miser is virtuous ; 
 
 Therefore some virtuous men are not learned. 
 
 Eepresenting the major, minor, and middle by the letters A, 
 J5, (7, it is evident that no part of B (virtuous men) is in- 
 cluded in C (misers) : their spheres, consequently, are quite 
 
 separate ( j ( ) But because some of the class A 
 
 S ~v" ~v 
 
 is included in JB, that is ( * Q B ), we are not on that ac- 
 
 ^_^-" . 
 
 count entitled to say that part of C is not A, as for anything 
 we know it may be included in the whole of it. The only 
 legitimate inference it is competent to us to draw in this case 
 is, that part of A which is included in B is not C. 
 Again, suppose it required to notify 
 
 Some A is B ; Some A is B ; 
 
 All .Bis C; or, Alibis C; 
 
 Therefore some C is A ; Therefore some C is B ;
 
 C. II. 2.] GEEMAN METHODS. 123 
 
 or its negative : 
 
 Some A is not : 
 
 All A is C; 
 
 Therefore some C is not S ; 
 the figures would evidently be : 
 
 OR 
 
 2. Ploucquet and Lambert's Method. 
 
 The method which Ploucquet introduced and Lambert 
 perfected, is more definite than Euler's, and consequently 
 of much easier application. It serves, also, to bring out 
 many inferences which Euler's notation hardly suggests, 
 from substituting for the sphere of a term the more logical 
 idea of its distribution. Thus a distributed term is de- 
 noted by an horizontal line , with the letter 
 
 S, P, or M, attached according as it is the subject, predicate, 
 or middle term of the syllogism : while an undistributed 
 
 term is marked by a row of dots in a 
 
 line with its significant letter. 
 
 Now premising that every affirmative judgment is repre- 
 sented by drawing one line under the other, the predicate 
 being always uppermost ; and every negative by drawing the 
 two lines apart, we may represent the argument adduced 
 by Dryden in defence of Christianity 1 : 
 
 No body of impostors would have conspired to cheat 
 men with a lie without temporal gain ; 
 
 The Apostles did this ; 
 
 Therefore they were not impostors. 
 
 As: 
 
 M 
 
 8 
 
 which signifies 
 
 No M is P; 
 But all Sis M; 
 Therefore no S is P. 
 
 1 Hind and Panther.
 
 124 NOTATION OF THE SYLLOGISM. [B. III. 
 
 Again : 
 All organised beings without volition are endued \vith 
 
 unconscious perceptions ; 
 But plants are organised beings ; 
 
 They are therefore endued with unconscious perceptions ; 
 would become, 
 
 P 
 
 M 
 
 8 
 
 From this notation, besides the two premises given, 
 
 (1) All M is P, 
 
 (2) All 8 is M, 
 we may infer 
 
 (3) Some P is M, 
 
 (4) Some M is 8. 
 
 3. -Sir W. Hamilton's Method. 
 
 The notation of Sir W. Hamilton surpasses all its prede- 
 cessors in its completeness and simplicity, and were it 
 not exclusively framed to meet the extensive changes which 
 the introduction of the new analytic would introduce into 
 logic, its practical value would be inappreciable. The former 
 systems of notation only embrace the extension of a syllo- 
 gism, this includes its intension, besides denoting the pre- 
 mises which may be converted without changing the mood 
 of the figure. To give the entire method would be useless, 
 as we have not adopted the system to which it corresponds. 
 Its outlines, however, are well worthy of inspection, as a spe- 
 cimen of learned ingenuity. 
 
 The middle term is invariably represented by its initial 
 letter M, while C and F stand for the two terms of the con- 
 clusion ; a colon (:) denotes the distribution of the term to 
 which it is annexed ; a comma (,) signifies it is not distri- 
 buted. "When the middle term consequently has (:) on one 
 side, and (,) on the other, its extension is determined by 
 the term with which either of those marks is associated in 
 judgment. The agreement of two terms is signified by ^ 
 and disagreement by =4- } the thick end of the bar denoting 
 the subject, the thin end the predicate when we regard the 
 extension of the terms ; but contrariwise when the syllogism
 
 c. ii. 3.] HAMILTON'S METHOD. 125 
 
 is interpreted according to its intension. Thus, in the one 
 case, C-. , M would denote " all G is some M," in the 
 other, " all M is some (7." 
 
 The terms are generally stated in the same line with a bar 
 drawn beneath them to indicate the conclusion ; but as in 
 the second and third figures there may be two conclusions 
 indifferently, a second bar is drawn above the terms to ex- 
 press the second of them. Thus, Oersted's argument : 
 All cases of magnetic polarity are cases of opposite pro- 
 perties in opposite directions ; 
 
 But some electric phenomena, viz. the voltaic pile and 
 electrified minerals, develope opposite properties in 
 opposite directions; 
 Therefore some electric phenomena are all cases of 
 
 magnetic polarity ; 
 would figure thus : 
 
 For, according to this system, it is of little moment whether 
 we infer from the premises, 
 
 Some electrical phenomena are all cases of magnetic 
 
 polarity, 
 or, 
 
 All cases of magnetic polarity are some electrical phe- 
 nomena, 
 
 as its author will allow no distinction between major and 
 minor premiss. 
 
 We may add, the mark -. -^ ' placed under a mood de- 
 notes that the premises may be converted without affecting 
 either the quantity or quality. But the sign ~^><^ between 
 
 two moods signifies that this transposition of the premises 
 cannot occur without the two corresponding syllogisms 
 changing places with each other. This may be easily per- 
 ceived, without further explanation, from the adjoining dia- 
 gram of syllogisms in the first figure :
 
 126 NOTATION OF THE SYLLOGISM. [B. III. 
 
 4. Use of Notation ; Equivalent Syllogisms. 
 
 The chief end of any adequate system of notation is to 
 present to the eye, by a species of symbolical language, all 
 the intricate relations which subsist between terms in a syl- 
 logism, so that no point may be overlooked which has any 
 bearing on the conclusion, and the inference be viewed in all 
 the various shapes which the premises allow it to assume. 
 It is not only serviceable in simply illustrating the rules of 
 syllogisms, though that utility is sufficiently great to chal- 
 lenge its admission into every logical system ; but it can, 
 moreover, be employed, by way of a "glaring instance," to 
 test the validity of an argument when the application of the 
 canon to its syllogistic form has been attended with a doubt- 
 ful result. 
 
 Another great advantage attending notation is, that, if 
 properly developed, it must not only represent the mutual 
 relations of terms, but to some extent of propositions and 
 syllogisms. It is in many cases very desirable to know what 
 premises can be converted without changing the mood of the 
 syllogism, i. e. without interfering with the quantity and 
 quality of each proposition in it ; what syllogisms in eacli 
 figure will pass into one another's place on the transposition 
 of the premises ; and also in how many figures the same ar- 
 gument may be stated; so that if its cogency be denied 
 in one, it may be presented in another. 
 
 It is obvious, though neither judgment or inference may 
 derive more intrinsic light or force from one mode of state- 
 ment more than another, that there are certain forms in 
 which an argument will strike conviction to some minds ; 
 which, if presented in another though equally conclusive 
 shape, it would have failed to effect ; and it becomes, there- 
 fore, of moment to the logician to be familiar with all the 
 modes in which a valid syllogism can be urged, in order 
 that when conviction does not attend his reasonings in one 
 form, he may produce them in another. All the artifices, 
 indeed, of mood, conversion, and figure, comprise only a 
 species of symbolical representation, witli a view to show 
 the various ways in which the relation between the terms of 
 an argument can be expressed while that relation remains 
 fixed and immutable. 
 
 With a view to exhibit the utility of this species of cipher
 
 O. in. 1.] EQUIVALENT SYLLOGISMS. 127 
 
 as far as equivalent syllogisms are concerned, let it be re- 
 quired to be shown in bow many ways tbe following argu- 
 ment may be proved : 
 
 Electricity will travel along a tied nerve, 
 
 The nervous fluid will not travel along a tied nerve ; 
 
 Therefore the nervous fluid is not electricity. 
 
 This is a syllogism in Camestres, and the permanent relation 
 of the terms would be represented in Lambert's method by 
 
 M 
 
 P 8 
 
 But by a glance at the lines it is obvious we can express the 
 same argument quite as conclusively in Cesare. Thus : 
 The nervous fluid will not travel along a tied nerve, 
 Electricity will travel along a tied nerve ; 
 Therefore electricity is not the electric fluid ; 
 or instead of asserting that no part of S agrees with M, we 
 may express the converse, which will lead to a syllogism in 
 Celarent of the first figure: 
 
 Nothing that travels along a tied nerve can be the elec- 
 tric fluid, 
 
 Electricity travels along a tied nerve ; 
 Therefore electricity cannot be the nervous fluid. 
 In this manner notation is pre-eminently useful in suggest- 
 ing all the inferences which may be drawn from the syllo- 
 gistic relation of terms, thus leaving the logician at liberty 
 to choose that which best suits his purpose, either in the 
 establishment or demonstration of fact, or in producing con- 
 viction in the mind of others. 
 
 CHAPTEE III. 
 
 KINDS OF SYLLOGISMS. 
 
 1. Complex Syllogisms. 
 
 EVERY form of argument yet considered has been of a 
 simple incomplex character, with a view to place the nature 
 of the syllogism in as clear a light as possible, that there 
 might be no difficulty in comprehending the full import of 
 its various properties, and the bearings of the rules which
 
 128 KTNDS OF SYLLOGISMS. [B. III. 
 
 legitimise its forms. But a large class of reasonings are 
 composed of syllogisms some complex, and others compound 
 in their characters, which it is obviously necessary to deal 
 with, either by resolving them into simple incomplex syllo- 
 gisms, and thus bringing them under the rules already given, 
 or by creating new rules by which their validity may be 
 tested on their own grounds. 
 
 Of these, perhaps embracing the largest class of reason- 
 ings, and certainly the most difficult to bring under distinct 
 rules, are complex syllogisms. They generally present a 
 simple incomplex minor premiss combined with a major pre- 
 miss and conclusion, in which incidental propositions are 
 introduced, and occasionally the complexity of the syllogism 
 is enhanced from the conclusion not being taken entire in 
 each of the premises, and consequently being only in part 
 compared with the middle term. Thus : 
 
 The sun is a thing insensible, 
 
 The Persians worship the sun ; 
 
 Therefore the Persians worship a thing insensible ; 
 
 in which worship, though excluded from the major, is intro- 
 duced in the minor and conclusion. 
 
 To reduce this class of syllogisms to a simple incomplex 
 form, we need only follow the rules already given for the 
 simplification of the propositions of which they are com- 
 posed, eliminating every part of the terms which have no 
 relation to the inference, and limiting the major to the exact 
 sense in which it is taken in the proposition. Thus, in this 
 syllogism : 
 
 The virtuous only are happy, 
 
 Some rich men are not virtuous ; 
 
 Therefore there are rich men who are not happy. 
 
 The major, being an exclusive proposition, is in reality com- 
 posed of two propositions, viz. : All the virtuous are happy, 
 and all who are not virtuous are not happy. But since the 
 force of the inference depends entirely upon the last proposi- 
 tion, we adopt it exclusively, and thus make the subject of the 
 major, all who are not virtuous, the predicate in the minor 
 premiss, which changes its quality, as,
 
 C. III. 1.] COMPLEX SYLLOGISMS. 129 
 
 All who are not virtuous are not happy, 
 
 Some rich men are among the number of those who are 
 
 not virtuous ; 
 Therefore some rich men are not happy 1 . 
 
 To denude the syllogism of all words which are irrelevant 
 to the inference, and set the terms in a clear light, it is fre- 
 quently necessary to transfer the active verb which generally 
 enters into complex propositions, to its passive tense 2 , as 
 
 The divine law commands us to honour our rulers, 
 Victoria is our ruler ; 
 
 Therefore the divine law commands us to honour Vic- 
 toria. 
 
 Although the term "rulers" in the major of this syllogism 
 appears to be the attribute, it is in reality the subject, since 
 we affirm of it that they are to be honoured on the authority 
 of the divine law. The syllogism should therefore stand : 
 
 Rulers are to be honoured (by the command of the 
 
 divine law) ; 
 
 But Victoria is our ruler ; 
 Therefore Victoria is to be honoured (by the command 
 
 of the divine law) ; 
 
 where the clauses in brackets being obviously incidental 
 only to the inference, may be omitted without affecting its 
 validity. 
 
 It often happens that a part of the premiss may be inci- 
 dental in one sense, and an essential constituent of the judg- 
 ment in another, as : 
 
 ' Many have cited such syllogisms to prove that the rule which 
 asserts that no inference can be drawn from two negative propositions 
 is false, without observing that the negation in the minor falls on the 
 term which is privative, and not on the verb, and that, as in the above 
 proposition, if the attribute of the minor was not taken in a privative 
 sense, the term would not have the same import in both propositions. 
 Of this kind of syllogism, the following is taken from 1'Art de Pensor 
 (part iii. ch. ix.): 
 
 That which has no parts cannot perish by the dissolution of its 
 parts, 
 
 The soul is a substance which has no parts; 
 
 Therefore, the soul cannot perish by the dissolution of its parts. 
 - See ante, p. 75, note. 
 
 K
 
 130 KINDS OF SYLLOGISMS. [B. III. 
 
 All philosophers maintain 1 that heavy things fall to the 
 
 ground without being impelled by anything ; 
 But this is an error ; 
 
 Therefore all philosophers may teach error. 
 Here the first part of the minor is the subject, for we affirm 
 of philosophers that they K teach a certain doctrine : but 
 should we argue, 
 
 All philosophers maintain that heavy things fall to the 
 
 ground without being impelled by anything; 
 But stones are heavy ; 
 
 Therefore stones fall to the ground without being im- 
 pelled by anything, 
 
 the minor, or complex proposition, would become the major, 
 and that part of it which was the subject before, would be- 
 come an incidental proposition, merely qualifying the attri- 
 bute and having no bearing on the inference. Thus : 
 Heavy things fall to the ground without being impelled 
 by anything (according to the teaching of philoso- 
 phers) ; 
 
 But stones are heavy ; 
 
 Therefore stones fall to the ground without being im- 
 pelled by anything (according to the teaching of 
 philosophers) . 
 
 It is therefore necessary, before eliminating from the terms 
 of the syllogism such words as are only incidental, to know 
 distinctly what is aimed at by the proof; as part of a propo- 
 sition may be a term in one sense, and only an incidental 
 expression qualifying a term in another 2 . 
 
 Some logicians 3 desirous to find a shorter process to the 
 validity of such syllogisms than their reduction to incomplex 
 forms and the application of the general rules afford, have 
 placed the entire artifice of reasoning in showing that the 
 conclusion is contained in one of the first propositions by 
 the interpolation of another, which establishes the inclusion ; 
 and since no argument can be vicious which is true to this 
 principle, they are disposed to accept it as an easy test by 
 which, without reference to mood and figure, the correctness 
 of every syllogism, however complex, may be ascertained. 
 
 1 As was the case anterior to the time of Galileo. 2 See ante, 
 
 pp. 79 and 90. 3 Arnauld and Nicol. See 1'Art de Penser, part iii. 
 ch. ii.
 
 C. III. 1.] TJKIYEESAL TEST OF SYLLOGISMS. 131 
 
 Thus, on being required to snow that every vicious man is 
 unhappy, we first endeavour to find a more evident proposi- 
 tion in which this is implicitly contained, as, Every man who 
 is the slave of his passions is unhappy (containing proposi- 
 tion) 1 ; but as this does not include the judgment which is 
 sought to be established expressly, we interpolate another 
 proposition to show that the containing proposition unde- 
 niably includes what we desire to prove, as, Every vicious 
 man is the slave of his passions (applicative proposition). 
 The syllogism would consequently be : 
 
 Every one who is the slave of his passions is unhappy, 
 Every vicious man is the slave of his passions ; 
 Therefore every vicious man is unhappy. 
 
 In affirmative syllogisms it is frequently optional which 
 premiss is assumed to be the containing or applicative proposi- 
 tion, as each will contain the conclusion in such case, only in 
 a different sphere, the major in that of extension, the minor 
 in the counter one of comprehension. Thus, in the above 
 example, the subject of the conclusion, "vicious," is con- 
 tained under the extension of the subject of the major, 
 ' slave of his passions," and the minor shows this. But the 
 minor contains it likewise, since "slave of his passions" 
 comprehends in its idea that of "unhappy," as the major 
 indicates. As the major, however, is nearly always the more 
 general proposition, it may be commonly regarded as the 
 containing proposition, and the minor only the applicative. 
 
 In negative syllogisms the affirmative proposition, whether 
 major or minor, will be the least general, and consequently 
 will form exclusively the applicative proposition, as in the 
 argument : 
 
 Every happy man is content, 
 
 No miser is content ; 
 
 Therefore no miser is happy. 
 
 It is more natural to say that the minor contains the conclu- 
 sion, and that the major, which is affirmative, proves the in- 
 clusion, than contrariwise. For the minor separating miser 
 from content, excludes it also from the term happy, since 
 that attribute, according to the major, is wholly contained 
 under the extension of content.
 
 132 KINDS OP STLLOGISMS. [B. III. 
 
 2. Conditional Syllogisms. 
 
 There are other kinds of syllogisms corresponding to the 
 different forms which the major proposition may assume, and 
 as this gives the name to the syllogism of which it forms a 
 part, the latter may be said to admit in some sort of the same 
 multiform division as propositions themselves. "We have 
 already dealt with that class of them which are simple, in- 
 complex, and complex, we proceed now to deal with com- 
 pound syllogisms, and take, as the first in order, that species 
 which is termed conditional. 
 
 These may be defined to be syllogisms in which the major 
 is a conditional proposition containing the entire conclusion. 
 For example : 
 
 If matter cannot move of itself, its first motion must 
 have been given to it by a spiritual being ; 
 
 But matter cannot move of itself ; 
 
 Therefore its first movement must have been given to it 
 by a spiritual being. 
 
 Since the consequent may be inferred from the concession 
 of the antecedent, and the denial of the antecedent from 
 the negation of the consequent 1 , we get two corresponding 
 kinds of conditional syllogisms ; the affirmative being called 
 constructive, the negative destructive. For instance, in the 
 proposition, "If the crops are bad, corn must be dear;" 
 should the antecedent be conceded, the first case applies, and 
 the consequent may be inferred. The argument would conse- 
 quently be : 
 
 If the crops are bad, corn must be dear ; 
 But the crops are bad ; 
 Therefore corn is dear. 
 
 This conditional is constructive. But if the consequent is 
 denied the second case applies, and the syllogism emerges in 
 a destructive form. Thus : 
 
 If any increase of population is desirable, some misery is 
 
 desirable : 
 
 But no misery is desirable ; 
 
 Therefore some increase of population is not desirable. 
 
 Hence conditional syllogisms, in addition to being faulty as 
 
 to matter when the condition is irrational, can with respect 
 
 1 See ante, p. 83.
 
 C. III. 2.] COMPOUND SYLLOGISMS. 133 
 
 to form be defective in two ways, viz., when we attempt to 
 infer anything from the affirmation of the consequent, or the 
 denial of the antecedent. For it is obvious from the conces- 
 sion of the consequent we can infer nothing, since the 
 same consequent may follow from other antecedents ; as in 
 the above example, corn may be dear from other causes 
 besides a failure in the harvest. Therefore it does not follow 
 from corn being dear that the harvest has failed. In like 
 manner we cannot infer from the denial of the antece- 
 dent, viz., that the crops are not bad, that they are not dear. 
 
 Yet arguments in which the latter fallacies are used, are 
 occasionally made to assume a very plausible shape : thus, 
 
 If such an administration had involved the country in 
 war, it would have been a bad administration ; 
 
 But it did not involve the country in war ; 
 
 Therefore it was not a bad administration. 
 Or, 
 
 If I refused to meet my liabilities, I should be a bad 
 member of society ; 
 
 But I do not refuse to meet my liabilities ; 
 
 Therefore I am not a bad member of society. 
 These we need not say are arguments which prove nothing, 
 since a bad member of society and mal-administration may 
 arise from various other sources besides those assigned. 
 When, however, there is an exclusion, either understood or 
 expressed in the major, no objection can be taken to this 
 kind of inference. As in Cicero's defence of Muraena: 
 
 "I could then only be accused with justice of acting 
 contrary to my law, if I maintained that Muraena purchased 
 the votes, and was justified in doing so. But I maintain 
 that he did not buy the votes, therefore I do nothing con- 
 trary to the law 1 ." 
 
 The same may be said of the argument urged in the follow- 
 ing passage of the ^Eneid : 
 " Si sine pace tua, atque invito numine Tree's 
 
 Italiam petiere, luant pecata, neque illos 
 
 Juveris auxilio. Sin tot responsa secuti, 
 
 Quaa superi manesque dabant ; cur nunc tua quisquam 
 
 Vertere jussa potest ? aut cur nova condere fata 8 ?" 
 
 1 O r at . pro L. Muraena, c. iii. Ramus cites it as an example of bad 
 reasoning, but he is evidently in error. 2 -35neid, x. 31.
 
 134 KINDS OF SYLLOGISMS. [B. III. 
 
 Tor, supplying the exclusive term in the major, the reason- 
 ing may be thus rendered : 
 
 If the Trojans had come into Italy contrary to the will of 
 the gods, they would then alone have been punishable ; 
 
 But they came not contrary to the will of the gods ; 
 
 Therefore they are not punishable. 
 
 If the exclusive term, however, could not be established, the 
 argument would be nugatory. These syllogisms may be 
 changed into a categorical, by the reduction of the major to 
 that form. 
 
 3. Disjunctive Syllogisms. 
 
 Those syllogisms are disjunctive whose major contains a 
 disjunctive proposition 1 ; whose object is to state an alter- 
 nate which leaves us at liberty, either by denying one part 
 to infer the other ; or, by affirming one part to reject the re- 
 maining. Of the first kind, Cicero's argument may be taken 
 as an example : 
 
 Those who have slain Caesar, are either parricides or 
 defenders of liberty ; 
 
 They are not parricides ; 
 
 Therefore they are defenders of liberty. 
 But it is not necessary that the alternative should be re- 
 stricted to two terms ; it may lie between several, as : 
 
 All sciences are either pure, inductive or mixed sciences ; 
 
 But astronomy is not a pure, or an inductive science ; 
 
 It is therefore a mixed science. 
 Gibbon's argument may serve as an instance of the second : 
 
 Mahomet was either an enthusiast or an impostor ; 
 
 But he was an enthusiast : 
 
 Therefore he was not an impostor. 
 
 Disjunctives are rarely defective, unless through the weak- 
 ness of the alternative which leaves a mean between the 
 opposed members. This, indeed, occurs in the last syllogism, 
 for there is nothing so antagonistic in the nature of an en- 
 thusiast and impostor as to prevent them being combined in 
 the same person, even at the same time, as was undoubtedly 
 the case with Mahomet. Of course when both members of 
 the major are true, we are not authorised, from the denial or 
 affirmation of the one to infer anything with regard to the 
 other, but only when the members are exclusive. 
 1 See ante, p. 82.
 
 C. III. 5.] COMPOUND SYLLOGISMS. 135 
 
 4. Copulative Syllogisms. 
 
 These syllogisms are only another form of disjunctives, 
 with the alternative expressed in the major by the copulative 
 conjunction "at the same time," "and," instead of ''either," 
 "or." For example : 
 
 A Government cannot be at the same time despotic and 
 the licenser of a free press ; 
 
 But the English Government permits a free press ; 
 
 Therefore the English Government is not despotic. 
 Now, granting the truth of the matter in the above syllo- 
 gism 1 , it is evident we can only from the concession of one 
 part deny the other ; but cannot conclude anything from the 
 denial of one part. Otherwise we might argue, 
 
 A Government cannot be at the same time despotic and 
 the licenser of a free press ; 
 
 But the English Government is not the licenser of a 
 free press ; 
 
 Therefore the English Government is despotic ; 
 which of course would be absurd, since despotism may arise 
 from a variety of other circumstances besides the violation of 
 freedom of discussion, and because matters may occasionally 
 take such a course as to warrant the present Government to 
 place restrictions on the press, with a view to preserve, 
 even liberty. 
 
 5. The Dilemma. 
 
 A syllogism with a conditional major, in which either the 
 antecedent or the consequent is disjunctive, is called a 
 dilemma. Thus, the argument of divines _ against temporal 
 felicity may be expressed in this form : 
 
 Man can only be truly happy on earth by yielding to 
 his passions, or by combating them ; 
 
 But either of these courses is attended with pain ; 
 
 Man cannot therefore on earth be truly happy. 
 Neither antecedent or consequent, however, is restricted to a 
 double member, as the word dilemma implies 2 , but either, or 
 
 1 Which some (Mr. Disraeli) are disposed to contest. * The 
 
 word literally signifies, " double proposition ;" hence the common ex- 
 pression of the "two horns of a dilemma." But the popular meaning 
 of the term arises from the condition of some one of the antecedents 
 being true, or one of the consequents false, though we cannot say which 
 is so.
 
 136 KINDS OF SYLLOGISMS. [B. III. 
 
 even both, may be compound to any degree, as in the argu- 
 ment of St. Augustine : 
 
 If children suffer misery, it must be either 1st. As 
 
 the consequence of sin committed in a previous life 1 . 
 
 Or, 2nd. The impotence of God, who has not the 
 
 power to prevent it. Or, 3rd. The injustice of God, 
 
 who inflicts it without a cause. Or, 4th. Original sin ; 
 
 But it is impious to allege the three first causes ; 
 
 Therefore the misery of children is to be attributed to 
 
 original sin. 
 
 Or, if the major premiss have a compound antecedent with 
 a simple consequent, the latter may be aflirmed of any one 
 member of the antecedent disjunctively granted. As : 
 
 Whether the soul perish with the body, or survive it in 
 
 the same or another form, death is to be feared ; 
 But either of these cases will happen ; 
 Therefore death is to be feared. 
 
 But should the different members of the antecedent have 
 each its separate consequent, then each member of the ante- 
 cedent being as before disjunctively granted, the consequent 
 can be only disjunctively inferred. For example : 
 
 If -iEschines joined in the public rejoicings he is incon- 
 sistent ; if he did not he is unpatriotic. But he either 
 joined or not ; therefore he is either unpatriotic or 
 inconsistent 2 . 
 
 The forms already given, which end in affirmative infer- 
 ence, are generally termed constructive ; there are, however, 
 others of a negative kind, in which, having denied the whole 
 of the consequent, or consequents, we deny the correspond- 
 ing antecedent. These are termed destructive. Thus : 
 If despotic Governments are conducive to the welfare 
 of society ; then the restriction of individual rights, 
 the publication of arbitrary enactments, and the re- 
 straint of public opinion is beneficial ; 
 But none of these are beneficial ; 
 
 Therefore despotic Governments are not conducive to 
 the welfare of society. 
 
 1 A belief of some Pagan philosopher. * The argument of 
 
 Demosthenes in the De Corona.
 
 C. III. 5.] PBINCIPLES OF THE DILEMMA. 137 
 
 There are many dilemmas in which the proposition con- 
 taining the alternative is understood, being sufficiently in- 
 dicated by the statement of each particular part of which it 
 consists. Thus, the argument urged by Antisthenes, that 
 we ought not to meddle with the affairs of the State, 
 which seems to have had great influence upon some of the 
 ancient philosophers : 
 
 If we conduct the affairs of State well, we shall offend 
 men; 
 
 If we conduct them iD, we shall offend the gods ; 
 
 Therefore it is not expedient to engage in them. 
 Of the same kind is the argument of Bias, quoted by Aulus 
 Gellius, in defence of the bachelorate : 
 
 If a wife is beautiful, she excites jealousy ($ 
 
 If she be ordinary, she disgusts (e 
 
 Therefore it is best not to marry. 
 In such cases the omitted proposition should be supplied 
 before the force of the dilemma is tested, as it may entirely 
 invalidate the conclusiveness of its matter. Thus, the 
 dilemma of Antisthenes, when fully expressed, would require 
 as its major : 
 
 " It is not expedient to engage in State affairs, if we 
 either displease god or men ;" 
 
 a proposition which bears the falsity of its matter on the face 
 of it. Pursuing the same course, the universal proposition 
 to the dilemma of Bias would be : 
 It is not wise to marry, if a woman creates jealousy or 
 disgust ; 
 
 a proposition which, even if admitted, would not establish 
 the conclusion, since many beautiful women so comport 
 themselves as to leave no room for jealousy ; and many ordi- 
 nary ones possess qualities of mind which cannot fail to 
 please all who approach them. Hence it is obvious, with 
 regard to the matter of dilemmas, that each particular con- 
 clusion should be necessary, and that the dividing member 
 should comprehend the entire subject to which they apper- 
 tain. 
 
 As dilemmas belong to the class of compound conditionals, 
 they are reducible to two or three simple syllogisms of that
 
 138 KITTDS OF SYLLOGISMS. [B. III. 
 
 kind, and the validity of their form may be tested by the 
 same rules. Thus, the dilemma : " If a man be wicked or 
 insane, he is unfit for society ; a criminal is either of these 
 two ; for if he knew the consequences of his act he was wicked ; 
 if he did not he was insane ; therefore he is unfit for society ;" 
 may be resolved into two simple conditional syllogisms, in 
 which " wicked" will form the attribute of one minor premiss, 
 and " insane" of the other. Dilemmas consequently admit of 
 being stated like pure conditionals, in a categorical form. 
 As: 
 
 The case of A being JB , is a case of C being D, or E 
 being F; 
 
 This is not a case of C being Z), or E being F ; 
 
 Therefore it is not a ease of A being B. 
 In the same manner constructive dilemmas may be reduced 
 to categoricals, and, if needs be, tested by the general rules 
 of the canon. 
 
 6. The Chain Syllogism, or Sorites. 
 
 "When a series of inferences occur in such order as to 
 make the predicate of one proposition the subject of the next, 
 till the attribute of the last of the premises is predicated in 
 the concluding proposition of the subject of the first, we have 
 what is termed a sorites 1 . Thus : A is B, G is D, D is E, 
 therefore A is J7, where the mind passes from proposition 
 to proposition, without expressing the conclusion until it 
 reaches the attribute which it seeks to connect with the sub- 
 ject of the first proposition. Of this kind of argument we 
 cannot adopt a better illustration than one given by Lord 
 Eldon, on the occasion of Laurence's injunction concerning 
 the pirated edition of his book on the Natural History of 
 Man : " I have a rational doubt whether some portion of this 
 book do not lean to materialism ; what leans to materialism 
 is inconsistent with the immortality of the soul ; what is in- 
 consistent with the immortality of the soul is contrary to 
 Scripture ; but as that which contradicts Scripture does not 
 come under the protection of the law, I have a rational doubt 
 
 1 Or, accumulating argument, from the Greek o-<apbs, a heap, though 
 we must confess the German name Kettenschluss, which we have adopted, 
 is more significant.
 
 C. HI. 6.] THE CHAIK SYLLOGISM. 139 
 
 whether the injunction can be maintained; therefore the 
 injunction is dissolved 1 ." 
 
 It will be observed that each intermediate proposition 
 between the first and last contains a middle term of the 
 sorites, which, on that account, is capable of being drawn 
 out into as many distinct syllogisms. In the major of the 
 first syllogism, the second proposition of the sorites must 
 be taken, while the first proposition will form the minor 
 premiss, and to each succeeding syllogism, the conclusion 
 of its predecessor will form the second premiss. Hence 
 the first proposition in the sorites is the only minor premiss 
 which is expressed. Prom this we may conclude that the 
 first proposition alone of all the premises can be particular ; 
 because in the first figure into which the reasoning of the 
 sorites falls, the minor may be particular but not the major : 
 and all the other propositions anterior to the conclusion are 
 major premises. It may likewise be inferred that in a sorites 
 there can be but one negative premiss, and that the last ; for 
 none other could be negative without involving, contrary to 
 the rule of the first figure, the implied syllogism in a nega- 
 tive minor. 
 
 A sorites may be exhibited in two ways by reversing the 
 order of the premises in the examples already given. Thus, 
 D is E, C is D, jB is C, A is B, therefore A is E. In this 
 form, which is called the Groclenien, from the name of its 
 originator, extension is more conspicuous, as the sorites 
 starts from its two widest terms, while in the common form 
 intension predominates. The former descends in extension 
 from the predicate to the conclusion ; the latter ascends in 
 intension from the subject 2 . 
 
 It may be remarked that a chain of conditional syllogisms 
 may be expressed in either of these forms. Thus, if educa- 
 tion be indispensable to the progressive development of so- 
 ciety, it is important that it should be well conducted. If 
 it is important it should be well conducted, an order of men 
 should be strictly trained for that purpose under the surveil- 
 lance of the State, But education is essential, &c., therefore 
 an order of men should be strictly trained, &c. Of course 
 if the sorites were destructive, the procedure would as- 
 sume the Goclenien form, and we must go back from the 
 
 ' Campbell's Lives of the Chancellors. 2 Thompson's Laws of 
 
 Thought, p. 284, 2nd ed.
 
 140 KINDS OF SYLLOGISMS. [fi. III. 
 
 denial of the last consequent to the denial of the first ante- 
 cedent. 
 
 6. Of the Enthymeme, or Imperfect Syllogism. 
 
 It is usual for logicians to denote one or two abridged 
 forms of arguments, commonly called enthymemes and pro- 
 syllogisms ; though as these distinctions only arise from 
 accidental forms of expression, there is no reason for their 
 admission into logic, any more than a score of others of the 
 same kind which might be mentioned. The enthymeme is 
 usually called a syllogism with one premiss suppressed ; but 
 as all the terms are comprised in the conclusion and the ex- 
 pressed premiss, the one omitted is commonly understood, 
 and may be readily supplied. Thus, Victoria is a sovereign 
 who respects the forms of the constitution, therefore her 
 subjects are free : the major premiss wanting to make the 
 syllogism conclusive from the form -of expression is, the 
 subjects of every sovereign who respects the forms of the 
 constitution are free ; but this is so easily understood as 
 to be dispensed with in the ordinary usage of language. 
 
 When one of the premises of a syllogism is itself an en- 
 thymeme, the concluding clause of that premiss is termed a 
 pro-syllogism, as the bracketed line in the argument : 
 
 Everything which concerns the public weal ought to be 
 
 under the control of the Legislature ; 
 But education is such (since property cannot be secure 
 
 without it) ; 
 Therefore education ought to be under the control of 
 
 the Legislature. 
 
 Sometimes the conclusion of the syllogism in common par- 
 lance furnishes a species of premiss from which a second con- 
 clusion is deduced, in which case the last proposition is 
 termed an episyllogism : A statesman who involved the 
 country in great debts could not be a good financier ; Pitt 
 involved the country in great debts, therefore he was a bad 
 financier, and (therefore he is unworthy of indiscriminate 
 panegyric).
 
 B. IV.] GENEBAL PBINCIPLES OF INFEBENCE. 141 
 
 BOOK IV. 
 
 GENEBAL PBINCIPLES OF 1NFEBENCE. 
 PBOEMITJM. 
 
 WHEN the truth of either premiss, or both, in a syllogism 
 is not intuitively evident, other arguments are required to 
 establish its validity, which gives rise to what are called 
 trains of reasoning, or combinations of inference. An ex- 
 ample of this kind has already been furnished in the sorites, 
 which is nothing else than a series of syllogisms stript of 
 the minor which is easily understood, and so arranged as to 
 connect an attribute or property with the subject of the first 
 propositions, apparently foreign to it, through a group of 
 inferences in which the connexion is intuitively discerned. 
 Thus restoring the suppressed premiss in each of the in- 
 ferences drawn by Lord Eldon, in the illustration already 
 cited, we should get the following train of reasoning. What- 
 ever contradicts Scripture is contrary to law ; this book con- 
 tradicts Scripture ; therefore it is contrary to law. Though 
 the major and minor premiss would be contested by a civilian 
 of the present day, in Lord Eld on' s opinion the latter was 
 only open to cavil, and he consequently sought to place it 
 beyond dispute by an additional inference : Whatever leans 
 to materialism contradicts Scripture ; this book leans to 
 materialism ; therefore it contradicts Scripture. But the 
 phrase " leans to materialism" is rather indefinite, and it 
 might be fairly argued that the " Natural History of Man" 
 did not fall within its sphere ; the judge, therefore, proceeds 
 to clench his argument by placing the book in the category 
 of things that lean to materialism, because it contradicts the 
 immortality of the soul. We in this manner obtain two syl- 
 logisms in corroboration of the minor premiss of the first 
 argument. Such combinations of inference it is evident will 
 grow more complex and involved in proportion as the two 
 terms of the conclusion is removed from the middle in the 
 syllogism whose validity we seek to establish ; as the farther 
 the distance, the more numerous will the intermediate links 
 become through which the connexion is demonstrated. 
 
 These trains of reasoning exemplify certain laws and
 
 142 GEKEBAL PBZSTCIPLES OF INEEEEKCE. [B. IV. 
 
 methods, are employed about different degrees of belief, and 
 rest upon various foundations of evidence. Each of these 
 divisions, developed in corresponding chapters, will form the 
 subject of the present book 1 . In this view it will only be 
 preliminary to the great design of logic, viz., the repre- 
 sentation of the valid forms of inference employed in the 
 construction of the moral and physical sciences, and will 
 serve (to use a Baconian phrase) as a kind of prodromi, or 
 anticipations of those principles of evidence to which all the 
 preceding parts of logic converge. From the exposition of 
 the laws of simple cases of inference to that of the multiform 
 functions which they fulfil in the construction of the two great 
 branches of knowledge, is manifestly too wide a step to be 
 taken at once, and it is but consulting the methodical expan- 
 sion of the science to interpose between them a survey of the 
 different grounds of evidence on which those inferences rest, 
 the primitive truths into which they can be resolved, together 
 with the laws and methods which they exemplify, and the 
 various degrees of belief which they excite in the subjective 
 
 1 The common school logics generally terminate with the first mem- 
 ber of this division, viz., Method, and leave the young logician in total 
 ignorance of the mental laws which the theory of reasoning is supposed 
 to illustrate, of the foundations upon which it is raised, and the 
 different forms which demonstration and induction assume in the 
 various sciences, to which the preceding subjects are subsidiary. Such 
 a procedure, which is not an unapt illustration of the play of " Hamlet" 
 with the part of the Prince omitted, doubtless arose from the 
 common habit of teaching the science in our universities before 
 a course of physics was entered upon ; but we hope, after Mr. 
 Mill's " System of Logic," the abuse will be corrected. If logic, 
 both in the continental and our home universities, is deemed an 
 essential propadeutic to the study of theology and ethics, it must be 
 deemed equally necessary to the study of natural philosophy. In 
 both cases we have distinct groups of knowledge raised out of 
 various combinations of inference ; and if it is essential in the pur- 
 suit of the moral sciences to have the general principles upon which 
 the evidence proceeds, in our grasp before we proceed to master the 
 particular details, the same course ought to be pursued in physics. 
 Hence, Sir John Herschel has very properly made this subject one of 
 the leading divisions of his Preliminary Discourse on the Study of 
 Natural Philosophy. Dugald Stewart (Philos. of the Mind, passim), 
 however, thought logic ought to follow, and not precede, the study of 
 the sciences, a view in which Dr. Whewell seems to coincide, by making 
 their philosophy supplementary to their history. We, notwithstanding, 
 deem this opinion a very erroneous one.
 
 C. I. 1.] ANALYSIS AND SYNTHESIS. 143 
 
 mind, that the reader may be presented not only with all the 
 mechanism of the formulae of reasoning, but have a clear 
 insight into the structure of knowledge which they are em- 
 ployed to raise, and a complete view of the foundations upon 
 which the edifice reposes. In pursuit of each branch of the 
 subject we shall have to encounter two objections of a very 
 formidable character, either of which, if admitted, would 
 prove fatal to the system of logic propounded in this work. 
 The first is, that which resolves all our knowledge into a series 
 of inductive generalisations; with its two necessary corollaries, 
 viz., that the interpolation of the major premiss in a syllogism 
 is an assumption of the thing to be proved (petitio principii) ; 
 and that there is no such thing as necessary truth existing, 
 unless what is of hypothetical creation. The second is, that 
 which denies the existence of anything like certainty either 
 in reasoning or in the first principles that inference assumes, 
 and which consequently attempts to rase every scientific 
 structure to the ground. The answer to these objections 
 will bring into court everything connected with the rationale 
 of evidence, and expose every artifice that human ingenuity 
 has contrived to convict its methods of falsehood and illusion. 
 
 CHAPTEE I. 
 
 UNIVERSAL METHODS OF INFEBENCE. 
 
 1. Analysis and Synthesis. 
 
 KEFLECTION cannot be exercised, and consequently no 
 modes of reasoning be pursued, without viewing the object 
 about which they are employed in either of two ways : viz., as 
 an obscure whole, whose parts are to be resolved, or as a group 
 of detached parts to be linked together in the form of a con- 
 stituted whole. The first process is called analysis, from a 
 Greek word, signifying decomposition 1 ; the last, synthesis, 
 from a term derived from the same source, designating re- 
 composition. These are the two vital functions of methods 
 the two essential accompaniments of all thought as systole 
 
 1 For the different modes of analysis, see History of Logic, pp. 2, 11, 
 and 15.
 
 144 ANALYSIS AND SYNTHESIS. [fi. IT. 
 
 and deastole are the living conditions of the animal or- 
 ganism. 
 
 This will be more evident on interrogating ourselves as to 
 the nature of truth. In what else can it consist, unless in 
 the relation of things to each other ; and by what other mode 
 can that relation be investigated, unless by mounting from 
 their primitive elements to their successive combinations ; or 
 by descending from these to the simple parts out of which 
 they arise ? Nature, by the process of growth and decom- 
 position going on within her, is continually weaving and un- 
 ravelling the complicated web of existence ; and, in whatever 
 position the threads may be placed, they can assume no other 
 relation than that of combination (synthesis) or disentangle- 
 ment (analysis). 
 
 Although each of these methods vary in some degree, ac- 
 cording to the subject-matter of the different sciences in 
 which they are employed, they nevertheless preserve in their 
 widest diversity those distinctive features which mark them 
 out as varieties of one species, and as such may be used to illus- 
 trate each other. Thus logical analysis, by which a process of 
 inference is resolved into syllogisms, and syllogisms into pro- 
 positions, and then again into the two terms and copula 
 which form the connecting link, or by which any of these parts 
 may be again resolved into the divisions which we have already 
 comprised under them, is perfectly analogous to the ana- 
 lysis which the chemist employs to get at the ingredients of 
 any mixture in his laboratory, or to that which geometricians 
 make use of when they convict any theorem of falsity, by 
 pointing out the ridiculous inferences to which the assump- 
 tion of its truth must lead. The same may be said of the 
 various synthetic processes which obtain in the different 
 sciences, as these are but the inverse methods of the cor- 
 responding analysis out of which they arise, and consequently 
 manifest in the same degree an opposite unity of method. 
 Distinct, however, as the two paths are by which the stream 
 of knowledge is either descended to its source or pursued 
 out into the wide arm which unites all its tributary branches, 
 they are commonly, more or less blended in every large train 
 of inference ; and where the investigation is of such a nature 
 as to allow either of the methods to predominate, they are 
 sometimes confounded together, through the process re-
 
 C. I. 1.] SYMBOLICAL PROOF HOW FAB ANALYTIC. 145 
 
 ceiving the name of the prevailing method. Thus sym- 
 bolical reasoning is generally termed analytic, because we 
 do not necessarily here, as in geometrical reasoning, proceed 
 by linking one truth to another till we reach the desired 
 result ; but commence with stating the unelicited truth, or 
 the given combination of known quantities in its symbolical 
 form, and then proceed, in conformity with certain axioms, 
 to trace what other truths are involved in the one first stated ; 
 resolving step by step the symbolical assertion with which 
 we began into others, which gradually reveal the meaning of 
 the unknown quantities which entered into the original 
 statement. Now the first process, which consists in forming 
 out of the quantities presented by the conditions of the ques- 
 tion one equation, is evidently synthetic, while the subse- 
 quent steps of the proof is analytic ; but as the latter com- 
 prise the main branch of the procedure, all symbolical rea- 
 soning became confounded with it. 
 
 With regard to the relative value of these two methods, 
 that must be determined according to the subject which pre- 
 sents itself for investigation. In physical science it is evi- 
 dent there can be no correct synthesis before analysis has 
 legitimated the use of that method, inasmuch as we can boast 
 of no revelations of the mysteries of nature but those which 
 arise from anatomising the interwoven mass of facts which 
 she presents, and acquainting ourselves with the mutual 
 bearings of their distinct parts. Thus, how vain would 
 have been the attempt to manufacture lapis-lazuli until we 
 had discovered that the components of the stone were silica r 
 alumina, soda, sulphur, and a trace of iron ; or to seek to 
 discover, at least without a number of wasteful experiments, 
 at what point of space the curved path of a given shot will 
 terminate, before examining the laws which the cannon-ball 
 obeys from the first moment the match has been applied. 
 We might, indeed, in the first instance, have accidentally 
 thrown together the five components of ultra-marine 1 in the 
 exact proportion required to produce the beautiful pigment 
 referred to ; but such an instance would have given us no 
 power to produce the combination at will, and still left us 
 dependent on the niggardly supplies which nature doles out, 
 
 1 As did really occur in 1710 in a furnace used for the manufacture 
 of alkali.
 
 146 ANALYSIS AIH> SYITTHESIS. [. IT.. 
 
 of this beautiful material. By chemical analysis, however, 
 we have wrung out of nature one of her important secrets, 
 and are thus enabled (verifying a prediction of Lord Bacon) 
 to produce- frequently what she does rarely, and to achieve in 
 a moment results which she takes centuries to consummate. 
 
 In physical science y therefore, the legitimacy of all syn- 
 thesis is in direct proportion to the .preceding analysis. If 
 we attempt to synthesise or construct a system of science 
 before the analysis of the parts to which it refers is complete, 
 the result is a false science ; just as, if we rest content with 
 simple analysis, and do not attempt its corresponding syn- 
 thesis, as far as its data would warrant such a procedure, the 
 result is an incomplete knowledge. But, if an error is to be 
 committed, the latter course is much preferable to the for- 
 mer, as an analysis, one day or other, is sure to find its syn- 
 thesis ; while, if we commence with synthesis, there is no 
 return to the true path unless through the demolition of the 
 vague hypothesis which such unwarranted synthesis has con- 
 structed. Of this truth the history of science is nothing less 
 than a series of illustrations. Aristotle, through leaping at 
 inference before a complete analysis of the facts upon which 
 his mind was employed, affirmed that the matter of the sun 
 was incorruptible ; and the falsity of the assertion was not 
 detected until the examination of the sun's disk by means of 
 the telescope discovered spots in that luminary. Ptolemy, 
 with a very incomplete analysis of celestial phenomena, at- 
 tempted to construct the whole theory of celestial mechanics. 
 The result was, that astronomy for nearly fourteen hundred 
 years was kept embedded in the ruck of fiction, and could not 
 advance until the orbs and epicycles with which he had peo- 
 pled space were swept away, and the analysis recommenced 
 from the point at which it had been broken off. Thus the 
 entire course of philosophy has been no other -than that of 
 analysis with synthesis following in its train ; and the im- 
 pediments which have constantly beset its path have sprung 
 from no other source than the rash commencement of such 
 synthesis before the corresponding analysis was made out. 
 
 The contrary principle, however, may be said to obtain, in 
 all cases where law and revelation are concerned, concerning 
 either particular doctrines or individual acts. For then, we 
 arrive at results, not through the dissection of the matter to 
 which they refer, but by linking successive cases to each
 
 C. I. 1.] SUBJECT-HATTEB OF SYNTHESIS. 147 
 
 other, in conformity with the laws enunciated in the revealed 
 proposition. Everything consequently must be made to meet 
 the truth which it expressed, either directly in itself or by its 
 immediate consequences, as coming from an impugnable 
 authority ; and hence arises the opinion 1 that, not alone in 
 the moral sciences, but in every complete system of knowledge 
 which professes to trace the relations of all science to each 
 other, and their mutual blendings and ramifications, the 
 synthetic element must predominate and give the tone to the 
 rest. This ground, however, is of too uncertain, a character 
 to warrant any kind of dogmatism, and the best course to 
 pursue, is that of conceding to each of the two great branches 
 of knowledge the predominance of their correlative methods, 
 while we refrain from thrusting forward a probable inference 
 in one department as sufficient ground for oversetting a legi- 
 timate conclusion in the other. 
 
 As in revelation we are not said to discover general laws, 
 but merely infer cases from laws already given, the synthetic 
 process, which is its method, is not said to discover truth, but 
 only to demonstrate it when discovered ; while that of ana- 
 lysis, which prevails in the physical sciences, brings new 
 truths to light, both with regard to particular facts, and the 
 general laws which are shown to arise out of them. Both, 
 therefore, may serve as verificatory processes to test each 
 other's legitimacy ; since as truth is always in unison with 
 itself, a fact which has only been analytically inferred, is 
 doubly confirmed when found to be in accordance with moral 
 truth, and to stand the test of the correlative method ; as a 
 principle, must shine forth with clearer lustre when it derives 
 renewed confirmation from the analytic examination of par- 
 ticular facts. There is consequently no fundamental oppo- 
 sition between the two methods, nor can they ever be viewed 
 as conflicting; unless from an erroneous conception of the 
 nature of the sciences, and the uses to which they are applied. 
 
 Though the direction of these methods must depend in a 
 
 1 Propounded by Gioberti in his Elementi dello Studio di Filosofia, 
 torn. ii. cap. ii., and covertly stated by Chretien in his work on Logical 
 Method, p. 218. These writers, in this case, are only the exponent* of 
 the views advocated by Catholic theologians both at Oxford and Rome; 
 but all the experimentalists and eclectics, with Victor Cousin at their 
 head, condemn this view. See ITntroduction a la Cours de PHistoire 
 de la Philosophic, by the latter. Troisieme Legon. 
 
 L2
 
 148 INDUCTION AND DEDUCTION. [B. IY. 
 
 great degree on individual sagacity, the rules which Descartes 
 laid down may not be without their use, if kept steadily 
 before the eye in all cases of investigation. They are, with 
 regard to analysis, as follows: 1st. Never to accept any- 
 thing as true which we do not clearly know to be so. 2nd. 
 To divide each of the difficulties we examine, into as many 
 parts as possible, and as may be necessary for resolving it. 
 3rd. To arrange our thoughts in order, by commencing with 
 objects the most simple and the most easily known, in order 
 to ascend by degrees to the knowledge of the most complex. 
 4th. To make, in relation to everything, the enumeration so 
 complete and general, that we may be assured of having 
 omitted nothing. The synthesis are thus given in the second 
 part of the same work on Method: 1st. To leave ^ no 
 ambiguity in the terms, by having due recourse to definition. 
 2nd. To assume only clear and evident principles, which 
 cannot be contested by any persons. 3rd. To prove demon- 
 stratively all the conclusions advanced, by employing no 
 other means than the definitions and principles (axioms) 
 already laid down. 
 
 CHAPTER II. 
 
 UNIVEESAL METHOD OF INFEBENCE. 
 
 1. Induction and Deduction Meaning of the Terms. 
 
 IF any train of reasoning be minutely examined, it will be 
 found to proceed either in a descent from the more general 
 to the more particular, resolving a whole 1 into its parts ; 
 (analysis), or in an ascent from the more particular to the 
 more general, or framing out of the particular parts a consti- 
 tuted whole ; (synthesis). The former is called deduction, the 
 latter induction. Thus the physical sciences are commonly 
 called inductive, because they consist of a series of generali- 
 sations, founded on the most circumstantially stated particu- 
 lars, and carried up through intermediate axioms to universal 
 laws, which comprehend in their statement every subordinate 
 degree of generality ; while the abstract sciences are usually 
 
 1 Which may be either of intension or extension. Sir W. Hamilton 
 restricts it to the former, see Ed. Kev. vol. Ivii., but he is evidently in 
 error.
 
 C. II. 1.] THEIR DELATION TO EACH OTHEE. 149 
 
 termed deductive, because they follow the inverse method of 
 proceeding from general axioms to particulars, by which these 
 axioms are traced back to their remote consequences, and all 
 the particular results deduced from them which are included 
 in the general proposition. Of course each branch of know- 
 ledge not only admits, but even exacts as the condition of its 
 perfection, the blending of the two methods, but they are 
 generally so designated, as one or the other element predomi- 
 nates in the proof and fashions its initiatory processes. 
 
 Every inductive train of inference, as well as deductive, is 
 capable of being resolved into its appropriate syllogisms, and 
 is consequently amenable to the laws of the universal canon 
 of reasoning ; the only difference between the two forms in 
 this respect being that, though the former equally ranges 
 through all the figures, it finds its most natural expression 
 in the third, while its deductive counterpart finds its most 
 direct form in the first. By employing the same symbols, 
 the correlation of the two processes may be thus exemplified : 
 Inductive. Deductive. 
 
 x, y, z are a. b is a. 
 
 x, y, z represent the class b. x, y, z are contained in b. 
 .'. b is a. .'. x, y, z are a. 
 
 or, or, 
 
 a contains x, y, z. a contains b. 
 
 x, y, z constitute b. b contains x, y, z. 
 
 .'. a contains b. .*. a contains x, y, z 1 . 
 
 In the syllogisms the order of the terms remains un- 
 changed, but that of the propositions is reversed ; the con- 
 clusion of the one forming the major premiss of the other. 
 Of the terms the major is common to both, but the middle 
 term in the deductive syllogism becomes the minor in the 
 inductive ; and the individuals which are the minor, or deter- 
 mined notion in the deductive syllogism, become the middle 
 term, or determining notion in the corresponding inductive 
 syllogism 2 . The one process, according to this view, is only 
 an inverted counterpart of the other. 
 
 1 Mr. Karslake, estimating the inductive by the deductive syllogism, 
 restricts the former to the 3rd fig. The scheme of Sir W. Hamilton in 
 the text presents the more correct doctrine. See Aids to the Study of 
 Logic, vol. i. p. 89, by W. H. Karslake, B.A. a Hence Aristotle
 
 150 INDUCTION AND DEDUCTION. [B. IT. 
 
 2. Different kinds of Induction, Formal and Material. 
 Syllogism erroneously confounded ivith Deduction. 
 
 Much confusion of thought has arisen through the absence 
 of distinction between the matter and form of induction, and 
 the propagation of the error thence resulting, that because 
 it proceeds in an inverted method to deduction, and is 
 generically applied to designate a distinct ^class of truths, it 
 must necessarily denote a species of inference not contem- 
 plated by the founder of logic ; a view which is countenanced 
 by the fact, that in the days when the laws of the syllogism 
 were evolved, no such thing as inductive science could be 
 supposed to exist. Hence that class of moderns who, like 
 Bacon and Dugald Stewart, will admit of no other correct 
 elementary process than induction, are led to throw aside the 
 syllogistic doctrine both as practically useless, and as an im- 
 perfect exposition of the theory of inference 1 . 
 
 seems to have had a correct idea of induction when he affirmed it to be 
 a syllogism in which the major is proved of the middle by means of the 
 minor; 'ETraycoyrj fj.ev ovv Kai 6 e eVaywy^s irvAAoytcr/ios TO 8ia TOV 
 erepov Qarepov ra> /x7a> croAAoyio'a(r&u. (Pr. Anal. ii. 23, 2.) 
 
 1 It is amusing to hear Bacon state his grounds for rejecting the 
 syllogistic theory, which he rather naively left to mob orators and 
 theologians, to whom he imagined correct reasoning was only a second- 
 ary matter: " At nos demonstrationem per syllogismum rejicimus . . . 
 quod syllogismus ex propositionibus constet, propositiones ex verbis, 
 verba autem notionum tesseraj ac signa sunt. Itaque si notiones ipsoe 
 mentis male ac temere a rebus abstracts fuerunt . . . omnia ruunt . . . 
 Rejicimus igitur syllogismum neque id solum quoad principia sed etiam 
 quoad propositiones medias." Introduction to the Instauratio Magna. 
 This extract clearly shows that Bacon was entirely ignorant of the 
 principles he condemns, or he could not have written middle propositions 
 for middle terms, or urged as a reason for the rejection of the school 
 logic the singular fact, that it was open to the illusion of language; for 
 what reasoning is not? Bacon in this extract rejects middle terms as 
 useless, yet he could not reason without them, and was necessarily as 
 unsparing in their use as St. Thomas Aquinas. 
 
 A great deal of the current notions about the inutility of logic springs 
 from the confusion which such loose writing tends to involve the old 
 and new methods. "We have seen a graduate escape from the hard 
 necessity of allowing himself to be convinced that he was arguing with 
 a middle term particular in both premises, by declaring that facts were 
 better than syllogisrr.6, ir-hen the forms of his argument would have 
 proved that men are ipdants because they require air. " I," he ex- 
 claimed, " produce facts like Bacon, you quibble about their combina- 
 tion with Aristotle."
 
 C. II. 2.] VIEWS OF THE JLNtllENTS AND MODEBNS. 151 
 
 The error appears to us to have arisen in a great degree 
 from the application of the term induction to the process in 
 which there is really no illative inference at all viz., the 
 objective process of investigating particular facts as prepara- 
 tory to illation, which is entirely intuitive, and also from 
 imagining, because the truths arrived at by the process of 
 illative induction are ordinarily tested by certain experimen- 
 tal canons of inquiry and the laws of the Calculus, that it is 
 entirely foreign to the class of truths which the syllogistic 
 theory contemplates. The confusion, however, will disappear 
 on considering that the syllogism, after all, only presents a 
 mode in which an inference may be tested as to the conclu- 
 siveness of its form, and that for this purpose its mechanism 
 is quite as available for inductive as for deductive reasoning, 
 in all cases where an illative inference has been drawn. Now, 
 if a train of reasoning can err on its formal side as well as 
 with respect to its matter, it is surely no good reason to 
 infer, because we are provided with a code of principles by 
 which the latter may be tested, that we are quite .at liberty 
 to neglect the rules which relate to the correctness of the 
 formal illation. 
 
 In both these respects with regard to induction, the 
 ancients and moderns appear to have entertained inverse mis- 
 conceptions. Bacon and his followers have marvellously 
 advanced the doctrine of material induction, but have entirely 
 mistaken the import of its formal laws, and the functions 
 they are calculated to discharge. Aristotle 1 , on the other 
 hand, was right with respect to the form ; while in relation 
 to material induction, or the mode of obtaining the materials, 
 and determining under what circumstances certain indi- 
 viduals could be said to constitute or represent a class, he 
 was obviously in error. For though in addition to the in- 
 duction per enumerationem simplicem, or that which required 
 every individual of a class to be tried, before they could be 
 affirmed to constitute a class, he seemed to admit the induc- 
 tion of a class from a few of the objects which it embraced, 
 founded on the general analogies of nature ; neither he or 
 his followers had any distinct conception of the kind of evi- 
 
 1 Aristotle attributes the discovery of induction to Socrates, deriving 
 the word eirayuyr) from the Socratic accumulation of instances serv- 
 ing as antecedents to establish the requisite conclusion.
 
 152 INDUCTION AND DEDUCTION. [B. IV. 
 
 dence required to warrant such, induction, but from a few or 
 a single instance, and even more frequently from no instance 
 at all, but only from some fancied analogy, they jumped at a 
 universal law, and strove to submit nature to the fanciful 
 hypothesis thus obtained, by concealing every objection 
 calculated to weaken or overthrow it. The moderns, with 
 Bacon at their head, therefore, justly allege, that in- 
 stead of proceeding from well-grounded particulars through 
 the platform of intermediate axioms up to general laws, 
 they rushed up to axiomata summa, and then attempted 
 to deduce the axiomata media, by which they ought to 
 have ascended; a method which of course involved them 
 in undue assumption, and proved the source of irretrievable 
 error 1 . 
 
 As an instance of the mistake of the moderns with regard 
 to formal induction, in addition to those already given, may 
 be cited the attempt to identify syllogism with deduction, 
 and the reduction of reasoning in the inductive form to the 
 first figure with a view to show that all reasoning is syllo- 
 gistic in the deductive sense of the term. Aldrich describes 
 induction as a kind of enthymeme or syllogism in Barbara 
 with its minor suppressed 2 ; viz., " This, that, and the other 
 magnet attract iron, therefore all magnets attract iron." 
 Though the illustration he gives, if thrown into a syllogistic 
 form, would really require a major to be supplied, and not a 
 minor. Thus, 
 
 "Whatever belongs to this, that, and the other magnet, 
 belongs to all ; 
 
 Attracting iron belongs to this, that, and the other 
 magnet ; 
 
 Therefore attracting iron belongs to all. 
 
 We are, consequently, obliged to infer that he inverted the 
 premises ; in which case the inference would be unintel- 
 ligible. 
 
 Archbishop "Whately, on the other hand, takes the sup- 
 pressed member of the syllogism in induction to be the major 3 , 
 and reduces that method of inference to the deductive form 
 in the following manner : 
 
 1 See Karslake's Aids to the Study of Logic, vol. i. p. 97. 2 Artis 
 Logicae Kudimenta, p. 175. 3 Whately's Logic, b. iv. c. i. 1.
 
 C. II. 3.] IN WHAT EESPECTS INDEPENDENT. 153 
 
 Whatever belongs to the individuals we have examined, 
 
 belongs, certainly or probably (as the case may be), 
 
 to the class under which they come. 
 Sheep, deer, and other individuals deficient in upper 
 
 cutting teeth, are found to ruminate ; 
 Therefore all animals deficient in upper cutting teeth 
 
 ruminate. 
 
 Although many instances of induction like the ones ad- 
 duced may be exhibited in a deductive form, yet this does 
 not prove that all can ; nor does the transformation add to 
 the cogency of the inductive inference, but rather weakens 
 its force, by representing it in an unnatural manner. Thus, 
 
 Sir Thomas More was incorruptible, 
 
 Sir Thomas More was a judge ; 
 
 Therefore some judge or judges are incorruptible, 
 
 would appear in the first figure as, 
 
 Sir Thomas More was incorruptible, 
 Some judge was Sir Thomas More ; 
 Therefore some judge is incorruptible ; 
 
 in which form there is not one trace of deduction, nor is the 
 inference strengthened, but despoiled of much of the illative 
 force it bore in the third figure. There is consequently no 
 object to be gained in such reduction, since each figure has 
 its own particular rules for testing the validity of every argu- 
 ment that falls within its confines, and none of the dicta, so 
 far as certainty is concerned, exercises a prerogative over the 
 rest. As long as the dictum de omni et nullo was considered 
 as the paramount law of correct inference, there was some 
 pretext for reducing all arguments to one of the four moods 
 of the first figure, to which that dictum is alone applicable, 
 and considering deduction as identical with syllogism ; but 
 since that view has been disclaimed, there is as much reason 
 and some think far more reason, as we shall presently see 
 for resolving all deduction into the inductive process, as there 
 is for the contrary procedure. 
 
 3. Theories of Seasoning. 
 
 The false views which arose from making deduction 
 synonymous with syllogism have invited attacks from dif-
 
 154 INDUCTION AND DEDUCTION. [B. IV. 
 
 ferent quarters on the whole doctrine of the school logic, 
 which, though varying in some degree in their form, re- 
 semble each other so far in their general features as to de- 
 note a common origin 
 
 facies non omnibus una 
 
 Nee diversa tamen ; qualem decet esse sororum 1 . 
 and, consequently, admit of being dealt with in an aggregate 
 form. The common principle from which they spring may 
 be traced to the assumption that all axioms are but gene- 
 ralisations from particular facts; that there are no such 
 things existing as a priori truths, given, as Kant would say, 
 as ultimate principles of our intellectual constitution; and 
 the consequent coroDary that all inference is from particu- 
 lars to particulars, and that general propositions being mere 
 registers of such inferences, when interpolated in an argu- 
 ment, add nothing to the proof, but simply refresh our 
 memories with the number of cases in which the law we are 
 about to apply to a new instance has been already observed. 
 Thus, when it is inferred, from the fact of the present Pre- 
 mier being a man, that he must die, the major premiss from 
 which we infer the conclusion is not all men are mortal, for 
 that would involve a petitio princvpii, but simply the number 
 of particular cases in which we have observed mortality to be 
 a mark of the class men 2 . Nor is the formula of previous 
 instances in which the inference has been drawn necessary 
 to be looked at on all occasions, as there are a great quantity 
 of particular inferences evident from the bare statement of 
 the minor. We would not require, in order to affirm that 
 the lines A, f, and B, C, from being equal to M, N, are 
 equal to each other, to recur to former cases in which we 
 had observed the truth of the axiom, that things which are 
 equal to the same thing are equal to each other. The bare 
 enunciation of propositions of this character is sufficiently 
 evident of itself, without any previous generalisation, to carry 
 
 1 Met. b. ii. 14. 2 This is Mr. Mill's view, but Dr. Brown will 
 not even concede so much, but affirms it is only necessary to know 
 that mortality is associated with the idea of man to predicate that 
 quality of any individual. Thus, " Prince Albert is a man ; therefore 
 Prince Albert is mortal." But the doctor does not seem to have been 
 aware that the knowledge of mortality being an essential constituent of 
 man's nature, previous to making the inference, was in reality the very 
 assumption of the major premiss, " all men are mortal," which he so 
 stoutly ignored.
 
 C. II. 3.] THEOBIES OF THE NOMINALISTS, 155 
 
 conviction to the most undisciplined understanding as soon 
 as they are understood. The syllogistic theory, therefore, is 
 not the universal type of reasoning, but inference from par- 
 ticulars to particulars through marks of marks. The conclu- 
 sion of an inference not being drawn from a general pro- 
 position, even when it may be advisable to consult it by way 
 of collateral security, but according to it; such general 
 proposition cannot be considered as the real antecedent or 
 premiss, but the particular facts from which that general 
 proposition was inferred. Accordingly the rules of the syl- 
 logism, and, in fact, every artifice which the peripatetic 
 logic embraces, beyond absolute definition, is perfectly use- 
 less in the sense of the Scotch school ; and the work should 
 be at once sent to the trunk-<makers, were it not as well, for 
 the purposes of curiosity, .and out of respect to the past, to 
 preserve so cumbersome a piece of mechanism, by which the 
 human species at least, for nearly two thousand years, con- 
 sented to guide the operations of the reasoning faculty 1 . 
 
 Some recent logicians, though entertaining fundamentally 
 the same views, do not go so far. Though we do not draw 
 the inference in reasoning from the general proposition, 
 where such is employed, it is necessary to preserve con- 
 sistency between the particular conclusion we infer from the 
 minor premiss and our former experience expressed by such 
 general proposition ; and the rules of the syllogism serve as 
 an indispensable guarantee for that purpose. The use of 
 the syllogism is consequently nothing else than the use of 
 general propositions in reasoning ; and these are only certain 
 formula generalised from the results of our former expe- 
 rience, to determine what inferences may be drawn in any 
 particular case. The work of drawing the inference is that 
 of applying the formula, and the rules of the school logic are 
 a system of security for the correctness of the application 2 . 
 
 This middle ground, between the Scotch school and the 
 peripatetic logicians, was raised with a view to defend the 
 syllogism from the charge of really assuming the conclusion 
 in the premises; an accusation that certainly had some 
 
 1 See Reid's Analysis of the Old Organon, Art. Categ.; Dugald 
 Stewart's Philosophy of the Mind, vol. ii. passim ; and Dr. Brown's 
 Lectures, passim. * Mill's System of Logic, vol. i. p. 269. He, how- 
 ever, does not give these rules, but somewhat naively refers his readers 
 to Dr. Whately for them, as evidently too trifling for his notice.
 
 156 INDUCTION AND DEDUCTION. [B. IV. 
 
 colour of plausibility so long as the syllogism was confounded 
 with deduction, and made to guarantee the cogency of every 
 inference that could be thrust into the four moods of the 
 first figure. For if we argue, from every man being a re- 
 sponsible agent, that the present Emperor of Eussia is 
 accountable for his actions, it is evident we assert no new 
 truth, but merely particularise, or draw out of the general 
 formula (major premiss), one of the single instances already 
 included under it. Such a form of reasoning it is conse- 
 quently contended is incompetent to advance us one step 
 in the progress of knowledge, or to corroborate any truth ; 
 since it falls into the sophism which renders the conclu- 
 sion a mere tautological repetition of the premises. Tet, 
 taking logic on the high ground of the deductive syllo- 
 gism with which its adversaries have confounded it, there is 
 need of little ingenuity to invalidate the charges alleged 
 against its method. For waving, at present, the question 
 how we come by the majority of general propositions, which 
 is really the cardinal point in dispute, it cannot be denied 
 that we frequently obtain such formula without realising 
 one-tenth of the meaning they are calculated, when fully 
 analysed, to convey ; and that we can only exhaust them of 
 their latent truth by casting about for middle terms, either 
 by experiment or reflection, which link them with other 
 classes of phenomena previously unknown to us, and thereby 
 extend our knowledge. For example, when Newton first 
 propounded his general law that material bodies attract eacli 
 other with a force proportionate to the product of their 
 masses directly, and the square of their mutual distance in- 
 versely, he hardly dreamt that the precession of the equi- 
 noxes could be deduced as a natural consequence of the 
 same principle. Nor did Pythagoras, when he first realised 
 the truth of the necessary relations between the base and 
 sides of a right-angled triangle, think of the consequent de- 
 velopment to which they subsequently conducted him in the 
 construction of the 47th proposition : at least, he is said to 
 have comported himself on the discovery of that famous 
 Theorem as Columbus in sight of a new world, or as Kepler, 
 when he found that the satellites of Jupiter verified his three 
 celebrated laws of the elliptical motion of the planets. 
 
 To take another branch of cases, which are generally 
 deemed more akin to the syllogistic scheme ; viz., those con-
 
 C. II. 3.] OBJECTIONS TO NOMINALIST DOCTRINES. 157 
 
 nected with the moral sciences, and concern either legisla- 
 tion, theological doctrine, or ethics. Whatever may be said 
 as to the rise of general propositions from the agglomeration 
 of particular instances in other sciences, it is evident they 
 are presented to us in these subjects at the outset in a gene- 
 ral form, and that all the subsequent stages of inferences 
 which these sciences embrace consist in the application of 
 such general formula, by means of middle terms, to particu- 
 lar instances never previously contemplated by us. All 
 these deductions lead to new truths, so far as tjuths can be 
 called new in the human sense of the term, and consequently 
 must be looked upon as resulting in a real addition to our 
 knowledge. What are all the doctrines, for instance, which 
 each denomination of Christians have raised upon the teach- 
 ing of Christ but so many inferences deductively inferred 
 (how far rightly or otherwise is not for us to say) from the 
 general scheme of doctrine he is reputed to have taught ? 
 To select a single case, it would be certainly going very far to 
 aver that the colossal system of doctrines that the patristic 
 fathers built on a few scattered texts of Scriptures were 
 assumed in the premises from which they were deductively 
 inferred ; and yet all these tenets were embraced as original 
 truths, latent, indeed, in the general propositions from which 
 they were drawn, but not fully realised by the primitive 
 Church, and that by the whole of Christendom in their 
 day, and are so held by the majority of professing Christians 
 now. 
 
 Now in all these cases, which extend over all the compart- 
 ments of knowledge, when a particular conclusion is deduced 
 from a general proposition, it is evident that the truth in- 
 ferred must be in some measure contained in the premises to 
 warrant the illation ; but it does not follow that it must be 
 explicitly involved but only in a virtual and implicit manner, 
 in which case there can be no direct assumption of the pre- 
 mises in the conclusion, in which the petitio principii consists. 
 The process of inference, in its deductive as well as its induc- 
 tive processes, is perfectly analogous in this respect to the 
 counter processes of natural truths which it seeks to evolve. 
 There is no effect which is not implied in the cause out of 
 which it springs 1 , nor any state of nature which has not its 
 
 1 Introduzione allo Studio dclla Filosofia da Gioberti, tomo secondo, 
 p. 221 ; and Teor. del Sovr. note 44, p. 406, by the same author.
 
 158 IKDTJCTIOIT AND DEDUCTION. [B. IT. 
 
 principles latently concealed in the state immediately pre- 
 ceding its existence. The phenomena, notwithstanding, are 
 substantially different, though secretly involved and inter- 
 laced in one web of mutual dependence, so that one series of 
 facts cannot arise until their principles have been furnished 
 at least in an inchoate state, by another. If, therefore, the 
 syllogistic theory is to be set aside on account of its implied 
 assumption of conclusion in the premises, we must set aside all 
 exposition of natural truths, and forego reasoning altogether 1 . 
 We do not, then, require Mr. Mill's theory to defend even 
 the deductive syllogism from a petitio principii ; nor, we fear, 
 can that theory be maintained without giving up the main 
 uses of the peripatetic logic. For, if as that logician some- 
 what strangely avers, the formal portion of inference must 
 alone be tested by the experimental canons of inductive in- 
 quiry ; while that part which merely refers to the consultation 
 of our former experience on the point at issue, and keeping our 
 inference in harmony with it, can only fall under the surveil- 
 lance of the syllogistic rules, the entire use of logic is at an 
 end 2 . The functions which it has to discharge relate entirely to 
 that part of inference which Mr. Mill denies its competency 
 to fulfil ; nor can it throw any light on the interpretation of 
 the general formula by which we seek to cover any particular 
 conclusion we have inferred. The latter supposition is r in 
 fact, ludicrous, and requires a very Quixotic imagination to 
 combine the two things in the same theory. "What help can 
 mood and figure with the heavy accompaniment of a group 
 of rules and canons which exclusively relate to pure in- 
 ference, lend to the interpretation of general propositions 
 formed from the results of one's individual experience ? The 
 
 1 Baron Galluppi, in his Lezioni di Logica, answers this futile objec- 
 tion in another way. While he allows the two terms of the conclusion 
 are fairly contained in the premises, he denies that the illation is con 
 tained, in which the truth of the conclusion exists. The latter he desig- 
 nates the formal part of the syllogism; the former the material. The 
 inference of course springs from the comparison of the two terms of 
 the conclusion with the middle, and as the result of that act is only 
 expressed in the conclusion, the premises can by no means be said 
 to contain it. The logicians whose opinions we combat in the text 
 confound the formal with the material part of the syllogism; but 
 though we see the latter intuitively, it does not follow we see the 
 former, as we have before observed, a middle term is necessary to 
 distinguish it. 2 See Mill's Logic : Functions of the Syllogism, where 
 he distinctly propounds the doctrine in the text.
 
 c. n. 4.] iiroircTiow -SOT PABAMOTTST. 159 1 
 
 syllogism, even in its deductive dress, which Mr. Mill takes 
 to be an essential part of its nature, has no more relation to 
 such a function than a flail has to the office of a windmill, or 
 a piston-rod to the uses of a compass. The canons of in- 
 ference were exclusively framed to guarantee the reasoning 
 process. To deny their competency in their proper sphere, 
 and apply them to objects in which,, as Mr. Mill asserts, no 
 inference is concerned, would be a burlesque upon the ordi- 
 nary notions of adaptability between end and means. 
 
