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EASY LESSONS 
 
 REASONING. 
 
 RICHARD WHATELY, D.D., 
 
 ARCHBISHOP OF DUBLIN. 
 
 THIRD AaiERICAN 
 
 FROM 
 
 FIFTH LOIVDON EDITION. 
 
 BOSTON AND CAMBRIDGE: 
 • JAMES ]\I U N R O K AND C O INI P A N Y . 
 1857. 
 

 Entered according to Act of Congress, in the year 1845, 
 
 Br JA]VIES MUNROE AND COMPANY, 
 
 In the Clerk's Office of the District Court of the District of Jtlassachusetts. 
 
 STEREOTTrED BY 
 
 S. N. DICKINSON & CO. 
 No. 52 VVashington Street, 
 
 BOSTON. 
 
PREFACE 
 
 The subject treated of in the following pages is one wMcli has 
 not usually been introduced into the course of elementary studies 
 for young persons of all classes. 
 
 It is supposed by some that the difference between a better and 
 a worse reasoner depends either wholly on natural ahllity^ or on 
 that combined with practice^ or on each man*s greater or less pro- 
 ficiency in the subjects he is treating of. 
 
 And others again consider a systematic study of the principles 
 of Reasoning as suitable only to a few persons, of rare endowments, 
 and of a peculiar turn of mind ; and to those, only in an advanced 
 stage of their education. 
 
 That this branch of study is requisite for all, and is attainable 
 by all, and presents not, necessarily, any greater difficulties than 
 the rudimente of Arithmetic, Geometry, and Grammar, — all this 
 cannot be so well e^dnced in any other way as by experiment. If 
 the perusal of these Lessons, or of the half of them, fail to satisfy 
 on this point any tolerably attentive reader, it is not likely he 
 would be convinced by any distinct argument to the same effect 
 that could be offered. 
 
 The work has ver}' little claim to novelty, except as to the 
 simplicity and familiarity of its form. But without making any 
 discovery^ strictly so called, of any thing previously altogether un- 
 known, it is possible — since ' discovery ' is a relative word — to be, 
 practically a discoverer, by bringing within the reach of thousands 
 some important branch of knowledge of which they would otherwise 
 have remained destitute all tlieir lives. 
 
 And in regard to the present subject, a fiimlliar introduction to 
 the study is precisely what has hitherto been wanting. The exist- 
 ing treatises upon it may be compared to ships, well freighted, but 
 which can only unlade at a few wharves, carefully constructed, in 
 
4 PREFACE. 
 
 advantageous situations. The want is, of small boats drawing very 
 little water, which can carry ashore small parcels of the cargo on 
 every part of the coast, and run up into every little creek. 
 
 Should the attempt to supply this deficiency prove as successful 
 as there is reason, from the trial that has been ali'eady made in the 
 (^Saturday Magazine,) to hope, an addition by no means unimpor- 
 tant will have been made to the ordinary course of elementary 
 education. 
 
 To frame, indeed, a system of rules that should equalize persons 
 of all varieties of capacity, would be a project no less chimerical 
 in this than in any other department of learning. But it would 
 certainly be a great point gained, if all persons were taught to ex- 
 ercise the reasoning faculty as well as the natural capacity of each 
 would permit; for there is good reason to suspect that, in this 
 point, men fail quite as often from want of attention, and of sys- 
 tematic cultivation of their powers, as from natural deficiency. 
 And it is at least worth trying the experiment whether all may 
 not be, in some degree, trained in the right exercise of a faculty 
 which all, in some degree, possess, and which all must, more or 
 less, exercise, whether they exercise it well or ill. 
 
 It was at one time contemplated to subjoin an Index of the 
 technical terms, with brief definitions of them, and references to 
 the Lessons and Sections. But, on second thoughts, it has been 
 judged best to omit this, and to recommend each student to draw 
 up such an index for himself. It is for students, strictly so called, 
 — that is, persons employed in acquiring an elementary knowledge 
 of the subject — that the work is chiefly designed : and for these, 
 no exercise could be devised more calculated to facilitate their 
 study than that of carefully compiling an Index, and also expand- 
 ing the Table of Contents, so as to give a brief summary of the 
 matter of each Lesson. And this being the case, it would not be 
 any real saving of labor to the learner to place before him such an 
 Index and Table of Contents already drawn up. 
 
 It may be worth while to suggest to the Teacher to put before 
 his pupils, previously to their reading each Lesson, some questions 
 pertaining to the matter of it ; requiring of them answers, oral or 
 written, the best they can think of without consulting the book 
 Next, let them read the Lesson, having other questions, such as 
 
PREFACE. 5 
 
 may lead to any needful explanations, put before tliem as they 
 proceed. And afterwards let them be examined, (introducing 
 numerous examples framed by themselves, and by the teacher,) as 
 to the portion they have learned, in order to judge how far they 
 remember it. 
 
 Of these three kinds of questions, — which may be called, L 
 Preliminary questions; ii. questions of instruction; and iii. ques- 
 tions o^ examination^ — the last alone are, by a considerable portion 
 of Instructors, commonly employed. And the elementary books 
 commonly known as * catechisms,* or ' books in question and 
 answer,* consist in reality of questions of this description. 
 
 But the second kind, — what is properly to be called instructive 
 questioning, — is employed by all who deserve to be reckoned 
 good teachers. 
 
 The third kind, — the preliminary questioning — is employed, 
 (systematically and constantly) but by few. And at first sight it 
 might be supposed by those who have not had experience of it, 
 that it would be likely to increase the learner's difficulties. But if 
 any well-qualified Instructor will but carefully and judiciously try 
 the experiment, (in teaching any kind of science,) he will be sur- 
 prised to find to how great a degree this exercise of the student's 
 mind on the subject will contribute to his advancement. He will 
 find that what has been taught in the mode above suggested will 
 have been learnt in a shorter time, will have been far the more 
 thoroughly understood, and will be fixed incomparably the better 
 in the memory. 
 
 1* 
 
INTRODUCTION 
 
 TO THE AMERICAN EDITION. 
 
 The author of this little work has not, so far as we know, 
 avowed himself. From internal evidence, one would infer very 
 decidedly that the work was prepared by Dr. Whately. It is 
 marked on every page by that same strong good sense and solid 
 learning which have rendered his works on Logic and Rhetoric so 
 eminently valuable as text-books for students. 
 
 Many persons of high reputation for their attainments in those 
 branches of learning to which they may have been devoted, have 
 failed disgracefully, in the attempt to furnish a suitable text-book 
 for the young student. Hence it is, that, although most depart- 
 ments of science and literature have been cultivated with con- 
 stantly increasing success, still the number of really good text-books 
 is exceedingly small. 
 
 The vanity of authorship has contributed much to this result. 
 The writers of text-books for colleges and schools, have been too 
 often tormented with the sorry ambition of saying something ori- 
 ginal, or something fine. They have been prone to forget that 
 originality, as such, is not to be sought for in a work for learners. 
 They have b*een impatient of the careful thought, and literary 
 self-denial, requisite to enable a man to say just what is necessary, 
 and no more. Often, too, mistaking prolixity for clearness, they 
 have burdened and perplexed the minds of the unlearned, with a 
 multitude of vague terms, suggesting many ideas partially, but 
 without giving distinct and sharply-defined views of any. 
 
 The highest merits of a text-book are brevity, strict method in 
 the arrangement, clearness and pertinency in the statement and 
 illustration of what are the admitted principles of the subject 
 treated upon. It is bare justice to say, that the elementary trea- 
 tises of Dr. Whately are free from most of the defects, and comprise 
 
INTRODUCTION. 7 
 
 most of tlie excellences above named. Whether he Is the author 
 of this work or not, it shows all the peculiar skill in arrangement, 
 power of definite statement, and graphic illustration, which so 
 strongly characterize his avowed works. To say the least, the 
 freest use has been made of Whately's thoughts and language. 
 
 The work contains the main principles of the Logic of Whately, 
 somewhat divested of their technical form, but not of their scien- 
 tific accuracy. There are also a few pages showing the application 
 of Logic to the purpose of conviction, which would more strictly 
 come under the head of Rhetoric. Although the author evidently 
 intended the vv^ork for the younger classes of learners, it contains 
 the distinct outlines of a system of Logic, and whoever thoroughly 
 masters this little work, and becomes able to apply its principles 
 to the analysis of arguments, will be no contemptible logician. 
 It is thought that this book will be admirably adapted to the 
 wants of the advanced classes in our High Schools and Academies, 
 as well as to the wants of those who wish for some acquaintance 
 with the theory of reasoning, and have not the time or the resolu- 
 tion to go through any larger treatise on the subject. As a text- 
 book for students in college, it is, doubtless, a more thorough work 
 than that of Hedge, which holds its place in the list of text-books 
 in some of our colleges. 
 
 However w^ell adapted this work may be to the young and 
 uninstructed, as a digest of the science and art of reasoning, 
 it may become still more valuable to them, as a discipline for 
 the mind. It cannot have escaped the notice of attentive ob- 
 servers, that the vast number of * simplified' books, which have 
 been prepared for the young, proposing to conduct them to learning 
 by a royal road, have had an injurious influence. The practice of 
 imparting knowledge in infinitesimal doses, diluted by leading 
 questions and useless explanations, till it becomes tasteless, is very 
 well, if the only object desired is to relieve the student from the 
 labor of thinking. Though this object be attained, the process 
 will have the effect to weaken the power of attention, to destroy 
 the robustness and vigor of the mind, and to pall that eager curi- 
 osity which nature intended to sustain us under the protracted 
 effort necessary to accomplish a difficult task. It cannot but have 
 a salutary influence upon a young or undisciplined mind, to be 
 
8 INTRODUCTION. 
 
 brought in contact with the clear and vigorous thinking of such a 
 man as the author of this little work. The comparative abstruseness 
 of the subject of the book, thus becomes one of its best recommenda- 
 tions. Strong studies only can make strong men. Besides, the really 
 efficient teacher will always find that the more difficult the subject, 
 (provided it be fairly within the grasp of the pupil,) the greater will 
 be the interest manifested. There is a pleasure in the act itself of 
 overcoming difficulty, which excites the generous mind, and throws 
 a lively interest around the investigation of the abstrusest subject. 
 
 There may be those who object to Logic as entirely barren and 
 useless. To such we would recommend a careful perusal of the 
 larger work of Whately. The conmaon objections to Logic, which 
 have been echoed by hosts of writers, from Locke and the Scotch 
 Metaphysicians, and have been rendered respectable by the au- 
 thority of those great names, have been disposed of by Whately in 
 such a way, that no scholar will again attempt to revive them. In 
 the minds of those, however, who readily admit the value of 
 Logic as a part of a course of college study, objections may 
 arise to its introduction as a constituent element of popular 
 education. 
 
 Still it is believed that the objections that may be urged against 
 the use of such a work as this, in schools and academies, will lie 
 with equal propriety against almost all the scientific instruction 
 ordinarily given in such institutions. The elements of Mathemat- 
 ics, of Natural Philosophy, of Chemistry, and Natural History, 
 have by general consent taken their place among the branches 
 taught in schools, and for good reason. These sciences relate to 
 the subjects with which, and upon which, we are constantly en- 
 gaged in the active duties of life. Aside from prudential consider- 
 ations, it is a gratification of the highest kind to the practical man, 
 to be able, in a partial manner even, to refer the phenomena of 
 nature around him to the general laws by which they are governed. 
 Although the knowledge of such men must, of necessity, be super- 
 ficial, compared with that of the man of science, still, it is gratify- 
 ing to reflect that from this slight acquaintance with natural laws, 
 the noblest practical inventions have often sprung. Not to limit 
 that much abused term practical^ to a narrow sense — how expansive 
 and elevating are such truths to the mind of the learner, however 
 
INTRODUCTION. 9 
 
 imperfectly conceived ! No teacher can have failed to perceive the 
 effect often produced by the first introduction into the mind of the 
 great principles of the laws of physics. The theory of reasoning 
 has, however, a more extended bearing upon man, — his enjoy- 
 ments and his capabilities, — than either, or all of these. If the 
 science and art of reasoning be applicable at all, it is applicable to 
 every thing. If it is of practical value to any, it is to all, and it 
 has the most important and intimate connection with every art 
 and science, and with the conduct of affairs in every possible situa- 
 tion in life. The process of reasoning, as such, being the same in 
 all cases. Logic has to do with every possible exercise of the rea- 
 soning faculty. The more accurate the definitions, and the more 
 obvious the data, of any science, the more easily can its deductions 
 be subjected to Logical Analysis. Consequently, Mathematical 
 reasonings, depending as they do upon postulates and definitions, 
 (which, referring to quantity and space, are capable of distinct and 
 unambiguous statement,) fall with the utmost readiness into logical 
 formulas. The constant business, then, of a reasonable being, is to 
 draw conclusions from things admitted. On the soundness of ar- 
 guments, as well as upon the truth of facts, we are constantly ac- 
 customed to stake the most vitally important interests. Not only 
 do our most valued interests constantly depend on the soundness 
 of our own conclusions, but often on the reasonings of others. We 
 are, under God, dependent for our national existence and national 
 blessings, on the soundness of the conclusions which are arrived at 
 by the millions of voters In our land. No attempt, however inad- 
 equate and feeble it may be, to infuse intellectual health into this 
 great mass of reasoning power, can be unworthy of our regard. 
 Is it a small matter that the rank and file of our voters should be 
 able to analyze and determine the soundness or unsoundness of 
 those arguments on Politics, or Public Economy, by which they 
 are urged to support, or destroy, systems of public policy ? IIow 
 often, -vvithln a few months, when listening to political haranguers, — 
 discoursing with a logic worthy of the grave-diggers in Hamlet, — 
 have we wished to be able to put into the possession of the lis- 
 tening throng around, a power of analysis, which, like the spear of 
 Ithuriel, might show In Its genuine form the grossness of the impo- 
 eition practised upon them. 
 
10 INTRODUCTION. 
 
 It may be said that Logic will not remedy the evil, for it 
 will not teach the ignorant political economy or history. True ; 
 but it will enable them, at least, to detect unsound reasoning, 
 when drawn from simple principles and familiar facts. Be- 
 sides, the great majority of those who are dupes of others, or 
 who deceive themselves by specious fallacies, suffer not so much 
 from ignorance of facts and principles as from vague ideas of the 
 relations which these facts and principles, bear to each other, and 
 to the cottclusions drawn from them. Unpractised in abstraction, 
 such persons are unable to fix the mind steadily upon the point at 
 issue in an argument, to the exclusion of what is irrelevant. It is 
 a wise remark of Dr. Barrow, that * confusion is the mother of 
 iniquity.' To no case does this maxim apply with more force than 
 to that confusion of thought, and indistinctness of mental vision, 
 which disqualify a man for ascertaining the justness or fallacy of an 
 argument, in reference to those subjects that vitally affect the 
 peace and welfare of society. The constant resort of sophistical 
 advocates, and politicians, and, indeed of errorists of every class, 
 is the false issue, or in logical language, the irrelevant conclusion. 
 Something is proved, triumphantly it may be, but not the thing 
 requisite, and the conclusion thus obtained is adroitly shifted, un- 
 der the cover of a cloud of words, and is affirmed with the utmost 
 seriousness, of an entirely different subject. So long as the com- 
 munity at large will be misled by fallacious reasoning, bad men 
 will make use of it for their own advancement. 
 
 Let students in our High Schools and Academies be as well 
 taught in the analysis of arguments, as they are in the elements of 
 other branches of learning, and it will not be unreasonable to hope 
 that a salutary effect may be produced upon those who assume to 
 instruct the people in Politics and Keliglon. Public men under- 
 stand their own interests too well to deal in counterfeits, when 
 there is much danger of detection. There is much said of the de- 
 plorably low standard of attainment to which professional men are 
 contented to arrive. The surest way to secure honesty and intel- 
 lectual ability, in the professions, is to create a demand for those 
 qualities, by instructing those from whom the substantial rewards 
 of professional merit must come. Let the study of a book like this 
 become general, and something, at least, will have been done 
 
INTRODUCTION. 11 
 
 towards staying the floods of solemn nonsense, that, by the aid of 
 the franking prh^ege, are yearly spread over our land. 
 
 It is to be hoped that this little work will receive the attention 
 from teachei^ and those interested in education, which its intrinsic 
 excellence and the importance of the subject demand. 
 
 June^ 1845. 
 
EASY LESSONS ON REASONING. 
 
 PART I. 
 ANALYTICAL INTEODUCTION. 
 
 LESSON L 
 
 N. B. In these Lessons, whenever two equivalent words or phrases are 
 employed, one of them is enclosed in angular [brackets,] instead of the 
 common mark of a (parenthesis.) 
 
 § 1. Every one is accustomed, more or less, to employ 
 Reasoning. There is no one that does not occasionally at- 
 tempt, well or ill, to give a Reason for any opinion he 
 entertains ; — to draw Conclusions from what he sees around 
 him, — to support those conclusions by some kind of Argu- 
 ments, good or bad, — and to answer the arguments brought 
 against him. 
 
 Now all these expressions, — ' giving a reason ' — ' draw- 
 ing a conclusion ' — ' bringing forward an argument ' — re- 
 late to one and the same process in the mind, that which is 
 properly called 'Reasoning.' And the same may be said of 
 several other expressions also; such as 'inferring' or 
 'drawing an inference,' — 'proving a point,' — 'establishing 
 a conclusion,' — ' refuting an argument,' — &c. All these 
 expressions, and some others besides, have reference, as we 
 have said, to the process of Reasoning. 
 2 
 
14 ANALYTICAL INTRODUCTION. \_Part I. 
 
 § 2. And this process, it is important to observe, is, in 
 iV^eZ/*, universally, the same; however different the subject- 
 matter of our reasoning may be, on different occasions. 
 
 The same is the case with Arithmetic. We may have to 
 add, or subtract, multiply, or divide, certain numbers, either 
 of Pounds-sterling, or of men, or of bushels of corn, &c. ; 
 but though these are very different things, the arithmetical- 
 process itself, in each of the operations, respectively, is always 
 the same. For instance, to ' multiply ' always means to take 
 one number a certain number of times ; whether it be men, 
 or miles, or days, that v^e are numbering. 
 
 So it is also with Grammar. The Nouns, and Yerbs, and 
 other Parts of Speech that Grammar treats of, may relate 
 to very different subjects, and may be found in various kinds 
 of Compositions ; such as works of Science, History, Poetry, 
 &c., but the rules of Grammar are the same in all. 
 
 So also the art of Writing (and the same may be said of 
 Printing) is in itself the same, however different may be the 
 kinds of subject-matter it is employed on. 
 
 Now the same is the case (as has been above said) with 
 Reasoning. We may be employed in reasoning on human 
 affairs, or on Mathematics, or on Natural-history, or Chem- 
 istry, or other subjects widely different from each other. 
 But in every case the Peasoning-process is, in itself, the 
 same. 
 
 § 3. Any Debate, [or Disputation] w^hen you are endeav- 
 oring to bring others over to your opinion, is one of the oc- 
 casions on which Peasoning is employed; and the word 
 * arguing ' is by some persons understood as having reference 
 only to cases where there is a dispute between those who are 
 maintaining opposite opinions. But this is a mistake. At 
 least, it is a mistake to suppose that the use of ' Arguments ' 
 • — if we understand by that, the use of Peasoning — is con 
 fined to the case of disputes; or even that this is ilio, principal 
 
Lesson i.] the keasoning-process. 15 
 
 employment of it. There is no set of men less engaged in 
 dispute and controversy than Mathematicians ; who are the 
 most constantly occupied in Reasoning. They establish all 
 their propositions by the most exact proofs ; so complete as 
 not even to admit of any dispute. 
 
 And in all other subjects, likewise, a sensible man, when 
 he wishes to make up his mind on any question, will always 
 seek for some sufficient ' Reason ' [or ' Argument '] on which 
 to found his conclusion. 
 
 Thus, a Judge, before whom any Cause is tried, is occupied 
 in weighing the Arguments on both sides, that are brought 
 forward by the respective Advocates. He (no less than 
 they) is engaged in Reasoning; though the Avoeates are 
 disputing, and the Judge is not. 
 
 A Physician, again, reasons from what he has read, and 
 heard, and seen, in order to draw his conclusions on medical 
 questions; — a Statesman, in political questions; — a Mer- 
 chant, in mercantile matters ; and so, of the rest. 
 
 § 4. But when any dispute does take place, between per- 
 sons of opposed opinions, it may be observed that the worst 
 educated, — those who are the most unskilful in reasoning, or 
 in clearly expressing their reasons, — are almost always the 
 most apt to grow angry, and to revile each other, and quarrel. 
 
 And even when they do not give way to anger, they 
 usually, after a long discussion, part, without distinctly under- 
 standing what the difference between them really consists in ; 
 neither of them having clearly expressed his own meaning, 
 or fully understood the other's. 
 
 Indeed, it often happens that two persons who are dis- 
 puting, do, in reality, disagree much less in their opinions 
 than they themselves imagine ; or, perhaps, not at all. And 
 hence it is that the word ^misunderstanding' has come to 
 signify, a quarrel ; because quarrels so often arise from men's 
 not clearly understanding each other's meaning. 
 
16 ANALYTICAL INTRODUCTIOK. \^Part I. 
 
 Again, it often happens that a person, not without good 
 sense, will give such weak and absurd reasons for his opinion, 
 — even v/hen it is a right one, — that, instead of convincing 
 others, he will even produce an opposite effect. 
 
 § 5. In order to avoid such inconveniences, and to conduct 
 the process of Reasoning as clearly, as correctly, and as 
 easily, as is possible, it is a great advantage to lay down ac- 
 curate explanations of the principles on which Reasoning 
 proceeds, and to employ, for the purpose, a technical lan- 
 guage ; that is, a regularly-foraied set of expressions, dis- 
 tinctly defined, and agreed on ; and to establish certain plain, 
 simple 7^ules, founded on, and expressed in, this technical 
 language. 
 
 Even in the common mechanical arts, something of a 
 technical language is found needful for those who are learn- 
 ing or exercising them. It w^ould be a very great inconve- 
 nience, even to a common carpenter, not to have a precise, 
 w^ell-understood name for each of the several operations he 
 performs, such as chiseling, sawing, planing, &c., and for the 
 several tools [or instruments] he works v/ith. And if we 
 had not such words as Addition, Subtraction, Multiplication, 
 Division, &;c., employed in an exactly defined sense, and also 
 fixed rules for conducting these and other arithmetical pro- 
 cesses, it would be a tedious and uncertain work, to go 
 through even such simple calculations as a child very soon 
 learns to perform with perfect ease. And after all, there 
 would be a fresh difficulty in making other persons under- 
 stand clearly the correctness of the calculations made. 
 
 You are to observe, however, that technical language and 
 rules, if you would make them really useful, must be not 
 only distinctly understood, but also learnt, and remembered, as 
 familiarly as the Alphabet; and employed constantly/, and 
 with scrupulous exactness. Otherwise technical language will 
 prove an incumbrance instead of an advantage ; just as a 
 
Lesson i.] the reasoning-process. 17 
 
 suit of elotlies would be, if, instead of putting them on, and 
 wearing tliem, you were to cany them about in your hand. 
 
 § 6. It has been, accordingly, found advantageous, in what 
 relates to the Reasoning-process, (as well as in the case of 
 mechanical operations, and of calculations,) to lay down ex- 
 planations, and rules, and technical terms ; answering to those 
 of Arithmetic, Grammar, and other branches of study. 
 
 And the technical terms and rules, of Grammar, are not at 
 all shorter, or easier to be understood and remembered than 
 those pertaining to the present subject. 
 
 You may, perhaps, meet with treatises professing much 
 more than what we here propose ; ■ — with works pretending 
 to teach ' the right use of Reason ; ' (not Reason 2*72^, or 
 ^Argumentation' merely, but the whole of the Human In- 
 tellect) and giving rules for forming a judgment on every 
 question that can arise, and for arriving at all truths in 
 any subject whatever. But such pretensions, however high- 
 sounding and attractive, are fanciful and empty. One might 
 as well profess to teach the ' right use of the bodily-organs,' 
 and to lay down a system of rules that should instruct a man 
 in all manual arts and bodily exercises at once. 
 
 If you do but teach a person to ride, or to draw, or to spin, 
 &c., something is gained : but if you should profess to lay 
 down a system of rules to teach all these at once, and also the 
 business of a shipwright, and a musician, and a watchmaker, 
 and everything else that is done by means of the bodily- 
 organs, you would teach, in reality, nothing all. 
 
 And so it is in all subjects. It is better to undertake 
 even a little, that it is possible to accomplish, than to make 
 splendid professions, which can only lead to disappointment. 
 
 After all, indeed, it cannot be expected that, in Reasoning, 
 any more than in other mental exercises, men of very un- 
 equal degrees of intelligence sliould be brought to the same 
 level. Nor is it to be expected that men will always be 
 2* 
 
18 ANALYTICAL INTRODUCTION. rPart I. 
 
 brought to an agreement in their conclusions. Different men 
 will have received different information respecting facts ; or 
 will be variously biassed, more or less, by their early preju- 
 dices, their interests, or their feelings. 
 
 But still, there is something gained, if they are taught, in 
 respect of the Reasoning-process itself, how to proceed right- 
 ly, and to express themselves clearly ; and if, when they do 
 not agree, they can be brought at least to understand wherein 
 they differ, and to state distinctly what is ' the point at issue,^ 
 (as it is called) between them ; that is, what is the real ques- 
 tion to be decided. 
 
 And it is just so, in the case of Arithmetic also. Two 
 persons may differ in their statements of an Account, from 
 their setting out with some difference in the numbers each 
 puts down ; — in the Items (as it is called) of the Account. 
 And no rules of Arithmetic can prevent such a difference as 
 this. But it is something gained if they are guarded (as 
 arithmetical rules do guard us) against differences arising 
 out of errors in the calculation itself. 
 
 LESSON 11. 
 
 § 1. We have said that in all subjects, and on all occasions, 
 the Reasoning-process is, in itself, the same. Whether you 
 are occupied in refuting an opponent, or in conveying instruc- 
 tion, or in satisfying your own mind on any point, — and 
 again, whatever kind of subject-matter it is that you are en- 
 gaged on, — in all cases, as far as you are (in the strict sense 
 of the word) reasoning, — that is, employing Argument — it 
 is one and the same process (as far as it is correctly con- 
 ducted) that is going on in your own mind. 
 
Lesson II.] THE REASONING-PROCESS. 19 
 
 And what this process is, must be the next point to be 
 inquired into. 
 
 Although (as has been said) all men do occasionally reason, 
 thej are often, at the time, as unconscious of it, as of the 
 circulation of their blood, and the various other processes 
 that may be going on within the body. And even when they 
 do, knowingly and designedly, use arguments, or are listening 
 to those of another, they will often be as much at a loss 
 to explain why one argument appears to them strong, and 
 another less strong, and another, utterly worthless, as if the 
 whole were merely a matter of taste ; like their preference of 
 one prospect, or one piece of music, to another. 
 
 In order, then, to obtain correct rules for forming a judg- 
 ment on this subject, and clear expressions for explaining 
 such judgment to others, it is necessary to analyze, — as it is 
 called, — (that is, take to pieces) the Reasoning-process. 
 And for that purpose, we should begin by examming the 
 most plain, short, and simple arguments, and inquiring on 
 what it is that their validity [or conclusiveness] depends, 
 examining also some of those appai*ent-arguments which are 
 not valid, and therefore are not, in reality, arguments at all, 
 though they are often passed off for. them, as counterfeit coin 
 is, for genuine. 
 
 § 2. You will perceive, on examination, that what is called 
 a ' Conclusion,' — that is, a Proposition proved by Argument, 
 — is drawn, in reahty, from two other Propositions. And 
 these are called its ' Premises ; ' from their being (in natural 
 order) ' premised^^ or put before it. 
 
 At first sight, indeed, some might suppose that a Conclusion 
 may follow from one Premise alone. For it happens oftener 
 than not, that only one is expressed. But in this case there 
 is always another Premise understood, and which is sup- 
 pressed from its being supposed to be fully admitted. 
 
 That this is the case, may easily be made evident, by sup- 
 
20 ANALYTICAL INTRODUCTION. [^Part I. 
 
 posing that suppressed Premise to be de7iied ; which will at 
 once destroy the force of the argument. For instance, if any 
 one, from perceiving that ' the World exhibits marks of de- 
 sign,' infers [or concludes] that ' it had an intelligent Maker,' 
 he will easily perceive, on reflection, that he must have had 
 in his mind another Premise also ; namely, that ' whatever 
 exhibits marks of design, had an intelligent Maker : ' since if 
 this last proposition were derded, the other would prove 
 nothing. It is true, that, in some cases, one proposition im- 
 plies another, by the very signification of the words, to every 
 one who understands those words; as, ^negroes are men; 
 therefore they are rational-beings : ' now ' rational-being ' is 
 implied in the very name ' man.' And such examples as 
 this, have led some people into the idea that we reason, — or 
 that we may reason, — from a single premise. But take such 
 a case as this ; some fossil-animal is discovered, which Natu- 
 ralists conclude to have been a ' ruminant,' from its ' having 
 horns on the skull.' Now, the laborers who dug up the 
 skeleton could not draw this inference, supposing they were 
 ignorant of the general law, ' that all horned animals are ru- 
 minat : ' — and they might be thus ignorant, though using the 
 name ' horned-animal ' in the same sense as the Naturalist : 
 for the name itself does not imply ' ruminant,' as a part of 
 its signification : and again, a Naturalist, at a distance, w^ho 
 knew the general law, but who had heard only an imperfect 
 account of the skeleton, and did not "know whether it was 
 horned or not, would be equally unable to draw the inference. 
 
 In all cases of what is properly called ' Alignment,' there 
 must be two premises assumed, whether they are both ex- 
 pressed or not. 
 
 § 3. Such an argument as the above, when all the three 
 propositions are stated at full length, and in their natural 
 order, is called a ' Syllogism.' And this is the form in which 
 all correct reasoning, on whatever subject, may be exhibited. 
 
Lesson ii.] the reasoning-process. 21 
 
 When one of the Premises is suppressed, — [or, under- 
 stoocT] which, for brevity's sake is usually the case, — the 
 argument is called, in technical language, an ' Enthymeme : ' 
 a name derived from the Greek, and denoting that there is 
 something left out, which is to be supposed [or understood] 
 as being well-known. 
 
 It is to be observed, that, when an argument, stated in 
 this last form, is met by opponents, their objection will some- 
 times lie against the assertion itself y that is made ; sometimes, 
 against ii^ force as an argument. They will say either 'I 
 deny what you assume,^ or ' I admit, indeed, what you say, 
 but I deny that it proves your conclusion.' For instance, in 
 the example above, an atheist may be conceived either deny- 
 ing * that that the World does exliibit mai'ks of design, or 
 again, denying f that ii follows from thence that it must have 
 had an intelligent Maker. 
 
 Now, you are to observe, that these are not, in reality, ob- 
 jections of different kinds. The only difference is, that, in 
 the one case, the expressed Premise is denied ; in the other, 
 the suppressed Premise. For ihQ force as an argument, of 
 either Premise, depends on the other Premise. If either be 
 denied, the other proves nothing. If both be admitted, the 
 Conclusion regularly drawn from them, must be admitted. 
 
 § 4. It makes no difference in respect of the sense of an 
 argument, whether the Conclusion be placed last or first; 
 provided you do but clearly mark out what is the Conclusion. 
 
 When it is placed last, (which is accounted the natural or- 
 der) it is designated by one of those conjunctions called 
 ^ illative,' such as ' therefore,' — ' thence,' — ' consequently.' 
 
 When the Conclusion is put first, the Premise is usually 
 called the ' Reason ; ' and this is designated (whether it comes 
 
 ^ As many of the ancient atheists did. 
 .-. t As most of the modern atheists do. 
 
22 ANALYTICAL INTRODUCTION. [^Part I. 
 
 last or first) by one of the conjunctions called causal,'' such 
 as ' since/ — ' because,' &c. 
 
 And here it is to be observed that each of these sets of 
 conjunctions have also another sense ; being used to denote, 
 respectively, sometimes ' Premise and Conclusion,' — some- 
 times ' Cause and Effect.' And much error and perplexity 
 have often been occasioned by not attending to this dis- 
 tinction. 
 
 When I say ' this ground is rich ; because the trees on it 
 are flourisliing ; ' or again, when I express the same sense in 
 a different form, saying, ' the trees on this ground are flourish- 
 ing ; and therefore it must be rich,' it is plain that I am em- 
 ploying these conjunctions to denote merely the connection of 
 Premise and Oonclusion ; or, (in other words) I am implying 
 that the one may be inferred from the other. For it is evi- 
 dent that the flourishing of the trees is not the cause of the 
 ground's fertility, but only the cause of my believing it. The 
 richness of the soil folloivs as an inference, from the luxuri- 
 ance of the trees ; which luxuriance follows as an effect [or, 
 natural consequence] from the richness of the soil. 
 
 But if, again, I say, ' the trees flourish, because the ground 
 is rich,' or (which is the same in sense) ' the ground is rich 
 and consequently [or therefore] the trees flourish,' I am 
 using the very same conjunctions in a different sense ; name- 
 ly, to denote the connection of Cause and Effect, For in this 
 case, the luxuriance of the trees, being a thing evident to the 
 eye, would not need to be 'proved; and every one would un- 
 derstand that I was only accounting for it, 
 
 § 5. But again, there are many cases also in which the 
 Cause is employed as an Argument, to prove the existence of 
 its Effect. So that the Conclusion Y^hioh follows, as an In- 
 ference, from the Premise, is also an Effect which follows 
 naturally from that same Premise as its Cause. 
 
 This is the kind of argument which is chiefly employed 
 
Lesson iii. fallacies. 23 
 
 when we are reasoning about the future : as, for instance, 
 when, from favorable or unfavorable weather, any one infers 
 that the crops are likely to be abundant, or to be scanty. 
 
 In such cases, the Gause^ and the Reason [or Proof] coin- 
 cide ; the favorable weather being at once the Cause of the 
 good harvest, and the Cause of our expecting it. 
 
 And this circumstance contributes to men's often con- 
 founding together ' Cause ' and — what is strictly called — 
 'Reason;' and to their overlooking the different senses of 
 such words as ' therefore,' ' thence,' ' consequently,' &., and 
 again, of such words as ' because,' ' inasmuch as,' &c., and 
 also, of the words ' follow,' ' consequence,' and several others ; 
 which have all of them that double meaning which has been 
 just explained. 
 
 LESSON III. 
 
 § 1. In such an argument as that in the example above 
 given, (in § 2, Lesson ii.,) it is clearly impossible for any one 
 who admits both Premises, to avoid admitting the Conclusion. 
 If you admit that, ' Whatever exhibits marks of design, had 
 an intelligent Maker,' and also, that ' the world exhibits 
 marks of design,' you cannot escape the Conclusion, that 
 ' the world had an intelligent Maker.' 
 
 Or again, if I say, ' All animals with horns on the head 
 are ruminant ; the Elk has horns on the head ; therefore it is 
 ruminant;' it is impossible to conceive any one's doubting the 
 truth of the Conclusion, supposing he does but allow the truth 
 of each Premise. 
 
 A man may, perhaps, deny, or doubt, and require proof, 
 that all animals thus horned do ruminate. Nay, it is con- 
 
24 a:nalytical introduction. \_Part i. 
 
 ceivable that he may even not clearly understand what 
 ' ruminant * means ; or he may have never heard of an 
 ^ Elk ;^ but still it will be not the less clear to him, that, 
 supposing these Premises granted, the Conclusion must be 
 admitted. 
 
 And even if you suppose a case where one or both of the 
 Premises shall be manifestly false and absurd, this will not 
 alter the conclusiveness of the Reasoning ; though ihQ conclu- 
 sion itself may, perhaps, be absurd also. For instance, ^ All 
 the Ape-tribe are originally descended from Reptiles or In- 
 sects : Mankind are of the Ape-tribe ; therefore Mankind are 
 originally descended from Reptiles or Insects : ' here, every 
 one * would perceive the falsity of all three of these proposi- 
 tions. But it is not the less true that the conclusion yb//o^^s 
 from those premises, and that if they were true, it would be 
 true also. 
 
 § 2. But it often happens that there will be a seeming con- 
 nexion of certain premises with a conclusion which does not 
 really follow from them ; although, to the inattentive, or un- 
 skilful, the argument will appear to be valid. And this is 
 most especially likely to occur when such a seeming-argu- 
 ment [or Fallacy] is dressed up in a great quantity of fine- 
 sounding words, and is accompanied with much vehemence 
 of assertion, and perhaps with expressions of contempt for 
 any one who presumes to entertain a doubt on the matter. 
 In a long declamatory speech, especially, it will often happen 
 that almosj^ any proposition at all will be passed off, as a 
 proof of any other that does but contain some of the same 
 words^ by means of strenuous assurances that the proof is 
 complete. 
 
 Sometimes, again, sound arguments will be distrusted as 
 fallacious ; especially if they are not clearly expressed ; and 
 the more, if the conclusions are such as men are not willing 
 to admit. 
 
 ^ Except certain French Naturalists. 
 
Lesson i.] arbitrary symbols. 25 
 
 And frequently, also, when there really is no sound argument, 
 the reader or hearer, though he believes, or suspects, that there 
 is some fallacy, does not know how to detect and explain it. 
 
