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 http://www.archive.org/details/cu31924031219920 
 
A TREATISE ON 
 
 LOGIC, 
 
 OB, 
 
 THE LAWS OF PUEE THOUGHT; 
 
 COMPKISING BOTH 
 
 THE ARISTOTELIC AND HAMILTONIAN 
 , ANALYSES OF LOGICAL FORMS, 
 
 AND SOME CHAFTEBS OF 
 
 APPLIED LOGIC. 
 
 By FRANCIS BOWEN, 
 
 ALFORD PROFESSOR OF MORAL PHILOSOPHY IN HARVARD COLLEGE. 
 
 " Nam Deque decipitur ratio, nee decipit unquam." 
 
 CAMBRIDGE: 
 SEVER AND FRANCIS, 
 
 BOOKSELLERS TO THE UNIVERSITY. 
 
 1864. 
 

 RMELL>^ 
 
 OQjJYi 
 
 Entered according to Act of Congress, in the year 1864, by 
 
 SEVER AND FRANCIS, 
 
 in the Clerk's Office of the District Court of the District of Mass&chasettB. 
 
 University Press: 
 
 Welch, Bigelow, and Company, 
 
 c ambri dge . 
 
PREFACE. 
 
 THE revival of the study of Logic, at least in 
 England and America, as an important ele- 
 ment of a University education, dates only from the 
 publication of Dr. Whately's treatise on the subject, 
 little over thirty years ago. Yet so much has been 
 accomplished for the advancement of the science 
 during this short period, that this treatise, with all 
 its excellences, must be admitted to be now as far 
 behind the times as were the compilation by Al- 
 drich, and the meagre compendium by Dr. Watts, 
 the use of which it superseded. Dr. Whately lived 
 long enough to be able to appropriate to himself 
 the epigrammatic boast, that he had labored so ef- 
 fectually as to render his own work useless. With- 
 out the interest which was awakened in the study 
 of the science by the publication of his book and 
 the discussions which it excited, it is not too much 
 to say that many of the valuable works upon Logic, 
 which have appeared during the last thirty years, 
 either would not have been written, or would have 
 lacked some of their most interesting and impor- 
 tant features. Sir William Hamilton's own labors 
 in this department, by which he certainly accom- 
 plished more for the science than has been done by 
 any one man since Aristotle, began with an elabo- 
 
iv PREFACE. 
 
 rate article on Dr. Whately's treatise in the Edin- 
 burg Eeview, a paper which, as he has himselt 
 declared, contains the germs of all his subsequent 
 discoveries. Besides what Hamilton has accom- 
 plished, the publications within this period of Pro- 
 fessor Mansel, Dr. Thomson, Mr. De Morgan, Mr. 
 Boole, Mr. J. S. Mill, and a host of others, have 
 given an entirely new aspect to the science. Among 
 recent American works upon Logic, honorable men- 
 tion ought to be made of those by Mr. Tappan, and 
 by Dr. W. D. "Wilson of Geneva. 
 
 The only hope that this volume may be found 
 to be of some use consists in the fact, that, as I was 
 the last to enter the field, I have been able to profit 
 by the labors of my predecessors. Certainly it 
 could not have been written without their aid, and 
 one of the chief objects held in view in the prepa- 
 ration of it has been to gather together, and digest 
 into system, their several improvements and eluci- 
 dations of the science. At the same time, the 
 work would not have been carried on in the same 
 spirit in which they began it, if I had not ventured 
 respectfully to dissent from some of their doctrines, 
 and even to present some opinions which will very 
 likely be found to have no other merit than that 
 of originality. As Le Clerc remarks, in introducing 
 his own lucid and thoughtful compendium of the 
 science to the reader's notice, " si, in hacce Logica, 
 nihil esse novi, aut pleraque nova dixerim, ledorem perinde 
 fefeUeroy 
 
 When Dr. Whately wrote, it was not so frequent 
 a practice as it has since become for English schol- 
 ars to profit by the labors of their German breth- 
 ren, and hence some of the greatest deficiencies 
 of his book. It cannot be said that the study of 
 Logic ever declined in the schools of Germany, as 
 
PREFACE. 
 