 The only things which can be of any service in the inter" 
 pretation of general propositions are a clear perception 
 combined with a capacious memory ; and Dugald Stewart 
 was consequently more consistent when entertaining the 
 same principles with Mr. Mill, he rejected the syllogistic 
 theory altogether, and resolved all reasoning into intuition 
 and remembrance. 
 
 4. General Truths exist independent of Experience. 
 Even in the supposition that all general propositions are 
 the result of experience, it would by no means follow that 
 the school logic was practically useless ; since such an hypo- 
 thesis could not preclude an argument from being incon- 
 clusive as to form, or present us with any means of detecting 
 its inconclusiveness different from that of throwing it into the 
 syllogistic form and bringing it under the universal canon of 
 inference. Nevertheless, the assumption would tend to weaken 
 the syllogistic doctrine, since it would show that reasoning, at 
 least in its elementary stage, was purely restricted to one pre- 
 miss, there being no common principle to> serve as major until 
 a number of particular inferences had become agglomerated 
 into a general proposition. Now, we fairly put it to each 
 one's consciousness, whether such an exposition of the 
 manner in which he registered his first inferences is correct. 
 When a child has once felt the consequences of playing with 
 fire, does it ever trust itself again with the dangerous ele- 
 ment ? What need has it of a second, experience to certify 
 that sugar is sweet and acids bitter ? Do the number of in- 
 stances in which these objects are felt through the course of 
 the longest life add a single iota of strength to the first in- 
 ference ? If no one can say that they do, without contra- 
 dicting the general experience of his species, then is that first 
 inference a general proposition not singly inferred from the
 
 160 INDUCTION AND DEDUCTION. [B. IV. 
 
 individual case, but from a constituent principle of our intel- 
 lectual constitution taken in conjunction with it, which in- 
 teriorly assures us, that whatever qualities we have found in 
 combination with particular phenomena, will invariably ac- 
 company the subsequent repetitions of that phenomena*. 
 
 If our inferences never travelled beyond the particular 
 cases out of which they spring, it would not only follow that 
 each repetition of the inference would act as an additional 
 guarantee for applying it to an indiscriminate number of 
 similar cases, but that all the relative degrees of certainty, as 
 well in different minds as in each individual's consciousness, 
 would arise exclusively from the number of times the par- 
 ticular coincidence, or disagreement, about which it was 
 employed had been experienced. To this indisputable conse- 
 quence of the assumption of the empirical nature of all 
 general propositions each one's experience gives the lie. For 
 though there are a class of facts that absolutely follow that 
 law (as those connected with contingent events), and re- 
 sult in general propositions of an empirical character, 
 there are other classes of truths which do not require 
 any sensible experience to assure the mind, that they in- 
 clude every concrete case to which they are capable of being 
 applied as abstract propositions, the truth of which the 
 mind perceives intuitively in its ideas ; while there is an ad- 
 ditional class which require one exemplification of the in- 
 ference, but after that are so indubitable and certain in their 
 character, as to be instinctively generalised on the spot, and 
 extended to every subsequent instance of the same pheno- 
 mena. The indispensable corollaries of the doctrine, that all 
 general propositions are only agglutinations of particular in- 
 ferences, do not agree with the facts of which each one's 
 own consciousness is a steady witness ; the principle itself is, 
 consequently, to be rejected as untenable. 
 
 Mr. Mill has attempted to confound abstract, or necessary 
 truths, with those of a physical character, by resolving them 
 into hypothetical notions, and making the necessity, which 
 
 1 Sir W. Hamilton will not admit this principle, because it does not 
 necessitate, but only inclines. We should like to know if the worthy 
 Edinburgh professor ever so far doubted of the burning qualities of fire 
 as to put his hand into a flame twice, or ever refused to eat bread 
 because he mistrusted its nutritive properties. With all due respect 
 to so high an authority, the practical exemplification of the principle 
 he lays down would be a mark of insanity.
 
 C. II. 4.] NECESSABY AND CONTINGENT TETJTH. 161 
 
 we suppose to accompany them, the simple result of habit, in 
 conformity with the consequence which we have attributed 
 to his principle. But here, again, this acute philosopher is 
 strangely at strife with himself. For if such propositions 
 be hypothetical^ true, it is evident they must be held neces- 
 sarily so, as long as the hypothesis is maintained, otherwise it 
 would be competent to any one to aver that the same thing 
 could be and could not be at the same time. It is, there- 
 fore, absurd to say, with such a doctrine in the foreground, 
 that their necessity springs from habit 1 . 
 
 But does the necessity of necessary truths spring from 
 their hypothetical character, and can the latter mark be 
 supposed to exist in combination with them ? "We think 
 neither of these cases can be maintained. In the first place, 
 there is a class of necessary truths, even conceded by Mr. 
 Mill 2 to bear no evidence of hypothesis about them, which 
 are, notwithstanding, held by the mind with the same intui- 
 tive certainty as those which he deems of a suppositive cha- 
 racter. That the two sides of a triangle must be always 
 greater than the third ; that two straight lines cannot enclose 
 a space, and truths of a similar character, do not involve the 
 least particle of hypothesis in their statement, is universally 
 admitted, yet they are embraced as soon as enunciated, with 
 the same confidence as the propositions which refer to the 
 
 1 Dr. Whewell very properly distinguishes necessary from contingent 
 truth by the utter impossibility of the former being otherwise than it is. 
 Thus, to take a numerical instance : 3 and 2 are 5 ; we cannot con- 
 ceive them, by any freak of thought, to make 7 (Phil. Ind. Sciences, 
 i. 54, 55). In reply, Mr. Mill takes the inconceivability of the re- 
 verse of a proposition as the only sign of its necessity, and attempts to 
 prove the futility of such a mark by citing cases of doctrines (such as 
 the antipodes) once deemed inconceivable, which have nevertheless 
 subsequently taken their place as scientific truths. But this is playing 
 with the double sense of the word inconceivable in a manner which is 
 unworthy of a logician of Mr. Mill's attainments. The term evidently 
 can be, and is very frequently, applied by Dr. Whewell, to denote two 
 classes of objects; one which cannot be entertained without conflicting 
 with the primary laws of the reasoning faculty, and the other which, 
 like some of the truths of revelation, surpasses our comprehension, 
 simply because the truths it embraces belongs to a class of subjects 
 which, either through defective faculties, or want of means of informa- 
 tion, we are unfitted to realise. It would be doing injustice to Mr. 
 Mill not to suppose that he understood Dr. Whewell to take the term 
 in the passage animadverted upon in the former sense. ' Logic, 
 
 vol. i. Art. Demonstration and Necessary Truths. 
 
 M
 
 162 INDUCTION AND DEDUCTION". [u. IT. 
 
 equality of the radii of a circle that is supposed to depend 
 upon the possibility of abstracting length from breadth for 
 its acceptance. Whence comes the difference, if both classes 
 of necessary truths are held with the like uniform and un- 
 varying degree of certainty by the believing mind ? Even if 
 we were disposed to save Mr. Mill from the consequences of 
 his first inconsistency, which his words, however, will not 
 allow us to do, and assert that the truth of the purely sup- 
 positive group springs from their hypothetical character, 
 while that of the contrary class arises from habit, the dis- 
 tinction could serve no purpose, unless to overthrow Mr. 
 Mill's doctrines. For in that case the indisputable conse- 
 quence would follow, that the hypothetical class must be 
 granted as soon as the condition was expressed ; while that 
 series whose truth was the mere creature of habit and asso- 
 ciation, would be received with doubt at first, and go on in- 
 creasing in certainty according to the number of times the 
 phenomena in which they first took their rise was repeated. 
 But such a supposition is at war with the plainest truths that 
 consciousness reveals to us, and could not be entertained with- 
 out convicting the first principles of reasoning of imposture. 
 We can only escape from such false consequences by 
 ascribing the uniformity of belief, with which all abstract 
 truth is held, to the necessary relation between the classes 
 of our ideas out of which they spring a relation which is 
 assented to in the same moment as it is intuitively perceived, 
 and instead of depending on experience does not require one 
 confirmation from that source to assure the mind that it in- 
 cludes all the cases that actual reality can bring under its 
 judgment. When we say that two straight lines cannot en- 
 close a space, or affirm that the radii of a circle are equal, 
 there is no more hypothesis in the last proposition than 
 in the first; since we do not affirm that the things of 
 which we speak exist out of our conceptions, but that both 
 are necessarily true as beheld in the percipient mind. 
 Even viewed with relation to external objects, the only con- 
 dition that is required in either case, is the existence of space 
 and sensible lines to which they can be referred. For it is no 
 more necessary that such lines should exist without breadth 
 to realise the truth of the last case than that of the first ; 
 since the radii would still be equal, if drawn to the very edge
 
 C. II. 4.] THEEE CLASSES OF TBTJTHS. 
 
 of the circumference of the circle, and in that sense would 
 fulfil the condition imposed by the geometrical definition of 
 a straight line 1 . But the fact is, owing to defective instru- 
 ments, and the inexactness attending even the most delicate 
 manipulations, the mind's conceptions can never be fault- 
 lessly cast into physical embodiments : but this by no means 
 argues a want of reality in the conceptions themselves, but 
 is to be ascribed to the grossness of our sensible perceptions, 
 which are not fitted to embody abstract truth to a greater 
 degree of perfection than is requisite to attain man's end in 
 creation. If mathematical or abstract truth fall short of ab- 
 solute perfection when carried into the material world, phy- 
 sical truth is in the same predicament, ail concrete know- 
 ledge being only so many approximations to absolute reality. 
 But to call either it or mathematical truth hypothetical on 
 that account, would bring the whole structure of science 
 about our ears 2 . 
 
 From the foregoing considerations, we conceive ourselves 
 fully warranted in drawing a distinction between three classes 
 of truths existing in the mind ; two underlying all our in- 
 ferences from particular events, and the other furnishing 
 the occasions by which either class are called into action. 
 "When we restrict our judgment to a particular event, the 
 result is a simple intuitive truth. But when the inference 
 travels further than the affirmation of the agreement, or dis- 
 agreement of the terms in that particular case, a real illation 
 has taken place ; which, upon analysis, will be found to 
 consist in the combination of one of the first class of truths 
 (major) with the particular case (minor) which called it into 
 being. Thus, when a child has once perceived that moisture 
 is the effect of rain, it directly concludes that in all future 
 cases it cannot come in contact with that element without 
 getting soaked, from an interior conviction which assures 
 it that similar effects follow from like causes ; and which, 
 expressly evolved, constitutes the major proposition to the 
 
 1 Or the truth would be equally preserved if the line was considered 
 to be of equal breadth. * The doctrine of hypothesis originated 
 
 with Dugald Stewart. The only distinction between the two classes 
 of abstract truth which Mr. Mill strives to discriminate by introducing 
 the extraneous idea of hypothesis is, that one admits of direct, the 
 other of indirect, proof, or reductio ad absurdum. 
 
 M2
 
 164 INDUCTION AND DEDUCTION. [B. IV. 
 
 inference in question. If such a proposition be not in the 
 mind instigating the judgment to leap to the general con- 
 clusion, then, we say, there is no ground for illation. For 
 when the child forms a judgment in the absence of any such 
 a priori truth, it is strictly of a particular character. Thus, 
 it never concludes from the single fact that its nurse has 
 been angry to-day, that she will be so to-morrow, simply 
 because it has no general a priori judgment in the mind 
 that could form a major premiss in combination with the in- 
 dividual case to warrant the supposition. 
 
 Nor is it even necessary to concede, though it does happen 
 in many cases, that individual occurrences are required to 
 call the abstract truth into being with respect to every par- 
 ticular phenomenon. Before a child has experienced a prac- 
 tical exemplification of the truth that every sound must have 
 a cause, it is found to burst its drums and break its trum- 
 pets, with a view to explore the locality of the noise. Who 
 has not smiled at his teacher when first set to learn the de- 
 finitions of Euclid, for attempting to increase his knowledge 
 by the announcement of the fact, that things which are equal 
 to the same thing are equal to each other, a truism as long 
 familiar to his memory as his own identity. Such prin- 
 ciples as these accompany the first exercise of thought, 
 fashion the first judgments that the mind forms, and instead 
 of being dependent on particular inferences, comprise the 
 very elements out of which such inferences are evolved, and 
 present the only means of testing, or legitimating, their 
 validity. Had the divine economy ordered this otherwise, 
 and left the child entirely dependent for its knowledge upon 
 its own solitary experience, it would be the victim of de- 
 struction before leaving its nurse's arms ; and such a thing 
 as certainty could no more enter into the mind than the 
 idea of colour into the conception of a blind man. 
 
 Such a priori judgments, which we agree with Kant 
 in accepting as the ultimate elements of our intellectual 
 constitution, may be distinguished into two classes, viz., 
 those which have direct reference to external facts, and are 
 only true in the supposition that the laws of nature remain 
 and will continue immutable ; such, however, may be denied, 
 as we shall subsequently see in certain cases, without im- 
 peaching either the reasoning faculty or consciousness, of
 
 C. III. 1.] DEGREES OF CERTAINTY. 105 
 
 error. The other class refers to necessary truth arising 
 from the necessary relation between our ideas, and which 
 cannot be denied without destroying the terms which consti- 
 tute the proposition in which they are expressed. Into these 
 classes of abstract truths and single intuitive judgments, both 
 alike incapable of demonstration, we resolve all reasoning. 
 
 CHAPTEE in. 
 
 DIFFERENT DEGREES OF EVIDENCE. 
 
 1. Various Grades of Certainty. 
 
 THE elements into which we have resolved the syllogistic 
 process partly correspond to the three divisions of Aris- 
 totle, touching the modality of propositions, or the different 
 degrees of belief with which a judgment is held by the mind, 
 which the Stagyrite classes under the head of necessary, cer- 
 tain, and contingent (probable) 1 . The first term he refers to 
 that class which spring out of the necessary relation between 
 our ideas, and which are so absolutely true that they cannot 
 be denied without invalidating the reasoning principle itself. 
 In the scholastic sense, this class was usually styled meta- 
 physical ; and even God is declared incompetent to render 
 them otherwise than they are, the things which they desig- 
 nate remaining the same ; as the supposition would lead to 
 the confounding the intrinsic properties of things. Physical 
 truth, on the other hand, while capable of demonstrative 
 certainty, is altogether dependent on the continuance of 
 the laws of the external world, and consequently may be 
 abrogated when the author of them chooses to suspend their 
 functions. Physical truth, therefore, is confined to the 
 boundaries of the material world, to space and time, and is 
 dependent on the will of the Creator ; while metaphysical 
 truth exists absolutely and universally, and can in no in- 
 stance be supervened without the destruction of the concep- 
 tions which enter into its composition. The supposition that 
 Fresnel's law of the bifurcation of light in certain crystals 
 was suspended, would by no means involve the destruction 
 of either the crystallised bodies concerned or an illuminat- 
 
 1 Prior Anal. i. 8. Avayicdla : fV8exM a ' a :
 
 166 DIFFERENT DEGBEES OF EVIDENCE. [fi. IV. 
 
 ing medium ; but we could not for a moment conceive lying 
 to be a virtue, or a cylinder to be a sphere, without annihi- 
 lating all the conceptions which enter into the respective 
 terms of the judgment. 
 
 Contingent, or probable truth, comprises that wide class of 
 judgments which depend upon events whose operations we 
 are unable to investigate, and concerning which we cannot 
 predict anything but with a very doubtful degree of certainty. 
 That the weather will be fine to-morrow because it has been 
 so to-day is ajudgment that falls under this category, because 
 we can furnish no other grounds for it than mere conjecture. 
 This class of propositions is generally designated by the word 
 chance, accident, &c., and was frequently so deemed by Aris- 
 totle and the ancients. But there is no such thing as chance 
 or accident existing in nature, everything being controlled by 
 systematic laws, and produced by the action of regular 
 causes, the only difference being that, in the class of things 
 termed contingent, we are unable to penetrate into their 
 operation. The result of the Derby, for example, next year, 
 depends upon the superior qualifications of a certain horse, 
 the manner of treatment in the interim, and the honesty 
 with which his owner and rider make use of his speed in 
 the contest. But the issue at best can only be conjectured 
 with probable certainty, because we cannot foresee the re- 
 sult of these causes or ascertain how far they will operate. 
 
 To this list the scholastics added that of moral truth, 
 which, though when accompanied with strict marks of vali- 
 dity, falls somewhat short of demonstrative certainty, still ap- 
 proaches so nigh it that it may almost be ranked in the same 
 category. Such are the foundations upon which rest our 
 belief in the testimony of others, with regard to facts which 
 we have not seen, and which impel us to believe histo- 
 rical truth, when accurately verified, with the same tenacity 
 as we accept any scientific fact derived from our own inves- 
 tigation. For, that a number of men having no connexion 
 with each other, and influenced by no personal motives, 
 should conspire to cheat mankind with a lie, is a supposition 
 which we can no more entertain than any notion which im- 
 peaches the reasoning principle itself. Yet in all such pro- 
 positions there is room for cavil, as many find it difficult to 
 convince themselves that all the required conditions have been
 
 0. III. 2.] YAEIOTJS PHASES OF CBEDIBILITY. 167 
 
 fulfilled ; and when the testimony of individuals are incon- 
 sistent with the permanence and fixity of Nature's laws, 
 some philosophers choose to abide by the latter, as more cer* 
 tain than the human testimony, no matter how well sup- 
 ported, which seeks to set them aside. 
 
 2. Twofold Doctrine of Modality. 
 
 The question of the different degrees of belief by which 
 judgments are held, has been deemed of so unsatisfactory a 
 character by many modern logicians, as to be excluded from 
 the domain of the science, on the ground that the certainty 
 affects the predicate of a proposition and not the copula, and 
 as such does not come within the reasoning process. There 
 is no doubt a quasi species of modality which only concerns 
 the predicate, as when we say " the wine is uncommonly good," 
 " the sun is very hot ;" but this does not come within the 
 proper definition of the term, and consequently must not be 
 confounded with it. With regard to strict modality, the 
 copula, as the link of connexion between the two extremes 
 of a proposition, is undoubtedly modified by any variation of 
 the certainty which exist between their union. If two 
 weights are held together by a chain, any diminution or in- 
 crease of the firmness with which they are held together 
 must influence the chain uniting, and not the weights which 
 it holds. The consideration of modality, therefore, becomes 
 essential to any practical system of reasoning, for the con- 
 clusion can in no instance involve any further degrees of cer- 
 tainty than is contained in the premises ; and if we would have 
 the mind realise its full value, it is essential to know the 
 amount of certainty that accompanies each premiss in the 
 syllogism. Moreover, since the resolution of a point in dis- 
 pute 1 will often depend upon the relative value we attach to 
 different degrees of evidence, it becomes a matter of very 
 great importance to consider how far, and in what respect, 
 one class of judgments is more certain than 'another. 
 
 The complete doctrine of modality would consequently 
 embrace every degree of belief which the mind is accustomed 
 to attach to the different classes of its judgments, with the 
 corresponding motives, commencing with the lowest grade of 
 
 1 Such as of miracles.
 
 168 DIFFERENT DEGEEES OF EVIDENCE. . [B. TV. 
 
 probability and rising through the intervening shades of 
 belief to the highest metaphysical certainty. Each of the 
 divisions in that case already given, would admit of a minute 
 subdivision. Thus, for instance, the class of moral truths 
 might be arranged under four or five distinct heads. First, 
 under that of historical testimony, which even in itself has 
 different branches of certainty, that which relates to the de- 
 struction of Nineveh not being commonly received with the 
 same credence as we believe the burning of Moscow or occur- 
 rences of a more recent date. In this respect, time seems 
 to be, in some respects, the arbiter of the degree of belief 
 we may attach to a fact depending on the testimony of tra- 
 dition. The fate of Troy has long been considered of very 
 doubtful authenticity, and the early account of Eome is be- 
 ginning to loom through the twilight of fable, which may, if 
 the world last long enough, in the lapse of ages overspread 
 its entire history. Secondly, under that class of evidence 
 which relates to the existence of the soul in a future state, 
 the belief of an overruling Providence, and the impression 
 that man in the next life will be punished or rewarded for his 
 actions in this ; all which judgments being incapable of de- 
 monstration or any very rigid proof, are accepted by a cer- 
 tain class of minds with great distrust, and even in the judg- 
 ment of those really confiding in them, who form the vast 
 majority of the human species, rest upon other foundations 
 than the purely moral proofs which are alleged in their sup- 
 port. Thirdly, under that class of testimony which relates 
 to present facts, whose reality any one, if he chooses, may 
 go and convince himself of by the evidence of his senses. 
 This class of truths is the most certain of any others de- 
 pending on purely moral grounds, and men universally accept 
 them with the same amount of credence as they receive the 
 plainest revelations of their own consciousness. Fourthly, 
 under that of ethical doctrine ; for, though the majority of 
 mankind are disposed to call things by their right names, 
 and would really stone a man who ventured to preach up a 
 loose morality among them, there are not wanting many 
 philosophers of very acute penetration who affirm that, intrin- 
 sically, there is no more vice in adultery than in saying one's 
 prayers, and that the vulgar distinctions of virtue and wicked- 
 ness only spring from the conventional notions of society. 
 That such opinions, if practically acted upon, would destroy
 
 C. HI. 3.] CEITEEIA OF EVIDENCE. 169 
 
 the ligaments by which nations and communities exist, is 
 universally admitted ; and since man was born for society, it 
 becomes a matter not of very hard calculation to determine 
 how far it may be presumed that either God or nature 
 would make the condition of one of the great ends of his 
 destiny dependent on a delusion. 
 
 3. The same subject continued. Criteria of Evidence. 
 The Doctrine of sufficient reason. 
 
 The branches of physical truth may be divided into ex- 
 perimental and demonstrative. Both are received with suffi- 
 cient certainty to displace doubt ; but assurance is doubly 
 fortified and strengthened when physical truth has stood all 
 the tests of the demonstrative methods ; for we then receive 
 two different species of security for the existence of the fact, 
 or law, whose validity may have been in question, which is 
 tantamount to a confirmation from two distinct sources of 
 evidence. The metaphysical portion of the general division 
 may be considered under the heads of mathematical and 
 logical. The first member is sufficiently evident, having been 
 already dilated upon to some extent. The nature of the 
 latter will fully appear in considering the different criteria 
 which have been laid down by logicians for sustaining the 
 mutual dependence and harmony of the different branches 
 of evidence, both with themselves and with each other. 
 
 The first of these is, the principle of contradiction, viz., 
 " that the same property cannot be at the same time affirmed 
 and denied of the same subject." Thus, we could not main- 
 tain the existence of Kepler's laws while we believed in the 
 Ptolemaic theory of the heavens, for that would be plainly 
 tantamount to saying that the planets moved in complete 
 circles, at the same time that they described an elliptic 
 course through the heavens. Yet trite as even this principle 
 may appear, it is more frequently violated in moral judg- 
 ments than we imagine. For how often do we meet with 
 men who talk about the existence of a free press in con- 
 nexion with absolute monarchy, and who cast their lot with 
 despotism while they affirm that all their opinions and predi- 
 lections are in favour of absolute liberty ? Indeed, there are 
 a class of persons in whom this error is so deeply rooted, 
 that their statements only cease to be contradictory when 
 they become tautological.
 
 170 DIFFEBENT DEGBEES OF EVIDENCE. [B. IV. 
 
 The second criterion is the complement of the former, viz., 
 "that conceptions which agree with each other can be in 
 thought united or affirmed of the same subject at the same 
 time," and is designated the principle of identity. The third 
 is the principle of the excluded middle (lex exclusi niedii) : 
 " Either a given judgment must be true of any subject or 
 its contradictory, there is no middle course." The result of 
 this criterion is, that we cannot accept one proposition as 
 true without abandoning its contradictory as false, and vice 
 versa. If, therefore, we can prove that the contradictory of 
 any judgment is true, we impugn its veracity quite as much 
 as if we directly overthrew it. The principle of sufficient 
 reason 1 may be said to form the fourth criterion of evidence, 
 viz., " that every judgment must rest upon a sufficient ground 
 or reason," which excludes from the consideration of evidence 
 every belief rooted in ignorance, prejudice, or self-interest. 
 From this law it would follow : first, that we cannot grant the 
 reason without accepting what follows from it, which is the 
 foundation of syllogistic inference : secondly, that if all the 
 consequences are held to be true, the reason must be true ; 
 thirdly, that we cannot reject the consequence without re- 
 jecting the reason. Hence the mode of proof called reductio 
 per impossibile*. 
 
 Logical truth, however, does not communicate to the 
 mind a distinct degree of certainty from that of mathe- 
 matical. Both are accepted with the highest degree of belief 
 that can be supposed to exist, and are therefore properly 
 termed metaphysical 3 . Physical and moral truths, when con- 
 firmed by the strict marks which we shall presently offer, as 
 a test of their validity, are accepted with a similar degree of 
 belief, though it is hard to conceive this of so certain a cha- 
 
 1 Usually attributed to Leibnitz, since it first received entire de- 
 velopment at his hands; but the principle was long known in the 
 schools prior to his time. 2 Leibnitz (Wolfs Ontologia, 71), 
 
 Stachenan (Ontologia, 23 25), and Degerando (Hist. Comparee, 
 1 ed. b. i. c. iv.) confound the motive which leads us to believe a thing 
 with the cause of its existence. Now, though there is always a motive, 
 it does not follow that there is a cause for everything. The latter is a 
 pure prejudice of philosophers, from which even Bacon was not exempt. 
 3 Metaphysical truth is sometimes taken for absolute truth, as by Mr. 
 Thompson in his Laws of Thought; but, as we shall presently show, no 
 such thing exists.
 
 0. IV. 1.] ULTIMATE SOUBCES OF JUDGMENT. 171 
 
 racter as that which accompanies metaphysical judgments, 
 inasmuch as the hypothesis of their being false does not lace- 
 rate the reasoning principle itself, and has been maintained 
 with great strength of argument by a group of very able phi- 
 losophers. But moral testimony, which does not bear the 
 assigned marks of validity, or physical events which seem to 
 contradict the usual order of nature, or refer to future 
 results, into the causes of which we are unable to penetrate, 
 must be regarded as probable, but the precise amount of 
 credence with which they must be accepted, will form the 
 chapter of a subsequent book. 
 
 CHAPTER IV. 
 
 THE FOUNDATIONS OF EVIDENCE. 
 
 1. Number of Primitive Elements into which all Knowledge 
 can le resolved. Their Relation to each other. 
 
 THE motives which impel us to form those various judg- 
 ments we have just considered are stated differently by 
 logicians, according to the opinions they have formed on 
 the nature of knowledge. The widest division we have seen 
 is that of Galluppi, who resolves these motives into seven 
 distinct elements ; viz., consciousness, memory, external 
 sense, analogy 1 , reasoning, evidence (intuitive we suppose 
 he means), and authority; since it is impossible to demon- 
 strate the veracity of any one of these means of know- 
 ledge without falling into a petitio principii. Thus, when 
 Descartes denied the infallibility of any other primitive 
 fountain of knowledge, unless that solitary act of conscious- 
 ness which informed him of his own existence, and attempted 
 
 1 For analogy, Galluppi, in conjunction with some other logicians, 
 uses the word induction. May we be allowed to enter our protest 
 against this abuse in applying terms whose functions are already 
 sufficiently large, to designate an entirely distinct class of subjects with 
 which they have no connexion. If this habit proceed much further, 
 all distinctions of philosophical- nomenclature will become confounded, 
 and we shall be in the condition of geographers, who, owing to the cus- 
 tom of calling all the places in the New World after the titles of the Old, 
 cannot tell, when an occurrence is said to have happened at Windsor 
 or Halifax, whether it took place in Europe, Australia, or America.
 
 172 FOUNDATIONS OF EVIDENCE. [B. IV. 
 
 to demonstrate the veracity of the rest, he assumed the 
 infallibility of reasoning and memory, as no truth can be 
 proved without the exercise of these two motives of judg- 
 ments ; and when the scholastics, who were addicted to the 
 folly of demonstrating everything, attempted to prove the 
 veracity of memory by the veracity of Grod, they fell into as 
 palpable a sophism, inasmuch ^s the accuracy of tlie trains of 
 inference they employed depended on the infallibility of the 
 very faculty they were intended to establish. 
 
 These motives, however, are so related, that while many of 
 them can be exercised apart from the rest, each requires a 
 separate act of consciousness for the perception of its ex- 
 istence 1 . Thus, we believe in the existence of the external 
 world on the immediate authority of the senses ; but these 
 are entirely dependent for their action on the act of con- 
 sciousness, so that the existence of matter is certified to us 
 mediately through the act of consciousness. Again, no act 
 of memory can be exercised unless through the same 
 medium, and when that faculty assures us of our own 
 identity, consciousness is required as a means by which that 
 act of memory may become manifest to us. But though 
 consciousness 2 thus underlies every other primitive truth, 
 and is essential to their exercise, it has functions apart from 
 them, and, therefore, may be said to have a distinct existence 3 . 
 Thus it reveals to us immediately, and that without the aid 
 of any of the other faculties, the idea of our existence, with 
 that class of intuitive judgments which spring out of the 
 relation between our ideas. It consequently may be said to 
 enjoy a prerogative over the other motives of judgments, as 
 it not only is the direct means of communicating to us a 
 wide class of evidence, but is the grand basement on which 
 the certainty of the other motives rest, the supposition of 
 their invalidity involving in the impeachment of its veracity 
 the destruction of all knowledge. 
 
 1 Keid and Royard Collard, following the common-sense doctrine in- 
 stituted by Pere Buffier, erected consciousness into a distinct faculty, 
 even existing separately from perception ; but for this they are pro- 
 perly censured by Sir W. Hamilton. 2 The scholastic definition of 
 consciousness, or sensus iutimus, is perceptio qua mens de presenti suo 
 statu admonetur, and, as such, it is usually taken as synonymous with 
 conscientia. 3 The contrary opinion is maintained by Sir W. 
 
 Hamilton.
 
 C. IT. 2.] MEMORY UNIMPEACHABLE. 173 
 
 It may be observed that each of these means of evidence 
 affords an inlet for original information, except memory, and 
 that its function is simply to reproduce the past states or 
 modifications of the thinking mind. It is not, therefore, an 
 original, but an auxiliary, motive of judgment ; but one of so 
 important a character that it ranks next to consciousness 
 in the function of generating knowledge ; since, in the ab- 
 sence of its veracity, as we shall presently show, none of the 
 other motives could be of the slightest avail in constructing 
 a system of science. In examining into the nature of the 
 other motives, each will be found to have distinct oflices en- 
 tirely independent of one another, unless, indeed, evidence 
 which, according to our description of consciousness, can 
 have no place in the category, even in the narrow sense of 
 intuition, in which alone its claims could be considered. 
 For the judgments which intuitive evidence embraces are 
 either of a metaphysical character, or they refer to particular 
 coincidences in the external world. In the former case they 
 come immediately under the cognisance of consciousness, 
 and in the latter that of the external senses. Its presence, 
 consequently, in the list leads to a cross division, besides 
 being entirely unnecessary. But as, of the six remaining 
 principles, consciousness never becomes the subject of the 
 direct assaults of scepticism, unless through the medium of 
 the others, we need only inquire in what respect the veracity 
 of these may be placed out of the reach of its attacks. 
 
 2. Memory an ultimate source of Evidence. 
 "Without the faculty of remembering the past modifications 
 of our minds, every moment of life would be the first moment 
 for us. "We could not recal one experience, or register one 
 single judgment or inference; no science consequently could 
 exist. The only conclusion we could arrive at would be, 
 "I am," and nothing more. Any attempt, therefore, to im- 
 pugn the veracity of this faculty lays the axe to the root 
 of all knowledge, and even aims at the destruction of 
 personal identity. Sceptics have not neglected to avail 
 themselves of the compendious method thus offered for the 
 destruction of certainty, and have directed their attack in 
 two ways. 
 . First, it is contended that memory is faltering and uncer-
 
 174 FOUNDATIONS OF EVIDENCE. [B. IT. 
 
 tain, and in many cases has been convicted of deception. 
 "Who has not mistaken one object for another, or been fully 
 assured he "was in possession of a fact which, when he came 
 to search for it, either eluded his recollection or emerged out 
 of his consciousness in another form ? Our courts of justice, 
 and the system of arbitration to which mankind find it neces- 
 sary to have recourse, hourly present cases of men, each at 
 the instigation of this faculty, making the most conflicting 
 statements, and staking their veracity on the asseveration of 
 an oath. The answer to this objection is patent. "We only 
 vindicate the certainty of memory in all those obvious cases 
 in which its certainty cannot deceive us without arguing some 
 degree of mental derangement in the understanding of the 
 person who manifests it. For certainty of memory in such 
 cases is all that is required to legitimate the generation 
 of knowledge, so far as its operation is concerned ; but ii 
 men choose to tax their memory with burdens beyond its 
 strength, or if they fail to remember things which persons 
 who possess this faculty in any ordinary degree would easily 
 recollect, memory is not on that account to be declared inca- 
 pable of performing its ordinary functions, otherwise we 
 might argue that because man could not bear a camel's load 
 he was not able to sustain his body erect, or from the fact 
 that there were always a number of valetudinarians, that the 
 human organs were incapable of the performance of their 
 healthy functions. 
 
 Another attempt has been made to weaken the evidence 
 of memory, by depriving that faculty of the collateral secu- 
 rity which it derives from its connexion with consciousness. 
 For it is contended that consciousness never takes into ac- 
 count the objects of memory, but only of an act existing 
 within us called by that name. But this is a distinction 
 without a difference, for memory is nothing else than the 
 perception of the past modifications of our being : render 
 these illusory, or wipe out their existence from the act of 
 consciousness, and no act of memory can exist. Again, if 
 the testimony of consciousness be veracious, we must admit 
 all that it reveals; but it certifies to us the existence of 
 three distinct faculties, viz., that of the perception of things 
 actually existing ; of those which have been and are not ; of 
 those which are not and have never been. Now, if the 
 objects of memory had no existence, it would be confounded
 
 0. IV. 2.] MEMOEY A1TD PEBSOHAL IDENTITY. 175 
 
 with the last faculty, that of simple imagination ; or, in other 
 words, it would not exist in the manner in which conscious- 
 ness reveals its existence to us. We cannot, consequently, 
 admit the separation of the objects of memory from con- 
 sciousness without impeaching that faculty itself of error. 
 
 One of the principal functions of memory undoubtedly is, 
 to assure the consciousness of its individual identity ; but as 
 it fails to do this beyond a certain period of existence, it has 
 been pronounced unequal to its mission, and accused of 
 leaving one of the most essential truths without any tangible 
 foundation. For what certainty have we against our exist- 
 ence from eternity in a state of metempsychosis, or that we 
 have not been in the world for three thousand years, and 
 even inhabited the body of a crocodile or a sparrow ? All 
 that memory certifies is our existence down to a certain 
 period of time ; but with regard to the state in which we 
 existed anterior to that period, as the assumed first months 
 of our infancy, and the nine months' probation in the womb, 
 it says confessedly nothing. It is, consequently, charged 
 with leaving our personal identity uncertain, and, as a reflex 
 consequence of this defect, with rendering all knowledge 
 which is built upon the assumption of this truth, including 
 its own posterior acts, of an apocryphal character. 
 
 But this difficulty seems to arise from confounding the 
 functions of a faculty with the remembrance of the exercise 
 of those functions. It does not at all follow that because 
 memory ceases to recal the manner in which it assured con- 
 sciousness of the identity of me in the first moments of 
 existence, that it did not discharge that office. It is a neces- 
 sary condition of our being that, as we progress in years, the 
 remembrance of infancy become less and less distinct, until 
 we lose sight of its earliest stages altogether ; but if we con- 
 cluded, from the inability to recollect the acts of memory by 
 which our personal identity was revealed to us at the earliest 
 stages of existence, that no such acts took place, we might 
 also for a similar reason affirm the same result of those 
 periods of adolescence whose manner of existence have 
 likewise lapsed out of remembrance. For, in the same man- 
 ner as we feel assured that consciousness has always ac- 
 companied our being from the first dawn of life, though 
 we may not recollect the distinct acts in which it mani- 
 fested our existence to us, do we believe that memory,
 
 176 FOUNDATIONS OF EVIDENCE. [B. IT. 
 
 from the earliest stage of being, carried forward the experi- 
 ence of one moment to the next, and thus kept alive the 
 assurance that the percipient soul constituted one identical 
 person. Now, so long as this identity of me has been 
 always revealed by memory to our consciousness, whether 
 we remember the distinct acts or not, the link of identity 
 has always been preserved, and the assurance we feel that 
 this condition has been invariably fulfilled, could only be 
 contravened by recalling a moment of existence in which 
 some knowledge of the past was inaccessible to the mind ; an 
 act, of course, which is beyond human power. We then are 
 fully authorised to conclude that memory has steadily im- 
 pressed the existence of me upon the intimate sense, and 
 that from two principles. First, that memory itself certifies 
 the fact down to a certain stage of childhood ; and secondly, 
 that the amount of sensible experience, which she then 
 assures us we possessed, could spring from no other source 
 than the constant act of memory keeping the identity of 
 one constantly before the mind in transferring the experience 
 of one hour to the next 1 . 
 
 The denial of transmigration, or even the maintenance of 
 personal identity, is not dependent on the argument we have 
 adduced, which, as far as we know, is perfectly novel ; but 
 the aid of analogy is called in to assure the individual that 
 what he perceives to be the general law of the human species 
 has not been departed from in his case, and though memory 
 does not expressly guarantee his existence beyond a certain 
 period, or place the possibility of his eternal duration out of 
 court, that the immutability of nature's laws comes to the aid 
 of memory, and proves that his existence could not have 
 passed the limit of a certain time, and that in the interval 
 the identical nature of me has been preserved. 
 
 1 With regard to personal identity, it is necessary to distinguish 
 three things, which Locke confounds, viz., memory, consciousness, and 
 the object of memory. Memory is the object of consciousness; the 
 substantial and personal identity of me the object of memory. The 
 veracity of both is bound up with the reality of their objects. Per- 
 sonal identity consists in being able to affirm of one past and present 
 existence. Yet Locke makes it consist in the exercise of conscious- 
 ness, -whose only function is to declare the present. See Hum. Under, 
 b. ii. c. xxvii. 9, 10.
 
 C. IV. 3.] OBJECTIONS OF SEXTUS EMPIEICUS. 177 
 
 3. External Sense an ultimate Source of Evidence. 
 
 The belief in the existence of matter and its various confor- 
 mations in the outward world, is derived immediately from the 
 authority of the senses, but mediately is bound up with that 
 of consciousness, as sensation cannot exist without render- 
 ing us cognisant of the presence of the object felt. Thus, 
 when we affirm the existence of the desk on which we write, 
 the sense of sight and touch into which, indeed, vision and 
 all the other senses may be resolved vouch for the presence 
 of the object in question ; but the operation of both of these 
 senses are accompanied by consciousness, which guarantees 
 their reality, and assures us we are not speaking about a 
 mere image or vision, but of a substantial embodiment. 
 The authority of the external senses, as a legitimate motive 
 of judgment, may be, consequently, invalidated by convicting 
 them directly of deception, or by separating either the sen- 
 sations themselves or the objects about which they are 
 exercised from the domain of consciousness. It was the fate 
 of the ancient sceptics to follow the first course. Their 
 modern representatives have made quite as potent an attack 
 on human certainty by adhering to the second. 
 
 The reasons which impugn the authority of the external 
 senses as a certain means of knowledge have received their 
 most elaborate exposition at the hands of Sextus Empiricus, 
 and may thus be summarily expressed 1 . With regard to 
 
 1 Sextus, surnamed Empiricus, from the school of physicists to 
 which he belonged, flourished at the end of the second century. He 
 put the finishing stroke to scepticism, by investing it with the form and 
 method of a science in his three books entitled Hvppa)i>(ian> vn-orvTrat- 
 In this celebrated work Sextus defines scepticism as the faculty 
 of comparing the appearances of the senses and thoughts 
 re KOI voovpeva) with a view to arrive (Sta 7171* iv rots 
 s Trpdypast KOI \oyois lo'oo'dfvfiav) at a suspension of all 
 judgment (eVo^i)) on objects whose nature is obscure (urj\ov, afyavts). 
 Hence results a certain repose of the mind (arapagid) and perfect equa- 
 nimity of disposition (/lerptorra&la) . He admits the existence of re- 
 presentations and appearances (tpaivopjva) , and does not deny the 
 possibility of cognition, but the reality of the objects of it. The result 
 of this doctrine was his maxim ovSev ^oAXoi/, signifying that since 
 
 V
 
 178 FOUNDATIONS OF EVIDENCE. [B. IV. 
 
 external objects the senses excite different and sometimes 
 opposite sensations in men and animals : That atmosphere 
 
 everything was uncertain no one thing was to be preferred to another. 
 His system received a further development in his ten books against 
 the mathematicians (yrpos TOVS ^ad^anKovs) , in the last five of which 
 he sets in a strong light the uncertainty of the principles of those, (Dog- 
 matists) who maintain that absolute truth is accessible to man by 
 affirming it of their doctrines ; and denies certainty even to the sim- 
 plest axioms of geometry and arithmetic. His writings form a com- 
 plete storehouse of sceptical reasons, and have been pressed into active 
 service by modern sceptics, and by none more zealously than Mon- 
 taigne. At the commencement of his first treatise (b. i. c. 1, 4) he 
 divides philosophers into three classes, viz., dogmatists, who maintain 
 they have found truth ; academics, who affirm that it is impossible to 
 discover it; sceptics, who affirm neither. He repeats the latter distinc- 
 tion in his seventh book against the mathematicians ( 153). But in 
 one respect it does not hold ; since CEnesidemus, the reviver of the 
 third academy, taught substantially the same sceptical doctrines as 
 himself. The distinction, indeed, had its origin with Cicero (Acad. 
 Qusest. i. 12), who discriminated the opinions of Pyrrho from those 
 of Arcesilaus and Carneades, the founders, in his time, of the second 
 academy : for Pyrrho maintained that the existence of probability 
 and doubt itself was doubtful, while these philosophers held that though 
 everything was uncertain, still there was such a thing as probable 
 knowledge, into which it was wise to inquire. They divided probable 
 judgments into three distinct classes: TriQavr] (fravTasia, dTreprjia-Traa-- 
 TOS and 8iea>8evfJifvr) rj TrfpioSfvp-evr) tpavTa<ria (Cic. Ac. Qusest. ii. 
 9, 31, sqq. Sext. Adv. Math. vii. 159, sqq. 161, 167. Euseb. praepar. 
 Evang. xiv. 7, sqq.). The doctrine of doubt, or absolute suspension of 
 judgment, which the followers of the third academy maintained, did not, 
 however, originate with Pyrrho, but with the sophist Protagoras, who 
 flourished about the Ninety-second Olympiad, or 460 years before Christ, 
 which places him nearly a century in advance of his more famous disciple. 
 Of course there is nothing in the mere name of academician to denote a 
 distinct species of opinions, as obtains in that of dogmatists and sceptics, 
 since the word, as is well known, originated with the name of the owner 
 of the gardens near the gates of Athens, who bequeathed his beautiful 
 property to Plato as a convenient spot for the delivery of his philoso- 
 phical lectures. The distinction, therefore, cannot be introduced into 
 philosophy without a cross division. For the founders of the first 
 academy were undoubted dogmatists, though they taught opinion 
 which legitimately developed their own thesis, and led to the destruc 
 tion of the universal doubt which followed ; while the revivers of the 
 last academy were complete sceptics. The correct division of ancient 
 philosophical opinions would be that of dogmatism, probabilism, and 
 scepticism. Of the latter it is singular to observe the exact resemblance 
 in the general outline of its principles and methods to the Hegelian 
 system, at present so widely prevalent in Germany.
 
 C. IV. 3.] RELATIVE KNOWLEDGE UNASSAILABLE. 179 
 
 which is dark to man is perfectly luminous to bats and owls. 
 They also excite different impressions in the same individual 
 at different ages, and change the appearance of the objects 
 which they represent in proportion to the variations of dis- 
 tance, and awake different images according as they are 
 viewed through different media. The senses, therefore, can- 
 not convey to us any certain information respecting the 
 objects whose existence they seem to testify; and the as- 
 sumption of their competency to that end, on which all 
 physical science is reared, is a delusion. 
 
 But this objection can only be urged with consistency 
 against those who maintain that the absolute nature of sensi- 
 ble objects is attainable by man a vulgar error adopted by 
 the first philosophers of Greece ; but it does not invalidate one 
 tittle of our belief in the certainty of experience which con- 
 stitutes the basis of physical science, since it leaves its three 
 fundamental corner stones untouched : 1st. That our sensa- 
 tions are real modifications of our beings : 2ndly. That they 
 instruct us as to the existence of external objects : 3rdly. That 
 these objects have some relations with us or, in other words, 
 that they appear such as they appear, and excite in us sensa- 
 tions corresponding to the functions we fulfil with regard to 
 the healthy preservation of our being. ISTow physical science 
 demands the concession of no further principle than is in- 
 volved in these truths, to show apodictically the relation 
 which must exist between the objects which produce these 
 different sensations as they are conceived by our conscious- 
 ness. With regard to the absolute nature of the objects 
 themselves, whether they reveal to us the actual essence of 
 things as viewed by superior intelligences, or excite impres- 
 sions merely relative to the important ends which man has 
 been destined to fulfil in creation, science in reality pro- 
 nounces nothing. 
 
 The observation appears to have escaped this school of 
 philosophers, that men, notwithstanding the different varieties 
 of sensations, generally contrive to perceive the same rela- 
 tions between their sensations. Thus, whatever may be the 
 nature of crystal and light, all perceive the same relation 
 between crystallised bodies and the illuminating medium. 
 This uniformity of judgment about the relation of sensible 
 objects is amply sufficient to guarantee the inference of the
 
 180 FOUNDATIONS OF EVIDENCE. [B. IT. 
 
 laws which spring from this source, and connecting their 
 phenomena with rational truth to erect the superstructure 
 of physical science. 
 
 Again, if the argument of the sceptics be worth anything, 
 it places beyond doubt the existence of two facts viz., that 
 there are as many different ways of perceiving nature as there 
 are different species of beings and organisations, and, more- 
 over, that these have as many distinct ways of acting as there 
 are different states of the subject on which they act. In- 
 stead, therefore, of proving there is nothing certain, it really 
 establishes an important truth. In attempting to convict 
 its opponents' principles of imposture, it destroys itself. So 
 true is the saying of Pascal, that there is a force of truth 
 invincible to every scepticism, an independence of demon- 
 stration invincible to every dogmatism. 
 
 The sceptics say we are ignorant of things absolutely, and 
 can only pretend to an acquaintance with their relative 
 nature. But it is absurd to affirm that we know things re- 
 latively without being cognisant of the terms of the rela- 
 tions. The very idea of a body existing in a certain mode 
 postulates the existence of four things viz., existence ; ex- 
 istence of a thing distinct from me ; the existence in me of 
 certain sensations produced by a thing distinct from me ; and 
 that this thing is the cause, and is able to be the cause of 
 these sensations. So far, therefore, from destroying cer- 
 tainty by such an argument, the sceptics really establish the 
 theory they intend to overthrow. They find themselves in 
 the position of a class of animals whose instinct leads them 
 to seek the destruction of certain insects by performing the 
 very act which is essential to their preservation. 
 
 The objections which a modern school of philosophers have 
 urged against the testimony of sense, with respect to the 
 existence of an external world, have taken their rise in some 
 theories of perception, which it will be necessary to explain 
 and confute before we can place their nature in a true light, 
 or be well satisfied we have escaped from the hard necessity 
 of affirming that space and all the worlds which it contains, 
 together with " this great globe itself, its cloud-capped 
 towers, and gorgeous palaces, are but the splendid fabric of 
 a vision," of no substantial reality, and merely existing in 
 the mind as subjective states arising out of the pre-esta-
 
 C. IT. 3.] THEOBIES OF PEECEPTI02T. 181 
 
 Wished mechanism of its own nature. It has from time 
 almost immemorial been a belief that the human mind, being 
 a spiritual substance, was not cognisant of external objects 
 directly, but through the medium of certain spectra (species), 
 which by an action analogous to luminous bodies conveyed 
 the exact impress of the material substances which cast them 
 off through the external senses into the mind. From this 
 opinion no moderns presumed to dissent until a very recent 
 period 1 ; and even Descartes, in citing every opinion of an- 
 tiquity before the bar of reason to show cause why it should 
 not be consigned to the category of doubt, allowed this opinion 
 to maintain its place, with one important modification, that 
 " idea should be assumed in place of spectra as the inter- 
 mediate agent by which external objects were impressed upon 
 the mind 2 ." It was contended, however, that the presence 
 of such ideas in the mind could not be assumed as certain 
 evidence of the real existence of the external objects to which 
 they refer, as they only arose out of certain modifications of the 
 percipient being, and consciousness did not warrant us to 
 conclude the existence of anything beyond them. A chasm 
 was thus interposed between the existence of the internal 
 states of our consciousness and the material world, which 
 philosophers attempted to bridge over, by calling to their as- 
 sistance the veracity of G-od 3 ; or by ingenious theories, either 
 about seeing all things in the divine nature 4 , or concerning a 
 pre-established harmony between our internal states and the 
 objective world to which they refer, each, however, acting 
 independent of the other, and solely dependent for their 
 mutual correspondence on the divine will 5 . Such opinions, 
 of course, together with the hypothesis of perception, from 
 which they flowed, reduced the naked testimony of the 
 external senses at best to a probable character, and opened 
 
 1 In this part of the world Reid has the credit of being the first 
 philosopher to call the principle into question, but he got the proof of 
 its invalidity, at least as he represented it, from Pere Buffier, and 
 Pere Buffier obtained it from Arnauld. See the treatise of the latter, 
 Des Idees Vrais et Fausses, contre ce qu'enseigne 1'auteur de la re- 
 cherche de la ve'rite'. Cologne, 1683. a Genovesi thus very accurately 
 expresses Descartes's doctrine: Id quod fit menti pra?sens dum percipit 
 aut cogitat, quodque semper rei a mente distinct, et quidem aut 
 existentis, aut possibilis imago quaedam est. Genovesi (Logica Critica, 
 lib. ii. cap. 1). * Descartes. 4 Malebranche. * Leibnitz.
 
 182 FOUNDATIONS OF EVIDENCE. [B. IT. 
 
 a breach for the sceptic to renew his attack 1 upon the do- 
 main of certainty, in a quarter that Sextus Empiricus little 
 dreamt of trying the strength of, and with far better vantage 
 ground than that from which he had commenced his attack. 
 What Sextus and GEnesidemus did for the probabilities of 
 Carneades 3 , Hume and Condillac effected for the probabilities 
 of Descartes and Locke. They showed that in consistency 
 with their own principles no such thing as matter could 
 exist ; and that with their postulates in the background even 
 the reality of the appearances themselves might be validly 
 called in question. But that the principle itself is a true 
 theory of perception we have no other proof than the very 
 slender one, of the consentaneous belief of nearly all philo- 
 sophers up to a very recent date in its veracity. Of itself, it 
 is supported by no intrinsic grounds whatever. For even ad- 
 mitting its truth, it does not lessen the difficulties it was 
 called in to resolve, since it is quite as hard to understand 
 how external objects can generate spiritual ideas, as it is to 
 conceive their direct action on a thinking substance. If 
 matter be declared incapable of the latter, it is doubly so 
 of the former ; and Berkeley, Hume, and Condillac were per- 
 fectly justified with such a theory in their heads in wiping 
 out the external world altogether. 
 
 Moreover, this hypothesis has been introduced not only 
 without an object, but in total defiance of the revelations of 
 consciousness. If that principle can be said to assure us of 
 anything, it certainly is the existence of things external to us 
 by the sensations they excite in the mind ; and all men, even 
 including those who pretend to disbelieve it, act as if the 
 testimony was of an infallible character. The assumption of 
 the contrary doctrine is so contrary to the common sense of 
 mankind that it requires some advance in philosophy to en- 
 tertain it. It involves the supposition that perception can 
 exist without the reality of the object perceived, which seems 
 a contradiction in terms. The opposition of this theory to 
 the plainest instincts of consciousness may be further seen 
 from the fact that it is at strife with the idea that we have 
 
 1 As Descartes, Wolf, Malebranche, and even Locke, who adopted 
 Descartes's views on the subject maintained. See Hum. Under, b. iv. 
 3. 2 evXoyiorta.
 
 C. IT. 3.] MODEBN SCEPTICS ANSWEBED. 183 
 
 of sensation as a phenomenon, whose cause is identical with 
 the object which produces it. Now, sensation offers itself to 
 the consciousness as distinct from the object felt and the sub- 
 ject which feels, being essentially connected with both. It 
 manifests itself as an effect of the same object felt ; not being 
 able to refute the testimony of consciousness, we cannot 
 deny the objectivity of the sensation, and consequently the 
 existence of the body. Again : if we have a conception of a 
 body that is not present to our senses, that conception must 
 refer to this object solely as an object conceived, but not as 
 the cause of the conception. The absence of this double re- 
 lation of a conception to the same object converts the act 
 into one of pure imagination. "We consequently cannot 
 deny the presence of a body actually modifying our spirit in 
 a case of sensible perception, without confounding that act 
 with the operation of the imaginative faculty; and thus again 
 convicting consciousness of imposture in blending two acts, 
 which it assures us are perfectly distinct. 
 
 It is urged, however, that dreams manifest cases analogous 
 to those of sensible objects, even when no external agents exist 
 answering to the images excited in our mind. But, in the first 
 place, it may be replied that such impressions exist as simple 
 objects of the imagination, which are put to flight as soon as 
 consciousness awakes us to the real appearance of things. 
 "We do not embrace them with anything like the same de- 
 gree of certainty as the objects of the waking senses, nor 
 move our bodily organs to correspond with the illusions they 
 excite in us in the same manner as we dispose our actions to 
 suit the direct impressions of the sensible world. In such 
 states we are incapable of reflex acts of thought ; that is, we 
 are never able to distinguish between appearances and reali- 
 ties, and the first moment in which we feel inclined to ques- 
 tion the reality of the impressions in the sensorium we are 
 roused into a waking state and feel assured of the delusion. 
 That dreams owe their origin to the imaginative faculty must 
 be admitted, from the circumstance that the images which they 
 excite in us do not occur in the same order in which they exist 
 in nature, but arise capriciously out of past modifications of 
 the mind, which the fancy sets together in the most ill-sorted 
 and fantastic manner, in sport, as it were, witli the solemn 
 realities and conventionalisms of nature and society. That we 
 appear to accord to her pranks any semblance of belief arises
 
 184 FOUNDATIONS OF EVIDENCE. [B. IV. 
 
 from the attention of consciousness being entirely withdrawn 
 from the real world and fixed upon such representations of it 
 that imagination chooses to give, to the entire abstraction of 
 everything else ; but that consciousness accords entire belief to 
 such representations on that account is no more to be inferred 
 than that of a reader's assent to the truth of a tale which 
 entirely absorbs his attention, or that of a woman's belief in 
 the real characters of the mythic personages of a theatre be- 
 cause she swooned away at the finale of the play. The only 
 difference in these cases is the minor degree in which con- 
 sciousness is abstracted from surrounding objects, which con- 
 sequently leaves less play for the exercise of pure imagina- 
 tion a modification which is also displayed in dreams them- 
 selves, since some appear less real than others, while there 
 are others which accompany a half- waking state, whose illu- 
 sion is manifest from the commencement of the operation. 
 
 Again, the sensations excited by dreams never convey a 
 new class of objects into the mind, but simply reproduce 
 the old, and that according to the strength of the impression 
 by which those objects have been previously communicated 
 to the mind, or the number of times it has experienced their 
 presence. Hence, hounds in their sleep open for their 
 prey, but no other class of the canine species do, because 
 they have never hunted in their waking state: an orator 
 who has controlled the decisions of senates, or a general who 
 has commanded armies, imagine they hear in their sleep the 
 murmur of applause or the thunder of cannon ; but a plough- 
 man or a huckster never finds himself in the same predica- 
 ment, simply because he has never mounted either a breach 
 or a tribune. This principle is undeniable, being attested 
 by every one's experience. If, therefore, nothing enters the 
 mind in dreams but what has been there in some shape or 
 other in its waking state, these delusions, instead of weaken- 
 ing our belief in the existence of external bodies, really esta- 
 blish it ; or, in other words, they show the impression of the 
 existence to have been so strong as to act when the object 
 which originally produced it has passed away. 
 
 All the errors which have been propagated on the testimony 
 of external sense have sprung out of the supposition that the 
 veracity of consciousness can stand without the veracity of 
 the other media of knowledge ; but we have shown, at least as 
 far as two are concerned, that it assures us of their particular
 
 0. IV. 4.] EXTEBNAL SENSE UNITED WITH CONSCIOUSNESS. 185 
 
 existence both as to the relation of the exercise of the act and 
 the object, and therefore cannot be isolated from them. This 
 truth is further strengthened by the illogical consequences 
 in which its contradictory has landed its opponents: for 
 while Pere Buffier, with Eeid, formed the veracity of external 
 sense on the common sense of mankind as distinct from con- 
 sciousness, they fell into a palpable petitio principii ; since 
 they had previously assumed the universality of the belief, as 
 a mark of such testimony being a primitive truth. Or, in other 
 words, they first lay down the postulate that every truth which 
 is universally received is primitive, and must be received 
 on its own evidence ; and then show the testimony of the 
 external senses is such, by affirming of it the very character- 
 istic which they ought to have proved 1 . Though the Car- 
 tesians avoided this paralogism, by resting the veracity of the 
 senses on the veracity of God whose existence they placed 
 in the idea we have of the infinite, still they were guilty of 
 the inconsistency of affirming that consciousness was com- 
 petent to certify the presence of that idea, while it was unable 
 to assure us of the existence of finite bodies out of which 
 such idea may be said to spring. If, however, consciousness 
 may be said to warrant us in assuming anything, it is that 
 external things are not only the cause of our sensations, but 
 the objects we perceive along with our sensation ; or, in other 
 words, that our sensations are not only passive modifications, 
 but the immediate perceptions of things outside of us, and 
 we cannot invalidate such testimony without impugning its 
 veracity, and even calling into doubt our own existence 2 . 
 
 4. Analogy an ultimate Source of Evidence. 
 
 Consciousness and the external senses only make us 
 acquainted with particular facts. But physical science can- 
 
 1 Pere Buffier gives two other marks of primitive truth besides the 
 one in the text, viz. : The incapability they manifest of being esta- 
 blished by truths clearer than themselves; 2nd. That those who cavil 
 with them act upon the belief of their existence. See PEssai sur les 
 verit(?s primitives, c. 3 5. The gross instance of the fallacy in the 
 text reminds us of the common reply of the farmer when we ask him 
 why we may not ride over his field : " Why why why that's the 
 reason why." a For the consideration of spectral illusions, as 
 
 bearing on this subject, the reader is referred to the supplement of this 
 book in the Appendix.
 
 186 FOUNDATIONS OF EVIDENCE. [B. IV. 
 
 not draw any certain inference from them without a belief 
 in certain axioms: such as the stability of the course of 
 nature ; that individuals similar in their apparent qualities are 
 similar in their occult qualities ; that similar effects proceed 
 from similar causes, and other principles of the same import, 
 which, as they spring from an interior conviction of our 
 nature that the future will resemble the past, are designated 
 by the common term analogy 1 . As this principle is the 
 foundation of all our knowledge of nature, any attempt to 
 overset it must be viewed as a direct attack upon the 
 existence of the external world, and, therefore, must be met 
 before we attempt to expound the leading inferential forms 
 by which its laws are established. 
 
 But beyond the objections whose confutation we have 
 already attempted 2 , we meet with no direct assault upon this 
 principle, unless from the solitary pen of Hume, who con- 
 tended that the principle of analogy could not be maintained 
 without falling into the sophism so often adverted to. For 
 it is impossible to affirm a likeness between two things, one 
 of which we have never seen or heard of. We ought, there- 
 fore, to know the future in order to compare it with the 
 present; and the assumption of this knowledge, which is 
 required to be proved, is the only foundation on which 
 analogy rests. But this argument supposes that analogy is 
 an experimental truth, which Hume affirms it must be, if it 
 be any truth at all, since it is obviously neither neces- 
 sary or identical. The confusion, however, lurks in the 
 word necessary. It is not necessary, as we have already 
 shown, in the sense of the highest metaphysical truth, that 
 is, independent of all condition ; but it is necessary in the 
 supposition that it does not depend upon experience, but 
 has been blended with the primordial elements of the mind 
 with a view to guide its inferences with respect to the objects 
 which envelope and surround its being. In this sense the 
 
 1 We have shown in a former chapter we do not derive these axioms 
 from experience but from an instinct which precedes or is co-existent 
 with experience. The establishment of this truth shows that inductive 
 inference does not differ from demonstrative in the threefold character 
 of the judgments involved in its illation. 2 Of course those who 
 
 refuse to admit the testimony of sense as a certain motive of judgment, 
 place analogy in the same category as Wolf. Logica, p. 2, $$ 674, 677.
 
 c. IT. 4.] HUME'S OBJECTION TO ANALOGY. 187 
 
 word necessary is sufficient to raise it out of the category 
 of experimental truth, and rescue it from the objection 
 which is only brought against it as belonging to that 
 category. 
 
 But even on the ground of its being an experimental truth, 
 we think the view of this illustrious sceptic cannot be main- 
 tained. For it is undoubtedly in our power to regard every 
 moment of existence as future in relation to the first instant 
 which memory can recal, and every subsequent moment as 
 past relative to the objects which succeeded it, and future 
 with regard to the moments already past. Thus every instant, 
 unless the first, may be regarded as either past or future, and 
 running over these several moments we may perceive that 
 the course of nature has invariably presented the future like 
 the past, and from the comparison are entitled to infer 
 that it always will continue to do so, without the illogical 
 consequence which Hume attributed to such an illation. 
 
 It may be important to observe, that the analogy produced 
 by certain knowledge is not to be confounded with con- 
 jecture 1 . For though intellectual superiority consists, in 
 some degree, of the skill which is exhibited in employing the 
 experience of the past to foresee the future, yet the results 
 are never more than probable, as the will of man and the 
 capricious nature of human events, which refuse to submit 
 themselves to the calculations of the exact sciences, are liable 
 to defeat the wisest prognostications. The astronomer, fore- 
 seeing with certainty what will be the future relations of 
 celestial phenomena in a given time, is able to determine 
 the exact moment of the equinoxes, and predict lunar and 
 solar eclipses ; because a constant experience manifests to 
 him the laws of the motions of the heavenly bodies, and 
 mathematical knowledge applied to observation gives him 
 infallible results. But if he turn his horoscope on the future 
 of society, both the vacillating nature of the will and the 
 ignorance of the motives which determine its action in any 
 weighty crises, the sudden appearance of great men on the 
 scene, who unexpectedly found, overset, or remodel religious 
 governments and dynasties, prevent anything further than 
 
 1 Dngald Stewart appears to us to fall into this error. See Phil. 
 Mind, a. 3, v. c. 2.
 
 188 FOUNDATIONS OF EVIDENCE. [B. IT. 
 
 probability even in predictions which fall within our own 
 time ; while with regard to those which extend beyond it, 
 even probability, in some respects, is unattainable. If the 
 arms of the republic had been victorious at Filippi, what 
 would have been the future of Borne ? If Bonaparte's 
 father had not married a Corsican, and thus brought that 
 general into the world, what would have been the condition 
 of France now ? 
 
 . 5. Reason an ultimate Source of Evidence. 
 
 Another primitive motive of belief is reasoning, or the 
 necessity we feel in any legitimate argument of admitting 
 the conclusion when we have conceded the premises. The 
 legitimacy of such a motive cannot be proved without as- 
 suming the thing in dispute, and even those who deny its 
 authority can only make out their case by an appeal to the 
 authority which they call in question. Sextus Empiricus, 
 however, attacked the veracity of reasoning : first, on the 
 ground that the majority of men who employ its methods 
 come to different conclusions ; and, secondly, that since it is 
 impossible to prove everything, the whole structure of in- 
 ference rests upon assumed principles, and partakes of the 
 uncertain character of their foundation. The first argument 
 is logically vicious, as the conclusion contains an illation 
 more universal than the premiss, being tantamount to this : 
 " Some men have reasoned badly, therefore none can reason 
 correctly :" but as all men who reason admit the veracity of 
 the means of knowing, why does not their united agreement 
 in some particulars coerce the sceptics into the admission of 
 some truth, if the discrepancy of opinion which men manifest 
 furnish them with a motive for suspending their judgment ? 
 Even if the inference be granted it is at the expense of a 
 double inconsistency. 
 
 From the premiss of their second argument, that all 
 truth is incapable of being demonstrated, it does not at all 
 follow that no inference is certain, but points to a totally 
 opposite conclusion. That all the layers of stone which an 
 edifice comprises are not indented into corresponding layers 
 beneath them, but that the first pile rests upon solid rock, 
 if it go to establish anything, it surely is the security of the 
 building so situate. Now on such solid rock repose primitive
 
 C. IV. 6.] AUTHOBITY WHEN UNIMPEACHABLE. 189 
 
 truths, for they are vouched for by the direct evidence of 
 consciousness, than which there can be no higher security in 
 nature. But the sceptics seem to forget, in urging such 
 objections ; they suppose the authority of reason in the act 
 of destroying it, and thus commit palpable suicide on their 
 own principles. They are in the position of the woodman 
 who was so busy in felling the branches of a tree, that he 
 cut off the very bough on which he was standing 1 . 
 
 6. Authority an ultimate Source of Evidence, 
 
 As man is unable to exist in all times and places, or to 
 assure himself of the certainty of every link of evidence 
 which demands his attention, he cannot avoid resting his 
 belief on the authority of others if he would travel beyond 
 personal experience, and in fact does so with a confidence 
 not less certain than he accepts the evidence of his senses. 
 This certainty, which is termed moral, has been attributed 
 to analogy 2 , as we may be said to infer a thing will be 
 true under certain circumstances, which has always proved 
 so when the marks which attended its veracity has been 
 fulfilled. Thus, we have heard that there is such a place 
 as Egypt ; by subsequent travel we realise the truth of the 
 testimony by which we were led to believe in its existence. 
 "We read of the demonstrations by which Newton proved 
 that the inequalities of lunar motion was a consequence of 
 the universal law of force, and though we may not have ex- 
 amined the consecutive train of inference by which that fact 
 was established, we do not believe it with less certainty, from 
 having proved the correctness of similar testimony when we 
 applied the test of personal examination. 
 
 Thougli authority may, as a motive of judgment, derive 
 collateral support from such confirmations, we hardly think 
 the main trunk of its certainty springs from other ground 
 
 1 Hegel assumes the principle of contradiction, or that everything 
 has its opposite, which (Enesidemus taught in the middle of the second 
 century, as valid ground for refuting the conclusions of legitimate 
 inference; but of course it would be perfectly idle to prove against 
 him that one cannot be right and wrong at the same time. 2 By 
 
 Galluppi, Lezioni di Logica, 32. Locke on this account would allow 
 no certainty but what sprung out of direct personal experience.
 
 190 FOUNDATIONS OF EVIDENCE. [B. IT. 
 
 than that of the direct intuitive evidence of consciousness. 
 For postulating the durability of the laws of human nature, 
 it is quite as impossible to conceive a number of men, sepa- 
 rated by gaps of time and dwelling in different hemispheres, 
 who can have no personal interest in affirming the truth of 
 what they state, and no common ground for acting in 
 concert, should conspire to cheat the rest of their species 
 with a lie, as to imagine that two straight lines can enclose 
 a space, or that the whole should be greater than the parts 
 of which it consists. Moreover, the direct pledge of con- 
 sciousness is required to certify the infallibility of this motive' 
 of judgment ; as there are many truths resting upon authority 
 whose evidence is past and cannot be repeated, which it is 
 consequently impossible to bring under the cognisance of 
 any existing personal knowledge. We accept these, however, 
 when duly corroborated, with the same unhesitating belief as 
 others, whose truth is hourly confirmed by the evidence of 
 additional personal witnesses, and that for no other reason 
 than the impossibility we intuitively feel of conceiving the 
 testimony of man can be other than true under the circum- 
 stances we have supposed above. These conditions may be 
 thus formally stated : 1st. That the testimony be universal. 
 2nd. That it arise from nature. 3rd. That it be convenient to 
 no sect or class. And 4th. That the testimony when it relate 
 to present facts, increase with knowledge. 
 
 Authority has been attacked only in its theological rela- 
 tions, and that by two distinguished sceptics ; but the argu- 
 ment of one respects rather the fulfilment of the conditions 
 than the truth of the testimony, which rests upon them. 
 Gibbon states the evangelical account of the death of Christ 
 is not to be received, as it lacks the testimony of cotem- 
 porary writers. If that be so, of course the main condition 
 of the veracity of authority has not been fulfilled, and our 
 thesis remains untouched. But Hume boldly assumes the 
 hypothesis of the conditions being carried out, and asserts 
 that even when accompanied by such marks of evidence, 
 authority is not to be trusted, when the report it announces 
 conflicts with the permanence of the laws of nature. But 
 the objection, though urged against the reception of historical 
 testimony in the case of miracles, is really to be met on 
 other grounds. For if a Providence exist who has impressed
 
 B. V.] HTTME AGAINST MIEACLES. 191 
 
 those laws on material objects, the assumption that He has 
 suspended their action for His own wise designs, is the only 
 escape we have from the absurd conception that a number of 
 men, who could not possibly act in collusion, should conspire 
 to deceive people with no selfish object in view. But if 
 no Providence exist, and we believe Hume was not disposed 
 to rest his argument on that ground, the assumption that 
 those laws could be suspended without material agency could 
 not, of course, be entertained ; and the hypothesis of the 
 marks of the certainty of authority being in that case ful- 
 filled, must fall to the ground. The belief in miracles is thus 
 resolved into the belief in the existence of God. If that be 
 denied, the hypothesis can not hold ; if it be acknowledged, 
 it leads to a consequence it sustains the irrefragable nature 
 of authority, when founded on the unanimous testimony of 
 men. 
 
 These six fountains of evidence constitute the criteria of 
 truth in the widest sense. If there be one criterion which 
 exercises any prerogative over the rest answering to the 
 description of Cicero Insignis ilia et propria percipiendi 
 nota propria veri et certi nota 1 it is reason in its intense 
 and primitive purity 2 . 
 
 BOOK V. 
 
 METHODS OP SCIENTIFIC PEOOF AND INVESTIGATION. 
 PEOEMITJM. 
 
 HAYING traced in the foregoing pages the subordinate 
 compartments in which the structure of evidence may be 
 divided, and pointed out the foundations on which the edifice 
 rests, we may now proceed to treat of the general outlines of 
 the building, and show in what manner such of its parts as 
 are dissimilar fit into one another, and form by their union the 
 different branches of science of which the structure is com- 
 
 1 Degerando, Hist. Compar. Syst. Phil. b. ii. part ii. c. 4, pronounces 
 such criterion impossible, as indeed it is in the sense in which he takes 
 it, as a certain seal or stamp, whose impress will lead the reader to 
 detect truth without any examination. 2 Ac. Quaest. iv. c. 31, 31.
 