 § 3. Suppose, for instance, such seeming-arguments as the 
 following to be proposed: — (1.) ^ Every criminal is de- 
 serving of punishment ; this man is not a criminal ; therefore 
 he is not deserving of punishment:' or, again, (2.) 'All 
 wise rulers endeavor to civilize the People ; Alfred endeav- 
 ored to civilize the People ; therefore he was a wise ruler/ 
 There are, perhaps, some few persons who would not perceive 
 any fallacy in such arguments, even when thus briefly and 
 distinctly stated. And there are, probably, many who would 
 fail to perceive such a fallacy, if the arguments were en- 
 veloped in a cloud of words, and conveyed at great length in 
 a style of vague, indistinct declamation ; especially if the 
 conclusions were such as they were disposed to admit. And 
 others, again, might perceive, indeed, that there is a fallacy, 
 but might be at a loss to explain and expose it. 
 
 Now, the above examples exactly correspond, respectively, 
 with the following ; in which the absurdity is manifest : — 
 (1.) 'Every tree is a vegetable; grass is not a tree ; there- 
 fore it is not a vegetable ; ' and (2.) 'All vegetables grow; 
 an animal grows ; therefore it is a vegetable.' These last 
 examples, I say, correspond exactly (considered in respect 
 of the reasoning) with the former ones ; the conclusions of 
 which, however truBj no more foUoiu from the premises than 
 those of the last. 
 
 This way of exposing a fallacy, by bringing forward a 
 similar one, where a manifestly absurd conclusion professes 
 to be drawn from premises that are true, is one which we 
 may often find it needful to employ when addressing persons 
 who have no knowledge of technical rules ; and to whom, 
 consequently, we could not speak so as to be understood, con- 
 cerning the principles of Reasoning. 
 3 
 
26 ANALYTICAL INTRODUCTION. \^Part I. 
 
 Eut it is evidently the most convenient, the shortest, and 
 the safest course, to ascertain those principles, and on them 
 to found rules which may be employed as a test in every case 
 that comes before us. 
 
 And for this purpose it is necessary (as has been above 
 said) to analyse the Reasoning-process, as exhibited in some 
 valid argument, expressed in its plainest and simplest form. 
 
 § 4. Let us then examine and analyse such an example as 
 one of those first given : for instance, ' Every animal that has 
 horns on the head is ruminant; the Elk has horns on the 
 head ; therefore the Elk is ruminant.' It will easily be seen 
 that the validity [or ' conclusivenes,' or ' soundness '] of the 
 Argument does not at all depend on our conviction of the 
 truth of either of the Premises ; or even on our understand- 
 ing the meaning of them. For if we substitute some unmean- 
 ing Symbol, (such as a letter of the alphabet,) which may 
 stand for anything that may be agreed on — for one of the 
 things we are speaking about, the Reasoning remains the 
 same. 
 
 For instance, suppose we say, (instead of ' animal that has 
 horns on the head,') ' Every X is ruminant ; the Elk is X ; 
 therefore the Elk is ruminant;' the argument is equally 
 valid. 
 
 And again, instead of the word ' ruminant,' let us put the 
 letter ^ Y : ' then the argument ' Every X is Y ; the Elk is 
 X ; therefore the Elk is Y ; ' would be a valid argument as 
 before. 
 
 And the same would be the case if you were to put ' Z ' for 
 ^ the Elk : ' for the syllogism ' Every X is Y ; Z is X ; there- 
 fore Z is Y,' is completely valid, whatever you suppose the 
 Symbols X, Y, and Z to stand for. 
 
 Any one may try the experiment, by substituting for X, 
 Y, and Z, respectively, any words he pleases ; and he will 
 find that if he does but preserve the same ybrw of expression, 
 
Lesson iii.] arbitrary sy:\ibols. 27 
 
 it will be impossible to admit the truth of the Premises, with- 
 out admitting also the truth of the Conclusion. 
 
 § 5. And it is worth observing here, that nothing is so 
 likely to lead to that — very common, though seemingly 
 strange — error, of supposing ourselves to understand dis- 
 tinctly what in reality we understand but very imperfectly, 
 or not at all, as the want of attention to what has been just 
 explained. 
 
 A man reads — or even writes — many pages perhaps, of 
 of an argumentative work, in which one or more of the terms 
 employed convey nothing distinct to his mind : and yet he is 
 liable to overlook this circumstance, from finding that he 
 clearly understands the Arguments. 
 
 He may be said, in one sense, to understand ivhat he is 
 reading ; because he can perfectly follow the train of Reason-- 
 ing, itself. But this, perhaps, he might equally well do, if he 
 were to substitute for one of the words employed, X, or Z, or 
 any other such unknown Symbol ; as in the examples above. 
 
 But a man will often confound together, the understanding 
 of the Arguments, in themselves, and the understanding of 
 the words employed, and of the nature of the things those 
 w^ords denote. 
 
 It appears, then, that valid Reasoning, when regularly ex- 
 pressed, has its validity [or conclusiveness] made evident 
 from the mere form of the expresssion itself, independently 
 of any regard to the sense of the words. 
 
 § 6. In examining this form, in such an example as that 
 just given, you will observe that in the first Premise {' X is 
 Y, ') it is assumed universally of the Class of things (what- 
 ever it may be) which ' X' denotes, that ' Y' may be afiirmed 
 of them : and in the other Premise, Q Z is X') that 'Z' (what- 
 ever it may stand for) is referred to that Chiss, as compre- 
 hended in it. Now it is evident that whatever is said of the 
 whole of a Class may be said of anything that is compre- 
 
28 ANALYTICAL INTRODUCTION. [^Part I. 
 
 bended [or ' included/ or ' contained/] in that Class ; so that 
 we are thus authorized to say (in the conclusion) that ' Z ' is 
 
 Thus also in the example first given, having assumed uni- 
 versally, of the Class of '^Things which exhibit marks of 
 design/ that they ' had an intelligent maker/ and then, in the 
 other Premise, having referred ' The world ' to that Class, 
 we conclude that it may be asserted of ' The world ' that ' it 
 had an intelligent maker.' 
 
 And the process is the same when anything is denied of a 
 whole class. We are equally authorized to deny the same, 
 of whatever is comprehended under that Class. For instance 
 if I say, ' No liar is deserving of trust : this man is a liar ; 
 therefore he is not deserving of trust : ' I here deny ' deserv- 
 ing of trust,' of the whole Class denoted by the word ' liar ; ' 
 and then I refer ' this man ' to that Class ; whence it follows 
 that ' deserving of trust ' may be denied of him. 
 
 § 7. This argument also will be as manifestly valid, if (as in 
 the former case) you substitute for the words which have a 
 known meaning, any undetermined Symbols, such as letters 
 of the alphabet. ' No X is Y ; Z is X ; therefore Z is not 
 Y,' is as perfect a syllogism as the other, with the afirmative 
 conclusion. 
 
 To such a form all valid arguments whatever may be re- 
 duced : and accordingly the principle according to which they 
 are constructed, is to be regarded as the Univeksal Prin- 
 ciple OF Reasoning. 
 
 It may be stated, as a general Maxim, thus : ' Whatever is 
 said, whether affirmatively, or negatively,' [or ' whatever is 
 affirmed or denied '] ' of a whole Class, may be said in like 
 manner/ [that is ' affirmed in the one case, and denied in the 
 other,'] ' of everything comprehended under that Class.' 
 
 Simple as this Principle is, the whole process of Reasoning 
 is embraced in it. Whenever we establish any Conclusion, 
 
Lesson iii.] principle of reasoning. 29 
 
 — that is, show that one thing may allowably be affirmed, or 
 be denied, of another — this is always in reality done by re- 
 ferring that other to some Class of which such affii'mation or 
 denial can be made. 
 
 The longest series of arguments, when fully unfolded, step 
 by step, will be found to consist of nothing but a repetition of 
 the same simple operation here described. But this circum- 
 stance is apt to be overlooked, on account of the brevity with 
 which we usually express ourselves. A Syllogism, such as 
 those in the examples above, is seldom given at full length ; 
 but is usually abridged into an ' Enthymeme.' * (See Less. 
 II. § 3.) And moreover what is called ' an argument,' is 
 very often not one argument, but several compressed together ; 
 sometimes into a single sentence. As when one says, ' The 
 adaptation of the mstinct of suction in young animals to the 
 supply of milk in the parent, and to the properties of the 
 Atmosphere, as well as other like marks of design, show that 
 the world must have had an intelligent Maker.' For most 
 men are excessively impatient of the tedious formality of 
 stating at full length anything that they are already aware of, 
 and could easily understand by a slight hint. 
 
 LESSON IV. 
 
 § 1. We have seen that when an Argument is stated in the 
 regular fyrm, (as in the foregoing examples,) which is what 
 is properly called a ' Syllogism,' the validity [or conclusive- 
 ness] of the reasoning is manifest from the mere form of the 
 expression itself, without regard to the sense of the words ; 
 so that if letters, or other such arbitrary unmeaning Symbols, 
 
 * That is an argument witii one of die Premises understood. 
 3* 
 
30 ANALYTICAL INTRODUCTION. \_Part I. 
 
 be substituted, the force of the argument will be not the less 
 evident. Whenever this is not the case, the supposed argu- 
 ment is either sophistical and unreal, or else, may be reduced 
 (without any alteration of its meaning) into the above form ; 
 in which form, the general Maxim that has been laid down 
 will apply to it. 
 
 What is called an unsound [or fallacious] argument (tliat 
 is, an apparent-2^Tgam.QTit which is in reality none) cannot, of 
 course, be reduced into such a form. But when it is stated 
 in the form most nearly approaching to this that is possible, 
 and especially when unmeaning Symbols (such as letters) are 
 substituted for words that have a meaning, its fallaciousness 
 becomes evident from its want of conformity to the above 
 Maxim. 
 
 § 2. Let us take the example formerly given ; Every crim- 
 inal is deserving of punishment ; this man is not a criminal ; 
 therefore he is not deserving of punishment : this, if stated in 
 letters, would be ' every X is Y ; Z is not X ; therefore Z is 
 not Y.' Here, the term (^ Y ') ' deserving of punishment ' is 
 affirmed universally of the Class (X) ' criminal ; ' and it 
 might therefore, according to the Maxim, be affirmed of any- 
 thing comprehended under that Class ; but in the instance 
 before us, nothing is mentioned as comprehended under that 
 Class: only ^this man' ('Z') is excluded from that Class. 
 And although what is affirmed of a whole Class may be 
 affirmed of anything which that Class does contain, we are 
 not authorized to deny it of whatever is not so contained. 
 For it is evident that what is truly affirmed of a Class, may 
 be applicable not only to that Class, but also to other things 
 besides. 
 
 For instance, to say that ^ every tree is a vegetable ' does 
 not imply that ^ nothing else is a vegetable.' And so also, to 
 say that ' every criminal is deserving of punishment,' does not 
 imply that ' no others are deserving of punishment : ' for how- 
 
Lesson iy. apparent-argidients. 31 
 
 ever trite this is, it has not been asserted in the proposition be- 
 fore us. .And in analysing an argument we are to dismiss all 
 consideration of what might have been asserted with truth, 
 and to look only to what actually is laid down in the 
 Premises. 
 
 It is evident therefore that such an apparent-argument as 
 the above does not comply \A\h the Rule [or Maxim] laid 
 down ; nor can it be so stated as to comply with it ; and it is 
 consequently invalid. 
 
 § 3. Again, let us take another of the examples formerly 
 given ; ' All wise rulers endeavor to civihze the People ; 
 Alfred endeavored to civilize the People ; therefore he v/as a 
 wise ruler.' The parallel example to this, was, ' All vege- 
 tables grow ; an animal grows : therefore it is a vegetable.' 
 And each of these, if stated in Symbols, would stand thus : 
 every ' Y is X,' [or the thing denoted by Y is comprehended 
 under the Class for which X stands] ' Z is X ; therefore Z is 
 Y.' 
 
 Now in such an example, the quality of ^ growing ' [X] is, 
 in one Premise, affirmed universally of ' vegetable,' [' Y,'] 
 and it might therefore have been affirmed of anything that 
 can be referred to the Class of ' vegetable ' as comprehended 
 therein : but then, there is nothing referred to that Class, in 
 the other Premise ; only, the same thing which liad been 
 affirmed of the Class ' vegetable,' is again affirmed of another 
 Class, ' animals ' (Z) ; whence nothing can be inferred. 
 
 Again, talie such an instance as this ; ' food is necessary to 
 life ; com is food ; therefore corn is necessary to life.' Here, 
 * necessary to life ' is affirmed of ' food,' but not universally ; 
 for every one would understand you to be speakhig not of ' all 
 food,' but of ' some food,' as being ' necessary to life.' So that, 
 expressed in Symbols, the apparent-argument would stand 
 thus : ' Some X is Y ; Z is X ; therefore Z is Y ; ' in which 
 you m^y see that the rule has not been complied with ; since 
 
32 ANALYTICAL INTRODUCTION. J[Part I. 
 
 that which has been affirmed not of the whole of a certain 
 Class, [or, not universally^ but only of part of it, cannot on 
 that ground be affirmed of whatever is contained under that 
 Class. 
 
 § 4. There is an argument against miracles by the well- 
 known Mr. Hume, which has perplexed many persons, and 
 which exactly corresponds to the above. It may be stated 
 thus ; ' Testimony is a kind of evidence more likely to be false 
 than a miracle to be true ; ' (or, as it may be expressed in other 
 words, we have more reason to expect that a witness should 
 lie, than that a miracle should occur) ' the evidence on which 
 the Christian miracles are believed, is testimony ; therefore 
 the evidence on which the Christian miracles are believed is 
 more likely to be false than a miracle to be true.' 
 
 Here it is evident that what is spoken of in the first of 
 these Premises, is, ' some testimony ; ' not ' all testimony,' [or 
 any whatever,'] and by ^ a witness ' we understand, ' some wit- 
 ness,' not, ' every witness ; ' so that this apparent-argument has 
 exactly the same fault as the one above. And you are to 
 observe that it makes no diffisrence (as to the point now be- 
 fore us) whether the word ' some ' be employed, or a diffigrent 
 word, such as * most ' or ' many,' if it be in any way said or 
 implied that you are not speaking of ' alU For instance, 
 ' most birds can fly ; and an ostrich is a bird,' proves nothing. 
 
 § 5. In order to understand the more clearly, and to des- 
 cribe the more accurately, the fallaciousness of such seeming- 
 arguments as those of which we have just given examples, 
 and also, the conclusiveness of the sound arguments, it will be 
 necessary to explain some technical words and phrases which 
 are usually employed for that purpose. This is no less need- 
 ful (as was remarked in Lesson I.) than for an Artisan to 
 have certain fixed and suitable names for the several instru- 
 ments he works with, and the operations he performs. 
 
 The word ' Proposition,' (which we have already had occa-l 
 
Lesson iv.] technical words. 33 
 
 sion to use) signifies ' a Sentence in "which something is saior 
 
 — [or predicated] — that is, affirmed or denied — of another/ 
 That which is spoken of, is called the ' Subject * of the propo- 
 sition ; and that which is said of it is called the ' Predicate ; ' 
 and these two are called the ' Terms ' of the Proposition ; from 
 their being (in natural order) the extremes [or boundaries] 
 of it. 
 
 You are to observe that it matters not whether each of 
 these Terms consist of one word, or of several. For whether 
 a Proposition be short or long, there must always be in it, 
 one — and but one — thi£g of which you are speaking ; which 
 is called (as has been just said) the Subject of it : and there 
 must be (in any one Proposition) one thing, — and only one 
 
 — that is affirmed or denied of that Subject : and this which 
 we thus affirm or deny of the other, is called — whether it be 
 one word or more — the Predicate. 
 
 § 6. You are to observe also that though, (in our language) 
 the Subject is usually placed first ; this order is not at all 
 essential. For instance, ' it is wholesome to rise early,' or 
 ^ to rise early is wholesome,' or 'rising early is wholesome,' 
 are only thi-ee ways of expressing the same Proposition. In 
 each of these expressions, ' rising early,' (or ' to rise early,' 
 for these are only two forms of the Infinitive) is what you are 
 speaJdng of ; and ' wholesome ' is what you say [or predicate^ 
 of it. 
 
 W^ien we state a proposition in arbitrary SymhoJs, as ' X 
 is Y,' it is understood that the first term ( ' X ') stands for the 
 Subject, and the last (' Y') for the Predicate. But when we 
 use the teiTns that are significant^ [or, have a meaning] we 
 must judge by the sense of the words which it is that is the 
 Subject, and which the Predicate ; that is, we must ask our- 
 selves the question ' ^ATmt am I speaking of? and what am I 
 sapng of it ? ' 
 
 For instance, ' Great is Diana of the Ephesians ; ' here 
 
34 ANALYTICAL INTRODUCTION. \^Part I. 
 
 ^ great' is evidently the Predicate. Again, 'Thou art the 
 man ; ' and ' Thou hast given occasion to the enemies of the 
 Lord to blaspheme ; ' by asking yourself the above question, 
 you will perceive, that in the former of these examples, ' Thou * 
 is the Predicate, and in the latter, the Subject. 
 
 § 7. That which expresses the affirmation or denial, is call- 
 ed the ' Copula J For instance, if I say, ' X is Y,' or ' X is 
 not Y,' in each of these examples, 'X' is the Subject, and 
 ' Y ' the Predicate ; and the Copula is the word ' is ' in the 
 one, and ' is not,' in the other. 
 
 And so it is, in sense, though not always in expression, in 
 every Proposition. For either the Affirmative-copula, ' is ' or 
 the Negative-copula, ' is not,' must be always, in every Pro- 
 position, either expressed in those words, or implied in some 
 other expression. 
 
 Any Sentence which does not do this — in short, which does 
 not affirm or deny — is not a Proposition, For instance, of 
 these sentences, ' are your brothers gone to school ? ' ' they 
 are not gone ; ' 'let them go,' the second alone is a Proposi- 
 tion ; [or ' Assertion '] the first being a Question, and the last 
 a Command, or request. 
 
 LESSON V. 
 
 § 1 . AYe have seen that in every Proposition there is some- 
 thing that is spoken of ; which is called the Subject; and 
 something that you affirm or deny of it ; which is called the 
 Predicate. And it is evidently of great importance to under- 
 stand and express clearly, in each Proposition, w^hether the 
 Predicate is said of the whole of the Subject, or only of part 
 
Lesson v.] propositions. 35 
 
 of it : — in other words, whether it is 'predicated ^ universally^ 
 or '"particularly^ [^ partially J~\ 
 
 If, for instance, I saj, or am understood to imply, that ' all 
 testimony is unworthy of credit,' this is a very different asser- 
 tion from saying or implying, merely that ' some testimony is 
 unworthy of credit.' The former of these is called a ' Uni- 
 versal ' Proposition ; the Subject of it being taken universally 
 as standing for anything and everything that the Term is ca- 
 pable of being applied to in the same sense. And a Term so 
 taken is said (in technical language) to be ' distrihutedJ The 
 latter of the two is called a ' Particular Proposition ;^ iYiQ 
 Subject being talcen particularly^ as standing only for part of 
 the things signified by it : and the Term is then said to be 
 ' undistributed^ 
 
 The technical word ' distributed ^ (meaning what some wri- 
 \ ters express by the phrase ' taken universally') is used, as you 
 perceive in a sense far removed from what it bears in ordina- 
 ry language. But, — for that very reason, — it is the less 
 likely to lead to mistakes and confusion. And when once its 
 • technical sense is explained, it is easily remembered. When 
 1 1 say, ' birds come from eggs,' and again, ' birds sing,' I mean, 
 in the former proposition, ' all birds ; ' [or ' every bird ' ] in 
 ' the latter proposition, I mean, not, ' all^ but ^ some ' birds. In 
 the former case the term ^ birds ' is said to be ^ distributed ; ' 
 I in the latter ' undistributed.' You must be careful also to 
 ikeep in mind the technical sense (already explained) of the 
 word ' parti cidar,^ In ordinary discourse, we often speak of 
 
 * this particular person ' or thing ; meaning ' this individuaU 
 f But the technical sense is different. If I say 'this city is 
 J large,' the Proposition is not 'Particular,' but is equivalent to 
 
 a Universal ; since I am speaking of the ivhole of the Sub- 
 ject, which is, ' this single city^ But ' some city is large,' or, 
 
 * some cities are large,' is a particular proposition ; because 
 the Subject, ' city^ is taken not universally^ but partially. 
 
36 ANALYTICAL INTRODUCTION. [^Part I. 
 
 The distinction between a ' Universal ' proposition, and a 
 ^ Particular/ is (as I have said) very important in Reasoning ; 
 because, as has been akeady remarked, although what is said 
 of the whole of a Class may be said of anything contained in 
 that Class, the Rule does not apply when something is said 
 merely of part of a Class. ( See the example ' X is Y ' in 
 § 3 of the preceding Lesson.) 
 
 § 2. You will have seen that in some of the foregoing ex- 
 amples, the words ' all,' ' every,' or ' smj,' which are used to 
 denote the distribution of a Subject, and again, ' some,' which 
 denotes its non-distribution, are not expressed. They are often 
 understood, and left to be supplied in the reader's or hearer's 
 mind. Thus, in the last example, 'birds sing,' evidently 
 means ' some birds ; ' and, ' man is mortal,' would be under- 
 stood to mean ' every man.' 
 
 A Proposition thus expressed,, is called ' Indejinite ; ' it be- 
 ing left undetermined [_' undefined '] by the form of expression, 
 whether it is to be considered as Universal or as Particular. 
 And mistakes as to this point will often give a plausible air to 
 fallacies ; such as that in the last Lesson (§ 4.) respecting 
 ' Testimony.' 
 
 But it is plain that every Proposition must in reality he 
 either Universal or Particular ; [that is, must have its Sub- 
 ject intended to be understood as distributed, or, as not dis- 
 tributed] though we may not be told which of the two is 
 meant. 
 
 And this is called, in technical language, the distinction of 
 Propositions according to their ' Quantity;' namely, into Uni- 
 versal and Particular. ' Every X is Y' and ' some X is Y,' 
 are propositions differing from each other in their ' quantity/ 
 and in nothing else. 
 
 § 3. But the Predicate of a proposition, you may observe, 
 has no such sign as ' all ' or ' some/ affixed to it, which denote, 
 when affixed to the Subject, the distribution, or non-distribu- 
 
Lesson v.] quality and quantity. 37 
 
 tion of that term. And yet it is plain that each Term of a 
 proposition, — whether Subject or Predicate — must always 
 be meant to stand either for the whole, or for part, of what is 
 signified by it ; — in other words, — must really he either dis- 
 tributed or undistributed. But this depends, in the case of 
 the Predicate, not on the ' quantity ' of the proposition, but 
 on what is called its ' Quality ; ' that is, its being Affirmative 
 or Negative. And the invariable rule, (which will be ex- 
 plained presently) is, that the Predicate of a Negative-propo- 
 sition is distributed, and the Predicate of an Aflirmative, un- 
 distributed. 
 
 When I say ^ X is Y ' the term ' Y ' is considered as stand- 
 ing for part of the things to which it is applicable ; in other 
 w^ords, is undistributed. And it makes no difference as to 
 this point whether I say ' all X,' or ' some X is Y.' The Pre- 
 dicate is equally undistributed in both cases ; the only thing 
 denoted by the signs ' all ' or ' some,' being the distribution or 
 non-distribution of the Subject. 
 
 If, on the other hand, I say ' X is not Y,' whether meaning 
 that ' No X is Y,' or that ' some X is not Y,' in either case, 
 ^Y' is distributed. 
 
 § 4. The reason of this rule you w^ill understand, by con- 
 sidering, that a Term which may with truth be affirmed of 
 3ome other, may be such as would also apply equally well, 
 and in the same sense, to something else besides that other. 
 Thus, it is true that ^all iron is a metal,' although the term 
 ^ metal' is equally applicable to gold, copper, &c., so that you 
 could not say with truth that ' all metal is iron,' or that ' iron, 
 and that onlg, is a metal.' For the term ' iron ' is of narrow- 
 er extent than the term ^ metal,' which is affirmed of it. 
 
 So that, in the above proposition, what we have been com- 
 paring, are, the tvhole of the term ' iron,' and part of the term 
 * metal;' which latter term, consequently, is undistributed. 
 
 And this application applies to every affirmative proposi- 
 4 
 
38 ANALYTICAL INTRODUCTION. [^Part I, 
 
 tion. For tliougli it ma^ so happen that the Subject and the 
 Predicate may be of equal extent [or ' equivalent ; ' or as 
 some express it, ' convertible/] so that the Predicate which is 
 affirmed of that Subject could not have been affirmed of any- 
 thing else, this is not implied in the expression of the proposi- 
 tion itself. 
 
 In the assertions, for instance, that ' every equilateral trian- 
 gle is equiangular,' and that ' any two triangles which have all 
 the sides of one equal to all the sides of the other, each to 
 each, are of equal areas,' it is not implied that ' every equian- 
 gular triangle is equilateral,' or that ' any two triangles of 
 equal areas have their respective sides equal.' This latter in- 
 deed is not true : the one preceding it is true ; that is, it is 
 true that ' every equiangular triangle is equilateral,' as well 
 as that ' every equilateral triangle is equiangular : ' but these 
 are two distinct propositions, and are separately proved in 
 treatises of Geometry.** 
 
 If it happen to be my object to assert that the Predicate as 
 well as the subject of a certain affirmative proposition is to 
 be understood as distributed — and if I say, for instance, ' all 
 equilateral triangles, and no others, are equiangular,' — I am 
 asserting, in reality, not one proposition, merely, but two. 
 And this is the case whenever the proposition I state is under- 
 stood (whether from the meaning of the words employed, or 
 from the general drift of the discourse) to imply that the 
 whole of the Predicate is meant to be affirmed of the Sub- 
 ject. 
 
 Thus, if I say of one number — suppose 100 — that it is 
 the Square of another, as 10, then, this is understood by every 
 one, from his knowledge of the nature of numbers, to imply, 
 what are, in reality, the two propositions, that ' 100 is the 
 Square of 10,' and also that Hhe Square of 10 is 100.' 
 
 Terms thus related to each other are called in technical 
 language, ' convertible ' [or ' equivalent '] terms. But then, 
 
 i 
 
Lesson v.] conyektible terms. 39 
 
 you are to observe that when you not only affirm one term of 
 another, but also affirm (or imply) that these are ' ^onvertiUe* 
 terms, you are making not merely one assertion, but two, 
 
 § 5. It appears, then, that in affirming that ' X is Y,' I as- 
 sert merely that VY ' — either the whole of it, or part^ (it is not 
 declared^ which) is applicable to ' X ; ' [or ' comprehends,' or 
 * contains ' X.] Consequently, if any part of a certain Pre- 
 dicate be applicable to the Subject, it must be affirmed, — 
 and of course cannot he denied — of that Subject. To deny 
 therefore the Predicate of the subject, must imply that no part 
 of the Predicate is applicable to that Subject; in short that 
 the whole Predicate is denied of that Subject. 
 
 You may thus perceive that to assert that ' X is not Y ' is 
 to say that no part of the term ^ Y ' is applicable to ' X : ' (for 
 if any part were applicable, ' Y ' could be affirmed, and not 
 denied, of ' X ') in other words, that the whole of ' Y ' is de- 
 nied of 'X;' and that consequently 'Y' is distributed.' 
 "When I say, for instance, ' All the men found on that island 
 are sailors of the ship that was wrecked there,' this might be 
 equally true whether the whole crew or only some of them, 
 were saved on the island. To say therefore that ' the men 
 found on that island are not sailors of the ship, &c.' would be 
 to deny that any part of that crew are there ; in short, it 
 would be to say that the whole of that Predicate is ^?^applica- 
 ble to that subject. 
 
 § 6. And this holds good equally whether the negative pro- 
 position be ' universal ' or ' particular.' For to say that ' some 
 X is not Y ' (or — which is the same in sense — that ' all X 
 is not Y ') is to imply that there is no part of the term ' Y ' 
 [no part of the class which ' Y ' stands for~\ that is applicable 
 to the whole without exception, of the term ' X ; ' in short, that 
 there is some part of the term 'X' to which ^ Y' is wholly in- 
 applicable. 
 
 Thus, if I say, ' some of the men found on that island ai'c 
 
40 ANALYTICAL INTRODUCTION. \^Part I. 
 
 not sailors of the ship that was wrecked there/ or, in other 
 words, ' the men found on that island are not^ all of them, 
 sailors of the ship, &c.' I imply that the term ' sailors, &c.' is 
 wholly inapplicable to some of the ' men on the island ; ' though 
 it might perhaps be applicable to others of them. 
 
 Again if I say ' some coin is made of silver,' and ' some 
 coin is not made of silver ' (or in other words, that ' all coin 
 is not made of silver ') in the former of th^se propositions I 
 imply, that in some portion (at least) of the Class of ' things 
 made of silver,' is found [or comprehended] ' some coin : ' 
 m the latter proposition I imply that there is ' some coin ' 
 which is contained in no portion of the Class of ' things made of 
 silver ; ' or (in other words) which is excluded from the whole 
 of that Class. So that the term 'made of silver' is distribut- 
 ed in this latter proposition, and not, in the former. 
 
 Hence may be understood the rule above given, that in all 
 Affirmative-propositions the Predicate is undistributed, and in 
 all Negative-propositions, is distributed. 
 
 The ' Subject' is, as we have seen above, distributed, in a 
 Universal-proposition, (whether affirmative or negative,) and 
 not in a Particular. So that the distribution or non-distribu- 
 tion of the Subject depends on the ' Quantity ' of the proposi- 
 tion, and that of the Predicate on the ' Quality.' 
 
 LESSON VI. 
 
 § 1. The next thing to be learnt and remembered, is the 
 names of the three Terms that occur in a Syllogism. For 
 you will have perceived from the foregoing examples, that 
 there are always three terms ; which we have designated by , 
 
ZeSS07l VI.] TERMS OF A SYLLOGISM. 41 
 
 the Symbols X, Y, and Z. Each Syllogism indeed has, in all, 
 three Propositions ; and every Proposition has two Terms ; 
 but in a Syllogism each term occurs twice ; as, ^ X is Y, Z is 
 X; therefore Z is Y.' 
 
 Of these three terms, then, that which is taken as the Sub- 
 ject of the Conclusion (^ Z ') is called the ' Minor-term ; ' the 
 Predicate of the Conclusion [' Y '] is called the 'Major-term ; ' 
 (from its being usually of more extensive signification than 
 the ' Minor,' of which it is predicated) and the Term [_' X '] 
 which is used for establishing the connexion between those 
 two, is thence called the ' Middle-term^ [or ' medium of proof ,^'] 
 
 Of the two Premises, that which contains the Major-term, 
 {' X is Y,') is called the ' Major-premise ; ' (and it is, proper- 
 ly, and usually, placed first ; though this order is not essen- 
 tial) and that which contains the Minor-term (Z is X) is call- 
 ed the 'Minor-premised And in these two Premises, respect- 
 ively, the Major-term and Minor-term are, each, compared 
 with the Middle-term, in order that, in the Conclusion, they 
 may be compared with each other; that is, one of them 
 affirmed or denied of the other. 
 
 § 2. Now it is requisite^ as you will see by looking back to 
 the examples formerly given, that, in one or other of the 
 Premises, the Middle-term should be distributed. For if each 
 of the Terms of the Conclusion had been compared only wdth 
 part of the Middle-term, they would not have been both com- 
 pared with the same ; and nothing could thence be inferred. 
 
 Thus, in one of the above examples, w^hen we say ' food ' 
 (namely, 'some food,') ^is necessary to life,' the term ^food' 
 is undistributed, as being the Subject of a Particular-proposi- 
 tion : in other words, we have affirmed the term ' necessary to 
 life,' of part only, not the wliole^ of the Class denoted by the 
 term ' food : ' and again, when we say ' corn is food,' the term 
 ^ food ' is again undistributed, (according to the Rule given in 
 
 the last Lesson) as being the Predicate of an Affij-mative : — 
 
 4* 
 
42 ANALYTICAL INTKODUCTION. Part I. 
 
 in other words, though we have asserted that the term ' food 
 is applicable to ' corn/ we have not said (nor, as it happens, is 
 it true) that it is not applicable to anything else ; so that we 
 have not been taking this term ' food ' universally, in either 
 Premise, but, each time, ^particularly.' And accordingly 
 nothing follows from those premises. 
 
 So also, when it is said, ' a wise ruler endeavors to civilize 
 the People ; and Alfred endeavored to civilize the People ; ' 
 [or ' Y is X, and Z is X,'] the Middle-term is here twice 
 made the Predicate of an Affirmative-proposition, and con- 
 sequently is left undistributed, as in the former instance; 
 and, as before, nothing follows. For, (as was formerly 
 observed) we are not authorized to affirm one term of 
 another, merely on the ground that there is something which 
 has been affirmed of each of them : as the term ' growing ' 
 (in the example formerly given) is affirmed of ' vegetables ' 
 and also of ' animals.' 
 
 In each of these cases, then, such an apparent-argument is 
 condemned on the ground that it ^ has the middle-term undis- 
 tributed.^ 
 
 § 3. The other kind of apparent Syllogism formerly given 
 as an example, is faulty (as was then shown) from a different 
 cause, and is condemned under a different title. ' Every tree 
 is a vegetable ; grass is not a tree, therefore it is not a vege- 
 table : ' or, ' every X is Y ; Z is not X ; therefore Z is not Y.' 
 
 Here, the middle-term ' X ' is distributed ; and that, not 
 only in one Premise, but in both ; being made, first, the sub- 
 ject of a Universal-proposition, and again, the Predicate of a 
 Negative. But then, the Major-term, 'Y' which has not 
 been distributed in the Premise, is yet distributed in the Con- 
 clusion ; being, in the Premise, the Predicate of an Affirma- 
 tive, and in tlie Conclusion, of a Negative, We have therefore 
 merely compared part of the term [^ Y '] ' vegetable ' with 
 the Middle-term ' Tree ; ' [^ X '] and this does not authorize 
 
Lesson yi.] terms of a syllogism. 43 
 
 our comparing, in the Conclusion, the whole of that same term 
 with [Z] ' grass ; ' which, as was explained above, we must 
 do, if we deny the term ' grass' of a Vegetable/ 
 
 Nothing therefore follows from the Premises: for it is 
 plain that they would not warrant an affirmative Conclusion. 
 To affirm that ' grass is a vegetable,' (or, as one might equally 
 well, that, ' a house is a vegetable,' because it ' is not a tree,' 
 would not have even any appearance of Reasoning. No one 
 would pretend to affirm one term of another (as, Y, of Z) on 
 the ground that it had been affirmed of something (^ X ') 
 which had been denied of that other. 
 
 Such a fallacy as the one we have been above considering, 
 is condemned as having what is called in technical language, 
 an • illicit process ; ' that is, an unauthorized proceeding^ from 
 a term, w/zdistributed in the Premise^ to the same term, dis- 
 trihuted^ in the Conclusion : or, in other w^ords, taking a 
 term more extensively in the Conclusion than it had been 
 taken in the Premise ; which is, in fact, introducing an ad- 
 ditional term. 
 
 § 4. The examples that have been all along given, both of 
 correct-reasoning and of Fallacy, have been, designedly, the 
 simplest and easiest that could be framed. And hence, a 
 thoughtless reader, observing that the rules given, and the tech- 
 nical language employed, though not difficult to learn, are yet 
 less easy than the examples themselves to which these are ap- 
 plied, may be apt to fancy that his labor has been wasted ; and, 
 to say, ' w4iy, common-sense would show any one the sound- 
 iHess of the reasoning, or the unsoundness, in such examples 
 'as these, with less trouble than it costs to learn the rules, and 
 jjihe technical terms.' 
 
 I ■ And a beghmer in Arithmetic might say the same. For, 
 (the examples usually set before a learner, are, purposely, such 
 'easy questions as he could answer ' in his head ' (as we say) 
 I with less trouble than the arithmetical rules cost him. But 
 
44 ANALYTICAL INTRODUCTION. [^Part I.j 
 
 then, by learning those rules, through the means of such sim-' 
 pie examples, he is enabled afterwards to answer, with little 
 difficulty, such arithmetical questions as would be perplexing 
 and laborious, even to a person of superior natural powers, 
 but untaught. 
 
 It is the same, in the learning of a foreign Language. Tlie 
 beginner has to bestow more pains on the translating of a few 
 simple sentences, than the matter of those sentences is worth. 
 But in the end he comes to be able to read valuable books 
 in the Language, and to converse with intelligent foreigners, 
 which he could not otherwise have done. 
 
 And so also, in the present case, it will be found that, sim- 
 ple as are the examples given, not only all valid Reasoning, 
 on whatever subjects, may be exhibited, and its validity shewn, 
 in the form that was first put before you, but also, most of the 
 Sophistical-arguments, [Fallacies] by which men are every 
 day misled, on the most important subjects, may be reduced 
 into the same forms as those of the examples lately given. 
 
 Hume's argument against Miracles, as believed on Testimo- 
 ny , which was explained in a former Lesson, is an instance of 
 this. And numberless others might be given. 
 
 § 5. For example, there is an erroneous notion commonly 
 to be met with, which is founded on a fallacy that may be thus 
 exhibited as a case of undistributed middle-term : ' A man j 
 who is indifferent about all religion, is one who does not seek 
 to force his religion on others ; ' (for though this is far from 
 being universally true^ it is commonly believed) ' this man does 
 not seek to force his religion on others ; therefore he is indif- 
 ferent to all religion.' 
 
 Again, as an example of the other kind of fallacy above- 
 mentioned, the * illicit process' of the Major-term, we may 
 exhibit in that form the sort of Eeasoning by which one may i 
 suppose the Priest and Levite, in the Parable of the good Sa-| 
 maritan, to have satisfied themselves that the poor wounded! 
 