 it did in those of France, England, and this country. 
 Upheld, for a time by the genius of Leibnitz and 
 the indefatigable industry of Wolff, it was at last 
 reduced to rigorous system, its boundaries were 
 fixed, and its relations to Psychology and Metaphys- 
 ics accurately determined, by the master mind of 
 Kant. Though this great Metaphysician prepared 
 no distinct work upon the subject, the volume re- 
 lating to it which passes under his name being a 
 mere compilation from his loose notes by Jasche, 
 the science has profited more by his labors than by 
 those of any other Continental writer of modern 
 times. Indeed, the publication of his " Criticism of 
 Pure Eeason" formed hardly less an era in the his- 
 tory of Logic than in that of Metaphysics. In one 
 respect, it is true, it had an injurious influence, as 
 it established the practice, which has since become 
 wellnigh universal in Germany, of modifying the 
 doctrines of this science in order to furnish a basis 
 on which might be erected any peculiar scheme 
 of speculative Philosophy. Since Kant's time, a 
 multitude of treatises upon Logic have been pub- 
 lished by German writers, about half of them hav- 
 ing no other purpose than that of preparing the 
 way, and furnishing the materials, for some extrav- 
 agant speculations in Metaphysics. This mode of 
 treatment was carried to an outrageous extent by 
 Hegel, who labored to break down altogether the 
 boundary that had been established by Kant, and 
 whose elaborate work, bearing the name of Logic, 
 is a mere perversion and caricature of that science, 
 as it is metaphysical from beginning to end. Even 
 Trendelenburg, who has contributed more than 
 any other person to the rapid decline of Hegel- 
 ianism in Germany, is not free from blame in this 
 respect, his very able work, Logische Untersuchmgen, 
 
PEEFACE. 
 
 being devoted in great part to buUding up a phil- 
 osophical system of his own. •_ 
 
 But the very prevalence of this abuse m Uer- 
 many furnishes an additional motive for the study 
 of the subject. A key to German Metaphysics 
 can be obtained only by a thorough mastery of 
 the principles and the terminology of Logic. To 
 some persons, perhaps, this consideration may not 
 have much weight, as they will object, that it is 
 of little use to be able to open the door, if the 
 room Contains little more than rubbish. Still I 
 cannot but believe — and the opinion is founded 
 on considerable experience as an instructor in 
 both departments — that a fair knowledge of Log- 
 ic is a natural, and even an indispensable, prepara- 
 tion for the successful pursuit of Psychology and 
 Metaphysics; — may I not add, of any philosoph- 
 ical speculations whatever? It appears certain, 
 that the University lectures of Kant, Fichte, Schel- 
 ling, and Hegel could not have been made even 
 intelUgible, much less instructive, to hearers who 
 had not previously acquired at least the elements 
 of Logical science. Hence the multitude of man- 
 uals and text-books upon this subject, which have 
 appeared in Germany during the last three quar- 
 ters of a century, many of them having passed 
 through numerous editions, and each betraying 
 very plainly the particular system of Philosophy 
 to which it was intended to serve as an introduc- 
 tion. Some familiarity with the principles of Log- 
 ic appears essential for a thorough comprehension 
 even of the metaphysical doctrines of Sir William 
 Hamilton, which, both in their philosophical and 
 theological bearings, seem likely to exert a consid- 
 erable mfluence over English and American minds 
 for many years to come. 
 
PREFACE. vii 
 
 Hamilton's "Lectures on Logic" are marked 
 with the inevitable defects of a posthumous pub- 
 lication, the larger portion of which was probably 
 never intended by the author to be given to the 
 public ; and though very ably edited by Professor 
 Mansel and Mr. Veitch, they present a mass of 
 crude material from which a knowledge of the 
 peculiar doctrines of the writer cannot be ex- 
 tracted but with considerable difficulty. Indeed, 
 the " Lectures," which form the body of the book, 
 were evidently prepared in great haste, when the 
 author's appointment to the Professorship in this 
 department, in 1836, obliged him to collect at 
 short notice the materials for an extended course 
 of instruction. He appears to have met this sud- 
 den call by hurriedly translating a series of ex- 
 tracts from the most approved German text-books, 
 especially those of Krug, Esser, and Bachmann, 
 merely interpolating here and there some of the 
 comments, corrections, and additions which could 
 not fail to occur to so rich a mind as his, while 
 traversing so broad and familiar a field. These 
 Lectures, containing only a glimpse of one feature 
 of the peculiar system which has since become 
 identified with his name, he seems to have re- 
 peated from year to year, during his whole period 
 of office, with no material enlargement or altera- 
 tion of the manuscript, though doubtless inserting, 
 from year to year, many extemporaneous exposi- 
 tions of his corrections of the leading doctrines 
 of Logical science, as these occurred to him at suc- 
 cessive periods. The whole transaction seems to 
 me to afford an instructive comment on the futility 
 of what is called the Professorial mode of teaching, 
 which has always prevailed in the University of 
 Edinburgh, and which consists in getting up very 
 