 192 METHODS OF SCIENTIFIC PBOOF. [u. V. 
 
 posed. This, the leading portion of the treatise, though 
 capable of being pursued almost to an indefinite extent 1 , 
 easily admits of being brought within the limits we have 
 assigned to it, as the only two divisions of the sciences whose 
 methods are so radically distinct as to require separate 
 treatment, are the moral and the physical ; and the methods, 
 which each of the various sciences comprised in these 
 two groups embrace, are so homogeneous, as to be dis- 
 posed of in five or six sections. For the sciences, included 
 under the physical branch of the division, do not exact spe- 
 cific methods varying with every subject-matter about which 
 each is conversant but with the precise stage of development 
 at which they may have arrived. They commence with the 
 registry of simple facts and collections of instances, and from 
 thence ascend to the most universal laws or axioms, through 
 the medium of intermediate ranges of laws, gradually widen- 
 ing into them ; while the moral sciences, for the most part, 
 embrace the reverse process of descent from axioms of the 
 widest generality, through cases of gradually diminishing ex- 
 tent to the minutest particulars. The methods entered upon 
 at each of these stages are adapted to the further development 
 of all the sciences which have reached them ; but since the 
 same method by which a law of minor generality has been 
 connected with a multitude of particular facts, either by the 
 deductive or inductive mode of inference, can be of no avail 
 in connecting such minor law with one of wider generality ; 
 it is evident that, as the growth of sciences varies, the method 
 by which they are investigated must vary along with them. 
 In the physical sciences, however, this development may be 
 included in three stages, viz., the descriptive, the inductive, 
 commonly called the experimental, and the deductive or 
 exact stage ; the first corresponding to the position which 
 meteorology, and the second to that which chemistry and 
 crystalography at present occupies ; while astronomy and me- 
 chanics may be taken as examples of the third. The methods 
 by which any physical science is forwarded through its first 
 stage may be comprised under the head of observation, ex- 
 periment, classification, and nomenclature ; these lead to the 
 
 1 And for that reason, i. e. its seeming vagueness, probably hitherto 
 neglected in logical treatises.
 
 B. V.] DIVISION OF PHYSICAL METHODS. 193 
 
 discovery of proximate causes, and laws of the lowest degree 
 of generality, through the application of the canons of 
 experimental inquiry. The latter, consequently, form the 
 methods applicable at the second stage ; while, as a science, 
 is made deductive by the formation of theories, and by 
 bringing these to the test of quantitative laws, the nature 
 and use of hypothesis, with the functions that mathematics 
 play in the verification and construction of the exact sciences, 
 will comprise the last range of methods which enter into the 
 highest development of physics. To the complete explana- 
 tion of these different methods, it is essential that some 
 account be rendered of the general laws they are designed to 
 discover, both in their simple and complex states ; and to 
 this end we shall add a section to each of these tripartite 
 range of methods, explanatory of the nature of the facts and 
 laws they are intended to bring to light, how each are inter- 
 woven and fit into the universe of things, and the general 
 entanglement from which they are to be disembedded. But 
 as many events occur, or facts present themselves, even in 
 the physical world, whose laws, if they are amenable to any, 
 we cannot exactly ascertain, one of these sections will be 
 devoted to the exposition of the general characteristics by 
 which such facts or events are accompanied, and the methods 
 pursued to construct out of them general propositions, avail- 
 able either for scientific purposes or for practical utility. 
 Hence this part of the book will embrace six sections, three 
 comprising the various methods pursued in the construction 
 of the sciences, and the remaining half generalising the multi- 
 tudinous cases of phenomena with which those methods have 
 to deal. 
 
 The methods which the moral sciences embody are, in 
 many respects, identical with those already described, the 
 only points in which they much differ being the deduction 
 of individual laws and occurrences from abstract proposi- 
 tions, which we obtain from other sources than experience ; 
 and the dealing with multitudes rather than with individuals, 
 in order to neutralise as much as possible the uncertain 
 element introduced into these sciences by the action of the 
 human will. The complexity involved in mental, spiritual, 
 and social phenomena, demand more subtle agencies to trace 
 their laws than those which obtain in the material world ;
 
 194 DIVISION OE MOBAL METHODS. [B. T. 
 
 for, while the principles of the one seem eternal and immu- 
 table, those of the other are ever shifting with the current 
 of the hour, and continue to exhibit fresh phases at every 
 stage of their development. Hence one or two direct modes 
 of inference are inadequate to grasp the perpetually changing 
 nature of the phenomena they present ; multiplied and di- 
 verging lines of argument are required, such as those included 
 in the negative process and the cross-examining elenches, 
 whose functions in moral proof are precisely analogous to 
 those which the calculus performs in the physical sciences. 
 The explanation of these methods in conjunction with the 
 purely deductive sciences to which they are applied, as 
 theology and ethics, will constitute one section, while their 
 connexion with the mixed or inverse deductive sciences, as 
 politics or ethology, where empirical data are blended with a 
 priori principles, will comprise another. In connecting such 
 empirical facts with minor or general principles, either by 
 way of direct proof or verification, the canons of experi- 
 mental inquiry will be found directly available where the 
 nature of the phenomena requires us to proceed by the path 
 of induction; but in the case of analogy and approximate 
 generalisations, a distinct section will be required, on ac- 
 count of the shifting nature of the evidence and the in- 
 fluence in much of the data of the capricious element of 
 human volition. It will be observed that the methods in 
 this arm of the division are more irregular in their applica- 
 tion than those belonging to the physical branch; since, 
 instead of varying simply with the growth of the sciences, 
 they adapt their form to the specific matter with which each 
 is conversant. As the subjects, however, which they embrace 
 are not of so multiform a character, the methods are capable 
 of being included within less limits than those of the physical 
 sciences, embracing only the three sections we have assigned 
 them, an additional one however being added, by way of 
 preliminary exposition of the nature of liberty and necessity, 
 and the general objects, about which it is the province of the 
 subsequent sections to treat.
 
 C. I. 1.] LAWS ULTIMATE AND DERIVATIVE. 195 
 
 CHAPTEE I. 
 
 METHODS OF THE PHYSICAL SCIENCES. 
 
 1. The Nature, Grounds, and Limits of Physical 
 Investigation. 
 
 THE object of the inductive sciences may be said to be the 
 pointing out what uniformities are perpetually occurring in 
 nature, and placing in evidence the causes or laws upon 
 which their existence depend. We hear, for instance, a 
 sound when a musical chord is struck, and on instituting an 
 inquiry into the cause of the phenomena, find it to consist 
 in the communication of motion from the sounding body to 
 the adjoining particles of the air, and the propagation of 
 motion from particle to particle of such intermedium till 
 it reach those contiguous to the ear, which convey the 
 impression to the auditory nerves, and from thence to 
 the brain. The investigation, however, does not terminate 
 in extricating the ultimate cause of the phenomena, but 
 merely presents us with simpler causes, into which its com- 
 plexity may be resolved, viz., the cause of motion and sensa- 
 tion. Though we have no infallible proof that the latter 
 causes are ultimate, and indeed strong presumptive evidence 
 that they are complex phenomena, it is usual to place them 
 in the former category, at least until science enables us to 
 complete the analysis of the parts into which they are 
 capable of being resolved. "Whether ultimate causes or 
 laws are attainable by the methods upon which science 
 relies for its most successful prosecution, or whether man's 
 faculties are too gross to discern them in the undiscernible 
 molecules and corpuscular motions in which they may be 
 supposed to reside, it is not for man, in the present state of 
 science, to hazard an assertion. Suffice it to say, that those 
 properties which appear ultimate, such as the gravity of 
 matter, the mutual attractions and repulsions of its particles, 
 the equal pressure of liquids in all directions, are generally 
 considered in the light of original causes, while the unifor- 
 mities into which these enter as active agents are ordinarily 
 regarded as derivative ones. For example, the rise of mer- 
 cury in the Torricellian tube is nothing more than an in- 
 
 o2
 
 196 METHODS OF THE PHYSICAL SCIENCES. [B. Y. 
 
 stance of pressure on a fluid in one direction unopposed by 
 an equal pressure in the contrary direction, producing 
 motion which does not cease till equilibrium is restored. 
 But the uniformity in question is regarded as derivative, 
 since it is fully accounted for by the weight of the air acting 
 on a body which distributes the pressure communicated to it 
 throughout all its parts with equal intensity. Hence the 
 variations of mercury in the barometer in proportion to the 
 density of the atmosphere may be said to take place accord- 
 ing to a derivative law, while the two laws in which it 
 eventuates may be considered as ultimate, until we are able 
 to disentangle the skein of causes which compose their re- 
 sults, and estimate their effects in like manner. 
 
 As complex uniformities, like the instances we have ad- 
 duced, are virtually implied in the simpler ones of which 
 they are the spontaneous effects, and consequently do not 
 require a separate act of creative will to necessitate their 
 existence, the designation of laws of nature has been denied 
 them by an acute writer 1 , who seems disposed to restrict 
 the term to those laws which do not admit of subordinate 
 analysis. But the statement is upheld in the absence of a 
 distinction which is essential to the subject, as going to the 
 bottom of the dispute about the nature of the causes and 
 laws which it is the function of scientific methods to dis- 
 cover. For it is evident that laws may be considered ulti- 
 mate with respect to the bodies through which they mani- 
 fest their agency, which are, however, not the less resolvable 
 into the simpler elements or laws out of which the substance 
 arises whose properties they constitute. Thus, the cohesion 
 and capillarity of the parts of liquids perish when they are 
 resolved into the expansible fluids out of whose combination 
 they sprung ; but it is nevertheless certain that such co- 
 hesion arose from the increased attraction with which the 
 union of the elementary gases invested the minute particles 
 of which the resulting liquid was composed. Or, assuming 
 the reverse case of the conversion of an inexpansible ^fluid 
 into a solid a process of continual occurrence in the animal 
 system ; as the liquid approaches a viscid state, mobility 
 among its parts, or the law of the propagation of equal 
 
 1 Mill's Logic, vol. i. p. 383. In the example which he gives he is 
 peculiarly unfortunate, his third ultimate uniformity, as we instance 
 in the text, being only a corollary of the second.
 
 C. I. 1.] CAUSES AND LAWS. 197 
 
 pressure in all directions, gradually disappear, though there 
 cannot be the slightest doubt that the change is effected by 
 neutralising the peculiar combination of attractive and re- 
 pulsive properties which constitute the laws into which that 
 mobility may be resolved. Now, to grant that those laws 
 which are only ultimate in the extreme sense are solely entitled 
 to be regarded as laws of nature, would be to invalidate 
 even the claims of those to that designation which form the 
 boundary of the present state of scientific analysis, for there 
 are none so simple which chemistry does not promise to 
 resolve into more elementary laws ; while the concession of 
 ultimative properties in the relative sense would not afford 
 any ground for the theory that such only can be justly 
 termed laws of nature, as requiring a separate fiat of crea- 
 tive will ; since such laws arise out of mere combinations 
 of ulterior properties, which can be supposed to occur as 
 spontaneously as the ^combinations which give rise to de- 
 rivative laws into which they enter, without any specific in- 
 terference on the part of the ruler of the universe. 
 
 In reality with regard to absolute primordial elements 
 nothing is known, and the introduction of the terms ulti- 
 mate and derivative can only be accepted to distinguish those 
 laws whose elements are known from others whose causes lie 
 concealed. But notwithstanding the inquiries which it is the 
 object of physical science to institute into the laws of the ma- 
 terial universe, at best only conduct to the proximate causes 
 of things, they for the most part point out the nature of their 
 various properties, and frequently reveal the ingredients of 
 the substances of which they are composed. This leads to 
 a twofold division of laws really pertinent to their nature, 
 one as regards the action of substances, the other referring 
 to the elements which enter into their composition. Thus 
 it is a law or immutable condition of nature that if two- 
 thirds in volume of hydrogen be brought in close contact 
 with one-third of oxygen while the two gases are in an elec- 
 trified state, water will be produced ; or that if silica, alu- 
 mina, soda, sulphur, and a trace of iron be combined in 
 certain proportions the result will appear in the creation 
 of lapis lazuli ; just as much as it is a law that planets 
 move in ellipses round the sun, each describing equal 
 areas in equal times, or that in their orbits the squares of 
 the periodical times are proportional to the cubes of the dis-
 
 198 METHODS OF THE PHYSICAL SCIENCES. [B. T. 
 
 tances; although we know in the latter case that these 
 different properties of planetary motion are resolvable into 
 laws still more general, which may be in turn deduced from 
 the peculiar combination of centripetal and tangential force 
 in which they originate, while we are as certain that in the 
 former the proximate substances of which water and ultra- 
 marine-blue have been shown to consist admit of resolution 
 through different stages of more elementary substances into 
 the simplest results that chemistry has laid open to us. The 
 causes, therefore, which scientific methods seek to discover, 
 always imply laws, since they exist through their agency ; 
 but laws cannot be regarded without some laxity in the use 
 of language as synonymous with causes, unless when in 
 addition to the signification of the measure of the forces by 
 which other substances and properties act, they generate 
 new substances and new properties, or in other words new 
 laws. But the web of cause and effect is so intricately 
 blended in nature, that we know of no existing law which 
 does not produce, and may not be consequently deemed the 
 cause of its effect, so that philosophers are conjointly agreed 
 in viewing the two terms as interchangeable in the language 
 of natural science. The elliptical motion of a planet, for 
 instance, though the final result of certain elementary forces, 
 is one of the principal conditions on which the return of the 
 seasons depend, and the periodical succession of the seasons 
 is again an essential element in the production and renova- 
 tion of the internal economy of the planet. 
 
 The causes, then, whose discovery forms the object of 
 scientific pursuit, may be assumed to be the essential physical 
 conditions, or material agencies, on which the different 
 uniformities in nature invariably depend, whether such 
 agency be the derivative effect of original self-acting agents, 
 as is the notion of the development theory both in its 
 ancient and modern aspects, or are ultimate agencies them- 
 selves, or the result of ultimate agencies created and set in 
 action by the direct fiat of God, as is the Theistical doctrine. 
 Of the original agents, and the primary forces into which the 
 whole phenomena of the material universe may be resolved, 
 science takes no direct cognisance, unless through the medium 
 of the derivative and intermediate causes, whose action is 
 capable of sensible analysis. "Whether such agents exist, or 
 are appreciable by the human faculties, science takes no
 
 0. I. 1.] PROBLEM OF INDUCTIVE SCIENCE. 199 
 
 account. Attempts have been made to grasp them at an 
 earlier period of the earth, by seizing upon some vague 
 assumption as the radical element of all things, and seeking 
 to evolve out of it the constituent furniture of the universe. 
 But such efforts, beyond originating in casual discoveries of 
 trifling importance, have recoiled upon their promoters, and 
 left science, even after the toil of ages, much in the condition 
 of the stone of Sysiphus, with no ulterior prospect of ad- 
 vancement. Warned by the futility of such efforts, modern 
 inquirers are content to take such truths as the analysis of 
 sensible phenomena offers, being convinced that if remote or 
 primary elements exist, the only path by which they are 
 attainable lies through the proximate causes which express 
 their complex results; and as the investigation of these 
 afford ample room and verge for the employment of their 
 highest faculties and the augmentation of their dominion 
 over nature, they concentrate their attention on their dis- 
 covery with the assurance that if such proximate causes do 
 not conduct to primary elements, that the 'pursuit of ulti- 
 mate causes is hopeless. Accordingly, astronomers do not 
 seek to discover the origin of the planetary movements in 
 the application of a determinate projectile force in a deter- 
 minate direction, but take such force as already existing, 
 and endeavour to follow it out into its results, and trace 
 its laws, or the causes of its different combinations. In like 
 manner, philosophical chemists no more aim at determining 
 the one essential element out of which all matter is framed, 
 than sober geologists attempt to infer the origin of our 
 system, or the condition of the earth at Creation from the 
 present collocations of strata which compose its crust. The 
 discoveries, it is true, in these sciences, which the steady 
 adhesion to philosophic methods is constantly bringing to 
 light, are ever tending in this direction, but this approach, 
 like that of the asymptotes, may have a limit, and never reach 
 its object, though constantly approximating to it. On ac- 
 count of this direct tendency of scientific discoveries to 
 simplify the multifarious uniformities existing throughout 
 nature, and trace them through a gradually diminishing 
 series of subordinate uniformities to the fewest simplest 
 uniformities cognisable by the human faculties, the problem 
 which the scientific methods are intended to resolve may be 
 stated to be what are the fewest general elements into
 
 200 METHODS OF THE PHYSICAL SCIENCES. [B. V. 
 
 which the existing uniformities of nature may be resolved, 
 and what are the laws which guide such elements into their 
 complex results, and necessitate their existing collocations ? 
 
 As a preliminary step towards the solution of such problem, 
 it is important to remember that the grounds on which the in- 
 quiry proceeds are independent of experience, though all the 
 subsequent processes are either determined by the results of 
 experience or are amenable to them by way of verification. 
 We cannot help believing that certain properties which we 
 have once perceived to accompany certain substances will 
 invariably accompany them, and that the connexion be- 
 tween them has existed since such substances came into 
 being. We believe that wood will burn a century hence if 
 fire be applied to it, just as we believe it burned some four 
 thousand years ago iu Assyria, or as we believe it burns to- 
 day in Cochin China under similar circumstances. This class of 
 uniformities comprise the first spontaneous inductions which 
 the philosopher is obliged to accept, in common with the child 
 and the peasant 1 , as the groundwork of his reasonings, and to 
 employ them in the commencement as guiding marks by 
 which he may be led to discover the unknown uniformities 
 which exist in nature. To attempt their proof would involve 
 him in what logicians call a vicious circle ; just as much as if 
 he were to demonstrate any other primitive truth, since he 
 could not establish their cogency without the medium of the 
 truths already built upon the assumption of their correct- 
 ness. Were such inductions referable to mere experience 
 it is obvious they must wax strong by repetition, and be 
 consequently weaker in the child than in the adult, and ob- 
 tain greater credence now than in the infancy of the world. 
 But all that we know of our progressive state, and those of 
 our species, is in conflict with such a supposition. A child 
 believes that flour Avill continue to whiten and water to wet 
 any substance with which they are brought into contact, 
 when it has once experienced such effects, as firmly as it does 
 
 1 We are reminded of an apposite passage in Shakspeare, which our 
 readers will not blame us for quoting: 
 
 TOUCHSTONE. Hast any philosophy in thee, shepherd ? 
 
 CORIN. No more than that I know that the property of rain is to 
 wet, and fire to burn ; that good pasture makes fat sheep, and that a 
 great cause of the night is lack of the sun. 
 
 TOUCHSTONE. Such a one is a natural philosopher. 
 
 As You Like It, Act iii. Sc. ii.
 
 C. I. 1.] TWOFOLD NATUBE OF INDUCTIONS. 201 
 
 after a hundred thousand repetitions of the same impres- 
 sion ; nor have we any reason to believe that the faith of 
 the ancients in the permanence of similar uniformities was 
 inferior to our own 1 . 
 
 But whence comes it that credence in the permanent 
 nature of such phenomena is confined to a special class, and 
 that many qualities exist which the mind never expects 
 to find invariably concomitant with the substances in con- 
 nexion with which they first meet its gaze ? "We believe that 
 fire will burn and water will wet, but never expect those 
 objects to maintain the same colour. We should esteem it 
 little less than marvellous if, having once tasted the effects of 
 bread, we should, on recurring again to that aliment, find it 
 accompanied with the flavour of cinnamon-juice, and the unnu- 
 tritive properties of deal shavings : after meeting with a green 
 chameleon, however, we should be by no means startled on 
 a renewal of his acquaintance at beholding the same object 
 assume a bluish aspect. How is it that uniformity in one 
 case is never looked for beyond the immediate instance, 
 while in the other it is expected to occur at every repetition 
 of the object ? That some principle is at work beside mere 
 experience is evident from the fact, that however invariably 
 some properties may accompany certain objects, we never 
 place sufficient reliance on the uniformity to generalise such 
 
 1 Some may be disposed to quote the ode of Horace, ending with 
 Damnosa quid non imminuit dies? 
 ./Etas parentum, pejor avis, tulit 
 Nos nequiores, mox daturos 
 
 Progeniem vitiosiorem. Lib. iii. c, 6. 
 
 against the statement in the text, but the allusions of the bard simply 
 refer to a gradual paralysis of the powers of nature becoming effete 
 with age, and not to any capricious interchange of properties on the 
 part of the natural elements, which would invalidate our confidence in 
 the constancy of their effects. If the substances in nature decay, their 
 properties of course perish with them ; but no ancient of sane mind 
 ever doubted for a moment that while the substances continued in 
 their healthy state, they would manifest other properties than those 
 which his first experience had attributed to them. There is no ulti- 
 mate principle of our constitution which urges us to believe the uni- 
 verse will always remain as it is; against which the doctrines of Chris- 
 tianity and the tenets of the development theory alike contend ; but 
 only that while it does continue, the substances of which it is composed 
 will not manifest different properties than those on which their in- 
 ternal constitution depend.
 
 202 METHODS OF THE PHYSICAL SCIENCES. [B. V. 
 
 results or extend them beyond the instances we have ex- 
 perienced ; while in others, one single case impels the mind 
 to place no limit to the uniformity, but to make it co-equal 
 with space and time. The solution of the difficulty will be 
 found in the sheer impossibility of the mind to believe that 
 a thing can be otherwise than what it is ; or, in other words, 
 that a substance can exist and manifest properties conflict- 
 ing with those which depend on its internal organisation. 
 Now, no philosophical instruments are required, or, indeed, 
 the slightest process of investigation, to enable us to draw a 
 line in the common elements of nature between those pro- 
 perties of objects which spring from variable external agencies 
 and those which depend on their internal constitution. A 
 child has but to taste bread to feel that the nutritive proper- 
 ties it possesses springs from the peculiar constitution of the 
 several particles of which it consists : it has only to open its 
 eyes to perceive that certain substances may be accompanied 
 with a variety of colours, and thus infer that such quality is 
 not essential to their existence. A crowd of similar acci- 
 dental and essential uniformities are spontaneously offered 
 by nature ; and that written so legibly that the peasant, in 
 common with the philosopher, may read them ; the only 
 difference between the two minds being, that the one contents 
 itself with such as nature writes upon her surface, while the 
 other, searching for the crowd of uniformities that lie beneath 
 them, asks what facts are needed to enable it to come to a 
 sure conclusion, and then looks out for these. 
 
 As nature may be regarded as an immense web of causes 
 and effects, curiously intertangled and combined, the main 
 difficulty in this research lies in unravelling the various 
 threads, and estimating the influence of each fibre which 
 enters into their composition. If one consequent were only 
 the result of one antecedent, the investigation would be com- 
 paratively easy, but in the generality of cases the opposite is 
 the rule, one effect being commonly the product of a variety 
 of causes, the influence of each of which in producing the 
 phenomena in question it is necessary to estimate, if we 
 would come to a certain conclusion about its origin. For 
 instance, in the production of the neap tides there is the in- 
 fluence of the sun, moon, and earth, each neutralising one 
 another's attractive force, over a body which admits of 
 mobility among its parts to such a degree as to move in the
 
 C. I. 1.] PLURALITY OF CAUSES. 203 
 
 direction of the impulse communicated to it by three distant 
 bodies acting in contrary directions. In ordinary parlance, 
 among the conditions of an effect, one cause is commonly 
 selected to which the result is attributed, either through its 
 being the principal or the culminating agent in its production. 
 Thus, a person in a feeble state of health takes mercury, and 
 exposes himself while in that state to night air; the effect is 
 sudden cold, which is at once ascribed to the influence of the 
 atmosphere, though the result was doubtless as much attribu- 
 table to the mercury 1 and his weak condition : any statement, 
 therefore, of the cause of the cold which did not include the 
 three antecedent conditions must be considered imperfect. 
 Again, the death of the Duke of Wellington was attributed to 
 the effect of some fruit pie, of which he had voraciously eaten 
 the day preceding his demise, though no one could for a mo- 
 ment doubt that the great agent in the business was a general 
 decay in the digestive organs, which only required the slight 
 temporary derangement produced by the fruit in question 
 to completely incapacitate them for discharging those func- 
 tions on which life depends. In like manner, a boy rolls a 
 ball which, towards the end of its progress, is stopped by a 
 stone ; yet it is very probable that such an event would not 
 have taken place had not the resistance of the air and the 
 counteracting force of the earth's attraction weakened its 
 motion to such a degree as to prevent it overleaping the 
 stone, though the two latter causes are omitted in the 
 account of the phenomenon. When the culminating condition 
 is superficially the most conspicuous in the production of the 
 effect, it is invariably set down as the sole agent in the 
 business. Thus we say, that the Crown's assent to a Bill 
 makes it law ; or the casting vote of the Speaker was the 
 cause of the resolution on the part of the Commons, in whose 
 support it was given : and if we happen to be insisting on 
 the requisiteness of such condition at the moment, one of a 
 negative character is styled the cause of an effect with which 
 it could have no positive relation ; as, when we state, the cause 
 of the army being surprised was the sentinel being off his 
 post ; or, the body fell because it was unsupported. We must, 
 however, be aware, that as the absence of the sentinel neither 
 created the enemy, or made the soldiers sleep, it could not 
 
 |_ > Mill's Logic, vol. i. p. 400.
 
 204 METHODS OF TUB PHYSICAL SCIENCES. [B. V. 
 
 be the cause of their surprise ; and, moreover, that the mere 
 absence of a prop underlying a body could no more make it 
 fall, than the absence of any obstruction to its motion above 
 could make it ascend, or the removal of any lateral hin- 
 drance cause it to move horizontally. All such conditions 
 being mere negations, are equivalent to non-existence, and 
 from nothing, nothing can proceed. The real cause must 
 obviously be placed in the fact of the stone being within the 
 sphere of the earth's attraction, which impelled it to its surface 
 with a force in direct proportion to its mass. 
 
 The cause of a phenomenon is, therefore, that condition, or 
 aggregate of conditions, on which alone the effect depends. 
 Its essential mark is in invariable and unconditional con- 
 comitance with its effect, so that from its simple presence 
 the result follows without the interference of any other 
 agency. Mere invariable sequence between two phenomena 
 proves nothing, unless we can produce indubitable evidence 
 of the fact that the one is the tangible result of the agency 
 of the other. Day never ceases without introducing night, 
 and night without being followed by day: yet everybody 
 knows that day is caused by the sun illuminating our hemi- 
 sphere, and that whether the night preceded or not, the 
 appearance of that luminary in our sky would always be 
 attended with the same effect. Though we cannot help in- 
 ferring, having once witnessed certain agencies generate cer- 
 tain results, that wherever such causes operate unmolested 
 by any counteracting agency the same effects must ensue, 
 we cannot inversely take the presence of the effect as an 
 irrefragable sign of the agency of the same causes. Thus, 
 sugar can be produced from linen rags, under the agency of 
 sulphuric acid, as well as from beet-root and West Indian 
 cane. Honey would not at present furnish us with undeni- 
 able proof that the bee had been at work in hoarding its 
 sweets, for that substance can be produced by subjecting 
 starch to certain chemical processes. Death may be the 
 effect of a variety of causes ; nor can we infer from the mere 
 presence of a shell on a rock, whether it dropped from the 
 shallop of a pilgrim, the beak of a bird, or was swept there 
 by the ever- shifting waves of the sea. 
 
 The ultimate basis of such investigations evidently pro- 
 ceeds upon the principle that every natural phenomenon 
 must have a cause sufficient to account for its existence ; and
 
 C. I. 1.] CAUSAL AGENCY UN1VEESAL. 205 
 
 it is as well to ask ourselves at the outset of the inquiry, 
 what evidence have we of the truth of such a proposition, 
 and whether there is any limit to its generality in nature ? 
 If such a principle spring from mere experience, it is evident 
 we are unauthorised to apply it to any other class of effects 
 than those whose causes we have discovered ; and that a 
 great many of the present researches of philosophers may be 
 employed in looking out for causes that may not exist, and 
 eventuate in demonstrations of the indemonstrable, and ex- 
 planations of what cannot be explained. But such a belief 
 no rational intellect can practically entertain. Its adoption 
 would shut up the philosopher's laboratory as well as the 
 courts of justice, since we could neither predict future results 
 or infer from the present anything relative to the past. Among 
 the ancients, indeed, to whom the material universe was a 
 sealed book, some trace of such an opinion may be said to be 
 discovered in their doctrine of chance ; but that tenet by no 
 means implied that objects could be produced without any 
 sufficient cause, but simply that the causes which produced 
 them, not being under the influence of any deity, were the 
 result of capricious agency ; a notion which modern science 
 has completely destroyed by showing that the so-called 
 theistic agencies are nothing else than laws so dependent on 
 the internal constitutions of things, that when once the tie 
 has been fairly established, we can in no instance, without the 
 interposition of supernatural agency, infagine a separation. 
 Accordingly, the introduction of the word chance in the an- 
 cient philosophy, instead of strengthening the empirical view 
 of the question, only proves the utter repugnance of the 
 mind to the belief that an effect can exist without a cause ; 
 since, when man in entire ignorance of natural laws re- 
 ferred every successive uniformity in nature to the direct 
 action of a deity, rather than leave those phenomena 
 which bore upon their front the marks of no forethought 
 or design in their origin, without a cause, he at once as- 
 signed their production to agencies acting without rule or 
 principle, and called their parent chance. But had he dis- 
 enchanted space of his imaginary divinities, and transferred 
 their functions to the agency of general laws, he would have 
 wiped out of his vocabulary the word chance as a notion 
 impossible to be entertained. He would have found it as 
 repugnant to conceive a substance, acting according to other
 
 206 METHODS OF THE PHYSICAL SCIENCES. [B. T. 
 
 principles than those which accorded with its own constitu- 
 tion, as to conceive the same substance existing without a 
 cause ; and have ascended with the moderns the ladder of 
 scientific induction, applying the law of regular causal agency 
 to every corner of the universe. 
 
 As relations, however, may be said to exist between co- 
 existent as well as sequential phenomena, a distinction is 
 sometimes attempted to be drawn between those properties 
 which are merely derivative and the ultimate collocations of 
 matter from which they spring. Though we can give a 
 causal account of the manner in which the threads are inter- 
 woven which compose the fabric of the universe, and show 
 how 'the figures are produced which dot its surface, by un- 
 ravelling the skeins' of which the web consists, it is argued 
 that our power stops here ; that we cannot pursue our inves- 
 tigation into the cause of the primordial fibres, into which we 
 have decomposed the fabric, or produce any reasons for the 
 proportions in which such ultimate qualities are found to 
 co-exist. "We can trace the influence, for instance, of the 
 sun's attraction, and the tangential force imparted to each 
 planet among the movements of the heavenly bodies, and 
 derive all the phenomena which such motions involve from 
 the effects of their combination, but it is said we can give no 
 reason for the existence of the combination itself, nor trace 
 any coincidence between it and the proportions in which the 
 other elementary agencies of the universe are intermingled. 
 In referring existing phenomena to their ultimate elements, 
 through a series of complicated effects, we generally find, 
 according to this view, that derivative laws do not depend 
 solely upon the primary laws into which they are resolvable, 
 but imply in addition a certain mode of co-existence among 
 some of the original elements of the universe. Now this last- 
 mentioned element, which is not a law of causation, but a 
 collocation of causes, cannot be reduced to any law. Among 
 such elements we are unable to explain why one substance 
 exists in greater abundance than another, or why different 
 powers act through various degrees and directions in space. 
 The original elements of the universe may have existed in 
 the greatest disorder, but if they act according-to uniform 
 laws they cannot fail to produce regularity of some kind ; 
 just as the capricious arrangement of coloured bits of glass 
 in the kaleidoscope, through carrying the law of refraction
 
 C. I. 1.] FINAL CAUSES INADMISSIBLE. 207 
 
 into their subsequent movements, produces a beautiful im- 
 pression of order on the mind of the beholder 1 . 
 
 This reasoning, however, is founded upon assumptions 
 which are not in harmony with the actual progress of science, 
 and in reality conflicts with the results to which the religious, 
 deistic, and pantheistic cosmogonies would alike lead us. That 
 the universe grew out of primordial elements, existing in a 
 confused and disordered shape, discoveries of modern che- 
 mistry tends strongly to contradict, which show that the 
 ultimate particles into which matter may be resolved, though 
 bearing evidence of essential difference among themselves, 
 may be arranged in a very limited number of groups or 
 classes, all the individuals of which are exactly alike in all 
 their properties, and when placed in similar circumstances 
 exhibit no variety of deportment. Now, as the number of 
 such atoms defies the multiplying powers of the calculus to 
 compute, the inference is irresistible, that the uniformity 
 they exhibit has been impressed upon them by an external 
 agent, and that the evidence of variety which obtains among 
 their indiscerptible molecules is just that very combination of 
 properties by which such agent intended to produce that op- 
 position and consistence of parts necessary to generate the 
 great globe itself and the universe which it inhabits. From 
 the ends produced in such case we can infer the precise 
 collocation of original materials required to effect it ; just as 
 an architect can tell, on examining the design of an edifice, 
 the combination of wood, masonry, glass, and other materials 
 necessary to execute it. To call, therefore, such collocation 
 a confused heap of causes obeying no regulating principle or 
 law, is about as great a perversion of terms as imagination 
 can conceive. 
 
 To say that final causes are not admissible in any account 
 of this branch of scientific evidence is only correct in the 
 sense which would place ultimate ones under the same ban 
 of exclusion : of neither, inductive science, strictly speaking, 
 can be said to know anything. Chemistry distinctly shows 
 that the final results into which philosophical methods can 
 analyse sensible phenomena are compound atoms, which 
 admit of no further decomposition by any instruments that 
 human agency can grasp ; and with regard to the last word 
 
 1 Mill's Logic, vol. ii. p. 45.
 
 208 METHODS OF THE PHYSICAL SCIENCES. [B. V. 
 
 which mechanics have to say upon the origin of planetary 
 motion, viz., a certain combination of centripetal and tan- 
 gential force, Laplace has shown that both can be rationally 
 accounted for, on the admission of the simple hypothesis 
 that the sun, weakened by the enormous supplies of heat 
 emitted from its surface, has gradually cooled down, aban- 
 doning successive rings of vapour consequent on the in- 
 creased centrifugal force imparted to it by the diminution 
 of its bulk. Science, consequently, knows neither force or 
 substance bearing any semblance of an ultimate character ; 
 and to assume their existence in a certain manner, in any 
 account of its methods, is a case of unwarrantable hypothesis, 
 which may be said to be fairly disposed of if found to clash 
 with legitimate generalisations in any other department of 
 science. 
 
 But in reality the hypothesis in question necessitates the 
 doctrine of final causes, and is found inconsistent with it. 
 Among other conditions, it supposes a period when these 
 original collocations of matter began to act according to 
 regular laws, and in so doing involves itself in an inextricable 
 dilemma. For if matter did not commence to act as soon as 
 created, according to the uniform laws of the substances of 
 which it was composed, it must have existed either from 
 eternity or from some antecedent period of time in amor- 
 phous shapes, obeying no laws, or, in other words, exhibiting 
 no marks of change among its properties. Now this latter 
 supposition it is impossible to entertain, without weakening 
 our notions of that steady uniformity of nature's laws on 
 which all scientific methods are built. For what once hap- 
 pened might occur again. If it were possible for substances 
 to exist without manifesting any action, uniform or otherwise, 
 between their several properties, a suspension of all natural 
 laws, without the interference of an internal agent, might 
 take place to-morrow. We are consequently driven back by 
 the hypothesis to the notion of creation, but find it completely 
 at war with every notion of intelligent agency in the produc- 
 tion of the universe In fact, there are only two kinds of 
 cosmogonies possible : either the world must have been pro- 
 duced by a spiritual being, or the causes which we see at work 
 must have no limit to their existence either in time or space. 
 The absolute generality of the causal theory, as we have
 
 C. I. 2.] FIBST STEP IN SCIENCE. 209 
 
 enounced it, agrees with both. The hypothesis which would 
 circumscribe it within a limited range of phenomena will not 
 admit the one, and is completely sabred by the other 1 . 
 
 2. Observation 
 
 Prom the foregoing view of the nature and objects of 
 physical investigation, it follows that the first step in the 
 inquiry is the ascertainment of the particular effects of which 
 the universe consists, the several appearances, systematic or 
 irregular, which their properties manifest, that we may be in 
 a position, from a comparison of the results, to get some 
 glimpse of their causes, by pursuing the analogies they sug- 
 gest, and by subjecting the phenomena to such influences as 
 the nature of the case shall point out as most likely to re- 
 veal their latent origin. As long as the notion prevailed 
 that natural phenomena was the direct result of spiritual 
 agency; that the whole of the present facts which the 
 universe presents, instead of being the infallible product 
 of all the facts which existed at the moment previous, 
 were the immediate results of a divine intelligence, it could 
 hardly be deemed unwise in the philosopher to shut him- 
 self up in his room and to attempt to reason out the prior 
 states, or even the primordial elements of the existing frame 
 of things, apart from the fluctuating phenomena he saw 
 around him. But since the objects of nature have been 
 shown to be connected in a compact web of mutual relations 
 and dependencies, and to precede each other in a regular 
 order of sequence, each effect being generated by certain 
 material conditions, which immediately preceded its occur- 
 rence, every individual of which in turn were generated by 
 others, it is obvious if we would analyse this complexity 
 
 1 Though " metaphors are no arguments," as Lady Hermione says in 
 the " Fortunes of Nigel," we may observe in passing, that the regu- 
 larity springing from the capricious combination of coloured bits of 
 glass in the kaleidoscope is the effect of one unique substance acting in 
 accordance with its own laws, and that if any other substance were 
 introduced into the arrangement, in similar disorder, the most chaotic 
 confusion would ensue. The simile consequently fails in that precise 
 point where illustration was wanting. That a confused collection of 
 elements, without principle or method in the assortment of their parts, 
 can ever generate harmonious phenomena, though acting according to 
 the laws of their respective substances, we will believe when we see 
 but not till then.
 
 210 METHODS OF THE PHYSICAL SCIENCES. [B. Y. 
 
 with a view to attribute to every cause its effect, to every 
 antecedent the consequent which it produced, we have no 
 other course than to commence with examining the partial 
 threads of which the web is composed, viewing them in every 
 light that is calculated to afford any glimpse into their in- 
 ternal structure, and making a faithful record of the proper- 
 ties they exhibit in the various situations in which they have 
 been tried, that reason may be guided by the resulting evi- 
 dence, not only to lay its hands on the direct mechanism by 
 which they have been produced, but to compute the amount 
 of influence which they exercise over other elements, and the 
 modification they receive by being acted upon by other sub- 
 stances in return. Throughout the whole of this process 
 reason can only be considered in the light of a subordinate 
 agent. She can only interpret the facts which nature puts 
 in her possession : one single result of experience is suffi- 
 cient to dissipate her brightest theories. 
 
 The mode of collecting instances must have distinct re- 
 ference to the point we have in view, some requiring the 
 registered observations of individuals situated in different 
 hemispheres and centuries to establish anything in the 
 nature of evidence co-extensive with the subject, whilst 
 others are perfectly open to individual exploitation. If a 
 single person wished to discover the actual direction in which 
 changes of relative level are taking place between the exist- 
 ing continents and seas, it is evident that no exertion on 
 his part could achieve his purpose, unless made in consort 
 with observers scattered over every part of the globe. For 
 the only way in which the point can be decided is, to select 
 on the most prominent coasts, situated in different hemi- 
 spheres, such marks as seem unlikely to change during the 
 next century, and ascertain their true elevation above the 
 mean level of the sea in the interval, by instruments adapted 
 to the purpose. But such agencies, extending over genera* 
 tions and hemispheres, can only be set and maintained in 
 action by different governments; or, at least, by mutual 
 compact between scientific corporations. 
 
 The motives, however, which lead to the record of pheno- 
 mena may be various ; and provided the instance narrated be 
 a faithful and complete account of objects before unobserved, 
 their registry cannot fail to be of the highest moment to 
 that branch of science to which they bear reference. Thus it
 
 C. I. 2.] IMPORTANCE OF OBSERVATION. 211 
 
 had long been known that the cell is the type of vegetable 
 structure ; that the simplest, as well as the most complex, 
 plants are composed either of single cells or multiform aggre- 
 gations of the same vesicle ; but this truth was comparatively 
 of minor importance until Schwann, led by the observation 
 of the embryonic structure of certain tissues of animals, esta- 
 blished the fact that the animal, like the vegetable tissue, 
 originate in cells, and that all the laws of vegetable cellular 
 formation apply, in every essential particular, to the sim- 
 plest as well as the most complex organism of animal crea- 
 tion. Physiologists, previous to Schwann, had, while sub- 
 jecting animal tissues to the microscope, perceived the ap- 
 pearances which indicate their origin in similar germ cells to 
 plants, but passed them by as something mysterious, or too 
 unimportant to be inquired into. Schwann, on the other 
 hand, subjected them to minute examination, and by pur- 
 suing the analogy which the cellular structure of plants 
 pointed out to him, opened the way to the most startling 
 truths of the animal organism, and completely changed the 
 aspect of physiological science 1 . Again, a soap manufac- 
 turer observes that the residuum of his ley, when exhausted 
 of the alkali for which he employs it, produces a cor- 
 rosion of his copper boiler, for which he cannot account. 
 A scientific chemist, on analysing the matter, discovers one 
 of the most singular and important chemical elements 
 iodine, which is found to occur most appositely in support of 
 a variety of novel and instructive views then gaining ground 
 in chemistry, and thus exercised a marked influence over the 
 whole body of that science. The new substance is subse- 
 quently discovered to be a prompt cure for the goitre, being 
 traced through sea plants and other marine substances from 
 whose ashes the principal ingredients of soap is extracted to 
 sponge, which had administered some relief to the victims of 
 that disorder. Intelligent workmen, therefore, at this stage 
 of the inquiry, are capable of being of immense service to 
 philosophy, and might write their names in its annals if they 
 chose to record every singular instance that crossed their 
 path, and noted all the particular circumstances attendant 
 upon it. The habit of minutely observing and particula- 
 rising the results of such phenomena could hardly fail to 
 i Mikroscopische Untersuchungen iiber die Ubereinstimmung in der 
 structur und dem Wachsthum der Thiere & Pflanzen. Berlin, 1839. 
 
 P2
 
 212 METHODS OP THE PHYSICAL SCIENCES. [B. V. 
 
 suggest to intelligent minds analogies similar to those just 
 narrated, which might prove the germ of equally brilliant dis- 
 coveries. Physical science has advanced rapidly since Bacon 
 pointed out the great importance of this branch of the subject, 
 leaving a noble pattern both of the industry and zeal 1 with 
 which it should be prosecuted. But had each one felt in the 
 interim the extent to which he was capable of assuming fellow- 
 ship with so great a mind, it is hardly too much to say that 
 science would have been looking back on the positions she has 
 reached to-day as mere starting-posts in her dazzling career. 
 
 In geology, meteorology, and other sciences, which can 
 hardly be said to be out of the descriptive stage, and whose 
 objects are co-extensive with the globe we inhabit, the obser- 
 vations of great numbers of individuals, widely dispersed, 
 are of manifest importance, as constituting the only means 
 by which these sciences can be carried through their infancy, 
 and connected by a series of intermediate generalisations 
 with laws sufficiently ultimate to allow the deductive element 
 to become an agent in their progress. But to ensure the 
 widest advantage to the labours which all well-informed 
 persons might carry on, and to stimulate them in the pur- 
 suit, it ought to be an object with every scientific body to 
 point out in what direction certain groups of instances tend ; 
 what kind of facts are required either to turn the rising 
 generalisation into a law, or to test its accuracy ; what class 
 of persons are most favourably situated, either by their 
 calling or position, for meeting with them; and what at- 
 tendant circumstances are most likely to prove influential in 
 modifying the phenomena. By such division of labour the 
 inquiries of large masses of individuals would be stripped of 
 vague generality and concentrated upon critical objects ; and 
 the separate results of their experience transmitted to a com- 
 mon centre, might enable judges skilled in interpretation at 
 once to pounce upon the law. 
 
 In recording or observing facts, whether to answer any 
 
 1 His Sylva Sylvarum, in the attempt to extend which he sacrificed 
 his life. When dying he said the experiment which caused his death 
 " had succeeded excellently well." The elder Pliny, whose collection 
 of registries would have broken the back of an elephant, perished in 
 exploring the crater of Vesuvius. His note-books, four hundred in 
 number, have not come down to us. Aristotle afforded another great 
 instance of this kind of industry in his work on animals, but only frag- 
 ments of his labours have reached posterity.
 
 C. I. 2.] CANONS OF OBSEETATION. 213 
 
 definite question, or simply to register some peculiar pheno- 
 menon which has presented itself to us, we must be careful 
 to omit no circumstance in the account, as the neglected 
 condition, like one of the quantities in an algebraic state- 
 ment, might be essentially connected with the solution, and 
 so mar the revelation of the cause. For instance, the fall of 
 meteoric stones, being accompanied with flashes of fire, issuing 
 from a cloud, and a loud rattling noise like thunder, was long 
 confounded with that of thunderbolts ; but had it been ob- 
 served that the flash and sound occasionally emanated from a 
 very small cloud insulated in a clear sky, instead of attributing 
 them to electric agency, philosophers would have sought for 
 their cause in the very circumstance which separated them 
 from that phenomenon. In order to guard against such 
 omissions it is necessary to have each of our senses brought 
 in actual contact with the phenomenon, and let nothing 
 escape notice which affects any one of them. Thus, if light- 
 ning were to strike a house we inhabit, we ought to notice 
 the form, colour, and duration of the light we saw, and to 
 what objects it adhered ; whether any smell of fire was per- 
 ceptible, and if sulphurous, metallic, or such as would arise 
 from substances scorched with flash; what sounds were 
 heard, and whether we felt any shock, stroke, or peculiar 
 sensation, or experienced any strange taste in our mouths. 
 The modifying circumstances should then be noted, such as 
 the presence of conductors, the neighbouring objects, the 
 state of the atmosphere, and the disposition of the clouds. 
 After all this particularity the question how the house came 
 to be struck, would have to be determined : whether by what 
 is termed a returning stroke, or by a flash of lightning pass- 
 ing from the clouds to the earth. 
 
 Our record of observation should not only be circum- 
 stantial but faithful, or, in other words, consist of what we 
 have observed, and nothing else. "Without any intention of 
 perverting the description, we may distort simple facts by 
 clothing them in the views and language of an erroneous 
 theory. Thus, if we said the thunderbolt struck with vio- 
 lence the side of the house and beat in the wall, our hearers 
 would be led to believe, by the statement of a fact which we 
 did not see, that a solid, or ponderable projectile was con- 
 cerned. The smell of sulphur which is sometimes said to 
 accompany the electric fluid, is a remnant of the theory which
 
 214 METHODS OF THE PHYSICAL SCIENCES. [B. V. 
 
 made thunder and lightning the explosion of aerial gun- 
 powder, composed of nitrous exhalations. The elder chemists 
 were so addicted to the mischief of representing facts in the lan- 
 guage of idle theories, as to falsify the descriptions of innu- 
 merable important and curious experiments. In geology, par- 
 ticularly, the Vulcanists and Neptunists so far set the purposes 
 of language at defiance through this practice, that it was totally 
 impossible in their descriptions to get at the facts observed. In 
 like manner, Faujas de St. Fond, in his work on the volcanoes of 
 Central France, describes, with that particularity which belongs 
 to fact, craters existing nowhere but in his own imagination 1 . 
 It is of immense importance, with a view to guard against 
 such errors, and to secure our observations from the illusions 
 frequently practised on us by the senses, to verify or accom- 
 pany them with accurate numerical statements, according to 
 such measure of time, space, or quantity as they appear to 
 admit of. It was entirely to the omission of exact numerical 
 determinations of quantity that the blunders of the Stahlian 
 chemistry and the Ptolemaic system of astronomy are attri- 
 butable ; and the correct expansion of these, as well as the rest 
 of the physical sciences, may be said to have been in propor- 
 tion to the extent to which their objects have been open to the 
 legitimate application of this element. All phenomena more 
 or less admit of accurate measurement, to such a degree that 
 the very class which are so fluctuating and irregular in their 
 occurrence as to appear an exception, cannot be pressed into 
 the service of science by any other means. The thousand capri- 
 cious agencies by which the atmosphere is hourly influenced, 
 and the irregular action of winds, tides, and currents, must 
 ever prevent us from ascertaining either the general tempera- 
 ture, or the mean level of the sea at any particular locality, by 
 the unassisted senses. If we would reduce such irregular 
 
 1 Herschel's Discourse on the Study of Natural Philosophy, p. 130. 
 A vague and loose mode of looking at facts very easily observable, left 
 men for a long time under the belief that a body ten times as heavy as 
 another falls ten times as fast ; that objects immersed in water are 
 always magnified, without regard to the form of the surface; that 
 the magnet exerts an irresistible force ; that crystal is always found 
 associated with ice, and the like. These and many other examples 
 show how blind and careless man can be, even in registering the 
 plainest and commonest appearances; and prove that the mere 
 faculties of perception, although constantly exercised upon innu- 
 merable objects, may long fail in leading to any exact knowledge.
 
 C. I. 2.] USE OF EXPEEIMENT. 215 
 
 agents to any kind of law, or hinder them from defeating our 
 discovery of the laws of the elements with which they come 
 in contact, we must call in the assistance of instruments 
 adapted to measure the precise scale of their variation within 
 a given period and locality, and combine the mean amount 
 with the result 1 . 
 
 Observation, even where supported by exact measurement, 
 in many cases, will go very little way towards establishing 
 the cause of a phenomenon, unless we are able to vary the 
 concomitant circumstances, and view the cause, generate the 
 effect, or vary in exact proportion along with it. Though 
 there was every reason to attribute lightning to electric 
 agency, the fact was never considered definitely made out 
 until Franklin threw up his kite in the air at the approach of 
 a thunder-storm, and obtained the same sparks from his cord 
 as invariably accompanied its connexion with an electric ma- 
 chine. As nature is constructed for a widely different object 
 than that of facilitating our studies, it frequently happens, 
 indeed, that she refuses to afford the precise kind of variation 
 needed to establish the law we are in search of, and leaves us 
 to rack our invention to institute a case in point by direct 
 experiment. Thus, were it required to ascertain the principle 
 in the atmosphere which enables it to sustain life, we should 
 find no instance in which nature produces either oxygen or 
 azote in a separate state, to enable us, by immersing a living 
 animal alternately in both gases, to decide the question. "We 
 are exclusively indebted to experiment for the fact, that re- 
 spiration is supported by oxygen, and also for our knowledge 
 of the ingredients of which the atmosphere is composed. 
 
 Hence experiment, besides multiplying the advantages de- 
 rived from passive observation, accomplishes that which pas- 
 sive observation is seldom adequate to perform. It enables 
 us to march directly to our object and to link it indubitably 
 with its cause. By experiment we are enabled to study the 
 laws of nature in our laboratory, and subject the wildest 
 elements to our control ; to multiply our knowledge of their 
 several properties by introducing such agents among them 
 as seem calculated to reveal their laws. By experiment we 
 are enabled to bring theories to the touchstone of fact, and 
 prevent hypothetical fictions from spreading darkness over 
 
 1 This process concerns the doctrine of chance, which will be treated 
 of under the section of empirical laws.
 
 216 METHODS OF THE PHYSICAL SCIENCES. [B. V. 
 
 centuries, and making genius actually instrumental in push- 
 ing back science instead of becoming an impulsive lever in 
 its advancement. To this element is to be ascribed the 
 creation of physical science in the fifteenth century, and 
 much of its wonderful progress during the intervening years. 
 To its absence among the ancients must be mainly attributed 
 their entire ignorance of physical laws, and their subjection 
 of nature to imaginary divinities. 
 
 It is, however, of importance to observe that the use of 
 this great instrument is suggested in a large degree by the 
 results the mind has gathered from pure observation, which 
 generally takes the initial step in the physical sciences. Before 
 mounting to the cause of any phenomena, we patiently ob- 
 serve its effects and examine its laws. Here pure observa- 
 tion alone is applicable. But the results to which it arrives 
 suggest in what agencies it may originate, and experiment 
 is ever ready to bring such hints to the test, and where 
 nature does not present a case in point to create an instance 
 that will decide the question. Hence experiment is mainly 
 applicable in inquiring into the effect of a given cause. So 
 far as we are strictly concerned with investigating the causes 
 of a given effect the process is one of pure observation 1 . 
 
 3. The Methods of Experimental Inquiry. Discovery of 
 Minor Laics ; their Extension and Verification. 
 
 Having collected a certain number of instances bearing 
 upon the chosen point of inquiry, it remains to determine the 
 nature of the evidence which will entitle us to conclude that 
 u certain course is followed by a given effect, or under 
 what circumstances invariable sequence may be allowed to 
 establish a causal connexion between the phenomena. The 
 marks commonly adduced in evidence of such relation may 
 be generalised under four heads 3 , though in practice, the 
 actual signs by which causes reveal themselves are frequently 
 only corollaries from them, or are traceable not to one dis- 
 tinct cause alone, but to two or three in conjunction. It 
 mil then be sufficient, for an accurate knowledge of the 
 
 1 The reader is referred for classification and nomenclature to the 
 Supplement of this Book in the Appendix. 2 Bacon's Novum Orga- 
 nuni, commencement of 2nd book; Herschel's Pis. Stud. Nat. Phil, 
 p. 151; Mill's System of Logic, vol. i. p. 450.
 
 C. I. 3.] METHOD OF AGBEEMENT. 217 
 
 subject, to give the leading causes of induction in full, point- 
 ing out their specific ground, differences, and merits, and 
 leave their mode of application to be gathered from the in- 
 stances we shall adduce in illustration of their properties. 
 
 The first mark, by which we are generally led to infer the 
 presence of the relation we intend by cause and effect, is 
 uniform connexion, provided the circumstances in which the 
 concomitance has been observed are sufficiently various to 
 exclude doubt that it could have originated from any relation 
 but the one assigned. For instance, let the object in view 
 be to ascertain the cause of death produced by metallic 
 poisons. It is observed that arsenious acid, and the salts of 
 lead, bismuth, copper, and mercury, if administered, except 
 in the smallest doses, destroy life. Now this effect obviously 
 can only follow from the violation of some of the conditions 
 on which animal organism depends, so that the question 
 arises which of those conditions seems most likely to be 
 interfered with by the substances in question, and how can 
 metallic poisons be brought in contact with it. The most 
 obvious mode is to trace the effects of these substances on 
 the composite ingredients of the animal system, and observe 
 what law or vital function of organism they arrest or enfeeble. 
 If the effect obtain in the separate parts at different periods 
 of their formation in an isolated as well as in a combined 
 state ; and if the remotest quantities of such poisons tend to 
 disturb the same law of the animal economy, there could 
 remain no doubt that interference with its functions was the 
 effect of introducing them into the animal system and the 
 proximate cause of death in every case in which they were 
 administered. But the effect of placing solutions of metallic 
 poisons in contact with albumen, milk, muscular fibre, mem- 
 branes, and other animal products, is that the acid or salt 
 having left the water in which it was dissolved unites with 
 the animal substance, and destroys its tendency to decompo- 
 sition. The same effect is perceived in cases where death 
 has been produced by these poisons, the parts of the body 
 with which the poisonous substances have been brought into 
 contact not afterwards undergoing the law of putrefaction : 
 and when the poisons have been supplied in too small a 
 quantity to destroy life eschars are produced, through the 
 destruction of superficial portions of the tissues, which are 
 subsequently thrown off by the reparative process taking
 
 218 METHODS OF THE PHYSICAL SCIENCES. [s. V. 
 
 place in the healthy parts. Hence the conclusion is patent 
 that these metallic compounds, when taken into the system, 
 cause death, by arresting the law of decomposition. In the 
 instances adduced all point to the arrest of the same law, 
 and this could not have occurred with antecedents varying 
 according to every conceivable mode of which the case ad- 
 mits, unless they had generated the consequent apart from 
 every other agent. 
 
 In this illustration we have proceeded, according to the 
 general route of scientific inquiry, from the effect to the cause. 
 But it may happen that the effect of a cause is required to be 
 known, in which case we must find or produce the cause in such 
 a variety of circumstances that it may be fairly presumed that 
 the different instances could have no other antecedent in com- 
 mon. Then it is obvious that if any unvariable result appear 
 in each combination of consequents, that must be attributed to 
 the cause which is the only invariable element in every new 
 set of antecedents. Thus reversing the example already 
 adduced, as the effect of metallic poisons in every instance, 
 in which it can be brought into connexion with organic com- 
 pounds is to arrest the process of decomposition, we experi- 
 ence no hesitation in attributing that result to their agency. 
 
 But it must be observed that this method, which proceeds 
 by comparing instances to observe in what they agree, is not 
 of very wide application, as it is liable to be defeated by two 
 obstacles at every stage of the inquiry. Either nature may 
 not present, or experiment fail to obtain, instances in suffi- 
 cient abundance to ensure the variety necessary to lead to 
 a legitimate induction ; or the number of instances being 
 secured, counteracting causes may interfere to modify or 
 neutralise the agents at work, and so prevent the instance 
 from throwing any clear light on the inquiry. In a great 
 number of natural phenomena the effect is produced gradu- 
 ally, and frequently diminishes in strength, while the cause 
 often goes on increasing in intensity, so that the antecedents 
 of the one and the consequents of the other become diffi- 
 cult to trace. On the other hand, the effect often follows 
 the cause so instantaneously that the interval cannot be per- 
 ceived, and we are left without any marks to discriminate 
 the cause from the effect. Owing to the frequent occurrence 
 of these cases, the method of agreement in the generality of 
 inquiries is incapable by itself of leading to a certain resiilt.
 
 C. I. 3.] METHOD OF DIITEBENCE. 219 
 
 The second mark of causal relation between two pheno- 
 mena is invariable negation of the effect with absence of the 
 cause, and vice versa, unless some other cause be capable of 
 producing the same effect. This may be styled the method 
 of difference. In the former method we endeavoured to 
 obtain instances which agreed in the presence of the object 
 whose cause or effect was sought. In the present method 
 we require, on the contrary, instances resembling each other 
 in every respect but the presence or absence of the pheno- 
 menon we desire to study. Thus, if our object be to discover 
 if air be an essential condition of sound, we need only place 
 a watch under a glass receiver, and observe its ticks fade on 
 the ear as the air is withdrawn from the interior, until by the 
 completion of the exhaustive process they cease altogether. 
 Here we have an instance of the presence of motion in the 
 sounding body combined with the contiguity of the ear to 
 catch the beats, but unaccompanied with sonorous vibration ; 
 or, in other words, the absence of one of the essential con- 
 ditions the cause, with the negation of the effect. On 
 re-admitting the air, the beats are again found to strike the 
 ear, thus proving by the strongest evidence the dependence 
 of sound on that medium, and suggesting in some measure 
 the nature of its functions. Again, in the case of introducing 
 metallic poisons into the animal organism, if we can show 
 that death is prevented by administering an antidote which 
 shall hinder the acid from arresting decomposition by com- 
 bining with the animal tissues, we should exclude the effect by 
 taking away the cause, or, in other words, prove, by the 
 method of difference, that metallic poisons destroy life through 
 the agency in question. Now, such antidotes are afforded by 
 the application of sugar, sulphuric acid, or hydrated peroxide 
 of iron ; for each of these substances as soon as administered 
 prevent, by different agencies, the salts of copper from enter- 
 ing into combination with the animal tissues, and in this wise 
 preserve the law of decomposition intact 1 . Occasionally this 
 
 1 It may be observed in the two examples adduced that the instances 
 in the first case only differ by the absence or presence of the same cir- 
 cumstance, viz.: air under a glass receiver; while the difference of the 
 last consists in the introduction or exclusion of a single substance. 
 But as every substance may have innumerable properties, the suppo- 
 sition is just conceivable that these antidotes may counteract the 
 poison through some other mode than that of forming an insoluble
 
 220 METHODS OP THE PHYSICAL SCIENCES. [_B. V. 
 
 mark of causation, besides leading to the establishment of a 
 general fact, points to contrary, or opposing facts, as equally 
 established by the same evidence. Thus, if rust be produced 
 by confining iron filings in a closed vessel over water, the 
 enclosed atmosphere will be found to quench the flame, or 
 destroy the life of any animal immersed in it. Now this ex- 
 periment not only shows that the remaining gas of which the 
 enclosed atmosphere is constituted will not support life, but 
 that the ingredient of the atmosphere which supports flame 
 and animal life must be attributed to that which the iron 
 absorbs and which rusts it. It is to similar inferences we owe 
 almost all the inductions of daily life. "When a man is shot 
 through the heart, we learn by this process that it was the 
 gun-shot which killed him ; for he was in the fulness of life 
 immediately before, all circumstances being the same except 
 the wound. 
 
 Hence the method of difference stands on the ground that 
 whatever cannot be eliminated without the subtraction of 
 the phenomenon is connected with the phenomenon by law ; 
 while that of agreement has for its foundation, that what- 
 ever can be eliminated without removing the phenomenon is 
 not connected with the phenomenon by law. Of the two 
 methods, that of difference is more particularly open to ex- 
 periment ; while the other is commonly the resource we 
 employ where artificial experiment is impossible. In examin- 
 ing the nature of any effect with a view to ascertain its 
 origin, we compare its points of agreement in as many vari- 
 able circumstances as possible. The method of difference 
 tries the causes which such cases suggest by comparing two 
 instances exactly similar in every circumstance except the 
 cause in question. If, with the same set of circumstances 
 in which the presence of the cause is succeeded by that of 
 the effect, the absence of the cause is followed by its ne- 
 gation, what was simply a suggestion before becomes an 
 established certainty. We need hardly say, however, that 
 nature is not so propitious to our studies as to lavish such 
 instances upon us. If we want them, in eight cases out of 
 ten we must devise instruments by which they may be pro- 
 compound with it, in which case the evidence would fall to pieces. 
 Hence, as the first class of cases do not admit of this barely conceivable 
 uncertainty, the conclusions established by them belong to the highest 
 rank of physical certainties.
 
 C. I. 3.] INDIEECT METHOD OF DIFFEBENCE. 221 
 
 duced. The majority of the great truths established by the 
 method of difference, and they are the most important that 
 science reveals to us, have been extorted from nature by arti- 
 ficial experiment. On the other hand, in comparing instances 
 of agreement, we must rely on pure observation for the 
 result ; unless, indeed, we can produce the cause whose effect 
 is sought in sets^of circumstances, sufficiently various to ex- 
 clude doubt that the result common to every instance origi- 
 nates from any other source than itself ; a belief which, as it 
 grows with every instance, is never of that convincing nature 
 with that produced by the method of difference, which 
 enables us, by one well-chosen experiment, to lay our hand 
 upon the cause, and say indisputably it is there. In the 
 former method, as the circumstances are different in every 
 case, we can never be infallibly secure that the constantly- 
 recurring effect may not arise from some latent cause or par- 
 ticular combination of the various properties which substances 
 are apt to manifest in different situations, instead of being 
 generated by the constant antecedent whose effect that com- 
 bination may neutralise in each instance. Now the method 
 of difference, in its most rigorous sense, excludes even that 
 shadow of possible doubt. !For the two instances compared 
 only differ in one circumstance the absence or presence of 
 the phenomenon we wish to explore ; so that we actually see 
 the effect generated under our eyes. 
 
 The two methods, however, are not unfrequently combined 
 in scientific investigations, though the juncture arises from a 
 lax application of the method of difference in cases where 
 the rigorous employment of it is impossible. Sometimes the 
 phenomenon we wish to investigate is associated with a 
 number of properties combined in the same substance, which 
 we are incompetent to separate so as to render the production 
 of a substance impossible which shall exactly resemble the one 
 in question, except in the particular property we desire to 
 study. Suppose, for example, the polarisation of light is the 
 subject of inquiry. The complicated phenomena which are 
 designated by that name are impressed upon light in the act 
 of double refraction, or by ordinary reflection at the surface 
 of a transparent body. But we cannot produce any sub- 
 stance winch shall resemble either transparent bodies or 
 doubly refracting crystals, except in the one property of 
 polarisation. Our only mode is to examine in what kindred
 
 222 METHODS OF THE PHYSICAL SCIENCES. [B. V. 
 
 qualities polarisation, ordinary reflection, and double re- 
 fraction, individually agree and differ, and endeavour from 
 the resulting analogies to get at the causal relation. This 
 mode of inquiry combines the method of agreement with 
 that of difference taken in an indirect sense. The in- 
 stances which fall under the latter branch, instead of agreeing 
 in all but the presence or absence of the phenomenon in 
 question, may differ in many other qualities besides ; so that 
 although, when conjoined with the method of agreement, all 
 doubt may be eliminated where the individual inductions have 
 been sufficiently extensive, yet the possibility is never com- 
 pletely banished that the remaining differences may not have 
 had some share in producing the established connexion. 
 Thus we compare instances of bodies which undergo putre- 
 faction with those which do not manifest that tendency, and 
 discover that water is always present in the one case, and 
 absent in the other ; and find, moreover, that salt, which is 
 an admirable preventative of this tendency in animal sub- 
 stances, has a strong attraction for this element. Though the 
 evidence amounts to scientific certainty that the ingredients 
 of water, Combining with some properties of the substance 1 , 
 produce decomposition, we are not driven to the conclusion 
 with the same force as if the evidence had rested upon two 
 instances differing in nothing but the conjoined absence and 
 presence of the element in question. For, in the former 
 case, the possibility remains that putrefaction, or non-putre- 
 faction, in the instances compared, may arise from the pre- 
 sence or absence of other properties besides water. This 
 method, however, which unites all the advantages of the 
 method of agreement with a modified portion of the method 
 of difference, is undoubtedly one of the most universal in- 
 struments which science employs. Its use is simple and 
 obvious, and the conclusions to which it leads are less 
 exposed to cavil than those which entirely depend on the strict 
 method of agreement. 
 
 The precise sphere of the application of this method is co- 
 extensive with that large class of phenomena which, on account 
 
 1 It has been shown by Liebig that the properties in question are 
 carbon and azote, the hydrogen of the water combining with the for- 
 mer and producing carbonic acid, while the oxygen unites with the 
 azote and generates ammonia. Now carbonic acid and ammonia con- 
 stitutes the gaseous compound which animal and other azotised bodies 
 throw off in a state of decomposition.
 
 C. I. 3.] METHOD OF EESIDUES. 223 
 
 of the complexity of their nature, will not admit of the direct 
 method of difference ; and whose properties do not appear in cir- 
 cumstances sufficiently diverse to allow any cogent conclusion 
 to be drawn by the method of agreement. For instance, if we 
 wish to investigate the proximate cause of animal heat, the phe- 
 nomenon being constantly associated with the living organism, 
 can neither be detached from a crowd of other properties, 
 nor viewed in connexion with any variable combination of 
 them. Now, even if we should observe in a thousand cases 
 that all animals, whose respiratory system is well developed 
 and aerates the blood perfectly, are warm-blooded, we should 
 never be justified in attributing, with more than probable 
 certainty, the phenomenon in question to the change which 
 takes place in the blood by respiration ; but when we observe 
 that those whose respiratory system is imperfect do not 
 maintain a temperature much above the surrounding at- 
 mosphere, that inference assumes the character of scientific 
 certainty. 
 
 This method answers to what Bacon called negative and 
 positive instances, and has been happily termed by Mr. Mill 
 the indirect method of difference 1 . 
 
 The fourth mark of causation is that of residual pheno- 
 mena, which remain in many cases after subducting the 
 effects of all the known causes, and which point to an agency 
 that, from the nature of the circumstances, could only 
 generate their production. For instance, in the return of 
 comets, there is perceived that general agreement between 
 their observed and calculated places as to lead to the in- 
 ference that the sole cause of their orbitual motion is the 
 gravitation of the sun and planets ; but when the effect of 
 this cause is strictly calculated and subducted from the 
 observed motion, we find some diminution of its periodic 
 time, which cannot be accounted for by any other sup- 
 position than the resistance of a medium disseminated 
 through the celestial regions. Now, as there is good ground 
 from other quarters for believing that such a medium actually 
 exists, this anticipation of a comet's periodic time has been 
 ascribed to such a resistance 2 . We cannot, however, be cer- 
 tain that such residual phenomenon is actually produced by 
 the cause it suggests, unless we are perfectly assured of the 
 
 1 System of Logic, vol. L p. 462. 2 Professor Encke. See Her- 
 
 schel's Astronomy.
 
 224 METHODS OF THE PHYSICAL SCIENCES. [B. V. 
 
 existence of such cause, and can also prove that no other agent 
 could have produced the residual effect. Now, as this rarely 
 happens, the strict application of the method of residues is 
 limited to very few cases. It may, however, serve to suggest 
 causes which we may try to produce artificially, according to 
 one of the two first methods, or which can be explained and 
 proved deductively from known laws. The last case is one 
 of frequent occurrence, and constitutes one of the principles by 
 which science in our day has been so much extended. Thus, 
 in calculating the velocity of sound, although the general re- 
 sult was sufficient to show the correctness of the cause and 
 mode of its propagation through the air, yet the velocity was 
 a little above what could be legitimately ascribed to this 
 theory. Laplace at length surmising that the residual velo- 
 city might arise from the heat developed in the act of con- 
 densation which ensues at every vibration of the air, sub- 
 jected the idea to exact calculation, and the result was at 
 once the complete explanation of the residual phenomenon, 
 and an unexpected confirmation of the general law of the 
 development of heat by compression. 
 
 The fifth mark of causal connexion is increase or dimi- 
 nution of the effect with corresponding variation in the 
 cause, an example of which may be observed in the method 
 by which Pascal satisfied himself of the gravity of air. That 
 philosopher knew that if the weight of the incumbent air be 
 the direct cause of the elevation of the barometer, that the 
 column of mercury would sink in proportion as he ascended 
 the Puy de Dome*, as the pressure of the air would diminish 
 with every step he took. The result of the experiment verified 
 his conviction of Torricelli's views, and settled the dispute to 
 which they had given rise for ever. This method of investiga- 
 tion/ which is called that of concomitant variations, though 
 constantly employed in conjunction with the other methods, is 
 mostly of use in ascertaining the law of permanent causes, 
 which it is impossible either to exclude or to isolate ; which 
 we can neither hinder from being present, or contrive that 
 they shall be present alone. To these cases the other me- 
 thods are confessedly inapplicable. Suppose, for instance, it 
 arise as a suggestion that the oscillations of the pendulum 
 are produced by the earth's gravitation, we can in no case 
 exclude the earth as an influencing agent, nor can we argue 
 1 A high mountain in Auvergne.
 
 C. I. 3.] METHOD OF CONCOMITANT TAEIATIONS. 225 
 
 from its constant presence, that it causes the phenomenon in 
 question ; for by parity of reasoning we migh t affirm the 
 same of the sun, which is equally co-existent in all the ex- 
 periments. Now, though we cannot remove the earth, we 
 may modify its influence, and that to a sufficient extent to 
 enable us to decide upon the point in question. For if, as 
 Bacon suggested, the pendulum tends downward in its oscil- 
 lations by the influence of the earth's attraction, " it will 
 follow, the nearer it approach to the earth the stronger, and 
 with the greater force and velocity will the pendulum be 
 drawn to it ; but the further the pendulum be removed, the 
 weaker and slower will be its oscillations 1 ;" a suggestion 
 which Professors Airy and Whewell fully realised by compar- 
 ing the motions of a pendulum in Dolcoath Mine with a 
 chronometer balance, and striking the difference between the 
 velocity of the same, motions as previously ascertained at 
 certain elevations above the earth's surface. By the same 
 method Bacon also pointed out 2 that the tides might be 
 proved to originate in the influence the moon exerts on the 
 earth's surface, if it could be established that the variations 
 in the position of that satellite are attended by correspond- 
 ing variations in the time and place of high water. The 
 great Newton subjected the phenomena to the laws of the 
 calculus, and proving the concomitant variation to the nicest 
 degree of exactness, revealed the laws of one of the most 
 admirable contrivances in the economy of nature. 
 
 Hence it may be inferred, when objects vary according to 
 some fixed quantity which is the ordinary rule, that it is in- 
 dispensable to the establishment of causal connexion by this 
 method, that the phenomena should be submitted to quanti- 
 tative laws, and their mutual influence proved to increase or 
 diminish in the same proportion with the action of their 
 causes. Now in such cases we cannot determine the exact 
 proportion in which the relations vary, unless we know the 
 total quantities of which they consist. Thus in the case 
 of contraction of substance, since we neither know how 
 much heat there is in any body, nor what is the real dis- 
 tance between any of its particles on which its bulk de- 
 pends, we are not in a condition to infer that the con- 
 
 1 Novutn Organ, vol. ii. Instantiee Prerogatives. * NoYum Org. 
 
 vol. ii. Ibid.
 
 226 METHODS OF THE PHYSICAL SCIENCES. [B. V. 
 
 traction of the distance between them would follow the 
 diminution of the quantity of heat, according to the nume- 
 rical relation that the two quantities would vanish simul- 
 taneously. It would, therefore, be hazardous to conclude 
 that because the diminution of temperature in a body con- 
 tracts the space between its particles, that we could bring its 
 particles into contact, provided the process of exhaustion 
 was urged to its full extent. In conjunction with the uncer- 
 tainty that beyond the limits and in circumstances of which 
 we have no direct experience some contracting cause may 
 manifest itself, we have the doubt that the law of varia- 
 tion which the quantities exhibit within the observed 
 limits will hold beyond those limits. There are many laws 
 of variation in phenomena whose differences are inappre- 
 ciable when confined within narrow limits ; but which mani- 
 fest a wide discrepancy when the absolute amounts of varia- 
 tion are considerable. In such cases, therefore, when the 
 variations which fall within the sphere of observation are of 
 limited range, there is considerable danger, if the numerical 
 laws which express those variations be stretched to a consi- 
 derable extent beyond the limits originally calculated, that 
 they will fail to support the theoretical structures built upon 
 them 1 . 
 
 The employment of this method may be occasionally 
 attended with doubt as to which of the phenomena is 
 the operating cause. The only way to clear up the mat- 
 ter is by endeavouring to ascertain whether one set of 
 variations can be produced by means of the other. In the 
 case of heat, for example, by increasing the temperature of a 
 body we increase its bulk ; but by increasing its bulk we 
 diminish its temperature. The conclusion is obvious, that 
 heat is not an effect but a cause of increase of bulk. If ex- 
 periment, however, be not available in the case, we must 
 look out for instances produced by nature in cases where the 
 pre-existing circumstances are already known. 
 
 1 A striking example of such miscalculation may be observed in the for- 
 mulae by which it was computed, from the amount of coal that a steamer 
 of average horse-power would consume in a transatlantic voyage, that 
 no vessel could be found to carry fuel sufficient to supply the engines 
 which she carried throughout the journey; a computation which led 
 many to infer, before the experiment was tried, that the undertaking 
 was impracticable.
 
 C. I. 3.] GENEEAl CAUTIONS. 227 
 
 It will be observed not only tbat most of these methods 
 may apply to the same act of induction, and so operate to test 
 or verify the correctness of each other's processes ; but that 
 they are all, with the single exception of the method of differ- 
 ence taken in its most rigorous sense, exposed to the same 
 uncertainty ; viz., that the presumed effects may be brought 
 about by the action of other causes than the uniform ante- 
 cedents to which we attribute them ; or, at best, if they should 
 really act as influencing agents, that their ubiquity with the 
 effects does not make out direct causation, but only a colla- 
 teral effect of it. Such uncertainties, however, where the 
 conditions of each method have been satisfied in a suffi- 
 ciently large circle of instances, and especially where the 
 methods tend to verify each other's results, dwindle down 
 to an almost inappreciable value. They become, therefore, 
 objects of metaphysical, rather than of logical concernment. 
 In circumstances, however, which do not admit of rigorous 
 precision in the application of each method, a strong proba- 
 bility of causal connexion can only be considered to have 
 been established, or at most the collateral dependence of the 
 phenomena in question, on some common cause. Unless, for 
 instance, in the case of concomitant variations, we can really 
 ascertain that the phenomena do vary in exact proportion 
 to their mutual operations, the result is only one of strong 
 probability ; nor, indeed, can it be relied upon even when 
 made out by quantitative laws, if those laws only express 
 the results of observation restricted to narrow limits. 
 