Lesson vi.] common fallacies. 45 
 
 stranger had no claim on them as 2i neighbor ; — a kind ol 
 procedure of which one may find instances in real life in all 
 times ; 
 
 ' A kinsman or intimate acquaintance has a claim to our 
 neighborly good-offices : tliis man, however, is not a kinsman, 
 &c., therefore he has no claim, &;c.' Again ' A Nation which 
 freely admits our goods, ought to be allowed freely to supply., 
 us with theirs : but the French do not freely admit our goods: 
 therefore, &c.' Again, ' Nations that have the use of money, 
 and have property in land, are subject to the evils of avarice, 
 of dishonesty, and of abject poverty ; but savage nations have 
 not the use of money, &c. &c.' 
 
 And again, ' A kind and bountiful landlord ought to be ex- 
 empt from lawless outrage ; but this man is not a kind and 
 bountiful landlord ; therefore, &c.' 
 
 It will be found a very useful exercise to select for yourself 
 a number of other arguments, good or bad, such as are com- 
 monly to be met with in books or conversation, and to reduce 
 them to the most regular form they wdll admit of, in order to 
 , try their validity by the foregoing rules. 
 
 You must keep in mind, however, (what was said in the first 
 
 Lesson) that technical terms and rules will be rather an in- 
 
 ; cumbrance than a help, unless you take care not only to un- 
 
 ' derstand them thoroughly, but also to learn them so perfectly 
 
 ' that they may be as readily and as correctly employed as the 
 
 ■ names of the most familiar objects around you. 
 
 j But if you take the trouble to do this once for all., you will 
 
 '. find that in the end much trouble will have been saved. For, 
 
 y the explanations given of such technical-terms and general 
 
 I rules, when thoroughly learnt, once, will save you the necessi- 
 
 ty of going through nearly the same explanation over and over 
 
 again on each separate occasion. 
 
 In short, the advantage of technical terms is just like wliat 
 
46 ANALYTICAL INTRODUCTION. [_Part I 
 
 we derive from the use of an?/ other Common-terms.* When, 
 for instance, we have once accurately learnt the definition of 
 a ' Circle/ or have had fully described to us what sort of a 
 creature an ' Elephant ' is, to say * I drew a Circle,' or ' I saw 
 an Elephant,' would be sufficiently intelligible, without any 
 need of giving the description or definition at full length, over 
 and over again, on every separate occasion. 
 
 LESSON vn. 
 
 § 1. We have seen that all sound Reasoning consists in 
 referring that of which we would (in the conclusion) affirm or 
 deny something, to a Class, of which that affirmation or denial 
 may be made. Now, ^ the referring of anything to a Class,' 
 means (as you will perceive on looking back to the examples 
 that have been given) to orffirm of it a Term denoting a Class ; 
 which Term, you will have observed, is the Middle-term of 
 the Syllogism. 
 
 We are next led, therefore, to inquire what terms may be 
 affirmatively predicated of what others. 
 
 It is plain that a proper-name, or any other term that stands 
 for a single individual, cannot be affirmed of anything except 
 that very individual. For instance, ' Romulus ' — the 
 ' Thames ' — ' England ' — ^ the founder of Rome ' — ' this riv- 
 er,' &c., denoting, each, a single object, are thence called ' Sin- 
 gular-terms : ' and each of them can be affirmed of that single 
 object only, and may, of course, be denied of anything else. 
 
 When we say ' Romulus was the founder of Rome,' we 
 
 ^ This will be more fully explained in the subsequent Lessons. 
 
Lesson vii.] common-terms. 47 
 
 mean that the two terms stand for the same individual. And 
 such is our meaning also when we affirm that ' this river is 
 the Thames.' 
 
 On the other hand, those terms which are called ' Common * 
 (as opposed to ' Singular ') from their being capable of stand- 
 ing for any, or for every, individual of a Class, — such as 
 ' man,' ' river,' ' countiy ' — may of course be affirmed of 
 whatever belongs to that Class : as, ' the Thames is a river ; ' 
 * the Rhine and the Ganges are rivers.' 
 
 And observe, that throughout these Lessons we mean by a 
 ' Class ' not merely a Head or general-description to which 
 several things are actually referred, but one to which an indef- 
 inite number of things mighty conceivably ^ be referred ; name- 
 ly, as many as (in the colloquial phrase) may ' answer to the 
 description^ For instance, we may conceive that when the 
 first-created man existed alone, some beings of a Superior 
 Order may have contemplated him, not merely as a single in- 
 dividual bearing the proper-name ' Adam,' but also (by Ab- 
 straction, which we shall treat of presently) as possessing 
 those attributes which we call, collectively, ' human-nature ; 
 and they may have applied to him a name — such as 'Man' — 
 implying those attributes [that ' description^~\ and nothing 
 else ; and which would consequently suit equally well any of 
 his descendants. 
 
 \ When therefore anything is said to be ' referred to such and 
 ^such a Class,' we mean either what is^ or what might be a 
 ^ Class, comprehending any objects that are 'of a certain de- 
 'scription;' which description (and nothing else) is implied by 
 •the ' Common term,' which is a name of any, or all, of those 
 i objects. 
 
 § 2. A Common-term is thence called (in relation to the 
 "** Subjects ' to which it is applicable) a 'Predicahle ; ' that is, 
 oj^rma^zVeZy-predicable ; from its capability of being affirmed 
 of another Term. 
 
48 ANALYTICAL INTRODUCTION. \_Part I. 
 
 A Singular-term, on the contrary, may be the Subject of a 
 proposition, but not the Predicate : unless of a Negative-^vo- 
 position ; (as ' the first-born of Isaac was not Jacob ') or un- 
 less the Subject and Predicate be merely two expressions for 
 the same individual ; as in some of the examples above. 
 
 You are to remember, however, that a Common-term must 
 be one that can be affirmed of an indefinite number of other 
 terms, in the same sense^ as applied to each of them ; as ' veg- 
 etable,' to ' grass,' and to an ' oak.' For, different as these 
 are, they are both ' vegetables ' in the same sense ; that is, the 
 word ' vegetable ' denotes the same thing in respect to both of 
 them : [or, ' denotes something common to the two.'] 
 
 But there are several proper-names which are borne, each, 
 by many individuals ; such as ' John,' ' William,' &c., and 
 which are said to be, (in ordinary discourse) very common 
 names ; that is, \evj frequent. But none of these is what we 
 mean by a ' Common-term ; ' because, though applied to sev- 
 eral persons, it is not in the same sense, but always, as denot- 
 ing in each case, one distinct individual. 
 
 If I say ' King Henry was the conqueror at Agincourt,' 
 and, ' the conqueror of Richard the Third was King Henry,' 
 it is not in sense one term, that occurs in both those proposi- 
 tions. But if I say, of each of these two individuals, that he 
 was a ' King,' the term ' King ' is applied to each of them in 
 the same sense. 
 
 § 3. A Common-term, such as ' King,' is said to have sev- 
 eral ' Signijicates ; ' that is, things to which it may be applied : 
 but if it be applied to every one of these in the same sense, 
 [or denotes in each of them the same thing] it has but one 
 ' signification^ And a Common-term, thus applied, is said to ' 
 be employed ^ univocally.' 
 
 If a term be used in several senses, it is, in meaning, not 
 one term only, but several. Thus, when ^ Henry ' (or any 
 Other such name) is applied to two individuals to denote, in 
 
 I 
 
Lesson vii.] common terms. 49 
 
 each case, tJmt one distinct person, it is used not as 07ie term, 
 but as two ; and it is said to be aj^plied to those two, ' equivo- 
 cally.^ 
 
 The like often occurs in respect of Common-terrns also ; 
 that is, it often happens that one word or phrase, will be not 
 merely one but several Common-terms. 
 
 Take, for example, the word ' Case,' used to signify a kind 
 of ' covering ; ' and again (in Grammar) an inflection of a 
 noun ; (as ' him ' is the accusative [or objective] ca^e of 'he') 
 and again, a ' case ' such as is laid before a lawyer. This 
 word is, in sense, three ; and, in each of the three senses may 
 be applied ' univocally ' to several thmgs which are, in that 
 sense, signified by it. But w^hen applied to a hox and to a 
 grammaiical case^ it is used ' equivocally.' 
 
 § 4. That process in the mind by which we are enabled to 
 employ Common-terms, is what is called ' Greneralization ; ' 
 Common-terms being often called also ' Ce^ieraZ-terms 
 
 When, in contemplating several objects that agree in some 
 point, w^e ' abstract ' [or draw off'\ and consider separately, 
 that point of agreement, disregarding everything w^herein they 
 differ, w^e can then designate them by a Common-term, appli- 
 cable to them, only in respect of that which is ' common ' to 
 them all, and which expresses nothing of the differences be- 
 tw^een them. And w^e obtain in this way either a term de- 
 noting the individuals themselves thus agreeing considered in 
 respect of that agreement, (which is called a concrete-doxmviow- 
 term) or again, a term denoting that circumstance itself ivliere- 
 liw they agree ; which is called an a^s^rac^-common-term. 
 I Thus we may contemplate in the mind several different 
 I* kings ; ' putting out of our thoughts the name and individual 
 .character, of each, and the times and places of their reigns, 
 land considering only the regal Office wdiich belongs to all and 
 'each of them. And we are thus enabled to designate any or 
 tvery one of them by the 'common' [or general] term, 
 5 
 
50 ANALYTICAL INTRODUCTION. \_Part I. 
 
 ' king/ or again, by the term ' royalty ' we can express the 
 circumstance itself which is common to them. And so in the 
 case of any other common-term. 
 
 The 'Abstraction' which here takes place, is so called from 
 a Latin-word originally signifying to ' draw off;' because we 
 separate, and as it were, draw off, in each of the objects be- 
 fore us, that point, — apart from every other, — in which they 
 are alike. 
 
 It is by doing this, that ' Generalization ' is effected. But 
 the two words have not the same meaning. For though we 
 cannot ' generalize ' without ' abstracting^ we may perform , 
 Abstraction without Generalization. ^ 
 
 § 5. If, for instance, any one is thinking of ' the Sun,' with- 
 out having any notion that there is more than one such body 
 in the Universe, he may consider it without any reference to 
 its jplace in the sky , whether rising, or setting, or in any other 
 situation ; (though it must he always actually to some situ- 
 ation) or again he may be considering its heat alone, without 
 thinking of its ligJd; or of its light alone ; or of its apparent mog^ 
 nitude, without any reference either to its light or heat. Now 
 in each of these cases there would be Abstraction ; though 
 there would be no Generalization^ as long as he was contem- 
 plating only a single individual ; that w^hich w^e call the 
 ' Sun.' 
 
 But if he came to the belief (which is that of most Astro* 
 nomers) that each of the Jixed Stars is a body affording light 
 and heat of itself, as our Sun does, he might then, by abstract- 
 ing this common circumstance, apply to all and each of these 
 (the Sun of our System, and the Stars) one common-term de- 
 noting that circumstance ; calling them all, ' Suns.' And this 
 would be, to ' generalized 
 
 In the same manner, a man might, in contemplating a single I 
 mountain, (suppose, Snowdon) make its height alone, inde- f 
 pendently of everything else, the subject of his thoughts ; or 
 
Lesson Yii.] generalization. 51 
 
 its total hdk ; disregarding its shape, and the substances it is 
 composed of ; or again, its shape alone; and jet while thus 
 abstracting, he might be contemplating but the single indivi- 
 dual. But if he abstracted the circumstance common to 
 Snowdon, Etna, Lebanon, &c., and denoted it by the common- 
 term ' Mountain,' he would then be said to generalize. He 
 would then be considering each, not, as to its actual existence 
 as a single individual, but as to its general character, as being 
 of such a description as would a]3ply equally to some other 
 single objects. 
 
 § 6. Any one of these Common-terms then serves as a 
 "' Sign ' [or Representative] of a Class ; and may be applied 
 to, — that is, affirmed of — all, or any, of the things, it is thus 
 taken to stand for. 
 
 And you will have perceived from the above explanations, 
 that w^hat is expressed by a Common-term is merely an in- 
 adequate — incomplete notion [or ' view ' taken] of an indivi- 
 dual. For if, in thinking of some individual object, you re- 
 tain in your mind all the circumstances (of character, time, 
 place, (fee.,) w^hich distinguish it (or which might distinguish 
 it) from others, — including the circumstance of unity [or 
 singleness] — then any name by w^liich you might denote it, 
 w^hen thus viewed, w^ould be a Shigidar-tevm ; but if you lay 
 aside and disregard all these circumstances, and abstract [con- 
 sider separately] merely the points which are common — or 
 which conceivably might be common — to it w^itli other indi- 
 viduals, you may then, by taking this incomplete view [or 
 I ^ apprehension '] of it, apply to it a name expressing nothing 
 ithat is pecidiar to it; and w^hich consequently will equally 
 , well apply to each of those others ; in short, a Common-term ; 
 J such as those in the above examples. 
 
 I § 7. You are to remember, then, that there is not, in the 
 
 ' case of these ' general ' [or common] Terms, (as there is in 
 
 the case of Siiigular-tevms) some real thiiig corresponding to 
 
52 ANALYTICAL INTRODUCTION. [Fart I. 
 
 each Term, existing independently of the Term, and of which 
 that term is merely the name ; in the same manner as Leb- 
 anon ' is the name of an actually-existing single individual. 
 
 At first sight, indeed, you might imagine that as any ' in- 
 dividual man ' of your acquaintance, or ' Great Britain,' or 
 * the Sun,' &C.5 has an existence in Nature quite independent 
 of the 7iame you call it by, so, in like manner, there must be 
 some one real thing existing in Nature, of which the Common- 
 term ' Man ' or the term ' Island ' is merely the name. 
 
 And some writers will tell you that this thing, which is the 
 subject of your thoughts when you are employing a general- 
 term, is, the • abstract idea ' of Man, of Island, of Mountain, 
 &c. But you will fiijd no one able to explain what sort of a 
 thing any such ' abstract-idea ' can be : w^hich is one thing, 
 and yet not an individual, and which may exist at one and 
 the same time in the minds of several different persons. * 
 
 All the obscure and seemingly-profound disquisitions that 
 you may perhaps meet with, respecting these supposed ' ab- 
 stract ideas ' will but perplex and bewilder you. 
 
 Whether the writers of these disquisitions have themselves 
 understood their own meaning, we need not here inquire. 
 But the simple explanation that has been above given of the 
 origin and use of Common-terms, you wdll be able, with mo- 
 derate attention, clearly to understand. And you will find it 
 quite sufficient for our present purpose. 
 
 § 8. You will perceive from it that the subject of our 
 thoughts when we are employing a Common-term, is, the 
 Term itself, regarded as a ' Sign ; ' namely, a Sign denoting a 
 
 ^ The question here briefly alluded to, and which could not properly 
 be treated of at large in a short elementary work, is that which was at 
 one time fiercely contested, throughout nearly all Europe, between the 
 Two rival sects of Philosophers, the Realists and the Nominalists. 
 
 There are several well known w^orks in which the student may find it 
 fully discussed. — See Whately's Elements of Logic, B. iv. ch. 5. 
 
Lesson viii.] abstract-ideas. 53 
 
 certain inadequate notion formed [or, view taken] of an indi- 
 vidual which in some point agrees with [or ' resembles ' j some 
 other individuals : the notion being, as has been said, ' inade- 
 quate ' or ' incomplete,' inasmuch as it omits all peculiarity 
 that distinguishes the one individual from the others ; so that 
 the same single ' Sign ' may stand equally well for any of 
 them. 
 
 And when several persons are all employing and under- 
 standing the same Common-term in the same sense, and are 
 thence said (as some Writers express it) to have ' one and the 
 same Idea ' at once in the mind of each, this means merely 
 that they are (thus far) all thinking alike; just as several 
 persons are said to be all ' in one and the same posture,^ when 
 they have all of them their limbs placed alike ; and to be of 
 one and the same complexion when their skins are colored 
 alike. 
 
 LESSON vni. 
 
 § 1. It has been shown, how, by taking an inadequate 
 view of an individual, disregarding every point wherein it 
 differs from certain other individuals, and abstracting that 
 wherein it agrees with them, we can then employ a Common- 
 term, as a sign to express all or any of them : and that this 
 process is called ' generalization.' 
 
 It is plain that the same process may be further and fur- 
 ther extended, by continuing to abstract from each of the 
 Classes [or Common-terms] thus formed, the circumstance 
 wherein it agrees with some others, leaving out and dis- 
 regarding the points of difference ; and thus forming a still 
 more general and comprehensive term. 
 5* 
 
54 ANALYTICAL INTRODUCTION. \_Part I. 
 
 From an Id dividual ' Cedar/ for instance, you may arrive 
 in this manner, at the notion expressed by tlie Common-term 
 ' Cedar,' and thence again proceed to the more general term 
 ' Tree,' and thence again, to ' Vegetable,' &c. 
 
 And so, also, you may advance from any ' ten ' objects be- 
 fore you, (for instance, the fingers ; from which doubtless 
 arose the custom of reckoning by tens) to the general-term, — 
 the number ' ten ; ' and thence again, to the more general- 
 term, ' number ; ' and ultimately to the term ' quantity.' 
 
 § 2. The faculty of Abstraction, — at least the ready exer- 
 cise of it in the employment of Signs, [Common-terms] seems 
 to be the chief distinction of the Human Intellect from that 
 of Brutes. These, as is well-known, often display much in- 
 telligence of another kind, in cases where Instinct can have 
 no place : especially in the things which have been taught to 
 the more docile among domesticated animals. But the 
 Faculty of Language^ such as can serve for an Instrument of 
 Reasoning , — that is, considered as consisting of arbitrary 
 general SignSj — seems to be wanting in Brutes. 
 
 They do possess, in a certain degree, the use of Language 
 considered as a mode of communication : for it is well known 
 that horses, and dogs, and many other animals, understand 
 something of what is said to them : and some brutes can 
 learn to utter sounds indicating certain feelings or perceptions. 
 But they cannot, — from their total want, or at least great 
 deficiency, of the power of Abstraction — be taught to use 
 language as an Instrument of Reasoning. 
 
 Accordingly, even the most intelligent Brutes seem in- 
 capable of forming any distinct notion of number : to do 
 which evidently depends on Abstraction. For, in order to 
 count any objects, you must withdraw your thoughts from all 
 differences between them, and regard them simply as units. 
 And accordingly, the Savage Tribes (who are less removed 
 than we are from the Brutes) are remarked for a great defi- 
 
Lesson viii.] deaf-mutes. 55 
 
 ciency in their notions of number. Few of them can count 
 beyond ten, or twenty : and some of the rudest Savages have 
 no words to express any numbers beyond five. 
 
 And universally, it is in all matters where the exercise of 
 Abstraction is concerned, that the inferiority of Savages to 
 CiviHzed men is the most remarkable. 
 
 §. 3. That we do, necessarily, employ Abstraction in order 
 to reason, you will perceive from the foregoing explanations 
 and examples. For you will have observed that there can be 
 no Syllogism without a Common-term. 
 
 And accordingly, a Deaf-mute, before he has been taught a 
 language, — either the Finger-language, or Reading, — can- 
 not carry on a train of Reasoning, any more than a Brute. 
 He differs indeed from a Brute in possessing the mental 
 capability of employing Language ; but he can no more make 
 use of that capability, till he is in possession of some System 
 of arbitrary general-signs, than a person born blind from Cat- 
 aract can make use of his capacity of Seeing, till the Cataract 
 is removed. 
 
 You will find, accordingly, if you question a Deaf-mute who 
 has been taught Language after having grown up, that no 
 such thing as a train of Reasoning had ever passed through 
 his mind before he was taught. 
 
 If indeed we did reason by means of those ' Abstract-ideas ' 
 which some persons talk of, and if the language we used 
 served merely to communicate with other men, then, a person 
 would be able to reason, who had no knowledge of any arbi- 
 trary Signs, But there are no grounds for believing that 
 this is possible ; nor, consequently, that ' Abstract-ideas ' (in 
 that sense of the word) have any existence at all. 
 I You will have observed also, from what has been said, that 
 'the Signs [Common-terms] we are speaking of as necessary 
 jfor the Reasoning-process, need not be addressed to the ear. 
 The signs of the numbers, — the figures 1, 2, 3, 4, &;c., liave 
 
56 ANALYTICAL INTRODUCTION. \_Part I. 
 
 no necessary connexion with sound; but are equally under- 
 stood by the English, French, Dutch, &c., whose spoken lan- 
 guages are quite diiFerent, 
 
 And the whole of the ioritten-\2iHgVi2igQ of the Chinese is of 
 this kind. In the different Provinces of China, they speak 
 different Dialects : but all read the same Characters ; each 
 of which (like the figures 1, 2, 3, &c.) has a sense quite inde- 
 pendent of the sound. 
 
 And to the Deaf-mutes, it must be so with all kinds of 
 Language understood by them ; whether Common Writing, 
 or the Finger-language.* 
 
 * There have been some very interesting accounts published, by tra- 
 vellers in America, and by persons residing there, of a girl named Laura 
 Bridgman, who has been, from birth, not only deaf and dumb, but also 
 blind. She has, however, been taught the finger-language, and even to 
 read what is printed in raised characters, and also to write. 
 
 The remarkable circumstance in reference to the present subject, is, 
 that when she is alone, her fingers an generally observed to he moving, 
 though the signs are so slight and imperfect that others cannot make out 
 what she is thinking of But if they inquire of her, she will tell them. 
 
 It seems that, having once learnt the use of Signs^ she finds the neces- 
 sity of them as an Instrument of thought, when thinking of anything be- 
 yond mere individual objects of sense. 
 
 And doubtless every one else does the same ; though in our case, no 
 one can (as in the case of Laura Bridgeman) see the operation; nor, in 
 general, can it be heard; though some few persons have a habit of occa- 
 sionally audibly talking to themselves ; or, as it is called, ' thinking aloud.^ i 
 But the Signs we commonly use in silent reflection are merely mental 
 conceptions of uttered words : and these, doubtless, are such, as could be 
 hardly at all understood by another, even if uttered audibly. For we 
 usually think in a kind o^ short-hand, (if one may use the expression) like 
 the notes one sometimes takes down on paper to help the memory, which 
 consist of a word or two — or even a letter — to suggest a whole sen- 
 tence ; so that such notes would be unintelligible to any one else. 
 
 It has been observed, also, that this girl when asleep, and doubtless 
 dreaming, has her fingers frequently in motion : being, in fact, talking in 
 her sleep. 
 
Lesson viii.] habits of abstraction. 57 
 
 § 4. By the exercise of Abstraction, (it is to be further re- 
 marked) we not only can spf>arate, and consider apart from 
 the rest, some circumstance oelonging to every one of several 
 individuals before the mind, so as to denote them by a general 
 [' common '] term, — and can alia^by repeating the process, 
 advance to more and more general terms; — but we are also 
 able to fix, arbitrarily, on whatever circumstance we choose to 
 abstract, according to the particular purpose we may have in 
 view. 
 
 Suppose, for instance, it is some individual ^ Building ' that 
 we are considering : in respect of its materials we may refer 
 it to the class (suppose) of ' Stone-buildings,' or of ' wooden,' 
 &c., in respect of its use^ it may be (suppose) a ^ house,' as 
 distinguished from a Chapel, a Barn, &c., in respect of Orders 
 of Architecture^ it may be a ' Gothic-building,' or a ^ Grecian,' 
 &c., in respect of size^ it may be a ' large,' or a ' small build- 
 ing,' in respect of color ^ it may be ' white,' ' red,' ' brown,' &c. 
 
 And so, with respect to anything else that may be the sub- 
 ject of our reasoning, on each occasion that occurs. We arbi- 
 trarly ^:l on, and abstract, out of all the things actually exist- 
 ing in the subject, that one which is important to the purpose 
 in hand. So that the same thing is referred to one Class, or 
 to another, (of all those to which it really is referable) accord- 
 ing to the occasion. 
 
 For instance, in the example above, you might refer the 
 ^ building ' you were speaking of, to the Class [or Predicable] 
 of ' i^^/^e-buildings,' — or even of ^ white-o^>c^5,' — if your 
 purpose were to shew that it might be used as a land-mark ; 
 if you were reasoning concerning its danger from Jire, you 
 might class it (supposing it were of wood) not only with such 
 buildings^ but also with hay-stacks and other combustibles : if 
 the building were about to be sold, idong with, perhaps, not 
 only other buildings, but likewise cattle, land, farming im])le- 
 ments, &c., that were for sale at the same time, the point you 
 
58 ANALYTICAL INTRODUCTION. [^Part I. 
 
 would then abstract would be, its being an article of value. 
 And so, in other cases. 
 
 § 5. You thus perceive clearly that we are not to consider 
 each object as really and properly helonging to and forming a 
 portion of, some one Class only, rather than any other that 
 may with truth be affirmed of it : and that it depends on the 
 'particular train of thought we happen to be engaged in, what 
 it is that is important and proper to be noticed, and what, 
 again, is an insignificant circumstance, and foreign from the 
 question. 
 
 But some persons, who have been always engaged in some 
 one pursuit or occupation, without attending to any other, are 
 apt to acquire a narrow-minded habit of regarding almost 
 everything in one particular point of view ; that is, consider- 
 ing each object in reference only to their own pursuit. 
 
 For instance, a mere Botanist might think it something ' 
 strange and improper, if he heard an Agriculturalist classing 
 together, under the title of ' artificial grasses,^ such plants as 
 Clover, Tares, and Ryegrass : which, botanically, are widely 
 different. And the mere Farmer might no less think it 
 strange to hear the troublesome ' weed ' (as he has been used 
 to call it) that is known by the name of ' Couch-grass,' ranked 
 by the Botanist as a species of ' wheat,' the ' Triticum 
 repens,' the farmer having been accustomed to rank it along 
 with ' nettles and thistles,' with which it has no botanical 
 connexion. 
 
 Yet neither of these classifications [or ' generalizations '] 
 would be, in itself, erroneous and improper : though it would j 
 be improper, in a Work on Natural- History to class plants I 
 according to their agricultural uses ; or, in an Agricultural ; 
 Treatise, to consider principally (as the Botanist does) the 
 structure of their flowers. 
 
 So also, it would be quite impertinent to take into considera- 
 tion a man's learning or ability, if the question were as to the 
 
Lesson VIII. habits of abstraction. 59 
 
 allowance of food requisite for his support ; or his stature, if 
 you were inquiring into his qualifications as a statesman ; or 
 the amount of his property, if you were inquiring into his 
 state of health ; or his muscular strength, if the question were 
 as to his moral character : though each of these might he im- 
 portant in reference to a different inquiry. 
 
 The great importance of attending to these points, you will 
 easily perceive hy referring to the analysis of Reasoning 
 which has been above given. For as the proving of any 
 Conclusion consists in referring that of which something is to 
 be affirmed or denied, to a Class [or Predicable] of which 
 that affirmation or denial can be made, our ability in Reason- 
 ing must depend on our power of abstracting correctly, clearly, 
 and promptly from the subject in question, that which may 
 furnish a ' middle-term ' suitable to the occasion. 
 
PART 11. 
 COMPENDIUM, 
 
 LESSON IX. 
 
 § 1. We have now gone through, in the way of a slight 
 sketch, the Analysis of Reasoning. To analyse (as has been 
 already explained) means to ' take to pieces,' so as to resolve 
 anything into its elements, [or component-parts.] Thus a 
 Chemist is said to ' analyse ' any compound substance that is 
 before him, when he exhibits separately the simpler substan- 
 ces it is composed of, and resolves these again into their 
 elements. And when, again, he combines these elements into 
 their compounds, and those, again, into further compounds — 
 thus reversing the former process (which is called the ' ana- 
 lytical ') he is said to be proceeding synthetically : the word 
 * Synthesis ' — which signifies ' putting together,' — being the 
 opposite of ' Analysis.' 
 
 Accordingly, it has been shown in the foregoing Lessons 
 that every train of Argument being capable of being ex- 
 hibited in a Series of Syllogisms, a Syllogism contains three 
 Propositions, and a Proposition, two Terms. And it has been 
 shewn how ' Common-terms ' (which are indispensable for 
 Reasoning, are obtained by means of Abstraction from Indi- 
 vidual objects. 
 
 This analytical method is the best suited for the first intro- 
 duction of any study to a learner ; because he there sees, from 
 the very beginning, the practical application of whatever is 
 taught. But the opposite method — the synthetical — is the 
 
Lesson ix.] system of rules. 61 
 
 more convenient for storing up in the mind all that is to be 
 remembered. 
 
 We shall therefore now go over great part of the same 
 ground in a reversed order ; merely referring to such things 
 as have been already taught, and adding such further rules, 
 and explanations of additional technical-terms, as may be 
 needed. 
 
 § 2. The act of the mind in taking in the meaning 
 of a Term, is called, in technical language, the act [or 
 ^operation'] of ^Simple-apprehension;' that is ' mere-ajy-pve- 
 hension,' [or 'apprehension-only.'] When a Proposition is 
 stated — which consists, as we have seen, of two terms, one 
 of which is affirmed or denied of the other, — the ' operation ' 
 [or ' act ' j of the mind is technically called ' Judgment.' And 
 the two Terms are described in technical language, as ' com- 
 pared ' together, and as ' agreeing ' or as ' disagreeing,' accord- 
 ing as you affirm, or denT/, the one, of the other. 
 
 When from certain Judgments you proceed to another 
 Judgment resulting from them, — that is, when you infer [or 
 deduce] a Proposition from certain other Propositions — this 
 * operation ' is called ' Keasoning,' or ' Argumentation,' or (in 
 the language of some writers) ' Discourse.' 
 
 And these are all the mental operations that we are at pres- 
 ent concerned with. 
 
 Each of these operations is liable to a corresponding defect : 
 namely ' Simple-apprehension ' to indistinctness, ' Judgment,' 
 to falsity, and ' Reasoning ' to inconclusiveness ; [or falla- 
 cioueness.] And it is desirable to avail ourselves of any 
 rules and cautions as to the employment of language, that may 
 serve to guard against these defects, to the utmost degree tliat 
 )is possible : in other words, to guard, by the best rules we 
 jean frame, against Terms not conveying a distinct meaning ; 
 ^^ against /a^5e Propositions mistaken for true, — and against 
 apparent-arguments [or ' Fallacies ; ' or ' Sophisms '] which 
 6 .. - 
 
62 COMPENDIUM. \_Part II. 
 
 are in reality inconclusive^ though likely to be mistaken for 
 real [valid] arguments. 
 
 And such a System of Eules*, based on a scientific view of 
 the Reasoning-process, and of every thing connected with it, 
 is what the ancient Greeks, among whom it originated, called 
 the ' Dialectic-art ; ' from a word signifying to ' discourse on,' 
 or ' discuss' a subject. 
 
 § 3. You are to observe, however, two important distinc- 
 tions in reference to the above-mentioned defects : 1st, you 
 are to remember that which is, really , a Term, may be indis- 
 tinctly apprehended by the person employing it, or by his 
 hearer ; and so also, a Proposition which is false, is not the 
 less a real Proposition : but, on the other hand, any expres- 
 sion or statement which does not really prove anything, is not^ 
 really, an Argument at all, though it may be brought forward 
 and passed off as such. 
 
 2dly. It is to be remembered that (as it is evident from 
 what has been just said) no rules can be devised that will 
 equally guard against all three of the above-mentioned defects. 
 
 To arrive at a distinct apprehension of everything that may 
 be expressed by any Term whatever, and again, to ascertain 
 the truth or falsity of every conceivable Proposition, is mani- 
 festly beyond the reach of any system of rules. But, on the 
 other hand, it is possible to exhibit any pretended Argument 
 whatever in such a form as to be able to pronounce decisively 
 on its validity or its fallaciousness. 
 
 So that the last of the three defects alluded to (though not 
 the two former) may be directly and completely obviated by 
 the application of suitable rules. But the other two defects 
 can be guarded against (as will presently be shown) only in-^ 
 
 directly, and to a certain degree. I 
 
 . -Ij 
 
 ^ YoTi are to observe that a Science, properly, consists of general truihs'l 
 that are to be known : an Art, of practical rules for something that is to j 
 be done. 
 
 i 
 
Lesson ix.] the * dialectic art.' 63 
 
 In other words, rules may be framed that will enable us to 
 decide, what is, or is not, really a ' Term,' — really, a ' Prop- 
 osition,' — or really an ' Argument : ' and to do this, is to guard 
 completely against the defect of inconclusiveness ; since nothing 
 that is inconclusive, is, really, an ' Argument ; ' though that 
 may be really a ' Term ' of which you do not distinctly appre- 
 hend the meaning ; and that which is really a ' Proposition^ 
 may be sl false Proposition. 
 
 § 4. When two Terms are brought together (or ^ compared,' 
 as some express it) as Subject and Predicate of a Proposition, 
 they are (as was above remarked) described in technical lan- 
 guage, as ' agreeing ' or ^ disagreeing,' according as the one is 
 a£irmed or denied^ of the other. 
 
 This ' agreement,' however, does not (you are to obser^'e) 
 mean coincidence ; [or that the two terms are ' equivalent '] 
 for when I say ' Every X is Y,' or ^ Every Sheep is a rumi- 
 nant-animal,' this does not mean * X is equivalent to Y ; ' [or 
 ' X ' and ' Y ' are terms of equal extent'] indeed we know that 
 ' ruminant-animal ' is in fact a term of greater extent than 
 ' sheep ; ' including several other species besides. We only 
 mean to assert that it is a Class [or Predicable] comprehend- 
 ing under it, at least, the term ' Sheep ; ' but whether it does 
 or does not comprehend anything else besides, the proposition 
 before us does not declare. 
 
 Hence it is that (as was formerly explained) the Predicate 
 of an Affirmative-Y^YO-i^o^iiiow is considered as undistnhuted : 
 the Subject being compared with part at least of the Predi- 
 cate, and asserted to ' agree ' with it ; but whether there be, 
 or be not, any other part of the Predicate which does not 
 agree with that Subject, is not declared in the proposition 
 itself. 
 
 There are, it is to be observed, two apparent exceptions to 
 this rule : 1st, the case of a Proposition which gives a Defini- 
 tion of anything ; as when I say ' a triangle is a three-sided 
 
64 COMPENDIUM. [Part ii. 
 
 figure ; ' which would not be a correct definition^ unless it 
 were also true that ' every three-sided figure is a triangle ; ' 
 and 2dly by the case of an affirmative-Proposition, where 
 both terms are singular, and denote of course one and the 
 same Individual ; as ' Ishmael was the first-born of Abraham.' 
 
 In both these cases the Subject and Predicate are, in each 
 proposition, what are called ' convertible ' [or ' equivalent '] 
 terms. But then, to assert or imply both that a certain af- 
 firmative-proposition is true^ and also that its terms are equiv*^ 
 alent^ is to make (as was formerly remarked) not merely one, 
 but two assertions. 
 
 Now if I am understood to mean not only that it is true 
 that ' a triangle is a three-sided figure,' but also that this is the 
 definition of a ' triangle,' then, I am understood as making 
 two assertions ; that not only ' every triangle is a three-sided 
 figure,' but also that ' every three-sided figure is a triangle.' 
 But this is understood not from the Proposition itself, looking 
 to the form of expression alone, but from what we know, or 
 think, respecting the sense of the Terms themselves, or fro-n 
 what we suppose the speaker to have intended by those 
 Terms. For, all that is implied in the mere form of an 
 affirmative-proposition, — as ' X is Y ' — is simply that some 
 part at least of the term ' Y ' (whatever that Symbol may 
 stand for,) is pronounced to agree with the term ' X.' 
 
 § 5. And a like explanation will apply in the other case 
 also. If I understand from the sense of the terms in some 
 affirmative-proposition, that the Subject and the Predicate 
 are each a Singular-term, (denoting, of course, one and the 
 same individual) — as ' Ishmael was the first-born of Abra- 
 ham,' then I understand, as implied by the meaning of the 
 words (though not by the form of the Proposition) another 
 proposition also ; namely, that ' the first-born of Abraham was 
 Ishmael.' In short, it is from my knowledge of the sense of 
 the terms themselves that I understand them to be ' convert- 
 
Lesson ix.] convertible teems. ^ 
 
 ible ' [or equivalent] terms. For you may observe tliat a 
 Singular-term must, from its own nature, correspond to a 
 Common term taken universally ^ [or, ' distributed J inasmuch 
 as it cannot hut stand for the whole (not merely some part) of 
 that which it denotes. 
 
 In such cases as the above, then, that which is expressed as 
 one proposition, is so understood from the meaning of the 
 words as in reality to imply two. And there is, therefore, no 
 real exception to the rule, that an Affirmative-proposition 
 does not, hy the form of the expression^ distribute its Predicate. 
 
 § 6. That which pronounces the agreement or disagreement 
 of the two Terms of a Proposition [or which make it affirma- 
 tive or negative'] is called, as has been above said, the ' Cop- 
 ula.' And this is always, in sense, either ^ is ' or 'is not.' 
 For every Verb, except what is called the ' Substantive-verb ' 
 to ' be,' contains something more than a bare assertion of the 
 agreement or disagreement of two terms. It always contains 
 in it the Predicate (or part of the Predicate) also. 
 
 Thus, the proposition 'it rains' (which in Latin would 
 be expressed by the single word 'pluit') is resolved 
 
 Siibj. Cop. Prod. 
 
 into ' Pain — is — falling ; ' or in some such way. ' Jolm 
 
 Siibj. Cop. 
 
 owes William a pound,' is resolved into ' John — is — 
 
 owing [or indebted to] William, a pound.' And so in all such 
 cases. 
 
 Sometimes, indeed, even the Substantive-verb itself is both 
 Copula and Predicate ; namely, where existence alone is 
 affirmed or denied ; as ' God is ; ' ' one of Jacob's sons is not * ; ' 
 in which cases ' existing ' is the Predicate. 
 