PREFACE. 
 
 hastily a course of lectures during the teacher's 
 first year of office, and repeating them, parroWike, 
 from year to year, without any regular use of a 
 text/book or manual of instruction. If such lec- 
 tures contain anything really valuable, in addition 
 to what is already before the world, they are apt 
 very soon to find their way to the press ; if they 
 are of little worth, they are almost sure to be 
 repeated, with little alteration, to one class after 
 another, and with as little profit to the hearer as 
 exercise to the reader. It may be doubted wheth- 
 er the most fertile and best-trained minds, at least 
 in the speculative sciences, are capable of prepar- 
 ing every year an entirely new course of lectures, 
 without either filling them with crudities and tru- 
 isms, or lapsing into paradox and extravagance, 
 such as have too frequently characterized the pro- 
 ductions of German Professors. 
 
 With all his amazing activity of mind and pro- 
 digious erudition, Hamilton appears to have been 
 either too indolent, or too critical of his own labors, 
 to be able, without great delays, to digest his mate- 
 rials into a shape fit for publication. He was not 
 an adept in the very low, but very necessary, art 
 of book-making. But for his controversy with Mr. 
 De Morgan, I doubt whether he would ever have 
 worked up into form as much as he did of his 
 " New Analytic of Logical Forms," th& publication 
 of which was promised as far back as 1846. Stim- 
 ulated by opposition, however, though impeded 
 by ill-health during the later years of his life, he 
 appears to have labored strenuously, after the last- 
 mentioned date, to fulfil this promise. Death sur- 
 prised him long before he had completed his prep- 
 arations ; and out of the mass of fragmentary ma- 
 terials which were found among his papers, with 
 
PREFACE. IX 
 
 some aid from the few critical and controversial 
 articles that he had already printed, his editors 
 pieced together, with great difficulty, the imperfect 
 view of his improved system of Logic, which ap- 
 pears as a long Appendix to the volume of his 
 Lectures. The manuscripts which they selected 
 and arranged were judiciously printed just as he 
 left them, and with very little editorial comment. 
 The reader must gather from them as best he 
 may, always keeping in view the date attached 
 to each fragment, a connected view of Sir William 
 Hamilton's latest doctrines upon the subject. This 
 posthumous work has at least one odd character- 
 istic, as the body of the work and the Appendix 
 flatly contradict each other, by giving opposite 
 views of the science to which they relate. 
 
 These are the sources whence I have endeav- 
 ored to collect the materials for a general survey 
 of the science of Logic in its present state, em- 
 bracing what is common to all systems, and a re- 
 view of most of the questions relating to it which 
 are still open to discussion. Among English au- 
 thors, after Sir William Hamilton, I have been 
 chiefly indebted to Professor Mansel ; for without 
 the aid afforded by his Prolegomena Logica, and the 
 notes and supplementary matter appended to his 
 edition of Aldrich, of which Hamilton justly re- 
 marks that la sauce vaut mieux que le potsson, this 
 book would have cost me much more labor, and 
 yet would have wanted what are now its best 
 claims to notice. 1 have also derived much help 
 from the excellent " Outline of the Laws of 
 Thought," by Dr. Thomson, the present Arch- 
 bishop of York. Among the German writers, be- 
 sides all whose names have been already men- 
 tioned, I have made profitable use of Kiesewetter, 
 
X PREFACE. 
 
 Fries, Beneke, Dressier, and Drobisch, besides con- 
 sulting a host of others. Of the earlier logicians, 
 it seems to me that Burgersdyck, with the anno- 
 tations of Heereboord, gives the clearest account 
 of the science as it was taught in the schools be- 
 fore the influence of Descartes and Locke began 
 to be felt; and that the Port Royal "Art of 
 Thinking," of which an admirable translation, with 
 Notes and an Appendix, by Mr. Baynes, has re- 
 cently been published, is far the best of the trea^ 
 tises on the subject which were in use during the 
 eighteenth century. Throughout the work, I have 
 kept constantly in view the wants of learners, 
 much of it having been first suggested while at- 
 tempting to expound the science in my own class- 
 room. My highest ambition will be satisfied if it 
 should be found to be of use to other teachers. 
 
 Cambridge, March, 1864. 
 
CONTENTS. 
 
 CHAPTER I.. 
 
 Pagb 
 
 pstchological introduction 1 
 
 IntuitionB distinguished from Concepts ..... 1 
 
 The Nature of Thought 10 
 
 Relations of Thought to Language . . . . , 16 
 
 Mental Characteristics of Brutes .* . . . . .18 
 
 The Formation of Concepts . . . . . . 19 
 
 Language aids Thought ........ 21 
 
 And is often substituted for it 24 
 
 CHAPTER II. 
 