 Where the induction, however, has been established by 
 the fulfilment of all the conditions that scientific certainty 
 requires, we are not to throw our conclusions lightly aside 
 when a single fact starts up which seems to convict them of 
 error, but rather to set the outstanding exception apart for 
 future examination, being convinced that further inquiry 
 will either destroy its hostility to past results, or verify or 
 extend the facts which they have established. Tims the 
 objection was brought against the Newtonian theory of 
 gravitation, that it did not account for the perplexing ine- 
 qualities of the moon's motions, and several minor irre- 
 gularities in the planetary system, which seemed violent 
 outstanding exceptions to it. Further inquiry, however, 
 transformed these seeming discrepancies into the strongest 
 
 Q 2
 
 228 METHODS OP THE PHYSICAL SCIENCES. [fi. V. 
 
 confirmations which that theory could receive, and ex- 
 tended its influence from those globular masses which 
 Newton had previously included under it to every par- 
 ticle of matter in the frame of the universe. An additional 
 instance may be cited in the law of isomorphism, discovered 
 by Mitscherlich, which announced that certain distinct 
 groups of chemical elements of which all bodies consist are 
 so related that when similar combinations are formed of in- 
 dividuals belonging to two, three, or more of them, such com- 
 binations will crystallise in the same geometrical forms. To 
 this law there appeared a remarkable exception in arsenic 
 and phosphoric acid, which, though seeming to constitute 
 identical combinations with those included under Mitscher- 
 lich's law, yet refused to crystallise in similar forms. But on 
 further investigation, the compositions of the two salts were 
 found to deviate essentially from that similarity required by 
 the law of isomorphism, and a new phosphate of soda was pro- 
 duced, differing from that generally known under the name 
 of phosphoric acid, in containing a different portion of water 
 and agreeing in composition exactly with the arseniate, the 
 crystals of which, when examined, agreed precisely in form 
 with the arseniate. The removal of the objection conse- 
 quently led to a further verification of the law. Again, in 
 the same science, it has been observed 1 that, though am- 
 monia is a strong contradiction of the law which attributes 
 the alkaline quality of the alkaline and earthy bases to the 
 presence of oxygen combined with one or other of a peculiar 
 class of metals, that there are almost certain indications that 
 this exception is not a real one, but assumes that appearance 
 in consequence of some modifying cause not understood. 
 Such objections generally appear in the form of residual 
 phenomenon, which, when minutely examined, are invariably 
 found either to extend and corroborate the induction against 
 which they were brought, or give rise to an unexpected and 
 novel class of laws. 
 
 (1st.) As the processes by which nature conducts her opera- 
 tions are frequently of an analogous character, one of the 
 most ready means of extending single inductions is by dis- 
 covering cases in which, from the general constitution of 
 things, similar laws are able to act, and endeavouring to 
 
 1 Herschel, Stud. Nat. Phil. p. 154.
 
 C. I. 3.] EXTENSION OF INDUCTIONS. 229 
 
 establish results precisely analogous to those already adopted. 
 Thus, Schwann having observed that certain animal tissues 
 originated in cells, was led by the analogy of plants to the 
 discovery that all the organs of the animal structure, together 
 with the original foetus, took their rise in similar cells, and 
 reached their highest development by aggregations of the 
 same or slightly different vesicles. In like manner Young 
 was led to infer, from the fact that two vibrations of sounds 
 arriving at the same place by different routes, either strength- 
 ened or wholly or partially destroyed each other's effects, 
 that, if the undulatory theory was true, two rays of light 
 might be made to combine so as to produce darkness; a 
 fact which had no sooner been established than it led to the 
 explanation of optical phenomena of a most remote kind. 
 
 (2nd.) Another mode of extension is that of examining all 
 the cases which present the necessary conditions for bringing 
 the newly-revealed law into action ; a process, indeed, which 
 commonly leads to the discovery of special laws before un- 
 suspected, and explanations of others only empirically known. 
 Thus Faraday having established the fact that electricity is 
 evolved by all magnets, great or small, even including the 
 earth, provided a conductor move at right angles to the 
 direction of its poles, began to look out for fresh instances 
 in which these conditions meet. Now, in the northern 
 regions, where the earth's magnetic poles are nearly per- 
 pendicular to the horizon, all horizontal wheels made of 
 metal, running streams, and other conductors, moving at 
 right angles to the polar direction, must comply with the 
 conditions of the law and charge the air with electricity. Ill 
 these latitudes, therefore, a larger display of the phenomena 
 produced by this element must be expected, and we find it 
 in the Aurora Borealis 1 . 
 
 Another example of the latter kind of extension is to be 
 found in the mode by which Professor Graham was led, from 
 the general law that gases have a strong tendency to per- 
 meate animal membranes and diffuse themselves through the 
 spaces which they enclose, to establish a number of special 
 laws explanatory of various phenomena in connexion with 
 
 1 Faraday does not attribute the entire effect of this startling phe- 
 nomenon to his law, as it would be unscientific to do so. He is, how- 
 ever, fully justified in the inference that it has a great share in the 
 operation.
 
 230 METHODS OF THE PHYSICAL SCIENCES. [B. V. 
 
 the animal system. Thus malaria is accounted for by the 
 tendency in the animal body to absorb those gases rapidly, 
 which are not already contained in the system ; as, for in- 
 stance, carbonic acid and ammonia, the gases which putri- 
 fying bodies exhale. By the same law, the heat and in- 
 toxication consequent on the consumption of spirituous 
 liquors may be attributed to the rapid spread of vapour 
 throughout the system, as the alcohol is driven above the 
 boiling point by the temperature of the stomach. These, 
 with many other explanations of phenomena to which the 
 same law leads, are only so many special cases of its action, 
 and started into being as soon as its acute discoverer began to 
 inquire in what cases the law might be expected to operate. 
 
 Now there is no place in which a new element is so 
 likely to have influence as in those sciences whose subject- 
 matter is of a kindred character, or which manifest phe- 
 nomena of an analogous tendency. Hence it becomes im- 
 portant when a new induction has been established, that the 
 property or law to which it refers should be studied as many 
 ways as possible in connexion with laws which exhibit 
 similar relations. By this method of extension many classes 
 of facts viewed as the nucleus of so many distinct sciences 
 have been merged into each other, and afterwards included 
 in one or two general laws. Thus the class of properties con- 
 templated by magnetism has been resolved into two opposite 
 currents of electricity ; and there can hardly be a doubt that 
 the property of polarity may yet be similarly derived from 
 those of attraction and repulsion, and both in some measure 
 shown to have a direct connexion with gravitation. There 
 is nothing so instructive as this pursuit of the consequences 
 of a new law into cases where its operation is likely to 
 be traced; and illustrations of its successful action may 
 be encountered at every stage of scientific history. Thus, 
 Kepler having ascertained the orbit of Mars to be an 
 ellipse in which the sun was one of the foci, and that the 
 square of the periodical times was proportional to the cube 
 of the distance, sought the same laws in the motion of the 
 other planets, and found that each, together with the motions 
 of their satellites, were only so many additional instances of 
 their operation. By a similar extension of induction to ana- 
 logous cases, Galileo broke down the barrier which Aristotle 
 had erected between the laws of terrestrial and heavenly
 
 0. I. 3.] EXTENSION OF INDUCTIONS. 231 
 
 mechanics, and showed the motions they mutually exhibit 
 were resolvable into the same dynamical forces. Newton 
 had no sooner enounced the principle of gravitation than 
 illustrations of its action were found in every corner of the 
 universe, and every minute particle of matter included in 
 the operation of the same law. In like manner selenium 
 was hardly discovered by Berzelius in the vitriol works of 
 Fahlun, when it presently made its appearance in the subli- 
 mates of Stromboli, and the rare and curious products of 
 the Hungarian mines. And thus it is with every new law 
 and general fact. It is hardly enounced before its traces are 
 found everywhere, and every one is astonished at its having 
 remained so long concealed. 
 
 (3rd.) Since each natural phenomenon is united, through a 
 series of mutually dependent agencies, with every branch of 
 science, there is no induction which, by the outlay of a little 
 sagacity, is not capable of leading to the most important 
 results in whatever direction it may be applied. The laws of 
 light no sooner led to the formation of a correct theory of 
 vision than Kepler explained the functions in that act, of 
 each part of the eye ; and thus prepared the way for the 
 invention of the telescope and microscope, by which the 
 kingdoms of nature were ransacked at both ends, and man 
 endued, as it were, with a new sense to enable him to 
 explore her most minute as well as her grandest operations. 
 If we would, then, extend the boundaries of knowledge, each 
 induction must not only be looked at with a view to obtain 
 exemplifying cases, but also as a certain species of vantage 
 ground from which the unknown in other sciences may be 
 attacked with the greatest prospect of success. The precise 
 relation of each induction to the phenomena which surround 
 its confines, both in its own science and others to which it 
 manifests a direct relation, should be considered, with a view to 
 obtain further insight into their character, as well as instances 
 which extend and illustrate its action. It was owing to the 
 intimate nature which exists between crystalography and 
 optics that the laws of light led to the discovery of the 
 most important qualities of crystalline substances ; and those 
 bodies in turn extended our knowledge of the laws of light, and 
 even in some degree decided the merits of the rival theories 
 concerning its transmission. So true is the remark of Bacon, 
 that no natural phenomenon can be adequately studied in
 
 232 METHODS OP THE PHYSICAL SCIENCES. [B. V. 
 
 itself alone, but to be understood must be viewed in con- 
 nexion with all nature. 
 
 (1st.) Every additional instance of the application of the 
 induction to new cases not originally included in the law will, 
 of course, help as so many distinct illustrations of its truth to 
 verify the correctness of the process by which it was reached ; 
 nevertheless, when the cause or law which it has laid bare 
 assumes the form of an additional instance of a more general 
 cause already well known and recognised, the verification 
 cannot be considered complete until we trace the action of 
 the original cause as modified by the circumstances of the 
 particular case, and prove that the induction is corroborated 
 by the result. Thus the law that salt preserves animal 
 substances from putrefaction by its attraction for water, 
 could not be considered as completely established till Liebig 
 showed the phenomenon was a direct consequent of the 
 necessity of the presence of water to generate the gases 
 thrown off by bodies in a state of decomposition. And in 
 like manner the induction which led the same illustrious 
 chemist to the relative functions performed by the serum 
 and globules of the blood in the act of respiration, was not 
 fully verified until traced deductively from the chemical 
 properties of oxide of iron, the substance which the globules 
 secrete, and proved to be the precise consequences to which 
 those laws lead when modified by the extraneous conditions 
 on which respiration depends. 
 
 (2nd.) But when the law to which we are conducted is alto- 
 gether new, we cannot rely on its enabling us to extend our 
 views beyond the circle of instances from which it has been 
 obtained, unless it has previously enabled us to predict with 
 certainty what will take place in cases analogous to those 
 originally contemplated. In such inductions, therefore, one 
 of the most decisive means of verification consists in the 
 application of the newly-discovered law to extreme cases, 
 with a view to ascertain how far its effect is general. For 
 instance, though there could be no doubt, as Galileo had 
 convinced himself, by allowing various substances of different 
 weights to fall at the same instant from the tower of Pisa, 
 that the accelerating power of gravity is the same on all sorts 
 of bodies, yet as extremely light substances could not be tried 
 on account of the resistance of the air, the law could hardly
 
 C. I. 3.] VEBIFICATION OF INDUCTIONS. 233 
 
 be said to be established in its utmost degree of generality, 
 until the invention of the air-pump had enabled it to be put 
 to the test of an extreme case. A guinea and a feather, then, 
 dropped from the upper part of a glass cylinder exhausted of 
 air, struck the bottom at the same moment, and rendered 
 further doubt on the subject visionary. 
 
 (3rd.) Where the inductions arrived at like those of con- 
 comitant variations belong to that class which require the 
 application of the calculus, their verification cannot be con- 
 sidered complete without every case of trial is one of precise 
 measurement, and without some of the instances chosen are 
 of such a nature as to multiply any deviation till it amount 
 to an appreciable* result. Thus Kepler's three laws of 
 planetary motions were only confirmed in the instance of 
 Jupiter's satellites, by submitting the periodical appearances 
 of these bodies to the test of quantitative laws : nor could even 
 this computation be relied upon, till it was proved that if any 
 deviation existed it must have become apparent in the result. 
 The use of this branch of the verificatory process in har- 
 monising individual inductions with the results to which the 
 higher laws with which they are connected deductively lead, 
 is beautifully exemplified in the mode by which Newton 
 proved that the law of falling bodies, inferred by Galileo, 
 was only another expression of the law to which his theory 
 of gravitation had conducted him ; viz., that the gravity of 
 every material body is in the direct proportion of its mass. 
 Now to ascertain this, a mode of experiment was required 
 which not only neutralised the interference of the air, but 
 also enabled the trial to be made a great number of times 
 without loss or gain in the intervals. The object was accom- 
 plished by inclosing in a hollow pendulum at different times 
 equal weights of the most various substances that could be 
 found, and ascertaining the time required for the pendulum 
 so charged to make a certain number of oscillations. Each 
 substance having to fall and rise successively without loss of 
 time through the same identical spaces, it is clear that any 
 difference that might exist in the time of one such oscillation 
 could not fail to be multiplied and become sensible in the 
 result. But none such having been discovered, the law 
 above stated was considered verified both in respect of ge- 
 nerality and exactness.
 
 234 METHODS OF THE PHYSICAL SCIENCES. [u. V. 
 
 We shall now proceed to illustrate the general principles 
 laid down in this section bj an inquiry into a cause 1 whose 
 incomplete investigation requires the application of the main 
 points on which we have insisted. Such a phenomenon is pre- 
 sented by dew. Now, at the outset of the inquiry, we must 
 precisely determine what dew is, and separate it from rain, the 
 moisture of fogs, evaporation of steam, and other phenomena of 
 a kindred quality, and confine the term to what is really meant ; 
 viz., the spontaneous appearance of moisture on substances 
 exposed in the open air when no rain or visible wet is fall- 
 ing (b. i. c. iii. 1). In the second place, we must search 
 for or endeavour to produce a phenomena identical or pre- 
 cisely analogous to the object of our inquiry (b. v. 2), 
 which occurs, for instance, in the moisture which bedews a 
 cold metal or stone when we breathe upon it; in that 
 which appears on a glass of water fresh from the well in hot 
 weather; in that which appears on the inside of windows 
 when sudden rain or hail chills the external air; in that 
 which runs down our walls when a warm, moist thaw ensues 
 after a long frost. Now all these instances agree in one point 
 (1st meth.), the coldness of the object dewed in comparison 
 with the air in contact with it. But in the case of night- 
 dew, is it a fact that the object dewed is colder than the air ? 
 To ascertain this we need only place a thermometer in con- 
 tact with the dewed substance, and hang one at a little dis- 
 tance above it, out of reach of its influence. The result has 
 invariably decided the question in the affirmative. Whenever 
 an object contracts dew, it is colder than the air (1st meth.). 
 But is this chill an effect of dew or its cause ? That dews 
 are accompanied with chill is a common remark ; but vulgar 
 prejudice would make the cold the effect rather than the 
 cause. We must, therefore, collect more facts, or, which 
 comes to the same thing, vary the circumstances ; since every 
 instance in which the circumstances differ affords a fresh fact ; 
 and note the contrary or negative cases (3rd meth.) . 
 
 Now, in the first place, no dew is produced on the surfaces 
 
 1 See Wells on dew, Herschel's Study of Nat. Phil. p. 159, and 
 Mill's System of Logic, vol. i. p. 491. We have principally followed 
 the astronomer, who has invested Wells's lucubrations with such ele- 
 gant features as might have seduced Plato into a study which he 
 abhorred.
 
 G. I. 3.] WELLS'S THEORY OP DEW. 235 
 
 of polished metals ; but it is produced very copiously on glass, 
 both exposed with their faces upwards, and in some cases the 
 under side of a horizontal plate of glass is also dewed, which 
 last circumstance (2nd rneth.) excludes the fall of moisture 
 from the sky in an invisible form, that would naturally ex- 
 clude the vulgar attribution of the cause. In the cases of 
 polished metal and polished glass, the contrast shows that 
 the substance has much to do with the phenomenon (b. v. 
 2). Therefore, let the substance alone be diversified as 
 much as possible, by exposing polished surfaces of various 
 kinds. The result is a scale of intensity in the phenomenon 
 (5th meth.), those polished substances being found to be 
 most strongly dewed which conduct heat worst ; while 
 those which conduct heat best resist dew most effectually. 
 Here we encounter a law (5th meth.) of the first degree 
 of generality ; but if we expose rough surfaces instead of 
 polished, we occasionally find this law interfered with. Thus, 
 roughened iron, especially if painted over or blackened, 
 becomes dewed sooner than varnished paper. The kind of 
 surface, therefore, has a great influence. Expose then the 
 same material in very diversified states as to surface (2nd 
 meth.), and another scale of intensity becomes apparent ; 
 those surfaces which part with their heat most readily by 
 radiation are found to contract dew more copiously, and thus 
 we obtain (5th meth.) another law of the same generality 
 with the former, by a comparison of two classes of facts, 
 one relating to dew, the other to radiation of heat from 
 surfaces. 
 
 Again, the influence ascertained to exist of substance and 
 surface, leads to the consideration of that of texture (2nd 
 exten.), which presents us with remarkable differences on a 
 third scale of intensity, pointing out substances of a solid 
 texture, as stones, metals, &c., as unfavourable ; but those of 
 a loose texture, as cloth, wool, velvet, and others of a similar 
 class, as eminently hostile to the contraction of dew, and 
 these are precisely those which are best adapted to clothing, 
 since they impede the free passage of heat from the skin into 
 the air, so as to allow their outer surfaces to be very cold, 
 while remaining warm within (2nd exten., 1st verif.). 
 
 Lastly, among the negative instances it is observed that 
 dew is never copiously deposited in situations much screened
 
 236 METHODS OF THE PHYSICAL SCIENCES. [B. V. 
 
 from the open sky, and not at all in a cloudy night ; but if 
 the clouds withdraw even for a few minutes, and leave a clear 
 opening, a deposition of dew presently begins, and goes on 
 increasing. Here, then, a cause is distinctly pointed out by 
 its antecedence to the effect in question (2nd meth.). A 
 cloudless sky is, then, an essential condition, or, which comes 
 to the same thing, clouds or surrounding objects act as 
 opposing causes. This is so much the case, that dew formed 
 in clear intervals will even evaporate again when the sky 
 becomes thickly overcast (2nd exten., 1st verif.). 
 
 Assembling all these partial inductions, with a view to 
 raise from them a general conclusion, it may be observed 
 that all the inferences we have made point to that first 
 general fact the cooling of the exposed surface of the body 
 dewed below the temperature of the air. Those surfaces 
 which part with their heat outward most readily, and have it 
 supplied from within most copiously, become coldest if there 
 be an opportunity for their heat to escape, without being 
 restored to them from other objects. Now a clear sky affords 
 such an opportunity. It is a well-known law, that heat is 
 constantly escaping from all bodies in rays, or by radiation, 
 but is as constantly restored to them by the similar radia- 
 tion of surrounding objects (1st verif.). Clouds, therefore, 
 act as opposing causes, by replacing the whole, or a great 
 part, of the heat so radiated away, which can only escape 
 without being replaced through openings into infinite space 
 (1st verif.). Thus, at length, we arrive at the general proxi- 
 mate cause of dew, in the cooling of the dewed surface by 
 radiation faster than its heat can be restored to it by com- 
 munication with the ground, or by counter-radiation, so as to 
 become colder than the air, and thereby to cause a condensa- 
 tion of its moisture. 
 
 Thus the inquiry may be said to terminate by resolving 
 the laws of the phenomenon into two more general laws, viz., 
 the radiation of heat and the condensation of invisible vapour 
 by cold, which become in turn capable of similar investigation 
 and resolution into phenomena of wider generalisation. The 
 laws of radiation had, however, been previously established, 
 and received no new confirmation by the explanation of this 
 theory, which, indeed, they only tended to explain (2nd verif.) : 
 and the condensation of invisible vapour by cold had already
 
 C. I. 4.] STTMMAKY OF INDUCTION. 237 
 
 become a portion of physical inquiry. Thus, the explanation 
 of the laws of nature only lead to the resolution of a sensible 
 knot of complicated effects into others more simple but less 
 known, and so far only substitutes for a mystery which has 
 become familiar, a phenomenon still more strange. To ex- 
 plain natural laws means nothing more than to assign other 
 laws of a higher character, which, modified by peculiar circum- 
 stances, will lead to the particular consequences they include. 
 
 4. General Outline of the Inductive ^Method. Difficulties 
 and Limits Attending the Application of its special Canons. 
 
 From the example already given of Dr. Wells' s theory of 
 dew, may be obtained a correct idea of the relative functions 
 of the different rules of induction, and the mode in which 
 they generally combine in interweaving the partial inferences 
 of which the texture of scientific evidence is composed. The 
 process may be summarily collected under the following heads : 
 1st. The obtaining a precise idea of the nature of the thing 
 whose cause we are in search of, by separating it from 
 subjects which exhibit a superficial resemblance to it. 2nd. 
 The collection and examination of every instance that seems 
 to bear upon the inquiry, including those which manifest the 
 property in question, as well as kindred instances in which 
 the property is not produced. 3rd. The variation of these 
 instances, to reveal the law which they suggest as the proxi- 
 mate cause, or the artificial production of others calculated 
 to accomplish the same purpose. 4th. The connexion of 
 such law with others of which it may happen to prove a 
 special instance, or the pursuit of it into individual cases, 
 with a view to ascertain if it rationally accounts for the 
 peculiarities they manifest. Any law which concentrates 
 within itself the united evidence of such an investigation, 
 must be accepted as the real proximate agent of the pheno- 
 menon for which it accounts. 
 
 Hence it will be observed, that no single method is 
 ever sufficient by itself to raise a law of high degree of 
 universality. In the examination of instances where the 
 law inquired into is modified by extraneous circumstances, 
 each method is competent to draw whatever induction 
 seems warranted by the circumstances of the case ; but since
 
 238 METHODS OF THE PHYSICAL SCIENCES. [u. V. 
 
 a law of any degree of generality embraces several of such 
 inductions, the evidence by which it is established must in- 
 clude and harmonise all the methods, otherwise the law is liable 
 to be overset, through covering more ground than its founda- 
 tions are warranted to support. In the investigation of 
 some physical laws, however, one method is more available 
 than another, and that to a greater or less degree, according 
 as the nature of the concomitant circumstances admit of their 
 action. These laws it will be necessary to point out, with their 
 correlative methods, and the limits which some branches of 
 physical science oppose to their action even on the threshold 
 of investigation. 
 
 The methods of induction explained in the last section 
 proceed upon the assumption that every effect is so con- 
 nected with a constant proximate cause, that it is impossible 
 to meet with an instance of divorce between them ; so that we 
 may always infer, from the presence of the effect, the opera- 
 tion of the same cause we have previously assigned to it. 
 Now we have already had occasion to observe, that this is by 
 no means universally the case. The same effect may, and 
 often is, generated by different proximate causes, especially 
 where its nature is the result of many compound conditions 
 as death, motion, heat, moisture, &c., and this in so remark- 
 able a manner, that the producing agents which alternately 
 concur in the creation of the same property are frequently of 
 a very dissimilar and heteroclite character. What conditions, 
 for example, can be so various and changeable as those on 
 which heat depends ? It may be produced by friction, by 
 electricity, by percussion, by chemical action, and the pre- 
 sence of the sun. To argue, therefore, from the sensation of 
 heat, that any single one of these agents were, or had been, 
 occupied in its production, would be illusory in the extreme 1 . 
 
 1 An error which Mr. Mill accuses Bacon with committing in his in- 
 quisition into the cause of heat. We do not think Bacon's mistake lay 
 exactly where this distinguished logician places it. Bacon attempted 
 to trace the different sources of heat to one common law. So far his 
 investigation was scientific; hut he entered on the task before ac- 
 counting for the effects of the different proximate causes which pro- 
 duced it. Here lay his error, as we are not privileged to merge minor 
 causes into higher generalisations before ascertaining their special laws. 
 Mr. Mill says Bacon was wrong in seeking for an ultimate cause which 
 might have no existence. But if this censure be worth anything, it 
 would bastardise every attempt at scientific analysis.
 
 C. I. 4.] INTEBFEBENCE OF PLUBAL CAUSES. 
 
 We do not hazard the assertion that each of these proximate 
 causes of the phenomena may be resolvable into one common 
 property on which they ultimately depend, or that effects 
 generally, which are dependent on different proximate causes, 
 may not likewise be traced back to one source. Of ultimate 
 causes, as such, science takes no account : she is entirely occu- 
 pied with proximate ones, and since a variety of these may 
 lead to one common effect, it becomes important to consider 
 how this uncertainty affects her methods. 
 
 It is obvious that when one effect has a plurality of 
 causes, the method of agreement must be put out of court, 
 since we could not infer from the bare presence of a constant 
 antecedent in the instances we had examined, that it alone 
 had generated the single invariable consequent which accom- 
 panied it. But no other method is invalidated by it, at least 
 in the single inductions we make concerning each special 
 case. For if the constant effect varies exactly according to 
 a direct ratio with the accompanying antecedent, or if we can 
 produce two instances which differ alone in the absence or 
 presence of the assigned cause, we need no further evidence 
 that the antecedent produces the effect in the case in 
 question. We can, indeed, proceed further, and generalise 
 the inference, predicting that wherever the conditions are 
 which we have discovered, the same effect must follow, though 
 we cannot reverse the statement, and affirm the ubiquity of 
 the cause with the effect. In cases where the plurality of 
 the cause is doubtful, what amount of experience will warrant 
 us to venture the latter prediction must be a consideration 
 for a subsequent section. 
 
 But as the operations of nature are characterised by eco- 
 nomical simplicity, diversity of cause is by no means the 
 ordinary rule, and the uncertainty with which it surrounds 
 the application of the first method can easily be dissipated 
 by a proportionate multiplication and diversity of instances. 
 It is no more possible that a single antecedent discovered in 
 a crowd of most dissimilar cases should be attended with a 
 constant invariable antecedent without a causal tie between 
 them, than it would be for the same antecedent to vary in 
 direct proportion with the same consequent, amid a number 
 of unvariable phenomena without connexion with it. Such 
 an element of doubt, therefore, only requires the method of
 
 240 METHODS OF THE PHYSICAL SCIENCES. [B. V. 
 
 agreement to rest upon a proportionally greater number of 
 cases than any of the others, in order to invest the results to 
 which it leads with the same amount of scientific value. 
 
 The consideration of the different modes in which causes 
 compound their effects, will help us to further distinctions 
 with regard to the use of these methods, and conduct us to 
 the limits of inductive inquiry. This composition resolves 
 itself into two branches, each of which are in some measure 
 co-extensive with chemistry and mechanics. "When one 
 effect is compounded of many causes, the result either mani- 
 fests itself in a composition or mixture of the individual 
 causes which enter into it, or leads to the formation of a new 
 substance, having no analogous properties with the elements 
 from which it sprung. For example, in the case of motion, 
 if a body is propelled by two forces meeting it in transverse 
 directions, it will describe the diagonal of a square, and be 
 conducted to the precise point it would have reached had it- 
 been acted upon by the two forces separately. Hence, in 
 this branch of the subject, if we happen to know the effects 
 of the separate causes we can arrive deductively or a priori 
 at a correct knowledge of the effect that will result in any 
 given case from their conjunct agency. In the chemical 
 branch of the subject the composition of causes is attended 
 with results of an opposite character. If potash and tartaric 
 acid be mixed together in certain proportions, instead of 
 obtaining a mere mixture composed of the joint properties of 
 both, we obtain a solid saline substance quite different from 
 either potash or tartaric acid, and not betraying any sensible 
 mark to lead to their distinction. Not a trace of the original 
 properties is to be discovered in the compound result. This 
 explains why mechanics is a deductive or demonstrative 
 science and chemistry is not. In the one, we can compute 
 the effects of all combinations of causes, both actual and 
 possible, from the laws which govern those causes when 
 acting separately. In the other, we are left entirely to 
 experiment, every induction terminating with the peculiar 
 combination which led to it : nor can it include other 
 combinations in any generalisations until assured by expe- 
 rience of the actual truth of the facts whose recurrence under 
 certain conditions it predicts. 
 
 Now, of these compound effects, those which follow
 
 C. I. 4.] TWOFOLD COMPOSITION OF CAUSES. 241 
 
 chemical laws are the most easy to investigate by the direct 
 methods of induction ; owing chiefly to the simplicity of their 
 development, which arises from their ceasing to carry into 
 the complex result the properties of the different causes 
 which produced them. They appear, like ultimate properties, 
 disinvested of the involuted web of causal agencies, and 
 present marks so characteristic, that their presence cannot 
 fail to be distinguished among a crowd of surrounding phe- 
 nomena. The methods of induction consequently can meet 
 with no other difficulty in their solution than the failure 
 of instances to reveal their causes present, or the absence of 
 artificial experiments to produce them. On the other hand, 
 in mechanical composition the effects of the separate causes 
 do not terminate and cease to form any part of the phe- 
 nomena to be investigated, but carry their results onward 
 until they intermingle with the homogeneous effects of other 
 causes. They are no longer simple integers existing in a 
 distinguishable shape, but appear as insoluble quantities, 
 some of which cancel one another, while many others merge 
 into one sum, forming altogether a result, between which 
 and the causes that produced them, observation is often in- 
 competent to trace any fixed relation whatever. Moreover, 
 it is a common feature of these laws to have their causes 
 counteracted, and exhibit no marks of action in many cases 
 where they have spent their full effects. If two equal forces, 
 for example, act upon a body in lines diametrically opposite, 
 the body so impelled does not manifest the slightest tendency 
 to motion, but remains where it was, notwithstanding the act- 
 ing forces have each produced its own quantum of effect. Or 
 if a force act upon a body which it is unable to move, we do 
 not perceive any result proceeding from the operation of such 
 force, although an effect has been produced in the tendency 
 of the particles of the passive body to move in the direction of 
 the impulsive force. But how can we expect to find the law 
 of a tendency by an induction from cases in which the ten- 
 dency is counteracted? Could the laws of motion have 
 ever been brought to light from the observation of bodies 
 kept at rest by the equilibrium of opposing forces ? In this 
 department of science the inductive methods are obviously 
 inapplicable : we have no other resource than to study the 
 effects of each cause separately, and to infer, by deductive 
 
 B
 
 242 METHODS OE THE PHYSICAL SCIENCES. [B. V. 
 
 reasoning, the result that must eventuate from their combi- 
 nation in any given case. Happily Dynamics, which embraces 
 the greatest branch of the latter kind of causal composition, 
 is so far independent of the ^inductive methods as to have 
 reached its highest generalisations, and to lack nothing in 
 their application to particular facts, by the deductive method, 
 than a further simplification of mathematical analysis ; while 
 the remaining branches, which play a great part in every 
 science except chemistry and physiology, depend in a great 
 degree on the experimental methods only, with a view to 
 obtain accurate data to justify and extend the use of the 
 descending scale of inference. 
 
 And even in the two sciences just mentioned, there are 
 many phenomena which are amenable through a similar com- 
 position for causes to the same method, and the tendency 
 which chemistry and physiology manifest to multiply laws 
 of this kind leaves us not without a hope that they are 
 destined one day to become deductive. Though it would be 
 of course impossible to deduce all chemical and physiological 
 truths from the laws or properties of simple substances or 
 elementary agents, it is by no means difficult to believe what 
 the general analogy of these sciences already points out, that 
 such particular truths may be deduced from the laws which 
 ensue when these elementary agents are brought together 
 into some moderate number of simple combinations. The 
 great law of definite proportions already has discovered a 
 certain relation between the quantities of a compound and 
 those of its elements, which enables us to predict, provided 
 our data be accurate, the exact proportion in which two sub- 
 stances will combine before actual trial. And we are already 
 in possession of some particular generalisations which indicate 
 the possibility of forecasting similar results in relation to the 
 qualities of compounds. We have also the law of isomor- 
 phism already alluded to, and the curious fact revealed by 
 Berthollet, that two soluble salts mutually decompose each 
 other, whenever the new combinations which result produce 
 an insoluble compound, or one less soluble than the two 
 former pointing in the same direction. In like manner the 
 complicated phenomena of life may all be deducible from 
 comparatively simple laws, which, though depending upon 
 certain combinations of antecedents, may in more complex
 
 C. I. 5.] THE DEDUCTIVE PBOCESS. 243 
 
 circumstances be strictly compounded with one another, 
 and with the physical and chemical laws of the ingredients. 
 The details of the vital phenomena even now afford innu- 
 merable instances of the composition of causes ; and in pro- 
 portion as their laws are accurately studied, there is every 
 appearance that more facts will be brought to light which 
 will connect complex cases with higher generalisations, and 
 legitimate a further extension of the deductive element. 
 
 Here we have arrived at a perfect type of those cases in 
 which the inductive methods can be of little service, where 
 an unknown multitude of clashing and combining agencies 
 being engaged in the production of one phenomenon, require 
 the aid of instruments to unravel, more subtile and diversified 
 in their application, more potent and decisive in their results. 
 In the physical sciences such are supplied by the calculus in 
 its deductive range, and the ratiocinative process ; but these 
 cannot be applied unless experience furnish them with suffi- 
 cient data on which to proceed, or unless, in case of the data 
 being assumed, the result can be brought to the touchstone 
 of facts, and clearly shown to accord with their actual 
 combinations. In proportion as the experimental sciences 
 display similar effects and allow their various conjunct 
 results to be traced back, and, consequently, deduced from 
 the separate action of the simple agencies of which they are 
 composed, do they become deductive and amenable to the 
 highest processes of generalisation. 
 
 5. Nature of Scientific Deduction. Formation and Veri- 
 fication of Theories. 
 
 "We have already alluded to the employment of the de- 
 ductive method as essential to the verification of single 
 inductions when the law they reveal is found to be a mere 
 exemplification of a higher law acting in combination witli 
 peculiar circumstances. Two cases in point occur in the 
 inductive process which led Dr. "Wells to his theory of dew. 
 It is a law, for example, that moisture which falls from the 
 sky never appears on the under surface of substances ; so that 
 the theory would be materially confirmed if an instance of dew 
 could be brought which shut out that law as an acting prin- 
 ciple. Such an instance was produced in some horizontal
 
 METHODS OP THE PHISICAL SCIENCES. [B. V. 
 
 plates of glass with, their under surfaces dewed to the exclu- 
 sion of the upper, which enabled Dr. Wells to infer that the 
 fall of moisture from the sky could not have produced the 
 phenomenon in question. Again, it is a well-known law that 
 heat is continually escaping from all bodies by radiation, but 
 is as constantly restored to them by similar radiation from 
 surrounding objects. Now, if dew was caused by such a 
 modification of this law as the theory purported, it is clear 
 that in places where the sky was overcast and the neighbour- 
 hood much sheltered from the influence of the atmosphere 
 little or no dew could be deposited ; an inference borne out 
 by actual observation, for dew is never copious in situations 
 much screened from the open sky, and does not appear at 
 all in a cloudy night. Hence the theory harmonised with 
 the deductive inference to which the law led, and strengthened 
 the series of partial inductions that pointed to it as the 
 operating cause. 
 
 Hence it will be seen that the inductive and deductive 
 methods are closely blended together in the successful pro- 
 cess of scientific inquiry. We cannot establish, even by 
 induction, any law of a moderate degree of generality 
 without the assistance of its correlative method, nor can we 
 proceed in the scale of descent unless the data from which 
 we set out have been at some stage or other guaranteed by 
 preceding inductions, except, indeed, we reason hypotheti- 
 cally, in which case the result will have to be verified by 
 induction from the actual instances to which it leads. Thus 
 Dalton could not have inferred that a complete combination 
 between two elementary substances in chemistry would 
 ensue when their weights were found in a certain definite 
 proportion, unless by the method of agreement the law had 
 been previously ascertained to occur in a sufficient number of 
 instances to place its universality beyond the pale of doubt ; 
 nor could Newton have identified the central force of the solar 
 system with terrestrial gravity without proceeding from a law, 
 which, though proximately the fruit of a deductive process, 
 could not have been received unless verified by facts based 
 on the inductive method. The fact that the earth attracted 
 the moon with a force varying according to the inverse 
 square of the distance, and the proof that this would cause the 
 moon to fall, were that luminary at no greater distance from
 
 C. I. 5.] UNION OF INDUCTION AND DEDUCTION. 245 
 
 the earth's surface than terrestrial bodies, with a rapidity 
 precisely equal to the increasing ratio of their velocities, 
 could not have helped Newton to his object unless he had 
 previously ascertained that the sun attracted the planets with 
 the same force as the earth attracted the moon, by showing 
 not only that the force in question led at once to the in- 
 ference of Kepler's laws, but that no other supposition could 
 lead to them. Thus, the path by which we rise to know- 
 ledge must be often ascended and descended before we can 
 scale our way to any eminence, much less reach the summit. 
 No great principle can be reached by a single eifort, or by 
 confining ourselves to one method. In every science sta- 
 tions must be established, and communications kept open 
 between all well ascertained truths of law, that minor facts 
 may be verified by the higher generalisations to which they 
 lead, and the correctness of hypothesis decided by an appeal 
 to inductive laws. 
 
 There is, consequently, no necessary opposition between 
 deduction and induction. Both are essential steps in the 
 process by which any law is reached of moderate generality : 
 nor is there any reason why the physical sciences should be 
 called inductive rather than deductive, unless, indeed, that the 
 former element generally predominates at the earlier stages 
 of their progress. The sciences, however, which have not got 
 beyond their infancy, are correctly designated experimental, 
 by way of contrast to that branch of physics with which deduc- 
 tion is principally concerned, simply because they include no 
 cases of laws sufficiently general to admit of extensive ratio- 
 cination, and are consequently dependent on observation and 
 experiment for new accessions to their store of truths. But 
 in proportion as conclusions can be drawn in such sciences 
 respecting cases of a new kind, by processes which bring those 
 cases under old inductions, do they become deductive, and are 
 open to receive the aids attendant on this method. Thus, 
 when Kepler announced his three laws of planetary motions, 
 astronomy could not be called deductive. The laws them- 
 selves pointed to no inference below them, unless movement 
 in an elliptical orbit a fact already ascertained by the in- 
 ductive process which led to them. For the rest, they left 
 the science where they found it ; a mere mass of descriptive 
 and statistical details, without any common bond or con-
 
 246 METHODS OF THE PHYSICAL SCIENCES. [fi. V. 
 
 necting principle "between them. But when Newton showed 
 that Kepler's laws were only partial inferences of a centripetal 
 force, varying directly as the mass, and inversely as the square 
 of the distance from the central power, he linked together a 
 host of particular inferences, and established a principle which 
 ultimately contributed to identify terrestrial with celestial 
 gravity, and to account for all the motions, whether regular 
 or anomalous, of all the bodies of the solar system. Astro- 
 nomy, consequently, became at once eminently deductive: 
 an arch was raised high in air which connected all the in- 
 ferior stations which had been established, with the highest 
 point of ascent. In the sweeping application of this prin- 
 ciple to the deductive range of inference, no fact was left 
 without its law, and no law but what became included in its 
 wider proximate generalisation. Chemistry, on the other 
 hand, though pointing to results which seem to promise a 
 great extension and simplification of its complex laws, is still 
 an experimental science, and is likely so to remain until 
 some comprehensive principle like Newton's shall bridge 
 over a vast number of the smaller inductions, and connect 
 them through intermediate links with its most extensive 
 inferences ; a principle, in a word, which should enable us 
 to foresee the result of any new combination of elements 
 previously untried, and to dispense with actual analysis in 
 pronouncing at sight upon the ingredients of any new com- 
 pound submitted for inspection. 
 
 It is at this stage of the sciences, when they are throwing 
 off their experimental character, that the principles of number 
 and geometry are instrumental in widening their bases and 
 imparting to them the simplicity and generality of their 
 methods. When laws act according to some numerical 
 quantity, or their effect takes place in space, and consequently 
 involve motion and extension ; or when they exhibit variations 
 of qualities, in exact correspondence to variations of quantity, 
 the reasoning by which they are carried down to their indi- 
 vidual limits may include among their premises all the 
 theorems of mathematics from common arithmetic up to the 
 calculus of variations. The application of such laws to particu- 
 lar objects consequently becomes multiplied in a proportionate 
 extent, and since the truths of number already ascertained 
 appear infinite, there seems no boundary to the extension of
 
 C. I. 5.] LEGITIMATE USE OF HYPOTHESES. 247 
 
 those sciences which admit of their influence but the intricacy 
 of the problems to which the expression of their data lead. 
 The prolific generation of new truths, which proceeds from the 
 conjunction of a science already deductive with so potent an 
 agent as number, may be witnessed in the indefinite exten- 
 sion of the axioms of geometry, as soon as it was observed 
 by Descartes and Clairaut, that every variety of position in 
 points, directions in lines, or forms in curves or surfaces 
 corresponded with a peculiar relation of quantity between 
 one or two rectilineal co-ordinates in such a manner, that, if 
 the law were known according to which those co-ordinates 
 vary relatively to one another, every other geometrical pro- 
 perty might be inferred relating to the quantity or quality of 
 the line or surface in question. Thus it resulted that the 
 axioms of geometry were taken out of mere lines and figures, 
 and made co-extensive with the range of algebraical analysis, 
 receiving an accession actual or potential of new truths cor- 
 responding to every property of numbers which the progress 
 of the calculus had discovered or might in future bring to 
 light. 
 
 To legitimise the use of this instrument, however, and to 
 allow free scope for ratiocination, it is obvious, where par- 
 ticular results are to be investigated, that the general 
 principle must rest on prior inductive or deductive evidence, 
 or at least be the fruit of a well matured hypothesis, whose 
 consequences are able to be tested by a direct appeal to facts. 
 Lagrange, for instance, could not have been warranted to 
 deduce all the known properties of sound from the laws of 
 the propagation of motion through an elastic medium, unless 
 it had been previously established by experiment, that every 
 variety of sound was consequent upon a distinct and definable 
 variety of oscillatory motions among the particles of the air. 
 Where such preliminary principle is not reached, we may 
 indeed assume one, but the details of the hypothesis must 
 not only be shown to accord exactly with all the facts which 
 it presumes to explain, but it must likewise be proved that 
 no other supposition could account for them. Thus it would 
 not have been competent to Newton to assume that the moon 
 was drawn to the earth by a force varying as the inverse 
 square of the distance, simply because that ratio would allow 
 him to accoun for the falling velocity of terrestrial bodies by a
 
 248 METHODS OF THE PHYSICAL SCIENCES. [B. V. 
 
 similar attraction and identity of gravity with the central force 
 of the solar system. For in that case, he could not subse- 
 quently have proved that no other supposition of a force was 
 able to account for the law in question, save one extending to 
 the moon, and proportional to the inverse square. In the 
 proof, however, of the existence of the centripetal force, 
 varying in the same ratio, the assumption with which he 
 set out, viz., that the force which deflects a planet from its 
 rectilineal course and makes it describe a curve round the 
 sun, is a force tending directly towards the sun, was per- 
 fectly legitimate. For he not only demonstrated that the 
 hypothesis which the nature of the phenomena had suggested 
 led by direct deduction to the inference of Kepler's laws, 
 but he also proved that no other supposition could lead to 
 them. Now Kepler's laws were facts resting on the strongest 
 inductive evidence. The case, therefore, was completely made 
 out, and the hypothesis became a law established by the 
 method of difference. 
 
 Owing to the limited extent of the resources on which the 
 inductive processes depend, there is no greater instrument 
 for the discovery of scientific truths than the formation of 
 legitimate and well matured hypotheses. They allow pure 
 reason to wing its flight through the realms of science eman- 
 cipated from a servile attendance on facts, and to assert its 
 prerogative over them by interweaving on its way that mul- 
 tiplied and ever diverging thread of argument, through which 
 a few inductions are connected with a labyrinth of laws, and 
 nature coerced to reveal her mysteries, not one by one as in 
 the case of tardy experiment, but to surrender up hosts at 
 once as under the talismanic spell of a superior spirit. But 
 in order to effect this object, the law must be so completely 
 made out as to render it impossible, consistently with pre- 
 vious inductions, for any other theory to be true. Reason 
 must not do her work by halves. She must show that out 
 of all possible suppositions which the case admits of, the 
 theory which she produces, is the only one that exactly fits 
 into the exact frame of the phenomena involved in the 
 inquiry. Now this can hardly be, unless we have good 
 grounds for the belief that the causes which the hypothesis 
 assumes actually exist in nature, and perform a part in 
 phenomena analogous to the laws we would render an ac- 
 eount of. Thus, Newton correctly assumed that the planets
 
 C. I. 5.] FUNCTIONS OP HYPOTHESES. 249 
 
 were attracted towards the sun by a force exerted in the 
 centre of their orbits ; for, in every instance of similar 
 motion around him, of slung stones, of balls, or wheels re- 
 volving round a fixed point, he never failed to observe a 
 material tie existing in that direction, and could not imagine 
 that the bodies in question were retained in their circles by 
 any other force. The hypothesis consequently involved what 
 he designated a vera causa, or really existing cause producing 
 effects in nature similar to the phenomena he contemplated, 
 and limited the range of admissible suppositions to the 
 various possible numerical relations between the variations of 
 the distance and the variations of the attractive force. But 
 when Descartes ventured to explain the planetary movements 
 by the supposition of vortices acting in accordance with the 
 known laws of rotatory motion, he attributed a series of 
 effects to a cause which not only produced no analogous 
 instance in nature, but whose existence could in no single 
 case be demonstrated. Fictitious or random suppositions, 
 even if they coincide with fact, cannot be supposed to ex- 
 plain them. The inferences to which they lead, though, ever 
 so plausible, will partake of the doubtful character of their 
 origin, and as long as nature refuses to decide upon their 
 existence, no striking illustration of their coincidence with 
 actual facts can furnish more grounds for belief in their 
 reality than a vague probability 1 . 
 
 It is not, however, to be inferred, because we know of no 
 case in which the cause assigned by the hypothesis produces 
 the effect in question, that the supposition must be thrown 
 away as idle, or regarded as absolutely incapable of being 
 transformed into actual reality. Nature works so secretly, 
 and produces even similar effects by agents occasionally so 
 novel and diverse, that it would be the height of presump- 
 tion to suppose that she could not operate by other causes 
 than those of which we were already cognisant, and that 
 the augmentation of future coincidences between the doubt- 
 ful agent and the visible effects might not at some future 
 stage transform the alleged hypothesis into fact. Even if 
 this desirable result should not happen, yet if the hypothesis 
 enables us to group together several laws under wider gene- 
 
 1 These remarks may appear trite, but we refer the reader to b. i. 
 c. iii. 4 for the baneful influence which such visionary hypotheses 
 have exercised over science.
 
 250 METHODS OF THE PHYSICAL SCIENCES. [B. V. 
 
 ralisations, and sets experiment to work by suggesting 
 modes of action analogous to what obtains in similar cases, 
 it can hardly fail to promote the purposes of science, by 
 bringing to light many facts which would have lain concealed 
 were it not for the presumed proximate causes or ana- 
 logies it had pointed out. The undulatory theory of light 
 is one of the most favourable instances of hypotheses of this 
 character. Considering the manner in which this theory 
 ascribed the transmission of light to the vibratory motions of 
 an elastic ether, Dr. Young was led to infer, from an analogous 
 property of the transmission of sound through a similar 
 medium, the beautiful law already adverted to of the inter- 
 ference of the rays of light. But it is not to be lost sight of, 
 notwithstanding this theory very plausibly accounts for all 
 the known properties of light (and might consequently be 
 supposed, should it not prove an actual statement of the 
 proximate causes of optical phenomena, to be in some manner 
 connected with them, or at least to run so close a parallel 
 with them as to admit of some expression common to both), 
 that the Newtonian theory, which sets out from an opposite 
 point of view, is capable of rendering a no less rational 
 account of all the facts embraced by the same science, if we 
 admit the very reasonable supposition advanced by M. Biot, 
 of a rotatory motion of the particles of light about their axes. 
 These apparent agreements and clashing discrepancies ought 
 to make us extremely chary in placing any strong reliance on 
 theories, and refuse to regard any hypothesis as legitimate, 
 at least where a cause is to be investigated, unless the cause 
 assigned be already known to produce the effect in question, 
 in which case the supposition will be limited to the precise 
 mode of the dependence ; or, in other words, to the exact 
 law according to which the effect varies with variations in the 
 quantity of, or in relation to the cause. 
 
 It may happen, indeed, that the supposition do not relate 
 to causation, but only to the law of correspondence between 
 facts, which being effects of one common cause, accompany 
 each other in a certain fixed proportion. But as the laws of 
 such variations are always open to precise measurements, 
 there is no difficulty in bringing any hypothesis concerning 
 them to the touchstone of facts, and thus pronouncing on 
 their reality. It was known, for example, that the direction
 
 C. I. 0.] HYPOTHESES WHEBE INAPPLICABLE. 251 
 
 of the line of refraction varied in a certain proportion with 
 that of incidence, but the different false hypotheses by 
 which Kepler sought to discover the law of the variation, 
 were cast aside as soon as they were brought to the test of 
 measurement, and none subsequently framed stood its ground 
 for the same reason, until Willebrod Snell pointed out the 
 angular proportion of the two rays, and M. Fresnil showed 
 the law, together with that of the deviation of the extraordi- 
 nary refracted ray, were necessary inferences from higher 
 generalisations of an indisputable character. 
 
 We need hardly say that it is indispensable to the two con- 
 ditions already enumerated for transforming hypotheses into 
 correct exponents of general laws, that they coincide with all 
 the observed facts and inductions previously known which 
 those laws include. Hence the comparison of the inferences 
 to which they deductively lead, with the mass of established 
 truths which every important theory embraces, is one of 
 the most secure means of their verification. When the 
 cause assigned by an hypothesis is already known to produce 
 similar effects to those attributed to it, and is found to agree 
 with all the facts included in its generalisation, it can hardly 
 fail to be true, especially if the previous inductions arrived at 
 be of a very diverse character. In such case the hypothesis 
 will rest on the method of agreement, and the number of in- 
 ductive inferences which it meets, will, therefore, be required 
 to spring from such different quarters as to place it beyond 
 doubt that any hypothesis, bearing the character of a vera 
 causa, could fit them without being the actual agent in ques- 
 tion. 
 
 Hypotheses, however, are not available in all subjects. In 
 many the general principle to be reached can only be gained 
 by ascending inductively from the minor to the more general 
 laws which it includes ; which ascent is not without its ad- 
 vantage in enabling us to perceive how laws which we had 
 previously regarded as unconnected become particular cases, 
 either one of the other, or each of one still more general, and 
 at length blend all together in the general principle, which 
 is the object of our search. If chemistry ever pass the limits 
 of an experimental science we fear it can only be by a process 
 analogous to this. The proximate generalisations in which 
 its complex laws are now commencing to resolve themselves
 
 252 METHODS OF THE PHYSICAL SCIENCES. [B. V. 
 
 are so unlike any agents which we could have suggested a 
 priori, as to make the use of hypothesis on any large scale in 
 this science visionary in the extreme. "Where the principles 
 of a science are peculiar to itself, and exhibit no analogous 
 laws, or facts to other sciences whose agents are more 
 thoroughly understood, the condition of hypothesis is despe- 
 rate. We have no choice hut to proceed in tardy gradation 
 and toilsome ascent from law to law, until we trace out a 
 general principle that will allow ratiocination its deductive 
 range. 
 
 It must, in fine, be noted, that in all cases of reasoning 
 from general theories, whether obtained by the inductive or 
 hypothetical process, every step of the ratiocination must be 
 verified, if possible, by an appeal to facts ; since, even should 
 the theory prove true, an error committed in pursuing it into 
 detail would of course lead to wrong inferences, and inva- 
 lidate the general statement in which it was expressed. An 
 apposite illustration of the necessity of this step is to be found 
 in Newton's Theory of Sound, which, although accounting 
 correctly for the general principle, and leading to a numerical 
 conclusion for the actual velocity of sound which agreed in 
 general respects with reality, yet was found defective in an 
 essential point when Lagrange looked more closely at the 
 facts, owing to one or two important considerations being 
 overlooked by his predecessor in pursuing the subject into its 
 minor details. Hence, it is indispensable to the secure com- 
 pletion of the deductive inferential process, that all the de- 
 tails to which it leads should be verified by an extensive com- 
 parison with observed facts. 
 
 6. Empirical Generalisations ; Theory of Probability ; 
 and Analogical Evidence. 
 
 So far we have considered the methods by which concealed 
 laws, or universal propositions, admitting of no exceptions, 
 are hunted out and demonstrated: but in addition to the 
 positive truths, of which natural philosophy is constituted, 
 there are a large class of irregular occurrences in nature that 
 depend on causes so variable and uncertain as to incapacitate 
 science either from pronouncing on their anterior conditions 
 or predicting their return in any determinate instance. These
 
 C. I. 6.] USE OF PROBABLE GENEBALISATIOITS. 253 
 
 it is necessary to invest with as much scientific certainty as 
 the case admits of. Though we cannot reclaim them entirely 
 from the dominion of doubt, we may, nevertheless, ascertain 
 the precise extent to which they are to be trusted : and, in 
 many instances, raise important conclusions from them of a 
 practical nature. 
 
 The most favourable of these cases meet us in the shape 
 of phenomena, whose concomitant occurrence is so frequent 
 as to warrant the inference of some antecedent connexion 
 between them, without affording us any secure ground for 
 affirming the manner of its existence. Thus, the fact that most 
 dark-eyed persons have dark hair; that most Swedes have light 
 complexions ; that most stratified formations contain fossils ; 
 that most mineral springs possess salt, and other coincidences 
 of a similar character, being the effects of latent conditions 
 which are liable to be marred in particular cases by uncertain 
 laws, do not present any ground on which science can erect 
 a proposition of more than probable universality, The time 
 may arrive when the condition, both of their occurrence and 
 failure in every known case, will be traced to the action of 
 laws of a distinctive character. At least, the present advance 
 of science is raising many similar coincidences out of the 
 category of empirical generalisations, to the rank of scientific 
 truths : but as fast as science proceeds in this direction it 
 brings to light other coincidences of like nature ; so that it is 
 never likely the philosopher will lack occasion to apply them 
 in evidence, or that cases will not continue to occur in which 
 they alone will constitute the only landmarks by which he 
 can guide his way. 
 
 Now, it is obvious that until the conditions on which sucli 
 coincidences depend are in whole or part laid bare, that we 
 can place no further reliance on them than simple experience 
 warrants. If we have observed that nine Swedes out of every 
 ten have light complexions, the probability that the next 
 Swede we meet will possess that feature will of course 
 be in the same proportion. There are, however, some em- 
 pirical generalisations whose anterior conditions are in 
 some degree known, and whose truth, therefore, admits of 
 prediction from another source. Tor example, it may be 
 ascertained that most Prussians are arithmeticians, not only 
 from personal observation and the reports of travellers, but
 
 254 METHODS OF THE PHYSICAL SCIENCES. [B. V. 
 
 also from the fact of government schools existing in that 
 country, to which every parent is obliged to send its offspring 
 for a certain period, and in which the science of number is 
 taught. The approximation to universality may consequently 
 be easily calculated, without depending on a single result of 
 experience, by allowing for the casualties of sickness and 
 incapacity, within reasonable limits of error. Where the 
 marks of the individual coincidence are latent, as in the latter 
 case, we can sometimes ascertain whether the particular in- 
 stance of the generalisation is included under it, by other 
 marks which lead to its recognition. Thus, were it required 
 to be known that a particular witness in any case was an 
 instance of the empirical proposition that most men speak 
 truth, we need only ascertain his general character, and the 
 bearings of his testimony on his own interest, to make up 
 our minds with sufficient certainty on the subject. 
 
 Where the coincidence, however, is so rare as to create 
 doubt as to its dependence on any recognised law, or to 
 lead us to attribute its origin to mere casualty, notwith- 
 standing a similar rule holds, it is necessary here to point 
 out some particular cases of its application. Suppose, for 
 example, the object of inquiry be the connexion of rain 
 with a particular wind; it is not sufficient to observe 
 the number of times this phenomenon occurs with one 
 wind more than another, but we must also take into 
 account the relative proportion of periods in which the other 
 winds blow. If a west wind blows twice as often annually as 
 an easterly wind, which is the case in England, we have no rea- 
 son to infer that rain co-exists with the former wind through 
 some law common to both, which does not obtain in the latter, 
 simply because it rains twice as often with the first wind 
 as with the last. But if it rain more than twice as often, 
 we may conclude that there is some cause in nature tending 
 to produce both rain and a westerly wind, or that a westerly 
 wind has itself some tendency to produce rain. But should 
 it rain less than twice as often, we may draw, for the contrary 
 reason, a directly opposite inference. Hence, if we pursue 
 the inference which points to some kind of connexion be- 
 tween a particular wind and rain, we generally find the cause 
 to lie in the nature of the earth's surface over which the 
 wind passes ; those which have a long tract of water to sweep
 
 C. I. 6.] CASUAL AGENTS HOW ELIMINATED. 255 
 
 over, as the south-westerly, being generally accompanied 
 with wet ; while easterly winds are dry, on account of the 
 arid continents which prevail in that direction. But as we do 
 not know how far these causes affect the phenomena in ques- 
 tion, or how much they are assisted or marred by other 
 causes, unless by experience ; the coincidences they exhibit 
 can only be regarded in the light of an empirical law, and 
 their effects predicted within a proximate degree of exactness 
 by the method already given. 
 
 The largest number of empirical generalisations embrace 
 those phenomena which are conjointly the result of law and 
 casualty, or in which the effects of casual conjunctions of 
 causes are habitually blended with the affects of a constant 
 cause. To ascertain the precise effect that ought to be 
 ascribed to the cause invariably acting, as it is impossible to 
 proceed according to the ordinary method of eliminating 
 the action of the inconstant agents, our only resource 
 is, to observe the variations which arise from their combina- 
 tion with the constant cause, and strike an average of the 
 mean result. Should the trials prove sufficiently numerous 
 as to include all the various states in which the capricious 
 causes enter into combination with the invariable one, any 
 further repetition of the experiments will only exhibit the 
 same fluctuations, reducible to the same fixed average ; so 
 that we cannot go astray, if we assign the mean point at- 
 tending all the sets of experiments to the presence of the 
 constant agent alone capable of producing it, while we attri- 
 bute the oscillations about it, to the casual influences which 
 modify its action. For example, the state of the barometer 
 at any particular period depends upon the air's gravity, 
 which is liable to be modified by a multitude of capricious 
 agencies, such as clouds, rarefaction, evaporation, and the 
 like ; but if the fluctuations of the quicksilver be regularly 
 noted, they will be found to be reduced to a small number, 
 periodic in their occurrence, and constantly oscillating about 
 a certain fixed point. The conclusion, consequently, is irre- 
 sistible, that the mean height is to be attributed to the 
 ordinary gravity of the atmosphere, and the periodic fluctua- 
 tions to the daily interference of some constant agent with 
 ita natural density ; which, on examination, proved to be the 
 rarefaction of the air, occasioned by the increase of tern-
 
 256 METHODS OF THE PHYSICAL SCIENCES. [B. V. 
 
 perature as the day advances. The inconstant fluctuations 
 were then set down to the inconstant agents which pro- 
 duced them. It is by such observations we are enabled to 
 ascertain the sun's medium heat at any point of the earth's 
 surface, and the exact level of the sea on any particular 
 coast, or the height at which the water of the ocean would 
 stand if undisturbed by winds, waves, or tides. We also 
 afford an example of the same method when we repeat an 
 experiment, in order to escape the unavoidable errors of each 
 individual experiment, by taking the mean of the different 
 results. 
 
 From the discovery of the cause of the periodic fluctua- 
 tions in the barometer, it will be seen, that when we are not 
 aware of the presence of a constant cause in the anterior 
 conditions of the effect, it may be discovered by striking a 
 similar average of the mean result. For in that case, if the 
 effects of the different causes do not cancel each other, but 
 continually oscillate about a certain fixed point, we may infer 
 the presence of an invariable antecedent among the anterior 
 conditions, and detect that agent by some of the scientific me- 
 thods already treated of. In this manner loaded dice may be 
 discovered. For if, after a sufficient number of throws, we do 
 not find the average of the particular results to balance each 
 other, but exhibit a preponderance in favour of some particular 
 throw, we may infallibly infer that some constant cause is act- 
 ing in favour of that particular throw, and the precise amount 
 of its influence. Hence we may conclude, with the same de- 
 gree of assurance, an invariable agent to be absent among 
 the anterior conditions when the average result is zero, and 
 attribute each individual instance of the effect to pure 
 casualty. But in these cases it remains to be determined, 
 firstly, considering the average results of the coincidences of 
 a sufficient number of trials, or the anterior cases possible, 
 what is the amount of probability with which a particular 
 instance may be inferred ; and, secondly, with what amount 
 of probability, in the case of several causes to explain a 
 given effect, but of the presence of which in this particular 
 case nothing is known, may this effect be assigned to any 
 one of these causes. 
 
 The principles on which these problems depend for solu- 
 tion are laid down in a refined branch of mathematical
 
 C. I. 6.] DOCTB1NE OF PEOBABILITY. 257 
 
 inquiry, called the doctrine of probabilities, and may thus be 
 summarily stated 1 : the probability in favour of the occur- 
 rence of any particular instance out of the antecedent pos- 
 sibility of a multitude of others is, in the ratio, between the 
 number of cases in which the event occurs, and the sum of 
 all the cases, including those in which the event occurs, and 
 those in which it does not occur ; or when the anterior con- 
 ditions are known to be equally possible, in the ratio which, 
 the entire number bears to the single condition. Thus, in 
 play at cross and pile, the probability of cross is one half, 
 because it is found on an average that cross is thrown about 
 once in every two throws ; whereas in the cast of a die the 
 probability of ace is one-sixth, because in every hundred 
 throws ace will be found to comprise one-sixth of the 
 number. Secondly, the probability that the effect was pro- 
 duced by any one of the unknown causes which might have 
 been in operation, is, in the ratio of the probability of the 
 cause, multiplied by the probability that the cause, if it 
 existed, would have produced the effect. Suppose, for example, 
 that a woman was found drowned in low water : if the spot 
 lay on any part of the sea-coast, three possible causes suggest 
 themselves as the only agents by which the circumstance 
 could be produced. First, the person slipping off" the beach 
 in a state of stupor or intoxication, and not having sufficient 
 self-control to recover herself; or falling in while the tide 
 was sufficiently high to drown her: secondly, the being 
 drowned at sea, and subsequently cast ashore : thirdly, an 
 act of violence, by which she was detained under water until 
 suffocated. Now, if the woman was seen a few hours pre- 
 vious, perfectly rational, proceeding, during the ebb of the 
 tide, in the company of a man in the direction of the locality 
 where her body was discovered, and if a shriek was heard 
 shortly afterwards in the neighbourhood whence they had 
 proceeded ; if, in addition, it could be proved that the man 
 had been recently engaged in violent altercations with the 
 woman in question, a strong case of probability, almost 
 amounting to circumstantial evidence, would be made out in 
 favour of the cause last mentioned. The second cause would 
 be put out of court ; the only doubt left in the case being that 
 created by the first supposition that she had strayed some 
 distance from her attendant, and having fallen into the sea 
 1 Essai PhUosophique sur les Probabilites, par Laplace, pp. 18, 19. 
 
 8
 
 258 METHODS OF THE PHYSICAL SCIENCES. [B. V. 
 
 during a fit, perished before he could reach, her ; a supposi- 
 tion which, remaining circumstances taken into account, is 
 hardly appreciable, when compared with the culminating pro- 
 babilities on the other side of the question. 
 
 In the first case the causes to which the effect could be 
 attributed were neither equally likely to have existed, nor 
 equally certain to produce the effect. Had the woman been 
 attacked with epilepsy, for the first time in her life, the pro- 
 bability that the fit would have thrown her on the beach, is 
 much stronger than it should have caused her to be immersed 
 in the sea ; and even in the latter case, the probability that 
 she should have been drowned before her companion reached 
 her, is fainter still. The first cause, therefore, is made up of 
 a series of very faint probabilities, which weaken each other 
 in multiplied proportion, while the last cause admits only 
 of one probability, and that, when blended with the adjacent 
 circumstances, of a very strong character 1 . 
 
 There are two other cases of the second theorem of very 
 common application in judicial and scientific inquiry, viz., 
 where the supposed possible causes, though equally certain to 
 produce the given effect, are not equally certain to have existed 
 in the case in question ; and where their existence is equally 
 certain, without being, under the circumstances, equally likely 
 to have produced the effect. But in these cases, the proba- 
 bility in favour of any one cause will, of course, only lie in the 
 ratio of their unequal probabilities. Thus, if one cause existed 
 twice as often in nature as another, that is, occurred two hun- 
 dred times where the other has only existed one hundred, and 
 that one or the other must have existed where a certain effect 
 has been produced, the probability in favour of the more fre- 
 quent cause being the agent in question would be in the ratio 
 of two to one, which is the ratio of their antecedent proba- 
 bilities. Suppose, on the other hand, that the causes, though 
 equally frequent, are not equally likely to have operated in 
 one particular case ; that, for example, out of three times 
 that one cause occurs, it produces the effect twice for the 
 
 1 It may be in the recollection of the reader that the probabilities on 
 the side of the last cause were so culminating as to lead the jury to 
 convict Mr. Kirwan, whose case is here summarily stated; but that the 
 extreme penalty of the law was subsequently commuted, on account of 
 the slight element of doubt that still remained in favour of the first 
 supposition.
 
 C. I. 6.] ANALOGICAL EVIDENCE. 259 
 
 other's once, it is obvious that the antecedent probability in 
 favour of the more frequent cause will be as before, in the 
 ratio of two to one. The third case is but a compound of 
 these two, where the unequal probabilities of each set of 
 causes are multiplied or compounded together, and the 
 balance struck in favour of the greatest probability. 
 
 Another class of inferences, which lie equally out of the 
 range of direct scientific methods, and rest to a great extent 
 on probable evidence, are those which we draw concerning 
 the state of nature in circumstances, times, and localities, to 
 which our observations have not extended, either through 
 the durability which nature manifests throughout all her 
 works, or from her tendency to bring about similar effects by 
 similar agencies, and to work out her ends by designs which 
 leave no arrangement half completed, or void of the object 
 it was intended to meet. For example, from the fact that 
 the sea has gained one hundred yards on the Sussex coast 
 within the last century and a half l , we conclude that it will 
 continue to advance in the same proportion in succeeding 
 years. Again, because day and night on our globe depend on 
 the periodical passage of the spectator into and out of the 
 earth's shadow, consequent on the earth's rotation and the 
 illuminating property of the sun, we conclude the same phe- 
 nomenon occurs with the other planets, which also revolve 
 on their axes, and possess the sun's light in similar degree. 
 In like manner, because the earth has never swerved out of 
 its orbit, or exhibited any oscillations in its course destructive 
 of its present internal economy, since the memory of man, 
 we find no difficulty in believing it will continue to preserve 
 the same beautiful order throughout all coming time. It is 
 also no uncommon thing to draw analogies between the con- 
 dition of other planets and this earth, with a view to obtain 
 evidence of the nature of their inhabitants and their internal 
 structure. 
 
 Now each of these, and similar cases of inference, are to 
 be received with different degrees of probability, according 
 to the amount of evidence in each case, and the limits 
 of time and space to which each inference extends. It 
 is obvious that with regard to the succession of day and 
 
 1 The town of Brighton of Elizabeth's era is now deep enough 
 under the waves, and the erosion of the sea on the adjacent cliffa is 
 noticeable every year. 
 
 s2
 
 260 METHODS OF THE PHYSICAL SCIENCES. [u. V. 
 
 night in the remaining planets of the solar system, the sup- 
 position is of the strongest character, bordering in fact on a 
 complete induction; but if we extend it to other spheres 
 which revolve on their axes, the inference descends lower in 
 the scale of probability, since we are not certain, on account of 
 their absence from our system, that their rotatory motion may 
 be accompanied with the illuminating properties of another 
 sun, so related to them as to cause the phenomenon in question. 
 Again, it is an inference resting upon the strongest grounds 
 that the sun will rise to-morrow, and the earth continue its 
 usual daily round ; for both have continued to do so for the 
 last five thousand years ; and we know the laws on which 
 these occurrences depend have not exhibited the slightest 
 degree of deterioration in the interval. The supposition, 
 therefore, that these agencies will be counteracted to-morrow 
 by some cause, the effects of which have not appeared for five 
 thousand years, and whose approach we have not the slightest 
 grounds to anticipate, so far transcends human conception 
 as to be considered an impossibility. The effects of no cause 
 that science can take into account, which had not been per- 
 ceptible for five thousand years, could in one night grow up 
 to such startling magnitude as to become overwhelming. 
 But if we extend the inference from to-morrow to this day 
 ten thousand years, the inference loses its conclusive value ; 
 for there is nothing which is not perfectly consonant with 
 our idea of causes to hinder the belief that a cause, which for 
 five thousand years had produced no sensible effect, might 
 produce a very considerable one at the end of ten thousand. 
 In the inference from analogy, the strength of the proba- 
 bility will depend upon the extent of ascertained resemblance, 
 both compared with the amount of ascertained difference and 
 taken in connexion with the extent of the unexplored region 
 of unknown^properties. Thus, in ascertaining the amount of 
 probability in favour of the moon being inhabited, we must 
 not only take into account the general points of resemblance 
 between it and the earth, in its being a solid, opaque, and 
 nearly spherical body, containing active volcanoes, and re- 
 ceiving heat and light from the sun in about the same quantity 
 as the earth, and revolving on its axis ; but we must consider 
 its comparatively smaller dimensions, and the differences it 
 exhibits in having its surface more unequal, and apparently 
 volcanic throughout in having no atmosphere sufficient to re-
 
 C. II. 1.] STJEVET OF THE MOEAL SCIENCES. 261 
 
 fract light no clouds, and therefore inferentially no water; and 
 strike the balance according as the resemblances or differences 
 predominate which bear upon the subject for decision. If 
 mere point of similarity between the moon's and the earth's 
 internal economy were in question, it is obvious, according 
 to the above observations, the probabilities would about 
 balance each other. But when we consider that some of the 
 discrepancies in the moon refer to those objects which are 
 found indispensable to animal life on our globe, we must 
 conclude that if inhabitants do exist in the moon, the 
 conditions on which their life depends differ considerably 
 from those which obtain on the earth. There are, however, 
 other bodies in the solar system, between which and the 
 earth there is a much closer resemblance, which possess an 
 atmosphere, clouds, and water, and which exhibit strong 
 indications of snow in the Polar regions ; while as the ascer- 
 tained differences only refer to their average light and heat, 
 their velocity of rotation and intensity of gravity, and similar 
 unimportant circumstances, the argument of analogy pre- 
 sents a striking preponderance on the side of an internal 
 disposition of parts analogous to the earth, and in favour of 
 their being similarly inhabited. Nevertheless, when we con- 
 sider the immense distance of these planets, and contrast the 
 infinite number of properties they possess, of which we are 
 entirely ignorant, with the few we know, we must confess this 
 probability dwindles down to an almost inconceivable value. 
 
 CHAPTEE II. 
 
 METHODS OF THE MOEAL SCIENCES. 
 
 1. Nature of the Moral Sciences. In what respect their 
 
 Methods differ from the Physical. 
 
 WE intend to devote this chapter to a succinct analysis of 
 those methods by which truths are reached, appertaining to 
 the social, mental, and spiritual constitution of man, in con- 
 tradistinction to those which belong to the physical world. 
 The subjects of these methods not only differ from those 
 comprised in the last chapter by the whole diameter of mind 
 and matter, but are hardly at less variance with each other. 
 The two great branches of the spiritual sciences, theology 
 and ethics, being exclusively founded on revealed truths, and
 
 2G2 METHODS OF THE MORAL SCIENCES. [B. V. 
 
 the universal principles of the natural law, are directly 
 amenable to the geometrical or abstract deductive method, 
 which, from a few aphorisms or salient propositions, deduces 
 the complexity of truths of which those sciences consist ; 
 while sociology comprises a group of sciences depending for 
 the most part on the action of men on circumstances, and 
 the action of circumstances on men, the laws of which can 
 by no means be learned a priori, but must be gleaned from an 
 accurate examination of the past, and referred as a kind of 
 axiomata media to the higher principles of human nature. 
 Hence the methods of this division of the subject referring 
 to past sequences between successive stages of phenomena, 
 are very closely allied to those of physical inquiry ; while 
 those, like theology and ethics, appertaining to inferences 
 from laws already discovered, which admit of no modifying 
 or neutralising forces, but demand ubiquitous enforcement, 
 are open at once to the sweeping range of direct deduction 
 in its most obvious and least intricate form. Such sciences 
 do not comprise relations between successive phenomena, 
 but mere interpretations of universal formulas to meet 
 every variety of case which the intellect may devise for their 
 application. 
 