 You are to observe that the Copula has in itself no rela- 
 tion to time. If, therefore, any other tense besides the Present, 
 
 "^ Gen. 42. xiii. 
 6* 
 
66 COMPENDIUM. \^Part i. 
 
 of the Substantive-verb, is used, it is to be understood as the 
 same in sense with the Present, as far as the assertion is con- 
 cerned ; the difference of tense being regarded (as well as the 
 person and number) merely as a matter of grammatical pro- 
 priety : unless it be where the circumstance of time really does 
 affect the sense of the proposition. And then, this circum- 
 stance is to be regarded as part of one of the Terms ; as, ' this 
 man was honest;' that is, ^he is one formerly -honest J In 
 such a case, an emphasis, with a peculiar tone, is laid on the 
 word ^ was.^ 
 
 An Infinitive, you are to observe, is not a Verb, (since it 
 can contain no affirmation or denial) but a verbal-noun-sub- 
 stantive. And a Participle again, is a verbal-adjective. 
 
 A Participle, or any other Adjective, may be made a Pred- 
 icate, but not (by itself) a Subject of a proposition ; as ' this 
 grass is green,' ' that grass is mown.' 
 
 An Infinitive, though generally placed (in English) at 
 the end of a sentence, is almost always (when it is by 
 itself a Term) the Subject ; as 'I like to ride ; ' that is> 
 
 Sub. ... . ^^^^• 
 
 ^ To ride ' [or ' riding '] is — a thing I like.' 
 
 And observe that there is, in English, an Infinitive in ^ ing^ 
 the same in sound with the Participle, but different in sense. 
 When I say, ' Piding ' [or ' to ride '] ' is pleasant,' and again 
 nhat man is riding,' in the former sentence the w^ord 'riding' 
 is a Substantive, and is the Subject ; in the latter it is an 
 Adjective [Participle] and is the Predicate. 
 
 One Infinitive, however, is sometimes predicated of another 
 Infinitive ; as, ' seeing is believing ; ' ' not to advance is to fall 
 back ; ' Ho be born is not to be perfected.' 
 
 § 7. A Term may consist (as was formerly explained) of 
 one word, or of several. And care must be taken, when you 
 are examining a proposition, not to mistake for one of its 
 Terms a word which, though it might have been used as a 
 
Lesson IX.] clearness of expression. 67 
 
 Term, is, in that proposition^ only a part of a Term. Thus, 
 in one of the above examples, the word ' pound ' is not 
 one of the Terms, but only a part of the Term ' owing a 
 pound to William.' A description of some object will some- 
 times occupy a page or two, and yet be only the Predicate of 
 a single Proposition. 
 
 You are to observe also that one single sentence will often 
 imply what may be regarded as several distinct Propositions ; 
 each indeed implying the truth of the others, but having their 
 Terms different, according as we understand the drift (as it 
 is called) or design of what is uttered : that is according to 
 what we understand the person to be speaking of, (which is 
 the Subject) and what it is that he says [predicates] of it. 
 
 1 2 3 4 
 
 Thus ' He — did not — design — your — death ; ' may be 
 regarded as any one of at least four different propositions. If 
 (No 1) the word ' He ' be marked by emphasis in speaking, 
 or by Italics, it will be understood as the Predicate ; and the 
 drift of the sentence will be that ' whoever else may have de- 
 
 j signed your death, it was not he : ' if the emphasis fall on 
 No. 2, the Predicate will be ' designing,' [or ' by design '] 
 and the drift of the sentence will be that, ' though he may 
 
 , have endangered your life, it was not by design : ' and so with 
 the rest. 
 
 I You should endeavor, therefore, so to express yourself as to 
 
 ■ make it clearly understood not only what is the meaning of 
 each ivord you employ, but also w^hat is the general drift of 
 the whole sentence ; in short, what is the Subject of your 
 
 I Proposition, and what it is that you say of it. And, as far as 
 you can, you should make this clear by the structure of each 
 sentence, without resorting to the expedient of italics or under- 
 scoring oftener than is unavoidable. 
 
 There is frequently a great advantage, towards such clear- 
 ness, gained, by the English word ' it ' in that sense in which 
 
68 COMPENDIUM. [^Part II. 
 
 it stands (not as the neuter pronoun, answering to ' He ' and 
 ^ She/ but) as the representative of the Subject of a Proposi- 
 tion, of whatever Gender or Number ; so as to allow the Sub- 
 ject itself to be placed last : as — 
 
 Subj. Cop. Pred. Subj. 
 
 ^ It — is not — he — that had this design ; ' 
 or again — 
 
 Subj. Cop. Pred. Subj. 
 
 < It — is not — by design — that he did this/ &c. 
 
 LESSON X. 
 
 § 1. A Proposition is, as has been said, an act of judg- 
 ment expressed in words ; and is defined to be a ' Sentence 
 which asserts ; ' or, in the language of some writers, an ^ in- 
 dicative Sentence:' ^indicative,' [or 'asserting'] meaning 
 * that which affirms or denies something.' It is this that dis- 
 tinguishes a Proposition from a Question, or a Command, &c. 
 
 Propositions, considered merely as Sentences, are distin- 
 guished into ' Categorical ' and ' Hypothetical.' 
 
 The Categorical asserts simply that the Predicate does, or 
 does not, apply to the Subject : as ' the world had an intelli- 
 gent maker ; ' * Man is not capable of raising himself, unas- 
 sisted, from the savage to the civilized state.' The Hypo- 
 thetical [called by some writers ' Compound '] makes its 
 assertion under a Condition, or with an Alternative ; as ' If 
 the world is not the work of chance, it must have had an in- 
 telligent maker : ' ' Either mankind are capable of rising into 
 
Lesson x.] propositions. 69 
 
 civilization unassisted, or the first beginning of civilization 
 must have come from above.' 
 
 The former of these two last examples is of that kind called 
 ' Conditional-propositions * ; ' the ' condition ' being denoted 
 bj ' if,' or some such word. The latter example is of the 
 kind called 'Disjunctive;' the alternative being denoted by 
 ^ either ' and ' or.' 
 
 The division of Propositions into Categorical and Hypo- 
 thetical, is, as has been said, a division of them considered 
 merely as Sentences: for a like distinction might be extended 
 to other kinds of Sentences also. Thus, ' Are men capable 
 of raising themselves to civilization ? ' ' Go and study books 
 of travels,' are what might be called categorical sentences, 
 though not propositions* ' If man is incapable of civilizing 
 himself, w^hence came the first beginning of civilization ? ' 
 might be considered as a conditional question ; and ' Either 
 admit the conclusion, or refute the argument,' is a disjunctive 
 command. 
 
 At present we shall treat only of Categorical Propositions. 
 
 § 2. It has been above explained that Propositions (of this 
 class, — the Categorical) are divided according to their 
 ^ Quantity ' into ' Universal ' and ' Particular : ' — that an 
 * Indejinite-^Yoi^osiiion ' is in reality either the one or the 
 other ; though the form of expression does not declare ichich 
 is meant : — and also that a ' Singidar-^vo])Oiii\o\i ' is equiva- 
 lent to a ' Universal,' since its subject cannot but stand for the 
 whole of what that Term denotes, when that whole is one 
 single Individual. 
 
 You have also learnt that Propositions are divided, ac- 
 cording to their ' Quality,' into ' affirmative ' and ' negative.' 
 
 ^ Or ' hypothetical,' according to those writers who use the word ' com- 
 pound ' where we have used ' hypothetical.' 
 
70 COMPENDIUM. [^Part II. 
 
 The division of them, again, into ' true ' and ' false ' is also 
 called a division according to their ' quality ; ' namely, the 
 ' quality of the Matter : ' (as it has relation to the subject- 
 matter one is treating of) while the other kind of quality (a 
 proposition's being affirmative or negative) is ' the quality of 
 the expression^ 
 
 The ' quality of the matter ' is considered (in relation to 
 our present inquiries) as accidental, and the ' quality of the 
 expression ' as essential. For though the truth or falsity of a 
 proposition — for instance, in Natural-history, is the most 
 essential point in reference to Natural-history, and of a mathe- 
 matical proposition, in reference to Mathematics, and so in 
 other cases, — this is merely accidental in reference to an 
 inquiry (such as the present) only as to forms of expression. 
 In reference to that, the essential difference is between affirm- 
 ation and negation. 
 
 And here it should be remarked, by the way, that as, on the 
 one hand, every Proposition must be either true or false, so, 
 on the other hand, nothing else can be, strictly speaking, either 
 true or false. In colloquial language, however, 'true' and 
 ' false ' are often more loosely applied ; as when men 
 speak of the ' true cause ' of anything ; meaning, ' the real 
 cause ; ' — the ' true heir,' that is, the rightful heir ; — a ^ false 
 prophet,' — that is, a pretended prophet, or one who utters 
 falsehoods ; ' — a ' true ' or ' false ' argument ; meaning a valid 
 [real] or an apparent-sirgwcueni ; — a man ' true,' or ' false ' to 
 his friend ; ^. e, faithful or unfaithful &c. 
 
 A Proposition, you are to observe, is Affirmative or Nega- 
 tive, according to its Copula ; i. e. according as the Predicate 
 is affirmed or denied of the Subject. Thus ' not to advance, 
 is to fall back,' is affirmative : ' No miser is truly rich ' [or ' a 
 miser is not truly rich'] is a negative. 'A few of the sailors 
 were saved,' is an affirmative ; ' Few of the sailors were 
 
Lesson X.] categorical propositions 71 
 
 saved/ is properly a negative ; for it would be understood that 
 you were speaking of ' most of the sailors,' and denying that 
 they were saved. 
 
 Since then every Proposition must be either Affirmative or 
 Negative, and also, either Universal or Particular, Proposi- 
 tions are considered as divided (taking into account both 
 Quantity and Quality) into four Classes ; which, for brevity's 
 sake, are usually denoted by the Symbols A, E, I, O ; name- 
 ly A. Universal-affirmative, E. Universal-negative, I. Par- 
 ticular-affirmative, and O. Particular-negative. 
 
 § 3. Any two Propositions are, technically, said to be 
 ^ opposed^ to each other, when 'having the same Subject 
 and Predicate, they differ either in Quantity, or in Quality, 
 or in both.' 
 
 In ordinary language, however, (and in some technical 
 treatises) propositions are not reckoned as ' opposed ' unless 
 they differ in Quality, 
 
 It is evident that with any given Subject and Predicate, 
 you may state four distinct Propositions, A, E, I and O : any 
 two of which are said to be ' opposed.' And hence there are 
 (in the language of most technical writers) reckoned four 
 kinds of ' Opposition.' 1st, A and E, — the two Universals, 
 Affirmative and Negative, (always supposing the Terms the 
 same) are called ' Contraries ' to each other ; 2nd. The two 
 Particulars, I and O, ' Sub-contraries.^ 3rd. The two Affirm- 
 atives again, or the two Negatives, (A and I, or again, E and 
 O) are called ' Suhalterns,^ And 4th, those which differ both 
 in Quantity and Quality — as A and 0, or E and I, — are 
 called ' Contradictories! 
 
 It is usual to exhibit in a Scheme (such as that in p. 72) these 
 four kinds of ' Opposition ; ' by placing at the corners of a 
 Square the Symbols A, E, I, O, as representing, respectively, 
 the abovementioned four classes of Propositions. 
 
72 
 
 COMPENDIUM. 
 
 [^Pait II. 
 
 n. t. A - - - 
 
 i. /. [Every X is Y.J 
 c./ 
 
 Contraries. 
 
 - E. n,/. 
 
 [No X is Y.] i. ^ 
 
 c./. 
 
 03 
 
 g- 
 
 CD 
 
 3 
 
 P 
 
 % 
 
 if 
 
 cF 
 
 ..- 
 
 % 
 
 •3 
 
 (/2 
 
 n. #. 
 
 I - - 
 
 Subcontraries. 
 
 n./ 
 
 i./. 
 
 [Some X is Y.] 
 
 
 [Some X is not Y.] i. t. 
 
 c. t. 
 
 
 
 c.t. 
 
 You may substitute for the unmeaning Symbols X, Y, 
 (which stand for the Terms of the above Propositions) what- 
 ever significant Terms you will; and on their meaning, of 
 course, will depend, the truth or falsity of each Proposition. 
 
 For instance. Naturalists have observed that ' animals hav- 
 ing horns on the head are universally ruminant ; ' that, of 
 ^ carnivorous animals,' none are ruminant ; and that, of ^ ani- 
 mals with hoofs,' some are ruminant, and some not. Let us 
 take then, instead of ' X,' ^ animals with horns on the head,' 
 and for ' Y,' ^ ruminant : ' here, the real connexion of the 
 Terms in respect of their meaning — which connexion is called 
 the ' matter ' of a proposition — is such that the Predicate may 
 be affirmed universally of the Subject; and of course the 
 affirmatives Cwhether Universal or Particular) will be time, 
 
Lesson yii.] opposition. 73 
 
 and the ' negatives ' false. In this case the ^ matter ' is tech- 
 nically called ' necessary ; ' inasmuch as we cannot avoid be- 
 lieving the Predicate to be applicable to the Subject. 
 
 Again, let ^ X ' represent ^ carnivorous animal/ and ' Y ' 
 ^ruminant: ' this is a case of what is called ^ impossible mat- 
 ter ; ' (i, e. where we cannot possibly conceive the Predicate 
 to be applicable to the Subject) being just the reverse of the 
 foregoing ; and, of course, both the Affirmatives will here be 
 false, and both Negatives true. 
 
 And, lastly, as an instance of what is called ' contingent 
 matter,' — i. e, where the Predicate can neither be affirmed 
 universally, nor denied universally, of the Subject, take 
 * hoofed animal ' for ' X ' and ' ruminant * for ^ Y ; ' and of 
 course the Universals will both be false, and the Particulars 
 true : that is, it is equally true that ' some hoofed animals are 
 ruminant,' and that ' some are not.' 
 
 § 4. You will perceive, then, on examining such a Scheme, 
 that ' Contrary ' Propositions can never be both of them true, 
 though they may (viz. : in ' contingent-matter '] be both false : 
 that ' /Sw^contraries,' on the other hand, may be both true, but 
 never both false : that ' Contradictories ' [^diametricaUy-oppo- 
 site Propositions] must in every case be, one true, and the 
 other false : and that ' Suhalterns ' (of which the Universal is 
 called the ' Subaltenza/i^,' and the Particular the ' Subalter- 
 nate ') may be either both true, or both false, or the one true 
 and the other false. 
 
 These last Propositions, however, though reckoned, as has 
 been said above, by most dialectical writers, among those op- 
 posed, are not so accounted in ordinary discourse. 
 
 The four kinds of Propositions, A, E, I, O, have been, in 
 
 the Scheme, marked, each, with the letters t for ' true ' and 
 
 f for ^ false,' and also Avith the letters n, i, c, to denote the 
 
 three kinds of matter, (necessary, impossible, contingent,) in 
 
 7 
 
74 COMPENDIUM. \_Part ii. 
 
 order to point out which propositions are true, and which, 
 false, in each kind of matter. 
 
 The technical terms ^q have here explained, are needful 
 to be learnt, as being, some of them, in frequent use, and as 
 being convenient for the avoiding of circumlocution and of 
 indistinctness. 
 
 ' Contradictory-opposition ' is the kind most frequently al- 
 luded to, because (as is evident from what has been just said) 
 to deny^ — or to disbelieve^ — a proposition, is to assert^ or to 
 helieve, its Contradictory ; and of course, to assent to, or main- 
 tain a proposition, is to reject its Contradictory. Belief, 
 therefore, and Disbelief, are not two different states of the 
 mind, but the same^ only considered in reference to two Con- 
 tradictory propositions. And consequently, Credidity and 
 Incredulity are not opposite habits, but the same ; in refer- 
 ence to some class of propositions, and to their contradictories. 
 
 For instance, he who is the most incj^edulous respecting a 
 certain person's guilty is, in other words, the most ready to 
 believe him not guilty ; he who is the most credulous * as to 
 certain works being v^^ithin the reach of Magic, is the most 
 incredulous [or ^slow of heart to believe'] that they are not 
 within the reach of Magic ; and so, in all cases. 
 
 The reverse of helieving this or that individual proposition 
 is, no doubt, to dishelieve that same proposition ; but the vq- 
 Y^Y^Q o^ belief generally, i^ (not belief; since that implies be- 
 lief; but) doubt. 
 
 And there may even be cases in which doubt itself may 
 amount to the most extravagant credulity. For instance, if 
 any one should ' doubt whether there is any such Country as 
 Egypt,' he would be in fact helieving this most incredible 
 proposition ; that ' it is possible for many thousands of persons, 
 unconnected with each other, to have agreed, for successive 
 
 =^ As the Jews, in the time of Jesus, in respect of his works. 
 
Lesson x.] si3iple-c on version. 75 
 
 Ages, in bearing witness to the existence of a fictitious Coun- 
 try, without being detected, contradicted, or suspected/ 
 
 All this, though self-evident, is, in practice, frequently lost 
 sight o£ 
 
 § 5. A Proposition is said to be ^ converted^ when its 
 ^ Terms are transposed ; ' ^. e., when the Subject is made the 
 Predicate, and the Predicate the Subject. And when no 
 other change is made, this is called 'simple conversion.* 
 When for instance I say ' no carnivorous animal is a rumi- 
 nant,' the ' ^vccc^^-conversQ ' of this would be, ' no ruminant is 
 a carnivorous animal.' 
 
 The ' conversion ' of such a proposition as this, ' No one 
 [is happy who] is anxious for change,' would be effected by 
 altering the arrangement of the words in brackets, into * who 
 is happy.' 
 
 The Conversion of a Proposition is said to be 'illative^ 
 when the truth of the ' Converse ' is ' implied ' (looking mere- 
 ly to the form of expression) ' by the truth of the original 
 proposition : ' [or ' exposita '] which is the case in the exam- 
 ple above : it being evident that if the former of those Propo- 
 sitions (whatever may be the meaning of the Terms) be true, 
 the Converse must be true also. For to say that ' No X is Y,' 
 is to imply that ' no Y is X.' 
 
 You are to observe, however, that the Converse of a 
 true Proposition may happen to be true also, without the 
 Conversion's being ' illative ; ' that is, when the truth of that 
 Converse is not implied by the truth of the ' Exposita ' [the 
 (original proposition]. Thus, ' Every X is Y ' does not imply 
 khat ' every Y is X,' though it may happen that both proposi- 
 jtions may be true. 
 
 i For instance, that ' Every tree is a vegetable,' does not 
 4mply that ' Every vegetable is a tree ; ' and this last hap- 
 jpens in fact to be not true. But no more is it implied, when 
 ||I say, ' every equilateral triangle is equianguku',' that ' every 
 
76 COMPENDIUM. l_Part II. 
 
 equiangular triangle is equilateral ; ' for though both these 
 propositions are true, the one of them does not imply the other ; 
 and they are separately demonstrated as distinct propositions, 
 in geometrical treatises. 
 
 In order to understand why the simple-conversion of * every 
 X is Y/ into ' every Y is X/ is not ' illative/ you have only 
 to observe that, in the * Exposita,' [original proposition] ' Y 
 is undistributed, as being the predicate of an Affirmative ; 
 while, in the ' Converse,' it is ' distributed,' by being made the 
 Subject of a Universal, A new Term is therefore, in fact, 
 introduced ; since instead o^ paii of the Term ^ Y ' we have 
 employed the whole of it ; and the agreement or disagreement 
 of one Term with some part of another Term, does not imply 
 its agreement or disagreement with every part of it ; that is, 
 with the whole. For though a part is implied by a whole, a 
 whole is not implied by a part. 
 
 When, for instance, I say ' every tree is a vegetable ' I 
 am employing (as was formerly explained) the Term ' vegeta- 
 ble ' to stand only for part of its ' significates ; ' and this does 
 not authorize me to employ it (in the Converse) as standing 
 for all its Significates ; as in saying that ' every vegetable is a 
 tree.' 
 
 And vStrictly speaking, that is not a real ' conversion,' — but 
 only an ' apparent conversion,' — which is not * illative.' For, 
 (as has been above said) there is not a mere transposition of 
 the terms, but a 7ieiv term introduced, when a term which was 
 undistributed in the ' exposita,' is distributed [taken univer- 
 sally] in the Converse. 
 
 But as it is usual, in common discourse, to speak of ^ an 
 unsound argument,' — meaning, ' an apparent-^vgxxiaeiii, which 
 is in reality not an argument,' so, in this case also, it is com- 
 mon to say, for instance, that ' Euclid proves first that all 
 equilateral triangles are equiangular, and afterwards he proves 
 the Converse, that all equiangular triangles are equilateral ; 
 
 { 
 
Lesson x.] illatiye-conyersion. 77 
 
 or again, to saj, ' It is true that all money is wealth ; but I 
 deny the Converse, (in reality, the c//;^are/i^-converse) that all 
 wealth is money.' 
 
 § 6. Conversion, then, strictly so called, — that is, ^ illa- 
 tive-conversion,' — can only take place when no term is dis- 
 tributed in the Converse, which was undistributed in the 
 ' Exposita.' 
 
 Hence, since E [a Universal-negative] distributes both 
 terms, and I, [a Particular-affirmative] neither, these may 
 both be simply-converted illatively. As in the example 
 above, ^ no carnivorous animal is ruminant,' implies by the 
 very form of the expression, that ' no ruminant is a carnivo- 
 rous animal.' And so also ' some things which are strange 
 are believed,' im^plies that ' some things which are believed 
 are strange.' 
 
 We may also illatively-convert A [a Universal-affirmative] 
 by altering its ' Quantity ' from Universal to Particular. 
 For ' Every X is Y ' does imply that ' some Y ' (though not 
 that ' every Y ') 'is X.' So in the example above we might 
 allowably have stated (though not that ' all vegetables,' yet) 
 that ' some vegetables arc trees.' 
 
 This procedure is called ' conversion by limitatiGn : ' or 
 according to some writers, ' conversion per accidens.' And it 
 may be applied to E also ; as, for instance, in the example 
 above, you might have said ' Some ruminant is not carnivo- 
 rous ; ' though this would have been to come short of what 
 you were warranted in stating. 
 
 But in [particular-negative] the conversion will not be 
 illative, on account of the rule that the Predicate of a Nega- 
 tive is always distributed. The proposition, therefore, ' Some 
 X is not Y ' does not imply that ' some Y is not X ; ' since X 
 is distributed in the ' Converse ' and was not, in the ' Ex- 
 posita,' in which it was the Subject of a Particular. It is true 
 7* 
 
78 COMPENDIUM. [^Part ii. 
 
 that ^ some men are not negroes : ' but this does not imply 
 that ' some negroes are not men.' 
 
 A Particular negative [0] cannot be converted illatively, 
 except by changing its Quality from negative to affirmative, 
 (without altering the sense) by regarding the negation as 
 attached to the Predicate instead of to the Copula. Thus 
 
 S. ^ Cop. rr. 
 
 * Some X is not Y ' may be taken as an affirma- 
 
 S. Cop. Fr. 
 
 tive, namely, ' Some X is not Y ; ' and this latter 
 
 proposition [I] may of course be simply-converted illatively ; 
 
 jS. Cop. p. 
 
 as ' Some not Y is X.' 
 
 Thus, ^ Some men are not-negroes ' implies that ^ Some who 
 are not negroes are men ; ' or (as such a proposition is often 
 expressed) ' One may be a man without being a negro.' So 
 again ' Some who possess wealth are not happy,' implies that 
 
 * Some who are not-happy possess wealth.' 
 
 § 7. This procedure is technically called ' Conversion-by- 
 negation,^ [or, by ' Contraposition.'] It is applicable also to 
 [A] Universal-affirmatives. For, to affirm some Predicable 
 of a Subject, or [to assert the presence of some attribute] is the 
 same thing in sense as to deny its absence. Hence a Univer- 
 sal-affirmative may be stated as a VmYevsal-negative ; which 
 (as we have seen) may be simply-converted. 
 
 Thus Every ' X is Y ' is equipollent [or equivalent in sense'] 
 to ' No X is not Y ; ' which may be illatively converted into 
 
 * nothing that is not Y — is — X : ' or ' whatever is not Y 
 
 is not — X.' 
 
 So the proposition, ' Every true poet is a man of genius,' 
 may be stated as ^ No true poet-is — not-a-man-of-genius ; ' 
 which (being E) may be illatively converted into ^no one 
 who is not a man of genius is a true poet : ' (as such a propo- 
 sition is very commonly expressed) ' None hut a man of 
 genius can be a true poet ; ' or again, ' a man of genius alone 
 
Lesson x.] conversion-by-negation. 79 
 
 can be a true poet ; ' or again, ' One cannot be a true poet 
 without being a man of genius/ 
 
 And here it is worth remarking, by the way, that in such 
 examples as the above, the words ' may,' ' can,' ' cannot,' &c. 
 have no teference (as they sometimes have) to power ^ as ex- 
 ercised by an agent ; but merely to the distribution or non- 
 distribution of Terms : or to the confidence or doubtfulness we 
 feel respecting some supposition. 
 
 To say, for instance, that ' a man who has the plague may 
 recover,' does not mean that ' it is in his power to recover if 
 he chooses ; ' but it is only a form of stating a particular- 
 proposition : [I] namely, that ' Some who have the plague 
 recover.' And again to say, ' there may be a bed of coal in 
 this district,' means merely, * The existence of a bed of coal 
 in this district — is — a thing which I cannot confidently deny 
 or affirm.' 
 
 § 8. So also to say ' a virtuous man cannot betray his 
 Country ' [or ' it is impossible that a virtuous man should be- 
 tray &c.'] does not mean that he lacks the power, (for there 
 is no virtue in not doing what is out of one's power) but 
 merely that ^ not betraying one's country ' fonns an essential 
 part of the notion conveyed by the term ' virtuous.' We 
 mean, in short, that it is as much out of our power to conceive 
 a virtuous man who should be a traitor, as to conceive ' a 
 Square with unequal sides ; ' that is, a square which is not a 
 square. The expression, therefore, is merely a way of 
 stating the Universal-proposition [E] ' No virtuous man be- 
 trays his Country.' 
 
 So again, to say, ' a Aveary traveller in the deserts of 
 Arabia 7nust eagerly drink when he comes to a Spring,' does 
 not mean that he is compelled to drink, but that / cannot 
 a/void believing that he will ; — that there is no doubt in my 
 mind. 
 
 In these, and many other such instances, the words ' may,' 
 
30 COMPENDIUM. [^Part II, 
 
 ' mast,' ' can/ ' impossible/ &c. have reference, not to power 
 or absence of power in an agent, but only to universality or 
 absence of Universality in the expr-ession ; or, to douht or 
 absence of douht in our own mind, respecting what is asserted. 
 
 LESSON XI. 
 
 § 1. An Argument [or Act of Eeasoning expressed in 
 words] is defined ' an Expression in which, from something 
 laid down [assumed as true] something else is concluded to 
 be true, as following necessarily [resulting] from the other.' 
 That which follows from the other, is called (as was formerly 
 explained) the ' Conclusion ; ' and that from which it follows, 
 the ' Premises ; ' or in the language of some writers, the ' An- 
 tecedent.' 
 
 The above is the strict technical definition. But in ordi- 
 nary language the word ' Argument' is often employed to de- 
 note the Premises alone ; or, sometimes that one of the 
 Premises which is expressed, when the other is understood : 
 as when one speaks of proving so and so hy this or that argu- 
 ment ; meaning, by such and such a Premise. 
 
 And you may observe, by the way, that of the two 
 Premises, the Major (formerly explained) is, in common dis- 
 course, often called the ^ Principle,' and the Minor-premise, 
 the ' Peason.' 
 
 Frequently also in common discourse ' an Argument ' is used 
 to signify a ' Series of arguments,' leading ultimately to the 
 Conclusion maintained. 
 
 An Argument, if stated in such a regular form that ^ its 
 conclusiveness [its being really an Argumentl is apparent 
 
Lesson XI.] an argument defined. 81 
 
 from the mere form of expression alone, ^ (independently of 
 the meaning of the words) is then called a ' Syllogism.' As, 
 ' Every X is Y* ; Z is X, therefore Z is Y ; ' in which, as 
 was formerly explained, the truth of the Conclusion, — assum- 
 ing the Premises to be true, — must be admitted, whatever 
 Terms you may make X, Y, and Z, respectively, stand for. 
 
 You are to remember, therefore, that a Syllogism is not 
 (as some have imagined) a peculiar kind of argument ; but 
 only a certain form in which every Argument may be ex- 
 hibited. 
 
 § 2. One circumstance wliich has tended to mislead persons 
 as to this point, is, that in a Syllogism we see the Conclusion 
 following certainly [or necessarily] from the Premises; and 
 again, in any apparent-syllogism which on examination is 
 found to be (as you have seen in s^me of the examples) not a 
 real one [not ' valid '] the Conclusion does not follow at all ; 
 and the whole is a mere deception. And yet w^e often hear 
 of Arguments wdiicli have some weight, and yet are not quite 
 decisive ; — of Conclusions wdiich are rendered prohahle, but 
 not absolutely certain &c. And hence some are apt to im- 
 agine that the conclusiveness of an argument admits of de- 
 grees ; and that sometimes a conclusion may, probably and 
 'partially, — though not certainly and completely — follow from 
 its Premises. 
 
 This mistake arises from men's forgetting that the Premises 
 themselves will very often be doubtful ; and then, the conclu- 
 sion also will be doubtful. 
 
 As w^as shewn formerly, one or both of the Premises 
 of a perfectly valid Syllogism may be utterly false and ab- 
 surd : and then, the Conclusion, though inevitably following 
 from them, may be either true or false, we cannot tell which. 
 And if one or both of the Premises be merely probable, we 
 
 =^ See a])ove. Lesson IX. § 4. 
 
82 COMPENDIUM. [^Part ii. 
 
 can infer from tliem only a probable conclusion ; though the 
 conclusiveness, — that is, the connexion between the Premises 
 and the Conclusion — is perfectly certain. 
 
 For instance, assuming that ' every month has 30 days ' 
 (which is palpably false) then, from the minor-premise that 
 ' April is a month,' it follows (which happens to be true) that 
 April has 30 days : ' and from the minor-premise that ' Feb- 
 ruary is a month ' it follows that ' February has 30 days ; ' 
 which is false. In each case the conclusiveness of the Argu- 
 ment is the same ; but in every case, when we have ascer- 
 tained the falsity of one of the Premises, we know nothing (as 
 far as that argument is concerned) of the truth or falsity of the 
 Conclusion. 
 
 § 3. When, however, we are satisfied of the falsity of some 
 Conclusion, we may, of course, be sure that (at least) one of 
 the Premises is false ; since if they had both been true, the 
 Conclusion would have been true. 
 
 And this — which is called the ' indirect ' mode of proof — 
 is often employed (even in Mathematics) for establishing what 
 we maintain : that is, we prove the falsity/ of some Proposi- 
 tion (in other words, the truth of its contradictory) by showing 
 that if assumed, as a Premise, along with another Premise 
 known to be true, it leads to a Conclusion manifestly false. 
 For though, from a false assumption, either falsehood or 
 truth may follow, from a true assumption, truth only can 
 follow. 
 
 Let us now look to the case of a doubtful Premise. Sup- 
 pose it admitted as certain that ' a murderer deserves death,' 
 and as probable that ' this man is a murderer,' then, the Con- 
 clusion (that ' he deserves death ') is probable in exactly the 
 same degree. 
 
 But though when one Premise is certain, and the other, 
 only probable, it is evident that the Conclusion will be exactly 
 as probable as the doubtful premise , there is some liability to 
 
Lesson xi.] degrees of probability. 8S 
 
 mistake, in cases where each Premise is merely probable. 
 For though almost every one would perceive that in this case 
 the probability of the Conclusion must be less' than that of 
 either Premise, the precise degree in wliicli its probability i^^ 
 diminished, is not always so readily apprehended. 
 
 And yet this is a matter of exact and easy arithmetical cal- 
 culation. I mean, that, given the probability of each Premise, 
 we can readily calculate, and with perfect exactness, the 
 probability of the Conclusion. 
 
 As for the probability of the Premises themselves that are 
 put before us, that, of course, must depend on our knowledge 
 of the siibject-matter to which they relate. But supposing it 
 agreed what the amount of probability is, in each Premise, 
 then, we have only to state that probability in the form of a 
 fraction, and to multiply the two fractions together ; the 
 product of which will give the degree of probabihty of the 
 Conclusion.* 
 
 § 4. Let the probability, for instance of each Premise be 
 supposed the same ; and let it, in each, be § ; [that is, let 
 each Premise be supposed to have two to one in its favor ; 
 that is, to be twHice as likely to be true as to be false] then the 
 probability of the Conclusion wall be two thirds of tivo thirds ; 
 that is |- ; — rather less than one half. For since twice two 
 is four, and thrice three nine, the fraction expressing the 
 probability of the Conclusion will be four ninths. 
 
 For example, suppose the Syllogism to be ^ A man who has 
 the plague will die of it ; ' (probably) ' this man has the 
 plague ; ' (probably) therefore, (probably) ' he will die of it.' 
 We are — suppose — not certain of either Premise ; though 
 
 ^ Those who arc at all familiar with Arithmetic will liardly need to he 
 reminded that, — since afracfion is less than a unit, — what is called (not 
 strictly, hut fiGnirativcly) midtipJifing any thing- hy a fraction, mcan:^, tak- 
 ing it less than once ; so that, for instance, -o+§, that is a lialf nuiUiplied 
 (as it is called) by two-thirds, means two-thirds of a half; ?. e. .2 or J. 
 
84 COMPENDIUM. l^Part ii. 
 
 we think eacli to be probable : we have judged — suppose — 
 that of 9 persons with the symptoms this man exhibits, two 
 thirds, — that is, six — have tlie plague : and again, that two 
 thirds of those who have the plague — that is, four out of six 
 — die of it ; then, of 9 persons who have these symptoms, 4 
 may be expected to die of the plague. 
 
 Again ' Every X is Y ; f Z is X f , therefore Z is Y ' 
 (y^2-==2-) l^t ^^6 fractions written after each Premise express 
 the degree of its probability ; and the result will be that which 
 is given as the probability of the Conclusion. 
 
 For instance, ' A Planet without any atmosphere is unin- 
 habited : the moon is a planet without any atmosphere ; 
 therefore, the moon is uninhabited : ' supposing these Propo- 
 sitions to be those represented in the former example (of X, 
 Y, and Z) then the probability that ' the moon is uninhabited,* 
 will be two thirds of three fourths ; or one half; since f mul- 
 tiplied by three fourths gives x\=2--^ 
 
 In the examples just given, you will observe that the 
 probability of each Premise has been supposed more than ^ ; 
 that is, each has been assumed to be more likely to be true 
 than not ; and yet there is, for one of these Conclusions, only 
 
 ^ Some persons profess contempt for all such calculations, on the 
 ground that we cannot be quite sure of the exact degree of probability of 
 each premise. And it is true that we are. in most cases, exposed to this 
 unavoidable source of uncertainty ; but this is no reason why we should 
 not endeavor to guard against an additional uncertainty, wliich can be 
 avoided. It is some advantage to have no more doubt as to the degree 
 of probability of the Conclusion, than we have in respect of the Premises. 
 
 And in fact there are offices, kept by persons whose business it is, in 
 which calculations of this nature are made, in the purchase of contingent- 
 reversions^ depending, sometimes, on a great variety of risks which can only 
 be conjecturally estimated, and in effecting Insurances, not only against 
 ordinary risks (the calculations of which are to be drawn from statistical- 
 tables) but also against every variety and degree of ex^ra-ordinaiy risks ; 
 the exact amount of which no one can confidently pronounce upon. But 
 the calculations are based on the best estimate that can be formed. 
 
Lesson XI.] degrees of probability. 85 
 
 an even chance ; and for the other less. The supposed pa- 
 tient is supposed to be rather less likely to die of the plague 
 than not. 
 
 And of course when there is a long train of reasoning, — 
 the Conclusion of each argument being made one of the 
 Premises of a succeeding one, — then, if a number of merely- 
 probable Premises are introduced, the degree of probability 
 diminishes at each successive stage. 
 
 And hence it may happen, in the case of a very long train 
 of reasoning, that there may be but a slight probability for the 
 ultimate Conclusion, even though the Premises successively 
 introduced, should be, some of them, quite certain, and the 
 rest, more probable than not. 
 
 And hence, we often have to employ several distinct trains 
 of arguments, each tending separately to establish some degree 
 of probability in the Conclusion. 
 
 § 5. When you have two (or more) distinct arguments, 
 each, separately, establishing as probable, the same conclu- 
 sion, the mode of proceeding to compute the total probability, 
 is the reverse of that mentioned just above. For, there, — in 
 the case of two probable premises, — we consider what is the 
 probability of their being both true ; which is requisite in 
 order that the conclusion may be established by them. But 
 in the case of a conclusion twice (or oftener) proved probable, 
 by separate arguments, if these distinct indications of truth 
 do not all of them fail^ the conclusion is established. You 
 consider, therefore, what is the probability of both these indi- 
 cations of truth being combined in favor of any conclusion that 
 is not true. 
 
 Hence the mode of computation is, to state (as a fraction) 
 |the chances against the conclusion as proved by each argu- 
 ment; and to multiply these fractions together, to ascertain 
 the chances against the conclusion as resting on botJi the 
 arguments combined ; and this fraction being subtracted from 
 8 
 
86 COMPENDIUM. [^Part II. 
 
 unity, the remainder will be the probability ybr the conclusion. 
 