 Definition op Logic 30 
 
 The Form distinguished from the Matter of Thought . • 31 
 Universal distinguished from Special Logic . . , .34 
 Divisions of the Science ....... 36 
 
 Utility of the Study of Logic 38 
 
 CHAPTER III. 
 
 The Primary Axioms op Pure Thought 47 
 
 These Axioms reduced to one Principle .... 48 
 
 This Principle explicated into three Axioms . . . .49 
 
 Analytic distinguished from Synthetic Thought . « . 52 
 
 The Principle of Synthetic Thought explicated . • . .53 
 
 Hamilton's Postulate of Logic 56 
 
xii CONTENTS. 
 
 CHAPTER ly. 
 
 The Doctrine of Concepts 59 
 
 The Elements of a Concept 62 
 
 The twofold Quantity of Concepts 66 
 
 First and Second Intentions 70 
 
 The Relation of the two Quantities to each other ... 72 
 
 Infinitated Concepts 75 
 
 The Quality of Concepts 77 
 
 The Standards of Nominal and Heal Definition ... 84 
 
 The Relations of Concepts 86 
 
 The Laws of Homogeneity and Heterogeneity ... 90 
 
 Definition and Division 93 
 
 CHAPTER V. 
 
 The Doctrine of Judgments 105 
 
 109 
 . 112 
 
 120 
 . 123 
 
 125 
 . 127 
 
 128 
 . 132 
 
 141 
 
 The Nature of the Copula .... 
 The Predicables and the Categories . 
 The Quantity of Judgments, Aristotelic Doctrine 
 The Quality of Judgments, " " 
 
 Quantity as affected by Quality, " " 
 
 The Relation of Judgments .... 
 Conditional Judgments .... 
 The Hamiltonian Doctrine of Judgments 
 Explication of Propositions into Judgments . 
 
 CHAPTER VI. 
 
 The Doctrine of Immediate Inference 148 
 
 .(EquipoUence or Infinitation 152 
 
 Conversion ••....... 15c 
 
 Hamilton's Doctrine of Conversion 160 
 
 Opposition and Integration I go 
 
 Conspectus of Judgments and Immediate Inference, AristoteUc 
 
 Doctrine ... ,-„ 
 
 Hamilton's Doctrine of Opposition and Integration . . les 
 
CONTENTS. 
 
 xm 
 
 CHAPTER VII. 
 
 The Doctrine of Mediate Inference : the Aristotblio Anal- 
 
 Tsis of Stliogisms 174 
 
 175 
 . 180 
 
 187 
 . 190 
 
 194 
 . 197 
 
 202 
 . 207 
 
 212 
 . 215 
 
 219 
 . 222 
 
 226 
 
 The Canon of Categorical Syllogisms . 
 This Canon explicated into Six Rules 
 Dictum de omni et nvUo .... 
 
 Figure and Mood 
 
 Reduction to the First Figure 
 The Mood of a Syllogism ... 
 The Technicalities of Reduction exemplified 
 Conditional Syllogisms . . . . , 
 Disjunctive Syllogisms .... 
 Dilemmas or Hypothetico-Disjnnctives 
 Defective and Complex Syllogisms 
 
 Sorites 
 
 Conspectus of the Aristotelic Doctrine of Syllogisms 
 
 CHAPTER VIII. 
 
 The Hamiltonian Doctrine of Stllogisms .... 228 
 
 Analytic and Synthetic Order of Enouncement . . . 228 
 
 Reasoning in the two Quantities 234 
 
 The Doctrine of the Figures 239 
 
 The Unfigured Syllogism 244 
 
 Hamilton's System of Notation or Symbolization . . . 246 
 
 The Number of Moods increased by Quantifying the Predicate . 251 
 
 The worse Relation of Subject and Predicate . . . 253 
 
 Hamiltonian Table of Moods 256 
 
 Falsity of the Special Rules demonstrated .... 259 
 
 Applicability of the difierent Figures to Deduction and Induction 261 
 
 Conditional Syllogisms reduced to Immediate Inferences . . 264 
 
 CHAPTER IX. 
 
 Of Fallacies 267 
 
 Fallacies in dictione improperly so called .... 269 
 
 Division of Formal and Material Fallacies .... 271 
 
 Syllogisms of more than Three Terms ; Ambiguous Middle . 272 
 
CONTENTS. 
 