 Mental science, or psychology, is another department of 
 this division, [the laws of whose sequential phenomena for 
 the most part are also to be gleaned from experience ; but 
 whose co-existing principles are obtained by a deep analysis 
 of the individual consciousness, and educed by deductive se- 
 quence out of the primordial elements of the human mind. The 
 former branch of psychology is connected as an art with edu- 
 cation ; the latter with the inferential process, which, true to 
 its a priori character, was matured 1 as soon as the human 
 intellect began to exercise the reflex principle ; while educa- 
 tion, depending on experience, is daily adding to its past 
 results. This science consequently is open to receive the 
 double aids of the experimental and abstract deductive 
 methods, though little has yet been done, however much 
 may have been attempted, to harmonise the truths collected 
 from these two sources 3 . 
 
 Legislation, which belongs to the sociological branch, is not 
 amenable to the corresponding method, its leading principles 
 
 1 By Aristotle. - Dugald Stewart's Philosophy of the Human 
 
 Mind is the leading work of this character.
 
 C. H. 1.] CONNEXION OF THE MOEAL SCIENCES. 263 
 
 being deduced from the highest ethical laws, or rather being 
 so many practical inferences from those laws, to suit the 
 various occasions which arise for their application in civil 
 society. As such they are strictly amenable to the abstract 
 deductive method, and were, in fact, so intended to be 
 treated by Lord Bacon in the heads of his fountains of 
 equity 1 . 
 
 These sciences, so apparently diverse, have a close affi- 
 nity to each other. Ethics with psychology, forming by their 
 conjunction the science of human nature, may be said to 
 stand in the same relation to the sociological sciences as 
 mechanics to astronomy. They comprise the simple law of 
 which the latter sciences only afford the concrete exemplifi- 
 cation in all the diversity of circumstances in which human 
 nature has been placed. The highest results of the socio- 
 logical sciences are therefore only automata media, or laws 
 derived from the fundamental principles of ethics and psy- 
 chology, and when unresolved into them, must be regarded as 
 so many unverified and consequently empirical generalisa- 
 tions. Legislation is only a similar offshoot of the natural 
 law ; and since human nature, which includes the whole, is 
 but a direct emanation from the Deity, theology may be 
 said to be the fountain, or parent source of the rest. 
 
 While, however, there exist this close relationship between 
 the several groups of these sciences, they present, by no means, 
 a state of finish proportionate to their rank ; nor, until the lead- 
 ing branches are in a more forward state, can we anticipate 
 any large development of the laws of the complex phenomena 
 to which they lead. While the science of mechanics was in 
 its infancy, astronomy, which presents only a concrete exem- 
 plification of its laws, could not propound a single generali- 
 sation to be depended upon with any degree of assurance ; 
 and while the laws of mind are for the most part obscure or 
 uncertain, we cannot rely upon any axiom that sociology may 
 furnish beyond the instances in which its truth has been 
 observed. The moral sciences, instead of being developed 
 according to their rank in the scale, owe their expansion 
 more or less to the extent of the a priori element in them, 
 those depending on experience being the slowest in pro- 
 
 De Augmentis, b. vii. Bacon had, however, during his solicitor- 
 ship, written a treatise oil English laws in exemplification of the in- 
 ductive method.
 
 264 METHODS OF THE MORAL SCIENCES. [B. V. 
 
 gress and the most tardy of appearance. While ethics have 
 reached a high degree of perfection, the laws of mind are a 
 blank ; while legislation has emulated ethics in extent of re- 
 finement, the science of social progress has hardly burst from 
 its shell. 
 
 Combined with the disadvantages produced through the 
 absence of proportionate development between the higher 
 and lower groups of the moral sciences, there arises the 
 startling anomaly of the widest diversity of opinion between 
 large masses of men, even with regard to the fundamental 
 axioms and derivative principles of those which are in then* 
 more advanced stage. In physics this is never the case with 
 sciences that have advanced beyond the empirical stage. In 
 astronomy, indeed, there are a few temerous enough to con- 
 front the Newtonian mechanics, but with the generality of 
 civilised communities the Principia is taken as a correct 
 exponent of the truths it endeavours to demonstrate, and 
 this to so universal an extent, that the philosopher who rises 
 to impugn them, succeeds in nothing but the demonstration 
 of his folly 1 . With theology and ethics, and even poli- 
 tical economy, one of the sociological branches, the case is 
 far otherwise. Every person thinks himself at liberty to 
 propound what opinions he chooses concerning these sub- 
 jects ; and, unless he belong to a certain school whose tenets 
 on the leading points he accepts as irrefragable, every new 
 writer generally sets out with the Cartesian principle of 
 pulling down whatever has been previously erected, and 
 clearing the ground for a new structure upon foundations 
 for the most part at variance with those assumed by his pre- 
 decessors. If his labours are characterised by systematic 
 thought and bold flights of genius, he also succeeds in esta- 
 blishing a school, and instead of advancing the science upon 
 which his mind has been concentrated one step onward, he 
 
 1 The censure in the text only applies to those who admit the reality 
 of celestial phenomena as implied both in the Ptolemaic and Coperni- 
 can systems, while they ignore the superstructure which has been 
 raised upon them by Newton and his successors. Of course, with re- 
 spect to those who, like Bishop Berkeley and the present Cardinal 
 Archbishop of Lyons, deny or throw doubt on the reality of the New- 
 tonian premises on purely metaphysical grounds, the author ventures 
 no reproof, though he respectfully adduces the reasoning in b. v. c. iv. 
 3, as a complete answer to what has been advanced on this side of the 
 subject.
 
 C. II. 1.] DIFFICULTIES OF THE SUBJECT. 265 
 
 has only increased the diversity of lights in which the same 
 subject may be viewed. This divergence of opinion, between 
 men of eminently scientific character, upon moral subjects has 
 introduced among the unlearned classes of society the same 
 fluctuating and conflicting views, and led them to consider 
 moral topics, as much open to their lucubrations as the most 
 inferior subjects upon which their minds can be employed. 
 A man who would deem his ignorant neighbour mad were 
 he to speculate in sober earnest on the higher principles of 
 acoustics or thermology without knowing anything about 
 their elementary properties, pays him the greatest atten- 
 tion when he chooses to discourse on the highest functions 
 of government, or ventures to propound the principles by 
 which churches and empires should be governed. On every 
 subject respecting man, religion, and society, conceit of 
 knowledge still reigns without the reality, and if Socrates 
 were in this age to descend into our market-places he would 
 encounter the same dogmatic assurance as in his own. 
 
 Such clashing variety of opinion upon the most elementary 
 principles of the different moral sciences at once arises out of, 
 and is daily increased by, the obscure character of psycholo- 
 gical laws and the capricious action of human volition. Phy- 
 sical laws may often be obscure, but their effects admit of 
 certain calculation ; and the order of sequence, being constant 
 and inevitable when once discovered, enables us not only to 
 predict the future, in any given instance, but also to recon- 
 struct the past. Astronomy, for instance, will afford us data 
 for calculating the precise conditions of the heavenly bodies 
 at any distant epoch, already elapsed, or in the womb of 
 futurity, and that to so great an extent that even were all 
 the astronomical archives burnt they could be completely re- 
 placed, and the past history of the heavens entirely supplied by 
 the observation of the present. But with moral phenomena 
 the case is otherwise. Here the chief motive power is mind, 
 and we are not only ignorant of the laws through which it mani- 
 fests its agency, but the order of its production is so irregular 
 that we can never reckon upon the precise quality or degree 
 of its action. Were psychological laws discovered, at least in 
 sufficient abundance to verify many inductive generalisations 
 in sociological science, still there arises the question, in ex- 
 tending those laws to future cases, of the exact force in which 
 they will act. Now on this very hinge turns the fate of man
 
 METHODS OF THE MOEAL SCIENCES. [B. V. 
 
 and the destinies of nations. No psychological revelations 
 that man can expect to discover could have predicted the 
 advent of those minds who have established religions, over- 
 thrown empires, founded dynasties, pulled down altars, or 
 reformed creeds. This class of minds are distributed over 
 the masses of generations by no presumable law that we can 
 discover, but in the most anomalous and confused manner. 
 Occasionally their appearance is separated by centuries, 
 sometimes by gaps of years ; now they come in clusters, and 
 then they stand alone. But whenever they appear, revolu- 
 tion of language and manners, creation and overset of insti- 
 tutions follow ; conjoined states are erected into new nations, 
 and distinct empires fused down into one. Hence were the 
 laws of mind known, and the phenomena it manifests as sub- 
 ject to the regular action of causation as the creatures of the 
 material universe ; yet the uncertainty alone of the quality 
 of the agent would render any calculation, founded upon them 
 for any distance of time, chimerical in the extreme. 
 
 Although it is a principle of our nature to assign to every- 
 thing an efficient cause, yet so difficult is the task, in moral 
 inquiries, of tracing any proportion between the apparent force 
 of any moral causes we may select and their known operation, 
 that we are often obliged to deliver up that operation to chance, 
 or, more rationally, to the irresistible hand of the great Dis- 
 poser. The death of a man at a critical juncture, his disgust, 
 his retreat, his disgrace, have brought innumerable calami- 
 ties on a whole nation ; a common soldier, a child, a girl at 
 the door of an inn, have changed the face of fortune and 
 almost of nature. The effects to which such slight incidents 
 led, may, indeed, be traced through the intervening series of 
 eventualities which generated the result, but these are of so 
 casual and multifarious a character, and so much depend at 
 every link upon the determining agency of the will, that to 
 attempt to found upon them any conclusion of a scientific na- 
 ture, either for future guidance or present application, would 
 be a waste of thought. Such cases are never likely to happen 
 again, and even were their occurrence possible, no power 
 short of omniscience could enable us to grasp all the condi- 
 tions upon which each step of the sequence would eventually 
 depend, and forecast the result. The will, which is the deciding 
 agent in such circumstances, is no doubt strongly influenced 
 by motives, if not completely governed by them ; but we have
 
 C. II. 1.] OPERATION OF PREJUDICE. 267 
 
 no power to calculate its action in a single individual under 
 any trying circumstances, much less in cases where a thousand 
 volitions are concerned. The rules of causation may hold, 
 at least to an extent sufficient for the application of scientific 
 methods, but we lack the power to get at the conditions upon 
 which the effect depends. The task of diving into the human 
 breast and tracing the crowd of agencies which are control- 
 ling each volition, is even too great for its owner, who is often 
 uncertain enough of the issue ; but the insuperable difficulties 
 which hinder an external observer from grasping the same 
 conditions, become multiplied in infinitesimal proportion. 
 
 Even in subjects which have no relation to sequence, as 
 theology and ethics, the irregular agency of the will is mani- 
 fested in interfering with the inferential process and leading 
 the mind to modify or oppose conclusions which are at war 
 with its tendencies. Such speculations not being of a tan- 
 gible nature, cannot be brought to any other test than that 
 of pure reason ; and since it is the fate of great talents to be 
 almost invariably accompanied with deep sensibilities, it oc- 
 casionally happens that the strongest reason obeys the be- 
 hests of some more predominating passion, in dethroning the 
 true system and setting up a more convenient, but a false 
 system in its place. The absence of close compact inference 
 is easily supplied by ingenious sophisms and brilliant rhetoric ; 
 feeling and interest is listed on the side of argument, and 
 with the majority conviction is the result. When the tenets 
 established by -such a method became fostered in subsequent 
 ages by the associations of infancy and kindred, it is no 
 marvel they should thrive and flourish so as to perpetuate, 
 among the generations of vast communities, the opinions to 
 which they gave rise. It is to such influences, combined 
 with the action of the imaginative feelings, which these sub- 
 jects very largely call into operation, that conflicting 
 views on the more purely spiritual sciences are to be traced. 
 It is simply because this class of the abstract sciences can 
 only be built up by pure reason, that the generality of men 
 who allow prejudice and imagination to interfere with the in- 
 ferential process in them, are least able to decide between 
 the rival claimants of orthodoxy. Could we, indeed, shut out 
 human volition and the action of disturbing fancies, mankind 
 would no more differ about the conclusions to be drawn from 
 the primary elements of theology and ethics than with the de-
 
 268 METHODS OF THE MOEAL SCIENCES. [B. V. 
 
 ductions from geometrical postulates and definitions. "Were 
 prejudice and feeling, on the other hand, let in upon the 
 mathematical branch of these sciences, were it any one's 
 interest to impugn some of the derivative principles of the 
 calculus of variations, or did the overthrow of any proposi- 
 tions of the higher geometry strongly administer to any 
 party's gratifications, the world would not be long without a 
 new system, of conic sections and a fresh doctrine of limits. 
 
 Yet we are not to relinquish, on account of these disturb- 
 ing influences and great obstacles, the erection of an impos- 
 ing group of moral sciences, on grounds quite as solid as those 
 which refer to the material world. Notwithstanding the socio- 
 logical portion may not give 'us the same power to predict oc- 
 currences without a cloud of conditions, they will help us to 
 many generalisations of practical importance and theoretic 
 value, affording a guide to the statesman in the control of 
 communities, and throwing light, in the eyes of the philo- 
 sopher, on the ultimate laws of human nature. Upon such 
 generalisations, provided they arise from a wide induction of 
 historical phenomena, and enable us to account deductively 
 for any past occurrences to which they are capable of being 
 applied, no cavil or doubt can arise. They can be brought 
 to the touchstone of fact, and men cannot call in question 
 what they see: while with regard to those subjects which 
 admit of no such verification, but simply concern complex in- 
 ferences from a priori data, we must rely on the variety of 
 proof that correct reason is capable of receiving, and the in- 
 consistencies which are the never failing attendants of erro- 
 neous inference, for securing their derivative principles from 
 error. 
 
 2. The Sciences amenable to the Abstract Deductive Method. 
 The Functions of the Cross-examining Blenches and the 
 Negative Process. Examples of Scientific Praxis. 
 
 The moral sciences may be divided into two large groups 
 viz., those which consist of inferences drawn from a priori 
 resources, and others which in conjunction with many 
 branches of such inferences are raised out of generalisations 
 drawn from an extensive examination of the past. The last 
 group refers to coincidences between the order of succession,or 
 to the laws by which one state of phenomena generate another,
 
 C. II. 2.] PRINCIPLES OF ETHICS. 269 
 
 and is co-extensive with the sociological branch ; while the 
 first comprises the conclusions our reason obliges us to infer 
 from general principles, either co-existing within, or deli- 
 vered to us from external authority ; in which case, the sphere 
 of inference will extend over the ground from which we are 
 led to infer the existence of such indubitable authority, and 
 the fact that the revelations we receive come entirely from its 
 hands. The proof, however, is a priori and deductive even 
 throughout those links of it which deal with sequence be- 
 tween a certain order of facts ; depending not on the causal 
 tie between the facts themselves, but solely on the relation 
 which these bear, or the point of view in which they may be 
 considered, to the external authority, or to the co-existing 
 principles, whether natural or revealed, which are said to 
 have emanated from it. Now, such relation being decided 
 by the rational principles of the intellect, the proof at this 
 stage of the process is no less abstractedly deductive than 
 when the legitimacy of the general propositions having been 
 made out, we are only concerning ourselves with drawing 
 inferences from them. 
 
 The sciences which compose this group are evidently theo- 
 logy, ethics, legislation, and that portion of psychology whose 
 laws may be completely learned by a study of the co-existing 
 laws of the mental constitution without reference to the de- 
 pendence of one state of mind on another, or the connexion 
 between antecedent states and the present, which, of course, 
 involve generalisations from experience. The elementary 
 principles of each of these subjects may be regarded as so 
 many definitions, axioms, and postulates, from which the 
 complete body of their respective truths are evolved by a 
 process exactly identical with the geometrical method. For 
 example, the primary data of ethics and legislation are 
 certain irreversible and irrepressible convictions stamped on 
 every breast, by which each human creature is urged to fulfil 
 the destiny of his being, and preserve his faculties, appetites, 
 and feelings which make up his individual constitution, in 
 that healthy state of action and subordination which will 
 most conduce to his own happiness and the welfare of others. 
 Such convictions as admonish us to do injury to no man, to 
 preserve our veracity, to submit our passions to the control 
 of reason, and in general to abstain from actions which 
 awake censure or shame, all which principles are co-existent
 
 270 METHODS OF THE MOEAL SCIENCES. [B. V. 
 
 with human nature, and compose the spiritual instincts which 
 enter into its constitution. They comprise, in one word, the 
 natural code by which, in compliance with the mandate of 
 the Apostle, every man is bound to govern himself 1 . Some 
 persons, indeed, may be found to deny the existence of such 
 principles a priori, and resolve them into the mere creatures 
 of conventionalism ; just as there are persons who will deny 
 the existence of matter, or the commonest axioms of physical 
 science ; but the generality of men in every position of life 
 savage, civilised, or semi-barbarous bear witness to the in- 
 digenous character of their origin. Now, it is in the appli- 
 cation of these common principles to adjust the actions of 
 man with relation to himself, his Creator, and his species, 
 that ethics consists : so far as the violation of such prin- 
 ciples, either in their ultimate or derivative form, interferes 
 with the welfare of society, it is the business of legislation 
 to take cognisance of their influence. But the process in 
 either case is identical with the geometrical method. When 
 we examine any particular question that may arise with a 
 view to establish a new derivative proposition, we simply 
 survey the relations which the case bears to the main prin- 
 ciples and the subordinate ones already deduced from them, 
 and cast up the result. Should a new theorem be demon- 
 strated, the links of inference by which the previous pro- 
 positions led to its establishment are brought into systematic 
 connexion, and the new law takes its place in the series of 
 constructed truths, and performs its functions in the gene- 
 ration of others. 
 
 Thus, were it required to solve the ethical problem whether 
 any action is formally indifferent, it would be necessary to 
 examine first in what good or evil consists, and then con- 
 sider if there are any human actions which do not enter 
 into either category 2 . But the first case is determined by 
 the theorem previously established, that an act is good or bad 
 according as it accords or conflicts with the natural law ; the 
 sole point, then, for investigation is, whether any act can be 
 realised without doing either. Now, as a preliminary step 
 to the decision, we ought to distinguish everything which a 
 
 1 "For when the Gentiles which have not the law, do by nature the 
 things contained in the law, these, having not the law, are a law to 
 themselves." Romans ii. 14. 2 Summa Theologia of St. Thomas 
 
 Aquinas, pars. ii. sect. 1st, 2nd, and 3rd.
 
 C. II. 2.] THE NEGATIVE PROCESS. 271 
 
 human act includes that we may know in how many ways an 
 act is capable of being viewed in connexion with the natural 
 law : first, there is the material thing done with its attendant 
 circumstances ; secondly, the motive which incited the action. 
 As to the material object, it is evident many acts do not come 
 within the cognisance of the natural law. If we walk, or play 
 an instrument, abstracting from the purposes which urge us 
 to do these things, no good or evil can attach to the naked 
 act itself : but if either be executed with a good or bad pur- 
 port, the law is directly applicable, and will pronounce its 
 sentence. The question, then, is narrowed to the simple 
 case, whether any motive can be indifferent, which is easily 
 determined in the negative by the consideration that man is 
 bound to direct all his actions in harmony with the fixed 
 constitution of things, and to do nothing through levity or 
 without a rational motive. A conclusion, indeed, which is 
 doubly corroborated by the Christian law, which exacts an 
 account of every idle word and action 1 , and requires its fol- 
 lowers to consecrate the intention of all their actions to the 
 glory of the Supreme Being. 
 
 The establishment, however, of such propositions do not 
 end with direct proof: before they can be accepted as indu- 
 bitable truths, it is necessary not only to demonstrate their 
 certainty, but to show that every other mode of looking at 
 the question is illusory. This, which is called the negative 
 process, performs the same functions in moral evidence as 
 mathematics do in the physical sciences, at least as far as 
 verification is concerned, placing the demonstration beyond 
 the shadow of doubt by the decided manner in which 
 every objection is met, and by investing the proposition 
 with double proof, viz., the direct, and the reductio per impos- 
 sibile, which is so powerful in elementary geometry. Thus the 
 proof of the intrinsic moral nature of man's actions, arising 
 out of the natural law, is not only based on each one's indi- 
 vidual consciousness, and the universal consent of mankind ; 
 but it also rests on the fact that no other principle can be 
 assigned which will account for it. For if such exist, it 
 must be either the utility of society, or the free election of 
 Providence, or the manichean principle of two antagonistic 
 deities. The last supposition, implying a contradiction, is 
 philosophically absurd ; the second is contrary to the attri- 
 1 St. Matthew, xii. 26.
 
 272 METHODS OF THE MOEAL SCIENCES. [B. V. 
 
 butes of Q-od ; and the third is inadequate to explain the 
 keen perception of right and wrong which is found among 
 isolated savages, bound to each other by no links in the 
 way of treaties and compacts. Hence all other possible 
 cases being put out of court, the understanding bounds back 
 to the direct proof with a confidence equal to that with which 
 it embraces the strongest demonstration of physical science. 
 Ethics are connected with theology, natural and revealed, by 
 the principle which insists upon the worship of theDeity a law 
 that is as irrepressible and fundamental as any in its category. 
 Natural theology, however, to silence the cavils of atheists, 
 proves the existence of the Supreme Being by the a priori 
 argument that mechanism cannot exist without an artificer, 
 and that the evidence of design is on so stupendous a scale 
 in the universe as to require a Being of the grandest capacity 
 to project it. The demonstration of His infinite attributes 
 follows from the necessity of His existence as the fountain of 
 being ; and consists of many diverging lines of argument, each 
 strengthening one another and meeting in the same point. 
 The negative process is also employed to prove there is no 
 assumption which accounts for the existence of the universe 
 apart from the Creator, without landing its maintainers in 
 startling contradictions. Thus every step in this link of the 
 proof is purely deductive, certain common principles being laid 
 down, which we are compelled by the intellectual laws of our 
 nature to accept as the conditions of the world's existence, 
 from which are reasoned out successively the existence of the 
 Deity and all the qualities with which His nature is endued. 
 The other branch of proof by which His revealed will is esta- 
 blished is similarly deductive ; it being assumed to be impos- 
 sible that rational men could bear witness to certain truths 
 and miracles which they knew to be impositions, or of which 
 they were only half certain, with no other prospect of reward 
 for their pains than punishment and death. This assumption 
 rises out of the constitution of human nature. The case which 
 it involves is sufficiently evident from history. There are, 
 moreover, multiplied lines of inference corroborating the same 
 point, all of a strictly a priori kind : such as, the existence of 
 God being proved, the strong antecedent probability in favour 
 of revelation, and the consonance of the doctrines taught 
 with the natural attributes of Deity. As soon as the funda- 
 mental tenets appertaining to revealed dogma are thus esta-
 
 C. II. 2.] EXAMPLE FBOM PALEY. 273 
 
 Wished, the process of inference from them is quite of a 
 similar character with the ethical deductions already de- 
 scribed, and is amenable to the same verifications. With 
 respect to the moral b'ranch of them, or Christian ethics, thia 
 confirmation partakes of a duplicate character. For the 
 moral doctrines of Christ are in unison with the natural law, 
 and no inference from His teaching can be accepted which 
 conflicts with any portion of that law either in its ultimate 
 or in its derivative principles ; and every inference which 
 cannot be shown to have a strict connexion with it, must be 
 received with doubt, until resolved, like a complex law, into 
 the higher principles of natural ethics, and shown to be a 
 particular exemplification of them. 
 
 Of the former kind of argument an example may be ad- 
 duced from Paley. His thesis that the Christian ' religion 
 came from God, is made to rest with respect to historic 
 evidence on the premises that " a religion attested by 
 miracles is from God," and that the " Christian religion is 
 so attested 1 ." The minor proposition, about which only 
 men are to cavil, is proved by a syllogism in Barbara : " Ail 
 miracles attested by such witnesses as we have named are 
 worthy of credit. The Christian miracles are attested by such 
 witnesses ; they are therefore worthy of credit." The minor 
 premiss of the latter syllogism is then divided into the seve- 
 ral propositions of which it consists, each of which is esta- 
 blished separately. In the first place, it is proved that the 
 witnesses had no prospect but suffering from the nature of 
 the case, because they were preachers of a religion unexpected 
 and unwelcome to the Jews and the Gentiles. That they 
 actually suffered, is proved from the testimony of the Jewish, 
 Heathen, and Christian writers ; and that they voluntarily ex- 
 posed themselves to suffering, rests on the authority of the 
 same writers. In the second place, it is proved that what they 
 suffered for, was a miraculous story ; by the nature of the case, 
 as they could have had nothing but miracles on which to rest 
 the claims of the new religion ; by the allusions to miracles, 
 
 1 It is remarked by Dr. Whately that the minor of this syllogism 
 was admitted, while the major was denied, by the Pagans; but as the 
 case at present is reversed, Paley's argument goes to establish the 
 minor premiss, about which alone in these days there is likely to be 
 any question. Logic, Appendix, iii. 
 
 T
 
 274 METHODS OF THE MOEA.L SCIENCES. [B. T. 
 
 particularly to the Resurrection, both in Christian and profane 
 writers, as the evidence on which the Christian religion 
 rested. It is also shown by the same evidence that the 
 miracles in attestation of which they suffered, were such as 
 they professed to have witnessed. In the third place, it is 
 proved that the miracles thus attested, are what we call the 
 Christian miracles, by the nature of the case that it is im- 
 probable that a new fiction should have replaced the original 
 story ; by the incidental allusions of ancient writers, both 
 Christian and profane, to accounts agreeing with those of 
 the inspired writings ; by the credibility of the Scriptures, 
 established by several distinct arguments, each separately 
 tending to show that these books were, from the earliest 
 ages of Christianity, well known and carefully preserved 
 among Christians. Again, it is proved by similar premises, 
 that the early Christians not only submitted to new rules of 
 conduct, but that they did so in consequence of their belief 
 in miracles wrought before them. 
 
 The major premiss, that miracles thus attested are worthy 
 of credit, Paley next proceeds to establish ; first, by the im- 
 probability that men who could have avoided all their suffer- 
 ings had they lived quietly, should have provoked the knife 
 of the executioner, by pretending to have seen what they 
 never saw ; that they should go about lying, to teach virtue, 
 and persist, with a full knowledge of Christ's imposture, in 
 propagating the frauds, which met with such reprisals as the 
 crucifixion, and shed their blood in attestation of their reality : 
 secondly, by the fact that no false story ever has been so at- 
 tested ; which is shown by adducing the several stories that 
 can be produced as parallels to the Christian, and proving 
 either that they are not so attested, or that they are not pro- 
 perly miraculous. Hence the minor of the leading syllogism 
 is fully made out, and granting the major, which has been full}* 
 conceded since the pretensions of magic have been exploded, 
 viz., that a religion attested by miracles is from Grod ; the 
 conclusion inevitably follows that the Christian religion came 
 from God. 
 
 To avoid unnecessary prolixity in the analysis of this argu- 
 ment, we have left the obvious premiss in most of the syllo- 
 gisms unexpressed, it not being needful in the analysis of any 
 train of reasoning to express the implied premiss. When 
 wanted to reduce the syllogism to its strictly technical form,
 
 C. II. 2.] ANALYSIS OF DEDTJCTIYE SEASONING. 275 
 
 with a view to detect a lurking fallacy, tlie implied premiss is 
 promptly suggested by the leading premiss and conclusion. 
 In following out a process of this kind it is necessary to begin 
 with the last point established, and, tracing the reasoning 
 backwards, to examine on what grounds the inference is made. 
 The assertion will be the conclusion, the grounds on which it 
 rests, the premises. The premises must then be taken sepa- 
 rately, and the grounds on which they rest examined, accord- 
 ing to the plan we observed with the first conclusion. A 
 premiss must have been used as such, either because it 
 required no proof, or because it had been proved. In the 
 former case it must either be self-evident, or universally 
 admitted, or conceded by the opponents of the argument. 
 In the latter it must be regarded as a new conclusion, de- 
 rived from other assertions which are premises to it, which 
 are to be examined in turn, and if found correct, treated as 
 other conclusions derived from other assertions. If the 
 train of reasoning be correct, the analysis will continue till 
 the premises with which the whole commences are reached, 
 which, of course, should consist of assertions requiring no 
 proof; but if the chain be anywhere faulty some proposition 
 will arise in the course of it, either assumed as self-evident 
 or incorrectly deduced from other assertions 1 . 
 
 1 The substance of the directions in the text are taken from the 
 preface to Hind's Introduction to Logic. Dr. Whately exhibits the 
 logical analysis of a course of argument in the form of logical division. 
 Thus: 
 
 [Ultimate conclusion.] 
 
 ZisX 
 proved by 
 
 YisX Zis Y 
 
 proved by proved by 
 
 
 
 1 
 
 
 A IB Y 
 [suppose admitted.] 
 
 ZisA 
 proved by, &c. 
 
 the argument that 
 
 and by the 
 th 
 
 argument 
 at 
 
 SisX 
 &c. 
 
 YisB 
 &c. 
 
 CiaX 
 &c. 
 
 Yia C 
 &c. 
 T 2
 
 276 METHODS OF THE MOEAL SCIENCES. [B. T. 
 
 The branch of psychological science which falls under the 
 head of the abstract deductive method, is the study of the 
 structure of the intellectual constitution, with a view to 
 ascertain the laws through which the different faculties 
 manifest their statical agency, so far as the reasoning pro- 
 cess is concerned, and the estimation of evidence in all its 
 branches. These laws have been pretty extensively de- 
 veloped, in the Organon of Aristotle, and the Kritik of Kant, 
 who may be taken as fair exponents of the methods by 
 which their highest generalisations have been reached, and 
 the modes by which they are to be extended. No reflection 
 upon experience, or analysis of scientific proof, enabled the 
 Stagyrite to see the syllogism in the human mind, and point 
 out the nineteen different ways in which men may naturally 
 reason. He showed, from the necessity of the case, that 
 every conclusion required two premises ; that the three pro- 
 positions concerned were only capable of a limited number 
 of legitimate combinations ; that such combinations involved 
 distinct qualities in the propositions themselves, which arose 
 out of the relation of the subject with the predicate ; and 
 that the nature of the subject and the predicate implied the 
 logical properties of terms. The mode by which Aristotle 
 constructed in a few weeks the system which has employed,, 
 and is destined to employ, men's thoughts for decades of 
 centuries, was precisely identical to the method by which 
 the early mathematicians ran up the splendid series of 
 proofs which constitutes the lower geometry. Descartes in 
 a similar manner established his methods, and Kant con- 
 nected the derivative laws of the old philosophy and the new, 
 with the ultimate principles of the intellect. No attempt 
 has been made to expound the laws of the imaginative faculty, 
 by seizing one or two of its elementary principles, and making 
 them the parent source of the rest. Yet there is the same 
 mutual dependence between their functions as exist between 
 those of the reasoning faculty, and they only lack some genius 
 rivalling Aristotle in systematic and ratiocinative power to 
 yield up similar results.
 
 C. II. 3.] SCIENCE OP HUMAN NATUBE. 277 
 
 3. The Laws which regulate successive states of Mind. 
 The Sociological Sciences. The Concrete Deductive Method, 
 direct and inverse. 
 
 The remaining group of moral sciences concern the laws 
 of sequence between phenomena, whether individual or social. 
 In the former they regard the laws which generate particular 
 mental states, either with regard to the entire mind, or only 
 with reference to some of its dependencies. For instance, 
 the law of association of ideas unfolds the series of relations 
 existing between different classes of thoughts and feelings, 
 which make one suggestive of another : as such, this law is only 
 one of the hundred operating agencies by which the -mind is 
 constantly modified and gradually urged from one state into 
 another. Each of these single agencies work according to 
 constant laws, though their force varies in different persons. 
 Thus it is a law of memory, that a page' is sooner committed 
 by learning it by section, alternately closing the book and 
 looking at the passage only to catch the escaped word, than 
 to attempt to grasp the whole at once by keeping the eye 
 continuously on the sheet ; yet the precise force with which 
 the law operates is never found exactly the same in two 
 persons. The affections, appetites, feelings, and passions 
 have each also distinct principles of action as well as the 
 intellect, and though capable of being modified by many 
 circumstances, manifest invariably certain tendencies, which 
 are capable of being singly calculated within certain limits 
 of error. Now, besides the laws peculiar to themselves, each 
 of these phenomena have some properties in common. For 
 instance, it is a law that the force by which each of these 
 powers act increases in quick progression the power of its 
 action, so that if any one be indulged to the exclusion of the 
 others, that one is sure to predominate over the mind. It is 
 the study of these agents, both singly, and in unison with 
 each 'other ; their peculiar together with their common pro- 
 perties ; the uses for which nature designed them, and their 
 effects both in ourselves and others, that constitutes the 
 science of human nature in its largest extent ; a study how- 
 ever which, apart from writers of fiction, seems not to have 
 engrossed any portion of the attention of mankind. We 
 have no treatises on the passions or affections, yet the special
 
 278 METHODS OF THE MOEAL SCIENCES. [B. V. 
 
 treatment of each of these in the various points of view we 
 have marked out, is indispensable to a complete system of 
 education, and an accurate knowledge of the development of 
 society. 
 
 It is obvious, from the complex nature of the phenomena, 
 that we have no other mode of tracing the effects of the 
 agents we have considered, in any given case, than by follow- 
 ing out their laws singly, by comparing their relative strength, 
 by taking into consideration the circumstances concerned, and 
 forecasting the result deductively. It is precisely a case 
 of the composition of causes considered in the last chap- 
 ter, where the result, comprising a crowd of clashing and 
 strengthening forces, baffles every attempt to unravel the 
 knot of effects and to assign to each its separate cause, some 
 of which are entirely neutralised in the action, and others 
 blended into one result. The only obstacle to so complete a 
 prediction of the result as would attend a similar investiga- 
 tion in mechanical philosophy, is the uncertainty generated 
 by the action of the will, and the impossibility of estimating 
 all the influences which may direct its action in any given 
 case. Nor can we expect the progress of the science of 
 human nature will ever place us in so favourable a condition. 
 All our data, consequently, must express tendencies, not certain 
 effects ; and notwithstanding the inferences built upon them 
 will not warrant unconditional prediction in any case, they will 
 be of eminent importance as a guide to the knowledge both 
 of any person's conduct, under certain circumstances, and of 
 the special training required to produce certain habits of cha- 
 racter. In some instances, erroneous or incomplete data 
 may lead us into wrong conclusions, but these are not to be 
 set down to the subject's unfitness to be invested with 
 scientific formula, but simply to wrong calculations. "We 
 may rely upon the fact that causes are at work in instances 
 which appear the most complex and casual, and though com- 
 pounding their results, acting according to invariable law, 
 whose effects, were we in possession of all the data, are 
 capable of being computed a priori, even throughout their 
 most intricate combinations. 
 
 Nor are the moral sciences alone in this uncertain predica- 
 ment. There are elements in meteorology, in the motions of 
 fluid masses, and the laws of the tides, which must always
 
 C. II. ~3.] PROBLEM OP ETHOLOGY. 279 
 
 remain unfathomable, and for which allowance must conse- 
 quently be made in the calculations which compute their 
 effects in any given instance. We know, for example, the 
 great operating causes at work in the production of the tides, 
 and are able, under certain conditions, to compute their 
 general effects, even in unknown quarters of the globe ; but 
 if precise accuracy be required, the calculation wSl be of no 
 avail in any single instance. For there are causes of a local 
 or casual nature, such as the configuration of the bottom of 
 the ocean, the indentations of shores, the direction and 
 strength of the wind, which it is impossible to foresee, and 
 which are always sure to interpose, and in some single cases 
 may altogether conspire to defeat the result. In meteorology, 
 again, the chief proximate operating causes, and the laws 
 which regulate their influences, are so unknown that it is im- 
 possible to predict the order of antecedence and consequence 
 between its phenomena with more than a very moderate de- 
 gree of probability. Yet no one doubts that tidology is a 
 science, and that meteorology is destined to become one ; or, 
 in other words, that all the phenomena which these sciences 
 embrace are not generated by special causes, which act 
 throughout all their combinations in accordance with in- 
 variable laws, and that the general action of such causes is 
 sufficiently cognisable to the human intellect to admit of 
 being predicted within limits of time and space wide enough 
 to leave a broad margin for the realisation of purposes of 
 practical utility. Nothing further is claimed for the science 
 of human nature, and, indeed, hardly anything further is re- 
 quired. If we are able to foretel from a general examination 
 of any individual character what will be his conduct in any 
 given emergency, or what course of discipline will generate 
 certain states of mind, or what principles of action, in the 
 generality of instances, are at work in the production of the 
 varieties of habits, tempers, and characters, we need no 
 further theoretical knowledge to produce results of the 
 greatest practicable importance to our species. 
 
 It is not through any belief that such knowledge is unat- 
 tainable that the present backwardness of this science is 
 owing, but chiefly to the unscientific methods by which men 
 have sought to obtain it. They have generalised from the 
 smallest empirical data, and rushed into the highest regions
 
 "280 METHODS OF THE MOBAL SCIENCES. [_B. T. 
 
 of art before drawing out, or having any definite conception 
 of, the propriety of the theory which the art involved. 
 Having stumbled upon the agreement of certain states of 
 mind with a certain- anterior routine of practice, they inquire 
 no further, but chain themselves down to the system which 
 embodies the result. This crude generalisation of passive 
 experience is at the bottom of all our systems of civil, of mili- 
 tary, and ecclesiastical education, and constitutes the prescient 
 wisdom of those who are said to be observant of character 
 and profoundly read in the world. Without any idea of the 
 action of the individual laws at work, or correct insight into 
 the complex agencies which concur to the production of the 
 effect they have the temerity to predict, they consult the 
 note-book of their former experience, and decide according 
 to the superficial aspects of the case. This, to draw an illus- 
 tration from a science whose methods are inevery respect 
 analogical, is precisely as if a man, without any knowledge 
 of the internal structure of the human body, were to con- 
 struct a system of therapeutics, or to predict simply from 
 his past experience the effects of a certain medicine on any 
 constitution of body. If it is a universal complaint, that the 
 treatment of many disorders in the system is founded on 
 mere empiricism, the censure is doubly applicable to the 
 efforts commonly made to regenerate human nature. 
 
 One of the first steps required to cpnstruct this science 
 on its true foundation is the production of separate treatises 
 on the different groups of homogeneous phenomena which 
 enter into it, as respects the action of their particular laws 
 taken singly, and in conjunction with others. Something of this 
 kind Bacon intended for the intellectual faculties in the little 
 tract he wrote for Sir Henry Saville, the provost of Eton ; 
 but the treatise was limited solely to the improvement they 
 are capable of receiving by due attention to psychology in a 
 course of preliminary education, an attempt which Dugald 
 Stewart further followed out in his Philosophy of the Human 
 Mind. The latter work, however, notwithstanding the learn- 
 ing and the attainments of the author, from aiming at too 
 much within its limited compass, accomplished little. Had 
 the two volumes, in which the treatise is comprised, merely 
 examined the operations of one or two special faculties, a step 
 would have been made in the direction we point out. Upon 
 the passions and feelings we have not even an attempt at
 
 C. II. 3.] ETHOLOGY WHERE INDUCTIVE. 281 
 
 distinct treatises 1 . The early fathers and a modern class of 
 theologians, in their disquisitions on practical morality, have 
 marked out many derivative laws which this class of mental 
 phenomena manifest, but entirely with a view to the acquire- 
 ment of certain habits of virtue, and not to enlighten us on 
 the general nature of their action, though this, to some degree, 
 is their collateral effect. Of course, in connexion with the 
 purely mental consideration of each of these special classes 
 of subjects, the physical condition of the body ought to be 
 studied, as there is no doubt of the influence of temperament 
 in producing moral and emotional peculiarities, and also of 
 the relation of certain cerebral conformations with specific 
 intellectual qualities. 
 
 This branch of the process, which concerns the obtaining 
 materials out of which to construct a science of human nature, 
 is obviously one, to a great extent, of observation. The 
 world, however, has existed long enough to give us facts in 
 abundance if we will only take the trouble to look out for 
 them ; and every different position in which man has been 
 placed, every phase of character he has assumed, is a store- 
 house from which the most valuable results may be drawn. 
 The great fear, however, is, that in collating the experience 
 afforded by various institutions and countries, antipathies or 
 predilections in relation to one or other may interfere, and 
 make correct inference on any given point impossible : but 
 such prejudices must be cast aside, as we dismiss in natural phi- 
 losophy illusions of sense, or prepossessions in favour of any 
 ill-judged theory, being conscious that while such distortions 
 remain we are incapable of moral science. Indeed, more cau- 
 tion is required in divesting ourselves of such preconceived 
 notions in this division of the sciences than in physics. Tor 
 observation, here, is almost solely at work in the preliminary 
 process, with little or no help from artificial experiment, and 
 relying to a great degree on the methods of agreement and 
 concomitant variations : any perversion of fact, therefore, is 
 less likely to be eliminated by more extended observation than 
 where the five methods come into play ; and if it concern the 
 operation of any institution of magnitude, it will doubtless 
 
 1 Smith's moral sentiments hardly comes under this class, its aim 
 being to examine the feelings not so much with reference to the laws 
 of their own nature as to a particular theory viz., that of their empi- 
 rical origin.
 
 METHODS OF THE MOEAL SCIENCES. [B. V. 
 
 prevent our obtaining a correct notion of some important law 
 of human nature on which such institution relies for its suc- 
 cess, and so interfere with the process by which the specific 
 law is resolved into the ultimate principles of psychology. 
 
 It is only after a careful examination of the laws of the 
 homogeneous groups, both in their simple and conjunct action, 
 that we can expect to reach that general knowledge of the 
 order of antecedence and sequence in psychological pheno- 
 mena which will enable us, from a few combinations, to 
 rise to the general principles at work in the production 
 of their complex states, and connect them by deductive in- 
 ference with the axiomata media, from which they branch out 
 into ramified connexion with particular facts. jSTow, since it 
 is entirely in our power to modify such general principles by 
 directing them to a given end, man, by the faculty which 
 such knowledge would confer upon him, might become in 
 some measure his own automaton. He need only calculate 
 the human agencies at work in the production of a given 
 character to superinduce that character either upon himself 
 or others, that is, allowing that time permitted the operating 
 causes to work out the result, and that his physical and 
 mental constitution opposed no insuperable barrier to their 
 action. Knowing from the general laws of mind what actual 
 or possible combination of circumstances are capable of pro- 
 moting or preventing the production of certain qualities, it is 
 obvious he can not only predict the particular type of cha- 
 racter which would follow any assumed set of circumstances, 
 but generate any quality he wishes in others, if those circum- 
 stances should be in his power 1 . As the science, however, 
 in its elementary stages is inductive, and as all its subse- 
 quent processes concern tangible facts, the deduction of 
 specific qualities accruing from particular circumstances of 
 position, must always be verified by the recognised results 
 of actual experience. As in the physical concrete deductive 
 sciences, whose method the science of human nature assumes, 
 each a priori deduction must be compared with inductive 
 inference from particulars. The theoretic conclusion as to the 
 type of character which should be formed by any given set of 
 
 1 One of the facts which such investigations are calculated to bring 
 to light is, that men differ less in natural capacities than is commonly 
 supposed, and that much is set down to genius which is only the result 
 of artificial aids and methods.
 
 C. II. 3.] EMPIEICISM IN SOCIOLOGY. 283 
 
 circumstances, must be tested by the specific experience 01 
 those circumstances whenever obtainable ; and the whole con- 
 clusions of the science must undergo constant verification 
 and correction from the general observations of mankind 1 . 
 
 The phenomena of society are produced by the operation 
 of outward circumstances upon masses of human beings, but 
 as the laws in operation among the single individuals, which 
 compose the aggregate body, are those of human nature, it 
 follows that the phenomena of society are produced by 
 complex combinations of the principles which govern human 
 thought, feeling, and action. Hence, the social states are 
 quite as much the product of fixed laws as the individual 
 states ; the phenomena are only more complex, and the proxi- 
 mate principles more derivative, not, indeed, from the 
 number of laws in operation, but from the extraordinary 
 number and variety of the elements, or agents, which in obe- 
 dience to that small number of laws co-operate in producing 
 the effect. If the laws of human nature, when concerned 
 with individual phenomena, required the deductive method to 
 unravel the complexity of the results, the need for the appli- 
 cation of the same method to social phenomena is doubly in- 
 creased, when we consider that this group of subjects arises 
 out of a multiplication of the complexity considered in the 
 most intricate phenomena of individual character. If, in- 
 deed, in the latter subject crude empiricism was to be con- 
 demned, in sociology it is far more censurable ; since the laws 
 of human nature at this stage exist in far more complex 
 states, and present more intricate problems for solution than 
 are to be met with in individual character. 
 
 Up to this time, however, with few exceptions, the only 
 attempts made to modify social states, or even to theorise 
 upon the regeneration of society, have been of this character. 
 Apart from all consideration as to the organisation of any 
 particular state of society, men have advocated measures for 
 their amelioration, influenced by no other motive than that 
 the specifics recommended had been found good in other in- 
 stances; forgetting that one remedy could not cure all 
 diseases, and that what was salutary in one climate might 
 
 1 Mr. Mill treats these laws as a distinct science, under the name of 
 Ethology. In this and the other portions of his treatise he follows the 
 doctrine of Comte, but with such allowance for the free action of the 
 will as not to disturb the ashes either of St. Augustine or Pelagius.
 
 284 METHODS OF THE MORAL SCIENCES. [B. V. 
 
 prove poisonous in another. After a measure was deemed 
 good in itself, the only question which these philosophic poli- 
 ticians asked themselves was, how can we get the people to 
 adopt it ? No social arrangement that might be deemed 
 desirable was expected to encounter any obstacles from the 
 organism of the society to which it was to be applied, but solely 
 from the private interests or prejudices of the individuals 
 who constituted its members. Statesmen thus attempted to 
 master the pathology and therapeutics of the social system 
 before they had laid the necessary foundations in its physio- 
 logy to remove distempers without understanding the laws 
 of health ; and the result was such as it must always be when 
 men, even of conspicuous ability, attempt to deal with the 
 complex questions of a science before its simpler and more 
 elementary propositions have been established. 
 
 There is a close analogy between the organisation of dif- 
 ferent states of individual character and those of social com- 
 munities. In the latter, as in the former, there are homo- 
 geneous groups of phenomena capable of being studied apart 
 from the general subject, and forming in themselves the 
 nucleus of distinct sciences. Such are political economy ; 
 the science which concerns the formation of political charac- 
 ter, or the character belonging to each age and country ; and 
 the science of government. Each of these subjects takes into 
 consideration a distinct class of phenomena mutually de- 
 pendent upon one another, and not likely to be much inter- 
 fered with by the action of the other agencies which enter 
 into the organisation of society, at least beyond results which 
 are capable of being calculated and allowed for in every 
 instance. Thus political economy takes cognisance of such 
 phenomena of the social state as are generated by the pur- 
 suit of wealth. It makes entire abstraction of every other 
 human passion or motive, except those which may be regarded 
 as antagonist to the desire of gain : viz., aversion to labour and 
 desire of present enjoyment. Nor are its results, when the data 
 are fairly expressed, ever wide of the truth. For, notwithstand- 
 ing men in all cases are not influenced by the desire of obtain- 
 ing wealth with the least possible labour, upon which supposi- 
 tion the fundamental axioms of the science proceed, it cannot 
 be denied that in commercial speculations such assumptions 
 hold ; and since the principles of political economy are only
 
 C. II. 3.] SOCIOLOGY WHERE DEDUCTIVE. 285 
 
 applied to transactions of this nature, provided they exactly 
 express the laws of the tendencies to which they refer, they 
 are never likely to mislead. Now it is only when the phe- 
 nomena are so restricted to a definite class of subjects, that we 
 are favourably situated for acquiring a knowledge of the 
 minuter agencies which enter into the organism of the 
 social state, and calculating (a priori) by direct deduction 
 the eifect of any single law. For in such cases, the circum- 
 stances with which the new law will interfere are previously 
 known ; and no counteracting or disturbing agent can lie con- 
 cealed to mar the correctness of the calculation founded upon 
 their absence. For instance, suppose the effect is required 
 to be known of commuting a certain quantity of indirect for 
 direct taxation : will the result be an augmentation of the 
 wealth and productive labour of the community ? Such a ques- 
 tion is able to be answered by purely a priori considerations j 
 for the phenomena with which the law has to deal are distinctly 
 marked out by the nature of the case, and little inference is 
 required to calculate how far the changes in question are 
 likely to operate to the advantage of the community. The 
 result of such direct reasoning can of course be easily veri- 
 fied by an appeal to actual experiment. In this manner Peel 
 worked out those judicious alterations in the British tariff 
 which have already made his name illustrious among European 
 statesmen. It was commonly thought that during his first 
 trials he was picking his way by the empirical process of 
 observation, and thus making experiments on the nation as 
 M. Majendie used to try his specifics on dogs and rabbits. 
 But the fact was otherwise. Peel had convinced him- 
 self that such alterations were judicious, and the deliberate 
 manner in which he worked them out, was simply to afford 
 timely warning to the interests concerned, as well as to 
 realise the sage counsel of Bacon, " in all your innovations 
 imitate nature, whose changes are quiet and imperceptible," 
 &c. 
 
 But it is obvious that the conclusion arrived at in this 
 particular case could not be generalised and erected into a 
 universal proposition of political economy. Had Peel been 
 desirous to extend the same principle to any other European 
 country, his object should have been to ascertain how far its 
 financial condition was analogous to that of England, and to
 
 286 METHODS OF TIIE MOBAL SCIENCES. [B T. 
 
 what extent and in what direction the industry and habits of 
 the people were likely to be influenced by the change. If the 
 wealth of the nation was more equally distributed than in 
 England, were its merchants and principal speculators just 
 struggling into importance, and its artisans in a flourishing 
 condition, it is obvious that a commutation of a portion of 
 the customs and excise for a direct tax upon capital would 
 be attended with ruinous effects. It would be a blow against 
 the rising civilisation of the community calculated to strike 
 down those who manifested any aptitude to direct or manage 
 its resources, and prevent them from grasping those facilities 
 which might enable them to economise labour, to open new 
 commercial channels to the ' enterprise of their countrymen, 
 and found institutions of education and benevolence. Hence 
 the results of such speculations are necessarily hypothetical. 
 No branch of the sociological sciences will help us to a uni- 
 versal proposition, stating in every case the effect of any 
 given law, but simply enables us to adapt the law to suit the 
 circumstances of any given case. The separate study of the 
 structure of the homogeneous parts of the social organism 
 makes the statesman acquainted with all the phenomena 
 with which the contemplated law is likely to interfere, just 
 as the knowledge of any particular organ of the human 
 system enables the physician to state a priori what agencies 
 are destined to be neutralised, counteracted, or promoted by 
 the action of certain diets and medicine ; and it is the pro- 
 vince of the medical or political operator to frame a law whose 
 action on that particular function of the system is destined 
 to eliminate the unsound tendencies and promote the healthy 
 action of the vigorous parts. The several branches of the 
 sociological sciences will furnish him with a multitude of 
 generalisations for this purpose true under the circumstances 
 in which they were obtained. It depends on his own tact, 
 how far he may be enabled to bring the new case contem- 
 plated, under any one of these heads, in order that the same 
 specific may be applied with as little alteration of the text of 
 the law as the circumstances warrant : but it is obviously the 
 duty of every statesman, before he applies his law, however 
 cautiously its provisions may have been framed, to meet the 
 peculiar circumstances of the case, to examine if the kindred 
 sociological science will supply him with any instances of
 
 C. II. 3.] VEBIMCATIONS OF SOCIOLOGY. 287 
 
 the effects of similar laws on analogical phenomena, and so 
 verify his conclusions by actual experience. If such prece- 
 dents, however, cannot be found, if either the law, or the 
 circumstances to which it was applied, manifest any startling 
 discrepancies of character, or if he has reason to think that, 
 notwithstanding the generalisation is similar which form the 
 peculiarities of the case, many of the operating conditions 
 lie concealed, the only possible mode of verification open to 
 the statesman is to deduce from the principles involved in 
 his law as much of the phenomena to which it refers both 
 in past ages and different communities, as would be likely to 
 be affected by it, and show that the results of past experience 
 completely harmonises with the conclusions of his theory. 
 If his expectations of the effects of any given cause in an 
 assumed set of circumstances will not enable the statesman 
 to explain and account for all that portion of the social phe- 
 nomena existing in times past or present which that cause 
 would have a tendency to influence, it is a proof either that 
 the facts which ought to be taken into account are not 
 known, or that the theory is not sufficiently accurate to meet 
 all the consequences. In either case a statesman would do 
 well to reconstruct his theory, and not venture to predict 
 the future by inference from any data that could not be 
 brought in unison with the present and the past. 
 
 The .inquiries which concern these special branches of 
 social phenomena generally concern the effects which will 
 follow from single causes in a certain condition of social cir- 
 cumstances ; but there is also a second inquiry with relation 
 to the laws which preside over the general circumstances 
 themselves, and determine the order of sequence and ante- 
 cedence between one social state and another. It is found, 
 for example, when the history of past ages is consulted, among 
 the various states of society existing in the different regions 
 of the earth, that certain uniformities exist between succes- 
 sions of phenomena ; so that one feature of society never as- 
 sumes a particular state without affecting the co-existing 
 states in a more or less precisely determinate manner. For 
 example : among highly civilised communities the existence 
 of an extremely despotic monarchy is invariably attended 
 with laxity of moral ties, and, if perpetuated for a long period, 
 causes a decline of the arts, degradation of literature, and a
 
 288 METHODS OF THE MORAL SCIENCES. [B. V. 
 
 general retrogression of humanity. And, in like manner, 
 where insuperable harriers are erected between the classes 
 of any community, and the highest social functions are only 
 open to certain privileged castes, mankind are never sure to 
 emerge from a semi-barbarous state, or to make any advance 
 in civilisation. Such uniformities between certain states of 
 society and institutions are mere derivative laws from the 
 higher principles of human nature, and can readily be ac- 
 counted for a priori. For, if it be an axiom, as it assuredly is, 
 that the phenomena of society are mere creatures of mind, 
 and that the arrangements which they manifest, are more or 
 less in accordance with the fitness of things according to the 
 degree in which the mental agent manifests its supremacy ,- 
 it follows that every society will flourish or decay in propor- 
 tion as obstacles or inducements are flung in the way of its 
 influence, or according to the mode in which the institutions 
 of the country act upon its growth, or stimulate or depress 
 its development. Now, the existence of castes, or slavery to 
 any large extent, or an imprimateur clapped on the press, or 
 the gagging of public opinion has this direct tendency ; and 
 such exclusions and prohibitions cannot be perpetuated 
 through generations without engendering corruption of man- 
 ners, and turning society itself into an instrument for the 
 degradation of humanity. 
 
 The prosecution of sociology, nevertheless, in its present 
 stage, labours under great disadvantages, on account of the 
 backward state of psychological science, into which its laws 
 are destitaed to be ultimately resolved. "While the prin- 
 ciples of psychology fluctuate, no derivative uniformity ob- 
 servable between co-existing or successive states of social 
 phenomena can be verified by its connexion with the corre- 
 sponding psychological laws ; and the only mode of ascertain- 
 ing the correctness of generalisations obtained by an analytical 
 survey of history, is to resolve them into the simpler laws to 
 which they inferentially lead, and to test their correctness 
 at this stage by comparing the results to which they conduct, 
 both in social and psychological phenomena, with specific ex- 
 perience. Thus, in the cases already cited, of the obnoxious 
 character of those institutions which tend to depress intellect, 
 the principle into which the uniform phenomena were re- 
 solved obtains, not only in individual instances, but in every 
 single exertion of the human faculties. For those men are
 
 C. II. 3.] SOCIAL STATICS AND DYNAMICS. 289 
 
 the foremost of our species, in whom mind has most largely 
 predominated, and who have opposed the least obstacle to its 
 influence ; and every reflex act of thought directed to resolve 
 any problem, is more likely to obtain its purpose in propor- 
 tion to the continuity and vigour with which it is exercised, 
 or according to the abstracting power by which it shuts out 
 extraneous influence and fastens on its object : a truth, of 
 which Newton acknowledged the force when, on being asked 
 by what means he succeeded in revealing that wonderful law 
 which unlocked the mechanism of the heavens, he replied, 
 by always thinking about it. "When principles are reached 
 of this extensive kind, which account deductively for all the 
 social phenomena in which they can be supposed to possess 
 any large influence, if they may not be assumed to be the 
 ultimate psychological laws wanting in the case, at least they 
 may fairly be relied on as corollaries from them, and so far 
 allowed to form the standard of indirect verification. 
 
 The empirical uniformities which it is the object of obser- 
 vation to set apart, as most likely to lead to the discovery of 
 sociological laws, relate either to co-existent or successive 
 phenomena ; and according as this science is occupied in 
 ascertaining and verifying the former sort of uniformities, or 
 the latter, M. Comte gives it the title of social statics, or of 
 social dynamics, conformably to the distinction in mechanics 
 between the conditions of equilibrium and those of move- 
 ment ; or in biology, between the laws of organisation and 
 those of life 1 . The first branch of the science ascertains the 
 conditions of stability in the social union the nature of the 
 relation existing between the different parts of the social 
 organism in its healthiest state ; the second concerns the 
 laws of progress, or the theory of society in a state of con- 
 tinuous movement. It must, however, be observed, that the 
 study of social statics can never be so completely disentangled 
 from the second branch as not to be in a great degree modi- 
 fied and controlled by its laws, as the uniformities of co- 
 existence obtaining between social phenomena are mere 
 corollaries from the laws of causation by which the succes- 
 sive states of those phenomena are determined. The mutual 
 actions and reactions of cotemporaneous social states are 
 
 1 Cours de Philosophie Positive, iv. 325. 
 u
 
 290 METHODS OF THE MORAL SCIENCES. [B. V. 
 
 mere complex effects arising from the fundamental movement 
 going on among them. The mutual correlation, therefore, 
 between the different elements of each state of society is a 
 derivative law resulting from the laws of succession between 
 one state of society and another ; and if we make a provi- 
 sional abstraction for the purpose of marking the coincidences 
 between their simultaneous effects, it is not only with a view 
 to ascertain the elements of social stability and many unifor- 
 mities of practical importance, but also to approach closer to 
 the resolution of the fundamental problem of sociology, and 
 discover the laws according to which any state of society pro- 
 duces the state which succeeds it and takes its place. 
 
 Of the practical value of this division of the science there 
 cannot be a doubt to him who considers the flood of light 
 capable of being shed upon the laws of social phenomena by 
 regarding them in the two special states of mutual depen- 
 dence and correlation, and making the uniformities of co- 
 existence and succession act as verificatory tests of each other. 
 It is, moreover, through the study of the uniformities of co- 
 existence that we are led to observe the more recondite laws 
 which preside over the generation of successive states of 
 society, of which the derivative laws of correlation are mere 
 complex exemplifications ; and to form those general maxims, 
 of the widest possible utility in statesmanship, which embody 
 the elements of social union, the principles which consti- 
 tute the ligaments by which the different parts of the social 
 organism is bound together, the ingredients which enter 
 into those ligaments and tend to increase or corrode their 
 vigour, and the chief properties on which the healthy action 
 of the leading functions depend, both in their individual 
 states and conjunct agency. By this branch of sociology we 
 are able to determine, from the absence or the presence of 
 certain elements in any given society, the general features 
 which characterised its past condition, just as we may infer 
 from the state of the abstract sciences in any age the amount 
 of erudition possessed by its leading sages 1 . 
 
 In examining the elements of social stability the states- 
 man will not only regard the essential requisites whose 
 
 1 A case in point is furnished in the dissipation of the pretended 
 astronomical lore ascribed to the Egyptian priests, as soon as it was 
 known that abstract geometry did not exist among them.
 
 C. II. 3.] OBJECT OF SOCIAL DYNAMICS. 291 
 
 presence is indispensable to the perpetuity of its functions, 
 but the precise effect which has attended the relative degree 
 in which they have exerted their action. He cannot fail to 
 observe, for example, the effects of severe restraining disci- 
 pline in fashioning the heroic states of antiquity, and the 
 martial spirit infused into their population, both by the cultiva- 
 tion of a strong feeling of nationality, and by throwing open 
 the highest posts of command to the ambition of the meanest 
 soldier. He will not fail to observe the effect of an equitable 
 administration of justice in teaching men to respect law ; and 
 the diminution of national wealth in proportion as property 
 became insecure and as excessive commercial restrictions were 
 adhered to. Nor can it escape his attention that without 
 some form of religion no society can hold together long, and 
 that the degree of its influence may be taken as a fair index 
 of the soundness and durability of the concomitant parts. 
 The indispensable conditions for the foundations of the 
 social fabric may, indeed, be deduced a priori from the laws 
 of human nature ; but the precise degree in which they 
 ought to be combined, to bring about a certain result, must 
 be gleaned from a close examination of social phenomena, 
 and the knowledge so obtained afterwards verified by com- 
 parison with psychological laws, and the known results of 
 analogical combinations. By the pursuit of such methods 
 men have erected social fabrics in times of great anarchy, 
 founded empires on the ruins of old societies, and made the 
 mean capital of a petty state the meridian of the earth's 
 glory. "Witness Charlemagne, Frederic the Great, and Na- 
 poleon. 
 
 The great object of social dynamics is to trace each of the 
 principal features of every generation to its causes in the 
 generation immediately preceding it. This may appear, where 
 single states are concerned, to present little difficulty ; for 
 every element in each nation can have its causes distinctly 
 marked out among the aggregate conditions that constituted 
 the state of society in the preceding centuries. But such 
 special cases only compose the materials of the elements 
 which determine the leading qualities attaching in common 
 to vast groups of progressive communities, which it is the 
 aim of social dynamics to resolve in their complex causes, 
 in showing what group of antecedents have generated each 
 
 172
 
 292 METHODS OF THE MOEAL SCIENCES. [E. T. 
 
 of the general phases which constitute the character of any 
 one generation. The difficulty of establishing this filiation, 
 and mounting to the most general laws of the succession of 
 social states, is increased in proportion to the number of 
 distinct nations, and to the discrepancies of government, 
 which they involve ; for, according as men are kept under 
 the action of various, and often clashing agencies, the uni- 
 formities of succession, as well as of co-existence, become 
 more fragmentary, and present insuperable obstacles to the 
 science which seeks to evolve them out of general laws. 
 Nevertheless, this difficulty is not without its advantage, in 
 affording a more ample field for the verification of the middle 
 axioms of the science ; since the assumed general uniformity 
 may fairly be regarded as a derivative law of human nature, if 
 it accounts for all the phenomena which falls under its influ- 
 ence in so diversified a theatre. 
 
 As it is only through the intermediate uniformities that 
 we can hope to grasp the higher generalisations of the 
 science, the means of testing their correctness cannot be too 
 highly valued. Now this is afforded to us through the varie- 
 gated social phenomena which constitute the living society 
 of every age, and the different degrees of prosperity and 
 decline they manifest in the various stages of their existence. 
 If any uniformities of succession will enable us to explain 
 why some nations continue to remain as they have begun, 
 and scarcely seem to ebb and flow, while others have spent 
 their vigour at the commencement, and others blazed out 
 in glory a little before their extinction ; why the meridian 
 of some have been the most splendid, and others have fluc- 
 tuated, and experienced at different periods of their existence 
 different reverses of fortune ; it is evident that such uni- 
 formities, found available for scientific explanation in so many 
 contrary instances, may be relied upon as derivative laws, 
 even if they only make out the case so far as their influence 
 in the generation of the phenomena could be expected to 
 extend. Axioms of this nature, which can be brought to the 
 test of diversified experience, must form the first stepping- 
 stones to higher laws ; and if they can be deduced from the 
 ultimate principles of human nature, these higher generalisa- 
 tions which it is the object of sociology to reach, will be 
 brought within the limits of judicious conjecture, and the
 
 C. II. 3.] GENERALISATIONS OF SOCIOLOGY. 293 
 
 suggestion started easily verified by comparison, either with 
 the a priori law, or with the simpler uniformities already 
 revealed. 
 
 The laws of social dynamics have been hitherto sought by 
 two distinct paths, the consilience of which on any one 
 point, has been deemed to furnish a strong verification of the 
 generality of the resulting uniformity. The progressive 
 tendencies of society have been pursued both in individual 
 communities and large groups of nations, whose social ele- 
 ments bore in any respects a kindred character. The con- 
 clusion, in M. Comte's view, broadly announces the law that 
 the course of progressive states of society, as well as that 
 of separate nations and individuals, is marked by three dis- 
 tinct phases : the theological, which presides over the elemen- 
 tary stage ; the metaphysical, which is the distinguishing 
 characteristic of the middle ; and the sceptical, or positive 
 philosophic feature, which is the predominant element in the 
 third. This generalisation, however, notwithstanding some 
 striking coincidences, is not reconcileable with fact; nor 
 is one of so sweeping a nature likely to be gained while 
 the elementary laws of the science, which must form the 
 platform to such a principle, are not yet raised from 
 the ground. Similar empirical axioms have been gathered 
 from an analytical survey of social phenomena, of a less pre- 
 tentious character, and more within the limits of truth, but 
 still open to occasional exceptions, and of course unverified 
 by psychological laws ; such as the aphorism of Bacon, that 
 in the beginning of states arms flourish, while intellectual 
 qualities are predominant in their maturity, and mechanical 
 agencies characterise their decline ; and those of some French 
 historians, which imply that as society advances mental quali- 
 fications gradually assume control over animal force, and 
 masses prevail over individuals ; that the first occupation of 
 mankind is chiefly military, which becomes by degrees ab- 
 sorbed in productive pursuits, until the spirit of clanship is 
 entirely transformed into an agent of the industrial arts. 
 These generalisations, even if strictly true, only assume the 
 appearance of so many sage conjectures, and can be held of 
 no scientific value, until shown to arise out of psychological 
 principles, and connected with the more complex uniformi- 
 ties to which they are akin. The error of speculation in
 
 294 METHODS OF THE MOEAL SCIENCES. [B. V. 
 
 this branch of sociology appears to consist in grasping at 
 vague generalities, which seem to coincide with fact, but 
 leave us without knowledge to state why they do so. 
 
 Such generalisations, however useful they may prove in 
 the subsequent stages of the science, can be of no avail 
 before the science can hardly be said to have commenced. 
 To attempt to inaugurate the study of an a posteriori science 
 by the fashioning of such universal propositions, is like com- 
 mencing to erect a building by the formation of pediments 
 to which we have no reason to know that the edifice will 
 correspond. The only mode by which any advance can be 
 made in the construction of sociological science is by 
 mounting from the simplest and most evident unifor- 
 mities to those of a more universal and complex character, 
 and seeking at every step to infer what laws of human 
 nature are involved in their production. A successful in- 
 ference will lead us to connect many generalisations before 
 deemed empirical with the ultimate principles of psychology, 
 and to interweave them in a web of confirmatory relation with 
 the lowest uniformities of the science. Thus, stations will 
 ultimately become opened in all quarters, and cross-lines 
 interposed, so that no accurate generalisation can be drawn 
 from history without having its higher laws assigned, and 
 being fitted into its precise place in the system. This is 
 the invariable method by which all sciences that relate to 
 successive phenomena, which have reached a high degree of 
 development, have been cultivated. Nor can we see any- 
 thing in sociology to exempt it from its influence. Yet the 
 science was no sooner propounded by Vico, and began to 
 excite any degree of attention, than its cultivators entered 
 into hot discussion upon the last question that the science 
 even in the highest state of maturity could be expected to 
 resolve viz., whether there results from the progressive 
 movements of society either a cycle or a trajectory course ? 
 "Whether society revolves in an orbit, or moves in a straight 
 line and so never returns to any of its former states ? a 
 problem whose resolution has about the same relation to 
 the discovery of social laws, as the disquisitions of Thales on 
 the first element of all things, have to the Galilean physics 1 . 
 
 1 The work of Giambattista Vico, entitled, Principi di Scienza nuova 
 d'Intorno alia Commune Natura delle Nazione, first saw the light at 
 Naples in 1725. But the most eulogistic of his editors admit that he
 
 C. II. 4.] CALCTJIiATION OF PROBABILITIES. 295 
 
 4. Probable Inference. Example and Analogy. 
 
 The moral sciences have their department of probable 
 evidence as well as the physical, and that to a far greater 
 extent. Since, in addition to their subjects being less ad- 
 vanced and exposed to more uncertain, intricate, and fluctu- 
 ating agencies, there are many branches of evidence in them 
 where direct certainty is unattainable, and the most that can 
 be gained is a high degree of probability. By far the 
 greater portion of the inferences we draw with reference to 
 ordinary life, from the government of a kingdom to the 
 crossing of a street, is of this character. Did we wait for 
 grounds of complete certainty before we moved in the per- 
 formance of any action, we should ever stand still. Human 
 society would be in a state of perpetual blockade. Our 
 only resource in the generality of cases is to calculate 
 probabilities, and act upon them. "We perceive that a 
 specific point cannot be definitely established, and examine 
 all the probabilities capable of being adduced in its favour, 
 and weigh the aggregate amount with those against it. 
 In proportion to the exact degree in which one or the 
 other preponderate, ought to be our acceptance or dis- 
 trust of the proposition. When arguments tend to esta- 
 
 was quite incapable, on account of the narrow circle of his erudition, 
 to construct theories reducing to the philosophical union of causal con- 
 nexion the multifarious phenomena of history. Vico, as far as Greek 
 and Latin antiquity went, was erudite enough, and his historical 
 theorems and postulates receive plausible support from that side of 
 humanity; but he knew little either of the Oriental world or of the 
 Middle Ages ; and hence his abstract generalisations met with complete 
 discomfiture when applied to interpret the phenomena which these 
 stages of humanity present. His theory of the course of nations, being 
 exclusively modelled on the Boman world, is quite in conflict with 
 the vast confederations of European civilisation ; and he regards those 
 instruments on which the generality of the seers of the present age rely 
 for the indefinite amelioration of their species, as the principal agents 
 in bringing about that decline iu European commonwealths which, ac- 
 cording to his system, is again to reduce mankind to a state of primitive 
 barbarism. The press, in Vico's view, is an engine calculated to obscure 
 and weaken the judgment by the spread of useless facts (Op. lat. i. 
 p. 41); religious toleration, a mark of the entire want of sincerity in re- 
 ligious conviction (Scienza nuova, pp. 350, 424). The abandonment of 
 the ancient languages as a means of transmitting thought, according 
 to the same author, will lead to the destruction of taste and philoso- 
 phical acuteness (Opusc. p. 16). We need say no more to show the 
 reader that Vico can hardly be trusted as a telescope of the future.
 
 296 METHODS OF THE MOEAL SCIENCES. [B. T. 
 
 blish the point they are intended to support with various 
 degrees of probability, no bare summing up of the single 
 results will give us an accurate idea of the strength of the 
 cumulative evidence without taking into account the de- 
 flection of the converging lines of argument and the amount 
 of probability the conclusion receives, not only from the 
 number, but from the variety and opposite nature of the 
 proofs. For example, if a certain conclusion be made out by 
 three lines of argument, each establishing a probability in its 
 favour, varying as , -f, and - ; in adding up these fractional 
 probabilities, it ought to be taken into account, to what 
 degree the adduced reasons vary in their subject-matter ; 
 and if this be to any extent, an additional fraction should 
 be annexed to the aggregate sum to represent the im- 
 probability arising from the inference that a proposition 
 should be untrue which was supported by testimony of so 
 discordant a nature. There are likewise cases in which 
 some deduction must be made from the total result for 
 a contrary reason. For example, if the testimony of three 
 witnesses be taken who have been in collusion with each 
 other, in casting up the individual probabilities in favour 
 of each party's testimony an abatement must be made in con- 
 sideration of the identity of interest existing between them. 
 
 The latter is an instance of joining probabilities by way of 
 addition, the result of which is an aggregate probability greater 
 than the individual instances of which it is composed. There 
 is another mode by way of deduction, where the certainty 
 diminishes with every new instance of probability implied in 
 the proof; as when we adduce the testimony of one witness, 
 that he has heard a thing asserted by another, who was not 
 himself an original witness, but who obtained it from one 
 who professed to have ocular evidence of the fact. The 
 former chain of evidence was termed by Mr. Bentham a self- 
 corroborative chain ; the latter, a self-infirmative chain 1 . 
 
 Both are applicable to the summation of that class of pro- 
 positions, whether physical or moral, which approximate to 
 the truth, but do not universally obtain in all cases ; such as, 
 Most pious men are grave ; Most rulers are influenced by 
 self-interest ; The generality of aged persons are cautious. 
 
 1 Kationale of Judicial Evidence, book v.
 
 C. II. 4.] LIMITATION OF PEOBABILIT1ES. 297 
 
 Now, it often happens when such proximate generalisations 
 are connected with others in a given proportion, through a 
 term which is common to both, that it is required to be 
 known what probability will attach to the occurrence of the 
 new term with either of the other terms. Thus, if two out 
 of every three pious men are grave, and three out of every 
 four studious men are grave, what probability is there that 
 every pious and studious man will have the property of 
 gravity? The answer will obviously be -y-. For the pro- 
 bability against the supposition will arise out of the com- 
 pound of the single probabilities. Now, against the occur- 
 rence of the first there is the chance of , and against the 
 second -J, the compound result of which ( T ^) deduced from 
 unity assigns the probability we have determined upon. 
 Hence the aggregate probability is greater than the indi- 
 vidual ones f or -|. Again, suppose that proximate generali- 
 sations similarly connected were required to be dealt with 
 by way of deduction, the probability arising from two pro- 
 positions taken together in this case will be correctly mea- 
 sured by the probability arising from one abated in the ratio 
 of that arising from the other. Thus, if nine out of ten 
 charitable persons are religious, and five out of every twenty 
 inhabitants in London are charitable, the probability that 
 any metropolitan citizen is religious will be -^y, or somewhat 
 less than -i. It is evident that there can be many links to 
 such calculations, but each additional step only involves a 
 repetition of the principle we have laid down. 
 