 For instance, let the probability of a conclusion as estab- 
 lished by a certain argument be f : (suppose, that this man 
 is the perpetrator of a certain murder, frcjm stains of blood 
 being found on his clothes) and again, of the same conclusion 
 as established by another argument, f : (suppose, from the 
 testimony of some witness of somewhat doubtful character) 
 then, the chances against the conclusion in each case, respect- 
 ively, will be |- and -| ; which multiplied together give ;J-| or 
 •J against the conclusion. The probability, therefore, jTor the 
 conclusion as depending on these two arguments jointly (i, e. 
 that he is guilty of the murder) will be f , or two to one.=^ 
 
 As for the degree of probability of each Premise, that, as , 
 we have said, must depend on the subject-matter before us ; 
 and it would be manifestly impossible to lay down any fixed 
 rules for judging of this. But it would be absurd to complain 
 of the want of rules determining a point for which it is plain 
 no precise rules can be given ; or to disparage, for that reason, 
 such rules as can be given for the determining of another 
 point. Mathematical Science will enable us — given, one side 
 of a triangle and the adjacent angles, — to ascertain the other 
 sides ; and this is acknowledged to be something worth learn- 
 ing, although mathematics will not enable us to answer the 
 question which is sometimes proposed in jest, of ' how long 
 is a rope ? ' 
 
 Men are often misled in practice by not attending to these 
 circumstances, plain as they are, when pointed out. 
 
 § 6. It has been already explained that the Maxim [or 
 Dictum] applicable to every Argument when stated in the 
 clearest form, is, that ' whatever is predicated universally of 
 any term, may be predicated in like manner [affirmed, or de- 
 nied, as the case may be] of whatever is comprehended under 
 
 ^' See Lesson XVn., § 10. 
 
Lesson xi.] universal principle of reasoning. 87 
 
 that term : ' and that this, consequently, is the ' Universal 
 Principle ' of Reasoning. 
 
 And you may observe that this Dictum [or Maxim] may 
 in fact be regarded as merely the most general statement of 
 ^ An Argument,^ — not, this, or that individual argument; but 
 any and every ' Argument, abstractedly.' 
 
 For instance, if you say ' this man is contemptible because 
 he is a liar,' you evidently mean to be understood, * every 
 liar is contemptible ; this man is a liar ; therefore he is con- 
 temptible.' Now if you so far generalize this Syllogism as to 
 omit all consideration of the very terms actually occurring in 
 it, abstracting, and attending solely to, theyb?'m of expression, 
 you will have ' Every X is Y ; Z is X ; therefore Z is Y,' 
 and then if you proceed to make a still further abstraction, 
 saying, — instead of ' Every X ' — ' any-term-distrihuted' and 
 instead of ' Y ' — ' anything whatever affirmed of that term,' 
 and so on, you will have, in substance, the very 'Dictum' 
 we have been speaking of: which may be separated into 
 three portions, corresponding to the three Propositions of a 
 Syllogism : thus, 
 
 1. 'Anything whatever' (as *Y') affirmed of a whole 
 class (as ' X ') 
 
 2. under which class something else (as Z) is compre- 
 hended, 
 
 3. may be affirmed of that (namely ' Z ') which is so com- 
 prehended ; ' 
 
 These three portions into which the Dictum has been sepa- 
 rated, evidently answer to the Major-premise, IMinor-premise, 
 and Conclusion, of the Syllogism given above. And it is 
 plain that the like explanation will apply (if ' denied ' were 
 put for ' affirmed') to a Syllogism with a Jiegative conclusion. 
 So that the ' Dictum' is, in fact, as we have said, merely the 
 most abstract and general form of stating the Act of Reason- 
 ing y universally. 
 
88 COMPENDIUM. [^Part ii. 
 
 § 7. Some persons have remarked of this ' Dictum ' (mean- 
 ing it as a disparagement) that it is merely a somewhat cir- 
 cuitous explanation of what is 7neant by a Class. It is, in 
 truth, just such an explanation of this as is needful to the 
 student, and which must be kept before his mind in reasoning. 
 For you are to recollect that not only every Class [the Sign 
 of which is, a ' Common-term '] comprehends under it an in- 
 definite number of individuals — and of other Classes — dif- 
 fering in many respects from each other, but also most of those 
 individuals and classes may be referred, each, to an indefinite 
 number of classes (as was formerly explained) according as 
 we choose to abstract this point or that, from each. 
 
 Now to remind one, on each occasion, that so and so is re- 
 ferable to such and such a Class, and that the Class which 
 happens to be before us comprehends such and such things, 
 — this, is precisely all that is ever accomplished by Reasoning. 
 
 For you may plainly perceive, on looking at any of the 
 examples above, that when you assert both the Premises taken 
 in conjunction, you have, virtually, implied the Conclusion. 
 Else, indeed, it would not be impossible, (as it is) for any one 
 to deny the Conclusion, who admits both Premises. 
 
 § 8. Hence, some have considered it as a disparagement to 
 a Syllogism (which they imagine to be one hind of Argument) 
 that you can gain no new truth from it ; the Conclusions it 
 establishes being in fact known already, by every one who 
 has admitted the Premises. 
 
 Since, however, a Syllogism is not a certain distinct kind 
 of argument, but any argument wdiatever, stated in a regular 
 form, the complaint, such as it is, lies against Reasoning alto- 
 gether. 
 
 And it is undeniable that no new truths — in one sense of 
 the word — (and that, perhaps, the strictest sense) can ever 
 be established by Reasoning alone ; which merely unfolds, as 
 it were, and develops, w^hat was, in a manner, wrapped up 
 
Lesson XI.] information and instruction. 89 
 
 and implied in our previous knowledge ; but which we are 
 often as much unaware of, to all practical purposes, till brought 
 before us, as if it had been w^holly beyond our reach. 
 
 New truths^ — in the strictest sense of the word — that is, 
 such as are not implied in any tiling that was in our minds be- 
 fore, — can be gained only by the use of our senses, or from 
 the reports of credible narrators, &c. 
 
 An able man may, by patient Reasoning, attain any amount 
 of mathematical truths ; because these are all implied in the 
 Definitions. But no degree of labor, and abihty, would give 
 him the knowledge, by ' Reasoning ' alone^ of what has taken 
 place in some foreign country ; nor w^ould enable him to know, 
 if he had never seen, or heard of, the experiments, what would 
 become of a spoonful of salt, or a spoonful of chalk, if put into 
 water, or what would be Ae appearance of a ray of light when 
 passed through a prism. 
 
 § 9. These tw^o modes of arriving at any truth are per- 
 ceived by all men as distinct. And they are recognized in 
 the expressions in common use. The one is usually called 
 * information ; ' the other ' instruction*.^ We speak of trust- 
 ing to the information (not, the instruction) of our senses. 
 Any one who brings news from any place, or w^ho describes 
 some experiments he has witnessed, or some spot he has vis- 
 ited, is said to afford us information, 
 
 A Mathematician again, a Grammarian, — a Moralist, — 
 any one who enters into a useful discussion cancerning human 
 life, — any one in short who satisfactorily proves anything to 
 us by reasoning, — is said to afford us instruction. 
 
 And in conversing with any one who speaks judiciously, 
 dne sometimes says ' very true ! ' or ' that is a very just remark : 
 that never struck me before, &c.' In these and suchlike ex- 
 pressions, we imply both that wliat he says is not superfluous, 
 
 * It is not meant tliat this Ls the onli/ sense of these words. 
 8* 
 
90 COMPENDIUM. \_Part II. 
 
 but valuable and important, and also that we are conscious of 
 having ourselves possessed, in our own previous knowledge, 
 the germ of what he has developed, and the means of ascer- 
 taining the truth of what he has said ; so as to have a right to 
 bear our testimony Jo it. 
 
 But when any one gives us information about a foreign 
 Country, &c. though we may fully believe him, and be inter- 
 ested by what he tells us, we never think of saying ' very 
 true ! ' or ^ you are quite right.' We readily perceive that in 
 this case the knowledge imparted is new to us in quite another 
 sense ; and is what no reasoning alone could have imparted ; 
 being not implied in anything we knew already. 
 
 These two modes of attaining what are, in different senses, 
 new truths, (and which of course, are often mixed together) 
 may be illustrated by two different modes in which a man may 
 obtain an addition to his wealth. One man, suppose, has 
 property to a certain value, bequeathed to him : another dis^ 
 covers on his estate a mine of equal value. Each of these 
 is enriched to the same degree. But the former of them ac- 
 quires what he had, before, no right to; the latter merely 
 comes to the knowledge and use of that which was, before, 
 legally, his property ; though, till discovered, it brought him 
 no advantage. 
 
 Any mode of attaining knowledge, distinct from Reasoning^ 
 is, of course, foreign from the present inquiry. , 
 
 
 LESSON xn. 
 
 § 1. The Dictum [or INIaxim] above explained as the Uni- 
 versal-principle of Reasoning, will apply to a Syllogism in 
 such a form as that of the examples given. ' Every (or No) 
 
Lesson XII.] terms of the conclusion. 91 
 
 X is Y* ; Z (whether some Z or every Z) is X; therefore 
 ' — some, or every — Z is Y ; ' or ' No Z is Y ; ' or ' Some Z 
 is not Y ; ' as the case may be. 
 
 And in that form every valid argument may be exhibited. 
 
 But there are other Syllogisms in other forms, to which 
 the ' Dictum ' cannot be immediately applied, (though they 
 may be reduced into the above form) and which yet are real 
 Syllogisms, inasmuch as their conclusiveness is manifest from 
 {h^form of expression, independently of the meaning of the 
 Terms. 
 
 For instance, ' no Savages have the use of metals ; the an- 
 cient Germans had the use of metals ; therefore they were 
 not savages,' is a valid Syllogism, though the Dictum cannot be 
 applied to it as here stated. But it may readily be reduced 
 into the form to which the Dictum does apply ; by illatively- 
 converting the Major-premise, into ' men who have the use of 
 metals are not Savages.' 
 
 But the argument as it originally stood was a regular Syl- 
 logism ; and so are some others also in a different form ; 
 although the Dictum does not immediately apply to them. 
 
 Accordingly, certain rules [or ' Canons '] have been framed, 
 which do apply directly to all categorical Syllogisms, whether 
 they are or are not in that form to which the Dictum is im- 
 mediately applicable. 
 
 1st Canon. Two Terms which agree with one and the same 
 third, may be pronounced to agree with each other : and 
 
 2-d Canon. Two terms whereof one agrees and the other 
 disagrees with one and the same third, may be pronounced to 
 disagree with each other. 
 
 The technical sense of the words ' agree ' and ' disagree ' 
 have been explained in a former Lesson. 
 
 The two Terms which are each compared with the same 
 
 * See Lesson ix. j 7. 
 
92 COMPENDIUM. \^Part ii. 
 
 tliird, are the Terms [or ' Extremes '] of the Conclusion ; viz. : 
 the Major-term and Minor-term : and that third Term with 
 which they are separately compared in the two Premises, is 
 the Middle-term. 
 
 On the former of these two Canons rests the proof of af- 
 firmative-conclusions ; on the latter, of negative. 
 
 § 2. To take first a Syllogism in the form originally given : 
 ' Every X is Y ; Z is X ; therefore Z is Y : ' or again ' No 
 X is Y ; Z is X ; therefore Z is not Y : ' in these examples, 
 * Y ' and ' Z ' are in the tw^o Premises respectively, compared 
 with ' X : ' in the former example they are assumed to ' agree ' 
 with it ; and thence in the Conclusion, they are pronounced 
 (according to the 1st Canon) to 'agree' w^ith each other; in 
 the latter example, ' Y ' is assumed to 'disagree' with 'X' 
 and ' Z,' to ' agree ' with it ; whence in the Conclusion they 
 are pronounced (according to the 2nd Canon) to ' disagree ' 
 with each other. 
 
 Again, to take a Syllogism in the other form, such as that 
 in this Lesson, ' No Savages &c.,' or, ' No Y is X ; Z is X ; 
 therefore Z is not Y ; ' you wdll perceive that the 2nd Canon 
 will apply equally well to this as to the preceding example. 
 
 You will also find, on examination of the apparent-syllo- 
 gisms [fallacies] — of which examples were given in former 
 Lessons, and w^hose faultiness was there explained, — that 
 they transgress against the above ' Canons.' 
 
 Take for instance, ' Some X is Y ; Z is X ; therefore Z is 
 Y* ; ' and again ' Every Y is X ; Z is X ; therefore Z is Y ; ' 
 or ' every tree is a vegetable ; grass is a vegetable ; therefore 
 grass is a tree : ' in these (as was formerly explained) the 
 Middle-term is undistributed ; [taken particularly, in both 
 premises] the two ' Extremes ' therefore [Terms of the Con- 
 clusion] have been compared each with part only of the 
 
 ^ See the example from Hume, respecting Testimony 
 
Lesson xii.] terms of the conclusion. 93 
 
 Middle ; and thence we cannot say that they have each been 
 compared with one and the same third: so tliat we are not 
 authorized to pronounce their agreement or disagreement with 
 each other. 
 
 But remember, that it is sufficient if the Middle-term be 
 distributed in one of the Premises ; since if one of the ' Ex- 
 tremes ' (of the Conclusion) has been compared with 'part of 
 the ' Middle ' and the other, with the whole of it, they have 
 both been compared with the same ; since the whole must 
 include every part. And accordingly, in the form originally 
 given ^ Every X is Y ; Z is X ' &c. you may observe that the 
 Middle-term is distributed in the Major-premise, and undis- 
 tributed in the Minor. 
 
 § 3. Again, take the example formerly given, of ' illicit- 
 process ; ' [proceeding from a term undistributed in the Pre- 
 mise, to the same, distributed, in the Conclusion] as, ' Every 
 X is Y ; Z is not X ; therefore Z is not Y ; ' or, ' Every tree 
 is a vegetable ; grass is not a tree, therefore, grass is not a 
 vegetable ; ' here the ^ Extremes,' w^hich in the Conclusion 
 are compared together, are not really what had been com- 
 pared, each, with the Middle. For in the Conclusion, it is 
 the whole of the term ' vegetable ' that is compared with the 
 term ' grass ; ' (since negatives distribute the Predicate) though 
 it was only part of that term that had been, in the Premise, 
 compared with ' tree ; ' the Predicate of an ' Affirmative ' 
 being undistributed. 
 
 In this instance, therefore, as in the former one, the Canons 
 have not been complied with ; each of these apparent-syllo- 
 gisms having in reality four terms. 
 
 You will observe, also, that when the Middle-term is am- 
 higiious, there are, in sense, tico Middle-terms, though you 
 may have', apparently, a correct Syllogism : as ' Light is op- 
 posite to darkness ; feathers are ligltt ; therefore feathers are 
 opposite to darkness.' The word 'light' is here used equivo- 
 
94 COMPENDIUM. [^Part ir. 
 
 colly. (See the explanation in Lesson YII. § 3 of ^univocal' 
 and ' equivocal/) 
 
 So glaring an equivocation as this, could, of course, deceive 
 no one, and could only be employed in jest.* But when there 
 is a very small difference between the two senses in which 
 a Middle-term is used in the two Premises, then, though the 
 reasoning is not the less destroyed, the equivocation is the 
 more likely to escape notice. And men are practically de- 
 ceived in this manner, every day, both by others, and by 
 themselves. 
 
 § 4. For instance, there is an argument of Hume's (in the 
 Work referred to in a former example, and which is said to 
 have been convincing to some persons) which may be regu- 
 larly stated, thus: 'Nothing that is contrary to experience 
 can be established by testimony ; every miracle is contrary to 
 experience ; therefore no miracle can be established by testi- 
 mony.' Now the middle-term, ' contrary to experience,' ad- 
 mits of being understood in either of two senses ; sometimes 
 (and this is the strict and proper sense) it means ' what we 
 know by our own experience to be false ; as, for instance, if 
 several witnesses should depose to some act having been done, 
 at a certain time and place, by a person known to me, and in 
 whose company I was, at that time, and in a different place, 
 I should be enabled to contradict their testimony from my 
 own experience. 
 
 Sometimes, again, the expression is employed to denote 
 ' something which we have never experienced^ and have not 
 known to be experienced by others : ' which would be the 
 case with the ascent of a balloon, for instance, to one who had 
 never seen or heard of such a thing ; or with the freezing of 
 water, to a king of Bantam, mentioned by Hume. 
 
 * Most jests, it is to be observed, — such as puns, conundrums, &c. — ! 
 are mock fallacies. 
 
Lesson xii.] ambiguous middle-term. 95 
 
 Now if the Term ' contrary to experience ' be understood 
 in this latter senvSe in both Premises, then the Jia/W-Premise 
 of the Syllogism will be manifestly false ; since it would im- 
 ply that the king of Bantam, or any one living in a hot 
 Country, could have no sufficient reason for believing in the 
 existence of ice. And if the term be understood (in both 
 Premises) in the other sense, then the Minor will be false ; 
 since a Man cannot say that he knows by his own experience 
 (whatever he may believe or judge, and however rightly) the 
 falsity of every individual narrative of every alleged miracle. 
 
 But if the term is in each Premise to be so understood as 
 that each shall be true, then it is evident that it must be taken 
 as two different terms, (in sense, though not in sound) no less 
 than the term ' light ' in the former example. 
 
 § 5. As for the truth or falsity of any Premise, or the sense 
 in which any Term is to be undertsood, in this or that Propo- 
 sition, of course no fixed rules can be given ; as this must 
 evidently be determined, in each case, by the subject-matter 
 we are engaged on. 
 
 But though no rules can be given for detecting and ex- 
 plaining every fallacious ambiguity, it is useful to learn and 
 to keep in mind where to seek for it : namely, to look to the 
 Middle-t^rm (the argument having been first stated in a syllo- 
 gistic form) and to observe whether that is employed precisely 
 in the same sense in each Premise. 
 
 As for the Terms of the Conclusion, there is not much 
 danger of error or fallacy from any possible ambiguity in one 
 of these ; since in whatever sense either of these is employed 
 in the Premise, it will naturally be understood in the Conclu- 
 sion, in that same sense ; though in itself it might admit of 
 other meanings. 
 
 If, for instance, any one should conclude that the ' Plantain ' 
 is ' worth cultivation in places where it will flourish, because 
 it produces a vast amount of human food,' you would under- 
 
96> COMPENDIUM. \_Part II. 
 
 stand him to mean, both in the Premise and the Conclusion, 
 the fruit-bearing ' Plantain ' of the West Indies, and not the 
 herb that grows in our fields. 
 
 Sometimes, however, in a long train of Reasoning, a person 
 may be led into error, by remembering merely that a certain 
 Proposition has been proved, while he forgets in what sense it 
 was proved. 
 
 § 6. There are six rules commonly laid down, as resulting 
 from the two Canons above mentioned ; by which rules any 
 apparent Syllogism is to be tested : since none can be objected 
 to v/hich does not violate any of these rules ; and any appar- 
 ent-syllogism which does violate any of them, is not, in reality, 
 conformable to the above Canons. 
 
 i. A Syllogism must have three, and only three. Terms. 
 
 ii. It must have three, and but three Propositions. 
 
 iii. The Middle-term must be one only, [^. e, not douhW] 
 and, therefore, must be unequivocal^ and must be (in one at 
 least of the Premises) distributed, 
 
 iv. No Term is to be distributed in the Conclusion that was 
 not distributed in the Premise : [or, there must be no ' illicit- 
 process.'] 
 
 V. One at least of the Premises must be affirmative ; since, 
 if both were negative, the Middle-term would not have been 
 pronounced either to agree with each of the ' Extremes,' or to 
 agree with one and disagree with the other ; but to disagree 
 with hoth ; ' whence nothing can be inferred : as ' No X is Y ; 
 and Z is not X,' evidently affords no grounds for comparing Y 
 and Z together. 
 
 And vi. If one Premise be negative, the Conclusion must 
 be negative ; since — inasmuch as the other Premise must be 
 affirmative — the Middle will have been assumed to agree 
 with one of the ' Extremes,' and to disagree with the other. 
 
 All these rules will have been sufficiently explained in what 
 has been already said. 
 
Lesson xii.] terms of a syllogism. 97 
 
 And from these you Avill perceive that in every Syllogism 
 one Premise at least must be Universal ; since, if both were 
 Particular, there would be eitlier an undistributed JMiddle, or 
 an Illicit-process. 
 
 For if each Premise were I (Particular-affirmative) there 
 would be no distribution of any Term at all ; and if the 
 Premises w^ere I and O, there would be but one Term, — the 
 Predicate of [the particular-negative] — distributed ; and 
 supposing that one to be the IVIiddle, then the Conclusion 
 (being of course negative, by rule vi.) would have its Predi- 
 cate — the Major-term — distributed, w^hich had not been 
 distributed in the Premise. Thus ' Some X is Y ; some Z is 
 not X,' or again ' Some X is not Y ; some Z is X,' would 
 prove nothing. 
 
 And for the like reasons, if one of the Premises be Particu- 
 lar, you can only infer a Particular Conclusion : as ' Every 
 X is Y ; some Z is X,' v^dll only authorize you to conclude 
 ^ Some Z is Y ; ' since to infer a Universal would be an ' illicit- 
 process of the MinoV'term^ 
 
 § 7. What is called the ' Mood' [or ' Mode '] of a Syllo- 
 gism, is the designation of the three Propositions it contains 
 (in the order in which they stand) according to their respect- 
 ive Quantity and Quality ; that is, according as each Propo- 
 sition is A, E, I, or O. 
 
 Looking merely at the arithmetical calculation of permuta' 
 tions, (as it is called) all the possible combinations of the four 
 Symbols, by threes, would amount to 64. For each of the 4 
 admits of being combined, in pairs, w^ith each of the 4 ; [as A, 
 with A, with E, with I, and with 0, <S:c.) which gives 16 pairs ; 
 and each of these 16 pairs admits of being combined with each 
 of the 4 as a third ; which gives 16 X 4 = 64. 
 
 But it is plain that several of these combinations are such 
 as oould not take place in a Syllogism. For instance E, O, 
 0, could not be a INIood of any Syllogism, since it would have 
 9 
 
98 COMPENDIUM. \^Part II. 
 
 negative-premises (see Rule V.) nor I, O, O, which would 
 have both premises particular^ nor I, E, O, which would have 
 an illicit-process of the Major-term ; since the Conclusion, 
 being negative, would have the Major-term distributed, while 
 the Major-premise, being I, would have no term distributed. 
 And so with many others. 
 
 There will be found on examination to be in all only eleven 
 Moods in which any Syllogism can be expressed : and these 
 are, A, A, A, — E, A, E, — A, I, I, — E, I, O, — A, E, E, 
 _A, O, O, — A, A, I, — I, A, I, — E, A, O, — O, A, 0, 
 — A, E, O. 
 
 § 8. What is called the ' Figure ' of a Syllogism, is, the 
 situation of the Middle-term, in the two Premises respectively, 
 with relation to the two ' Extremes ' [or Terms] of the Con- 
 clusion, — the Major and Minor-terms. 
 
 It is evident that all the possible collocations of the Middle 
 must be four : since it must be either the Subject of the Major- 
 premise and the Predicate of the Minor ; or the Predicate of 
 each ; or the Subject of each : or the Predicate of the Major 
 and Subject of the Minor. 
 
 On looking to the examples originally given, you will see 
 that a Syllogism in that form \_' Every X is Y ; Z is X ; 
 therefore Z is Y '] has the Middle-term made the Subject of 
 the Major-premise, and the Predicate of the Minor, 
 
 This is called the First Figure ; and it is to Syllogisms in 
 this Figure alone that the ' Dictum ' above-mentioned will at 
 once apply. ; 
 
 § 9. If you look to the forms afterwards exemplified, (§ 1 I 
 of this Lesson,) as ' No savages, &c.' or ' No Y is X ; Z is X ; i 
 therefore Z is not Y,' you will see that the Middle is the 
 Predicate of each Premise. This is called the Second Figure, i 
 And in this, evidently none but negative Conclusions can be 
 proved ; since one of the Premises must be negative, in order; 
 that the Middle-term may be (by being the Predicate of al 
 JSfegative) distributed. 
 
Lesson xii.] mood of a syllogism. 99 
 
 Again, the Middle-term may be the Subject of each Premise. 
 And this is called the Third Figure, Thus ' Some X is Y ; 
 every X is Z ; therefore some Z is Y ; ' is a correct Syllo- 
 gism in the third Figure, being conformable to the first 
 Canon. 
 
 And the Syllogism here given as an example may be easily 
 reduced to the first Figure, by simply-converting the Major- 
 premise, and taking it for the Minor; [transposing the 
 Premises] which will enable you to infer the simple-converse 
 of the Conclusion : as ' Every X is Z ; Some Y is X ; there- 
 fore Some Y is Z : ' and this implies that ' Some Z is Y ; ' 
 since (as was explained formerly) the simple conversion of I 
 is illative. 
 
 For instance, ^ some painful things are salutary ; every 
 thing painful is an object of dread ; therefore some things 
 which are object-S of dread are salutary ; ' this, though a valid 
 Syllogism as it stands, may be reduced, in the manner above 
 stated, to the first Figure. 
 
 In this, or in other ways, any Syllogism in the third Figure 
 may be easily ' reduced ' (as the technical phrase is) to the fii*st 
 Figure. 
 
 In this third Figure you will find that none but Particular 
 Conclusions can be drawn. To infer a Universal would 
 always, you will find, involve an ' illicit-process of the Minor- 
 term.' For if the Premises are both Universal, which (as we 
 have already seen, (§ 6) they must always be, to warrant a 
 Universal Conclusion) then, supposing them to be A, A, there 
 wnll have been, — in this third Figure — no term distributed 
 except the Middle ; (affirmatives not distributing the Predi- 
 cate) and consequently no term can be distributed in the 
 Conclusion ; which must, therefore, be I. 
 
 And if the Premises be E and A, there will have been 
 (besides the Middle) only one term, — the Predicate of E, 
 distributed; and. consequently only one term can be dis- 
 
100 COMPENDIUM. \_Part II. 
 
 tributed in tlie Conclusion ; and that one must be the Predi- 
 cate of O ; since the Universal [E] would have both terms 
 distributed. 
 
 § 10. The third Figure might be called the 'exceptive^ or 
 the ' refutatorj ' Figure ; (or, agreeably to the expression 
 of the Greek writers, the ' enstatic ; ') as being a very natu- 
 ral form of expressing arguments which go to establish the 
 contradictory of some Universal Proposition that any one may 
 have maintained, or that may be generally believed. 
 
 For instance, if any one were speaking of ' metals ' as being, 
 universally^ ' conductors of heat,' you might adduce ' Platina ' 
 as an exception. Or should any one contend that ' no agent 
 incapable of distinguishing moral good and evil (as, for in- 
 stance, a madman) can be deterred from any act by appre- 
 hension of punishment,' you might refute this, by adducing 
 the case of a brute, — for instance, a dog — deterred from 
 sheep-biting by fear of punishment. And such arguments 
 would fall very naturally into the third Figure. 
 
 It is, especially, the most natural form in which to express 
 an argument — such as we often employ for the above pur- 
 pose — in which the Middle-term is a Singular-terwi ; as when, 
 for instance, you prove by the example of a certain individual,* 
 the contradictory of a Proposition (which would seem to most 
 persons a very probable conjecture) that a deaf and dumb 
 person, born blind, cannot be taught language. 
 
 The second Figure may be called the ' exclusive ' Figure ; 
 being a very natural form for arguments used in any inquiry 
 in which we go on excluding^ one by one, certain suppositions, 
 or certain classes of things, from that whose description we 
 are seeking to ascertain. 
 
 Thus, certain symptoms, suppose, exclude 'small-pox ;^ 
 that is, prove this not to be the patient's disorder; other 
 
 ^ See the Note on a former Lesson, oa the case of Laura Bridgeman. 
 
Lesson xiii.] figure of a syllogis^m. 101 
 
 symptoms, suppose, exclude ' Scarlatina ' &e., and so one 
 may proceed by gradually narrowing the range of possible 
 suppositions. 
 
 These three Figures are the only ones in which any argu- 
 ment would, designedly, be stated. For, as to what is called 
 the 4th Figure (in which the Middle-term is made the Pred- 
 icate of the Major-premise and the Subject of the Minor) 
 though a Syllogism so stated would be undeniably valid if 
 conformable to the rules (as ' every Y is X ; no X is Z ; 
 therefore no Z is Y ') this form is only a clumsy and inverted 
 way of stating what would naturally be expressed in the 1st 
 Figure ; as, in this example, might be done by transposing 
 the Premises, and simply-converting the Conclusion. 
 
 LESSON xm. 
 
 § 1. Besides (7a/(9^oncaZ-arguments, which we have been 
 treating of, Eeasoning is often expressed in a JTypothetical 
 form. And though such arguments may be reduced into a 
 categorical form, this is not necessary, except for the purpose 
 of pointing out the sameness^ in all cases, of the Eeasoning- 
 process. For you may exhibit in a hypothetical form, a per- 
 fect ' Syllogism ' as above defined. 
 
 A Hypothetical (or as some writers call it, a ' compound ') 
 Proposition, consists of ^ two or more Categorical-propositions, 
 united by a Conjunction, in such a manner as to make them 
 one proposition.' And the different kinds of hypothetical- 
 proposition are named after their respective Conjunctions; 
 9* 
 
102 COMPENDIUM. [^Pay-t II. 
 
 namely ' Conditional ' and ' Disjunctive*.' For instance, ' if 
 A is B, then X is Y ' is a Conditional-propositionf ; ' either 
 A is B, or X is Y ' is Disjunctive. 
 
 And each of these is a real Proposition^ ^. e,, asserts some- 
 thing ; and consequently is either true, or false ; which (as 
 was formerly explained) is peculiar to Propositions: and 
 each is also one Proposition, though consisting of several 
 parts [or ' members '] each of which, if taken separately, 
 would be itself a Proposition ; but the Conjunction (which is 
 called a Copula) makes the whole one Proposition. 
 
 § 2. For instance, ' the world is eternal,' is a proposition : 
 ^ records earlier than the Mosaic exist,' is another proposition ; 
 and ' if the world be eternal, records earlier than the Mosaic 
 must exist,' is a third proposition distinct from each of the 
 other, and . which may be true, though they be both false: 
 since it does not assert the truth of either of them, but only 
 the connexion between them. Again, should any one say ' if 
 the Northern-lights be shining, some great revolution of an 
 Empire is going on,' this would be, properly speaking, a false 
 Proposition, even should it turn out that each of the ' mem- 
 bers ' stated as a categorical-proposition, is true ; supposing it 
 admitted that they have no connexion with each other. 
 
 Observe, however, that no false Conclusion can be de- 
 duced from a false Conditional-proposition, when it so happens 
 that both its ' members ' (stated as categorical-propositions) 
 are true. 
 
 In the case of a Disjunctive-proposition on the other hand, 
 it is implied that one at least, of its ' members ' (stated as a 
 categorical-proposition) must be true, and that, if not, the 
 whole Proposition must be false. As ' this man was either at 
 
 ^ See Lesson X. 
 
 t Those writers who use the word compound proposition instead of %- 
 pothetical^ employ ' h}T30thetical ' to signify ' conditional.' 
 
Lesson XIII.] HYPOTnEXICAL-PROPOSITIOXS. 103 
 
 Oxford or at Cambridge ' would not be true, if he were not at 
 Oxford, and not at Cambridge. 
 
 And it is usually meant to be understood that only one of 
 the members can be true : for if this were not the meaning in 
 such an example as the foregoing, it would have been more 
 correct to say ' this man was either at Oxford, or Cambridge, 
 or hotli^ 
 
 § 3. A Hypothetical-5yZ/<9(/^5;?^ is one in which the reasoning 
 itself turns on the hypothesis; not, every syllogism that has 
 in it a hypothetical premise ; for the ' hypothesis ' may be a 
 portion of one of the Terms, and the syllogism may be merely 
 categorical. 
 
 For instance, ' Real miracles are evidence of a divine com- 
 mission ; if the works of Jesus were acknowledged miraculous 
 by the unbelieving Jews, they must have been real miracles ; 
 therefore, the works of Jesus (if they were acknowledged, 
 &c.) are evidence of a divine commission ; ' is a categorical 
 syllogism; the hypothesis being merely a portion of the 
 Minor-term. 
 
 And so also with such an example as ' Every X is either 
 Y or W ; Z is X ; therefore Z is either Y or W.' 
 
 In a hypothetical-syllogism, properly so called, — that is, in 
 which the reasoning is based on a hypothetical-premise, that 
 premise is called the Major^ and the other — which is cate- 
 gorical — is called the Minor-premise. 
 
 We will speak first of CbwcZz^/oyzaZ-syllogisms. 
 
 There are in a Conditional-proposition two members, [cate- 
 gorical-propositions] whereof one is asserted to depend on the 
 other. That on which the other depends is called the ^ Ante- 
 cedent ; that which depends on it, the Consequent ;^ and the 
 connexion between the two, (expressed by ' if,' or ' supposing') 
 is called the ' consequence' 
 
 (Oonsenuencc) (Antecedent) 
 
 For instance 'If this man is a murderer 
 
104 COMPENDIUM. \_Part II. 
 
 (Consequent) (Consequent) 
 
 he deserves death.' 'The English are well olF- 
 
 (Consequence) (Antecedent) 
 
 if thej know their own advantages. 
 
 The natural order is to place the ' Antecedent ' /r5^ ; 
 but this (as you will see from the example above) is not 
 essential. 
 
 § 4. The meaning, then, of a Conditional-proposition, is, 
 that ' the Antecedent being assumed to be true, the Consequent 
 is to be granted as true also.' And this may be considered in 
 two points of view : 1st, allov/ing that the Antecedent is true, 
 the Consequent must be true ; 2ndly, supposing the Antece- 
 dent were true, the Consequent would be true. 
 
 Hence, there are two kinds of Condition ah syllogism ; 1st, 
 if the Antecedent be (in the minor-premise) granted to be 
 true^ the Consequent may (in the Conclusion) be inferred : 
 2ndly, if the Consequent be not true — that is, if its Contra- 
 dictory be assumed in the minor-premise — the Antecedent 
 cannot be true ; that is, its Contradictory may, in the Conclu- 
 sion, be inferred : since if the Antecedent had been true, the 
 Consequent (which we have assumed to be false) would have 
 been true also. 
 
 A Syllogism of the former kind, is called ' Constructive ; ' 
 of the latter kind, ' Destructive! 
 
 For instance, ' if A is B, X is Y : ' let this be the major- 
 premise ; then if you add, ' but A is B ; therefore X is Y,' 
 this forms a Constructive-syllogism : if you say ' X is not Y ; 
 therefore A is not B,' this is a Destructive-syllogism. Thus, 
 ' if this river has tides, the sea into which it flows must have 
 tides ; ' then if I add ^ this river has tides,' it follows in Con- 
 clusion, that ' the sea into which it flows has tides ; ' which 
 is a Constructive-syllogism. If I add, ' the sea into which it 
 flows has not tides,' it follows that ' this river has not tides.' 
 
 § 5. And here observe, by the way, that, in hypothetical- 
 arguments, we are not concerned with the distinction between 
 
Lesson xiii.] conditional-proposition. 105 
 
 affirmative and negative Conclusions, For, of the two mem- 
 bers of a Conditional-propositioiij either, or Loth, may be 
 affirmative, or may be negative ; so that we may establish tlie 
 truth ' constructively ' of either an affirmative or a negative 
 Consequent; or may (^destructively') establish the falsity — 
 that is, infer the Contradictory — of either an affirmative or a 
 negative Antecedent. 
 
 For instance ' if no miracles had been displayed by the first 
 preachers of the Gospel, they could not have obtained a hear- 
 ing ; but they did obtain a hearing ; therefore some miracles 
 must have been displayed by them,' is a Destructive-condi- 
 tional-Syllogism. 
 
 The Consequent, as has been said, depends on the Ante- 
 cedent ; so that, if the Antecedent be true, the Consequent 
 will be true also ; but as the Antecedent does not depend on 
 the Consequent, nothing is proved by denying the Antecedent, 
 or again, by assuming the truth of the Consequent. Suppose 
 it granted that 'if A is B, X is Y,' though it may indeed so 
 happen that X is Y, only on that condition, — that is, that if 
 X is Y, A is B, — this is not implied by the original asser- 
 tion : so that (merely assuming that original assertion,) 
 to add that ' A is not B,' or again, to say ' X is Y,' proves 
 nothing. 
 
 For instance, ' if this man has committed theft he deserves 
 punishment ' does not authorize me to proceed either to say 
 ^ he has not committed theft ; therefore he does not deserve 
 pun -shment ; ' or again, ' he deserves punishment ; therefore 
 he has committed theft.' For it is (in this case) evident that 
 a man may deserve punishment for some other offisnce. 
 
 § 6. And you may observe, that the fallacy of affirming the 
 Consequent and thence inferring the truth of the Antecedent, 
 answers to the fallacy (in Categoricals) of undistributed mid- 
 die, or to that of negative-premises ; as may be seen from the 
 iibove example. For to say ' every one who has committed 
 
106 COMPENDIUM. \_Part II. 
 
 theft deserves punishment; and this man deserves punish- 
 ment/ would evidently be a case of undistributed-middle. 
 And again, if instead of saying ' if this man has a fever he is 
 not fit to travel ; and he is not fit to travel ; therefore he has 
 a fever,' you say ' no one who has a fever is fit to travel,' &c. 
 there will be the fallacy of two negative-premises. 
 
 The Fallacy again, of denying the Antecedent and thence 
 inferring the denial of the Consequent, would correspond (in 
 Categoricals) either to an 'Illicit-process of the Major-term/ 
 or to the Fallacy of ' two negative -premises,' or that of intro- 
 ducing palpably ' more than three terms.' For instance, sup- 
 pose instead of saying ' if this man has committed theft &c.' 
 you say, ' Every one who has committed theft deserves pun- 
 ishment ; this man has not committed theft, &c.' this would 
 be an illicit-process of the Major. Or again, suppose, instead 
 of saying ' if this man has a fever, he is not fit to travel ; but 
 he has not a fever ; therefore he is fit to travel,' you say ' No 
 one who has a fever is fit to travel ; this man has not a fever 
 &c.' this would be to employ ' two negative-premises.' Again, 
 ' If this army is not brave it will not be victorious ; it is brave ; 
 therefore it will be victorious ; ' would, if expressed categor- 
 ically, have palpably more than three terms. 
 
 § 7. It is plain from what has been above said, that a Con- 
 ditional-proposition may be illatively converted^ by taking the ' 
 Contradictory of the Consequent for an Antecedent, and (of 
 course) the Contradictory of the Antecedent, for a Conse- 
 quent. ' If A is B, X is Y ' implies that ' if X is not Y, 
 A is not B.' ' If all wages be regulated by the price of food, 
 an English laborer will have higher wages than an Ameri- 
 can ; ' this manifestly implies, that, ' if an English laborer has 
 not higher wages than an American, all wages are not regu- 
 lated by the price of food.' 
 
 This corresponds to the conversion of the categorical-propo- 1 
 sition A, ' by negation ; ' [_' contraposition,'] every Conditional- 
 
Lesson xiii.] conditional-proposition. 107 
 
 proposition corresponding in fact to a Universal-affirmative- 
 Categorical : the Antecedent answering to the Subject^ and the 
 Consequent^ to the Predicate, 
 
 It is evident, that if you thus convert the Major-premise 
 [the hypothetical-premise] of any Conditional-syllogism, you 
 change the Syllogism from ' Constructive' to Destructive,' 
 or vice versa, from Destructive to Constructive. 
 
 The Proposition ^ if A is B, X is Y ' may be considered as 
 amounting to this ; ' The case [or supposition] of A being B, 
 is a case of X being Y.' And then to say (as in the Minor- 
 premise and the conclusion, of a constructive-conditional syl- 
 logism) 'A is B; and therefore X is Y/ is equivalent to 
 saying ' the present [or the existing] case is a case of A being 
 B ; therefore this is a case of X being Y.' 
 
 Or again, ' if the Stoics are right, pain is no evil ; but pain 
 is an evil ; therefore the Stoics are not right,' (which is a 
 destructive-conditional syllogism) may be reduced to a Cate- 
 gorical, thus : ' To say that pain is no evil - - is not - - true ; 
 to say that the Stoics are right - - is - - to say that pain is no 
 evil ; therefore to say that the Stoics are right - - is not - - 
 true.' 
 
 This Syllogism is in the first Figure. The argument might 
 be exhibited in the third Figure, thus : ' that pain is no evil is 
 not true ; but that is maintained by the Stoics ; therefore some- 
 thing maintained by the Stoics is not true.' 
 
 In some such way (taking care always to preserve the 
 same sense) any argument may be exhibited in various differ- 
 ent forms of expression, (the choice of wdiich is merely a 
 matter of convenience) so as to point out and impress on the 
 mind that the reasoning-process itself is always essentially one 
 and the same, and may ultimately be referred to the ' Die- 
 tum ' formerly mentioned. 
 
 § 8. In a disjunctive-preposition, as has been already ob- 
 served, it is implied that at least some one of the ' members ' 
 
108 COMPENDIUM. \_Part II. 
 
 must he true. If, therefore, all except one be (in the minor- 
 premise) denied, the truth of the remaining one may be in- 
 ferred. 
 
 For instance, ^ either the Gospel was an invention of im- 
 postors, or it was a dream of fanatics, or a real revelation ; 
 it was neither of the two former ; therefore it was a real rev- 
 elation.' 
 
 But if there be more than two members, and you deny (in 
 the minor-premise) one or more of them, but not all except 
 oncj then you can only draw a disjunctive Conclusion ; as, 
 ' this event occurred either in Spring, Summer, Autumn, or 
 "Winter ; it did not occur in Summer or in Winter ; therefore 
 it occurred either in Spring or in Autumn.' 
 
 In a Disjunctive-proposition it is (as has been said above) 
 usually understood that the members are exclusive ; i, e. that 
 only one, of them can be true : and you may, on that supposi- 
 tion, infer from the truth of one of them (assumed in the 
 Minor) the Contradictory of the other, or others. As ' either 
 A is B, or C is D, or X is Y ; but A is B ; therefore C is 
 not D, nor is X Y.' 
 
 § 9. A Disjunctive-Syllogism may readily be reduced to a 
 Conditional, by merely altering the form of the Major-pre- 
 mise ; namely, by taking as an 'Antecedent the Contradictory 
 of one or more of the members ; everything else remaining as 
 before. Thus, in the example lately given, you might say, 
 ' If this did not occur in Summer nor in Winter, it must have 
 occurred either in Spring or in Autumn ; ' &c. 
 
 A Disjunctive-proposition, you are to observe, is, (as well 
 as a Conditional) always affirmative. For, either kind 
 of Hypothetical-proposition always affirms the connexion of 
 the members of it [categorical-propositions contained in it] 
 whether these be affirmative or negative propositions. 
 
 And the contradiction of a Hypothetical-proposition must, 
 therefore, consist in denying this connexion ; which is done, 
 
Lesson xiy.] dilemma. 109 
 
 not in a Plypothetical, but in a Categorical-proposition. When 
 it is asserted that ' if A is B, X is Y/ you would contradict 
 this by saying ' it does not follow that if A is 13, X must be 
 Y;' or by some such expression. Or when it is asserted 
 that ' either A is B, or X is Y/ you might contradict this by 
 saying 'it is 2>ossihle that neither A is B, nor X, Y ; ' or you 
 might contradict a Disjunctive-^^roposition by two or more 
 Categorical propositions ; namely, by asserting separately the 
 Contradictory of each member ; as ' either some Z is Y, or 
 else some W is not X,' might be contradicted by ' no Z is Y, 
 and every W is X.' 
 
 LESSON XIY. 
 
 § 1. It will often happen that you will have occasion to 
 employ that complex kind of Conditional-syllogism (consisting 
 of two or more such syllogisms combined) wdiich is commonly 
 called a ' Dilemma,^ 
 
 When you have before you as admitted truths two (or more) 
 Conditional-propositions, with different Antecedents, but each 
 with the same Consequent, and these Antecedents are such 
 that you cannot be sure of the truth of any one of them, sepa- 
 rately, but are sure that one or other must be true, you will 
 then, naturally be led to state both of the Conditional-proposi- 
 tions, first ; and next, to assert disjunctively the Antecedents ; 
 and thus to infer the common Consequent. As ' if every A is 
 B, X is Y ; and if some A is not B, X is Y ; but either every 
 A is B, or some A is not B ; therefore X is Y.' 
 
 This kind of Argument was urged by the opponents of Don 
 Carlos, the pretender to the Spanish Throne ; which he 
 10 
 
110 COMPENDIUM. [^Part II. 
 
 claimed as heir-male, against his niece the queen, by virtue 
 of the Salic-law excluding females; which was established 
 (contrary to the ancient Spanish usage) by a former king of 
 Spain, and was repealed by king Ferdinand. They say ' if a 
 king of Spain has a right to aUer the law of succession, Carlos 
 has no claim : and if no king of Spain has that right, Carlos 
 has no claim ; but a king of Spain either has or has not, 
 such right; therefore (on either supposition) Carlos has no 
 elaim.' 
 
 § 2. When several Conditional-propositions have different 
 Consequents as well as different Antecedents, then we can 
 only disjunctively infer those Consequents : that is, we can 
 only infer that (supposing some one or other of the Antece- 
 dents true) one or other of the Consequents must be true. As, 
 ^ if A is B, X is Y ; and if C is D, P is Q ; but either A is 
 B, or C is D ; therefore either X is Y, or P is Q.' Thus, ^ if 
 the obedience due from Subjects to Kulers extends to reli- 
 gious worship, the ancient Christians are to be censured for 
 refusing to worship the heathen idols ; if the obedience, &c., 
 does not so extend, no man ought to suffer civil penalties on 
 account of his religion ; but the obedience, &c., either does 
 so extend, or it does not ; therefore either the ancient Chris- 
 tians are to be censured, &c., or else no man ought to suffer 
 civil penalties on account of his religion.' 
 
 So also, ' if man is capable of rising, unassisted, from a sav- 
 age to a civilized state, some instances may be produced of a 
 race of Savages having thus civilized themselves ; and if Man 
 is not capable of this, then, the first rudiments of civilization 
 must have originally come from a super-human instructor ; 
 but either Man is thus capable, or not ; therefore either some j 
 such instance can be produced, or the first rudiments, &c.' 
 
 § 3. And when there are several Antecedents each with a 
 different Consequent, then, we may have a Destructive- 
 dilemma : that is, we may, in the Minor-premise disjunctively 
 
Lesson xiY.] dilemma. Ill 
 
 deny the Consequents, and in the Conclusion disjunctively 
 deny the Antecedents. Or again, you may have a Dilemma 
 partly Constructive and partly Destructive; that is, in the 
 Minor-premise (which in a Dilemma is always a Disjunctive- 
 proposition) the members — suppose, for instance, there are 
 two, — may be, one of them, the assertion of the Antecedent 
 of one of the Conditional-propositions, and the other, the con- 
 tradictory of the Consequent of the other Conditional. 
 
 Suppose we say, 'if X is not Y, A is not B ; and if P is 
 not Q, C is not D ; but either A is B, or C is D ; therefore 
 either X is Y, or P is Q ; ' this would be a Destructive-Di- 
 lemma ; and you may see that it corresponds exactly w^ith the 
 example given a little above, only that we have, here, con- 
 verted both of the Conditional-propositions. See § 7 of the 
 preceding Lesson. If we had converted one only, and not, the 
 other, of the Conditionals, (as ' if A is B, X is Y ; and if P is 
 not Q, C is not D ; ' &c.,) then the Dilemma would have been 
 partly Constructive and partly Destructive. For, as has been 
 formerly explained, the Difterence between a Constructive 
 and a Destructive Syllogism consists merely in the form of 
 expression, and it is very easy to reduce either form into the 
 other. 
 
 It may be worth while to observe, that it is very common 
 to state the J/mo?'-premise of a Dilemma first ; in order to 
 show the more clearly that the several Categorical proposi- 
 tions w^hich are, each, doubtful, wdien taken separately, may 
 be combined into a Disjunctive-proposition that admits of no 
 doubt. And this Minor-premise being disjunctive, some have 
 hence been led to suppose that a Dilemma is a kind of dis- 
 jiinctive argument ; though it is really, as w- e have shown, a 
 Conditional. 
 
 The name of ' Z^/lemma, again, has led some to suppose, 
 that it must consist of two members only ; though it is evident 
 that there may be any number. 
 
112 COMPENDIUM. [^Paii II. 
 
 § 4. When there is a long series of arguments, the Conclu- 
 sion of each being made one of the Premises of the next, till 
 you arrive at your ultimate Conclusion, it is of course a tedious 
 process to exhibit the whole in the form of a series of Syllo- 
 gisms. This process may in many cases' be considerably 
 abridged, without departing from the strict syllogistic-form: 
 [that is, such a form as shows the conclusiveness of the rea- 
 soning, from the expression alonSj independently of the mean- 
 ing of the Terms, and equally well when arbitrary Symbols 
 are used to stand for the Terms.] 
 
 What is called a ' Sorites ' (from a Greek word signifying 
 a heap, ov pile) is such an abridged form of stating a train of 
 arguments. When you state a series of propositions in v/hich 
 the Predicate of the first is made the Subject (distributed) of 
 the next, and the Predicate of that, again, in like manner, the 
 Subject of the next, and so on, to any length, you may then 
 predicate in the Conclusion the Predicate of the last Premise 
 of the Subject of the first. 
 
 Thus ' A (either " some " or " every ") is B ; every B is 
 C ; every C is D ; every D is E ; &c. therefore A is E ; ' or 
 ' no D is E ; therefore A is not E.' Thus, also, ^ this man is 
 selfish ; whoever is selfish is neglectful of the good of others ; 
 whoever is neglectful of the good of others is destitute of 
 friends ; and whoever is destitute of friends is wretched ; 
 therefore this man is wretched.' 
 
 § 5. To such a form of argumentation the ' Dictum ' for- 
 merly treated of may be applied, with one small addition, 
 which is self evident. ' Whatever is affirmed or denied of a 
 whole Class, may be afiirmed or denied of whatever is com- 
 prehended in \_any Class that is wholly comprehended in"] that 
 Class.' This sentence, omitting the portion enclosed in brack- 
 ets, you will recognize as the ' Dictum,' originally laid down : 
 and the words in brackets supply that extension of it which 
 makes it applicable to a ' Sorites,' of whatever length ; since 
 
Lesson xiiv.] sorites. llfi 
 
 it is manifest that that clause might be enlarged, as far as you 
 will, into ' a Class that is wholly comprehended in a Class, 
 which again is wholly comprehended in another Class, &c.' 
 
 You will perceive, on looking at the above examples, that, 
 though the first of the propositions of a Sorites may be either 
 Universal or Particular, all the succeeding Premises must be 
 Universal; since, else, the ' Dictum,' as stated just above, 
 would not apply. 
 
 You will perceive also that, though the last of the Premises 
 may be either Negative or Affirmative, all the preceding ones 
 must be Affirmative^ in order that the Dictum may be appli- 
 cable. Thus, in the example, first given, it is allowable to 
 say ' no D is E ; therefore A is not E ; ' but then it is neces- 
 sary that ' C ' should be comprehended in ' D ' (not excluded 
 from it) and ' B ' likewise in ^ C,' and ' A ' in ' B,* since other- 
 wise the ' Dictum ' would not be applicable. 
 
 § 6. It will be seen, on examining the examples, that there 
 are, in a Sorites, as many Middle-terms as there are interme- 
 diate propositions between the first and the last ; and that it 
 may be stated in just so many separate syllogisms in the 1st 
 Figure ; which is the simplest and most common form of a 
 syllogism. 
 
 The first of these syllogisms will have for its il/cyor-pre- 
 mise the second of the propositions in the series, and for its 
 J/mor-premise, the first of them : and the Conclusion of this 
 first syllogism will be a proposition which is (in the Sorites) 
 not expressed but understood ; and which will be the Minor- 
 premise of the next Syllogism. And of this next syllogism 
 the Major-premise will be the third that is expressed in the 
 Sorites ; and so on. 
 
 For instance, (1st,) ^ every B is C; A is B ; [therefore A 
 is C;'] and (2dly) 'every C is D;' ['A is C; therefore A 
 is D,'] &c. 
 
 10* 
 
114 COMPENDIUM. \_Part II. 
 
 The portions enclosed in brackets are those which in the 
 Sorites are understood. 
 
 The only Minor-^YQxm&Q expressed in the Sorites is the first 
 proposition of the Series ; all the succeeding minor-premises 
 being understood. 
 
 And hence it is that (as has been above said) this first is 
 the only one of all the Premises that may allowably be a 
 Particular : because, in the first Figure, though the Minor 
 may be either Universal or Particular, the Major (as you see 
 from what was formerly said, of the ' Dictum,') must always 
 be Universal; and all the premises in the Sorites except the 
 first, are J[fa;*or-premises. 
 
 In this way may also be explained what was above said, 
 that the last of the premises of a Sorites is the only one that 
 can allowably be a Negative : since if any of the others were 
 negative, the result would be that one of the Syllogisms of 
 the Series would have a negative minor-premise ; which, in the 
 first Figure (as you will see by again referring to the ' Dic- 
 tum ') is inadmissible. 
 
 § 7. A series of Conditional-sjlhgisms (which correspond, 
 as has been shown, to Categorical-syllogisms in the first 
 Figure) may in like manner be abridged into a Sorites ; by 
 making the Consequent of the first proposition the Antecedent 
 of the next ; and so on : and then drawing the Conclusion by 
 either asserting the Jirst Antecedent, and thence (construc- 
 tively) inferring the last Consequent, or else, denying the 
 last of the Consequents, and (destructively) inferring the 
 Contradictory of the first Antecedent. ' As, ' If A is B, C is 
 D ; and if C is D, E is F ; and if E is F, G is H,' &c. : and 
 then, if the Sorites be ' Constructive,' you add ' but A is B ; 
 therefore G is H ; ' or, if ' destructive,' ' but G is not H ; 
 therefore A is not B.' 
 
 The foregoing are all the forms in which Reasoning can be 
 
Lesson xiv.] enthymeme. 115 
 
 exhibited Syllogistically ; i. e. so that its validity shall be man- 
 ifest from the mere form of expression. 
 
 For, an Enthymeme, (see Lesson II. § 3) is manifestly not 
 syllogistic; since it is possible to admit the truth of the one 
 premise that it is expressed, and yet to deny the Conclusion. 
 
 An Enthymeme may indeed be such (since it contains all 
 the three Terms requisite for a Syllogism,) that we can read- 
 ily perceive what the premise is that ought to be understood, 
 and which if supplied, would make the Syllogism complete : 
 as ' Z is X ; therefore Z is Y ; ' [or ^ the Elk has horns on the 
 head ; therefore it is a ruminant '] this would be syllogistic, 
 if you were to prefix ' Every X is Y ; ' but whether this be 
 the Premise actually meant to be understood, we can only 
 judge from the sense of the words that are expressed, and from 
 what we believe respecting the subject-matter in hand, and 
 the design of the Speaker. 
 
 In a Syllogistic form, on the other hand, — w^hether Cat- 
 egorical, or Hypothetical, and whether at full length, or 
 abridged into a Sorites — that which is actually expressed in 
 the Premises is such that no one can possibly suppose these 
 true (whatever be the meaning of the Terms^ or whether we 
 understand them or not) ivithout admitting the truth of the 
 Conclusion thence drawn. 
 
 § 8. As for any arguments that are not expressed in a 
 regular form, of course no precise rules can be laid down for 
 reducing them into such a form ; since any arguments to 
 which such rules do apply, must evidently be, on that very 
 ground, pronounced to be already syllogistic. Some general 
 remarks, however, (drawn chiefly from what has been taught 
 in the foregoing Lessons) may be practically serviceable in 
 !he operation of reducing arguments into regular form. 
 
 i. It has been remarked (in Lesson HI. § 7) tliat men are 
 very impatient of tedious prolixity in Eeasoning; and that 
 the utmost brevity, — the most compressed statement of argu- 
 
116 COMPENDIUM. \^Part II. 
 
 mentation, — that is compatible witli clearness, is always 
 aimed at, and is, indeed, conducive to clearness. And hence 
 (as was pointed out) a single sentence, — or even a word, — 
 will often be a sufficient hint of an entire syllogism. 
 
 And it may be added, that such a sentence will sometimes 
 be in the form, not of a Proposition, but of an Exclamation^ 
 — a Question, or a Command; and yet will be such as read- 
 ily to suggest to the mind a Proposition. 
 
 For instance, in some of the examples lately given, one 
 might say (in place of one of the Propositions) ' Choose which 
 you will of these two suppositions ;*' or ' Who can doubt that 
 so and so follows ? ' 
 
 The message to Pilate from 'his wdfe* furnishes an instance 
 of a single word {'just ') suggesting a Major-premise, w^hile 
 the Conclusion is stated in the 'form of an exhortation : ' have 
 thou nothing to do with that just man.' And the succeeding 
 sentence must have been designed to convey a hint of Argu- 
 ments for the proof of each of the Premises on which that 
 Conclusion rested. 
 
 § 9. ii. Kemember that (as was formerly shown) we may 
 change any proposition from Affirmative to Negative, or vice 
 versa, without altering the sense : it being the same thing, for 
 instance, to affirm of any one the term ' not happy,' or to 
 deny ' happy.' So that an argument may be valid which might 
 appear, at the first glance, to have ' negative premises.' 
 
 But if the above experiment be tried in an argument that 
 is really faulty on that ground, the only effect will be, to change 
 one fallacy into another : as ' A covetous man is not happy ; 
 this man is not covetous ; therefore he is happy : ' here, if 
 you take 'happy' as the predicate of the Major, you have 
 negative-premises : if you take ' not happy ' [or ' unhappy '] 
 ^s the term, you will hdiw^four terms. 
 
 Matt. 27, 19. 
 
Lesson XIV.] conversion-by-negation. 11/ 
 
 On the other hand, ^ no one is happy ^vho is not content ; 
 no covetous man is content ; therefore no covetous man is 
 happy/ is a valid syllogism. 
 
 That the Conversion-by-negation [contra-position] of a Uni- 
 versal-affirmative, is illative^ has been formerly explained. 
 And it is very common, and often conducive to clearness, to 
 state such a proposition (A) in the form of this its converse 
 (E) ; as, for instance, instead of 'every motive that could 
 have induced this man to act so and so, must have been purely 
 benevolent,' to say ' no motive but pure benevolence could 
 have induced him to act so.' 
 
 iii. Remember that one single sentence (as was formerly 
 explained. Lesson IX. § 7) may imply several distinct propo- 
 sitions, according to the portions of it which you understand as 
 the Subject, and as the Predicate. For instance, ' It is the duty 
 of the Judge to decide for him who is in the right ; this plain- 
 tiff is in the right ; therefore it is the Judge's duty to decide 
 for him,' might be understood as having jive terms : but ac- 
 cording to the d?^ift of the first premise (considered as a part 
 of this argument) what you are speaking of is, not, ' the duty 
 of the Judge,' but ' the person who is in the right ; ' of whom 
 you assert that ' he is fairly entitled to the Judge's decision on 
 his side.' And if thus stated, the argument will be seen to be 
 valid. 
 
 And here it may be remarked, that to state distinctly as 
 Subject and Predicate, that which is really spoken of^ and that 
 which is said o/it, will be often the best and most effectual 
 exposure of a Fallacy ; which will always be the more likely 
 to escape detection, the more oblique and involved is the ex- 
 pression. 
 
PART III. 
 SUPPLEMENT, 
 
 LESSON XV. 
 
 § 1. There are some other technical-terms, which it la 
 useful to be familiar with, and which we will therefore now 
 proceed to treat of in a supplementary Lesson. They are such 
 as are usually introduced in an earlier place, previously to the 
 matter of the last ^ve Lessons. But it has been thought 
 better to postpone everything that was not indispensable for 
 the right understanding of what has been said concerning the 
 several forms of Syllogism. 
 
 A ' Common-term,' v/e have seen, is so called from its 
 expressing what is common to several things ; and is thence 
 called also a ' Predicable,' inasmuch as it can be affirmatively- 
 predicated, in the same sense [_' univocally '] of certain other 
 terms. It is evident that the word ' Predicable ' is relative^ 
 i. e. denotes the relation in which some Term stands to some 
 other, of which it can be predicated. And this relation is of 
 different kinds : in other words, there are several Classes [or 
 Heads] of Predicables. 
 
 When you are asked concerning any individual thing, 
 ^ what is it ? ' the answer you would give, if strictly correct; 
 would be what is technically called its ' Species : ' as ' this is 
 a pen ; ' ' that is a man ; ' ' this is a circle ; ' ' that is a mag- 
 net^ &c. 
 
 And the ' Species ' of anything is usually described in tech- 
 nical language as expressing its 'whole Essence ; ' meaning, 
 the whole of what can be expressed by a Common-ievm : for 
 
Lesson xv.J difference. 119 
 
 it is plain, that, (as was formerly shown) it is only by taking 
 an inadequate view of an ' Individual,' so as to abstract from 
 it what is common to it with certain other individuals, disre- 
 garding all that distinguishes it from them (including its actual 
 existence as a single object) — it is only then, I say, that we 
 can obtain any Common-term. 
 
 § 2. When the same question ' what is this ? ' is asked re- 
 specting a Species^ the term by which you answer, is, that 
 Predicable which is technically called the ' Genus ' of that 
 Species. As, ' what is a 'pe7i ? ' answer ' an Instrument ; ' [a 
 kind, or species of Instrument] ' what is a circle ? ' ^ a curvili- 
 near-plane-figure : ' so also ' a magnet ' would be said to be ^ a 
 Species [or kind] of Iron-ore,' &c. 
 
 When you are asked ' what kind of [or " what sort of "] 
 instrument is a pen ? ' you would answer, one ' designed for 
 ivriting ; ' this being what characterizes it, and distinguishes it 
 from other instruments : ' what kind of animal is Man ? ' the 
 answer would be ' rational ; ' as distinguishing the Species 
 from other animals ; ' what kind of plane-curvilinear-iigure is 
 a circle ? ' answer, ^ one whose circumference is- everywhere 
 equidistant from the Centre ; ' which circumstance distinguish- 
 es it from an Ellipse : &c. 
 
 Such a Predicable, then, is technically called the ' Differ- 
 ence ; ' [or, by the Latin name, ' Differentia '] in popular 
 language, frequently, the ^ Characteristic,' or the ' distinguishing 
 point.' And the ' Difference ' together with the ' Genus,' are 
 technically spoken of as ' constituting ' [' making up '] the 
 ' Species.' 
 
 Any quality [or ' attribute '] which invariably and pecu- 
 liarly belongs to a certain Species, but which yet is not that 
 which we fix on as characterizing the Species, is technically 
 called a ' Property ; ' [or ' Proprium '] of that Species. Thus, 
 ^risibility' [or the faculty of laughter] is reckoned a ' Prop- 
 erty ' of Man : one of the ' Properties ' of a Circle, is, that any 
 Single drawn in a semi-circle, is a right-angle : &c. 
 
120 SUPPLEMENT. \_Part III. 
 
 The power of ' attracting iron ' might be taken as the ' dif- 
 ference ' [or ' characteristic '] of a magnet ; and its ' Polar- 
 ity ' as a ' Property : ' or again, this latter might be taken 
 as its Difference, and the other, reckoned among its Prop- 
 erties. 
 
 For it is evidently a mere question of convenience, whichy 
 in any such case, we fi^L on as the Characteristic of the Species 
 we are contemplating. And either the one arrangement, or 
 the other, may be the more suitable, according to the kind of 
 pursuit we may be engaged in. 
 
 An Agriculturist, for instance, (see Lesson 8, § 5) would 
 not characterize each kind of plants in the same way as a Bot- 
 anist, or again, as a Florist : no more would a Builder, and a 
 Geologist, and a Chemist, characterize in the same way the 
 several kinds of stones. 
 
 § 3. Any Predicable which belongs to some (and not to 
 other) mdividuals of the same Species, [or which ' may be 
 present or absent, the Species remaining the same 'j is called 
 an ' Accident J 
 
 And these are of two kinds. A ^ Separable-accident ' is 
 one which may be removed from the Individual ; ' [or, which 
 may be absent or present, in that which we regard as one and 
 the same individual] as, for instance (in an example formerly 
 given) the ' Sun ' is regarded as the same individual thing, 
 whether ' rising,' or ' setting,' or in any other situation rela- 
 tively to the spot we are in : ' rising,' therefore, or ' setting/ 
 are separable accidents of the Sun. 
 
 So, also, to be in this or that dress, or posture, would be a 
 separable accident of an individual man ; but to be a native 
 of France, or of England, or to be of a certain character, 
 would be an * inseparable accident.' 
 
 It is by inseparable-accidents that we commonly distinguish 
 one Individual from another of the same species. And to 
 enumerate such Accidents is called ' giving a Description/ 
 (See § 10.) 
 
Lesson xy.] division. 121 
 
 Of course, it is only from individuals that any ' Accident * 
 can be ' inseparable ; ' for anything that is inseparable from a 
 Species^ [or, which forms a part of the signification of a Term 
 by which we denote a certain Species] is not an Accident, but a 
 Property. 
 
 § 4. Some writers enumerate among Properties such Predi- 
 cables as are pecidiar but not universal ; that is, which do not 
 apply, each, to every individual of a certain species, but are 
 'peculiar to that species : as Man alone can be ' virtuous,' — 
 can be a ' philosopher,' &c. which are attributes not belonging 
 to man. But these are more correctly reckoned Accidents ; 
 though Accidents peculiar to the Species. 
 
 Some again speak of ' Properties,' which are universal but 
 not pecidiar ; as • to breathe air ' belongs to the whole human 
 species, but not to that species alone. Such a Predicable, 
 however, is not, strictly speaking, a Property of the Species 
 ' Man,' but a Property of a higher [more comprehensive'] 
 Species, ' land-animal ; ' which stands in the relation of ' Ge- 
 nus ' to the species ' Man.' And it would be called, ac- 
 cordingly, in the language of some writers, a ' generic-^Yo\)' 
 erty ' of Man. A Property, strictly so called, of any Species 
 under our consideration, would be called its ' specijic-^vo^Qviy.^ 
 
 Predicables, then, have been usually divided into these 
 five heads : ' Genus, Species, Difference, Property, and Ac- 
 cident.' 
 
 You are to remember, that, as every Predicable is so called 
 in relation to the Terms of which it can be (affirmatively) 
 predicated, so, each Common-term is to be regarded as belong- 
 ing to this or that Head of Predicables, according to the Term 
 to which it is, in each instance, applied, or which may be ap- 
 plied to it. Thus, the term ' Iron-ore ' is a Species in respect 
 of the term ^ Mineral,' and a Genus in respect of the term 
 * Magnet ; ' and so, in other instances. 
 
 § 5. AYhen we ^ enumerate distinctly ' [or ' separately '"] 
 11 
 
122 SUPPLEMENT. [^Part III. 
 
 the several things that are signified by one Common-term, — ► 
 as the several species included under some Genus — we are 
 said to ' divide ' that Common-term. Thus, ' natural-produc- 
 tions ' are divided into ' Animal, Vegetable, and Mineral ; ' 
 and each of these again may be subdivided into several ' mem- 
 bers ; ' and so on. 
 
 Perhaps the word ' distinguish, if it had been originally 
 adopted, would have been preferable to ' divide : ' (which, 
 however, has been so long in general use in this sense, that 
 it could not now be changed) because ' Division ' being (in 
 this sense) a metaphorical word, the 'Division' we are now 
 speaking of is liable to be confounded with 'Division' in 
 the other (which is the original and proper) sense of the 
 word. 
 
 ' Division,' in its primary sense, means separating from each 
 other (either actually, or in enumeration) the parts of which 
 some really-existing single object consists : as when you di- 
 vide ' an animal ' (that is, any single animal) into its several 
 members ; or again, into its ' bones, muscles, nerves, blood- 
 vessels,' &c. And so, with any single Vegetable,' &c. 
 
 Now each of the parts into which you thus ' physically ' 
 (as it is called) divide ' an animal,' is strictly and properly 
 a ' part,' and is really less than the whole ; for you could not 
 say of a bone, for instance, or of a limb, that it is ' an Animal.' 
 
 But when you ' divide ' — in the secondary sense of the 
 word ' (or, as it is called, ' metaphysically ') — ' Animal,' that 
 is the Genus ' Animal,' into Beast, Bird, Fish, Keptile, Insect, 
 &c., each of the parts [or ' members '] is metaphorically called 
 a ' part,' and is, in another sense, more than the whole [the 
 Genus~\ that is thus divided. For you may say of a Beast or 
 Bird that it is an ' Animal ; ' and the term ' Beast ' implies 
 not only the term ' Animal,' but something more besides ; 
 namely, whatever ' Difference ' characterizes ' Beast ' and sep- 
 arates it from ' Bird,' ' Fish,' &c. 
 
Lesson xv.] division. 123 
 
 And so also any Singular-term [denoting one individual] 
 implies not only the whole of what is understood by the Spe- 
 cies it belongs to, but also more ; namely, whatever distin- 
 guishes that single object from others of tlie same Species : as 
 ' London ' imphes all that is denoted by the term ' City/ and 
 also its distinct existence as an individual city. 
 
 § G. The parts [_' members '] in that figurative sense with 
 wlndi we are now occupied, are each of them less tJian the 
 whole^ in another sense; that is, of less comprehensive significa- 
 tion. Thus, the Singular-term ' Romulus ' embracing only 
 an individual-king, is less extensive than the Species ' King ; ' 
 and that, again, less extensive than the Genus ' Magis- 
 trate,' &c. 
 
 An ' i/idividual,' then, is so called from its being incapable 
 of being (in this figurative sense) divided. 
 
 And though the two senses of the word ' Division ' are 
 easily distinguishable wdien explained, it is so commonly 
 employed in each sense, that through inattention, confusion 
 often ensues. 
 
 We speak as familiarly of the ^division' of Mankind into 
 the several races of ' Europeans, Tartars, Hindoos, Negroes,' 
 &c. as of the ' division " of the Earth into ^ Europe, Asia, Afri- 
 ca,' &c., though ' the Earth ' [or ' the World '] is a Singular- 
 term, and denotes what ^ve call one Individual, And it is 
 plain w^e could not say of Europe, for instance, or of Asia, 
 that it is ^ a World.' But w^e can predicate ' Man ' of every 
 individual European, Hindoo, &c. 
 
 And here observe that there is a common colloquial incor- 
 rectness, (increasing the liability to confusion) m the use of 
 the ^vord ' division,' in each of these cases, to denote one of the 
 'parts ' into which the wdiole is divided. Thus, you will some- 
 times hear a person speak of Europe as one ' division ' of tlie 
 Earth ; or of such and such a ' division ' of an Army ; meaning 
 'portion.^ And so, again, a person will sometimes speak of 
 
124 SUPPLEMENT. \_Part UK. 
 
 ^ animals that belong to the feline division of the Carnivora,' 
 [ilesh-eating-animals] meaning, that portion of the class ' Car- 
 nivora.' 
 
 § 7. Division, in the sense in which vv^e are here speaking 
 of it, (the figurative) is evidently the reverse process to ' Gen- 
 eralization.' (See Lesson VII. § 4.) For as, in general- 
 izing^ you proceed by laying aside the differences between 
 several things, and ahstracting that which is common to them, 
 so as to denote them, — all and each, — by one Common-term, 
 so, in dividing, you proceed by adding on the differences, so as 
 to distinguish each by a separate term. 
 
 When you take any Common-term to be divided and sub- 
 divided, for any purpose you have in hand, — as, the Term 
 ^ Animal ' in a w^ork on Zoology, — that Term is called your 
 ' Summum [highest] geniis^ the several Species into which 
 you proceed to divide it, and which are afterwards divided 
 each into other Species, are called, each of them, a ' Subal- 
 tern ' Species or Genus ; being, each, a Species in relation to 
 that which can be predicated of it, and a Genus, in relation to 
 the Species of which it can be predicated. 
 
 Thus ' Iron-ore ' (in the example lately given) is a Subal- 
 tern Species, or Genus, in relation to ^ Mineral ' and to ^ Mag- 
 net,' respectively. 
 
 Any Species that is ^ not made a Genus of any lower Spe- 
 cies ' in the division you happen to be engaged in, — or, in 
 other words, which is not regarded as any further divisible 
 except into individuals, — is usually called (by the Latin 
 name) ^ injima Species ; ' that is, the ' lowest Species.' 
 
 ' Proximum Genus ' is a technical name often used to denote 
 the ' Genus-next-ahove ' [or ' nearest,'] the Species you may 
 be speaking of: as 'Iron-ore' would be the 'nearest' [proxi- 
 mum] Genus, of Magnet ; and ' Mineral ' would be its more 
 remote Genus ; that is, the Genus of its Genus. 
 
 § 8. It is usual, when a long and complex course of Di- 
 
Lesson xv.] tree of division. 125 
 
 vision is to be stated, to draw it out, for the sake of clearness 
 and brevity, in a form like that of a genealogical 'IWe* 
 And, by carefully examining any specimen of such a ' Tree/ 
 (going over it repeatedly, and comparing each portion of it 
 with the explanations above given) you will be able perfectly 
 to ^:iL in your mind the technical terms we have been ex- 
 plaining. 
 
 Take, for instance, as a ' Summum-genus,' the mathemati- 
 cal-term 
 
 * Plaue-superficial-figurc ' 
 
 Mixed Figure Eectilinear Figure Curvilinear Figure 
 
 (of Rcct. and Curv.) ] 
 
 r ^ j 1 
 
 Triangle Quadrilateral, &c. Circle Ellipse, &c. 
 
 Such a ' Tree of division' the Student may easily fill up for 
 himself. And the employment of such a form will be found 
 exceedingly useful m obtaming clear views in any study you 
 are engaged in. 
 
 For instance, in the one we have been now occupied with, 
 take for a Summum-Genus, ' Expression ; ' (i, e, ' expression- 
 in-language ' of any such mental-operation as those for- 
 merly noticed) you may then exhibit, thus, the division and 
 subdivision of — 
 
 11% 
 
126 
 
 TREE OF EXPRESSION. 
 
 [^Part III. 
 
 
 
 'tl ^ 
 
 o 
 
 c3 
 
 o-^ 
 
 - c 'ti .tp 
 
 cog 
 
 Ph 
 
 bo 
 
 
 -Is. 
 ^ s 
 
 op 
 
 e.): 
 S 
 
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 XJl 
 
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 g5 
 
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Lesson xv.] rules for dividing. 127 
 
 § 9. The rules for dividing correctly, are, 
 
 i. That the whole [or Genus-to-be-divided] be exactly 
 equal to all the Parts [or Members] together. Nothing, 
 therefore, must be included^ of which the Genus can 7iot 
 be (affirmatively) predicated; — nothing excluded, of which 
 it can, 
 
 ii. The Members [Parts] must be ^ contradistinguished,' 
 (or, as some writers express it, ' opposed ') and not include 
 one another ; which they will do if you mix up together tuo 
 or more hinds of division, made by introducing several dis- 
 tinct classes of differences. 
 