 Proximate truths of this kind may, however, occasionally 
 be transformed into universal propositions of scientific accu- 
 racy, by assigning some mark which clearly separates the 
 accordant from the exceptional cases; and reasonings de- 
 pendent upon them may be carried to any length we please, 
 by taking care, in the introduction and composition of every 
 fresh generalisation, to annex the sign on which its uni- 
 versality depends. For instance, the proposition Most per- 
 sons who have uncontrolled power employ it ill, may be in- 
 vested with a universal character, either by assigning the 
 features which invariably characterise licentious despots; 
 viz., weakness of judgment and will, with depraved habits, 
 or by assuming the opposite qualities to these as exceptional 
 cases. Thus, All persons of weak judgment and depraved
 
 298 METHODS OF THE MOEAL SCIENCES. [B. V. 
 
 habits who have uncontrolled power employ it ill ; or, All 
 persons who have uncontrolled power employ it ill, provided 
 they are not persons of unusual strength of judgment and 
 confirmed habits of virtue. Now, if we annex to this pro- 
 position another of a similar character, as, All absolute 
 monarchs have uncontrolled power who are independent of 
 the active support of their subjects, we may deduce from both 
 the universal conclusion that all absolute monarchs employ 
 their power ill who do not need the active support of their 
 subjects, unless they are persons of unusual strength of 
 judgment and confirmed habits of virtue. It is of no con- 
 cern how rapidly such conditions accumulate, provided we 
 assign the distinguishing rank to each proposition, and ex- 
 press the aggregate with every additional conclusion. 
 
 Occasionally, as in reasonings which concern large masses, 
 and do not in the slightest degree affect the actions of iso- 
 lated individuals, proximate generalisations are all that is 
 required, even to establish a conclusion of scientific value. 
 Neither the general or the statesman desires complete accu- 
 racy in the data on which they found their respective mea- 
 sures for the guidance of the numbers over whom they pos- 
 sess control. It is enough for them to know that most 
 persons comport themselves in a particular way, since their 
 speculations refer almost exclusively to cases in which vast 
 groups of men are acted upon simultaneously, and in which, 
 therefore, what is done or felt by most persons determines 
 the result produced by or upon the general body. In these 
 cases proximate truths assume the nature of precise gene- 
 ralisations with reference to the results to which they are in- 
 tended to lead. The properties of multitudes can only be 
 ascertained by approximations of this nature, but they are 
 not the less strictly amenable on that account to scientific 
 law than those of individuals. 
 
 The probable inferences in the moral sciences which corre- 
 spond to those drawn in the physical, from the resemblance 
 of their objects to phenomena whose properties for the most 
 part lie beyond the grasp of our faculties, may be ranged 
 under the head of example and analogy. We are not able to 
 penetrate beyond the vista of the present, and form indu- 
 bitable inferences with respect to the future effects of certain 
 actions upon any specific individual ; for, being ignorant of the
 
 C. II. 4.] ARGUMENT OF EXAMPLE. 299 
 
 impulsive forces which generate individual character, and the 
 laws according to which they act, we want all the data that 
 could help us to a conclusion of scientific value ; yet we augur 
 the complexion of those effects, and in the generality of cases 
 find we are not far short of the truth. These conclusions 
 are found to predict in many cases with tolerable accuracy 
 what will be the future position of a character chiefly de- 
 pendent on fame, on knowledge, and talent, for success; 
 and that with no further data on the part of their framers 
 than what is afforded by superficial observation. They 
 know what has occurred in past instances will occur again 
 if similar conditions supervene, and they leap from the re- 
 semblance of properties to that of effects. This is strictly 
 the argument of example. It is induction on practical mat- 
 ters, the laws of whose action are hidden from us, but whose 
 uniformities we nevertheless predict, grounding our inference 
 upon the effects which the laws have exhibited in the past. 
 Of this kind of loose induction Horace will afford us an 
 example: "If my father," says the poet, "wished to per- 
 suade me from squandering my estate in profligate living, he 
 would point to some spendthrift who had ruined himself 1 ." 
 The father of the bard left him to infer from the example of 
 Barrus, and the son of Albus, who had both impoverished 
 themselves by luxurious living, that those who so act com- 
 monly come to ruin. The staple argument of most people 
 assumes a similar form. They judge simply from past effects ; 
 and according to the constancy with which the uniformity in 
 question has obtained, they imply its occurrence in future. 
 
 To such kind of inference there can be no objection, if not 
 stretched further than the limits in which it has been ob- 
 served warrant ; but the evil is, that men leap from a few 
 casual instances of successive or concomitant uniformity to a 
 wide generalisation, implying a law of causation between the 
 phenomena concerned. Having observed that the country 
 prospered under unfair institutions, or that trade flourished 
 
 " Insuevit pater optimus hoc me : 
 Ut fugerem, exemplis, vitiorum quaeque notando. 
 Cum me hortaretur parce, frugaliter, atque 
 Viverem uti contentus eo quod mi ipse paressetu, 
 Nonne vides Albi ut male vivat filius? atque 
 Barrus inops? magnum documentum ne patriam rem 
 Perdere quis velit." HOT. Serm. L 4.
 
 300 METHODS OF THE MOEAL SCIENCES. [B. V. 
 
 during the last war, they arrive at the sweeping conclusion, 
 without looking into the circumstances of the case, that such 
 institutions are essential to the welfare of the community, 
 and that commerce is increased by foreign war. But pre- 
 vious to any inference being made, men should not only 
 regard things as they are, but look to the causes which pro- 
 duce them, and endeavour to discover their mutual inde- 
 pendence. If the uniformity seem to be connected with no 
 law that we can discover, the extent to which it is to be 
 relied upon, is simply a case of calculation by the ordinary 
 laws of probability : where, however, it appears as the result 
 of a causal tie between the sequential or concomitant pheno- 
 mena, the laws of which, however, we cannot calculate, we 
 may regard the uniformities as universal laws, and predict 
 their occurrence in all instances which do not present coun- 
 teracting obstacles to their agency. The discovery, however, 
 of such conflicting agencies, and the nature of the law on 
 which the uniformities themselves depend, are necessary to 
 raise them out of the category of conditional truths, and 
 invest their prediction with scientific certainty. 
 
 Analogical evidence, in a strictly moral sense, comprises 
 that kind of inference which is drawn from mere resem- 
 blance of relations 1 ; as if from the assumption that the colo- 
 nies stand in the same relation to the mother country as a 
 child to its parent, any one were to argue that unconditional 
 
 1 " Every one knows," says Bishop Berkeley, in his Minute Philo- 
 sopher, " that analogy is a Greek word, used by mathematicians to 
 signify a similitude of proportions. For instance, when we observe 
 that two is to six in the same proportion (ratio) as three is to nine, 
 this similarity or equality of proportions (ratios) is termed analogy. . . . 
 The schoolmen tell us that there is analogy between intellect and sight ; 
 forasmuch as intellect is to the mind what sight is to the body ; and 
 that he who governs the state is analogous to him who steers a ship." 
 It would, however, greatly contribute to philosophical exactness if the 
 word were confined to one of the three senses for which it is now too 
 indiscriminately used. We have called, in conjunction with most 
 metaphysicians*, the grounds of analogy those on which the physical 
 sciences rest. If this term be accurate, another ought to be found to 
 distinguish resemblance of qualities, and a third, distinct from the two 
 preceding, to express similarity of relation. While the three meanings 
 are huddled together under one name, confusion of ideas must ine- 
 vitably ensue. 
 
 * See Foundations of Evidence, p. 171, with note.
 
 C. II. 4.] ARGUMENT OF ANALOGY. 301 
 
 obedience to all the degrees of the central authority was the 
 clear duty of the colonists ; or from the similarity of relation 
 existing between a nation and its rulers, and a joint-stock 
 company and its board, that the people were perfectly at 
 liberty to choose their own governors, cashier them for mis- 
 conduct, and in case of need to frame a government for 
 themselves. In this narrow sense, however, analogy is rather 
 suited for illustration than argument, nor can we adduce any 
 example in which its force arises above that of weak proba- 
 bility. Arguments which arise from the direct similarity of 
 things are weak enough when the evidence does not amount 
 to a complete induction ; but when we introduce the element 
 of the similarity of relation of things, the amount of proba- 
 bility dwindles in rapid proportion, and exhibits an inherent 
 inferiority of conclusiveness. 
 
 It, however, very frequently happens that analogical argu- 
 ment is capable of meeting both cases, and rests its inference 
 not only on similarity of relation, but on the direct resem- 
 blance between the things themselves. As an instance of 
 the high conclusive force which double analogies of this kind 
 are capable of attaining, we may adduce Butler's famous 
 argument in favour of the divine origin of Christianity. The 
 proof may be said to consist in close compact inference from 
 the resemblance of the system of nature and the economy of 
 God's visible dispensation in the natural world, to the system 
 of religion and the economy of God with regard to the present 
 and future state of our moral being. We may also regard it 
 as an argument by strict analogy, inferring the truth of the 
 Christian religion from the fact that it puts forth the same 
 relations to man and its author as the system of nature. If 
 we grant, therefore, that God created nature, we cannot well 
 avoid the conclusion that the Christian scheme, so similar to 
 it in its deepest and broadest relations, should have sprung 
 from the hands of the same artificer. The force, however, of 
 the argument in the last case is derived from the strength 
 which attends it in the former, or may be said to be con- 
 founded with it. From the evidence of design and profound 
 adaptation of parts to meet certain ends which the Christian 
 religion exhibits, we infer its divine origin, just because similar 
 evidence in the case of nature has led mankind to the conclu- 
 sion that it came from God. The conclusiveness of the proof 
 does not proceed from mere similarity of relation, but from the
 
 302 METHODS OF THE MOEAL SCIENCES. [B. Y. 
 
 fact of that resemblance arising out of vastness of design, and 
 intricate and elaborate co-ordination of parts with reference 
 to a constituted whole which mark both systems, and stamp 
 them as the works of the same author. The degree of con- 
 fidence to be placed in this and similar analogical arguments 
 will depend, of course, on the amount of similarity as con- 
 trasted with that of dissimilarity involved in the case, taken 
 in conjunction with the extent of our knowledge of the indi- 
 vidual subjects whose properties are compared. If the unex- 
 plored region of unascertained properties be large, or if we 
 have reason to think that many remain concealed whose dis- 
 covery might affect the probability to which the recognised 
 resemblances point, faint stress indeed should be laid upon 
 the evidence. 
 
 Notwithstanding the argument of analogy in the cases 
 already contemplated, is never able to reach/above a high de- 
 gree of probability, it may occasionally form the ground of rigid 
 scientific inference in disproof of the position of an adversary. 
 Though it cannot help the philosopher to a certain conclusion 
 on any one point, it can enable him by means of what the 
 ancients called tWrao-is 1 , to demolish every position which his 
 adversary takes up against it. Evidence which may be inade- 
 quate to establish a complete inference, may be amply suffi- 
 cient for refutation. If the peculiar character of the subject 
 prevented Butler from demonstrating with scientific rigour 
 the divine origin of the Christian faith, he, at all events, 
 annihilated, with the analogical weapon, the position assumed 
 by the deists of his day, viz., that the Christian religion could 
 not be true since it contradicted and falsified the natural pre- 
 sumptions and intuitive convictions of mankind, by proving 
 that the system of nature involves difficulties of no less 
 startling a character. He thus overthrew a falsely assumed 
 principle by the allegation of an unanswerable fact 2 . 
 
 1 Instance brought forward to disprove the general principle of an 
 adversary. See Karslake's Aids to the Study of Logic, vol. ii. p. 83. 
 2 Butler himself seems to have regarded his argument in this light, 
 for he writes: "If there be an analogy or likeness between that 
 system of things and dispensations of Providence which revelation in- 
 forms us of, and that system of things and dispensation of Providence 
 which experience, together with reason, informs us of, i. e. the known 
 course of nature, this is a presumption that they both have the same
 
 B. VI.] FALLACIES. 303 
 
 BOOK VI. 
 
 FALLACIES. 
 PEOEMniM. 
 
 As we have followed the reasoning process in every diver- 
 sified combination it assumes in science, and laid bare the 
 mechanism by which every description of scientific truth is 
 reached, it only remains for us to notice the variety of illu- 
 sions to which the process is exposed, the different forms in 
 which error is capable of simulating reason and deceiving 
 mankind. To some extent, indeed, this has been already 
 performed. At every stage of the scientific process certain 
 errors were to be guarded against and corresponding decep- 
 tions pointed out ; yet, since many remain unnoticed, and all 
 are more or less connected in a chain of mutual dependence 
 and relation, it becomes essential to a scientific view of the 
 subject, to allot to them a distinct portion of the treatise. 
 
 Fallacies are commonly divided into two grand classes ac- 
 cording as they interfere either with the canons of the syllo- 
 gism ; or introduce false premises, or lead to a conclusion 
 different to that of which proof is required. The first are called 
 fallacies in dictione, or formal fallacies, in which the conclusion 
 does not follow from the premises. The latter are termed 
 extra dictionem, or material fallacies, which are good as far as 
 the reasoning is concerned, but false as to the matter, the 
 premises being either wrongly assumed, or the conclusion 
 foreign to the subject. The first kind may be considered under 
 two heads. The fallaciousness of some being evident from 
 the bare form of the expression, without regard to the mean- 
 ing of the terms, such as undistributed middle, illicit process, 
 and negative premiss ; while that of others requires the mate- 
 rial sense of the middle term to be inquired into before the 
 ambiguity can be cleared up, which happens in all cases of 
 ambiguous middle term, except its non-distribution. Of 
 
 author and cause; at least so far as to answer objections against the 
 former being from God, drawn from anything which is analogical or 
 similar to what is in the. latter; for an author of nature is here sup- 
 posed." Introduction to the Analogy. See Karslakc's Aids, &c., vol. 
 ii. p. 83.
 
 304 FALLA.CIES. [B. VI. 
 
 these we shall treat in two chapters under the head of formal 
 fallacies and fallacies of language. 
 
 The material fallacies, in their moral and physical rela- 
 tions, may be ranked under premiss unduly assumed, and 
 irrelevant conclusion. The former class will lead to the 
 consideration of non causa pro causa in all the various phases 
 it is capable of assuming in both order of sciences, as incom- 
 plete enunciation, groundless assumption, false analogies, and 
 petitio principii, or the assumption of a premiss, either iden- 
 tical with the conclusion or unfairly implying it. Irrelevant 
 conclusion will comprise that large magazine of fallacies so 
 commonly drawn upon by vulgar dialecticians, such as ap- 
 peals to the passions, shifting ground, eternal raising of 
 objections, and use of complex terms, which enable the dia- 
 lectician, while employing the same words, to make out his 
 case in a sense quite foreign to the matter in dispute. An 
 additional chapter on this branch of fallacies will exhaust 
 the subject. 
 
 There is no fallacy which does not fall naturally under 
 one of the foregoing heads. Even those sophisms which 
 arise from self-love, interest, or passion, and which so power- 
 fully influence civil concerns, ordinarily involve some of the 
 intellectual obliquities above referred to, and are capable of 
 being hunted out and condemned on the same grounds. The 
 idola of Bacon might appear to be fallacies of another genus, 
 and have been so characterised by Dr. Whewell ; yet, on a 
 close analysis, they will be found mere exemplifications of 
 the fallacies above enumerated, only expressed in a more 
 popular form. For, what else is characterised by Bacon's 
 illusions of the Forum (idola Fori), but the common ambi- 
 guities of language ; or what other thing does he caution his 
 readers against, under the name of illusions of the tribe and 
 illusions of the den (idola tribus, idola specus), but the fal- 
 lacies of groundless assumption and unwarrantable induction ? 
 In reality, no fallacies have risen out of the application of the 
 inferential process to modern science, which had not been 
 already provided for under the heads of the old logical 
 division. 
 
 It must not be assumed, from the strict manner in which 
 we have laid down the boundaries of the different fallacies, 
 that each is only capable of being referred to one distinct
 
 C. I. 1.] TWOFOLD DIVISION. 305 
 
 head. It occasionally happens that one fallacy may present 
 so many different aspects, according to the light in which it 
 is looked at, as to be referable to one or two heads, under 
 both the formal and material division ; in which case, the 
 only resource is to place it among that class to which it 
 bears the nearest kinship. This is most frequently the case 
 with dialectical fallacies, where the sophist either envelopes 
 his false principle in a variety of disguises, or avoids its 
 distinct statements in the elliptical language of ordinary 
 reasoning by a suppressed premiss, leaving his hearers to 
 supply one which is either untrue or does not establish 
 the conclusion. In the latter case the fallacy may not 
 only have as many relations to one genus as another, but, 
 until the sophist has drawn his inference, it remains a matter 
 of doubt to what particular head it may be referred. For 
 example, if a man, after dwelling on the abuses of religion, 
 proceed to infer that the system so deformed is false, we must 
 suppose him to assume either that every power distorted 
 from its natural uses cannot come from God, which is a 
 palpable falsehood, or that every false religion is corrupt, 
 which, however true, proves nothing, the middle term being 
 undistributed. Now, in the former case, the fallacy would 
 be referred to the head of extra dictionem ; in the latter, to 
 that of in dictions. It is a matter of no concern to the 
 sophist whether his hearers assent to the false premiss or 
 to the unsound syllogism, as long as they can be brought 
 to admit the conclusion 1 . 
 
 CHAPTER I. 
 
 FOBMAL FALLACIES. 
 
 1 . Illicit Process and Undistributed Middle. 
 
 To this head may be referred all those forms of reasoning 
 which violate any of the canons of pure inference, as laid 
 down in the book on syllogisms. Of this kind is the fallacy 
 so much in vogue of supposing the conclusion false because 
 the premiss is false, or because the argument is illegitimate ; 
 
 ' Whately's Logic, chap. v. 
 X
 
 306 FORMAL TALLACIES. [B. VI. 
 
 as if any one should show the futility of an argument ad- 
 vanced to prove the Divine existence, and thence infer that 
 God did not exist. In reality, the discarded argument ought 
 to go for nothing : its refutation proves nought beyond its 
 individual weakness, nor can it be extended further without 
 involving an illicit process of the major. Thus, supposing 
 the existence of God was rested on the universality of the 
 belief, and a nation was adduced as destitute of belief, the 
 sophism by which such a refutation would be erected into a 
 disproof of the existence of the Deity would be Whatever is 
 universally true must be believed ; the existence of God is 
 not universally believed, therefore it is not true ; in which 
 true is taken universally in the conclusion, and only par- 
 ticularly in the major premiss. In like manner, others are 
 inclined to infer the truth of the premises from that of the 
 conclusion, which involves the fallacy of undistributed middle : 
 As what is universally believed is true ; the existence of God 
 is universally believed, therefore it is true ; where the term 
 universally believed is taken twice particularly. Tet it may 
 be fairly assumed, if an able reasoner produce no other argu- 
 ments in defence of his position than such as are easily 
 exploded, that his opinions are untenable, and that the con- 
 verse of his doctrine is true. Hence no greater damage can 
 accrue to a cause than to leave its defence in the hands of 
 feeble advocates, since ordinary people take their exposition 
 as an accurate measure of all that can be said in its favour. 
 Nothing is more common to persons who are fluctuating 
 between two sets of tenets, than to become firmly attached 
 to one of them through hearing a weak-minded advocate 
 argue against them. 
 
 Another fallacy akin to the present is mistaking a con- 
 trary for a contradictory proposition, or inferring, against the 
 rules of opposition, that because one view is false its contrary 
 must be true. Thus, if any one were to argue from the fact 
 that the cholera was a visitation from God, that its causes 
 did not depend upon any physical laws, he would fall into a 
 fallacy of this kind. For there is not such direct opposition 
 between the two cases that both cannot be true together, 
 which is the law of contraries. In fact, the probabilities 
 are strongly in favour of the latter supposition ; since we 
 know nothing of pestilence that may not be traced to some
 
 .C. II. 1.] FALLACIES OF HYPOTHETICALS. 307 
 
 kind of material agency, though we cannot lay our hands 
 upon the precise combination of causes in which some of 
 them take their rise. This fallacy appears in the form of 
 undistributed middle. "Whatever does not depend on phy- 
 sical laws is a visitation from God ; the cholera is a visitation 
 from God ; therefore it does not depend on physical laws. 
 
 It may be observed, that the infraction of the rules of 
 hypotheticals viz., proceeding from the denial of the ante- 
 cedent to that of the consequent, or from the establishment 
 of the consequent to the affirmation of the antecedent, also 
 involves illicit process of the major and undistributed middle. 
 Thus, if the existence of God be universally believed, it must 
 be true ; but it is not universally believed, therefore it is not 
 true ; and if the existence of God be true it must be uni- 
 versally believed, but it is not universally believed, therefore 
 it is not true. 
 
 CHAPTEE II. 
 
 TEEBAL FALLACIES. 
 
 1. Ambiguous Middle. 
 
 IK the case of undistributed middle, the extremes of the 
 syllogism are compared with two different parts of the same 
 term : we have now to consider a series of fallacies in which 
 the middle, being used in two different senses in the two pre- 
 mises, is compared with two different terms. The first class 
 of them may be referred to the head of fallacies of equivo- 
 cation. Of this kind is the argument of Plato 1 , which is 
 generally taken up by those who advocate a system of 
 national education as a panacea for everything: No one 
 desires evil knowing it to be so; to do wrong is evil, 
 therefore no one desires to do wrong cognisant of the true 
 nature of what he desires, but only in consequence of 
 ignorance. No one could assent to the major unless the 
 term evil were restricted to that class of objects which either 
 interfered with our own happiness, or frustrated that of 
 others in matters where our own interests were not con- 
 
 1 In his Gorgiaa. 
 x2
 
 308 VERBAL FALLACIES. [B. VI. 
 
 cerned. In the minor, however, the term is taken in its 
 most general sense, and being in that character applied to 
 the major term, leads to a palpably wrong inference. Yet 
 from this argument Plato inferred that virtue is a branch of 
 intelligence, and is to be produced by intellectual cultivation ; 
 and made the proposition the basis of his ethical system, 
 in which he was followed by most of the philosophical 
 schools among the later Greeks 1 . With a similar " paltering 
 with words in a double sense" were the arguments of the 
 ancients relative to the summum bonum infected, the word 
 good being at one time intended to mean what was good for 
 oneself, and at another what was good for other people. 
 The proper mode of dissipating such verbal ambiguities is 
 by drawing a distinction, and granting or denying the pro- 
 position according to the different meanings implied in the 
 statement. Of the use of this instrument the scholastics 
 were the most powerful masters ; and it still furnishes in the 
 continental universities one of the most powerful weapons of 
 theological controversy. 
 
 Another example of ambiguous middle may be instanced 
 in the argument by which many set themselves against a 
 judicious reform of the electoral system. Thus, whatever 
 interferes with the influence of property is pernicious ; the 
 measure in question interferes with the influence of pro- 
 perty, &c. Now, the major should never be accepted in an 
 unrestricted sense ; because property may exercise a perni- 
 cious as well as a beneficial influence, according as it is 
 administered ; and if the proposed measure simply tended to 
 deprive the possessor of property of the power to abuse his 
 influence, the objection would, of course, fall to the ground. 
 There are a class of words which, from being indiscriminately 
 applied to distinct meanings, are peculiarly liable to lead 
 those who employ them into fallacies of this character. 
 Of this kind is the word same, which sometimes denotes 
 similarity, but is as often employed to point out identity ; 
 as when we say : " The same person whom we observed 
 yesterday," we do not mean an individual resembling the 
 one whom we saw in dress and features, but the same 
 identical person ; but if the word is applied to a house or 
 a stone, the expression by no means signifies identity, but 
 
 1 Mill's System of Logic, vol. ii. p. 446.
 
 C. II. 1.] EQUIVOCAL AND PABONYMOUS WOBDS. 309 
 
 mere similarity of ^relation. From this double signification 
 of words arise frequent cases of ambiguous middle, as in the 
 argument of Bishop Berkeley to prove the existence of an 
 eternal mind : " Ideas cannot exist without a mind in which 
 they inhere ; I have the same idea to-day as I had yester- 
 day ; but this would be impossible, unless there was a mind 
 in which it could exist during the interval of its absence." 
 Here Dr. Berkeley confounds, under the word same, resem- 
 blance with identity, and uses the term in the latter sense 
 when he ought only to have employed it in the former 1 . 
 
 OccasionaDy this fallacy assumes the form of an interro- 
 gation, in which many questions are asked under the guise 
 of one ; so that whatever answer is given the sophist may 
 bring under the response the cases to which it does not 
 apply. To detect the ambiguity it is necessary to answer 
 each question separately. Thus, the question discussed by 
 Cicero in the third book of the He Officiis, whether anything 
 vicious is expedient, belongs to the fallacy of interrogation ; 
 from the ambiguity of the word expedient, which sometimes 
 means conducive to temporal prosperity, sometimes con- 
 ducive to the greatest good. Now, if the reply to this 
 question be in the negative that is, if the latter sense be 
 applied to the word expedient, it is the custom of the sophist 
 to introduce the former. For example : What is vicious is not 
 expedient ; whatever conduces to wealth and aggrandisement 
 is expedient ; therefore it cannot be vicious. If the response 
 be affirmative, of course the order will be reversed : Some- 
 thing vicious is expedient ; whatever is expedient is desirable ; 
 therefore something vicious is desirable. 
 
 Another group of fallacies under this head arises from 
 men taking for granted that paronymous words i. e. those 
 which spring from one root must convey exactly the same 
 meaning. This assumption is of common occurrence, as few 
 express the terms in precisely the same words throughout 
 the discourse, but continually vary them to suit the structure 
 of the sentence, and to divest their style of a pedantic air. 
 Nor is the practice at all illogical, so long as the variety of 
 expressions in which the terms are clothed point to the 
 same identical meaning ; but since paronymous terms do not 
 invariably do so, the assumption, when not carefully watched, 
 
 1 Mill's System of Logic, vol. ii. p. 451.
 
 310 VERBAL FALLACIES. [B. TI. 
 
 is often likely to mislead. Thus, if any one inferred from 
 the fact that theorists and projectors are unfit to be trusted, 
 that his neighbour ought not to be trusted because he has 
 formed projects or theories ; he would imply that the bad 
 sense which we attach to mere theorists and projectors is 
 equally applicable to any one who forms theories and pro- 
 jects, which is by no means the case. It is not indispensable 
 to sophisms of this kind that the fallacy lurk in the middle 
 term. Though classed under that head, it may lie in one of 
 the terms of the conclusions. Thus : To be acquainted with 
 the guilty is a presumption of guilt ; this man is so acquainted, 
 therefore we may presume that he is guilty. This argument 
 proceeds on the supposition of an exact correspondence 
 between presume and presumption, which, however, does not 
 exist ; for presumption is commonly used to express a kind 
 of slight suspicion, whereas to presume amounts to abso- 
 lute belief 1 . Such fallacies being built on the grammatical 
 structure of language, are usually termed Fallacia figure 
 dictionis. 
 
 As an additional instance of this class we may cite the use 
 of the word representative, which, from the verb which forms 
 its root, is taken not unfrequently to mean, in the case of a 
 member of a legislative assembly, a person who is bound to re- 
 present the exact opinions of the majority of his constituents on 
 all points, and never to act on his own responsibility; whereas, 
 law and usage has defined the term to mean one who is 
 chosen to represent the interests of a certain constituency 
 according to the best dictates of his own judgment, and un- 
 biassed by any undue extraneous influence. Such a person 
 may consult the opinions of his constituents before making 
 up his mind on a question that may concern them, but he is 
 not bound either to be their spokesman, or resign his seat, 
 though he may pursue the latter course from motives of 
 delicacy. 
 
 Under the head of ambiguous middle may be ranked the 
 fallacy of division, which consists in the middle term being 
 used in the major premiss collectively and in the minor dis- 
 tributively ; and the fallacy of composition, which simply re- 
 verses this order, taking the distributive sense first and the 
 collective sense after. Of these the most glaring examples 
 
 1 Whately's Logic, ch. v.
 
 C. II. 1.] FALLACIES OF DIVISIOK A.JTD COMPOSITION. 311 
 
 are : Seven is one number ; five and two are seven ; therefore 
 five and two are one number ; or the reverse : Five and two 
 are two numbers ; seven is five and two, therefore seven is 
 two numbers. Of the last kind is the Owenite fallacy, di- 
 rected against the doctrine of human responsibility : He 
 who necessarily goes or stays is not a free agent ; you must 
 necessarily go or stay, &c., in which the major is " he who is 
 compelled to go or compelled to stay, is not a free agent," 
 which can be readily conceded ; but as the minor changes the 
 middle term into sheer compulsion to take the alternative of 
 these two courses, the conclusion is abortive. Such, likewise, 
 is the fallacy which leads many to speculate in lotteries, 
 which is thus stated by Dr. Whately 1 : The gaining of a high 
 prize is no uncommon occurrence ; and what is no uncommon 
 occurrence may reasonably be expected ; therefore the gain- 
 ing of a high prize may reasonably be expected. The con- 
 clusion, being evidently confined to the person who makes the 
 inference, must mean " reasonably expected by a certain in- 
 dividual ;" therefore, for the major premiss to be true, the 
 middle term must be understood to mean, " no uncommon 
 occurrence to someone particular person ;" but the minor, 
 which has been placed first, can only be true in the sense of 
 no uncommon occurrence to some one or other, and thus 
 gives rise to the fallacy of composition. 
 
 This fallacy is of frequent occurrence in civil concerns, as 
 is instanced in the mode in which people lose sight of the 
 aggregate results of acts in their separate insignificance. 
 Thus the profligate forgets while he infers that each single 
 indulgence can be of little harm to his constitution, that the 
 collective amount may undermine its vigour; nor do the 
 avaricious seem to be aware, while they attempt to convince 
 their own conscience and others that they are not bound to 
 subscribe to this or the other benevolent institution, that the 
 practical conclusion which they draw is that all charity may 
 be dispensed with. 
 
 The last verbal fallacy we shall notice is tkefallacia acci- 
 dentis, together with its converse, fallacia a dicto secundum 
 quid ad dictum simpliciter; in each of which the middle is used 
 m one premiss to signify something considered in its absolute 
 essence, and in the other to imply, besides its simple nature, 
 
 1 Logic, ch. v.
 
 312 VEEBAL FALLACIES. [E. TI. 
 
 the accidents and relative conditions it is liable to assume. 
 Thus, in thefallacia accidentis we draw a simple, unrestricted 
 absolute conclusion from one that is only true by accident, 
 as if we were to decry antimony because (on account of its 
 misapplication) it produces bad effects ; or to attribute to elo- 
 quence all the evils to which its abuse leads ; or to medicine 
 the errors of certain ignorant practitioners. Of a similar kind 
 is the fallacy of the epicureans, who concluded the gods must 
 have human form, because, among all creatures in the world, 
 men alone had the use of reason. The gods, said these philoso- 
 phers, are very happy ; none can be happy without virtue ; 
 there is no virtue without reason ; and reason is found nowhere 
 except in the human form : it must be avowed, therefore, 
 that the gods have the human form. Eeason, however, is not 
 essential to the human form, but only accidentally connected 
 with it : it was, therefore, puerile to conclude that because 
 the gods were endowed with mind they must also have hands, 
 feet, and other human appurtenances. The converse fallacy 
 of passing from what is true in some respects to what is true 
 absolutely, may be instanced in another argument of this 
 school of philosophers to prove the same proposition. The 
 gods must be invested with the human form, because that form 
 is most beautiful, and everything beautiful must be in God. 
 For, as the human figure is not beautiful absolutely, but only 
 in relation to bodies, it does not follow -that it must be in 
 God, who is only the inheritor of absolute perfection : i. e. 
 perfection without any imperfection. The following is a 
 similar fallacy, which Cicero puts into the mouth of Cotta to 
 disprove the existence of God : If God exist, he must be in 
 possession of all virtue ; but we can attribute no virtues to 
 God like those in men, therefore no deity exists 1 . It did not 
 
 1 " How," says Cotta, " can \ve conceive God, since we can attribute 
 no virtue to Him? For shall we say that He has prudence? But since 
 prudence consists in the choice between good and evil, what need can 
 God have for this choice, not being capable of any evil? Shall we say 
 He has intelligence and reason ? But reason and intelligence serve to 
 discover to us that which is unknown from that which is known. Now 
 there can he nothing unknown to God. Neither can justice be in God; 
 because this relates only to the intercourse of men ; nor temperance, 
 since He has no desires to moderate; nor strength, since He is susceptible 
 of neither pain or labour, and is not exposed to any danger. How, 
 therefore, can that be a God which has neither intelligence or virtue?" 
 Cicero, Natura Deorum, b. iii.
 
 C. III. 1.] OBLIQUE ASSUMPTIONS. 313 
 
 strike the framer of this argument that there was just a 
 possibility that virtue in man might only exist in a relative 
 state from the imperfection it exhibits, and that the source 
 from which it was derived might be traced back to its full 
 plenitude in God. To deny that there is no virtue in God, 
 because the imperfect virtue which exists in , man cannot be 
 ascribed to Him, is tantamount to the assertion that because 
 no rivers can exist in the sea, the ocean has no water ; or is 
 equivalent to saying that the fact which proves God to have 
 no intelligence is that nothing can be hid from Him ; that, 
 in other words, He sees nothing, because He sees everything ; 
 that He can do nothing, because He can do everything ; that 
 He enjoys no happiness, because He possesses all happiness. 
 It is, as if a rustic, who having never seen any houses but 
 those covered with thatch, and having heard that there were 
 no roofs of this nature in towns, should conclude that there 
 were no houses in towns, and that the dwellers in them were 
 exposed to all the inclemencies of the weather. 
 
 CHAPTEE III. 
 
 MATEEIAL FALLACIES. 
 
 1. Non Causa pro Causa. Fallacy of Groundless 
 Assumptions. 
 
 THE largest group of material fallacies may be assigned to 
 undue assumption of premiss ; which is in fact the cause of 
 iiearlv all the sophisms which have obstructed the progress 
 of science, either in the shape of incongruous theory, false 
 objections, or any erroneous statement of fact. The false 
 
 remiss is not unfrequently introduced as a thing quite in- 
 ubitable, of which mankind never ventured to exercise the 
 slightest doubt ; just as Charles the Second made the mem- 
 bers of the Eoyal Society believe, that a live fish did not 
 increase the weight of any vessel of water in which it was 
 placed, by requesting an explanation of the phenomenon 
 as a real fact. Sometimes the groundless statement is in- 
 troduced as " a well-known fact, universally admitted," 
 or " a circumstance not a little remarkable ;" or it may 
 be covertly insinuated, by way of illustrating the pre- 
 tended fact which is so assumed. Thus, the opponents of
 
 314 MATEBIAL FALLACIES. [B. TI. 
 
 Copernicus argued that the earth did not move ; because, in 
 that event, a stone let fall from the top of a high tower would 
 not reach the ground at the foot of the tower, but at a little 
 distance from it, in a contrary direction to the earth's course. 
 In the same manner (said they) as a ball ivhen dropped from 
 the mast-head of a ship in full sail does not fall exactly at 
 the foot of the mast, but nearer to the stern of the vessel. The 
 Copernicans might have silenced these objections by drop- 
 ping a ball from the mast-head; as it turned out upon 
 actual experiment that it does fall at the foot as the theory 
 requires. But the spurious fact was so plausibly stated that 
 the Copernicans admitted its truth, and struggled vainly to 
 make out a difference between the two cases. 
 
 To this head may be referred that wide class of fallacies 
 which ascribes objective existence to abstractions. From 
 the abstract principle that nature abhors a vacuum, philoso- 
 phers formerly taught that vessels full of water break when 
 they freeze, and by the contraction of the water leave a 
 vacuum which nature cannot endure. It has, however, been 
 discovered that the fracture arises from a contrary reason ; 
 since water when frozen occupies more space than in a state 
 of fluidity, and consequently breaks the vessels which do not 
 afford room for the expansion. Of a similar nature were the 
 abstractions which corroded the .bulk of the Aristotelian 
 physics ; such as the abstract perfection of circular motion, by 
 which the Stagyrite attempted to prove that the planets move 
 in perfect circles ; and the assumption that generation and 
 corruption only happen between contraries, which led him to 
 infer that the heavenly bodies were incorruptible, simply 
 because circular motion had no contraries 1 . Extreme in- 
 stances of this tendency to substitute a priori conceptions for 
 actual realities, may be found in the abstract notions by which 
 many of the ancients sought to resolve the principles of the 
 universe. Some placed the explanation of all phenomena in 
 the "TO curfipov," or infinitude of things ; others in the TO ov 
 and the TO ^ ov, that is to say, in entity and nonentity; 
 while an authority,' which was destined to command opinions 
 for nearly two thousand years, settled this important point 
 by deciding that matter, form, and privation were to be con- 
 sidered the principle of all things. 
 
 1 Galileo Systema Cosmicum, Dial. L p. 30.
 
 C. HI. 1.] FALLACIES OF THE GBEEK PHILOSOPHEES. 315 
 
 Another prejudice that leads to the fallacy of groundless 
 assumption, is the notion that differences in nature corre- 
 spond to distinctions in language ; extreme instances of 
 which may be found in modern as well as in ancient inquiries. 
 "With the Greeks, however, this fallacy was most conspicu- 
 ously prominent, partly on account of the philosophic struc- 
 ture of their own language, which led them to imagine that 
 all its generalisations of natural phenomena were exact tran- 
 scripts of reality ; and partly because their own ignorance of 
 every other language debarred them from, perceiving the true 
 functions of language, or from drawing a distinction between 
 terms loosely abstracted from things by vulgar perception, 
 and others which had been scientifically invested with a 
 determinate connotation. Hence they never [dreamt it was 
 necessary to distinguish things which their language con- 
 founded, or to combine objects that the popular phraseology 
 of the country had kept apart ; but they set on analysing and 
 sifting the general terms of their language, as if the vague 
 notions they embodied, had been formed by some inspired 
 process, and warranted by Heaven to reflect the exact reality 
 of things. Accordingly, when Thales was asked what is the 
 greatest thing ? he replied, Place ; for all other things are in 
 the world, but the world is in it. In Aristotle we have the 
 consummation of this mode of speculation. Thus, in in- 
 quiring into the existence of void, or empty space, he enu- 
 merates the different senses in which we say one thing is 
 contained in another. For example, the part is in the 
 whole, as the finger is in the hand ; the species is in the 
 genus as man is included in animal; the government of 
 Greece is in the king, and various other senses are exem- 
 plified, but of all these the most proper is when we say a- 
 thing is in a vessel, or, generally, in a place. Then examining 
 what place is, he comes to the conclusion that if about a 
 body there be another body including it, it is in place, and 
 not, if otherwise. Proceeding, then, to the question of, a 
 void, he, as usual, examines the different senses in which the 
 term is used, and adopts, as the most proper, place without 
 matter. He then proves that so blank a thing cannot exist, 
 from such arguments as these : In a void there could be no 
 difference of up and down ; for as in nothing there are no 
 differences, so there are none in privation or negation ; but a 
 void is merely a privation or negation of matter ; therefore,
 
 316 MATEBIAL FALLACIES. [u. TI. 
 
 in a void bodies could not move up and down, which it is in 
 their nature to do. "When we compare such attempts to 
 extract facts out of the loosest forms of language with the 
 scientific reasoning of our day, we may cheerfully allow the 
 ancients their decided supremacy in the walks of sculpture 
 and eloquence, in consideration of our more splendid domi- 
 nion over nature. 
 
 "We are not unfrequently led to take our own conceptions 
 of the possible, as furnishing the actual limits to which its 
 boundary extends ; nor is this unfair, if the things we place 
 outside the line be really impossible, in the light of being 
 absolutely inconceivable without over-riding some of the 
 elementary principles of the thinking faculty. Thus it 
 would be by no means wrong to assume that the same object 
 cannot be in two places at the same time ; that something 
 can spring out of nothing ; or that the laws of number can 
 be otherwise than what they are. But the evil is, that men 
 confound this strict sense of the word impossibility, with that 
 which belongs to what is purely inconceivable ; on the score 
 of the matter which is placed in that category being entirely 
 strange to them, and requiring some strain on their concep- 
 tions before they can bring their mind to entertain it. Thus 
 St. Augustine denied the existence of the antipodes, be- 
 cause he could not see how it could be brought about ; 
 and Bacon rejected the Copernican system simply because 
 he could not conceive so great a void in the celestial regions 
 as that system assigns to them. In like manner the Carte- 
 sians waged war against Newton's law of gravitation, assum- 
 ing the principle that a thing cannot act where it is not ; and 
 so plausible did the objection seem to that great astronomer, 
 that he imagined a subtile ether to line space, through the 
 medium of which the attraction of the various planetary 
 bodies might be conveyed to each other. " It is inconceivable" 
 said Newton, in propounding this theory, " that inanimate 
 brute matter should, without the mediation of something 
 else which is not material, operate upon and afiect other 
 
 matter without mutual contact That gravity should 
 
 be innate and essential to matter so that one body should act 
 on another through a vacuum, is to me so great an absurdity 
 that I believe no man who has a competent faculty of 
 thinking in philosophical matters can ever fall into it." It 
 does not appear to have struck Newton, that with regard to
 
 0. m. 1.] FALSE SENSE OF " INCONCEIVABLE." 317 
 
 the mere inexplicability of the phenomena, that motion by 
 impact is quite as mysterious as impulsion at a distance, with 
 no intermediate agencies between ; and that since the latter, 
 as we are fully assured, is the ordinary mode by which one 
 spiritual substance acts upon another, we can find no diffi- 
 culty, if circumstances require it, to invest material sub- 
 stances with a similar property. 
 
 The same conception of impossibility has been at the 
 bottom of most of the absurd theories of modern times, from 
 the vortices of Descartes to the Neptunian system of geology. 
 In metaphysics it has exercised rampant sway, as may be wit- 
 nessed in the theories of Malebranche and Leibnitz to ac- 
 count for the conformity of states of mind with peculiar dis- 
 positions of bodies without direct contact, which these phi- 
 losophers believed impossible. Leibnitz attributed the fact 
 of such dissimilar substances acting in concert to a " pre-esta- 
 blished harmony" existing between them ; which caused their 
 motions to beat always in unison, just as two clocks which, 
 though unconnected, strike simultaneously, and always point 
 to the same hour. Malebranche's theory of "occasional 
 causes" was a refinement on this conception. Instead of 
 supposing the clocks originally arranged so as to strike 
 together, he held that when the one strikes God interposes, 
 and makes the other strike in correspondence with it. 
 
 No prejudice is so apt to lead men to assign real causes in 
 nature to the agency of pure chimeras, as that of mistaking 
 their subjective notions for objective laws; as may be witnessed 
 to a great extent in astrologers, who, referring every natural 
 production to the influence of the stars, made out that there 
 must be an immoveable heaven beyond the celestial orbs, 
 because the earth produces different things in different 
 countries ; just as if India could not produce ivory, and Sabea 
 precious drugs, and Italy wine and oil, unless there were an 
 immoveable heaven to present a diversified and unchangeable 
 aspect towards different portions of the globe. To the influence 
 of this prejudice may be ascribed the popular notion, that the 
 advent of comets and eclipses always portend great evils to 
 subjects and princes ; which has caused an infinite waste of 
 stout prophesying and prediction to the no small terror of 
 nations. Had the chronologies of Helvicus borne the most 
 distant approximation to truth, Borne would have been de- 
 stroyed some scores of times ; nor has it been for want of
 
 318 MATEEIAL FALLACIES. [B. VI. 
 
 similar forethought in modern times that Paris and London 
 have not as often undergone the same fate 1 . The marvel, 
 however, is not that direful mortalities and plague, or the 
 death of some great potentate happen to coincide with the 
 arrival of a comet or an eclipse, but that they fall out so 
 often without them ; for such celestial phenomena come 
 round so frequently, that we are inclined to suspect by the 
 laws of chance that wars and pestilence should be oftener 
 associated with them. Moreover, there is no reason why 
 causes so general and removed as these should have any con- 
 siderable effect on the earth, or act at one point more than 
 another, or threaten a king rather than a tobacconist. 
 
 With the latter class of groundless assumptions may be 
 ranked the inclination to take refuge in omens and au- 
 guries as exponents of the future, which is so prevalent 
 among the inferior orders of our day, and which exercised 
 so potent an influence over the destinies of the ancient 
 empires. Even Dr. Johnson would not go abroad on Fri- 
 day, through a pre-existing notion that he must encounter 
 misfortune ; and we all know that no Italian host will 
 dine thirteen together, or sit down with a party of eleven. 
 If an ancient general missed his footing in landing on any 
 expedition, the omen told so fearfully on the courage of the 
 soldiers, that the chances of his success were consider- 
 ably diminished. Hence Caesar, who was much in advance 
 of his time in all respects, on accidentally stumbling in effect- 
 ing an embarkation on the African coast, had the presence of 
 mind to convert the direful presage into a favourable one, by 
 exclaiming, "Africa, I embrace thee." Frequently the omen 
 took the form of a lucky or unlucky name, which the gods 
 were supposed to send in prognostication of a future event. 
 Thus the Greeks, as Herodotus tells us, were encouraged in 
 their enterprise on then 1 way to Mycale by the arrival of a 
 deputation from Lamos ; from the fact that one of the indi- 
 viduals comprising it was called Hegisistratus, or the leader 
 of armies. 
 
 Another fallacy no less generally diffused, may be noticed in 
 the practice of blending our own inferences with descriptions 
 of what we have seen, so as to confound the conclusions 
 
 1 What Cervantes did for the old romancers, Dean Swift accom- 
 plished for this class of propheciers : none have survived the renowned 
 predictions of his Isaac Bickerstaif.
 
 C. HI. 1.] INFEEENCE CONFOUNDED WITH PEECEPTION. 319 
 
 drawn from fact with actual observation. Thus it was stoutly 
 maintained by the anti-Copernicans, that the system of 
 the Danish astronomer could not be true, because they saw 
 the sun rise and set ; the stars revolve in circles round the 
 pole ; and they felt the earth to remain immoveable under their 
 feet. But we now know that their alleged experience con- 
 sisted entirely of inferences from a set of phenomena equally 
 reconcileable both with the Ptolemaic system, and with that 
 against which they objected. To the same absence of ability 
 to discriminate between inference and the perception on which 
 inference is grounded, may be attributed many of the marvel- 
 lous stories by which posterity is astounded and amused. A 
 wandering meteor in a churchyard is sufficient to call up in 
 the mind of a rustic the presence of a supernatural visitor ; 
 nor could many observant travellers of antiquity get rid of 
 the impression derived from the sight of some Africans in a 
 state of abject abasement, that they belonged to a race of men 
 whose heads grew out of their breasts, and not from their 
 shoulders. * It is singular to observe how full of conjectural 
 inference is the most naked statement that can be wrung 
 out of an illiterate person concerning the facts which he saw. 
 He observes a sheet of lightning strike a house, and imme- 
 diately asseverates his conviction that he saw a bolt drive in 
 the wall, and not unfrequently goes in search of it. Every 
 word in his description has its surmise, and each sentence is 
 accompanied with a theory. So far, as Dugald Stewart ob- 
 serves, is a plain ungarnished statement of natural fact from 
 being a result of nature, that the capacity to perform it may 
 be regarded as unequivocal evidence of a mind trained by 
 long and successful study to the most difficult of all arts, the 
 interpretation of nature 1 . 
 
 A common assumption, and one by no means confined to 
 vulgar minds, is the habit of assigning anything as a cause 
 which precedes another, or exists in casual connexion with it. 
 Thus, because the wealth and power of the country increased 
 under the old electoral system, and during the continuance 
 of the Test Act, it was a standing argument with a large 
 portion of the community when the abolition of such things 
 were talked of, that the prosperity of England was owing to 
 their influence. Eor a similar reason it has been assumed that 
 
 1 Elements of the Philosophy of Mind, vol. ii ch. ii. sec. 5.
 
 320 MATEEIAL FALLACIES. [E. VI. 
 
 the national debt is the cause of the national prosperity ; 
 that, because in mediaeval times provisions were more equally 
 distributed, a low degree of refinement is more favourable 
 to the enjoyment of the masses of a community than a high 
 state of civilisation 1 . In the same manner it was concluded 
 that the star which is called the dog-star is the cause of the 
 heat which prevails during the time of its ascension, and the 
 increased mortality which attends its zenith in warm cities. 
 Virgil himself, unless his language may be deemed figurative, 
 was guilty of this fallacy when he wrote : 
 
 Aut Sirius ardor : 
 
 Ille sitim morbosque ferens mortalibus segris 
 Nascitur, et laevo contristat lumine ccelum. sEn. x. 273. 
 
 Now if there were any truth in such conjectures, it would 
 follow that in those countries where the situation of the star 
 above the horizon is most perpendicular, heat should be the 
 most severely felt ; but so far is this from being the case, that 
 its greatest altitude is accompanied with extreme cold. Sucli 
 fallacies, though receiving a distinct name in the scholastic 
 logic, as that of post hoc, ergo propter hoc, or cum hoc, ergo 
 propter hoc are only violations of the cautions with which we 
 have surrounded the method of agreement ; and all infractions 
 of similar rules with respect to the other methods may be 
 regarded as so many distinct fallacies, and invested with 
 corresponding designations. 
 
 2. Incomplete Enumeration. 
 
 One of the most common infringements of a principle 
 affecting the validity of three of the experimental methods is 
 that of incomplete enumeration, or of forming a conclusion 
 upon the effects or causes of certain phenomena before ex- 
 amining all the circumstances in connexion with them. This 
 is the fallacy of inductio per enwnerationem simplicem, which 
 Bacon censured as one of the primary sources of the errors 
 which infected the ancient systems of philosophy. Men, 
 after observing a few facts, grasped at the most sweeping- 
 generalisations, being impatient of the tardy results of passive 
 observation, and having no idea of the experimental mode of 
 investigation. Hence in everything which concerns natural 
 
 ' Nov. Org. Aph. 46. 

 
 C. III. 2.] INCOMPLETE ENUMERATION. 321 
 
 phenomena their theories went astray, as they assumed in- 
 stances which nature either flatly contradicted, or failed to 
 corroborate by actual fact. On such loose inductions Bacon 
 attempted to throw ridicule by citing the case of an ancient 
 sceptic who, on being shown by a Pagan priest the register 
 of those who had discharged the benefactions they had made 
 to the gods on condition of their preservation from impend- 
 ing shipwreck, as a proof of the miraculous interposition of 
 God, drily asked, where were the names of those registered 
 who, after making similar vows, had perished. 
 
 Yet instances of such loose reasoning are by no means 
 wanting in modern times, even among men of great 
 eminence, and are to be traced in many of the ordinary 
 axioms of civil intercourse. Locke, for example, in his 
 Treatise on Education, seriously advises all parents and go- 
 vernors of children to inure them to great hardship, dining 
 them at all hours in the day, bathing them in snow during 
 winter, and habituating them to long fasts and fatigues ; 
 because, he remarks, those who have undergone such dis- 
 cipline never fail to carry a robust body through manhood, 
 and live to extreme old age : but had this distinguished 
 metaphysician taken pains to collect the number of those 
 who had died under the experiment, he would most likely 
 have modified his opinion. Another instance occurs in the 
 plausible notion so generally entertained by the old political 
 economists, that men of lavish expenditure encourage in- 
 dustry, while the mere hoarder confers no benefit on society 
 by his gains 1 . Here, then, are two sets of phenomena in- 
 volved, one open and palpable to the senses, while the other 
 lies under the surface, and cannot be reached unless by a 
 penetration which, irrespective of sense, follows out things to 
 their natural results. The fallacy consists, as most sophisms 
 of this kind commonly do, in losing sight of the latent effects, 
 and restricting the generalisation to mere sensible pheno- 
 mena, as if they were the only instances concerned. The 
 generous expenditure of the liberal is observed to feed 
 labour, encourage industry, and stimulate the arts : every 
 tradesman flourishes with whom they have connexion, and no 
 misery is seen at their gates. It is, however, overlooked 
 
 The first paradox was maintained by Coleridge, the second by 
 Rousseau. 
 
 Y
 
 822 MATEEIAL FALLACIES. [B. Til 
 
 that the money of the avaricious, as far as the great masses 
 of the community are concerned, is more usefully employed; 
 for their savings, after passing into the hands of their banker, 
 or having been invested in the funds, is lent to some mer- 
 chant or manufacturer, and employed in hiring spinners and 
 weavers, or opening some new channel of commercial enter- 
 prise, and thus gives occupation and bread to far more hands, 
 at one venture, than the money of the generous employ 
 during the whole of their career. But the careless observer 
 does not see what becomes of the miser's money. The 
 vulgar impression is, that it is locked up in an iron chest, 
 which is not opened unless at the dictation of stern neces- 
 sity ; while the number of flourishing tradesmen that the 
 profusion of the liberal feeds, is at once evident to the most 
 obtuse vision ; and this in so palpable a manner, that no 
 one ever thinks of the far greater group of artisans whom 
 it might employ in industrial and far more remunerative 
 occupations. Hence comes the prejudice universal previous 
 to the time of Adam Smith, and even not yet exploded among 
 the majority of the educated classes, that prodigality encou- 
 rages industry and parsimony oppresses it 1 . 
 
 3. Fallacy of False Analogies. 
 
 Analogies, whether including similarity of relations or 
 resemblance between the properties of objects themselves, 
 are generally introduced in discourse either for the purpose 
 of mere illustration, or of moving the intellect to the recep- 
 tion of certain opinions in the shape of direct evidence, or 
 by way of argument and illustration combined. In the two 
 latter cases only it falls under the cognisance of logic ; the 
 former branch of the subject belongs to the rhetorician. 
 
 An error in analogical reasoning may occur either in over- 
 estimating the probative force of the proof, or in asserting or 
 implying resemblance in points which are essential to the 
 argument, simply from resemblance in other features which 
 are indifferent to it. It is to the last case that the fallacy 
 in question more particularly applies. A common instance 
 may be cited in the inference commonly drawn in favour of 
 despotic government, from the similarity of relation which 
 holds between a prince and his subjects and a father and his 
 
 1 Mill's System of Logic, vol. ii. p. 400.
 
 C. HI. 3.] FALSE POLITICAL ANALOGIES. 323 
 
 family. The common people of every community are always 
 in a state of infancy, and since paternal authority is neces- 
 sary to promote the happiness of children, it is argued that 
 the superior sagacity of the prince ought to interpose by 
 direct mandate to advance the welfare of his subjects. Nor 
 would the inference be at all unfair, if the analogy agreed 
 in the essential point which contributes to make paternal 
 government the best possible form for the administration of 
 private concerns viz., the affection of a father for his family 
 and his superior wisdom and experience. But it is just in 
 this very point where it breaks down. For experience shows 
 that we can never rely upon the existence of these properties 
 in political despots ; evil favourites in many cases getting 
 between them and their subjects, and creating jealousies and 
 misunderstandings which involve either one or both in ruin. 
 Were parental management likely to be disordered by similar 
 causes, the result would be anything but good government. 
 Another instance of this fallacy may be adduced in the 
 common opinion that states, by the very constitution of 
 things, have the same periods of infancy, manhood, and de- 
 crepitude that are found in the individuals who compose 
 them, that after the enjoyment of a certain amount of 
 vigorous action decay must stamp its furrows upon empire 
 just as it writes its wrinkles on the human body. Loose 
 generalisations of this sort from history may furnish simi- 
 litudes to illustrate or adorn ; but if obtruded in the shape of 
 analogies from whence to reason, they will occasionally be 
 found upon examination rather to turn the argument the 
 opposite way than make out the conclusion. Thus, in the 
 present case, the decay of the vital powers in natural bodies 
 are traceable to the spontaneous progress of those very 
 changes of structure which in their earlier stages constitute 
 their growth to maturity; while so far is this from being 
 the case in political bodies, that the advance of those changes 
 cannot, unless by palpable mismanagement, have any effect 
 but the still further continuance of growth. Hence the 
 analogy in question establishes an opposite conclusion to 
 what it was intended to make out. For, if it prove any- 
 thing, it certainly is this, that bodies politic can only die 
 of disease or violent death ; or, in other words, that they 
 can have no old age. 
 
 T2
 
 324 MATEEIAL FALLACIES. [B. VI. 
 
 Tliis sophism, which scholastics termed a non tali pro tali, 
 is generally allied with that of petitio principii, the analogy, 
 which is the very thing to be proved before it can be ad- 
 duced in evidence, being first assumed and argued from as if 
 universally admitted. In this form it is frequently used to 
 throw ridicule upon an opponent's reasoning, when he has in- 
 cautiously let slip one or two loose expressions which admit 
 of being illustrated by a burlesque parallelism. A ludicrous 
 example of the fallacy in this guise may be found in the 
 parliamentary debate on unlawful societies in Ireland, which 
 took place in 1824 1 . "True philosophy," Mr. Mackintosh 
 had said, in alluding to the word hate applied by the Catholic 
 Association to the Orangemen of Ireland, " true philosophy 
 will always contrive to lead men to virtue by the instru- 
 mentality of their conflicting vices. The virtues, where 
 more than one exist, live in harmony together. But the 
 vices bear a mortal antipathy to each other, and furnish to 
 the moral engineer the power by which he can keep them 
 under control." "Admirable!" replied Mr. Canning ; "but 
 the poor man who has but one vice must be in a very poor way 
 no fulcrum, no moral power for effecting his cure ; whereas 
 his more fortunate neighbour, who has more vices than one 
 in his composition, is in a very fair way, indeed, of becoming 
 an honest member of society. How would the honourable 
 gentleman like to have this doctrine introduced into his 
 domestic establishment ? If I had a drunkard in my house- 
 hold and dismissed him on account of this fault, it would be 
 totally out of my power to recommend him to the honour- 
 able gentleman. But if I had the good fortune to discover 
 he was also a thief, might I not with a safe conscience send 
 him with an excellent recommendation, saying, I send you a 
 man whom I know is a drunkard, but whom I am happy to 
 inform you is also a thief; you cannot do better than employ 
 him ; you will make his drunkenness counteract his thieving, 
 and bring him out of the conflict a very moral personage." 
 This felicitous exaggeration is founded on a misconception 
 of the word vice, confounding it with crime, and then se- 
 lecting two cases which instead of being conflicting are in 
 reality accessory to each other. It may be remarked that 
 the most brilliant raillery of this logical statesman may be 
 traced to a dexterous employment of analogical fallacies. 
 1 Hansard.
 
 C. III. 3.] FALSE PHILOSOPHICAL ANALOGIES. 325 
 
 There is no more effective weapon in dispute than the fallacy 
 of a non tali pro tali sharpened with an ironical edge. 
 
 Under this head may be classed those fanciful analogies 
 upon which many of the ancients founded physical theories, 
 and which have drawn some of the moderns into inferences 
 quite at war with common sense. Thus Pythagoras, finding 
 that the relative distances of the planets bore an exact pro- 
 portion to the divisions of the monochord, concluded that 
 the action of these bodies in their orbitual motion gave rise 
 to the fictitious music of the spheres 1 ; as if the melody of 
 the harp entirely depended on the proportion of certain dis- 
 tances between the strings, and not in the least on the sound- 
 ing-board or wires of the instrument. It has been similarly 
 held, that because certain combinations of numbers prevailed 
 in some natural phenomena, they must run through the whole 
 of nature ; as, that there must be four elements, since there 
 are only four possible combinations of hot and cold, wet and 
 dry ; that there must be seven planets, because there were 
 seven metals, and even because there were seven days in the 
 week. Kepler himself limited the number to six, simply 
 because there were only five regular solids: besides, six 
 was a perfect number that is equal to all its factors viz., 
 2 + 2 + 2 or 3 + 3, which was an additional reason why 
 there must be exactly six planets. The Pythagorians, in a 
 similar way, were unanimous in thinking that the decimal 
 number, as it surpassed most others in perfection, must be 
 found in every celestial combination ; and being acquainted 
 with only nine heavenly bodies, to make up the enumeration, 
 stoutly maintained that there was an antichthon or counter- 
 earth on the other side of the sun invisible to us. Even Huy- 
 
 1 Shakspeare's delightful allusion to this conceit in the Merchant of 
 Venice will, no doubt, be familiar to many of our readers: 
 "How sweet the moonlight sleeps upon this bank; 
 Here we will sit, and let the sounds of music 
 Creep in our ears : soft stillness and the night 
 Becomes the touches of sweet harmony. 
 Sit, Jessica : look how the floor of heaven 
 Is thick inlaid with patterns of bright gold ; 
 There's not the smallest orb which thou behold'st 
 But in his motion like an angel sings, 
 Still quiring to the young-eyed cherubims: 
 Such harmony is in immortal souls ; 
 But while this muddy vesture of decay 
 Doth grossly close it in, we cannot hear it." Act v. sc. 1.
 
 MATERIAL FALLACIES. [B. YI. 
 
 gens was persuaded that when the number of the heavenly 
 bodies had reached twelve, that further look-out was useless ; 
 even Divine power could not go beyond that sacred number. 
 Of a similar kind was the assumption of the ancients, that 
 because nature in many objects realised their abstract ideas 
 of perfection, that a similar adherence to the most perfect 
 imaginable entities ought to pervade the entire universe. 
 This was a most convenient principle, which dispensed with 
 all examination of instances, and enabled them to come to a 
 conclusion upon the laws of any natural phenomenon with 
 little expenditure of thought. Thus, if any action of nature 
 was to be investigated, the ancients had only to ask them- 
 selves in how many possible ways a thing could be brought 
 about, and select the most perfect, as the sure course which 
 nature followed. For instance, because the heavenly bodies 
 were perfect, they must move in circles, and that with uniform 
 motion ; for irregularity of movement would be censurable in 
 men, and could not be tolerated in the celestial regions. Nor 
 was the force of such reasoning lost upon some of the moderns ; 
 for the Copernicans alleged in favour of their system, that it 
 placed fire in the centre of the universe, the only position which 
 the noblest element could consistently occupy in conformity 
 with that precedence given to dignity, and those customary 
 rules of etiquette which prevailed in other parts of the universe. 
 
 4. Petitio Principii. 
 
 The fallacy of petitio principii, or begging the question, 
 consists either in arguing in a circle or assuming a premiss 
 which unfairly implies the conclusion. The theologian would 
 furnish an instance of the first, were he to prove the au- 
 thority of the Church from Scripture, and the inspiration of 
 Scripture from the authority of the Church. To prove the 
 existence of God on the same authority, or to argue that a 
 government was good because we ought to support it, would 
 afford an extreme instance of the second. 
 
 Notwithstanding Aristotle is very circumstantial in the 
 description of this fallacy 1 , no philosopher fell so frequently 
 into it as himself. As an instance of his performances in 
 this way, we may adduce his proof of the earth being the 
 central spot of the universe : 
 
 1 Arist de Soph. Elenc. cap. xxviL
 
 C. III. 4.] FALLACIES OF PHBENOLOGY. 327 
 
 The nature of heavy things is to tend to the centre of the 
 
 universe, and of light things to fly off from it ; 
 But experience proves that heavy things tend towards 
 
 the centre of the earth, and that light things go off 
 
 from it, 
 Therefore the centre of the earth is the same as the 
 
 centre of the universe. 
 
 It is clear that heavy things tend towards the centre of 
 the earth ; but how could Aristotle deduce from this fact that 
 they tend to the centre of the universe, unless by assuming 
 in the major that the two centres are identical, which is the 
 very thing he had to prove ? 
 
 There is no fallacy in the category which is apt to put on 
 more disguises, and to hoodwink men more readily into false 
 principles, or to present them with more plausible reasons 
 for their errors, than the assumption of the thing in dispute. 
 Sometimes it appears in support of a bad generalisation to 
 explain away the outstanding exceptions which conflict with 
 the theory. Thus, when it was objected to the psychological 
 system of Grail and Sphurzheim, that Voltaire (if the phreno- 
 logical busts were accurate) had the organ of veneration very 
 large; it was alleged by the phrenologists that the reverence 
 of that philosopher for the Deity was so great that he scouted 
 all existing forms of worship, simply because they fell below 
 his idea of the majestic and sublime nature of that worship 
 which befitted so great a Being. Goethe's deficiency in 
 ideality, and Mozart's want of harmonic perception when 
 judged by the phrenological standard, were accounted for in 
 a similar manner. These individuals had the organs very large, 
 but owing to the casual thinness of the plates of the skull, and 
 the transparent tenuity of the muscle at that particular spot, 
 the organ did not protrude on the upper surface. It is ob- 
 vious that such a convenient system of answering objections 
 amounted to this : The system of phrenology is true, there- 
 fore no exceptions to the theory exist which cannot be 
 rationally accounted for, and proved to accord with it ; which 
 is one of the most glaring instances of reasoning in a circle 
 that the vagaries of philosophy afford 1 . 
 
 1 These instances do not invalidate the entire system, but only the 
 hasty generalisations which led its framers, in a night and a day, to 
 assign to every inch of the cerebrum the precise feeling and faculty of 
 which it was the organ. The tripartite division of the brain which this
 
 328 MATEEIAL FALLACIES. [B. VI. 
 
 Occasionally this fallacy comes before us in the shape of 
 mistaking a sign of a thing for the thing itself a mistake, 
 however, of so gross a nature that it could not possibly pass 
 current, unless a large space of time interfered as an agent 
 in the deception. In past ages, for example, certain opinions 
 were casually associated with peculiar interests, and though 
 the interests have long been buried with the circumstances 
 in which they had their origin, yet the opinions are still 
 taken as presumptive proof of their tangible existence. A 
 glaring instance of mistaking a sign, from which one might 
 fairly infer a certain phenomenon, for a cause of it, occurred 
 in the arguments of those who resisted Boman Catholic 
 claims. The greater part of the enactment commonly known 
 by the name of the Penal Laws, was framed at the epoch of 
 the revolution, and was enforced with a view to discover the 
 partisans of the Pretender. The creed of the Catholic, as 
 Canning remarked, was not his guilt, but the means of de- 
 tecting it. The creed was simply a sign or badge of those 
 who had a leaning to a prince outlawed by the constitution. 
 But to uphold the penal laws after the attachment had ex- 
 pired, and the political danger passed away, was, as if a 
 magistrate having received information that a murder had 
 been committed by a man who wore spectacles and a wig, 
 and having apprehended a man distinguished by these ap- 
 pendages, should, upon its being ascertained that no murder 
 was committed, still refuse to relinquish his man, persisting 
 that the spectacles and the wig were conclusive evidence of the 
 murder. All believers in transubstantiation being suspected 
 of an attachment which the law deemed treasonable to the 
 possessor of the throne, their creed was taken as a certain 
 badge of the treason, and exposed its professors to severe 
 punishment. But when the foreign attachment with the 
 exiled family had ceased, the Catholic was punished for be- 
 lieving in transubstantiation. 
 
 One of the most notable disguises which this fallacy puts 
 on, is to assign as the original cause of a thing in dispute an 
 eifect or collateral consequence of the very principle which is 
 sought to be explained away. By such a procedure Gibbon 
 endeavours to undermine that part of the evidence adduced 
 
 system assumes, cannot, we think, be doubted; but, then, it had been 
 pointed out long before by Galen, and was a favourite theory of Hip- 
 pocrates.
 
 C. III. 4.] BEGGING THE QUESTION. 329 
 
 to prove the divine origin of Christianity, which is derived 
 from the marvellous speed with which it subjected the world 
 to its tenets. "We need no miraculous interposition, argues 
 the historian 1 , to account for what is fully explainable by 
 human agency ; and he immediately collects under distinct 
 heads the causes which had conjointly operated to the wild- 
 fire spread of the Christian doctrine. The principal of these 
 are the pure lives of its professors ; the inflexible firmness 
 with which they adhered to their principles, despite of rack, 
 gaol, and all the horrid instruments of death ; the zeal they 
 manifested in the propagation of their doctrines, and the 
 subserviency of all other views to that end ; the social bond 
 of brotherhood perpetuated among their members, and the 
 regularities of daily worship. But Gibbon forgot in stating 
 these and similar reasons as natural agents in the spread of 
 Christianity, that he was assuming the very thing in dispute. 
 It is obvious that the features he alleged so far from being 
 natural, were about the most startling phenomena that could 
 present themselves in a corrupt state of society corroded by 
 moral pestilence of every kind : so that his pretended proof 
 leaves the swift propagation of Christianity quite as in- 
 explicable on human grounds as it was before. This kind of 
 explanation is not a whit better than the light let in upon 
 the foundations of the earth by the cosmogony of the Indians. 
 " The world rests upon an elephant, and the elephant upon a 
 tortoise," say the Brahmins. But, then, what does the tor- 
 toise rest upon ? 
 
 A similar instance of this fallacy in its most concealed 
 guise is presented in the reasoning, by which Hobbes and 
 Eousseau rest the mutual obligations of members of a civil 
 community upon a supposed social compact, apart from all 
 motives of utility and interest. According to the latter, 
 sovereigns are compelled to provide for the welfare of their 
 subjects, and subjects are bound to maintain dutiful allegiance 
 to their sovereigns, by the terms of a contract entered into by 
 their barbarous progenitors in renouncing savage life, and 
 agreeing to establish a political society. In the same manner 
 Hobbes, throughout his Leviathan, deduces with elaborate 
 skill, the obligations which men are under, to obey even the 
 most despotic mandates of their rulers, from a promise made 
 by their ancestors, at the foundations of society, to leave their 
 1 Decline and Fall, eh. xvi.
 
 330 MATERIAL FALLACIES. [B. VI. 
 
 destinies in their hands. A great deal of good ingenuity, 
 however, might have been spared by these philosophers had 
 they reflected that even if the compact had been drawn out 
 in precise terms, and the document on which it was written 
 hermetically sealed, and transmitted to future generations, it 
 could only have bound the race of men who subscribed it. 
 In no further case could it have held without the admission 
 of the very principle of expediency and interest they discarded 
 as a ground of obligation. Thus we are forced back by the 
 conclusion they adopted, to the enunciation of the operating 
 motive their reasoning endeavoured to exclude. To have 
 established that conclusion, they should have proved not 
 only that a social compact did exist, but that it was an all- 
 sufficient ground to link generations of men together in sup- 
 port of the same institutions and the same line of policy. 
 But they assumed this which was the radical point in the 
 argument, and consequently proved nothing. 
 
 Occasionally this fallacy masks itself in mere forms of 
 expression, either assigning as a reason for a thing expressed 
 in the abstract the same thing re-stated in the concrete, or 
 making the concrete statement first, and then alleging as proof, 
 the same thing expressed in a concrete form. Thus the load- 
 stone attracts amber by reason of its magnetic virtue ; the 
 poppy has a soporific virtue because it lulls to sleep. These 
 sort of pretended explanations, though ungallantly termed 
 ladies' reasons, are by no means confined to the gentler sex. 
 The gravest philosophers have dealt in them, and none, per- 
 haps, so much as the Stagyrite himself. The English lan- 
 guage, on account of the diverse character of its origin, which 
 has crowded it with words nearly synonymous in meaning 
 but widely different in expression, is peculiarly suitable to this 
 form of begging the question. For a sophist can, if he chooses, 
 bring forward a proposition expressed in words of Saxon 
 origin, and pretend to prove it by giving utterance to the 
 very same sentiment in language of Norman derivation, or 
 vice versa. This is the common mode of reasoning adopted 
 by a peculiar class of political speakers. " The measure 
 under consideration is the best fitted to meet the circum- 
 stances of the case (Saxon propos.) ; because it provides for 
 all the exigencies that can be supposed to be involved in the 
 question" (JS"or. proof). " The bill before the House is 
 calculated to elevate the character of the education of the
 
 C. III. 5.] IBBELEVANT CONCLUSION. 331 
 
 country (Nor. prop.) ; for it raises the general standard of 
 instruction throughout all the schools 1 " (Sax. proof). So 
 true is the saying of Hobbes, that words are the counters of 
 wise men but the money of fools. 
 
 The reader must be on his guard against what Bentham 
 termed " begging question appellatives," which assume the 
 question under the guise of stating it. Thus, were a person 
 to argue that because liberal institutions were beneficial to 
 the country, that a Whig government ought to be preferred ; 
 he would assume the point in dispute by the use of the word 
 liberal, the connexion of which term with such institutions 
 being the very matter which requires proof. Instances of 
 this kind of begging the question are presented in all dis- 
 cussions in which words of a laudatory or a vituperative 
 character are used. For instance, the opponents of the 
 recent establishment of the Roman Catholic hierarchy in 
 these dominions, in all their arguments' on the subject set 
 out with the assumption of the act being an aggression, and 
 thence proceeded to show it was a wanton outrage on the 
 feelings of the country. Whether right or wrong, elaborate 
 reasoning on the point might have been dispensed with, for 
 the conclusion was palpably begged in the statement of the 
 premiss. 
 
 5. Ignoratio Elenchi. 
 
 The concluding fallacy we have to advert to is called by 
 Aristotle ignoratio elencM 2 , or ignorance of the contradictory 
 of an opponent's assertion, which we fall into when, instead 
 of proving the contradictory or elenchus of our adversary's 
 proposition, we attempt to establish something else re- 
 sembling it : but as it is substantially the same thing to 
 prove what was not denied as to disprove what was not as- 
 serted, the fallacy may be employed for the apparent esta- 
 blishment of our own proposition as well as for the feigned 
 refutation of that of an opponent's. Though the Stagyrite 
 is as carefully minute in his description of this fallacy as of 
 the last, his own reasonings will afford not the least striking 
 specimens of its practice. Thus he assumes that Parmenides 
 and Melissus admitted only a single principle of all things ; 
 as if they had understood by this principle that of which 
 
 1 The phrases in question are selected from Hansard. Every par- 
 liamentary debate affords many choice specimens of similar inanities. 
 2 De Soph. Elen. c. v.
 
 332 MATERIAL FALLACIES. [B. VI. 
 
 all things are composed, and refutes them on that ground ; but 
 his reasoning was nothing to the purpose, since they meant 
 the single and unique principle from which all things have 
 derived their origin which is God. In like manner, he 
 attributed to his predecessors, ignorance of the principle of 
 privation, viz., that a thing could not exist before it was made, 
 and treated them as clowns and fools, for not employing 
 it, in the explanation of natural phenomena. Whereas no 
 one could be ignorant of so palpable a truth, and he must 
 have been blind indeed, who could have expected it to unlock 
 for him, the least of the mysteries of nature. 
 