 Thus, if you were to divide ' Books ' into ' Ancient, Mod- 
 ern, Latin, French, English, Quarto, Octavo, Poems, Histo- 
 ries,' &c., (whereof a ' modern-book ' might be ' French,' or 
 * English,' — a ' Poem,' or a ' History,' &c., a ' Quarto-book,' 
 ^ ancient ' or ' modern,' &c.) you would be mixing together 
 four different kinds of divisions of Books ; according to their 
 Age, Language, Size, and Subject. 
 
 And there are what are called Cross-divisions ; (because 
 they run across each other, like vertical and horizontal sections 
 of anything) being divisions formed according to ' distinct 
 classes of Differences : ' or, in other words, ' on several distinct 
 principles of Division.' 
 
 It is a useful practical rule, whenever you find a discussion 
 of any subject very perplexing, and seemingly confused, to 
 examine whether some ' Cross-division ' has not crept in unob- 
 served. For this is very apt to take place : (though, of course, 
 such a glaring instance as that in the above example could not 
 occur in practice) and there is no more fruitful source of in- 
 distinctness and confusion of thought. 
 
 When you have occasion to divide anything in several 
 different ways, — that is, ' on several principles-of-division,' 
 — you should take care to state distinctly hoio many divisions 
 you are making, and on what principle each proceeds. 
 
128 SUPPLEMENT. [^Fart in. 
 
 For instance, in the ' Tree ' above given, it is stated, that 
 ' Propositions ' are divided in different ways, ' according to ' 
 this and that, &c. And thus the perplexity of Cross-divisioa 
 is avoided. 
 
 § 10. iiiiy. A Division should not be ' arbitrary ; ' that is, 
 its members should be distinguished from each other by ' Differ- 
 ences ' (see above § 7) either expressed or readily understood ; 
 instead of being set apart from each other at random, or with- 
 out any sufficient ground. For instance, if any one should 
 divide ' coins ' into ' gold-coins,' ' silver,' and ' copper,' the 
 ground of this distinction would be intelligible ; but if he should, 
 in proceeding to subdivide silver-coin, distinguish as two 
 branches, on the one side, ' shillings,' and on the other ' all 
 silver-coins except shillings,' this would be an arbitrary Di- 
 vision. (See below, § 13.) 
 
 ivly. A Division should be clearly arranged as to its Mem- 
 bers : that is, there should be as much subdivision as the oc- 
 casion may require ; and not a mere catalogue of the ' lowest- 
 Species,' omitting intermediate classes \J subaltern '] betv/een 
 these and the ' highest genus : ' nor again an intermixture of 
 the ' subaltern,' and ' lowest-species,' so as to have, in any two 
 branches of the division. Species contradistinguished and placed 
 opposite, of which the one ought naturally to be placed higher 
 up [nearer the ' Summum '] and the other lower down in the 
 Tree. 
 
 For instance, to divide ^ plane-figure ' at once, into ^ equi- 
 lateral-triangles, squares, circles, ellipses,' &c., or again ' vege- 
 table,' into ' Elms, pear-trees, turnips, mushrooms,' &c., or 
 again to divide ' Animal ' into ' Birds, Fishes, Reptiles, Horses, 
 Lions,' &c. would be a transgression of this rule. 
 
 And observe that, (as was formerly remarked) although 
 such glaring cases as are given by way of examples could 
 not occur in practice, errors precisely corresponding to them 
 may, and often do, occur ; and produce much confusion of 
 thought and error. 
 
Lesson xv.] definitions. 129 
 
 § 11. When you state the Genus that any Species belongs 
 to, together with the Difference tliat constitutes it [' charac- 
 terizes ' it, so as to separate it from the rest] you are said to 
 give a ' Definition ' of that species. 
 
 As, ' the Magnet,' (meaning, a ?ia^?<rc//-magnet) is defmed 
 ^ an iron-ore, having an attraction for iron : ' a ' Triangle,' a 
 * three-sided figure : ' a ^ Proposition,' * an indicative ' [affirm- 
 ing or denying ' Sentence.' ' Iron-ore ' — ' Figure ' — ' Sen- 
 tence,' are evidently each the Genus^ in these definitions re- 
 spectively ; and the other part, the Difference, 
 
 This is accounted the most perfect and proper kind of De- 
 finition. And the two portions of which it consists — the 
 ' Genus ' and the ' Difference,' are called technically the 
 ' metaphysical parts : ' as not being two real parts into which 
 any individual-object can be actually divided, but only differ- 
 ent views taken [or notions formed] of a Class of objects, by 
 our mind. 
 
 What is called a ^physical-definition,' is made by an enu- 
 meration of such parts of some object as are actually separa- 
 hie ; such as are the Subject, Predicate, and Copula of a 
 Proposition ; — the root, trunk, branches, bark, &c. of a 
 Tree, &c. 
 
 A Definition which proceeds by enumerating several Prop- 
 erties, — or, in the case of an individual — Inseparahle-acci- 
 dents, is called a ^ Description ; ' or, according to some writers, 
 an ^ Accidental- Definition.' 
 
 It is evident that an Individual can be defined only by a 
 Description ; that is, by stating the Species and (not ' Prop- 
 ei'ties ; ' since they belong to all the individuals of the Species ; 
 but) the Inseparahle-acci dents* As ' Alexander the Great ' 
 
 would be described as ' a King ' ' of Macedon, who subdued 
 
 __SP: 
 
 Persia; ' ' Paris,' ' Tiie capital. . .City. . .of France.' 
 
 § 12. Definitions have also been distinguished — according 
 
130 SUPPLEMENT. [^Part nil 
 
 to the ohject designed to he effected by each, — into ' Nominal' 
 and ' Eeal.' 
 
 A Nominal-definition is usually described as being one 
 which explains merely the meaning of the word defined; 
 and a Real-definition, that which explains the nature of the 
 thing signified by that word. 
 
 Now it may naturally occur to you to ask, are not these 
 (at least, in defining a Common-term) the same thing ? Since 
 the object of our thoughts, when we employ a Common-term, 
 is, (see above, Lesson VII. § 7,) — not any such really-exist- 
 ing-ihing as those imaginary abstract-ideas some speak of, but, 
 — the Term itself, regarded as a ' Sign ' &c., as was formerly 
 explained. 
 
 And in many cases, accordingly, the 'Nominal' and the 
 ' Real ' definition do coincide. But by a iVbmmaZ-definition 
 is meant, (strictly speaking) one which expresses exactly 
 what the Name itself conveys to every-one who understands 
 that name : and nothing beyond this. And any Definition 
 may be called (in a greater or less degree) a i^eaZ-definition 
 which explains anything — more or less — beyond what is 
 necessarily implied in the Name itself. 
 
 Thus, any one who gives such an account of some one of 
 the ' metals,' for instance, or of the ' Sun ' as modern research- 
 es would enable him to give, would be advancing beyond a 
 mere Nominal-definition ; since, in this latter, — the mere ex- 
 planation of the words ' iron ' or ' sun ' — v/e, and our ances- 
 tors 500 years ago, would coincide ; since both they and we 
 use those words in the same sense ; though they knew much 
 less than we do, of the nature of those things. 
 
 In the ease of strictly -5c?267z^(/?c-terms, the Nominal and the 
 Real-definition may be regarded as coinciding. Thus, the 
 mathematical-definition of a circle, may be considered as strict- 
 ly ' Nominal,' inasmuch as it denotes precisely the same as 
 the word ' Circle,' and nothing beyond ; every name being (in 
 
Lesson xv.] rules for defining. 131 
 
 Mathematics) regarded as merely the ' definition abridged. 
 And again, it may be regarded as so far a ' Real-iliSm\\ov\* 
 that it conveys all that can belong to the thing spoken of, since 
 there can be no property of a Circle tliat is not in fact implied 
 in the definition of a Circle ; or, which is the same thing, in 
 the name, ^ Circle.' It is, therefore, as much of a real-defini- 
 tion as can^ conceivably, be given, of a Circle. 
 
 And, so with other scientific-terms. In respect of these, in 
 short, the meaning of the name^ and the nature of the things 
 are one and the same. 
 
 And accordingly, in Mathematics, the Definitions are the 
 Principles from which our reasonings set out. 
 
 On the other hand, since a ' diamond ' or a ^ planet ' or ' a 
 sheep ' &c. have, each of them (that is, each individual of any 
 such Species) a real, actual existence in nature, independently 
 of our thoughts, any of these may possess attributes not im- 
 plied in the meaning w^e attach to the name ; and which are to 
 be discovered by observations and experiments. Any expla- 
 nation, however, of the nature of any object beyond what is 
 implied in the signification of its name, is not usually called a 
 ' Definition ; ' but the word ^ Description ' is often used to de- 
 note such an explanation. 
 
 § 13. What we are concerned with at present is 'Nominal- 
 definition ; ' it being important, wuth a view to Reasoning, to 
 ascertain the exact sense in which each Term is employed, 
 and especially, to guard against any ambiguity in the Middle- 
 term of any argument. 
 
 The Rules [or cautions] commonly laid down in various 
 treatises for framing a Definition, are very obvious : namely, 
 i. That a Definition should be ' adequate ; ' i. e. compre- 
 hending neither more, nor less, than the Term to be defined. 
 For instance if, in a definition of ' Money ' you should specify 
 its being ' made of metal,' that would be too narrow, as ex- 
 cluding the shells used as money in some parts of Africa : if, 
 
132 SUPPLEMENT. \_Part lU. 
 
 again, you would define it as an ' article of value given in ex- 
 change for something else/ that would be too wide^ as it would 
 include things exchanged by barter ; as when a shoemaker, 
 who wants coals, makes an exchange with a collier, Avho wants 
 shoes.* 
 
 And observe, that such a defect in a Definition cannot be 
 remedied by making an arbitrary exception; (such as was 
 alluded to above, § 10,) as if, for instance, (and it is an instance 
 which actually occurred,) a person should give such a Defini- 
 tion of ' Capital ' as should include (which he did not mean to 
 do) ' Land ; ' and should then propose to remedy this by de- 
 fining ' Capital,' any ' property of such and such a description, 
 except LandJ 
 
 ii. The other caution usually given, is, that a definition 
 should be clearer than the Term defined : clearer, that is, to 
 the persons you are speaking to : since that may be obscure to 
 one man, which is intelligible to another. 
 
 And this rule evidently includes (what some give as a iiird 
 rule) a caution against excessive prolixity, excessive brevity, 
 and ambiguous language. 
 
 * See Lesson I. on Money Matters, 
 
PART IV. 
 F ALL ACIE S. 
 
 LESSON XVL 
 
 § 1. Although sundry kinds of Fallacies have been from 
 time to time noticed in the foregoing Lessons, it will be worth 
 while to make some further observations thereon. 
 
 By a ' Fallacy ' is commonly meant ' any deceptive argument 
 or apparent-argument, whereby a man is himself convinced, 
 — or endeavors to convince others — of something which is 
 not really proved.' 
 
 Fallacies have been usually divided into two Classes ; those 
 in the form^ and those in the matter : though the difference 
 has not been in general clearly explained. 
 
 The clearest way of proceeding will be to consider a ' Fal- 
 lacy-in-form ' as one in which the Conclusion does not really 
 follow from the Premises ; and a ^ Fallacy-in-matt er ' as one 
 where the Conclusion does follow from the Premises, though 
 there will be still something faulty in the procedure. 
 
 In this latter case (where the Conclusion does follow) one 
 may either object to the Premises as being ' unduly assumed,* 
 or to the Conclusion as irrelevant ; that is, different, in some 
 way, from what ought to have been proved, — namely, from 
 what was originally maintained, — from what had been under- 
 taken to be established, — from what the particular occasion 
 requires, &c. 
 
 These that have been mentioned (as the ' Fallacies-in-form,' 
 and ' in matter ') must evidently include ever^j possible Falla- 
 cy ; since whatever objection can be brought against any ar- 
 12 
 
 ^ 
 
134 FALLACIES. \^Part IT. 
 
 gument or apparent-argument, must be an objection either 
 against the Conclusion, or against the Premises, or against 
 the connexion between the premises and conclusion ; that is, 
 against the co7iclusiveness of the apparent argument. 
 
 § 2. ' Fallacies-in-form/ [in which the Conclusion does not 
 really follow from the Premises] are such as we have already 
 given examples of, as violations of the rules above-ex- 
 plained : such as ' undistributed-middle,' — ' illicit-process,' &c. 
 
 Among others was noticed the fault of an ' equivocal Mid- 
 dle-term,' taken in one sense in the one premise, and in a dif- 
 ferent sense in the other. And since this Fallacy turns on 
 the meaning of words, and not on the mere form in which the 
 argument is expressed, some may be disposed to rank it rather 
 under the Head of ' Fallacies-in-matter.' 
 
 The most convenient course, however, will be to keep to 
 the division already laid down ; and, accordingly, to reckon 
 the Fallacy of ' equivocal-middle ' along with all the others in 
 which the Conclusion does not follow from the Premises. 
 
 And in truth the technical rules do apply to this, — the 
 * Fallacy of equivocation ' — as soon as it is ascertained that 
 the Middle-term is employed in two different senses, and con- 
 sequently is, in reality, not one, but two terms. 
 
 But of course the rules of Syllogism do not, alone, enable 
 us to ascertain the meaning or meanings of any Term. That 
 must be judged of from our knowledge of the subject-matter, 
 — from the context, [or general drift of the discourse] — and 
 often from what we know or beheve concerning the writer or 
 speaker. 
 
 And the same may be said, in many cases, in respect of not 
 only the signification, but also the distribution or non-dis- 
 tribution, of a Term ; on which depend the Fallacies of ' un- 
 distributed-middle ' and ' illicit-process.' For when a Propo- 
 sition is expressed indefinitely (as, ' Man invents arts ; ' ' Man 
 is mortal;') we are left to judge from the subject-matter, 
 
Lesson xyi.] enthymeme. 135 
 
 &c., whether it is to be understood as Universal or as Par- 
 ticular. 
 
 And again, the sign ' all,' which, in an Affirmative proposi- 
 tion, denotes Universality) in a Negative-proposition, general' 
 ly^ though not invariably, indicates a Particular ; that is, usu- 
 ally, though not always, the negation is understood as a negation 
 of universality. For instance, of these two propositions, ' all 
 they that trust in him shall not be confounded,' and ' we 
 shall not all sleep,' the one would be understood as Universal, 
 and the other as Particular. 
 
 Observe, also, that the sign ' all ' is sometimes understood 
 as meaning ' Si\l-collectively ; ' sometimes ' every -one, sepa- 
 rately' As ' all the apples on that tree are enough to fill a 
 bushel : ' i. e. all together : and ' they are all ripe ; * i. e. 
 every one. 
 
 § 3. You are to observe that we cannot always decide ab- 
 solutely as to vjhich Class we should pronounce some particular 
 fallacy to fall under, those in ' form,' or those in ' matter : ' 
 because it will often happen, when an argument is stated 
 (which is usually the case) as ^lH Enthymeme, that the suppressed 
 premise may be either one which is false, but which would, if 
 granted, make the Syllogism complete : or else one which is 
 true, but which would not complete a regular Syllogism. 
 Now, on the former supposition, the Fallacy would be in the 
 ^matter; ' on the other supposition, it would be in the 'form,' 
 
 For instance, in this Enthymeme, ' The Country is dis- 
 tressed ; therefore it is misgoverned,' we cannot decide abso- 
 lutely whether the premise meant to be understood, is ' every 
 Country that is distressed is misgoverned ; ' which would make 
 the syllogism correct, but would not be admitted as true ; or, 
 ' every Country that is misgoverned is distressed ;' which would 
 leave the Middle-term undistributed. 
 
 And again, when both Premises are expressed, it will often 
 happen (as in an example formerly given) that we have the 
 
136 FALLACIES. \^Part IV. 
 
 alternative of either denying the truth of one of the premises, 
 
 — supposing the Middle-term used in the same sense in both, 
 
 — or denying the conclusiveness of the argument, supposing 
 the Middle-term used in each premise in such a sense as to 
 w.alce that ^premise true. If by ' contrary to ex'perience ' you 
 mean two different things, in the two premises, respectively, 
 then, each is, by itself, true, but they prove nothing: if you 
 mean by it the same in both premises, then, one of them is 
 untrue. 
 
 § 4. But observe, that when you mean to charge any argu- 
 ment with the fault of ' equivocal-middle,' it is not enough to 
 say that the Middle-term is a word or phrase which admits 
 of more than one meaning ; (for there are few that do not) 
 but you must show, that in order for each premise to be ad- 
 mitted, the Term in question must be understood in one sense 
 (pointing out what that sense is) in one of the premises, and 
 in another sense, in the other. 
 
 And if any one speaks contemptuously of ' over-exactness ' 
 in fixing the precise sense in which some term is used, — of 
 attending to minute and subtle distinctions, &c., you may reply 
 that these minute distinctions are exactly those which call for 
 careful attention ; since it is only through the neglect of these 
 that Fallacies ever escape detection. 
 
 For a very glaring and palpable equivocation could never 
 mislead any one. To argue that ' feathers dispel darkness, 
 because they are light^ or that ' this man is agreeable, because 
 he is riding^ and riding is agreeable,' is an equivocation which 
 could never be employed but in jest. And yet, however slight 
 in any case may be the distinction between the two senses of 
 a Middle-term in the two premises, the apparent-argument 
 will be equally inconclusive ; though its fallaciousness will be 
 more likely to escape notice. 
 
 Even so, it is for want of attention to minute points that 
 houses are robbed, or set on fire. Burglars do not in general 
 
Lesson xvi.] equivocation. 137 
 
 come and batter down tlie front-door ; but climb in at some 
 window whose fastenings have been neglected. And an in- 
 cendiary, or a careless servant, does not kindle a tar-barrel in 
 the middle of a room, but leaves a lighted turf, or a candle- 
 snuff, in the thatch, or in a heap of shavings. 
 
 In many cases, it is a good maxim, to ' take care of little 
 things, and great ones will take care of themselves.' 
 
 § 5. Of the Fallacies of ' undistributed-middle ' and of ' il- 
 licit-process,' &c. (which have been formerly explained) no 
 more need be said in this place. 
 
 But in respect of the ' Fallacy of equivocation,' it is worth 
 while to notice briefly some of the different modes in which a 
 word or phrase comes to be employed in several senses. 
 
 i. That may be reckoned an accidental equivocation, in which 
 there is no perceived connexion between the different senses. 
 Thus ' pen ' is an instrument for writing, or an enclosure for 
 cattle ; ' turtle ' a kind of bird, and a kind of tortoise ; and 
 ' case ' is used (as was noticed in Lesson YII. § 3,) in three 
 senses. Of this kind is the ambiguity of several proper- 
 names (as John, Thomas, &c.) also noticed in the same 
 place. 
 
 ii. There are several words which are ambiguous from be- 
 ing employed in what is technically called a 'first intention ' 
 and a ' second intention^ 
 
 A ' Second-intention ' of any word is that signification which 
 it bears in reference to some particular art, science, study, 
 pursuit, or system ; and its first-intention is its ordinary collo- 
 quial sense when there is no such reference. 
 
 Thus, the ordinary signification of the words ' ship,' ' beast,' 
 and ' bird,' every one knows ; but sailors limit the word ^ ship ' 
 to vessels of a certain construction ; ' beast ' is the word ap- 
 plied by farmers in some parts, especially, and exclusively, to 
 the ' ox-tribe ; ' and ' bird ' is used in a ' Second-intention ' to 
 signify 'partridge.' 
 
 12* 
 
138 FALLACIES. \_Part TV. 
 
 § 6. It is evident that a word may have several different 
 * Second-intentions/ according to the several systems, &c. 
 into which it may be introduced as one of the technical-terms. 
 
 Thus ' line ' is technically employed in Geometry, in Ge- 
 ography, in the Military-art, in the art of Angling, in Print- 
 ing, &c. 
 
 The word ^ Species ' is employed by Naturalists in a cer- 
 tain ' Second-intention ' when they are speaking of organized- 
 beings. 
 
 The ordinary sense [' first-intention '] of the word, is that 
 which has been explained in these Lessons : but Naturalists 
 restrict it to such a class of animals or plants as are supposed 
 to have descended from a common stock. 
 
 In ordinary discourse any one would say that a ' Grey- 
 hound' or a 'Mastiff' is a kind [' Species'] of dog: but a 
 Zoologist would say (in technical language) that these are 
 only * Varieties,' and that all dogs are of one Species. So 
 also, in common discourse any one would speak of ' Cauli- 
 flower,' and several others, as ' kinds ' of ' Cabbage : ' but the 
 Botanist reckons all these as ' varieties ' of the single Spe- 
 cies, Cabbage. 
 
 Those, in short, which are (in the technical language of 
 these Lessons) the ' lowest-Species ' that the Naturalist treats 
 of, are called by him, not Species, but Varieties ; and again 
 those classes under which his Species come, he never calls 
 Species of a higher Genus, but Genera, Orders, &c. 
 
 Much confusion of thought has often arisen from over- 
 looking this technical-sense [' second intention '] of the word 
 ^ Species.' 
 
 In some instances the ' second-intention ' [or philosophical 
 sense] of a word, is, — instead of being more limited, — more 
 extensive than the ' first-intention ' [or, popular sense.] 
 
 Thus ' affection,' which is limited, in popular use, to ' love,' 
 is employed by philosophers as comprehending both ' benevo- 
 
Lesson xvi.] analogy. 139 
 
 lent and malevolent affections.' So also ' charity,' which is 
 often, in popular use, confined to ' almsgiving' — ' flower,' tc 
 such flowers as have 'conspicuous petals,' — and 'fruit' to 
 such fruits as are ' eatable,' have each a technical second- 
 intention, which is more extensive. 
 
 § 7. iii. A word will often be employed to denote (in dif- 
 ferent senses) to things which have a ' resemblance,^ or ' anal- 
 ogy^ to each other. 
 
 A ' blade,' of grass, or of a sword, have the same name from 
 the direct resemblance betw^een the things themselves. But 
 instances of this kind are far less common than those in 
 which the same name is applied to two things, not from 
 their being themselves similar, but from their having similar 
 relations to certain other things. And this is what is called 
 ' Analogy.' 
 
 Thus, the ' sweetness ' of a ' sound ' and of a ' taste ' can have 
 no resemblance : but the w^ord is applied to both, by analogy, 
 because as a ' sweet ' taste gratifies the palate, so does a ' sw^eet ' 
 sound, the ear. 
 
 Thus also w^e speak in the ^ secondary ' [or ^ transferred,' 
 or ' analogical '] sense of the ' hands ' of a Clock — the ' legs * 
 of a Table, — the ' foot ' of a Mountain, — the ' mouth ' of a 
 E-iver, &c. which words in their ' primary ' [' proper,' or orig- 
 inal] sense, denote the ' hands ' of a man, — the * legs, foot, 
 and mouth ' of animals ; from the similar relations in which 
 they stand to other things, respectively, in reference to use, 
 position, action, &c. 
 
 The words pertaining to Mind may in general be traced up, 
 as borrowed (which no doubt they all were, originally) by 
 Analogy, from those pertaining to Matter : though in many 
 cases the primary sense has become obsolete. 
 
 Thus, ' edify^ ' in its primary sense of ' build upf ' is dis- 
 
 * See Peter, i. ch. 2, v. 5. t See Johnson's Dictionary. 
 
140 FALLACIES. [^Part IV 
 
 used, and the origin of it often forgotten ; although the sub- 
 stantive ' edifice ' remains in common use in a corresponding 
 sense. 
 
 When, however, we speak of ' weighing ' the reasons on 
 both sides, — of ' seeing,' or ' feeling ' the force of an argu- 
 ment, — ' imprinting ' any thing on the memory, &c. we are 
 aware of these words being used analogically. 
 
 It is an analogical sense that ' Division,' ^ Part,' and 
 several other technical terms have been employed in these 
 Lessons. 
 
 § 8. There are two kinds of error, each v^ery common — 
 which lead to confusion of thought in our use of analogical 
 words : 
 
 i. The error of supposing the things themselves to be similar, 
 from their having similar relations to other things. 
 
 ii. The still commoner error of supposing the Analogy to 
 extend further than it does ; [or, to be more complete than it 
 really is ;] from not considering in what the Analogy in each 
 case consists. 
 
 For instance, the ' Servants ' that we read of in the Bible, 
 and in other translations of ancient books, are so called by 
 Analogy to servants among us : and that Analogy consists in 
 the offices which a ' servant ' performs, in waiting on his mas- 
 ter, and doing his bidding. It is in this respect that the one 
 description of ' servant ' ' corresponds ' \J answers'] to the other. 
 And hence some persons have been led to apply all that is 
 said in Scripture respecting Masters and Servants, to these 
 times, and this Country : forgetting that the Analogy is not 
 complete, and extends no further than the point above-men- 
 tioned. For the ancient ' servants,' (except when expressly 
 spoken of as ^zVet^-servants) were Slaves ; a part of the Mas- 
 ter's possessions. 
 
 § 9. iv. A word will often (in different senses) be applied 
 to two things, connected, not by Resemblance or Analogy, but 
 
. Lesson xyi.] analogy. 141 
 
 bj the circumstance of time or place, as being ' Cause and 
 Effect/ or ' Part and Whole,' &c. 
 
 Thus, when we saj, ' the fire gives heat' and * I feel heat' 
 it is plain that the ^heat' of the fire is not a sensation in the 
 fire, and cannot resemble or be analogous to a sensation ; but 
 is tlie cause of the ' sensation ' of ' heat ' in me. 
 
 This kind of transfer of a word from its ' primary ' to a 
 Secondary sonse, is called ^ Metonymy' It is thus we speak 
 of a ' Crown," or a ' Throne ' for ' regal-power ' ' the sword,' 
 for ' war ; ' a ^ voice,' for a ' declaration ; ' and a man is said 
 to be ' worth ' such and such a sum of money ; meaning that 
 lie, posseses property that is worth so much, &c. 
 
 Much confusion of thought, and many Fallacies, have arisen 
 from inattention to this source of ambiguity.* It seems strange, 
 but it is quite true, that things have often been in this way 
 confounded together, which have not the least resemblance or 
 analogy to each other. 
 
 A remarkable instance of tliis is to be found in the ' pri- 
 mary ' and ' secondary ' uses of such words as ' same ' — ' one ' 
 — ' identical,' &c. In the primary sense they imply ' numer- 
 ical unity,' [individuality] and do not imply, necessarily, any 
 similarity. For when we say of any grown man that he is 
 the ' same person ' whom we remember to have seen when an 
 infant, this is, not from his now resembling an infant. Another 
 infant, now, would be much more like what he then was. 
 
 In the secondary sense, on the other hand, these words 
 imply nothing hut exact — or nearly exact — similarity. For 
 instance, if a man finds in a mine some metal which turns out 
 to be gold with a small alloy of copper, he would say, it is the 
 same metal of which coins, or of which watches are made : 
 
 ^ The ambiguity of the word ' Division,' when used to sif^nifv one 
 o^ i\iQ portions into which anything is divided (See Lesson XV., § C,) is of 
 this kind. 
 
142 FALLACIES. \^Part IV. 
 
 not meaning, of course, that one single piece of metal cat 
 be in two places at once ; but only, that there is a perfect 
 similarity. 
 
 So, also, several persons are said to be in one and the same 
 posture, when they are all placed alike ; and to have ' one and 
 the same ' idea in their minds, when they are all thinking 
 alike. (See Lesson VIL § 8.) 
 
 § 10. Now the mode in which these words have been thus 
 transferred (to the utter bewilderment of the inattentive) is 
 this: one single word, — such as ^gold,' or ^man,' or tri- 
 angle,' or ' fever,' — will equally well apply to any one piece 
 of gold, or individual man, or triangle, or fever, &c. And so 
 also will one single Definition [or Description] of a triangle : 
 and hence the things themselves come to be called ' one^ — 
 — the ' same^ ' identical,' &c., because all the individuals thus 
 named or described, are (according to the modern phrase, 
 which is very correct) ' of the same description/ 
 
 In the transferred [secondary] sense, accordingly, you may 
 observe, that things are often spoken of as ' very neaily the 
 same, but not quite ; ' there being some small difference be- 
 tween them. In the ' primary ' sense on the other hand, 
 ' unity,' — ' identity ' &c. do not admit of degrees. For in- 
 stance, ' This man ' either is or is not the same person whom 
 I saw formerly when he was an infant or child ; and that, 
 whether he differ much or little, from what he then was. 
 
 But what helps to introduce confusion, is, that ' identity ' 
 in the primary sense, is in many csisesjudged of, and inferred, 
 from similarity. For instance, a man may be ready to swear 
 to some picture as the one which he had lost, from his per- 
 ceiving a perfect similarity; and yet it might, perhaps, be 
 afterwards proved to his satisfaction, that it was 7iot that one, 
 but an exact copy. 
 
 § 11. Besides the causes of ambiguity that have been just 
 mentioned, it is to be observed that there are several words 
 
Lesson xvi.] ellipsis. 143 
 
 which it is customary to employ ellipticaUy ; that is, in com- 
 hination with something understood ; and that men are apt to 
 forget when it is that such a word is used with, and when 
 without, this ellipsis. 
 
 For instance, we speak of such a one possessing £10,000 ; 
 (though, perhaps, he may not actually possess ten pounds in 
 money) meaning, that his whole property would exchanrje for 
 that sum. And, ordinarily, such a mode of speaking leads 
 to no practical inconvenience. But there is no doubt that 
 it has contributed to foster that enormous practical error 
 known among Political Economists * as the ' Mercantile 
 System.' 
 
 So also we speak commonly of ' the example of such a one's 
 punishment serving to deter others from crime!' And usu- 
 ally, no misapprehension results from this, which is, in truth, 
 an elliptical expression. But sometimes sophistical reasoners 
 take advantage of it, and men who are not clear-headed are 
 led into confusion of thought. Strictly speaking, what deters 
 a man from crime, in such cases as those alluded to, is, the 
 apprehension oi himself suiFering punishment. That appre- 
 hension may be excited by the example of another's being 
 punished ; or it may be excited without that example, if pun- 
 ishment be denounced, and there is good reason to expect 
 that the threat will not be an empty one. And on the other 
 hand, the example of others suffering punishment does not 
 deter any one, if it fail to excite this apprehension for him- 
 self; if, for instance, he consider himself as an exempt per- 
 son as is the case with a despot in barbarian countries, or 
 with a madman who expects to be acquitted on the plea of 
 insanity. 
 
 So also, when any one speaks of being in distress from be- 
 ing * out of worh^ and of his ^ seeking for employment,' we 
 
 ^ See Senior's and Whatcly's Lectures on Political Economy. 
 
144 FALLACIES. \Pa7't IV. 
 
 understand him to mean ' work by which he can earn a suh^ 
 sistence.' But great errors have often been committed by 
 writers who have lost sight of the elliptical character of the 
 expression, till they have practically forgotten in their rea 
 sonings that the thing really desired is, not the labor, but the 
 ffam. 
 
 To this head may, perhaps, be referred the ambiguity 
 (which has been a source of endless confusion) formerly no- 
 ticed (Lesson 11.,) of such words as ' because,' &c., and again 
 ' therefore,' and several others. 
 
 When, in accminting for the wetness which I perceive on 
 the ground, I say, ' the ground is wet because it has rained,' 
 I mean (speaking at full length) to assign the ' rain ' as the 
 ' cause of the wetness : ' when, again, I infer that ' it has rained 
 because the ground is wet ' the meaning of the word ' because ' 
 is, if fully expressed, that I assign the wetness as the ' cause 
 of my belief^ 
 
 The same may be said of such words as ' may,' ' possible,* 
 &c., and again, ^ must,' 'necessary,' &c. (See Lesson X., 
 §8.) 
 
 When I say of a man forcibly carried off by enemies, * he 
 must go wherever they conduct him,' I mean, ' he cannot avoid 
 going : ' when I say that on his release ' he must eagerly re- 
 turn to his home,' I mean that '/cannot avoid drawing thai 
 conclusion^ 
 
 So also, if I say of a man in health and at liberty, ' he may 
 go out or stay within,' I mean that neither going nor staying 
 is unavoidable to him : but when I say of a man who is sick, 
 that ' he may recover,' I do not mean (as in the former case) 
 that ' this depends on his choice^ but that ' I am not led una- 
 voidably to the conclusion, that he will recover, or that he will 
 not recover.' 
 
 § 12. There are also other ways in which a Term may be 
 so modified in its sense as not to have precisely the same 
 meaning in both premises. 
 
Lesson xvi.] fallacies-of-division. 145 
 
 For jou are to remember that even any one word which is 
 not itself one of the Terms, but only a small portion of one of 
 them, may be so understood as to affect the sense of the whole 
 Term. Even a difference in the position of a word in respect 
 of the rest, may greatly alter the sense. 
 
 For instance, ' He who believes his opinion always right, 
 deems himself infallible ; you always believe your opinion 
 right ; therefore you deem yourself infallible.' Here, the 
 premises are both true ; for any opinion which you did not 
 believe to be right, would plainly not be your opinion ; and it 
 would be difficult to deny that a man considers himself infalli- 
 ble, who should believe that his opinion is invariably right. 
 But the different situation of the word ' always ' gives a differ- 
 ent sense to the Middle-term in the two premises. To ' think 
 your opinion always right,' means, to have a general convic- 
 tion respecting the whole of your opinions collectively^ that 
 none of them is ever wrong : but ' always to think your opin- 
 ion right,' means, ' to have a particular conviction, on each 
 occasion, separately^ that your opinion, on that occasion, is 
 right.' 
 
 A Fallacy of this character, — that is, where the Middle- 
 term is taken collectively in one premise, and dividedly in the 
 other, — is technically called the ' Fallacy-of-o?^V^5^o?^,' or of 
 ' composition ; ' according as the Middle-term is understood in 
 a collective-sense in the Jia/or- premise, and in a divided-sense 
 in the Minor ; or vice versa. 
 
 A glaring example would be ' all the apples from that tree 
 are worth 205. ; this is an apple from that tree ; therefore it is 
 worth 2O5.' 
 
 Such a fallacy has helped to give plausibility to what has 
 been called ' the doctrine of necessity.' For instance, ' He who 
 necessarily goes or stays ' (in reality, ' who necessarily goes, 
 or again, who necessarily stays ') is not a free-agent ; you 
 necessarily go or stay; (that is, — taking these two things in 
 13 
 
146 FALLACIES. [^PaH IV. 
 
 connection^ — you ' necessarily take the alternative ') ' there- 
 fore you are not a free agent.' 
 
 § 13. The way in which this Fallacy usually occurs in 
 practice, is, when something is proved separately concerning 
 each one of several things belonging to some class ; and then 
 this is considered as having been proved concerning the whole 
 class collectively ; that is, concerning those things taken in 
 connexion with each other. 
 
 A man, for instance, swallows a certain drug, and is seized 
 with alarming symptoms : you show that these symptoms may 
 possibly have arisen from other causes : the same drug is 
 swallowed by another man, who is seized with like symptoms ; 
 and you show that other causes may have produced the symp- 
 toms in him : the same may be shown, suppose, in each separate 
 case (considered each by itself) out of 100 ; and then you 
 assume that it has been proved that all the men who have 
 taken the drug and exhibited like symptoms may have been 
 affected, all of them, by natural causes. 
 
 This kind of argument has been employed to refute the ac- 
 counts given by the Evangelists of the miracles they record ; 
 that is, explaining some one of the recorded cures — considered 
 hy itself y as an accident ; and then the same with another, and 
 another ; and so on. 
 
 Sometimes again a Middle-term is ambiguous from being 
 understood in one premise in conjunction with certain circum- 
 stances actually pertaining to it, at a particular time, &c., and, 
 in the other premise, independently of those circumstances. A 
 glaring example would be, if any one should pretend to prove^ 
 (which would of course be only as a jest,) that because what 
 you have on your back was the covering of a sheep, therefore 
 the sheep wore a coat of blue or red broadcloth. This is called, 
 in the technical language of the Latin treatises, ' Fallacia 
 accidentis.' 
 
 It is evident that when any ambiguity, of whatever kind, in 
 
Lesson xvi.] irrelevant-conclusion. 147 
 
 a Middle-term, is suspected, the natural course is to seek for, 
 or to demand, a Definition of it. Only, remember that it 
 would be impertinent to insist, in every such case, on a com- 
 plete definition, beyond what is requisite for removing any 
 doubt as to the argument before us ; i. e. as to tlie IMiddle -term's 
 being employed in the same sense in both premises. 
 
 For instance, if there were a discussion respecting a person's 
 having swallowed ^ jpoison^ and some ambiguity connected v/ith 
 the reasoning, were suspected in the employment of that 
 word, it would not be necessary to give a definition such as 
 should extend to ' every poison,' including such as savages use 
 for their arrows .-because the supposed question relates only 
 to poisons taken into the stomach. 
 
 § 14. The Fallacies-in-matter are divided (as has been 
 said) into two kinds : ' undue-assumption- of -a-premise^^ and 
 ' irrelevant'ConclusionJ 
 
 It is to be observed that no one is to be charged with falla- 
 C20w5-proceeding merely because he argues from Premises 
 which we deny ; or because the Conclusion he draws is not 
 the one we would wish to see proved. For neither of these 
 implies any deception. 
 
 One man may assume facts or principles which another will 
 not admit ; but provided he does this openly and knowingly, 
 there is no Fallacy in the case. 
 
 Or again, we may, (suppose,) wish to have it pointed out 
 and proved ivho is the perpetrator of such and such a crime ; 
 but if the accused party prove that it was not he, we have no 
 right to demand more. 
 
 But if any one is convinced by an argument based on some 
 Premise which he would not have admitted if distinctly put 
 before him, there is in this case a Fallacy. 
 
 And so there is, if any one is satisfied, or endeavors to sat- 
 isfy others, by proving some conclusion different from wliat 
 he had originally maintained ; or from Avhat was originally 
 
148 FALLACIES. [^Part IV. 
 
 proposed as the Question : or, (which comes to the same) 
 which is the contradictory, not, of what he had originally de- 
 niedj but of some different proposition. Tliis is properly the 
 Fallacy of ' irrelevant-conclusion.' 
 
 § 15. Under the former of these two classes of Fallacy 
 comes what is, technically, called ' begging the Question ; ' 
 that is, assuming as a Premise the very Proposition which, — 
 m other words, — is proved as the Conclusion. The way in 
 which tliis is usually done is that w^hich is commonly called 
 ' ea:guing in a circle ; ' that is, proving some conclusion by 
 means of a Premise which is itself deduced — more or less 
 remotely — from premises deduced from that very Conclu- 
 sion, assumed as a Premise. As if yon were to prove that A 
 is B, because C is D ; and that C is D, because E is F ; and 
 so on, till at length you come to infer that Y is Z because 
 A is B, 
 
 Of course the narrower the Circle, the less likely it is to 
 escape the detection, either of the reasoner himself, (for men 
 often deceive themselves in this way) or of his hearers. When 
 there is a long circuit of many intervening propositions before 
 you come back to the original Conclusion, it will often not be 
 perceived that the arguments really do proceed in a ' Circle.' 
 Just as when any one is advancing in a straight line (as we 
 are accustomed to call it) along a plain on this Earth's sur- 
 face, it escapes our notice that we are really moving along the 
 circumference of a Circle, (since the earth is a globe) and 
 that if we could go on without interruption in the same line, 
 we should at length arrive at the very spot we set out from. 
 But this we readily perceive, when we are walking round a 
 small hill. 
 
 For instance, if any one argues that you ought to subjnit to 
 the guidance of himself, or his leader, or his party, &c. because 
 these maintain what is right ; and then argues that what is so 
 maintained is right because it is maintained by persons whom 
 
Lesson xyi.] fallacy-in-matter. 149 
 
 you ouglit to submit to ; and that these are, himself and his 
 party ; or again, if any one maintains that so and so must be a 
 thing morally wrong, because it is prohibited in the moral 
 portion of the Mosaic-law, and then, that the prohibition of it 
 does form a part of the moral (not the ceremonial, or the civil) 
 portion of that Law, because it is a thing morally wrong ^ — 
 either of these would be too narrow a Circle to escape detec- 
 tion, unless several intermediate steps were interposed. And 
 if the form of expression of each Proposition be varied every 
 time it recui-s, — the sense of it remaining the same, — this 
 will greatly aid the deception. 
 
 Of course, the way to expose this Fallacy, is to reverse this 
 procedure : to narrow the Circle by cutting off the interme- 
 diate steps ; and to exhibit the same proposition, — w^hen it 
 comes round the second time, — in the same words. 
 
 § 16. In all cases, an unduly-assumed premise (i. e. one 
 which would not be admitted if clearly stated, and deliberately 
 considered) is the more likely to escape detection, the longer 
 the train of argument is, and the greater the number of well- 
 established propositions introduced. Wlien this artifice is 
 employed, a dull or thoughtless hearer is apt to say, ' there is 
 much truth in what has been urged.' And so, perhaps, there 
 is. There may have been introduced, in the course of the 
 reasoning, twenty propositions, all of them true, except one : 
 the denial of which one w^ould nullify the whole train of argu- 
 ments. A chain which has only one faulty link, is not indeed 
 the stronger, but is the more likely to appear strong, by the 
 addition of a great many sound links. 
 
 It also contributes to this kind of deception, to suppress the 
 unduly-assumed premise ; stating the argument as an Enthy- 
 meme expressing the true premise, and giving proofs of the 
 truth of that, as if everything turned on the establishment of 
 that premise. 
 
 So also, in Fallacies of the other class, — the ' irrelevant- 
 13* 
 
150 FALLACIES. [_Part IV. 
 
 conclusion ' — it often aids the deception, to suppi^ess the Con^ 
 elusion itself: bringing forward arguments which do indeed 
 go to prove a Conclusion, somewhat like the one required, 
 though not the very one : and then (instead of expressly stat- 
 ing the conclusion that really does follow, or again, that which 
 had been originally maintained) a man will say ' the inference 
 from this is plain : or ^ I have thus established my point ; ' 
 or the position of our opponents is thus completely over- 
 thrown,' &c. 
 
 § 17. The two kinds of ' Fallacy-in-Matter,' are very com- 
 monly combined in one course of argument : that is, a false or 
 a doubtful premise will be assumed as having been proved by 
 arguments which go to prove, not that^ but another proposi- 
 tion, somewhat like it. 
 
 For instance, instead of proving that ' this Prisoner has 
 committed an atrocious fraud,' you prove that ' the fraud he is 
 accused of is atrocious : ' instead of proving (as in the well- 
 known tale of Cyrus and the two coats) that ' the taller boy 
 had a right to force the other boy to exchange coats with him,' 
 you prove that ' the exchange would have been advantageous 
 to both : ' instead of proving that ' a man has not the right to 
 educate his children or to dispose of his property, in the way 
 he thinks best,' you show that the way in which he educates 
 his children, or disposes of the property, is not really the 
 best : instead of proving that ' the poor ought to be relieved 
 in this way rather than in that,' you prove that the poor ought 
 to be relieved ;' instead of proving that ' an irrational-agent — 
 whether a brute or a madman - — can never be deterred from 
 any act by apprehension of punishment,' (as for instance a dog, 
 from sheep-biting, by fear of being beaten) you prove that 
 ^ the beating of one dog does not operate as an example to 
 other dogs,' &;c., and then you proceed to assume as prem- 
 ises, conclusions different from what have really been estab- 
 lished. 
 
Lesson xvi.] fallact-in-matter. 151 
 
 The chief difficulty in detecting any Fallacy of whatever 
 kind, in oar own reasonings, or another's, arises (as was for- 
 merly remarked) from its being usually stated in an obliciue, 
 indirect, and somewhat inverted and perplexed form of ex- 
 pression ; and more especially when diluted, as it were, with 
 a multitude of words : just as poison is more likely to escape 
 detection when disguised and diluted by being mixed up with 
 a quantity of innocent ingredients, than when presented in a 
 small concentrated dose. 
 
 The validity, or the fallaciousness, of any course of reason- 
 ing, w^ill then be made the most evident, when examined ac- 
 cording to the foregoing rules, after laying aside all redundant 
 words put in for mere embellishment of style, and stating the 
 whole in the most simple language, and in regular order, as 
 briefly as is compatible with perfect clearness. 
 
PART V. 
 DIFFERENT KINDS OF ARGUMENTS. 
 
 LESSON XVII. 
 
 § 1. It remains to make a few remarks on the 'finding 
 [according to the Latin writers, Inventio7i'\ of arguments ; ' 
 the foregoing Lessons relating only to the rules for passing 
 judgment on arguments. 
 
 It is to be observed, in the first place, that the words ' infer* 
 and 'proved (which we have frequently had occasion to em- 
 ploy) denote, not, two different things, but the same thing 
 considered in two different points of view. He who ' infers ' 
 (correctly) proves ; and he who ' proves ' infers : and yet the 
 two expressions are not synonymous. 
 
 So also, the 'road from London to Liverpool' and the 
 
 * road from Liverpool to London,' are rot different things; 
 but the one expression calls to mind the thought of a journey 
 from the Metropolis to the Seaport ; and the other, the re- 
 verse. And in like manner, the word ' infer ' fixes the mind 
 first on the Premises and then on the Conclusion ; the word 
 
 * prove,' on the contrary, leads the minds /rom the Conclusion 
 (in this case called the ' Question ') to the Premises. 
 
 Hence, we say commonly ' what do you infer from that ? ' 
 How do you prove this ? ' namely, this Conclusion, 
 
 And the corresponding Substantives are often used to denote- 
 that which is, in each instance, last in the mind : ' inference ' 
 being often used to signify a Conclusion [Proposition-inferred,"] 
 and ' proof,' a Premise, 
 
Lesson xyii.] different kinds of arguments. 153 
 
 When, then, any long train of reasoning is carried on, we 
 proceed — in ' inferring,' and in * proving ' — in opposite di- 
 rections : our object being, in the one case, to ascertain from 
 all that we know on a certain subject, ivJiat Conclusion is to 
 be drawn ; and in the other case, — when we are satisfied as 
 to the Conclusion — to consider by what arguments we shall 
 establish it. 
 
 § 2. In the former case, from established ' data ' [certain 
 known facts, and acknowledged principles] we infer so and so ; 
 and from this conclusion, in conjunction with other known 
 truths, we infer something else ; and so on, till we have ascer- 
 tained what is decisive of the question before us, or as much 
 as we are able. 
 
 In the latter case, we proceed upwards from the Premises 
 which will establish the Conclusion we are maintaining, to 
 the arguments which will prove those Premises : and so on, 
 till we arrive at something that is admitted. And from this, 
 — when we have to convince others — ^ve generally proceed 
 through the same train of reasoning, in a reversed order, ' 
 downwards^ till we have arrived at the Conclusion to be es- 
 tablished. 
 
 We are sometimes then employed in what may be called 
 * seeking for a Conclusion^ and sometimes again, in ' seeking 
 for Middle-terms,^ 
 
 For instance, a Judge is inquiring Avhether the estate does, 
 or does not, belong by law to the claimant : the Suitor (or his 
 Advocate) is seeking for proofs that the estate is his. The 
 Natural-philosopher, when investigating^ inquires, ' what is 
 the cause of the tides ; ' the Physician, ^ what is this patient's 
 disease ; ' and each, when he has satisfied himself, and is 
 proceeding to teach or to convince others, sets himself, — like 
 the Advocate, — to seek for proofs ; sometimes employing 
 the same that had led himself to the conclusion, and some- 
 times different ones ; according to what he judges will serve 
 
154 DIFFERENT KINDS OF ARGUMENTS. \_Part V. 
 
 best to satisfy the understanding of others, that ' the cause of 
 the tides is so and so ; ' or that ' such and such is the patient's 
 disease.' 
 
 And in thus laying before others this process of reasoning, 
 a man will sometimes proceed in the same order in whieh he 
 had sought for the arguments, (that is, beginning from the 
 Conclusion, and proceeding upwards) or again, sometimes, 
 in the reverse order ; setting out from something that is ad- 
 mitted, and proceeding downwards^ towards the ultimate Con- 
 clusion.* 
 
 § 3. In treating of the operation of seeking for Middle- 
 terms — in other words, for Arguments to establish, on each 
 occasion, the Conclusion maintained — we are naturally led 
 to inquire concerning the different hinds of Arguments one 
 often finds alluded to in books, or in conversation. 
 
 These are in general very indistinctly described, and con- 
 fusedly enumerated. 
 
 "We hear persons speaking of ' Syllogistic reasoning,' and 
 such as is not ' Syllogistic ; ' — of ^ Categorical, or Hypotheti- 
 cal Arguments,' — of 'Demonstrative, and Probable' [or 
 Moral] Reasoning ; of ' Direct and Indirect Arguments ; ' — 
 of A priori Arguments,' ' Arguments from Testimony,' — from 
 ' Analogy,' — from ' Example,' — by ' Parity-of-reasoning,' 
 &c., without any distinct account being given of these and other 
 modes of procedure. 
 
 In reality, to enumerate thus confusedly the several kinds 
 of Argument, is to commit the fault formerly noticed in refer- 
 ence to ' cross-divisions ; ' there being, in this instance, no less 
 than four different divisions ; which ought not to be blended 
 together. 
 
 ist. The division of Arguments into irregular and syllo- 
 gistic, and of Syllogisms again, into Categorical and Hypo- 
 
 ^ See the notice in Lesson IX. of the Analytical arid Synthetical order. 
 
Lesson xvii.] different kinds of arguments. 155 
 
 thetical, &c. is a division, strictly-speaking, not of Arguments 
 Jiemselves, but of the forms of stating an argument. For it 
 is manifest (as above explained) that one individual argument 
 may be stated either in a Hypothetical or in a Categorical 
 form, and in the first figure, or in the second, &c. 
 
 iily. The division of Arguments into probable and demon* 
 strative, is evidently according to the subject-matter : and is, 
 strictly, not a division of Arguments, considered as Arguments, 
 but rather, of the Propositions they consist of, in respect of 
 the ' matter ' of those Propositions. 
 
 § 4. iiird. Arguments are divided into ' direct ' and ' indi* 
 rect^ according as your object is to establish either the truth of 
 the Conclusion, or the falsity [the ' Contradictory'] of one of 
 the Premises. For when we arrive, by sound reasoning, at a 
 false Conclusion, it is plain that one at least of the Premises 
 must be false. 
 
 In short, every valid Argument may be stated in the form 
 of a Conditional-Proposition : ^If the Premises are true, the 
 Conclusion is true : ' then, supposing you admit the Premises 
 to be true, you must admit the truth of the Conclusion: 
 (which corresponds to a Constructive Conditional-syllogism) 
 and hence, also, supposing you find the Conclusion false, 
 you must admit that the Premises, or one of them, cannot 
 but be false ; since if they were both true, the Conclusion 
 w^ould be true : and this corresponds to a Destructive Condi- 
 tional-syllogism. 
 
 Now the above is evidently a Division, not, strictly speak- 
 ing, of Arguments, but of the purposes for which any Argu- 
 ment may be designed : namely, either to prove its Conclu- 
 sion, or to disprove one of its Premises. 
 
 For the same individual Argument may answer both pur- 
 poses, to difiTerent persons. For instance, ' Whatever is main- 
 tained by the Stoics (or by such and such a philoso}>her, sect, 
 party, &c.) must be admitted ; that pain is no evil (or such 
 
156 DIFFERENT KINDS OF ARGUMENTS. [^Part V. 
 
 and such a doctrine, whatever it may be, in each instance) is 
 so maintained ; therefore this must be admitted : ' now a zeal- 
 ous partizan will be so fully convinced of the Premises that 
 he will assent to the Conclusion : others may be so revolted 
 by the Conclusion, that they will thereupon reject the Major- 
 premise. 
 
 The Argument, therefore, will, to the one, be ' direct,' and 
 to the other ' indirect.' 
 
 § 5. ivly, "When we speak of arguing from a Cause to an 
 Effect, or of arguing from Testimony to the truth of what is 
 attested, or again, from a known case to an unknown similar 
 case, &c. these kinds of Argument are distinguished from 
 each other ^according to the relation existing between the 
 Premises and the Conclusion^ in respect of the subject-matter 
 of each.' 
 
 This, then, and this alone, is properly a division of Argu- 
 me7its, as such. 
 
 When we say, for instance, that in arguing from the ' fall 
 of rain' to the consequent 'wetness of the roads,' the Premise 
 is a Cause, and the Conclusion drawn, an Effect, it is evident 
 we are not speaking of the mere syllogistic connexion of the 
 Premise and Conclusion ; (which, as was formerly explained, 
 is always the same) nor again are we speaking of the subject- 
 matter of thos-e Propositions (as in the iid Head) considered, 
 — each by itself, — merely as Propositions, independently of 
 the Argument : for ' Cause,' and ' Effect ' are relative words ; 
 and the Premise is called a Cause of that Effect which is 
 inferred in the Conclusion. So that it is the relation, in re- 
 spect of matter, of the Premise to the Conclusion, that we are 
 speaking of. 
 
 And so also in respect of Arguments from Testimony, and 
 the other kinds that have been alluded to. 
 
 § 6. Arguments, then, may be divided, first, into two class- 
 es : ist. such as might have been used to account for the Con- 
 
Lesson xvii.] two classes of arguments. 157 
 
 elusion, supposing it had been already granted ; and uYy, those 
 which could not. Or, in other words, ist. Arguments from 
 Cause to Effect ; and iily, all other kinds. 
 
 For mstance, if I infer from ' a fall of rain,' that ' the roads 
 must be wet,' I am using an Argument of the Ibrmer Class ; 
 [an ' A-prion- Argument '] since if it were knoivn^ and re- 
 marked by any one, that the roads are wet, I should account 
 for that fact by informing him that it had rained. 
 
 Or again, if a person were known to have committed a mur- 
 der, and it were inquired how he came to perpetrate such a 
 crime, then, any one would be said to account for it, [to show 
 why he did it,*] by saying that he w^as a man of ferocious and 
 revengeful character ; or that he was known to bear malice 
 against the deceased ; or to have an interest in liis death, &c. 
 And these very circumstances might have been used (sup- 
 posing the charge not proved) as an argument to cast suspicion 
 on liim. 
 
 On the other hand, if his guilt were inferred from the testi- 
 mony of some witnesses, or again, from his clothes having been 
 bloody, or from his having about him some property of the de- 
 ceased, these would be arguments of the other class, since they 
 are such as could not have been employed to account for the 
 fact, supposing it established. 
 
 § 7. The Arguments of this latter class may be subdi- 
 vided into two kinds ; which may be called Arguments from 
 ^ Sign,' and Arguments from ' Example ; ' [or ' Instance '] 
 each of which may also be further subdivided. 
 
 ^. As far as any circumstance is what may be called a 
 * Condition,' — more or less necessary, — to the existence of 
 a certain effect, phenomenon, event, result, law, &c. ; in other 
 words, as far as it is a ^ Condition ' of the truth of some asser- 
 
 * It is to be observed that tlie word ' Avhy ' lias tlircc different senses ; 
 viz. from what cause 7 by what proof ? for ^\'\\iii purpose f 
 14 
 
158 DIFFERENT KINDS OF ARGUMENTS. \^Part V 
 
 tion or supposition, — so far it (the ' condition ') may be infer^ 
 red [or ' concluded '] from the truth of that assertion or sup- 
 position, — from the existence of that effect, &c. 
 
 If it be a ' Condition ' absolutely essential to something which 
 we know or assume to be true, it may, of course, be inferred 
 with complete certainty: and the nearer we approach to 
 this case, the stronger will be the probability. 
 
 Thus, in the instance just above, when a man is suspected 
 of a murder, from being found near the spot, his clothes bloody, 
 and property of the deceased about him ; the perpetration of 
 the murder by him is just so far probable, as it is presumed 
 to be a Condition of the existence of the ' Signs ; ' i. e. so far 
 as it is presumed that otherwise his clothes would not have 
 been stained, &c. [or that they would not have been stained 
 unless he had committed the deed.] 
 
 So also the w^etness of the roads is a ' Sign ' that rain has 
 fallen,' just so far as we suppose that otherwise the roads would 
 not have been wet ; — in short, that the fall of rain was a 
 condition of that wetness. 
 
 To this head we may refer all mathematical reasonings. 
 Every property, for instance, of a Triangle, may be regarded 
 as a ' condition ' of the supposition that ' a Triangle,' is what 
 is defined. A figure would not he a Triangle, unless its angfes 
 were equal to two right angles,' &c. 
 
 It is to be observed, that although in many Arguments from 
 ' Sign ' — as when we infer wetness of the roads from a fall 
 of rain — we infer a Cause from an Effect, this is not inas- 
 much as [or ' so far forth as '] it is a Cause, but inasmuch as 
 it is a Condition, For we should no less infer from finding a 
 certain spot wet, that it had been left uncovered; though the 
 mere absence of covering could not be properly called a Cause 
 of its wetness. 
 
 And in like manner, a man's having been alive on a certain 
 day, might be inferred as a necessary ' Condition ' (though 
 (>®rtainly not a ' Cause ') of his dying the next day. 
 
Lesson xvii.] arguments from sign. 159 
 
 § 8. ' Testimony ^ h one, kind of 'Sign.' For it evidently 
 has weight just so far as we suppose the truth of what is 
 attested, to be a necessary ' Condition of the testimony ; that 
 is, just so far as we suppose that the testimony would not have 
 been given, unless the thing attested had been true. 
 
 The different degrees of weight due to different Testimonies 
 must, of course, depend on a great variety of circumstances : 
 of which we must, on each occasion, judge in great measure 
 from the particulars of the case then before us. 
 
 There are two remarks, hovv^ever, on this point, which are 
 needful to be kept in mind : ist. we should remember the dif- 
 ference between Testimony to ' matters-of-^/ac^ ' and to ' mat- 
 ier^-oi-opinionJ When the question is about 2ifact, v/e look 
 merely, or chiefly, to the honesty of the witness, and to his 
 means of oUaining information : when the question relates to 
 doctrine [or opinion] of any kind, his ahility to judge must 
 equally be taken into account. 
 
 By a ' matter [or " question "] of fact,' is commonly under- 
 stood something which might, conceivahly^ be submitted to the 
 senses ; and about which it is supposed there could be no dis- 
 agreement among persons who should be present, and to whose 
 senses it should be submitted. 
 
 By a ' matter-of-opinion,' again, is meant anything whereon 
 an exercise oi judgment would b<3 called for on the part of 
 persons having the same objects presented to their senses ; and 
 who might, conceivably, disagree in their judgment. 
 
 Suppose, for instance, a man is accused of a murder ; 
 whether he did or did not strike the blow, or fire the shot, 
 &c., would be a question oi fact ; whether he did so wil- 
 fully and. maliciously (which is necessary to constitute an 
 act, murder) would be a question of \^' judgment,''] or opinion. 
 
 And observe, that the distinction does not at all turn oh the 
 greater or less degree of certainty attainable in tlie two cases 
 respectively. For instance, whether King Richard the 3d 
 
160 DIFFERENT KINDS OF ARGUMENTS. \_Part V* 
 
 didj or did not, put to death his nephews in the Tower (which 
 is a ' question o^ fact,) is very doubtful, and a matter of dis- 
 pute among historians : but ivhat sort of an act it was, if he 
 did commit it, is a ' matter of opinion/ but one on which no 
 one would be likely to doubt. 
 
 § 9. In most cases this distinction is very obvious : but it 
 sometimes happens that a person is supposed, — and supposes 
 himself — to be attesting 2^ fact, when in truth he is giving an 
 opinion ; that is, either stating the inference he draws from 
 the fact he has witnessed ; or again, professing to attest a fact 
 which he has not really witnessed, but which he concludes to 
 have taken place, from something he did witness. 
 
 An instance of the former kind is, when some one who is in 
 attendance on a sick person, bears witness that the patient 
 was benefitted, or was disordered, hy taking such and such a 
 medicine. He was an eye-witness, perhaps, of the medicine's 
 being swallowed, and of the subsequent change for the better 
 or for the worse ; but that the medicine caused that change, 
 (though he may be very right in believing that it did) is evi- 
 dently his judgment » 
 
 As an instance of the other kind, a man, suppose, will attest 
 that he saw such one killed : though, perhaps, he did not see 
 him dead ; but saw him receive a wound which he judged 
 (perhaps very rightly) could not fail to occasion speedy death. 
 
 For it is to be remembered that there may be, and often 
 are, ' questions-of-opinion ' relative to facts ; i, e., we judge 
 from such and such circumstances, that so and so is, or is not, 
 Ukelg to occur ; or to exist. It is a fact that there is, or 
 that there is not, a great lake in the interior of New-Hol- 
 land ; but till that interior shall have been explored, every- 
 one is left to form his opinions, and to judge according to 
 probabilities. 
 
 And hence, it should also be remembered that men are apt 
 to reason unconsciously ; and thus to suppose themselves bear- 
 
Lesson xvii.] matter of opinion. 161 
 
 ing testimony (as has been said) to something their senses 
 have witnessed, when in truth they are stating their own in- 
 ferences therefrom. 
 
 The process which usually takes place is this : their senses 
 furnish them with one Premise, (the Minor) the other is sup- 
 plied by their own mind ; and the Conclusion drawn from 
 these two (as you may see in the above examples) is what 
 they describe themselves as having witnessed, 
 
 § 10. iily. The other remark to be borne in mind, is, that 
 w^hen several independent witnesses [witnesses between whom 
 there could have been no collusion'] attest the same thing, the 
 weight of their testimony depends on this agreement, and not 
 on the weight of each considered separately, or on the mere 
 addition of these together. 
 
 Thus, if a stranger, or one on whose veracity I have no re- 
 liance, gives me intelligence of some remarkable transaction, 
 or state of things, which he professes to have w^itnessed, de- 
 scribing fully all the details, I may, perhaps, think it more 
 likely than not that the whole story and all the particulars, are 
 a fabrication. But if I receive the same account from another, 
 and again from another person, (equally undeserving of cred- 
 it) who could not have had any communication with the first, 
 nor could have had access to any source of false information 
 common to them all, I should at once believe them ; because 
 the chances would be immeasurably great against several 
 persons (however likely, each, to invent a story) having, in- 
 dependently, invented the same story. 
 
 And the force of evidence in such an argument depends 
 mainly on the number and minuteness of the 2)artictdars in the 
 thing attested ; because the chances are thus increased against 
 an accidental coincidence. 
 
 The same rule applies not only to ' Testimony/ but to other 
 ' Signs ' also. As when, (to refer to an example in tlie pre- 
 ceding Lesson,) a person after swallowing a certain drug is 
 14* 
 
162 DIFFERENT KINDS OF ARGUMENTS. [^Pttrt V. 
 
 attacked with such and such symptoms ; which may have been 
 accidental ; if the same symptoms follow in another case, and 
 another, &c., we are convinced at length that these cannot 
 have been accidental coincidences, but that the drug caused 
 the symptoms. 
 
 § 11. When we reason from a known case to another, or 
 others, less known, under the same Class, this is called argu- 
 ing from ' Example,' — by ' Induction,' — from ' Experience,' 
 — by ' Analogy,' — by ' Parity-of-reasoning,' &c., all of which 
 expressions, though not exactly synonymous, denote a process 
 substantially the same. And the two cases, — the known and 
 the unknown, — are said to be ' analogous,'' or ' parallel cases ; ' 
 the common Class which they both fall under, being, the point 
 of Resemblance or Analogy between the two. 
 
 Thus, we show from the example of the French Revo- 
 lution, and that of England in the time of Charles the 1st, 
 that the extreme of Democracy is likely to lead to a military 
 Monarchy. 
 
 It is in this sense that we speak of ' making an Example * 
 of one who is punished for any faults ; so as to deter others 
 by the expectation that a like fault in them will lead to their 
 punishment. 
 
 And it is thus that we learn to anticipate such and such 
 weather, in certain situations, at certain seasons ; and in short, 
 become acquainted with the general Laws of Nature, 
 
 In all these cases we proceed, strictly speaking, by Analo- 
 gy. But this word is most usually employed in those argu- 
 ments where the correspondence between the two cases is not 
 so complete as to w^arrant a certainty in our conclusions. 
 When the two cases do correspond completely, or nearly so, 
 we usually employ the word Experience. 
 
 Thus, a man would be said to be convinced from ' Expe- 
 rience ' that such and such a kind of diet, or of medicine, or 
 of weather, is wholesome or unwholesome to himself; if he 
 
Lesson xvii.] argument by induction. 163 
 
 had invariably observed like effects on a number of men, he 
 might, perhaps, speak of Experience as having convinced him 
 that this diet, &c. was wholesome or unwholesome for the 
 whole human Species ; though in this, he would be more lia- 
 ble to mistake : but if he conjectured the same with respect 
 to some other Species of animal, every one would say that he 
 was reasoning by ' Analog}^' 
 
 § 12. And here observe, that it is not strictly correct to 
 speak of ' Knowing by Experience ' such and such a general 
 truth ; or that so and so will take place under such and such 
 circumstances. Not but that we may often have the most 
 complete and rational assurance of general truths, or future 
 events ; but, properly speaking, what we knovj, ' by experi- 
 ence,' is, ihQ past only; and those individual events which 
 we have actually experienced ; and any conviction concerning 
 a general rule and concerning future occurrences, is what we 
 judge from Experience.* 
 
 And this distinction is important to be remembered, be- 
 cause, although (as we have said) there are numberless cases 
 in which the conclusion thus drawn is not liable to mistake, 
 many persons are apt — as was above remarked — to make 
 mistakes as to wliat it is that they themselves, — or that oth- 
 ers, — are, on each occasion, bearing witness to. 
 
 A mere fact, or a number of individual facts, however 
 strange they may seem to us, — that are attested by a person 
 whose veracity we can fully rely on, we are justified in be- 
 lieving, even though he be a man of no superior judgment. 
 But if he states some general fact [or ' law '] as a thing ex- 
 perienced by him, we should remember that this is his in- 
 ference^ from his experience. It may be a very correct 
 one ; and it may be one in which no great ability is needed, 
 
 =^ See the instance formerly cited from Hume of the argument that 
 miracles ai'c contrary to experience,' &c. 
 
164 DIFFERENT KINDS OF ARGUMENTS. [^Part V. 
 
 for forming a correct judgment ; but still the case is one in 
 which his ability^ as well as veracity^ is to be taken into 
 account. 
 
 For instance, a Farmer or a Gardener will tell you that 
 he ' knows by experience ' that such and such a crop suc- 
 ceeds best if sown in Autumn, and such a crop again, if sown 
 in Spring. And in most instances they will be right : that 
 is, their Experience will have led them to right conclusions. 
 But what they have actually known hy experience, is, the 
 success or the failure of certain individual crops. 
 
 And it is remarkable, that for many ages all Farmers and 
 Gardeners without exception were no less firmly convinced 
 — and convinced of their knowing it by experience — that the 
 crops would never turn out good unless the seed were soion 
 during the increase of the Moon : a belief which is now com- 
 pletely exploded, except in some remote and unenlightened 
 districts. 
 
 § 13. In all cases. Arguments of the Class we are now 
 speaking of, proceed on the supposition (which is the Major- 
 premise) that ' what takes place, — or has happened — or 
 which we are sure would happen — in a certain case, must 
 happen, or take place, in a certain other similar [or analogous] 
 case ; or in all such cases.' 
 
 The degrees of probability of this Major-premise will, of 
 course, be infinitely various, according to the subject-matter. 
 In the investigation of what are called ' physical-laws,' a sin- 
 gle experiment, fairly and carefully made, is often allowed to 
 be conclusive ; because we can often ascertain all the circum^ 
 stances connected with the experiment. Thus, a Chemist, 
 who should have ascertained by trial, that a specimen of Gold, 
 or of some other metal before him, would combine with Mer- 
 cury, would at once conclude this to be a property of that 
 metal universally. 
 
 In human transactions, on the contrary, it would be thought 
 
Lesson xvii.] invented example. 165 
 
 very rash to draw a conclusion from a single occurrence ; or 
 even from two or three. We make, in such cases, a wide 
 ' Induction ' (as it is called) of a number of individual instan- 
 ces, [or ' examples '] before we venture to conclude universal- 
 ly? — 01* even as a general rule — what is likely to be, for in- 
 stance, the result of such and such a form of Government, — 
 of the existence of Slavery, — of the diffusion of Education, — 
 of Manufactories, &c. 
 
 § 14. We have said that we sometimes argue not only from 
 what has actually happened in certain cases, but also from 
 what we feel certain woidd happen in such and such a sup- 
 posed case. Of this description are instructive ' Fables ' [or 
 ' Parables,' ' Apologues,' ' Illustrations '] in which a general 
 maxim [or ' principle '] is inferred from a supposed case, 
 analogous to that to which we mean to apply the maxim. 
 
 Thus, the imprudence of a man who should hastily join the 
 disciples of Jesus, without having calculated the sacrifices re- 
 quired, and the fortitude expected of him, is illustrated by the 
 supposed case of a man's beginning to build a house without 
 computing the cost. 
 
 So also Socrates argued against the practice of some of 
 the Greek republics, who chose their Magistrates by lot, from 
 the supposed case of mariners casting lots, ivho should have 
 the management of the vessel, instead of choosing the best 
 Seaman. 
 
 And Nathan's parable brought home to David a sense 
 of the enormity of his own crime. Indeed, the ' golden 
 rule ' of supposing yourself to change places with your neigh- 
 bor, and reflecting what you would, then, think it right for 
 him to do towards you, is merely an admonition to employ 
 in one (very numerous) class of cases, such a mode of rea- 
 soning. 
 
 In every employment of what may be called {' fictitious ' 
 jr] ' invented example,' [reasoning from a supposed case] the 
 
166 DIFFERENT KINDS OF ARGUMENTS. [^Part Y 
 
 argument will manifestly have no weight, unless the result 
 that is supposed in the imaginary case, be such as one would 
 fully anticipate. 
 
 On the other hand, real instances have weight, even thougl 
 they be such as one would not have expected. For instance, 
 that all animals with horns on the head, should chew the cud, 
 and should be destitute of upper cutting-teeth, is what no one 
 would have originally conjectured ; but extensive observation 
 has so fully established this as a universal rule, that a natu- 
 ralist, on finding the skeleton of some unknown animal with 
 horns on the skull, would at once pronounce it a ruminant, and 
 would be certain of the absence of upper incisors. 
 
 § 15. When an Argument of the Class now before us, 
 [from Example, Analogy, &c.] is opposed by denial of one 
 of the Premises, it is usual, in ordinary discourse, to say, 
 either, \ the statement is not correct^' which is denying the 
 JH^'/ior-premise, — or ' this case does not apply ^ [or is ' not in 
 point '] — or does not hold good in reference to the one be- 
 fore us ; ' or ' the cases are not parallel : ' which amounts 
 (as you will see on examination) to denying the Major-Pre- 
 mise. 
 
 Thus, if any one recommends to this patient a certain med- 
 icine, as having been found serviceable in cases of Typhus, 
 it might be either denied that it did prove serviceable in 
 those cases, which would be a denial of the Minor) or again 
 it might be denied that this patient's disorder is the same as 
 those : which would be a denial of the J^%*or-premise. 
 
 And here observe, that two things may be very unlike in 
 most respects, and yet quite alike — i. e. the Analogy may 
 hold good — in the one point that is essential to the argument : 
 or again, they may disagree in that one, though they are anal- . 
 ogous in many other points. 
 
 And it is from inattention to this distinction, that just argu- 
 ments from Analogy are often rejected, and fallacious ones 
 admitted. 
 
Lesson xvii.] analogy. 167 
 
 § 16. For instance, in the Parables alluded to above, if a 
 man should object that ' a lamb is a very different thing from 
 a wife,' and ^ a ship from a Republic,' the differences, every 
 one would see, do not affect the Analogy in question. 
 
 On the other hand, there is an Analogy in many respects 
 between all ' valuable- Articles ' that Man uses ; as corn, and 
 iron or lead, and again (what are called the precious-metals) 
 gold and silver. And as an increased supply of most of these 
 articles, while it lowered their price, would not diminish 
 their usefulness, and -would thus prove a general benefit, some 
 might infer that this would hold good in respect of gold and 
 silver. 
 
 If the earth should yield two bushels of corn, or two tons 
 of iron or lead, for one that it now yields, these articles 
 would be much cheaper ; while a bushel of corn would be as 
 useful in feeding us, as now ; and so, wdth most other articles. 
 
 But if the supply of gold or silver w^ere thus doubled, the 
 chief use of these being for coin, and the utility of coin de- 
 pending on its vahce, the only important change would be, that 
 a sovereign or a shilling would be twice as large as now ; 
 and, therefore, twdce as cumbrous. So that no advantage 
 would result. 
 
 It is manifest that in a train of Reasoning, it will often 
 happen, that several of the different kinds of argument we 
 have spoken of will be combined. Thus we may, perhaps, 
 have to prove by several examples, the existence of a cer^ 
 tain ' Cause ; ' and from that Cause to infer a certain ' Effect ; ' 
 and that effect again may be employed as a ^ Sign ''to infer 
 a certain ' Condition,' &c. 
 
 In this, and the preceding Lessons, several interesting sub- 
 jects have been very slightly touched on, which may be found 
 
168 CONCLUSION. [^Part v. 
 
 more fully treated of, and the views now taken more devel- 
 oped, in treatises on those several subjects.* 
 
 If you proceed, in following up this course of study, to pe- 
 ruse such treatises, you will have been prepared, it is hoped, 
 to find that perusal the easier and the more interesting, from 
 what has been explained in these Lessons ; and you will be 
 the better able to understand what is valuable in other 
 Works on such subjects, and to detect anything that may be 
 erroneous. 
 
 ^ In the Elements of Rhetoric, Part I., the subjects of this last Lesson 
 are more fully treated of. 
 
CONTENTS. 
 
 [To be filled up by the Student.] 
 
 Part I. ANALYTICAL INTRODUCTION. 
 
 Lesson I., p. 13. 
 
 Lesson II., p. 18. 
 
 15 
 
CONTENTS. 
 
 Lesson III., p. 23. 
 
 Lesson IY., p. 29. 
 
 Lesson V., p. 84. 
 
CONTENTS. 171 
 
 Lesson VL, p. 46. 
 
 Lesson YII., p. 46. 
 
 Lesson VIIL, p, 53. 
 
CONTENTS. 
 
 Part II. COMPENDIUM. 
 
 Lesson IX., p. 60. 
 
 Lesson X., p. 68. 
 
 Lesson XL, p. 80. 
 
CONTESTTB. 17S 
 
 Lesson XEL, p. 90. 
 
 Lesson XIIL, p, 101. 
 
 Lesson XIV., p. 109. 
 
 15 
 
CONTENTS. 
 
 Part IIL SUPPLEMENT. 
 
 Lesson XV., p. 118. 
 
 PART IV. FALLACIES. 
 
 Lesson XVL, p. 133. 
 
CONTENTS, 175 
 
 Part V. 
 DIFFERENT KINDS OF ARGUMENTS. 
 
 Lesson XYIL, p. 152. 
 
176 
 INDEX. 
 
 [Index to be made by the Student.] 
 
 Lesson. § Page. 
 
INDEX. 177 
 
 Lesson. § Page. 
 
178 INDEX, 
 
 Lesson. § Page. 
 
INDEX. 179 
 
 Lesson. § Page. 
 
180 INDEX. 
 
 Lesson. § Page. 
 
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