 This is the standing sophism of polemical writers, and 
 accompanies all controversy which is much connected with 
 the passions, or which engages the attention of an over-heated 
 crowd of disputants. The field of debate is so large that 
 the combatants either join issue on the wrong points or do 
 not join issue at all. One goes to the east, another to the 
 west ; one loses the principle in dispute, and wanders amidst 
 a crowd of irrelevant details : one mistakes contraries for 
 contradictories ; another particulars for universals ; and after 
 many hours' storm, they know not what they have been dis- 
 cussing 1 : one is above, another below, another at the side ; 
 each either making out a case which his adversary admits, or 
 pursuing a line of argument which, when fully established, 
 has not the slightest bearing on the point in dispute : one 
 tugs at a word or similitude, or takes up a collateral pro- 
 position having no essential connexion with the main argu- 
 ment, and, overthrowing that, makes his pretended triumph 
 resound over the field : another, being rather shattered by 
 reasons, appeals to the prejudices of his auditory, and over- 
 whelming his more rational antagonist with ridicule and 
 abuse, comes off the apparent victor of the contest 2 . 
 
 1 Hence it is not unusual, after a protracted debate in the House of 
 Commons, for the cooler thinkers to preface their observations with re- 
 minding the House of the real nature of the point on which they are to 
 join issue ; and the longer the subject in question has been under the 
 consideration of the House, the greater the necessity has appeared for 
 these premonitory exordiums. The same precaution is generally taken 
 by judges in summing up, after trials of protracted length. 2 Ben 
 
 Jonson satirically expressed the vain disputes of a certain class of 
 divines by Inigo Lanthorne disputing with his puppet in Bartholomew 
 Fair: "It is so; it is not so; it is so; it is not so," &c. The majority 
 of theological disputes, we fear, practically amount to the same result.
 
 C. III. 5.] FORMS OF IEEELEVANT CONCLUSION. 333 
 
 The various kinds of irrelevant conclusions contained in 
 the above description, have distinct names assigned to them 
 by logicians, according to the matter they embrace. Thus, 
 all unfair use of personal opinions (argumentum ad Tiomi- 
 nem), of popular prejudices (argumentum ad populutn), and 
 respected authorities (argumentum ad verecundiam), are 
 classed under the head of the fallacy of appeals to the 
 passions ; as attempts to decide the question on other 
 grounds than the reason of the thing (argumentum ad rein), 
 or than that of the dispassionate exercise of the individual 
 judgment (argumentum ad judicium). It is not that such 
 appeals are not allowed, but that more should be built upon 
 them than what the circumstances of the case necessarily 
 warrant. For instance, were we to prove, from the peculiar 
 circumstances, character, or avowed opinions of an individual, 
 that he was bound in consistency to admit a certain con- 
 clusion, and thence to argue that the proposition was true, 
 we should seek to establish a relative and particular conclu- 
 sion for one absolute and general, and thus be guilty of 
 irrelevant inference : or should we attach more than probable 
 weight to the argument, that a certain course was the best to 
 pursue, under the circumstances ; simply because a certain 
 authority had recommended its adoption, we should fall into 
 the same fallacy, by mistaking a relative for an absolute degree 
 of certainty. It is, however, often legitimate and even neces- 
 sary to use such arguments in order to silence those who will 
 not yield to fair argument, or to convince those whose weak- 
 ness and prejudice will not allow them to assign to any reason 
 its true weight. With this view Jesus Christ silenced the 
 cavils of the Jews when they reproached him with healing on 
 the Sabbath, by citing the parallel case of drawing out a beast 
 from a pit on the same day, which none of them would have 
 deemed sinful. The argument (ad Jiominem), however, was 
 not pressed further by our Lord than to convict his objectors 
 of gross inconsistency. 
 
 Another form of this fallacy is that of shifting ground, 
 when an adversary, after having vainly attempted to maintain 
 his position, covertly exchanges it for another instead of 
 honestly giving up the dispute. To this is akin the fallacy 
 of objections, by which people conclude that because argu- 
 ments can be alleged against any plan, theory, or system, 
 it ought to be rejected, or that it cannot be true : when it
 
 334 MATERIAL FALLACIES. [B. YT. 
 
 ought to be shown, in order to warrant them to hold such 
 an opinion, that the objections against the adoption of the 
 thing are stronger and more numerous than those urged 
 in its favour. This is the main fallacy of sceptics, who con- 
 clude that Christianity cannot be true as long as strong 
 objections can be urged against any portion of the evidence 
 on which it rests ; and of bigoted anti-innovators, who oppose 
 all reforms on the ground that no alteration can be pro- 
 posed against which they cannot urge strong and unanswer- 
 able objections. But did such reasoning hold, and men 
 choose to delay accepting any proposition until all the ob- 
 jections that could be brought against it were unequivocally 
 disposed of, it is obvious that society could not advance a 
 step in the way of speculative belief or of useful reforms. 
 
 An ordinary case of this fallacy is exhibited when we 
 prove only a part of what is required, and dwell on that to 
 the exclusion of the rest. Thus, if a man is charged with 
 an offence, and some portion of the evidence adduced against 
 him be of equivocal character, a skilful advocate will com- 
 pletely sink the sound part of the allegations, and expatiate 
 on the others as if they constituted the only proof before 
 the court. Hence in advancing more than can be well 
 maintained, we expose the entire line of evidence to a com- 
 plete overthrow ; for a clever tactician will seize on the weak 
 point introduced, and by dwelling upon that part of his 
 adversary's argument, make it appear that it involves the 
 whole question at issue, and resound his triumph over the field, 
 as if he had demolished all the outworks of his opponent's 
 position. Wo person, therefore, should lay down a principle 
 without guarding or restricting it by modifications, since a 
 clever antagonist is always sure to avail himself of his neglect 
 in this particular, by pushing his principle over the boundaries 
 of moderation. This course is frequently pursued in par- 
 liamentary rejoinders; and frequently afforded Canning a 
 way to the citadel of his adversary, when reason and justice 
 had fortified every other path against him. There is no 
 principle, however just in theory, however reasonable in 
 argument, or expedient in practice, which is not capable in 
 its naked state of being carried to an extreme length, or 
 represented in so ludicrous a light as to make it shiver in 
 the hands of its nunciator as a weapon of reasoning. One 
 of the most glaring examples of this kind of irrelevant
 
 0. III. 5.] THE LAST TWO FALLACIES COMBINED. 335 
 
 conclusion occurred in the debate on the institution of a 
 commission of inquiry into the state of the universities. 
 The principal opponent of the ministerial proposition took 
 up the ground, that government had no right to inquire into 
 the state of municipal or corporate bodies; a principle of 
 which no one can dispute the justice so long as the movements 
 of those societies do not interfere with the interests of the 
 commonwealth, or impede the progress of the community ; 
 matters, of course, over which the government have complete 
 control. The defender of the universities, however, neglected 
 so to restrict it, and the minister threw ridicule on his op- 
 ponent by representing many cases in which a wise govern- 
 ment could not abstain from interfering with corporate 
 societies. The onus which lay on the minister, of proving 
 that the universities presented a case for public interference 
 was thus lost sight of, in the feelings excited by the con- 
 futation of the principle in the sense to which its propounder 
 did not intend it to apply. 
 
 "With the last form of ignoratio elenchi may be classed 
 the common case of substituting a particular for a universal 
 conclusion, or of proving something to be possible when it 
 ought to have been proved highly probable; or probable 
 when it ought to have been proved necessary ; or contrary 
 instead of contradictory; or improbable when it ought to 
 have been proved impossible. Aristotle complains of this 
 last branch of the fallacy as giving an undue advantage to 
 the respondent 1 . Many a guilty person owes his acquittal 
 to this ; the jury considering that the evidence brought does 
 not demonstrate the absolute impossibility of his innocence, 
 notwithstanding the chances are innumerable against it. 
 
 This fallacy is not unfrequently combined with that of 
 getitio principii, when the premiss implying the conclusion 
 is assumed on the ground of something resembling it having 
 been already established. An instance of this kind occurs 
 in the speech of Cleon concerning the Mitylenians, who urges 
 the justice of putting the revolters to death ; which, as Dio- 
 totus, a subsequent speaker, remarked, was nothing at all to 
 the purpose, since the Athenians were not sitting in judgment, 
 but in deliberation, of which the proper end was expediency 2 * 
 A similar illustration of the hybrid form of this fallacy may 
 be seen in the objection urged against a scheme of national 
 1 Rhet. b. ii. * Thucidydes, quoted by Dr. Whately. 

 
 33G MATERIAL FALLACIES. [B. TI. 
 
 education ; which assumes that the humbler classes, if pro- 
 perly instructed, would not submit to the low drudgery of 
 their station, from the fact that those few at present who 
 scrape together a little knowledge are apt to think them- 
 selves gentlemen and become discontented with their posi- 
 tion. Now the force of the argument rests on the perfect 
 similitude between the two cases, which is most gratuitously 
 assumed. For when education is universal it must cease to 
 be a distinction, which, as Archbishop Whately remarks, is 
 most likely the very circumstance which renders such indi- 
 viduals too proud for their employment. 
 
 The combination of these two fallacies is very usual in 
 parliamentary debates ; and Canning's speeches afford several 
 instances of then: employment and detection. One of the 
 most striking of the latter will be found in his reply to 
 Mr. Perceval in the debate on Horner's resolutions, which 
 emanated from the bullion committee of 1811. That states- 
 man having referred to the continuance of our triumphs in 
 the Peninsula and our conflicts with Napoleon as a reason 
 for perpetuating an exclusive paper-currency, Mr. Canning 
 replied : " I will not pay my right honourable friend so ill a 
 compliment, as to suppose that he is not himself perfectly 
 aware that in thus shaping his argument he has, in fact, rather 
 assumed or omitted the question in dispute. The question 
 is not whether we shall continue the war in the Peninsula 
 with all our heart. Who doubts, who dissuades that deter- 
 mination? That point might have been assumed without 
 hazard of contradiction. But my right honourable friend 
 argues that point as if it were disputed, and assumes without 
 argument that which was necessary for him to prove viz., 
 that to the continuance of the war and our successes in the 
 Peninsula it is essential that the present system of cur- 
 rency should remain unchanged. Just as fairly might I 
 assume without argument that a change in our currency is 
 necessary to this same purpose of continuing the war, and 
 then retort upon my right honourable friend his own ex- 
 postulations against fettering the energies and cramping the 
 exertions of the country. In either case the point which is 
 alone in dispute remains to be decided."
 
 APPENDIX. 
 
 MODEBN SCHOOLS OP LOGIC. 
 
 A DISTINCTION is sometimes sought to be erected be- 
 tween the different modern schools of logic, as if the 
 predominant elements in each contained something neces- 
 sarily antagonistic to one another. Thus we find the 
 verbal school of logicians including men whose views 
 differ so widely as Hobbes, Dr. "Whately, and the school- 
 men set up in antagonism to the sensational or pheno- 
 menal school, which numbers Bacon, Helvetius, Comte, 
 and Mill among its chief expositors ; and these again con- 
 trasted by way of opposition with the conceptualist school 
 of logic, of which Kant is the chief exponent 1 . The student 
 having been introduced to these different varieties of logical 
 sects, is told that he can make only one choice, and that the 
 set of tenets which is pointed out for his acceptance must 
 necessarily place him in antagonism with the opposite 
 schools. 
 
 It must not, however, be overlooked, as the functions of 
 words, conceptions, and things, are conjointly admitted in 
 every rational system of logic, that there is no necessary anta- 
 gonism between these separate elements in logic, further, 
 indeed, than what may arise from the importance of any one 
 being so unduly exaggerated as to exclude or unduly inter- 
 fere with the functions of the others, in the inferential process. 
 Each school, with the exception of one or two extreme sec- 
 tions, admit that words are only the embodiments of the 
 mind's conceptions, while the latter are only so many ways of 
 regarding external phenomena, so that there is in reality 
 
 1 Essay on Logical Method, by Charles P. Chretien, ch. v. p. 94. 
 Oxford. 1348.
 
 338 APPENDIX. 
 
 nothing to prevent the main body of their individual 
 opinions from being collected into one system of logic, and 
 thus to exclude that sectarianism in this department of 
 philosophy which is the disgrace of religion. What is there 
 in Mill beyond his nominalist views which interferes with 
 Kant's logical doctrines as propounded by Jahsche ? or in 
 "Whately's exposition of the scholastic logic, which conflicts 
 with either, unless matters of metaphysical concernment, 
 which have no claims to be acknowledged in logic, as the 
 ground of antagonistic schools ? Mill's nominalist views 
 would certainly, if carried out to their extreme conse- 
 quences, upset the scholastic theory of logic, but as a proof 
 that he did not consider his purely logical opinions at all 
 conflicting with those put forth by that school, he refers his 
 readers to Dr. Whately's treatise, as containing views 'in a 
 great measure supplementary to his own. In eliminating, 
 therefore, in the foregoing treatise, the conflicting metaphy- 
 sical opinions of the different schools of logical writers, we 
 have found nothing in the body of their logical doctrines 
 which refused to combine harmoniously in one system. 
 
 In referring, however, to the extreme sections of some of 
 these schools, we might find matter to legitimate an opposi- 
 tion of logical doctrines; but this, so far from leading 
 to the distinction upon which we have animadverted, would 
 really take it to pieces. Thus the extreme exponents of the 
 verbal school are Hobbes and Condillac, who, denying alto- 
 gether the antithesis between thought and language, assert 
 the identity of each, and make every question purely verbal. 
 With Hobbes, logic is only a peculiar kind of mental arith- 
 metic : " Season is nothing but reckoning (that is, adding 
 and subtracting) of the consequences of general names 
 agreed upon for the marking and signifying of our thoughts. 
 Logicians," he further says, " add together two names to 
 make an affirmative, and two affirmatives to make a syllo- 
 gism, and many syllogisms to make a demonstration, and 
 from the sum or conclusion of a syllogism they subtract one 
 proposition to find the other 1 ." Condillac, though in other 
 terms, expresses precisely the same doctrines 2 . With him 
 reasoning is only a kind of algebraical computation, and 
 
 1 Leriathan, ch. v. a Hist. Introd. p. 19.
 
 MODEEN SCHOOLS OF LOGIC. 339 
 
 definition the only weapon in the logical armoury ; and the 
 greatest results to which the most successful scientific re- 
 searches can lead is a well-assorted language : " Science, c'est 
 une langue bien faite." There is nothing, however, in these 
 views, even so far as verbal logic is concerned, to place them in 
 the same category with those entertained by "Whately and the 
 scholastic logicians. While the scholastics, and their modern 
 representatives, overstrained at one time the conceptual and 
 rational faculties, and at another placed too much reliance 
 on the powers of language to explain fundamental differences 
 of principle 1 , they nevertheless admitted the reality of external 
 phenomena and the correlative functions of language and 
 conception in the elaboration of thought. Hobbes and Con- 
 dillac, on the other hand, denied as rigidly the distinction 
 between mind and [matter, and implied that reason was a 
 consequence of our bodily organisation, and depended on 
 speech for its existence. They consequently belong to that 
 group of logicians who, with Locke and Dugald Stewart, 
 ignore the functions of the school logic as far as proposi- 
 tions and syllogisms are concerned, and as such stand in 
 direct opposition to that school of logicians with whom they 
 are sometimes classed. 
 
 There is, notwithstanding, among the general body of 
 logicians who admit the syllogistic theory with proper 
 limitations, a tendency to give undue expansion to one ele- 
 ment in the triad to which we have alluded; the a priori 
 school, placing too much stress either on words or on con- 
 ceptions, while the nominalist branch are too apt to degrade 
 the former and place external phenomena in the ascendant. 
 Thus it cannot be denied that one of the chief defects of 
 Whately' s exposition of the Aristotelian logic is the attempt 
 to seek for the origin of every dispute in verbal equivoca- 
 tion 2 , and to measure the powers of thought by the verbal 
 
 1 Home Tooke, who took Shakspeare's expression that " the lip ia 
 parcel of the mind" (Merry Wives of Windsor, act i. sc. iv.) as a great 
 philosophical axiom, refused to admit there was anything simple or 
 complex, general or abstract, in ideas apart from the terms them- 
 selves. (Div. of Purley, p. i. ch. ii.) ' These views have been advocated 
 by French and the leading High Church divines, and were cherished 
 by De Maistre. (See his criticism on Bacon, art. Syllogism, in the 
 collection of his posthumous works.) 2 Thus he resolves the dis- 
 
 pute on Arianism and Sabellianism, which for nearly two centu- 
 
 z2
 
 340 APPENDIX. 
 
 conventionalisms by which men choose to invest its mys- 
 terious processes with external embodiment. Thus in treat- 
 ing of hypothetical and inductive arguments, he compels 
 methods of reasoning which when viewed in the thinking 
 mind are clearly distinct from the deductive process and 
 from each other to bow to an artifice of language and submit 
 to the unvarying formula of the deductive syllogism. His 
 manifest aim is to underrate the number of real questions at 
 issue among mankind, and to increase in proportion the 
 number of verbal; differences. In dealing with contending 
 disputants he either accuses them of an equivocation, t. e. 
 that they mean the same thing by different words, or use 
 the same word to signify distinct things or he looks for 
 some formal error in the argument of one of the parties, to 
 which he assigns the discrepancy, rather than refer the cause 
 to some broad difference of principle underlying the whole 
 discussion 1 . In a similar spirit it is the tendency of con- 
 ceptional writers to confound logic with metaphysics 3 , and to 
 make both language and external realities submit themselves 
 to the domineering influence of mental theories. 
 
 Mr. Mill's " System of Logic," on the other hand, may be 
 taken as an instance of the undue preponderance given to 
 external phenomena, and the subjugation of language and 
 conception to phyaics. The favourite notions of logic are 
 transferred from the inner to the outer world: sequence 
 causation with abstract and general terms are held to be de- 
 rived from phenomena, and not to be the conditions of the 
 mind's perceiving them. Logic, in this view, is represented 
 
 ries divided the opinions of some of the leading minds of Christendom, 
 into a mere play upon the words one and same. We need hardly say 
 that there is no difference of opinion, however fundamental, which could 
 not be explained away in like manner. Thus the dispute between the 
 Spinozists and the Christians, with respect to the existence of God, 
 might be resolved into a mere verbal shuffling upon the word Deity. 
 Both classes of disputants really admit the same power existing from 
 eternity, and endued with creative energies the only difference being 
 that one call it Nature, and the other God; but what is there in a 
 mere nominal discrepancy to keep the Spinozists and the Christians 
 apart so long as they imply in substance the same thing? l Chre- 
 
 tien, Log. Meth. p. 101. - As is observed in the title of Mr. Thom- 
 son's Logic, viz., Laws of Thought. Logic, however, has nothing to 
 do with laws of thought further than these are involved in the process 
 of inference.
 
 MODEBN SCHOOLS OF LOGIC. 341 
 
 not as dealing with conceptions, but as employed directly 
 about things. In like manner, words are considered as signs 
 rather of things than of our conception of them 1 ; and pro- 
 positions are treated not as connecting two ideas or concep- 
 tions, but two things. The mind is thus thrown on the out- 
 ward world for the conditions of its laws, and is deprived of 
 the dignity of independent action, which its superior nature 
 would lead us to think was its natural prerogative. 
 
 There is, however, no conflicting opposition between the 
 main body of the strict logical doctrines of these several 
 schools, but only in the exaggerated expansion they are apt 
 to receive from the hands of zealous partisans. 
 
 1 VoL i. p. 28.
 
 342 APPENDIX TO BOOK I. 
 
 APPENDIX TO BOOK I. 
 
 CHAPTER II. 1, 2. 
 Nominalism and Realism, 
 
 A PEW lines of Porphyry on the predicables of Aristotle, 
 raising the question long before agitated between the Stagy- 
 rite and Plato, as to whether universal conceptions or gene- 
 ral ideas which include classes have any existence out of 
 the human mind, gave rise to the angry disputes concern- 
 ing nominalism and realism which disturbed the repose of 
 Christendom from the eleventh to the fifteenth century, and 
 which had previously evoked the same stormy discussions 
 among the doctors of Islam. The question both in the 
 Mussulman and Christian camp had assumed a more com- 
 plicated form from being involved in theological quarrels; 
 and as 'long as the most vital dogmas of religion were 
 thought to depend on the issue, the fire of spiritual zeal in- 
 vested these debates, which almost cotemporaneously excited 
 the passions of two hemispheres, with an interest to which 
 the most absorbing discussions of the present epoch can 
 furnish no parallel, and which were frequently silenced, but 
 never suppressed, by the mandates of the civil, and the 
 anathemas of the spiritual, authorities. 
 
 Now, when all the smote has been cleared away, and the 
 question has been again presented free from any adventitious 
 element, it does not appear to have derived much elucidation 
 from the searching investigation of so many learned doctors, 
 though the inquiry, if we take the Mussulman abbas into 
 account, extended over a period of six centuries. These 
 gentlemen, after a fearful waste of time and zeal, left the 
 question just where they found it, with the exception of 
 Avicenna, who is said to have started the doubtful theory of 
 conceptualism, which Abelard and Occham had the poor merit 
 of transplanting into the Christian arena of the dispute. 
 This theory, however, though not directly broached by Aris- 
 totle, would evidently impress itself on any reader of the pre-
 
 NOMINALISM AND REALISM. 343 
 
 dicables as the very solution of the difficulty which the Stagy- 
 rite had embraced : its formal originators have, therefore, 
 little claim to novelty, except, indeed, for the improper use 
 to which they applied it, in accounting not only for the mode 
 in which class notions or general ideas enter into the mind, 
 but also in confounding this with their absolute existence a 
 point which Aristotle very properly left undecided. 
 
 With regard, indeed, to the mode in which the mind ac- 
 quires universals or class ideas, philosophers are generally 
 united in assigning the process of abstraction which we have 
 attempted to explain in the text. In every object there is 
 always some property analogous to others in surrounding ob- 
 jects, which compel us, as it were, to generalise in a particular 
 way. Thus we place houses in one class and men in another ; 
 nor are there any people so uncultured as to rank some houses 
 and some men in one category because they are red, or to con- 
 found tastes and sounds together because, in many cases, 
 they are accompanied with agreeable sensations. In like 
 manner, the mind traces among classes of phenomena similar 
 organisations and properties within them, and, having formed 
 conceptions out of these classes, always applies the name wher- 
 ever it meets with an individual instance of the general pro- 
 perty. Such designations have generally led to the classifi- 
 cations we meet with in zoology and botany, where animals 
 and plants are ranged into classes to bring out in bold relief 
 the most striking differences of their organisation ; and ac- 
 cording as such conceptions in the mind are founded upon 
 the real properties of external objects, and classified accord- 
 ing to their importance in creation, are they to be relied 
 upon as correct representations of class properties in nature. 
 Now if creation had a spiritual designer, it is impossible to 
 resist the conclusion that, before He evolved the world 
 out of chaos, such class properties existed in His mind as 
 archetypes or moulds after which the fabric of existing things 
 was fashioned to which they correspond. If the same 
 vertebral column is found in a hundred species of animals, 
 occasionally joined to large powerful limbs, and sometimes to 
 small rudimental ones, we are compelled upon the Christian 
 hypothesis of creation to infer that this part of the frame was 
 pre-ordained to be the connecting link of these species, and 
 that in forming a class of vertebrate animals, we are seeking
 
 344 APPENDIX TO BOOK I. 
 
 after a form or idea which existed in the divine mind when 
 animals were created. Universals or class ideas, therefore, 
 may be said in this view to exist without the mind of man, in 
 as far as they are in another mind. The divine mind stampa 
 them on material things ; the human mind reads them there. 
 The controversy is thus resolved into questions which are 
 extrinsic to pure philosophy, and would, perhaps, never have 
 arisen, had not natural theology been confounded with it. 
 Plato, through his love of system-making, would explain 
 everything, and regarding nature as a sealed book, he 
 taught his followers that they might easily put themselves 
 in possession of all the truths it contained by a priori spe- 
 culations on the divine mind, in which the original designs 
 existed upon which nature had been modelled. This, 
 though to a certain extent true as regards morals and 
 aesthetics, was absurd as regarded the material creation ; and 
 Aristotle very naturally challenged the whole doctrine as 
 an assumption in the department of philosophy ; being an 
 attempt to explain what was certain by what was mystical 
 and obscure. How do these ideas, asked the Stagyrite, exist 
 in the divine mind? "Whether as an attribute or a sub- 
 stance ; and if the latter, as the Platonists maintained, how 
 can the universal exist in the singular? Again, Eoscelin 
 and the scholastic nominalists required to know if such 
 ideas existed in the divine mind from eternity, or were sub- 
 sequently evolved out of it by an after process of thought ? 
 If the first case, other substances existed from eternity 
 besides God, which is inconsistent with the divine existence 
 as a necessary being ; if the latter, the attribute of his im- 
 mutability was set aside. Again, must there be an idea for 
 every sensible object ? If so, before Socrates could be born 
 there must have been an eternal idea of Socrates; which 
 would lead to a multiplication of ideas too great even for the 
 imagination to grasp. Then there arose the multifarious 
 questions concerning the mode by which they entered into 
 the mind, and how they became connected with the things 
 to which they belonged. To say that the things participate 
 in, or are copies of the ideas to which they correspond, was, 
 the nominalists alleged, to avoid the difficulty by vague meta- 
 phorical language. In this manner it was by no means diffi- 
 cult to show that the Platonist realism jarred with its own 
 hypothesis, through the exaggerated view which it took
 
 NOMINALISM AND EEALISM. 345 
 
 of a principle having its foundation in truth. Aristotle 
 confronted Plato's doctrine, because it closed the era of 
 physical inquiry ; and the scholastic nominalists, because it 
 clashed with the plainest facts of our own consciousness, 
 with regard to the mode by which we come into possession 
 of class conceptions. 
 
 The nominalists, however, erred by the tendency they 
 manifested to push the doctrine concerning class concep- 
 tions to the other extreme, in asserting that these universals 
 were mere names, and were not only unconnected with any 
 class properties in nature, but had not even a mental con- 
 ception to support them. But unless general names can be 
 assumed at will, it must be admitted that they are inseparably 
 attached to the general qualities which they connote. Be- 
 tween the individual object and the general name, we must 
 insert the notions for which the name stands ; as between 
 Socrates and the name " man" there intervenes the mental 
 notion of the properties which make man. Nominalism 
 thus, in its strict sense, is indefensible ; and those who held it 
 deserve the censures which were heaped upon them as the 
 virtual destroyers of philosophy. Their theory tends to re- 
 present the operation of thought as purely mechanical, and 
 to invert the obvious facts of the case by making reason a 
 function of language, instead of viewing language as a con- 
 sequence of reasoning. 
 
 To escape the absurdities of the ultra-nominalist theory, 
 Abelard, and subsequently Occham, alleged that general 
 names signify general notions dependent on the abstracting 
 powers of the mind, but though independent of single ob- 
 jects, without any real substantial entity corresponding to 
 them in nature. They made no distinctions between moral 
 and physical notions, or attempted to explain how we obtain 
 the general ideas of goodness, virtue, and beauty from the 
 faint exemplars of surrounding objects ; nor did they attempt 
 to reconcile their theory with the existence of the divine mind, 
 or the Christian hypothesis of creation. This theory of univer- 
 sals, which is called conceptualism, is, therefore, open to grave 
 objections. Even so far as the mode is concerned by which 
 the mind comes into possession of general notions, it only 
 accounts for those which are derived from physical creation; 
 while, if followed out to its extreme consequences, it would 
 strip that creation of an intelligent artificer.
 
 846 APPENDIX TO BOOK I. 
 
 In rejecting, however, the nominalist view of universals, 
 both in its ultra and moderate coneeptualist aspect, we do 
 not venture to recommend the acceptance even of a modified 
 view of the realist doctrine, on the ground that the claaa 
 ideas which the mind abstracts from physical objects must, 
 in the present state of science, be correct representations 
 either of the primary ideas in the divine mind, or of their 
 correlative properties in nature. The process by which the 
 mind seeks to attain these universals often leads to erroneous 
 results; and even when we attempt to arrange them in 
 subordination to each other, in few cases can we positively 
 assert that the arrangement is a correct expression of their 
 gradation in nature. Viewed as a statement of abstract truth, 
 if the zoological system of Linnaeus was right, that of Cuvier 
 is wrong. Only when we are assured on the best evidence 
 that we have attained to the real nature of things, and under- 
 stand their relative positions in the scale of creation, can we 
 rely on the validity of our class terms as correct exponents 
 of natural universals 1 . Until we are certain that our class 
 conceptions have reached this point of accuracy, they will 
 only stand as symbols of a provisional classification, which 
 greater research, or more skilful analogies, may at any mo- 
 ment supersede. 
 
 In summing up this important controversy, we may take, 
 as far as regards morals and aesthetics, the Platonic theory of 
 universals to be in the main correct; while in relation to 
 physical truths we must accept such universals as purely 
 conceptual which simply correspond to artificial systems of no- 
 menclature ; as, for instance, the Linnsean system of botany ; 
 or those of whose correspondence to the actual order of 
 things in the external world we have no direct certainty. 
 "With respect to those general conceptions which may be 
 fairly relied upon as correct exponents of outward realities, 
 they may be regarded in the Platonic sense as copies of the 
 designs existing in the divine mind at the period of creation ; 
 while the coneeptualist view must be adopted with reference 
 to their origin in the human mind from an analysis of things. 
 The ultra-nominalist account of universals we discard alto- 
 gether, and place the correct theory in a combination of 
 Abelard's views with Platonic realism. 
 
 1 Chretien, Logical Method, p. 76.
 
 CATEGORIES IN LOGIC. 347 
 
 CHAPTEB II. 6. 
 The Categories of Aristotle. 
 
 These categories have been cited in the text as an example 
 of correct division, and also as an appendage to that part of 
 the Aristotelian logic which refers to the hunting out of 
 genera and proximate species in the process of definition. 
 They are, however, in a practical system of logic of no real 
 value, and were very properly banished by Arnauld to meta- 
 physics. 
 
 Some dispute has arisen whether the categories referred 
 to things, to words, or to conceptions; and, according as 
 they have been deemed a division of one of these three 
 subjects, they have been exposed to much criticism. Chre- 
 tien asserts 1 , that the ten predicaments are purely "an 
 analysis of the leading parts of speech and certain modifica- 
 tions of them," and endeavours to point out the mode in 
 which they might have been obtained by any philosophical 
 grammarian. As such he allows the correctness of the 
 division, but questions their utility beyond the specimen 
 they afford of subtile analysis. Kant, on the other hand, 
 accepts the predicaments in an exclusive sense as a division 
 of the conceptions which dwell in the pure understanding ; 
 and endeavoured to make it more complete by the addition 
 of post-predicaments, or five supplementary categories. It 
 was not difficult, in this erroneous view of the case, to cavil 
 with the Aristotelian division as blending empirical and 
 deduced conceptions viz., motion, action, and passion, with 
 primary notions ; and also to show, by extending the term 
 conception to mere subjective conditions of thought, that 
 there were many such conceptions not even implied in the 
 predicaments of the Stagyrite. Kant, on these grounds, sub- 
 sequently substituted for the old list of predicaments and 
 post-predicaments a new division of categories viz., Unity, 
 Plurality, Totality, Affirmation, Negation, Limitation, Inde- 
 pendence, Dependence, Inter-dependence, Actuality, Possi- 
 bility, and Necessity, which he defined as ^the " subjective 
 conditions of thinking, or the rules which the understanding, 
 
 1 Logical Method, p. 119.
 
 348 APPENDIX TO BOOK I. 
 
 foregoing all the given diversity of consciousness, lays at the 
 foundation of nature by means of its own essential laws." 
 
 The predicaments of Aristotle have again been accused of 
 incorrectness, on the ground of being strictly a division of 
 things. In this light Mill fairly shows that they are open 
 to a charge of cross-division, quality, and relation for in- 
 stance, running into each other in the case of habit, and 
 position falling under relation as a species under a genus. 
 Mr. Mill then proceeds to state his own categories of all 
 nameable things in the following order: 1st. Peelings, or 
 states of consciousness ; 2nd. Minds which experience these 
 feelings ; 3rd. Bodies or external objects which excite certain 
 classes of these feelings, together with the powers or pro- 
 perties whereby they excite them ; and 4th. The successions 
 and co-existences, the likenesses and unlikenesses between 
 feelings and states of consciousness. 
 
 Aristotle's categories, however, are not to be judged ex- 
 clusively on any of the grounds above enumerated, being 
 intended, as Mr. Mill indeed admits, as an enumeration of 
 the most extensive conceptions, or summa genera, into which 
 all things capable of being named can be distributed. They 
 are not names of things, or of words, or of conceptions apart 
 from each other, but simply a division of things into the 
 most extensive conceptions that the mind is capable of dis- 
 tributing them, and as such correspond, of course, to the 
 natural divisions of language which is framed on the model 
 of those conceptions. Kant's view of the Aristotelian cate- 
 gories was, therefore, entirely a mistaken one. Mr. Mill, 
 notwithstanding his correctness with respect to the point of 
 view in which the predicaments are to be considered, is, we 
 think, in error as respects the superiority of his own 
 categories in a logical system. Waiving the objection that 
 it confines spiritual existence to human minds, and, there- 
 fore, does not seem exhaustive, the generalisations which it 
 involves cannot be assumed, on Mr. Mill's own principles, 
 to be correct, till inductive science has worked its way up 
 to the boundaries of knowledge and thrown aside the curtain 
 which hides the universal frame of things. In a word, as 
 logical it is out of place ; as a correct distribution of name- 
 able things, even shutting out the spiritual world, its correct- 
 ness and usefulness are only conjectural.
 
 CATEGOBIES IN LOGIC. 349 
 
 Of the list of categories already given to the world, the 
 peripatetic is the only one which aims at Baking a distinct 
 place in logical science ; and so far, indeed, as the scholastic 
 conception of this science is concerned, it will be found to 
 answer the requirements of its framer. Being devised at a 
 period when nothing beyond language was very philosophi- 
 cally elaborated, it may be faulty in giving too great a pre- 
 ponderance to the verbal element ; but we must not lose 
 sight of the fact, that considering the narrowness of the 
 human faculties, no division of this kind, which aims at the 
 distribution of every nameable thing under the highest heads 
 in which they are conceived by divine intelligence, can 
 possibly be devised without being open to many objections. 
 Aristotle's attempt, to say the least of it, is the most perfect 
 that has been made. All the others seem to be quite inde- 
 pendent of logic, being conceived more or less in reference to 
 the metaphysical system adopted by their framers. The 
 Pythagorian, Platonic, and Stoic schools among the Greeks, 
 had each its corresponding tables. And in modern times the 
 word has come to denote the distinctive classification of each 
 metaphysician, whatsoever his system leads him to discuss, 
 or howsoever he divides it. Thus, Reid tells us that the 
 categories of Locke are three Substance, Modes, and Eela- 
 tions ; and those of Hume two Ideas and Impressions ; and, 
 he adds, amusingly enough, that an excellent mathematician 
 of his day desired to substitute for the peripatetic predica- 
 ments two only viz., Data and Qu&sita. 
 
 CHAPTEB IY. 1. 
 Use of Language in Logic. 
 
 Some confusion has originated in former treatises from 
 the absence of a distinct conception with regard to the rela- 
 tion of language to thought in logic. Dr. Whately, for ex- 
 ample, has defined logic as the art of employing language 
 properly for the purposes of reasoning, and thus implied, 
 either that thought and language are invariably united, or 
 that the mere words, by which the results and the process of 
 inference are expressed, form the substantial element about
 
 350 APPENDIX TO BOOK I. 
 
 which the science is employed. The latter is to mistake the 
 shadow for the substance ; the former involves a false meta- 
 physical hypothesis. 
 
 Even taking the high ground of the Scripture theory in its 
 literal sense with regard to the origin of language 1 , it implies 
 no more than that man was endowed with the power of 
 framing words to correspond to his conceptions: as such 
 it dissevers thought and language, and allows the latter no 
 other value than as its vehicle and exponent. There is, how- 
 ever, a wide school, principally consisting of High Church 
 divines, who believe that words are something more than 
 mere signs who stoutly contend that they are vital powers, 
 and seem inclined to reverse the ingenious remark of Hobbes, 
 that words are the counters of wise men, but the money of 
 fools 2 . We have, notwithstanding the crowd of assertions in 
 favour of this view, met with nothing like a single reason 
 in its favour. That words may be employed as strong 
 impulsive forces may be easily admitted by any one who 
 has observed the power which the skilful rhetorician ex- 
 ercises over the crowd, or the influence of language in the 
 advancement or deterioration of society; but that words 
 derive this power from any other source than their sym- 
 bolical character, no one can maintain with even the sem- 
 blance of argument. If words are used as the signs of things 
 and conceptions, it is very natural they should, as Bacon 
 alleges 3 , react upon the intellect, and limit and, in some 
 measure, control its operations ; but from this surely nothing 
 can be inferred except the liability with certain minds, from 
 the constant association of language with thought, to mistake 
 words for realities, and believe that they command language, 
 when in reality language commands them. 
 
 1 Gen. ii. 19. 2 Trench expressly does so, and goes out of his way 
 to call the Malmesbury philosopher " one of England's false prophets." 
 Study of Words, p. 25, 3rd ed. " There is a sense of reality about 
 children which makes them rejoice to find there is a reality about 
 words." Ibid. Their reality, however, is derivative, and not primary. 
 There is nothing in Trench's valuable treatise whichreally conflicts with 
 Hobbes's views, unless his uncharitable expression and the reversal of 
 Hobbes's brilliant aphorism. 3 " Credunt enim homines rationem 
 
 suam verbis imperare. Sed fit etiam ut verba vim suam super intel- 
 lectum retorqueant et reflectant."
 
 USE OF JiANGtrAGE UT LOGIC. 351 
 
 Words being simply instrumental in aiding the mind to 
 travel much further by means of general terms than it could 
 without their aid, can only be considered in logic so far as 
 their employment either tends to assist or to defeat the 
 process of inference ; and, as with instruments of another 
 kind, our care' should be that they faithfully transmit the 
 properties they were intended to convey, and not "palter 
 with us in a double sense," or be allowed to float about 
 either with a loose, unsettled, or inaccurate connotation. 
 
 CHAPTER IV. 2. 
 Abuse of General Terms. 
 
 As an instance of the disputes to which the employment 
 of general terms may give rise in fundamental questions of 
 law or government, Trench adduces the Latin word Bene- 
 ficium. This word, it appears, anciently implied either benefit 
 or benefice, either we suppose on account of the advantages 
 that accrued to the minister from the possession of the 
 revenues, or the benefits that were believed to flow to the 
 people from his pastoral functions ; and is used in both senses 
 by "Wicliff in his translation of the Bible (1 Tim. vi. 2). As 
 the term, however, was early connected with the conflicting 
 claims of imperial and priestly jurisdiction, it was not long be- 
 fore its bifold signification was turned to account. Pope 
 Adrian IV., writing to the Emperor Frederic I. against cer- 
 tain lay encroachments on the spiritual authority, reminded 
 the Emperor " that he had placed the imperial crown upon 
 his head, and would willingly have conferred even greater 
 Seneficia upon him than this." Had the word been accepted 
 without a remonstrance, it might have been afterwards ap- 
 pealed to as an admission on the part of Frederic that he held 
 the empire as a feud or fief (for beneficiwm was then the 
 technical word for this, though the meaning has been much 
 narrowed since) from the Pope the very point in dispute 
 between them. The word, however, was repelled by the 
 Emperor, whereupon the Pope appealed to the etymology,
 
 352 APPENDIX TO BOOK I. 
 
 that Beneficium was but bonum factum, and protested that he 
 meant no more than to remind the Emperor of the " benefits" 
 which he had done him, and which he would have willingly 
 multiplied still more 1 . 
 
 CHAPTER IV. 3. 
 Transitive Application of Words. 
 
 The transformation of words from one distinct sense to 
 another, without either widening or diminishing their appli- 
 cation, may be taken as one of the most general laws of 
 language. A striking example of it may be adduced in the 
 application of the term " classics" to denote, according as the 
 object either refers to languages or books, those of the highest 
 excellence. Thus, when we speak of the classical languages, 
 we refer exclusively to the Greek and Latin, because these 
 tongues have been always considered by Europeans as exem- 
 plars after which they might improve their own. In like 
 manner we refer to the works of Milton or Dryden, Racine 
 or Boileau, as English and French classics, the productions 
 of these authors being ranked as the best of their kind by the 
 general body of their countrymen. The word " classics," or 
 classici, however, was attended at first with a very different 
 signification. This word was originally applied by the po- 
 litical economists of Rome to designate men who possessed 
 the largest income Roman society being divided into classes 
 according to the amount of property its respective members 
 possessed, with a view that each might be rated in proportion 
 to his ability to contribute towards the expenses of the state. 
 The individuals in the foremost rank were called classici, in 
 contradistinction to men of the second, third, or fourth class, 
 who are termed infra classem. When the Roman political 
 system was broken up, and the term wandered about without 
 a meaning, it was associated by an obvious analogy with the 
 works of the ancient writers ; since, at the time when the 
 appellation was bestowed, no works were written either in 
 the East or the "West except in Greek and Latin, and it could 
 
 1 We have not verified the accuracy of this statement, but give it on 
 Trench's authority, and almost in his own words. Study of Words, 
 p. 157, 3rd ed.
 
 CHANGES IN THE MEANING OF WOEDS. 353 
 
 not be considered that the mediaeval writers were able to rival 
 the Pagans in the use of their own tongue. By degrees, how- 
 ever, as the barbarous dialects of Europe took " the form and 
 pressure" of the ancient languages, and men felt sufficient 
 confidence in their stability to make them the vehicle of their 
 literary bequests to posterity, the term classics made another 
 leap, and is now applied in conjunction with its mediaeval 
 signification to designate the best writers in any of the modern 
 languages. 
 
 As an instance of the disputes to which the transitive 
 application of words occasionally give rise, we may cite the 
 history of the word sacramentum. This word is first met with 
 in the Roman law as signifying a deposit or pledge, which 
 in certain suits defendant and plaintiff were alike obliged to 
 risk upon the condition that the loser of the action should 
 forfeit his, to the nearest temple. Hence the name sacra- 
 mentum or consecrated thing was applied to the property 
 thus offered as a guarantee of sincerity. "We next find the 
 word used in connexion with the military oath by which the 
 soldiers of the Eepublic bound themselves never to desert 
 their standards, or turn their back upon the enemy. From 
 being applied to denote the sacredness which the Kornaiis 
 attached to their military engagements, it soon became 
 synonymous with any oath whatever. 
 
 The early Christian writers in appropriating all the terms 
 of a solemn or sacred character in the heathen vocabulary, 
 and applying them to the nascent theology, were not always 
 careful to avoid a bifold meaning. As something peculiarly 
 sacred was attached by the ancients to the solemnity of an 
 oath, the first Christians applied the word sacrament to 
 designate in particular a class of actions which were also 
 deemed of peculiar sanctity in their system, and in return 
 for which divine grace was communicated to the soul by 
 certain ordained ceremonies ; and solemn engagements were 
 entered into by the recipients to continue true to the fulfil- 
 ment of certain duties. But the early Christian writers also 
 applied the word sacramentum in a loose, secondary, or 
 analogous sense to denote any sacred transaction that had 
 some special solemnity or sanctity attached to it ; as the incar- 
 nation, the lifting up of the brazen serpent, the giving of the 
 manna; which in time led the two senses to become confounded. 
 
 2A
 
 APPENDIX TO BOOK I. 
 
 Hence the controversy has arisen, how many sacraments 
 the early Church acknowledged of divine institution. The 
 Catholic stoutly maintains there are seven, while the Lutheran 
 will only admit two, explaining away the passages cited 
 against him from the early fathers which call matrimony, 
 extreme unction or confirmation sacraments, as so many uses 
 of the word in its second signification 1 . 
 
 CHAPTER IT. 4. 
 Twofold Law of the Transformation of Names. 
 
 A crowd of examples might be produced from French or 
 any similar treatise in illustration of this law ; nor is the ob- 
 servance of the course which words take in obedience to it 
 without historical or even moral significance. Thus, with 
 regard to the specialisation of words of general meanings to 
 denote some peculiar object or function, we could not form 
 a very favourable idea of Roman chastity at the time when 
 Conciliatrix was employed to designate a female pander ; or 
 of French and English manners from the particular application 
 of the word "esteem" in the reigns of Louis XIV. and the 
 second Charles. More favourable instances of specialisation 
 may be noticed in our day in the use of the word " irregular" 
 to characterise a person of profligate manners, or of "the 
 acceptance of a consideration" to signify the receipt of a 
 salary. This tendency to denote things by words which 
 convey the faintest impression of their disagreeable pro- 
 perties is not confined to the refined classes of society, but is 
 occasionally apparent among the commonalty, as in the appli- 
 cation of the word " love-child" to designate illegitimate 
 
 1 Trench defends the latter view on the ground of its adaptation to 
 the old Roman signification. " The remembrance of the use of sacra- 
 ment to signify the plighted troth of the Boman soldier to his imperator, 
 was that I think which specially wrought to the adaptation of the 
 word to baptism ; wherein we also, with a manifest allusion to this 
 oath of theirs, pledge ourselves to fight manfully under Christ's ban- 
 ner, and to continue his faithful soldiers and servants to the end." But 
 Trench forgets that by a similar parity of reasoning confirmation 
 ought to be placed in the same category.
 
 TEANSFOEMATION OF NAMES. 355 
 
 children, or the word " tally" to a female living with a man. 
 out of matrimony 1 . 
 
 Instances of the contrary law of generalisation are still more 
 common. The word bigot (bigote), for example, from being 
 in the Spanish language the name for moustache, which in 
 that country was deemed a mark of resolution and firmness 2 , 
 came to be employed in this country as a by-name for Roman 
 Catholic, and on account of the unhappy notoriety of Spain 
 in religious persecution, the term was afterwards extended 
 indiscriminately to all those who exhibited any symptoms of 
 exclusiveness or of a persecuting spirit in matters of religion. 
 In like manner the term rivals was originally confined to those 
 who dwelt on the opposite banks of the same river, from the 
 disputes which they had at diiferent periods concerning their 
 right to turn off the stream into their own fields, or keep the 
 sluices open as it suited their convenience. Prom this the 
 term was gradually extended to conflicting claimants of every 
 kind, and finally included all persons engaged in unfriendly 
 competition with each other. 
 
 CHAPTEB IV. 
 
 Primary and Secondary Intentions. Analogical use of 
 Terms. 
 
 The first intention of a term is a certain vague and general 
 signification of it in contradistinction to one more precise and 
 limited which it bears in some particular art or science, 
 that is called its second intention. Thus a " line" expresses 
 a certain idea of extension which constitutes its primary sig- 
 nification, and which nearly corresponds with the employment* 
 of the term in mathematics ; while in military art it signifies 
 a certain form of drawing up ships and troops ; in geography 
 a certain division of the earth ; in angling a string to catch 
 fish. These, therefore, constitute its secondary intention, 
 the term in each being employed not in its broad, naked sig- 
 
 1 Extreme instances of the law of specialisation generally go under 
 the name of Euphemism. * Hombre de bigote is the Spanish for a 
 
 man of resolution, and tener bigotei, in the same tongue, means to stand 
 firm. 
 
 2 A2
 
 356 APPENDIX TO BOOK I. 
 
 nification, but expressing something foreign in addition, ac- 
 cording to the purposes for which it is employed. 
 
 Occasionally words are turned from their* primary signifi- 
 cation and used in an analogical sense, as we talk about 
 " weighing reasons," or when we attribute the sense of sweet- 
 ness to sounds ; nor can error arise from this employment of 
 terms so long as we do not take the analogy for more than it 
 is worth, or imagine that things must be similar in themselves 
 because they have similar relations to each other. But this 
 error, as we have seen in the word sacrament, will sometimes 
 happen ; men confounding the primary with the analogical 
 meaning of the term, and deeming the one signification in 
 many cases of no more importance than the other. The same 
 destiny has attended the word servant. Because this word 
 was applied to persons under the Jewish law whose lives and 
 property were completely at the mercy of their masters, some 
 persons in our day seem inclined, from the old word being 
 still in use, to exact the same peremptory service from those 
 Avho serve them, as if the ancient duty of slaves still attached 
 to persons in an analogous position. In a similar manner, 
 because we can hardly speak of the operations of the spirit 
 without employing the terms which are commonly used to 
 express analogous physical action, it has been alleged that 
 no such thing as spiritual substance exists, and that thought 
 must be an attribute of matter ; or, in other words, because 
 mind and body have similarity of relation they must be iden- 
 tical. 
 
 There are two more classes of words which are apt to intro- 
 duce confusion, as far as an accurate rendering of thought is 
 concerned : viz., those which under one name apply to several 
 distinct things ; and others vulgarly called synonymes, which, 
 while differing slightly from each other, are associated with 
 one meaning. As an example of the first kind, we may take 
 the word "stock," which from being anciently the past par- 
 ticiple of " to stick," came to designate everything into which 
 the idea of "fixedness" entered in a definite manner. Thus 
 we have live-" stock," the stock of a gun, stock in trade ; 
 the " stock" -dove, the stock which goes round the neck, the 
 family stock, the village stocks, the stocks in the public 
 funds, the stocks on which ships are built, and an infinity of 
 other stocks of an analogous kind. In like manner we find
 
 ANALOGICAL USE OF TEEMS. 357 
 
 the word "post" from the Latin positus, that which is 
 " placed," applying to a variety of objects into which the idea 
 of that participle enters : as a military station, an office for 
 letters, a piece of timber placed in the ground, and an official 
 position. The same term is also used in a verbal sense, as to 
 "post" a ledger, and also adverbially, as to travel "post," 
 " post" -haste, &c. The same variety of meanings occurs 
 with the word "case," and hundreds of other terms in the 
 English language. 
 
 When the diiference of meaning between the several signi- 
 fications of one word is not clear, great confusion is likely to 
 arise from their use. Thus, when we say the " rose smells 
 sweet," " I smell the rose," the term " smell" refers to two 
 objects widely different. In the first sentence we speak of a 
 quality in the flower ; in the second, of a certain sensation in 
 our minds. On this ambiguity have been founded the striking 
 paradoxes of those who maintain there is 110 heat in fire, and 
 no cold in ice. In the same manner the term "certain," as 
 used with reference to the state of the speaker's mind, as " I 
 am certain of the fact," or to denote the accuracy of any in- 
 telligence, points to two different objects ; and philosophers 
 have not been wanting to avail themselves of such equivoca- 
 tion to deny the existence of certainty altogether. 
 
 In guarding against similar ambiguities of speech, all lan- 
 guages -are not equally fortunate. The Greek and the 
 German are much more philosophically accurate than the 
 Latin ; and the Latin in this respect may be said to surpass 
 the French, Italian, and Spanish, while our own language is 
 behind each of the latter triad in the same quality, however 
 much it may surpass them in strength and copiousness of 
 diction. Thus, the German takes care in using the same 
 word in different senses to make some change in the spelling, 
 or in the gender of the term, or in his mode of forming the 
 plural, that the meaning may be distinguished. In this 
 manner, we find der Band to signify a book, dieBdnde books ; 
 das Band a tie and ribbon, die Bande ties, and die Bander 
 ribbons. In like manner die Worte signify spoken words, 
 and die Wdrter written words ; die Strausen mean ostriches, 
 die Strduse bouquets of flowers. A similar arrangement oc- 
 curs in Italian to distinguish the primary and analogical 
 meaning of words. Thus, lefondamenta means the founda-
 
 358 APPENDIX TO BOOK I. 
 
 tions of a house, or material edifice, but when applied to the 
 first elemeuts of an art or science ifondamenti must be used. 
 In like manner we have le membra to denote the members of 
 the human body, and i membri the members of society, or of 
 any other social corporation. The same distinction may be 
 traced between the words le frutta and ifrutti, le coma and 
 i corni, and many others. The same subtilty of distinction 
 is manifest in the employment of the Spanish and Italian pro- 
 noun, which entirely excludes the possibility of those mis- 
 takes which sometimes occur in the English use of the same 
 article of speech. 
 
 In German and Greek a systematic order of distinction is 
 observed to make words correspond by a little alteration, 
 generally on the final Byllable, with all the shades of difference 
 in which they can present themselves to the subject mind. Ac- 
 cordingly we find a distinction preserved in the two languages 
 between the same term used in the concrete and in the ab- 
 stract, and also between the result of an act and the act itself, 
 so that it would require a person to be in some respects a phi- 
 losopher to understand their simplest conventionalities. Thus 
 we find in the Greek re^vij, the abstract term for art ; but 
 rexvai, the concrete name for the exercise of any particular 
 art ; and in German That, an action or deed ; Thatigkeit, or 
 activeness ; so Kenntschaf't and Kenntniss. In like manner 
 n-pasis, the doing of anything, TrpayfM, the thing done ; so 
 8os and 8a>pov, Xrj-^is and X^/xa, &c. In English, however, 
 there is no similar arrangement, and we are frequently obliged 
 to use the same word in different senses. Thus, " learning" 
 may either mean the act of acquiring knowledge, or know- 
 ledge itself; " shot," the materials of ramming a gun, or the 
 act of firing it, and so with others. 
 
 Confusion is also apt to rise from the opposite practice of 
 using many words to express the same sense, especially when 
 such terms are on the eve of being desynonymised, or when 
 the shade of distinction that begins to obtain among them is 
 far from being universally acknowledged. The English lan- 
 guage is, perhaps, more open to confusion of this kind from 
 the various elements of foreign words which have become 
 amalgamated with it in the course of history, and which 
 have given it many names for the same thing. Thus from 
 Norman Latin and Greek sources, in addition to our native
 
 WOBDS NEASLT SYNONYMOUS. 359 
 
 Saxon, we have shepherd and pastor, feeling and sentiment, 
 handbook and manual, love and charity, freedom and liberty, 
 numeration and arithmetic, supposition, theory, and hypo- 
 thesis, almighty and omnipotent, unreadable and illegible, 
 reason and understanding, fancy and imagination, poetry and 
 poesy, burdensome and onerous, keenness and subtlety ; and 
 so with duplicate verbs : to heal and to cure, to whiten and 
 to blanch, to soften and to mollify, to cloak and to palliate, 
 and many others. Now, notwithstanding each of these 
 duplicates, words were used originally in the same sense, they 
 have now separated from one another, and acquired separate 
 meanings to answer the varieties of fresh thoughts and feel- 
 ings which society acquires in advancing to a high state of 
 civilisation. Hence, as this desynonymising process is con- 
 stantly going on, mistakes are apt to arise from the use of 
 words in a sense exactly equivalent, when a broad distinction 
 is acknowledged between them 1 . 
 
 1 See Coleridge, Biog. Lit. v. i. p. 90, and Lit. Eem. v. i. p. 219, and 
 v. ii. p. 365, and Table-talk, p. 140, and Trench, Study of Words, 
 Lect. v. p. 142, from whom these quotations are taken.
 
 360 APPENDIX TO BOOK IY. 
 
 APPENDIX TO BOOK IV. 
 
 CHAPTEE I. 1. 
 Analysis and Synthesis. 
 
 WHAT we have advanced on analysis and synthesis in the 
 text mainly refers to the applied sciences, where it is usual 
 when the tentative process of analysis is complete, to con- 
 struct the synthesis by way of verification, and also to employ, 
 the latter method of statement in teaching as more scientific 
 and complete. Analysis, however, is not always thus subor- 
 dinate to synthesis, as may be shown by any simple instance 
 from the analytical mathematics. In a common algebraical 
 equation one or more unknown quantities are given, and the 
 consequences are traced backward till those quantities become 
 known. It is not considered necessary to show, by reversing 
 the process, that the results obtained actually fulfil the con- 
 ditions which the unknown quantities were assumed to fulfil 
 in the original formula. 
 
 Another instance in which analysis is perfect without any 
 corresponding synthesis is found in the ordinary process 
 of deliberation, which has sometimes gained, in consequence, 
 the name of practical analysis. Those who deliberately desire 
 any object which they have reason to suppose within their 
 reach, begin by assuming it is attainable by them, and then 
 proceed to consider on what antecedent conditions the attain- 
 ment of the object depends, and to what conditions these in 
 turn are subject. Thus they continue precisely as in mathe- 
 matical analysis, until they arrive at certain elementary con- 
 ditions, which their own consciousness tells them are within 
 their power certain acts of their individual will, and the 
 natural expression of it in word or deed. The analysis is 
 perfect when the agent can clearly perceive that all the actions 
 or means on which the result depends are fully within his 
 power, and when he is conscious of the force of his own will 
 to bear him through them. The analytical process is com- 
 plete in itself, because the subsequent actions which corre- 
 spond to them do not reverse the order of thought, as in cor-
 
 ANALYSIS IN THE AETS. 361 
 
 rect synthesis, although the result of the actions should 
 verify the accuracy of the analyser's speculative inferences. 
 
 It remains to consider in what mode art avails itself of 
 these methods. "With respect to aesthetics, it does not appear 
 they have any but a faint application, on account of their a 
 priori nature, and the consequent reverse method of pro- 
 cedure which obtains in the fine arts in contradistinction to the 
 applied Sciences. It often happens that principles are really 
 involved in the works of an artist which the artist himself has 
 probably never realised except in their abstract form. He 
 exemplifies the laws of science not in consequence of any 
 particular study of them, but in virtue of that taste and keen 
 perception of beauty which imagination continually feeds 
 within him, and which is only casually influenced in the 
 highest genius by exterior observation and the study of the 
 phenomenal world. 
 
 Perhaps in this field the most common use of analysis is in 
 investigating the causes of defects. Something offends ; we 
 know not why. But in the endeavour to refer it back to 
 first principles, we shall discover that some rule has been 
 transgressed, some harmony violated, some canon of incon- 
 sistency broken. Thus very early attempts at art, through 
 the want of consistency, often fail at the first touch of 
 analysis. Notwithstanding the parts may be right in them- 
 selves, on no possible hypothesis could the whole be true. 
 The same reason is fatal to the attempt of a Chinese artist to 
 depict all the six sides of an interior at once ; and to the con- 
 ventional Egyptian representation of a man, in which the 
 head, body, and lower members are depicted in three incom- 
 patible positions ; and to the head of Minerva, on the archaic 
 coins of Athens, in which the full eye, which figures appro- 
 priately in the front face, is transferred without modification 
 to the profile. 
 
 In the earlier stages of the fine arts this seems to be the 
 only use of analysis. In their most flourishing state there is 
 nothing of that doubt and indecision which the analytical 
 process implies. Great works are owing to the magic of 
 genius, and not to any artificial study of particulars or 
 formal process of thought. But when invention waxes cold, 
 and the mind relies less readily on its own resources than 
 the imitations of the past, then analysis steps in. It gives
 
 362 APPENDIX TO BOOK IV. 
 
 rules according to which the highest processes of genius has 
 spontaneously produced certain effects ; and these rules will 
 fall under the leading idea of the art, so far as the nature of 
 the case admits, according to the ordinary methods of science. 
 These remarks are strictly confined to esthetics, including 
 not only music, painting, and poetry, but other works of an 
 analogous kind which appertain to the highest order of 
 genius. The case is different with many mechanical arts, in 
 which an opportunity is afforded for strict consequence in 
 the formation of the rules which can be deduced from certain 
 empirical principles by means of the laws of space and 
 number. Of this nature are many practical exemplifications 
 of the laws of hydraulics, and pneumatics, and projectiles. 
 Here the synthetical arrangement is more than a form, and 
 the method of art, by'coinciding with its type, loses its indi- 
 viduality, and melts into that of applied science 1 . 
 
 CHAPTEE IV. 3. 
 The Senses an ultimate Source of Evidence. 
 
 Notwithstanding spectres and apparitions are generally 
 brought in proof of the reality of sensible impressions, they 
 are sometimes adduced on the contrary side ; so that it is in 
 some measure necessary to consider them here to complete 
 the argument of the text. 
 
 If, as some contend, the senses can convey such delusive 
 impressions as to lead persons who are usually accounted 
 sane, to mistake the figures engendered by their own mind for 
 realities, and converse with them as creatures of flesh and 
 blood, why may not the senses generally be labouring under 
 a similar delusion, and generating around us a world of 
 shadows which have no existence out of the mind ? Of the 
 fact that the senses have thus grossly imposed upon the 
 minds of many there can be no doubt. Eespectable physicians, 
 of whose veracity there can be no suspicion, have stated 
 many striking instances of such deceptions ; and the victims 
 themselves have pined away, and in many cases died, of the 
 
 1 Chretien, Logical Method, p. 205.
 
 CAUSES OF APPABITIONS. 363 
 
 suffering produced by their shadowy tormentors, and the in- 
 ability on their part to get rid of the impression that they 
 were something more than mere shadows. Dr. Gregory tells 
 us of a patient who daily, as the evening clock struck six, en- 
 countered a witch in form, something like those which* are 
 said to have greeted Macbeth on the heath of Pores, and 
 who was so distressed by the grimaces of his weird visitor 
 that he languished and finally died of a broken heart. Thus 
 the Duke of Olivarez, in Le Sage, who was worried to death 
 by the presence of an apparition, which he fancied always 
 pursued him, was no imaginary character. 
 
 "We find another case still more striking, vouched for on 
 the most indisputable authority 1 , in a lawyer who was first 
 haunted by a cat, which subsequently took the shape of a 
 gentleman usher, and appeared with cap, plume, and sword, 
 like the ghost of Beau Nash, and then denuded itself of 
 flesh and clothes altogether, taking the form of a skeleton. 
 The last metamorphosis was fatal to the life of the sufferer. 
 Sir David Brewster also narrates a series of remarkable 
 apparitions to which a lady of his acquaintance was subject, 
 sometimes assuming the garb of deceased friends, occasionally 
 the shape of absent ones, and in every instance comporting 
 themselves as to speech and behaviour like substantial crea- 
 tures. She encountered her husband in the drawing-room, 
 and held some moments' conversation with him at a time 
 when he must have been two hundred miles distant, and she 
 spoke to friends at her toilette who must have been rotting 
 in their shrouds some five years before. 
 
 These apparitions would be certainly marvellous, and might 
 throw grave .doubt upon the testimony of the senses, if they 
 did not admit of lucid explanation. But this, fortunately, is 
 not wanting. We can not only theoretically account for the 
 cause, but point out many instances of the cessation of the 
 apparitions consequent on its removal. Spectral illusions, 
 as Dr. Hibbert has shown, are nothing more than ideas, or 
 the recollected images of the mind, which in certain states 
 of bodily indisposition have been rendered more vivid than 
 actual impressions ; or, to use other words, that the pictures 
 in the mind's are far more vivid than pictures in the body's 
 eye. The mind's eye may be said to be the body's eye, and 
 1 Sir Walter Scott, Letters on Demonology and Witchcraft.
 
 364 APPENDIX TO BOOK IV. 
 
 the retina the common tablet on which both classes of im- 
 pressions are painted, and by means of which they receive 
 their visual existence according to the same optical laws. 
 
 In the healthy state of the mind and the body, these two 
 classes of impressions on the retina are nicely adjusted. The 
 mental pictures are transient and feeble, and in ordinary 
 states never capable of disturbing or effacing the direct 
 images of objects. The two opposite impressions could not 
 co-exist. The same nervous fibre which is carrying from the 
 brain to the retina the figures of the memory, could not at 
 the same moment be carrying back the impressions of exter- 
 nal objects from the retina to the brain. The direction of the 
 mind's attention to one of the two classes of impressions 
 necessarily produces the extinction of the other. Hence, in 
 darkness and solitude, when external objects no longer inter- 
 fere with the pictures of the mind, they become more vivid 
 and distinct, and in the state between waking and sleeping 
 the intensity of the impression approaches to that of visible 
 objects. With studious persons, who are much occupied 
 with the operations of their own minds, the mental pictures 
 are much more distinct than in ordinary persons, and in the 
 midst of abstract thought external objects even cease to make 
 any impression on the retina. A philosopher in his study 
 experiences a temporary deprivation of his senses : noises 
 and objects are conveyed to his eyes and ears, and his nerves 
 actually receive the impressions of light, sound, and touch, 
 but he fails to realise them. Now pictures of the mind and 
 spectral illusions are equally impressions on the retina, only 
 differing in vividness ; and frightful apparitions are nothing 
 more than the results of a disordered imagination acting on 
 some accidental disarrangement of the vital functions. 
 
 The substantial correctness of this reasoning is evident 
 from the state of those persons subject to such hallucina- 
 tions, and the disappearance of the malady as soon as they 
 returned to a healthy condition. Thus, the crowd of persons 
 whom Nicholai 1 imagined he saw constantly moving and 
 acting in his sight, gradually faded away as soon as he sub- 
 jected himself to a course of medical treatment ; and the 
 ugly spectres with which the bright imagination of Tasso 
 
 1 A bookseller of Berlin, who had the courage to lay his case before 
 the philosophical society of that capital.
 
 CAUSES OF APPABITIONS. 365 
 
 peopled his cell, and who sometimes contested with him his 
 daily meal, grew imperceptibly less palpable as he recovered 
 his health, and only annoyed him during inveterate periods 
 of sickness. Again, the lady whose spectres were recounted 
 by Sir David Brewster, convinced herself of their emptiness 
 by standing in the positions and sitting in the same chairs 
 the apparitions occupied, and finding nothing where they 
 appeared to stand or sit but vacuity. All parity is conse- 
 quently destroyed between such impressions and those which 
 follow from the presence of tangible objects in the external 
 world. Like the ordinary illusions of the visual organ, on 
 pressing one eye or straining both, the apparitions are seen 
 doubled ; which of course could not be, had they, like sensible 
 objects, any solid reality. They, therefore, must be classed with 
 shadows ; nor does their relation to that category throw the 
 remotest doubt on the reality of the outward phenomenal 
 world, with which, beyond the mere impression, they have 
 nothing in common 1 . 
 
 1 For a further elucidation of the subject, see Eding. Journ. (new 
 series) No. iv. p. 218 19, No. vi. p. 244, and No. viii. p. 261.
 
 366 APPENDIX TO BOOK V. 
 
 APPEISDIX TO BOOK V. 
 
 < 
 
 CHAPTEB I. 2. 
 Classification and Nomenclature. 
 
 WHEN we attempt to arrange natural objects in groups, 
 according as they possess similar properties, and again to 
 range these groups in regular gradation corresponding to the 
 rank which each holds in the department of nature to which 
 it belongs, the result is a system of classification. Considering 
 the vast number of different objects embraced in each of the 
 tripartite divisions of nature, and the necessity of having the 
 evidence of all brought to bear on scientific inquiry at that 
 stage of the proceeding in which their testimony is likely to be 
 of any value, the importance of such classifications, and the 
 care with which they should be framed, so as to bring not only 
 all the properties of the objects they embrace into notice, but 
 also the causes on which these properties depend, cannot be 
 too much overrated. According, indeed, as these classifications 
 are loosely or accurately framed will the respective sciences to 
 which they correspond lag tardily behind, or exhibit signs of 
 progress. When the facts of a case are lucidly and com- 
 pletely stated, a clever judge is not long in coming to a just 
 decision. When any branch of natural phenomena is ar- 
 ranged in that form which is best calculated to bring out in 
 bold relief all the striking properties it embraces, and the 
 elements upon which those properties mainly depend for 
 their origin and development, a sagacious observer seldom 
 fails to get into the secret recesses of the phenomena and to 
 pounce upon the law. 
 
 Such classifications have failed hitherto principally from 
 their framers selecting arbitrarily some subordinate or non- 
 essential point of agreement as the basis of their system, and 
 thus throwing into the same group objects which in the 
 general aggregate of their properties present no resemblance, 
 and into different and remote groups others which have the 
 closest similarity. Thus, the Linnsean arrangement of plants 
 according to the number of stamens and pistils, or Tourne- 
 fort's system, founded on the shape and the division of the
 
 CLASSIFICATION BY GEOUPS. 867 
 
 corolla, are positively mischievous ; since they direct the 
 attention to those properties in plants which are of the least 
 interest, and thus hinder the mind from regarding them in 
 the groups which have the greatest number of the most 
 striking properties in common. Artificial arrangements of 
 this kind hardly deserve the name of scientific classifications. 
 They are more properly divisions in which the taste of the 
 framer, or the particular end he may have in view, rather than 
 the footprints of nature, serve as the guiding principle of the 
 arrangement. 
 
 the classifications by which science is advanced are widely 
 different from these. Instead of agreeing in nothing but 
 arbitrary heads, from which the most important natural 
 relations are rejected, these relations themselves are sought 
 out and adopted as the basis of the system, and every object 
 ranged in accordance with them, so as to represent the 
 various kinds which exist in nature as much as possible in 
 the precise order in which they occur, and bring into view 
 the most distinctive properties they exhibit. Classifications 
 in natural history, for example, which have any claim to be 
 natural, are founded upon those distinctions of kind winch 
 run throughout nature, and which place impassable limits 
 between the different groups to which they refer ; and not 
 upon any arbitrary choice of the naturalist. These kinds are, 
 of course, determined by the properties which are so funda- 
 mentally distinct as to interpose an insuperable barrier be- 
 tween the classes into which they enter ; and such characters 
 are selected to be a mark or type of the kind which point to 
 the greatest number of subordinate properties in common 
 with each group. Distinctions of kind, however, are not 
 numerous enough to supply the whole basis of a classifica- 
 tion. Very few, for instance, of the genera of plants, or 
 even of the families, can be pronounced with certainty to be 
 kinds. The great distinctions of Vascular and Cellular, 
 Dicotyledonous or Exogenous, and Monocotyledonous or 
 Endogenous, are perhaps differences of kind, since the lines 
 of demarcation which divide these classes seem to go through 
 the whole nature of the plants. But the different species of 
 a genus, or genera of a family, usually have in common only 
 a limited number of characters. A Rosa does not seem to 
 differ from, a Kubus, or the Umbelliferse from the Banun-
 
 368 APPENDIX TO BOOK T. 
 
 culacese, in much else than the characters botanically as- 
 signed to those genera or families. Notwithstanding such 
 distinctions are marked out by properties limited in number, 
 they may be eminently natural, provided those properties 
 are important, and the objects contained in each group 
 resemble each other more than they resemble anything which 
 is excluded from it. But then these lower groups are to be 
 arranged into higher classes and made, when it is possible, to 
 correspond to kinds, the latter serving as a kind of exemplars 
 or types of the subordinate classes which are grouped around 
 them. 
 
 Such arrangements as we have described have reference to 
 distinct compartments of natural history. There are, how- 
 ever, other classifications of a similar tendency which enter 
 into every science, and which are based upon any prominent 
 resemblance or analogy, whether as regard objects or laws. 
 As soon as such point of agreement is perceived between any 
 phenomena, they constitute themselves into a group or class 
 which may become enlarged to any extent by the accession 
 of new phenomena bound together by the same point of 
 resemblance. In this manner the materials of science become 
 grouped in classes, such as chemistry furnishes examples of 
 in its various groups of acids, alkalies, sulphurets, &c., or 
 optics in those classes of phenomena ranged under the heads 
 of periodic colours, double refraction, &c. ; and that re- 
 semblances themselves become traced, which it is the busi- 
 ness of induction to generalise and include in abstract pro- 
 positions. 
 
 The preceding kinds of classification refer not to any 
 specific end, but are simply framed with a view to put the 
 mind in possession of the whole of the properties and rela- 
 tions of objects embracing any wide department of nature ; 
 that when, in the course of its inquiries, any startling facts 
 occur, or any theory is formed, it may bring to the contem- 
 plation of either one or the other all the knowledge which 
 can possibly bear upon the subject. But classification is not 
 confined to this method of arrangement by groups, nor do its 
 advantages flow in any one channel. There is another kind 
 which still bears more directly on the successful issue of 
 scientific inquiry, and that is when we select as the ground- 
 work of the classification some particular phenomenon whose
 
 CLASSIFICATION BY SEEIES. 3G9 
 
 laws are to be investigated, and range all the objects which 
 bear any resemblance to it in regular gradation, according to 
 the degree in which they seem to possess the property the law 
 of which is sought. This has been termed classification by 
 series 1 . Suppose, for example, the law of transparency was the 
 subject of inquiry, the collection of the most striking instances 2 
 of this phenomenon would be the first step in the investiga- 
 tion, as most likely to lead, by the method of concomitant 
 variations, to the discovery of the cause. Hence classifica- 
 tion by series often brings together a number of objects 
 which have nothing in common except the one peculiar pro- 
 perty which is taken as the head of the classification ; as in 
 that of colourless transparency, the list would comprise ob- 
 jects differing most widely in their nature, such as water, air, 
 diamond, spirits of wine, glass, &c. ; while the arrangement 
 by groups, as in the botanical families of Euphorbiaceae, 
 TJmbelliferae, &c., or in the chemical classes of alkalies, 
 metals, &c., bring together those objects which have most 
 properties in common, and appear to possess a natural rela- 
 tion. 
 
 But every class formed on a positive resemblance of cha- 
 racters draws with it the consideration of a negative class, in 
 which the resemblance does not subsist at all, or the contrary 
 takes place. Now it is important, as Herschel observes, to 
 distinguish between cases in which there is a real opposition 
 of quality, or a mere diminution of intensity, in some quality 
 susceptible of degrees, till it becomes imperceptible. For 
 example, between transparency and opacity, there would at 
 first sight appear a direct opposition ; but on nearer con- 
 sideration, when we consider the gradations by which trans- 
 parency diminishes in natural substances, we shall see reason 
 to admit that the latter quality, instead of being the opposite 
 of the former, is only its extreme lowest degree. On the 
 other hand, the opposite electricities ; the north and south 
 magnetic polarities ; the alkaline and acid qualities of che- 
 
 1 Mr. Mill assigns the merit to Comte of being the first to treat 
 systematically this branch of classification (vol. ii. p. 321); but the 
 subject was developed by Hunter in his physiological arrangements 
 long before Comte had published his work. a Enumerated by 
 Bacon in the second book of the Nov. Org. under the head of preroga- 
 tive instances. 
 
 2B
 
 370 APPENDIX TO BOOK V. 
 
 mical agents, and many other cases, exemplify not merely 
 a negation of quality as levity or opacity, but an active oppo- 
 sition. Both these modes of classification were distinguished 
 by Bacon in his positive and negative instances, and have 
 their peculiar importance in the inductive process, by afford- 
 ing an opportunity of tracing a relation between phenomena 
 by way of contrast, and by the observation of a correspond- 
 ence in the scale of intensity 1 . 
 
 With regard to nomenclature, three things are particularly 
 desirable ; first, completeness, or a name for each definite 
 object; secondly, precision, or the necessity of one name 
 applying to that object and to nothing else ; thirdly, expres- 
 siveness, or that the name either denote the peculiar proper- 
 ties of the object or the position which it occupies in the 
 system. Now science possesses two splendid examples of 
 systematic nomenclature which combine these requirements ; 
 that of plants and animals, constructed by Linnasus and his 
 successors, and that of chemistry, which we owe to the illus- 
 trious group of French cliemists who flourished towards the 
 close of the eighteenth century. There is, however, an 
 essential difference between the two systems, which assigns 
 the palm of perfection in this department to the latter. In 
 chemistry the compound substances possess one property 
 (the chemical composition), which is of itself sufficient to dis- 
 tinguish the kind, being a sure mark of all the other pro- 
 perties of the compound. All, therefore, that was required 
 to meet the third condition of a systematic nomenclature was 
 to give a name to every compound expressive of its chemical 
 composition. But in botany and zoology no one property is 
 of such a prominent nature as to allow itself to be taken as 
 indicative of the others ; Linnsous therefore was obliged to 
 
 1 The two modes of classification by groups and series may be com- 
 bined in zoology on the supposition that the investigations concern the 
 laws of animal life, since all the natural groups which zoology em- 
 braces may be arranged in that precise order which is most calculated 
 to reveal the law in question. But in any other compartment such 
 a combination is hopeless. As in botany, for instance, were the phe- 
 nomena of vegetative life to be inquired into, there is no arrangement 
 of the different classes of plants in a serial gradation which could throw 
 the remotest light on the subject, since their leading groups present 
 no cases of variations in the particular point assumed as the basis of 
 investigation.
 
 FOBMAL AKALT3IS IK PHYSICS. 371 
 
 express the nearest natural affinities of the kind, in lieu of 
 its distinctive properties, by incorporating into its name the 
 name of the proximate natural group, of which it is one of 
 the species. Thus the name of every species was made to 
 consist of the name of the genus, or natural group next above 
 it, with a word added to distinguish the peculiar species. On 
 this principle is founded the admirable binary nomenclature 
 of botany and zoology. Linnaeus found about seventeen 
 hundred generic names, with a moderate number of specific 
 names, sufficient to designate with precision the ten thou- 
 sand species of vegetables known in his time ; and, notwith- 
 standing the number of generic names has since greatly in- 
 creased, the augmentation has not kept pace with the multi- 
 plication of known species 1 . 
 
 CHAPTEB I. 3, 4. 
 Formal Analysis in Physics. 
 
 To exemplify the mode by which the inductive inferences 
 may be thrown into a corresponding series of syllogisms, and 
 thus laid open to formal analysis, we subjoin the following 
 example from Mr. Thomson's Outlines of the Laws of 
 Thought : 
 
 " In Sir Humphrey Davy's experiments upon the decompo- 
 sition of water by galvanism, it was found that besides the 
 two components of water, oxygen and hydrogen, an acid and 
 aii alkali were developed at the two opposite poles of the 
 machine. As the theory of the analysis of water did not give 
 reason to expect these products, they were a residual phe- 
 nomenon, the cause of which was still to be found. Some 
 chemists thought that electricity had the power of producing 
 these substances of itself; and if their erroneous conjecture 
 had been adopted, succeeding researches would have gone 
 upon a false scent, considering galvanic electricity as a pro- 
 ducing rather than a decomposing force. The happier insight 
 of Davy conjectured that there might be some hidden cause 
 of this portion of the effect ; the glass vessel containing the 
 water might suffer partial decomposition, or some foreign 
 
 1 WheweU's Hist. Induct. Scien. i. 489, and Mill's System of Logic, 
 ii. p. 316. 
 
 2u2
 
 372 APPENDIX TO BOOK V. 
 
 matter might be mingled with the water, and the acid and 
 alkali be disengaged from it, so that the water would have no 
 share in their production. Assuming this, he proceeded to 
 try whether the total removal of the cause would destroy the 
 effect, or at least the diminution of it cause a corresponding 
 change in the amount of effect produced. By the substitu- 
 tion of gold vessels for the glass without any change in the 
 effect, he at once determined that the glass was not the cause. 
 Employing distilled water, he found a marked diminution of 
 the quantity of acid and alkali evolved ; still there was enough 
 to show that the cause, whatever it was, was still in opera- 
 tion. Impurity of the water then was not the sole, but a con- 
 current cause. He now conceived that the perspiration from 
 the hands, touching the instruments, might affect the case, 
 as it would contain common salt, and an acid and an alkali 
 would result from its decomposition under the agency of 
 electricity. By carefully avoiding such contact, he reduced 
 the quantity of the products still further, until no more than 
 slight traces of them were perceptible. "What remained of the 
 effect might be traceable to impurities of the atmosphere, de- 
 composed by contact with the electrical apparatus. An ex- 
 periment determined this ; the machine was placed under an 
 exhausted receiver, and when thus secured from atmospheric 
 influence, it no longer evolved the acid and the alkali. 
 
 " A formal analysis of these beautiful experiments will illus- 
 trate the method of applying the rules of pure logic in other 
 cases. 
 
 "I. Statement of the case, the residual cause being still undiscovered. 
 ' The decomposition of water by electricity, produces oxygen and 
 hydrogen, with an acid and an alkali.' 
 
 II. Separation of the residual from the principal cause. 
 
 a. ' The decomposition of water produces oxygen and hydrogen.' 
 
 b. ' The production of an acid and alkali in the decomposition of 
 water may be caused by action on the glass vessel containing the 
 water.' (Problematical Judgment A.) 
 
 III. The latter Judgment disproved by a syllogism in Mood E A O, 
 Fig. iii. with a conclusion that contradicts it. 
 
 ' A case in which I employ a vessel of gold cannot involve any 
 
 decomposing action on a glass vessel, 
 ' A case in which I employ a gold vessel still gives the acid and 
 
 the alkali, 
 ' Therefore cases of the production of the acid and alkali are not 
 
 always cases in which glass is decomposed.'
 
 FOBMAL ANALYSIS IN PHYSIOS. 373 
 
 IV. Another attempt to suggest the residual cause. 
 
 ' The acid and alkali are produced by the decomposition and im- 
 purities in the water employed.' 
 Syllogism in A A I, Fig. iii. tending to prove this, 
 ' An experiment with distilled water must admit less impurity, 
 ' An experiment with distilled water gives less acid and alkali, 
 ' Therefore sometimes with less impurity we have less acid and 
 alkali.' 
 
 V. ' The contact of moist hands' may be an additional cause of the 
 
 residual phenomenon. 
 Improved syllogism in A A I, Fig. iii. to include this concurrent 
 
 cause. 
 ' An experiment with distilled water, and apparatus kept from 
 
 contact of hands will admit still less impurity ;' 
 ' An experiment, &c. results in the production of still less acid 
 
 and alkali, 
 ' Therefore sometimes with still less impurity we have still less 
 
 acid and alkali.' 
 VL Amended syllogism. A A A. Fig. iii. 
 
 ' A case where we use these precautions in vacua is a case of no 
 
 impurity,' 
 
 ' A case where we use, &c. in vacua is a case of no acid and alkali, 
 ' Therefore a case of no impurity is a case of no acid and alkali.' 
 VII. Immediate inference from last conclusion. 
 
 ' Cases of no- impurity are cases of non-production of acid and 
 
 alkali,' 
 ' Therefore all cases of production of acid and alkali are cases of 
 
 some impurity;' 
 which was to be proved. 
 
 " An example like this brings into a strong light many of 
 the characteristics of inductive reasoning. Forms usually 
 considered to be deductive are here freely employed. The 
 later steps tend to confirm the earlier, on which, however, 
 they themselves depend ; so that a mutual confirmation is ob- 
 tained from setting them together. When the chemist sub- 
 stituted gold vessels for the glass, and inferred from the con- 
 tinuance of the effect under this change that the glass could 
 have nothing to do with its production, it was formally 
 possible in the then state of knowledge that the glass might 
 be the cause in the one experiment, and the decomposition of 
 the gold in the other. But the later steps, which showed 
 that the effect varied with the variations in a circumstance 
 wholly distinct from the decomposition of glass or gold, re- 
 duced the possibility of maintaining such a view to the very 
 lowest amount. Even the premisses of particular syllogisms
 
 374 APPEKDLX TO BOOK V. 
 
 in the chain are sometimes tested and corrected by the con- 
 clusion, although formally the conclusion should entirely de- 
 pend upon the premisses. The experimenter expected to find 
 that the use of distilled water would exclude all impurity ; 
 and he intended that his premiss should assert as much ; hut 
 when it turned out in the conclusion that the supposed pro- 
 ducts of the impurity were still present, he was reduced to 
 the choice between abandoning that cause and recasting his 
 premiss so as to admit that the cause was still present 
 ' the use of distilled water gives less impurity.' " 
 
 CHAPTEB I. 5. 
 
 Mathematical Reasoning. 
 
 Sir "W. Hamilton has written an essay to disparage mathe- 
 matical reasoning as a mental discipline, and quoted a host 
 of writers who support the same view. His arguments, how- 
 ever, do not seem to us to go farther than to condemn an 
 exclusive devotion to this species of learning as injurious to 
 the mental faculties, and in this view can prove nothing. 
 Excess in every study warps the mind to a degree propor- 
 tionate to the intellectual capability of the learner ; nor do 
 we see anything in the isolated pursuit of mathematics 
 calculated to produce this derangement more conspicuously 
 than an exclusive devotion to classics or to metaphysics, or 
 any other department of learning. For our part, if we are 
 to be bored with learned monoculists, we should prefer the 
 company of D'Alembert to Person, of Lagrange to Dr. 
 Bentley, desirous that the discourse should turn rather on 
 substances than words, on realities than shadows. 
 
 The most that can be said is that the exclusive study of 
 mathematics seems to injure the more common and useful 
 mode of inference viz., that by induction. Mathematical 
 truths being, so to speak, infallible, the moral feelings, if 
 neglected by their study, become less sensitive to the various 
 degrees of certainty attending probable inference. As when 
 one sense is carried to great perfection, the others are 
 usually less acute; so mathematical reasoning seems in 
 some degree to injure the other modes of ratiocination. 
 Thus Napier wrote nonsense on the historical evidence con- 
 nected with revelation, though he invented logarithms;
 
 BACON'S CHAKT OB KNOWLEDGE. 375 
 
 Galileo published a most absurd criticism on the finest 
 modern epic in the same month in which lie expounded the 
 correct laws of motion ; and JXewton played the deuce with 
 chronology and the prophecies of Daniel, while he was un- 
 folding the arcana of the heavens. 
 
 Division of the Sciences. 
 
 Having treated logic as the science of inference, it will 
 not form an inappropriate conclusion to a work of this 
 character, if we direct the reader's attention to the various 
 subjects in which its methods and rules are employed. As 
 in the categories we found several tables differing from each 
 other by the broad lines of demarcation set up by the dif- 
 ferent metaphysical systems on which they were projected, 
 so in the classification of the various departments of human 
 knowledge we meet with a similar diversity of arrangement, 
 with this difference that the ancient attempts have been long 
 ago abandoned as imperfect, owing to the false views which 
 their framers entertained of physical science 1 . 
 
 The modern attempts at a general classification of the 
 sciences may be said to commence with Bacon, whose pro- 
 iection, though surprising for his age, is based on a false 
 principle. Considering all human knowledge as relative, 
 Bacon was led to believe that the sciences would unfold 
 themselves in natural order, if mapped out in relation to the 
 three distinctive powers of the mind, Memory, Imagination, 
 and Reason ; as, however, these faculties are simultaneously 
 engaged in the production of every mental work, the most 
 complete confusion was the result of carrying Bacon's prin- 
 ciple into detail. Formal science was confounded with real, 
 experimental with deductive, relation of law and relations 
 of theory with relations of facts groups of sciences con- 
 nected w4th the closest affinity divorced from each other, 
 and the most heterogeneous subjects forced into the bonds 
 
 1 Mr. Thomson discriminates a table of categories from a division 
 of the sciences, by assigning to the former the function of pointing out 
 the different attributes with which a conception may be clothed, and 
 to the latter that of separating the different districts of knowledge 
 with the leading and subordinate conceptions which belong to them 
 from one another.
 
 376 APPENDIX TO BOOK V. 
 
 of association. The history of minerals, of vegetables, of 
 animals, being confounded in this chart with the history of 
 nations and the history of man, would place the labours of 
 Boswell, in company with the labours of Cuvier and the 
 researches of Hunter, by the side of the researches of Gib- 
 bon. Botany, zoology, and chemistry were separated from 
 their histories and joined to metaphysics. Painting and 
 music were ranked under the head of artes voluptarias with 
 cookery and cosmetics. The anatomy of the human frame 
 was severed from the anatomy of animals, and the doctrine of 
 angels and spirits confounded with natural theology. 
 
 After Bacon, whose chart was adopted by Diderot and 
 D'Alembert as the basis of their celebrated Encyclopaedia, 
 no similar attempt was made until Locke's time, who en- 
 larged the Greek classification, as follows : 
 
 aj sica 
 
 TEconomics. TLogic. 
 
 Practica... < Politics. S^eiam*?) ...... \ Rhetoric. 
 
 |_Ethics. ^Grammar. 
 
 "With the exception of Smith and Turgot, who followed 
 Locke, the subject has not been philosophically considered by 
 any writer of public importance down to very recent times. 
 Dugald Stewart, in reviewing the past efforts to construct a 
 genealogical chart of the sciences, pronounced the labour 
 hopeless, at least in his generation. 
 
 Coleridge, however, imagined he saw in the relations of 
 necessity and the relations of choice a clue to the entire 
 labyrinth of human knowledge in the systematic order in 
 which it is viewed by superior intelligences ; and after a 
 vague and sanguine development of his theory, in a style 
 suited rather to the dim magnificence of poetry than to 
 philosophic disquisition, he surveys the domain of knowledge 
 from 
 T1 , r ("Formal i. e. purely intellectual. 
 
 t +vT Necessary relations { -R , (Moral sciences. 
 point of the ^Real j Mixed ^^ 
 
 intellect, I 
 
 Cause and effect, 
 and thence or 
 
 proceeds to (. Relations of theory
 
 COLEBLDGE'S AND BERTRAM'S DIVISION. 377 
 
 But as this division was far from exhausting the sub- 
 ject, Coleridge found himself obliged to institute a distinct 
 head under "Miscellaneous," to which he consigned one- 
 third of the Encyclopedia Metropolitana, whose ground- 
 work was taken from his plan. To profess, however, to map 
 out all the compartments of knowledge, and annex as a sequel 
 to the chart a voluminous chapter of miscellanea, is precisely 
 the case of Smalgruenius, who wrote a work entitled " De 
 Omnibus Rebus" and afterwards added a supplementary 
 treatise, "De Quibusdam Aliis." 
 
 But the chart is as theoretically wrong as it is prac- 
 tically worthless. Eelations of necessity, and relations of 
 cause and effect, instead of being co-ordinate branches of 
 philosophy, are, considered abstractedly, no less intimately 
 connected, than a general law with one of its particular ex- 
 emplifications. "We cannot, without subverting our mental 
 constitution, consider matter otherwise than as subject to the 
 great law which regulates the procession of phenomena, than 
 we can believe that two and three make six, or that the 
 whole is less than its part. Even in the objective light that 
 Coleridge seems to have regarded the causal relation, far from 
 being confined to any peculiar class of sciences, it runs 
 through them all, and claims a co-extensive dominion with 
 the empirical element itself. Instead, therefore, of being con- 
 centric with the transcendental relation, the laws of cause 
 and effect, as here considered, are as subordinate to it as 
 "Scientia activa," in Bacon's sense, is subordinate to the 
 primary philosophy. Throughout the entire range of the 
 sciences, with the single exceptions of logic and mathematics, 
 necessary and causal relations are more or less interwoven 
 with each other, and to regard them as separate branches 
 leading to distinct groups of science, is to revive in a worse 
 form the error of Bacon, which we have pointed out in the 
 text. 
 
 Bentham in his Chrestomathia, adopting the bifurcate 
 division which Eamus took from the Isagoge of Porphyry, 
 attempted to draw a similar genealogical tree of the sciences, 
 but found the first rough sketch so unpromising that he did 
 not attempt to pursue the subject into detail. He fixed his 
 point of departure, of course, in utility, which he divided into 
 being in general, and what is not being ; the first branch 
 giving rise to metaphysics and the natural sciences, in so far
 
 378 APPENDIX TO BOOK V. 
 
 as they relate to the essences of things ; the latter to the 
 formal sciences, and those which embrace the accidents or 
 changes to which all bodies spiritual or corporal are liable to 
 undergo. It is needless to dwell upon a division which, if 
 practically adopted, would confound all human knowledge, in 
 obliterating the old landmarks which have, since science had 
 a name, served to map out the boundaries of its diversified 
 dominions, and in splitting up each subject heretofore con- 
 sidered unique and inseparable, into elements as various and 
 multiform as the shifting light of opinion may choose to 
 invest them with. 
 
 It was reserved for Ampere to distance all his competitors 
 in constructing a chart of universal knowledge as theore- 
 tically perfect as it is practically useful, by adopting Du- 
 gald Stewart's fundamental division of matter and mind, 
 and classifying everything he considered, in either of the two 
 categories. The questions he asked himself concerning each 
 science were, what subjects did it embrace, and in what 
 point of view was it regarded by others ? The first led him 
 to fix its boundaries, and assign its correlations ; the second 
 to determine its place in the chart, and the groups of sciences 
 by which it should be surrounded. In every other respect 
 the order followed is precisely analogous to that adopted by 
 Linna3us in the classification of the vegetable kingdom. 
 Having divided his field into the two great kingdoms of 
 matter and mind, Ampere groups the sciences whose bounda- 
 ries he had previously laid down, in distinct families or kinds, 
 which he collects into species of a higher order ; and then 
 proceeds to assign the leading branches or genera into which 
 the cognate kingdom is divided, and in which the species of 
 the scientific groups are included. The kingdom and 
 branches with their subordinate orders and distinct families 
 of sciences are connected with each other by a bifurcate divi- 
 sion which separates the experimental sections the pro- 
 dromi, as Bacon calls them from those which refer to the 
 perfect sciences, and thus keeps distinct throughout, the 
 deductive and empirical departments of knowledge. At the 
 head of each rank stands its peculiar and leading idea. The 
 subordinate orders being at once divergent and concentric, 
 branching out into the numerous sciences of which they are 
 composed, as well as guiding to the unique trunk whence
 
 AMPEBE'S TABLES. 379 
 
 they spring. "When we say that no groups of sciences are 
 found together but those which reflect mutual light on each 
 other, and whose proximity is therefore desirable in the 
 study of the same art or profession ; and that the knowledge 
 of no science in the chart presupposes the acquisition of any 
 which have not gone before, we have given the highest testi- 
 mony in favour of its practical utility. We subjoin the 
 tables in extenso, which Ampere spent the best part of his 
 life in constructing. The Latin verses which follow point 
 out the leading conception of each science in the chart, to 
 which they bear literal reference, and enable the classical 
 reader by a slight mnemonic effort to grasp the leading divi- 
 sions of human knowledge in their most minute scientific 
 speciality, and in that order most calculated to favour their 
 study and development.
 
 380 
 
 AMPEEE'S TABLES. 
 
 CLASSIFICATION OP HUMAN KNOWLEDGE; OR, SYNOP- 
 TICAL TABLES OP THE SCIENCES AND ARTS. 
 
 FIRST TABLE. DIVISION OF KNOWLEDGE INTO Two KINGDOMS, 
 AND OF EACH KINGDOM INTO SOB-KINGDOMS AND BRANCHES. 
 
 FIRST KINGDOM. 
 
 Kingdom. 
 
 Sub- Kingdoms. 
 
 Branches. 
 
 Cosmological Sci- 
 ences 
 
 f A. Cosmologies, pro- 
 perly so called... 
 
 ( I. Mathematics. 
 I II. Physics. 
 r III. Natural Sci- 
 
 
 
 N ences. 
 
 
 
 1 IV. Medical Sci- 
 V. ences. 
 
 SECOND KINGDOM. 
 
 Kingdom. 
 
 Sub-Kingdoms. 
 
 Branches. 
 
 
 f~C. Noologics, properly 
 so called 
 
 5 V. Philosophies. 
 | VI. Dialegmatics. 
 
 Noological Sciences 
 
 -1 
 ! D. Social Sciences 
 
 f VII. Ethnological 
 j Sciences. 
 Ivm. Political Sci- 
 
 SECOND TABLE. DIVISION OF EACH BRANCH INTO SUB-BRANCHES 
 AND SCIENCES OF THE FIRST ORDER. 
 
 FIRST KINGDOM. 
 
 
 Branches. 
 
 Sub-Branches. 
 
 Sciences of the First 
 Order. 
 
 A. 
 
 I. Mathema- 
 tical Sci- 
 ences 
 
 II. Physical 
 
 " a. Mathematics, pro- 
 perly, so called 
 5. Physico-mathema- 
 tical Sciences 
 " c. Physics, properly so 
 called 
 
 5 1 . Arithmology. 
 1 2. Geometry. 
 5 3. Mechanics. 
 1 4. Uranology. 
 C 5. General Physics. 
 ( 6. Technology. 
 
 
 Sciences 
 III Natural 
 
 d. Geological Sciences 
 
 " e. Phytological Sci- 
 ences ... 
 
 5 7. Geology. 
 I 8. Oryctotechny. 
 ( 1. Botany. 
 7 2 Agriculture. 
 
 
 Sciences 
 
 /, Zoologies, properly 
 so called 
 
 5 3. Zoology. 
 1 4. Zootechny. 
 
 B.- 
 
 
 " g. Physico-medical 
 {Sciences 
 
 5 5. Medical Physics. 
 ( 6. Hygiene. 
 
 
 IV. Medical 
 
 Sciences 
 
 h. Medical Sciences, 
 properly so called. 
 
 C 7. Nosology. 
 ] 8. Practice of Medi- 
 (. cine.
 
 AMPEBE'S TABLES. 
 
 381 
 
 SECOND TABLE continued. 
 
 SECOND KINGDOM. 
 
 Branches. 
 
 Sub-Branches. 
 
 Sciences of the First 
 Order. 
 
 C V. Philoso- 
 phical 
 Sciences 
 P *t 
 
 f f. Philosophies, pro- 
 \ perly so called ... 
 
 / k. Moral Sciences 
 
 j 1. Psychology. 
 \ 2. Metaphysics. 
 5 3. Ethics. 
 ( 4. Thelesiology. 
 
 i 
 
 VI. Dialegma^ 
 
 tical Sci- 
 L ences.... 
 
 f 1. Dialegmatics, pro- 
 N perly so called ... 
 
 / m. Eleutherotechnics . . 
 
 3 5. Glossology. 
 1 6. Literature, 
 j 7. Technesthetics. 
 i 8. Pedagogy. 
 
 C VII. Ethnologi- 
 
 f n. Ethnologies, pro- 
 \ perly so called ... 
 
 C 1. Ethnology. 
 1 2. Archeology. 
 
 J ences.... 
 
 / o. Historical Sciences. 
 
 ( 3. History. 
 1 4. Hierology. 
 
 j 
 
 C p. Ethnorytics 
 
 ( 5. Nomology. 
 
 VIH. Political 
 
 
 \ 6. Military art. 
 
 v Sciences 
 
 / 5. Ethnegetics 
 
 V 7. Social economy. 
 
 
 
 1 8. Politics. 
 
 THHID TABLE. DIVISION OF EACH SCIENCE OF THE FIRST ORDER 
 INTO SCIENCES OF THE SECOND AND THIRD ORDERS. 
 
 FIRST KINGDOM. 
 
 Sciences of the First 
 Order. 
 
 Sciences of the Second 
 Order. 
 
 Sciences of the Third 
 Order. 
 
 A.J 
 
 / 
 
 1. Arithmology .. 
 
 2. Geometry 
 V 
 
 ' a. Elementary Arith- 
 mology 
 
 "11. Arithmography. 
 12. Mathematical 
 Analysis. 
 "13. Theory of func- 
 tions. 
 14. Theory of proba- 
 bilities. 
 "21. Synthetical Geo- 
 metry. 
 22. Analytical Geo- 
 metry. 
 "23. Theory of lines 
 and surfaces. 
 24. Molecular Geo- 
 metry. 
 (continued) 
 
 6. Megethology 
 
 f c. Elementary Geome- 
 Itry .. 
 
 d. Theory of Forms ...
 
 382 
 
 AMPERE'S TABLES. 
 
 THIRD TABLE continued. 
 
 Sciences of the First 
 Order. 
 
 Sciences of the Second 
 Order. 
 
 Sciences of the Third 
 Order. 
 
 A, 
 B.< 
 
 /3. Mechanics-.... 
 
 4. Uranolpgy 
 
 5. General Phy- 
 sics 
 
 6. Technology ... 
 7. Geology 
 
 ,- e. Elementary Mecha- 
 nics 
 
 (31. Cinematics. 
 \ 32. Statics. 
 f33. Dynamics. 
 I 34. Molecular Me- 
 chanics. 
 (41. Uranography. 
 1 42. Heliostatics. 
 i43. Astronomy. 
 44. Celestial Mecha- 
 nics. 
 51. Experimental 
 Physics. 
 52. Chemistry. 
 ( 53. Stereonomy. 
 t 54. Atomology. 
 ("61. Technography. 
 -| 62. Industrial Cer- 
 doristics. 
 T63. Industrial Eco- 
 nomy. 
 64. Industrial Phy- 
 sics. 
 "71. Physical Geo- 
 graphy. 
 72. Mineralogy. 
 "73. Geonomy. 
 74. Theory of the 
 Earth. 
 f 81. Mining. 
 I 82. Docimacy. 
 C 83. Oryxionomy. 
 ( 84. Mineral Physics. 
 [11. Phytography. 
 i 12. Vegetable Ana- 
 tomy. 
 : 13. Phytonomy. 
 14. Vegetable Phy- 
 siology. 
 : 21. Geoponics. 
 22. Agricultural 
 Cerdoristics. 
 23. Agronomy. 
 24. Agricultural 
 Physiology. 
 (continued) 
 
 ] /. Transcendental Me- 
 chanics 
 
 (g. Elementary Urano- 
 loo'V... 
 
 h. IJranognosy 
 
 C i. Elementary general 
 Physics 
 
 I k. Mathematical Phy- 
 *- sics . 
 
 r I. Elementary Tech- 
 nology ... 
 
 m. Comparative Tech- 
 L nology 
 
 f n. Elementary Geo- 
 
 | o. Comparative Geo- 
 
 lojTV... 
 
 \8. Oryctotechny 
 fl Botany 
 
 (p. Elementary Oryc- 
 totechny 
 
 q. Comparative Oryc- 
 totechny 
 
 {a. Elementary Botany 
 b. Phytognosy 
 
 2. Agriculture ... 
 
 {c. Elementary Agri- 
 
 d. Comparative Agri- 

 
 AMPEBE'S TABLES. 
 
 383 
 
 THIRD TABLE continued. 
 
 Sciences of the First 
 Order. 
 
 Sciences of the Second 
 Order. 
 
 Sciences of the Third 
 Order. 
 
 , 
 
 3. Zoology 
 
 4. Zootechny .... 
 
 5. Medical Phy- 
 sics 
 
 6. Hygiene 
 7. Nosology 
 
 8. Practical Me- 
 \ dicinc 
 
 s e. Elementary Zoo- 
 \ losrv . . . 
 
 (31. Zoography. 
 } 32. Animal Ana- 
 (. tomy. 
 f 33. Zoonomy. 
 3 34. Animal Physio- 
 (. logy. 
 (41. Zoochresy. 
 ( 42. Zooristics. 
 ( 43. CEcionomy. 
 \ 44. Threpsiology. 
 ?51. Pharmaceutics. 
 52. Traumatology. 
 ( 53. Dietetics. 
 \ 54. Phrenygietics. 
 ( 61. Crasiography. 
 \ 62. Crasioristics. 
 ( 63. Hygionomy. 
 { 64. Prophylactics. 
 (71. Nosography. 
 ^ 72. Pathological 
 { Anatomy. 
 r 73. General Thera- 
 \ peutics. 
 1 74. Medical Phy- 
 ( siology. 
 t 81. Semiography. 
 1 82. Diagnostics. 
 C 83. Special Thera- 
 peutics. 
 (.84. Prognosy. 
 
 v./. Zoognosy 
 
 ( g. Elementary Zoo- 
 j techny 
 
 1 h. Comparative Zoo- 
 (_ techny 
 
 f i. Medical Physics, 
 \ properly so called 
 
 / k. Biotology 
 
 C I. Crasiology 
 
 j m. Hygiene, properly 
 (, BO called 
 
 {n. Nosology, properly 
 so called , 
 
 
 f p. Semiology 
 
 1 q. Medical Practice, 
 (. properly so called 
 
 
 
 SECOND KINGDOM. 
 
 Sciences of the First 
 Order. 
 
 Sciences of the Second 
 Order. 
 
 Sciences of the Third 
 Order. 
 
 C 
 
 fa. Elementary Psycho- 
 
 JlOfiTV... 
 
 (11. Psychography. 
 (12. Logic. 
 
 G.ll. Psychology ... 
 
 1 b. Psychognosy 
 
 (13. Methodology. 
 {14. Ideogeny. 
 (continued)
 
 384 
 
 AMPERE'S TABLES. 
 
 THIED TABLE continued. 
 
 Sciences of the First 
 Order. 
 
 Sciences of the Second 
 Order. 
 
 Sciences of the Third 
 Order. 
 
 H 
 
 D. 
 
 2. Metaphysics... 
 3. Ethics 
 
 C c. Ontothetics 
 
 (21. Elementary Ont- 
 ) ology. 
 1 22. Natural Theo- 
 C logy. 
 (23. Comparative 
 Theology. 
 ( 24. Theodicy. 
 (31. Ethography. 
 1 32. Physiognomy. 
 ( 33. Practical Morals. 
 1 34. Ethogeny. 
 (41. Thelesiography. 
 1 42. Diceology. 
 r43. Apodictical 
 Morals. 
 (. 44. Anthropotelics. 
 (51. Lexiography. 
 1 52. Lexiognosy. 
 (53. Glossonomy. 
 ^ 54. Philosophy of 
 { Languages. 
 (61. Bibliography. 
 1 62. Bibliognosy. 
 ^63. Literary Criti- 
 ^ cism. 
 ~) 64. Philosophy of 
 (_ Literature. 
 (71. Terpnography. 
 1 72, Terpnognosy. 
 ( 73. Technesthetical 
 j Criticism. 
 j 74. Philosophy of the 
 f Fine Arts. 
 (81. Pediography. 
 \ 82. Idioristics. 
 ( 83. Mathesiology. 
 ^ 84. Theory of Edu- 
 l cation. 
 (11. Ethnography. 
 12. Toporistics. 
 (13. Comparative 
 Geography. 
 14. Ethnogeny. 
 (continued) 
 
 [_d. Ontognosy 
 
 e. Elementary Ethics 
 f Ethognosy 
 
 4. Thelesiology... 
 5. Glossology .... 
 
 6. Literature 
 
 7. Technesthetics 
 8. Pedagogics ... 
 j 1. Ethnology .... 
 
 " g. Elementary Thele- 
 sioraphy 
 
 _ h. Thelesiognosy 
 z'. Lexiology 
 
 \^k. Glossognosy 
 
 1. Bibliology 
 
 m. Comparative Lite- 
 
 1 n Terpnology 
 
 1 o. Comparative Tech- 
 ^ nesthetics 
 
 C p. Pedagogics, pro- 
 perly so called .... 
 
 [_ q. Pediognosy 
 
 f a. Elementary Ethno- 
 \ logy... 
 
 1 b. Comparative Eth- 
 (. nology
 
 AMPERE'S TABLES. 
 
 385 
 
 THIRD TABLE continued. 
 
 Sciences of the First 
 Order. 
 
 Sciences of the Second 
 Order. 
 
 Sciences of the Third 
 Order. 
 
 D. 
 
 /2. Archeology ... 
 3. History 
 
 -/* c. Mnemiology 
 
 (21. Mnemiography. 
 1 22. Mnemiognosy. 
 f 23. Archeological 
 Criticism. 
 C24. Archeogeny. 
 t31. Diegematics. 
 \ 32. Chronology. 
 f 33. Historical Criti- 
 \ cism. 
 "j 34. Philosophy of 
 (_ History, 
 j 41. Hierography. 
 ( 42. Symbolics. 
 C 43. Controversy. 
 ^44. Hierogeny. 
 f51. Nomography. 
 \ 52. Jurisprudence. 
 {53. Comparative Le- 
 gislation. 
 54. Theory of Law. 
 f 61. Hoplograpby. 
 1 62. Tactics. 
 ( 63. Strategy. 
 1 64. Nicology. 
 (71. Statistics. 
 1 72. Chrematogeny. 
 C 73. Dianemetics. 
 1 74. Coeuolbology. 
 (81. Ethnodicy. 
 \ 82. Diplomacy. 
 ( 83. Cybernetics. 
 1 84. Theory of Power. 
 
 1 d. Comparative Ar- 
 (. cheology 
 
 f e. Elementary History 
 
 1 f. Comparative His- 
 f torv... 
 
 4. Hierology 
 5. Nomology 
 
 6. Military Art... 
 
 7. Social Eco- 
 nomy 
 
 \ g. Sebasmatics 
 
 1 h. Comparative Hiero- 
 logy 
 
 f i. Nomology, properly 
 \ so called 
 
 (. k. Legislation 
 
 C /. Hoplismatics 
 
 j m. Military Art, pro- 
 (. perly so called .... 
 
 V n. Chrematology 
 
 1 o. Social Economy, 
 (. properly so called 
 
 ( p. Syncimenics 
 
 If. Politics 
 
 j g. Politics, properly so 
 (. called 
 
 
 2c
 
 TERSE S 
 
 BENEVOLO LECTOEI. 
 CARMEN MNEMONICUM. 
 
 PRO(EMITJM. 
 
 Ut Mundum* noscas, moles A et 
 vita B notandas : 
 
 A. Mensura et motus primunii, 
 
 mox corpora 11 et omne, 
 
 B. Viventum genus 1 " ct vitam quse 
 
 cura tuetur iv . 
 
 Ad Mentera** referas qua; 
 menti c aut gentibus D insunt : 
 
 C. Nunc animum T , nunc signa 
 
 animi prodentia sensus-n, 
 
 D. Nunc populos disces et qua 
 
 ratione regendi'. 
 
 PROLEGOMENA. 
 
 A. 
 
 I. HJEC ubi cuncta animo rap- 
 
 tim peragrare libebit, 
 Jam numeros 1 , spatium 2 . 
 vires 3 et sidera 4 noris ; 
 II. Corpora 5 , fabrorumque 
 
 artes 6 tractabis, et orbem 7 
 Lustrabis ; latebras penitus 
 rimabere terrre 8 . 
 
 B. 
 
 III. Herbarum inquires genus 1 , 
 
 agricolaeque labores 2 ; 
 Jam quae sint 3 , jam quos 
 hominum fingantur in 
 usus 4 , 
 
 IV. Et quibus aegrescant rige- 
 
 antve 5 animalia disces ; 
 Nunc firmanda salus 6 , nunc 
 
 tempus noscere morbos 7 , 
 Nunc segrislethum durosque 
 
 arcere dolores 8 . 
 
 V. Turn mentem 1 , res atquc 
 
 Deum 2 medi tabere et inter 
 Affectus hominum 3 virtus 
 
 ut libera regnet 4 ; 
 VI. Turn voces 5 et scripta 6 simul, 
 
 turn noveris artes 
 Ingenuas 7 , et qua? pueri sit 
 cura magistro 8 . 
 
 D. 
 
 VII. Mox populos 1 , monurnenta 2 
 
 et facta 3 notabis ; 
 Quos gentes servent ritus, 
 
 quod numen adorent 4 ; 
 VIII. Jura fori, leges populorunv 
 
 et rnunia disce 
 Bellantum 6 , mox gentium 
 
 opes 7 scrutare, ducesque 
 Ut paci valeant et bello im- 
 
 ponere morem 6 .
 
 AND MNEMONIC. 
 
 387 
 
 SYNOPSIS. 
 
 A. 
 
 1 . Si scrutari aveas quidquid cog- 
 
 noscere fas est, 
 Compones prim urn numeros 11 , 
 
 igiiota requires 12 ; 
 Nunc incrementa 13 et casus 14 , 
 
 nunc discere formas 
 
 2. Est opus 21 , et formis numero- 
 
 rum imponere signa 22 ; 
 
 Noscere quae gradiens generet 
 curvamina punctum 23 ; 
 
 Primave concrescant queis re- 
 rum elementa figuris 24 ; 
 .'5. Et motus 31 , et cum pulsum in 
 contraria vires 
 
 Corpus agunt,ubi stare queat 32 , 
 quorsumve moveri 33 ; 
 
 Quo pacto haerescant, trepident 
 quo corpora prima 34 ; 
 
 4. Sidereasque vices 41 , tellus quos 
 
 erret in orbes 42 ; 
 Quasque regant vastos leges per 
 
 inania motus 43 ; 
 Impulsus quae causa latens, 
 
 atque insita rerum 
 Seminibus quo; vis undo astra 
 
 per astheris alti 
 Volvuntur spatia et cursus in- 
 
 flectere discunt 41 . 
 
 5. Prceterea scire in terris ut 
 
 cuncta genantur, 
 Ut moveant sensum, formas 
 
 vertantur in omnes 51 ; 
 Queis nexis inter se elementis 
 
 corpora constent 52 ; 
 Necuon materiae leges 53 vires- 
 
 que atomorum 54 
 
 6. Noscendaj, et variae quas usus 
 
 protulit artes 61 . 
 Turn quaestus 62 operumque 
 
 mod os conferre memento, 
 Ut potiora legas 63 causasque 
 
 evolvere tentes 04 . 
 
 7. Tumjuga, turn campos disces 
 
 et flumina 71 , tellus 
 Corporibus 72 stratisque 73 quibus 
 
 conficta sit intus; 
 Hacc ut longa dies imis forma- 
 
 verit undis, 
 
 Utque eSerbueriut olim igui- 
 
 vomi undique montes 74 ; 
 8. Eruat ut caecis occlusa metalla 
 latebris 
 
 Fossor, et ardenti tractet mol- 
 lita vapore 81 ; 
 
 Nee dubias telluris opes rimare 
 priusquam 
 
 Impensas, lucrum 62 , leges 83 , 
 causasque laborum 
 
 Et terraj ut subeas tutus pene- 
 tralia noris 84 . 
 
 B. 
 
 1. Jam quae plantarum species 
 
 ubicumque vigescant 
 Scire juvat 11 ; jam quas celent 
 
 sub tegmine partes 12 ; 
 Utque pares paribus recte 
 
 sociehtur 13 , ut arbor 
 Herbaque nascantur, crescant 
 
 et semina fundat 14 ; 
 
 2. Agricola ut laetas fruges ferre 
 
 imperet arvis 21 , 
 Qua sint cuique solo foenus 22 
 
 culturaque 23 , et unde 
 Langueat ilia seges, gravidis 
 
 haec nutet aristis 24 ; 
 
 3. Quas soboli tradant generatim 
 
 auimalia formas 31 , 
 Corporis et qua3 sit compages 
 
 intima 32 , vito3 
 Qua? leges 33 , gliscatque artus ut 
 
 vita per omnes 31 . 
 
 4. Nee tibi turpe puta, jucunda 
 
 per otia ruris, 
 Bombyces nutrire, et oves 
 
 vitulosque tueri ; 
 Turn captare feras, turn lino 
 
 fallere pisces 41 ; 
 Noscere quis pecudum sump- 
 
 tus 42 , qua; cura bubulco 4 *; 
 Cur uunc utilius viridantia 
 
 gramina carpant, 
 Nunc pecora in stabulis melius 
 
 saturentur opimis 41 . 
 
 5. Vitam multa juvant animan- 
 
 turn, multaque lacdunt;
 
 388 
 
 YERSES EXPLANATORY 
 
 Saepe graves possunt expellcre 
 
 toxica morbos 51 ; 
 Nostraque nunc laedit, nunc 
 
 sanat corpora ferrum 52 ; 
 Ilia nocent alimenta, haec 
 
 prudens sumere malis 53 , 
 Sedulus insanos animi com- 
 
 ponere motus 54 . 
 0. Non tamen ars medica est ulli 
 
 tentanda priusquam 
 Noscat ut infundant nobis 
 
 natura genusque 
 Jam varies habitus 61 , quorum 
 
 scrutabere signa 61 ; 
 Ut quod cuique nocens, quod 
 
 cuique sit utile noris 83 ; 
 Tune morbo disces venienti oc- 
 
 currere 64 , et omnis 
 
 7. Naturam 71 sedemque 72 mali, 
 
 medicamina 73 , causas 74 , 
 
 8. Queisque notis detur morbos 
 
 dignoscere 81 , et segri 
 Scire quis 82 et qua sit languor 
 
 sanabilis arte 83 , 
 Quis metus immineat, qua; spes 
 
 sit mixta timori 84 , 
 
 C. 
 ;. Mentem nosse velis" : utpossit 
 
 cernere verum 12 ; 
 Utque nova inveniat, vel ponat 
 
 in ordine nota 13 
 Qusaras, et quo pacto ab origine 
 
 cogitet 14 ac se 
 '2. Noscere non tantum valeat, 
 
 sed resque 21 Deumque 22 . 
 Turn subeunt scrutanda tibi 
 
 commenta sophorum 23 ; 
 Humana ratione Deo qua3 
 dantur inesse 24 ; 
 
 3. Affectus hominum, studia, ob- 
 
 lectamina, curae 31 ; 
 Quae tibi corda notae, quse 
 
 morum arcana recludunt 32 ; 
 Quod decet et quae sunt me- 
 
 tuenda optandaque 33 , etunde 
 Indolis omne genus 34 ; quaa 
 
 mentibus insita nostris 
 
 4. Libera vis animi 41 , justo se- 
 
 cernit iniquum 42 ; 
 
 Qua: recti ffiternae leges 43 ; qua.- 
 
 prasmia sontes 
 Insontesque manent 44 : stimulos 
 
 haec mentibus addunt 
 Ut nova discendi semper rapia- 
 
 mur amore. 
 
 5. Jam verborum usus 51 , et verbis 
 
 quae sit origo 52 ; 
 Diversos ut apud populos 
 
 mutentur 53 , et undo 
 Concessa humani generi tarn 
 
 mira facultas 
 Quidquid inest animo ut voces 
 
 expromere possint 54 , 
 
 6. Assidua evolves cura. Kunc 
 
 alma poesis, 
 Nee minus arridens interdum 
 
 sermo pedestris, 
 Pectora mulcebunt 61 , scripta 
 
 explorare libebit 62 ; 
 Et quae digna legi indignis 
 
 secernere 63 , et arte 
 Noscere qua sacrum nomen 
 
 mereare poetae 64 ; 
 
 7. ^des, suave melos, picturac et 
 
 daedala signa 71 ; 
 Necnon unde placent 72 , artis 
 
 pracepta modusque 73 , 
 Principium et ratio 74 pergunt 
 
 dulcedine mentem 
 Pellicere ad studium longosque 
 
 levare labores, 
 
 8. Nunc puerum edoceat sapientis 
 
 cura magistri 81 , 
 Discipuli ingeuium tentet 82 , 
 
 fingatque vicissim 
 Ad studium veri 8 * prasscripta- 
 
 que muuia vitae 84 . 
 
 D. 
 
 1. Inde loca' 1 , inde situs datur 
 
 explorare locorum 12 , 
 Prisca licet conferre novis 13 , et 
 
 verba habitusque 
 Corporis, ut valeas populorum 
 
 exordia nosse 14 . 
 
 2. Jam veterum monimenta 
 
 virum 51 , jam scire memento
 
 AND MNEMONIC. 
 
 389 
 
 Qua retegant 2 *; ut vera queas 
 
 dignoscere fictis' 3 , 
 Qua, fuerint exstructa manu, 
 
 qua condita causa 24 . 
 
 3. Factaque perquires 31 , factorum 
 
 tempora 32 , veris 
 Unde fides 33 , quae causa olim 
 
 concusserit orbem, 
 Cum tot bella forent, tot regna 
 
 eversa jacerent, 
 Ambirentque novae return fas- 
 
 tigia gentes 14 . 
 
 4. Jam nosces ritus et dogmata 
 
 relligionum 41 , 
 Symbola quas celant mysteria 
 
 sacra profanos 41 , 
 Et quo sit cultu . veneranda 
 
 aeterna potestas 43 , 
 Quoque modo oblitos aevi prae- 
 
 cepta prioris 
 Diffusus late populos invaserit 
 
 error 44 . 
 .3. Quae sint, quae fuerint leges et 
 
 publica jura 51 , 
 Quae solerti egeant praesertim 
 
 interprete noris 52 ; 
 
 Quaeque nova instituenda, sevo 
 cum prisca fatiscunt, 
 
 Nunc exempla decent 53 , et nunc 
 enitere recti 
 
 Legibus aaternis humanas pro- 
 mere leges 54 . 
 
 6. Disce et queis armis arcendi 
 
 finibus hostes 61 ; 
 Quo pacto instaurandae acies* 4 , 
 
 quo bella gerenda 63 , 
 Fregerit et virtus ingentes 
 
 saepe catervas 64 . 
 
 7. Mox et opes 71 , mox unde 
 
 fluant 72 , populisque parentur 
 Nunc facilis victus 73 , nunc 
 
 laetae munera vitae, 
 Et sortem ut mutare queat 
 
 gens inscia rerum, 
 Cum segnes torpent mentes 
 
 meliora perosse 74 . 
 
 8. Foedera quid jubeant 81 , qua 
 
 sint servanda sagaci 
 Arte 82 , et secura cives ut pace 
 
 fruantur 83 ; 
 Quae fluxa et quae sit mansura 
 
 potentia regum 84 .

 
 INDEX 
 
 A. 
 
 ABELARD adopts the conceptualist 
 theory, 342, 345 
 
 Absolute terms, 35 
 
 Abstract and concrete terms, 34 
 
 Abstract deductive method, its ap- 
 plicability to the moral sciences, 
 268 
 
 Abstraction, the principal act by 
 which the mind arrives at con- 
 ceptions, 37 
 
 Abstraction and generalisation, 37 
 
 Abuse of general terms, disputes 
 arising from, 351 
 
 Academies, the various, their doc- 
 trines, 178 
 
 Accident, 39; how distinguished 
 from property, 41 
 
 Adrian IV., Pope, his use of the 
 word beneficium, 351 
 
 Agreement, method of, 217 
 
 Airy and Whewell, their observa- 
 tions on the pendulum, 225 
 
 Ambiguous middle, fallacy of, 307 
 
 Ampere, his chart of universal 
 knowledge, 378 
 
 Analogical evidence, its value, 259 
 
 Analogical use of terms, confusion 
 occasioned by the, 356 
 
 Analogy, various meanings of the 
 term, 300; an ultimate source of 
 evidence, 185; Hume's objec- 
 tion, 187 
 
 Analogy, logic of, 21 ; argument of, 
 301; its high conclusive force, 
 301 
 
 Analysis, methods of, 2 ; analysis 
 and synthesis, 143, 360 
 
 Analysis, formal, in physics, 371 
 
 Analytic, the New, 28, 92; con- 
 sidered with reference to mood 
 and figure, 115 
 
 Antisthenes, dilemma of, 137 
 
 2 
 
 Apparitions, explanation of, 362 
 
 Argument of example, 299; of 
 analogy, 301 
 
 Aristotle, logical doctrines of, 4; 
 glaring error in, 7 ; ascribes the 
 discovery of induction to So- 
 crates, 151 ; his fallacies, 315; 
 opponents of his system, 10 
 
 Association of ideas, law of, 277 
 
 Assumptions, groundless, fallacy 
 of, 313 
 
 Attributes, essential and contin- 
 gent, 33 
 
 Authority an ultimate source of 
 evidence, 189 . 
 
 Avicenna, the theory of concep- 
 tualism attributed to, 342 
 
 B. 
 
 Bacon, Lord, not so opposed to the 
 views of Aristotle as commonly 
 reputed, 13; his error, 45; mis- 
 took the formal laws of induc- 
 tion, 151; his devotion to ob- 
 servation and experiment, 212; 
 his aphorisms on the progress of 
 society, 293 ; his Chart of Know- 
 ledge, 375 
 
 Bacon, Roger, the inductive me- 
 thod recommended by, 14 
 
 Barbara, syllogism in, 152 
 
 Baynes, Spencer, his proposed al- 
 terations in logic, 28 
 
 Begging the qyestion, fallacy of, 
 326, 329 ; instance of, from the 
 phrenologists, 327; from Gibbon, 
 329 
 
 Belsham, an indifferent writer on 
 logic, 25 
 
 Beneflcium, employment of the 
 word, 351 
 
 Bentham on evidence, 296; his 
 classification of the sciences, 377
 
 392 
 
 INDEX. 
 
 Berkeley, Bishop, on analogy, 300 
 Bias, his argument in defence of 
 
 the bachelorate, 137 
 Bigot, history of the word, 355 
 Brighton, of the time of Elizabeth, 
 
 submerged by the sea, 259 
 Brown, condemnation of logic by, 
 
 25 
 
 Butler, Bishop, his famous argu- 
 ment in favour of the divine 
 origin of Christianity, 301 
 
 C. 
 
 Calculation of probabilities, 295 
 Canning, detection of fallacies by, 
 
 336 
 
 Casual agents, elimination of, 255 
 Categorical propositions, 80; re- 
 duction of other propositions to 
 the categorical form, 83 
 Categories, or Predicaments, Aris- 
 totle's enumeration of, 47, 347; 
 ludicrous illustration of, 48 ; 
 Kant's new division of catego- 
 ries, 347 
 
 Causal agency, universality of, 205 ; 
 final causes inadmissible, 207; 
 plural causes, 239 
 Causal method, its author, 10 
 Causes, plurality of, 203, 239 ; two- 
 fold composition of, 241 ; final 
 causes inadmissible, 207 ; Male- 
 branche's theory of occasional 
 causes, 317 
 
 Causes and laws in physical sci- 
 ence, 197 
 
 Certainty, various grades of, 165 
 Chain syllogism or sorites, 138 
 Charles II., his fallacious question 
 
 to the Koyal Society, 313 
 Christianity, argument of Butler 
 in favour of, 301 ; of Paley, 273; 
 of Gibbon against, 329. See 
 Miracles 
 
 Classics, history of the word, 352 
 Classification by groups, 367 ; by 
 series, 369; of the sciences, 375 
 Classification and nomenclature, 
 
 366 
 
 Combinatorial art of Raymond 
 Lully, foundation of the, 22 
 
 Complex terms, 51; illustration, 
 from iron, 52 
 
 Composition, fallacies of, 311 
 
 Compound expressed propositions. 
 80 
 
 Comte, M., value of his division of 
 sociology into statics and dyna- 
 mics, 290; his empirical axioms 
 on the progressive tendencies of 
 society, 293 
 
 Conception, conditions of, 33 ; di- 
 visible into the qualities which 
 distinguish co-ordinate species. 
 43 
 
 Conceptions, formation of distinct. 
 49 ; distinct and confused, 53; 
 double mode of resolving, 54; 
 observation and experiment 
 tests of accurate conception, 58 ; 
 double capacity of, 60; in rela- 
 tion to signs, 60 
 
 Conceptualism, definition of, 345: 
 ascribed to Avicenna, 342 
 
 Conceptualist school of logicians. 
 337 
 
 Concio, an opponent of the Aris- 
 totelian system, 10 
 
 Conclusion, irrelevant, fallacy of. 
 331 
 
 Concomitant variations, methods 
 of, 225 
 
 Concrete deductive method, direct 
 and inverse, 285 
 
 Condillac, an opponent of the 
 Aristotelian system, 10 ; de- 
 velopes the views of Locke, 19 
 
 Conditional propositions, 83; re- 
 duction of, to categorical, S3 
 
 Connotative and non-connotative 
 terms, 34 
 
 Contingent, different senses in 
 Avhich used, 88 
 
 Contingent or probable truth, what 
 comprised under, 166; how dis- 
 tinguishable from necessary 
 truth, 161 
 
 Contradiction, principles of, 189 
 
 Conversion of propositions, 97 
 
 Copulative propositions, 81 
 
 Crackenthorpe, a writer on logic. 
 26 
 
 Credibility, various phases of, 167
 
 IKDEX. 
 
 393 
 
 Criteria of evidence, 169 
 
 Cross - examining elenches, func- 
 tions of the, 271 
 
 Crousaz, on probability and cau- 
 sality, 21 
 
 D. 
 
 Deduction, 148; confounded with 
 syllogism, 150 
 
 Deduction, scientific, nature of, 
 243; not necessarily opposed to 
 induction, 245 
 
 Deductive reasoning, analysis of, 
 275 
 
 Definition, logical, its end, 67; 
 how far real, 68; nominal, 71; 
 scientific, 7 1 ; other classes, 74 
 
 De Morgan inclines to the views of 
 Sir William Hamilton, 28 
 
 Descartes, general principle of his 
 system, 14 ; his rules for the 
 direction of the mind, 15; his 
 error, 16 
 
 Dew, principles of physical inquiry 
 applied to the investigation of 
 the phenomena of, 234 * 2^ 
 
 Difference, method of, 219 ; in- 
 direct method of, 221 
 
 Differentia, 39 
 
 Dilemma, the, 135; principles, 137 
 
 Disjunctive propositions, 82; re- 
 duction of, to categorical, 83 
 
 Division, fallacies of, 311 
 
 Dreams, examination of, 183 
 
 E 
 
 Eldon, Lord, syllogism by, 138,141 
 
 Elements, primitive, of knowledge, 
 171 ; their relation to each other, 
 172 
 
 Elenches, cross-examining, func- 
 tions of the, 271 
 
 Empirical generalisations, impor- 
 tant conclusions arrived at from, 
 253 
 
 Enthymerae, or imperfect syllo- 
 gism, 140 
 
 Enumeration, incomplete, fallacy of, 
 320 
 
 Equivocal and paronymous words, 
 fallacy of, 309 
 
 Essences, real and nominal, 68 
 
 Ethics, principles of, 269 
 
 Ethics, how connected with theo- 
 logy, 272 
 
 Ethology, the science of, 279 ; cause 
 of the backwardness of, 279; 
 where inductive, 281; how 
 treated by Mill, 283 
 
 Euclid, the author of many falla- 
 cies attributed to the Stoical 
 school, 3 
 
 Eudemus, an early writer on logic, 7 
 
 Euler, logical notation of, 23; his 
 notation of the syllogism, 120 
 
 Evidence, different degrees of, 165; 
 criteria of, 169; foundations of, 
 171; memory, 173; external 
 sense, 177, 362; analogy, 185; 
 reason, 188; authority, 189 
 
 Experience, general truths inde- 
 pendent of, 1 59 
 
 Experiment in physical science, 
 use of, 214 
 
 Experiment and observation the 
 first steps in physical science, 
 209 
 
 Experimental inquiry, methods of, 
 216 
 
 Extension of inductions, 228 
 
 Extension and intension, 42 
 
 External sense an ultimate source 
 of evidence, 177,362; objections 
 of Sextus Empiricus, 177 
 
 F. 
 
 Fallacies, classes of, 303; formal. 
 
 305; verbal, 307; material, 313 
 False analogies, fallacy of, 322; 
 
 political, 323; philosophical, 325 
 Faraday on the magnetism of the 
 
 earth, 229 
 Final causes inadmissible, 207 
 
 G. 
 
 alen, his treatise on logic, 8 
 alluppi, logical treatise of, its 
 high character, 24, 25 
 General terms, abuse of, 351 
 reneral truths independent of ex- 
 perience, 195 
 
 Generalisation and abstraction, 37 
 generalisations, empirical, impor- 
 tant practical conclusion drawn 
 from, 253
 
 394 
 
 INDEX. 
 
 Genovesi, logical treatise of, its 
 character, 24, 25 
 
 Genus and species, 38 
 
 German school of logic, 20, 24 
 
 Gibbon, unsoundness of his argu- 
 ment against Christianity, 329 
 
 Graham on the law of the diffusion 
 of gases, 229 
 
 Greek philosophers, fallacies of 
 the, 315 
 
 H. 
 
 Hamilton's (Sir William) logical 
 notation, 23; his proposed al- 
 terations in logic, 28; his nota- 
 tion of the syllogism, 124; con- 
 demns mathematical reasoning, 
 374 
 
 Hegel, his development of Kant's 
 principles, 24 
 
 Hippocrates, the basis of phreno- 
 logy a favourite theory of, 328 
 
 Hispanus, Peter, his verses on 
 logic, 115 
 
 Hobbes, instance of unsound rea- 
 soning from, 329 
 
 Human nature, science of, 277 
 
 Human responsibility, the Owenite 
 fallacy regarding, exposed, 311 
 
 Hume's objection to analogy, 187; 
 to miracles, 190 
 
 Hypotheses, legitimate uses of, 
 247; where inapplicable, 251; 
 functions of, 249; empirical 
 generalisations, 252 
 
 Hypotheticals, fallacies of, 307 
 
 I. 
 
 Idea, different definitions of, by 
 Aristotle, Descartes, and Locke, 
 72 
 
 Implied, or tacit compound pro- 
 positions, 85 
 
 Ignoratio elenchi, fallacy of, 331 
 
 Illicit process and undistributed 
 middle, fallacy of, 305 
 
 Incomplete enumeration, fallacy of, 
 320 
 
 " Inconceivable," false sense of, 317 
 
 Induction, different kinds of, 150; 
 twofold nature of, 201 ; summary 
 of, 237 ; its formal laws mistaken 
 by Bacon and his followers, 151 ; 
 
 not necessarily opposed to de-' 
 duction, 245 
 
 Induction and deduction, 148; in 
 what respects independent, 15& 
 
 Inductions, extension of, 229; veri- 
 fication of, 233 
 
 Inductive method, general outline 
 of the, 237 
 
 Inductive science, problem of, 199 
 
 Inference, two kinds of, 101 ; uni- 
 versal canon of, 102; general 
 principles of, 141 ; universal 
 method of, 143, 148; analysis 
 and synthesis, 143; induction 
 and deduction, 148 
 
 Inference confounded with per- 
 ception, 319 
 
 Inquiry, experimental, methods of, 
 216; scientific, 191 
 
 Intension, definition of, 42 
 
 Interference of plural causes, 239 
 
 Iron, illustration of a complex term 
 from, 52 
 
 Irrelevant conclusion, fallacy of, 
 331 ; various forms of, 333 
 
 Isomorphism, law of, 228 
 
 J. 
 Judgment, ultimate sources of, 171 
 
 K. 
 
 Kant separates pure and applied 
 
 logic, 24; his new division of 
 
 categories, 347 
 Kepler's laws of planetary motion, 
 
 233 
 Kirwan, an indifferent writer on 
 
 logic, 25 
 Kirwan, the doctrine of probability 
 
 illustrated from the case of, 257 
 Knowledge, primitive elements of. 
 
 171 ; their relation, 172 
 
 L. 
 
 Lambert on logical notation, 22; 
 his notation of the syllogism, 
 123 
 
 Language, use of, in logic, 60, 349 ; 
 confusion arising from the tran- 
 sitive application of words, 63, 
 353; greater or less distinctness 
 of various languages, 357
 
 395 
 
 Laws in physical science, 197; 
 twofold division of, 197 
 
 Leibnitz, his logical labours, 20 
 
 Linnaean nomenclature, the, 370; 
 why inferior to the French che- 
 mical nomenclature, 370 
 
 Locke, an opponent of the Aristo- 
 telian system, 18; his views de- 
 veloped by Condillac, 19; his 
 definition of real essence, 68; 
 his classification of the sciences, 
 376 
 
 Logic, foundation of, laid by So- 
 crates, 2; Plato's method, 3; 
 Aristotle's Organon, 4 ; his incon- 
 sistencies, 5; early commenta- 
 tors on Aristotle, 8 ; the Scholas- 
 tics, 8, 345 ; attacks on Aristotle, 
 9; Bacon, 12; Descartes, 15; 
 Mariotte and the Port Royalists, 
 17; Locke and Condillac, 18; 
 Leibnitz, Wolf, and the German 
 school, 20; introduction of logi- 
 cal notation, 22; Italian and 
 English logicians, 25; the New 
 Analytic, 28 ; Terms, their ma- 
 terial relation, 33; formal rela- 
 tion, 37 ; with regard to things, 
 49; in relation to signs, 60; 
 Propositions, 74; division of, 77; 
 with regard to matter, 78; to 
 form, 87; Syllogisms, 100; pro- 
 perties, 102; the New Analytic 
 tested, 117; notation, various 
 methods of, 120; kinds of syllo- 
 gisms, 127; Inference, general 
 principles of, 141 ; universal me- 
 thods, 143; different degrees of 
 evidence, 165; foundations of 
 evidence, 171; miracles, 191; 
 Methods of Scientific Proof and 
 Investigation, 191; in physical 
 science, 195; in moral science, 
 261; Fallacies, 303 ; formal, 305; 
 verbal, 307; material, 313; spec- 
 tral illusions, 362 
 Logic, modern schools of, 337 ; no 
 real opposition of doctrine, ex- 
 cept with extreme partisans, 
 341 
 
 Logical division, nature and rules 
 of, 43 
 
 Logical notation, various schemes 
 
 of, 22 
 Logicians, conceptualist school of, 
 
 337; sensational, 337; verbal, 
 
 337 
 Lully, Raymond, foundation of his 
 
 combinatorial art, 22 
 
 M. 
 
 Malebranche's theory of occasional 
 causes, 317 
 
 Mariotte and the Port Royalists, 
 endeavour of, to reconcile the 
 Aristotelian and Cartesian me- 
 thods, 17 
 
 Material fallacies, various classes 
 of, 313 
 
 Memory an ultimate source of 
 knowledge, 173 
 
 Methods of proof, in the moral 
 and physical sciences, 193 
 
 Middle, ambiguous, fallacy of, 307 ; 
 undistributed, 305 
 
 Mill, John Stuart, places logic on 
 its legitimate foundation, 28; 
 on propositions, 76; on syllo- 
 gisms, 158; on ethology, 283; 
 gives undue preponderance to 
 external phenomena, 340; his 
 objections to Aristotle's predica- 
 ments, 348 
 
 Mind, laws which regulate succes- 
 sive states of, 277 
 
 Miracles, Hume's objection to, 19^ / fo 
 
 Mitscherlich's discovery of the law 
 of isomorphism, 228 
 
 Modality, twofold doctrine of, 167 
 
 Mode and substance, distinction 
 between, 34 
 
 Moon, question as to its having 
 inhabitants, 260 
 
 Moral sciences, methods of the, 
 193, 261 ; their nature, 261 ; how 
 their methods differ from those 
 of the physical, 262; connexion 
 of the moral sciences, 263; diffi- 
 culties of the subject, 267 ; the 
 sciences amenable to the ab- 
 stract deductive method, 268; 
 the sociological sciences, 277; 
 probabilities, 295 ; example and 
 analogy, 299, 301
 
 396 
 
 INDEX. 
 
 Moral truth falls short of demon- 
 strative certainty, 166 
 
 N. 
 
 Names, twofold law of the trans- 
 formation of, 64; examples of, 
 354 
 
 Necessary and contingent truth, 
 161 
 
 Negative process, its functions in 
 the elucidation of the moral 
 sciences, 271 
 
 Newton, his examination of the 
 laws cf the tides, 225 
 
 Nizolius, an opponent of the Aris- 
 totelian system, 9 
 
 Nominal definition, 71; neglect of, 
 occasions interminable disputes, 
 73 ; confounded by Aristotle and 
 the Scholastics with the defi- 
 nition of things, 73 
 
 Nominal essences, definition of, 68 
 
 Nominalism and realism, 342 
 
 Notation, logical, introduction of, 
 22; of the syllogism, various 
 methods, 120 
 
 O. 
 
 Observation in physical science, 
 
 209 ; its importance, 211; canons, 
 
 213 
 Observation and experiment the 
 
 first steps in physical science, 
 
 209 
 Occasional causes, Malebranche's 
 
 theory of, 317 
 Occham adopts the conceptualist 
 
 theory, 342, 345 
 CEuesidemus teaches the principle 
 
 of contradiction, 189 
 Omens, belief in, a material fallacy, 
 
 318 
 Opposition of propositions, 94 ; 
 
 scheme of, 97 
 Owen, his fallacy regarding human 
 
 responsibility, 311 
 
 P. 
 
 Paley, examination of an argu- 
 ment by, 273 
 
 Paronymous words, fallacy of, 309 
 Particular propositions, how dis- 
 tinguished from universal, 87 
 
 Pascal, his verification of the hypo- 
 thesis of the gravity of air, 224 
 
 Patrizzi, an opponent of the Aris- 
 totelian system, 10 
 
 Peel, Sir Robert, his gradual altera- 
 tions in the British tariff justi- 
 fied, 285 
 
 Perception, theories of, 111 
 
 Perception, inference confounded 
 with, 319 
 
 Personal identity, 175 
 
 Peter Hispanus, his verses on logic. 
 115 
 
 Petitio principii, fallacy of, 326 
 
 Phenomenal or sensational school 
 of logicians, 337 
 
 Phrenology, fallacies of, 327; its 
 basis sound, but as old as Hippo- 
 crates, 328 
 
 Physical investigation, nature, 
 grounds and limits of, 195 
 
 Physical sciences, methods of 
 proof in the, 192; nature, grounds 
 and limits of investigation, 195; 
 observation and experiment, 
 209; methods of experimental 
 inquiry, 216; general cautions. 
 227 
 
 Physics, formal analysis in, 371 
 
 Planets, question as to their being 
 inhabited, 260, 261 
 
 Plato, his conceptions of analysis 
 and synthesis, 3 
 
 Ploucquet on logical notation, 22 ; 
 his notation of the syllogism. 
 123 
 
 Plural causes, interference of, 239 
 
 Porphyry gives rise to the disputes 
 on nominalism and realism, 342 
 
 Positive and negative terms, 35 
 
 Praxis, scientific, examples of, 275 
 
 Predicables, the five, 41, 48 
 
 Predicaments, Aristotle's enume- 
 ration of, 47, 347 ; ludicrous il- 
 lustration of, 48 
 
 Predication, modes of, 93 
 
 Prejudice, operation of, in the 
 moral sciences, 267 
 
 Probabilities, calculation of, 295; 
 limitation of, 297 
 
 Probability, theory of, 252 
 
 Proof, scientific, methods of, 191
 
 IKDEX. 
 
 397 
 
 Property, 39; distinguished from 
 accident, 41 
 
 Propositions, their constituents. 
 74; division of, 77; considered 
 with regard to matter, 78; sim- 
 ple, 79 ; compound, 80; reduction 
 of, 83 ; with regard to form, 87 ; 
 quantity, 87; quality, 89; dis- 
 tribution of terms, 90 ; opposition 
 of, 94; conversion of, 97; quan- 
 tification of the predicate pro- 
 posed instead of conversion, 98; 
 shown to be useless, 99 
 
 Q. 
 
 Quantification of the predicate, or 
 New Analytic, 92 ; considered 
 with reference to mood and 
 figure, 115 
 
 Quantity and quality of propo- 
 sitions, 87, 89 
 
 Question, begging the, 326, 329; 
 instances, 327, 329 
 
 Quiditas, or essential nature, 66 
 
 R. 
 
 Ramus, an opponent of the Aris- 
 totelian system, 10 ; mode of 
 logical division ascribed to him, 
 really employed by Aristotle 
 and the Scholastics, 44 
 
 Real and nominal essences, GS 
 
 Realism and nominalism, 342 
 
 Reason an ultimate source of evi- 
 dence, 188 
 
 Reasoning, on what founded, 32; 
 theories of, 153; Nominalist the- 
 ories, 155; objections, 157 
 
 Reasoning, mathematical, injurious 
 to other modes of ratiocination, 
 374 
 
 Regnault, his attempt to popu- 
 larise logic, 22 
 
 Relative and absolute terms, 35 
 
 Residues, method of, 223 
 
 Royal Society, Charles IL's ques- 
 tion to the, 313 
 
 Rudiger, introducer of the logic of 
 analogy, 21 
 
 o. 
 
 Sacramentum, history of the word, 
 353 
 
 Saunderson, a writer on logic, 26 
 
 Scepticism reduced to a science by 
 Sextus Empiricus, 177 
 
 Sceptics, their objections to the 
 evidence of the senses, answered, 
 179, 183 
 
 Scholastics, the, their merits and 
 defects, 8, 345 
 
 Sciences, division of the, 375; Ba- 
 con's Chart of Knowledge, 375 ; 
 Locke's classification, 376; Cole- 
 ridge's, 376; Bentham's, 377; 
 Ampere's tables, 378; explana- 
 tory and mnemonic verses, 386 
 
 Scientific definition, often pro- 
 visional, 71 
 
 Scientific praxis, examples of, 275 
 
 Scientific proof and investigation, 
 methods of, 191 
 
 Sensational or phenomenal school 
 of logicians, 337 
 
 Senses, evidence of the external, 
 177; sometimes deceptive, 362 
 
 Sextua Empiricus, impugns the 
 authority of the external senses, 
 177 
 
 Simmias of Thebes, an early wri- 
 ter on logic, 3 
 
 Simon of Athens, an early writer 
 on logic, 3 
 
 Simple complex propositions, ex- 
 ample of, 79 
 
 Singular propositions, when ranked 
 with universal, 87; when rec- 
 koned particular, 87 
 
 Social statics and dynamics, what, 
 289 ; practical value of this di- 
 vision of sociology, 290 ; object 
 of social dynamics, 291 
 
 Society, progressive tendencies of, 
 293; Bacon's aphorism, 293; 
 Cornte's generalisations, 293; 
 such generalisations premature, 
 294 
 
 Sociological sciences, the, 277; em- 
 piricism in, 283; where deduc- 
 tive, 285; verifications of, 287; 
 divisions of M. Comte, their 
 practical value, 290; generalisa- 
 tions, 293 
 
 Socrates employs the interrogatory 
 mode of disputation, 1 ; lays the
 
 398 
 
 INDEX. 
 
 foundation of logic proper, 2; 
 his pupils, 3; discovery of in- 
 duction ascribed to him, 151 
 
 Sorites, or chain syllogism, 138 
 
 Species, definition of, 38 
 
 Spectral illusions, explanation of, 
 362 
 
 Stewart, Dugald, condemnation of 
 logic by, 25 ; the syllogism dis- 
 carded by him, 159 
 
 Subaltern genera and species, defi- 
 nition of, 39 
 
 Subalternans, what kind of propo- 
 sitions so called, 95 
 
 Subcontraries, qualities of, 95 
 
 Substance and attribute, distinc- 
 tion of, 33 
 
 Syllogisms, 100; properties of, 102; 
 figures, 108; moods, 113; nota- 
 tion, 120; kinds, 127; complex, 
 127; conditional, 132; disjunc- 
 tive, 134; copulative, 135; the 
 dilemma, 135; chain syllogism, 
 or sorites, 138; enthymeme, or 
 imperfect syllogism, 140; de- 
 duction confounded with syllo- 
 gism, 150 
 
 Svnthesis, 143; its subject-matter, 
 147 
 
 T. 
 
 Tacit, or implied compound propo- 
 sitions, 85 
 
 Terms, definition of, 32; material 
 relation of, to each other, 33 ; 
 formal relation, 37; terms with 
 regard to things, 49 
 
 Test, universal, of syllogisms, 131 
 
 Theophrastus, an early writer on 
 logic, 7 
 
 Theories, formation and verifica- 
 tion of, 243 
 
 Thomson attempts to popularise 
 the New Analytic, 29; formal 
 analysis in physics, explanation 
 of, by, 371 
 
 Transformation of names, twofold 
 law of the, 64 
 
 Transitive application of words, 
 confusion arising from the, 63, 
 352 
 
 Trench, his idea of the reality of 
 words, 350 ; his censure of 
 Hobbes, 350 
 
 Truths, three classes of, 163; ge- 
 neral, independentof experience, 
 159; necessary and contingent. 
 161; logical, 170 
 
 U. 
 
 Undistributed middle, fallacy of, 
 305 
 
 Union of induction and deduction, 
 245 
 
 Universal canon of inference, 102; 
 test of syllogisms, 131 
 
 Universal propositions, how dis- 
 tinguished from particular, 87 
 
 V. 
 
 Verbal fallacies, 307 ; enumeration, 
 
 307312 
 
 Verbal school of logicians, 337 
 Vico, unphilosophical views of, 294 
 
 \V. 
 
 Wallis, a writer on logic, 26 
 
 Watts's Logic, indifferent cha- 
 racter of, 46 
 
 Wells's theory of dew, 235 
 
 Whately, Archbishop, his views of 
 the office of logic, 26; his defini- 
 tion of logical division ques- 
 tioned, 43; his exposition of the 
 Aristotelian logic, 339 
 
 Whewell and Airy, their observa- 
 tions on the pendulum, 225 
 
 Wolf, an eclectic, his attempt to 
 reconcile the old and new me- 
 thods in science, 20; his suc- 
 cessors in Germany, 21 
 
 Words, confusion arising from the 
 transitive application of, 63, 352 
 
 Z. 
 
 Zeno the Eleatic, the earliest known 
 logician, 1 
 
 THE END. 
 
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