 Undistributed Middle ; Composite and Divisive sense 
 Illicit Process of the Major and Minor Terms 
 The Sophism of EubuUdes, the Liar 
 Sophisms respecting the Quality of the Reasoning 
 Violation of the Canons of Hypothetical Reasoning 
 Material Fallacies ; petitw principU 
 Falhioy of the Impossibility of Motion . 
 Igrwratio denchi ...•••• 
 Argumentum ad ignorantiam . . ■ • 
 Nm Causa pro Causa; post hoc, ergo propter hoc . 
 Ignava Batio ....■'•■ 
 Achilles and the Tortoise 
 
 278 
 281 
 288 
 290 
 293 
 294 
 296 
 298 
 300 
 306 
 309 
 312 
 
 CHAPTER X. 
 
 Applied Logic .....-••• 
 Science formed by Analysis and Synthesis . 
 
 Classification in Science 
 
 The Relation of Cause and Effect .... 
 
 Necessary Cognitions a priori 
 
 These Cognitions not mere Laws of Thought 
 
 Elements of our Concepts of Individual Objects 
 
 The preliminary Classifications of Science . 
 
 Science advances through the improvement of Classifications 
 
 Failure of the attempts made to classify the Sciences 
 
 314 
 817 
 322 
 324 
 328 
 330 
 334 
 340 
 343 
 346 
 
 CHAPTER XI. 
 
 Cemonstkative Rbasonino akd Deductive Evidence . . 351 
 Demonstration applicable to mere Concepts, not to Real Things 352 
 
 Why Mathematical reasoning is demonstrative . . . 353 
 
 Mathematical evidence not a mere perception of identity . . 359 
 
 Distinction between Pure and Applied Mathematics . . 361 
 
 The Conclusion not deduced from the Major Premise . . 362 
 
 The only New Truth is that enounced in the Sabsumption . 364 
 
 Particular facts not learned, but proved, by Reasoning . .367 
 
 Different classes of Major Premises 371 
 
 Technical terms used in the Construction of Science . . 374 
 
CONTENTS. 
 
 XV 
 
 CHAPTER XII. 
 
 Induction and Analogy 376 
 
 Want of Universality in the Sumption fatal to strict Keasoning 376 
 
 Induction and Analogy are means for discovering Truth . . 380 
 
 Difference between them illustrated 381 
 
 Analogy is Aristotle's Reasoning from Example . . . 382 
 
 Analogy leads only to Probable Conclusions . . . 383 
 
 Induction presupposes the correctness of previous Classifications 385 
 
 Uniformity of Nature the basis of Induction . . . 388 
 
 This Maxim not an Ultimate Fact 389 
 
 And not first obtained by Induction ..... 391 
 
 But derived from the Principle of Causality .... 395 
 
 What is Physical Necessity 400 
 
 All Induction proceeds by simple enumeration .... 401 
 
 A universal Logic of Induction cannot be established . . 403 
 
 A General Fact, a Law of Nature, and a Cause distinguished . 405 
 
 How a Law of Nature is discovered ..... 409 
 
 Physical Causes proved by the Laws of Nature subsumed under 
 
 them .......... 414 
 
 Induction discovers, the Law of Causality proves . . . 416 
 
 CHAPTER XIII. 
 
 The SotjECES of Evidence and the Causes of Ekkor 
 Intuition the basis of all Certainty 
 Intuition of external objects as external . 
 Memory as a Source of Evidence 
 The art of Writing an auxiliary to Memory 
 The experience of others a necessary aid 
 Testimony distinguished from Authority . 
 And Veracity from Competency . . • . 
 Hume's Argument against Miracles examined . 
 The Criticism of Tradition and Ancient Writings 
 The Theory of Probabilities .... 
 Moral Causes of Error . • . 
 
 419 
 419 
 421 
 423 
 426 
 427 
 428 
 430 
 432 
 433 
 437 
 445 
 
LOGIC. 
 
 CHAPTER I. 
 
 PSYCHOLOGICAL INTRODUCTION. 
 
 Intuitions distinguished from Concepts. — Mental Characteristics of Brutes, 
 — Relations of Thought to Language. 
 
 THE beginning of all knowledge is in single acts of the 
 Perceptive or Acquisitive faculty, each of which re- 
 lates immediately to an individual object or event. Such 
 acts are called Intuitions or Presentations; the former is the 
 more generally received appellation. Each Intuition gives 
 us a knowledge of its object so far only as this object is 
 perceived now and Aere, and also as it is owe, or undivided, 
 though not necessarily indivisible. To recognize, or know 
 over again, the object as similar to another thing perceived 
 on a former occasion or in a different place, or to analyze it 
 into its parts or attributes, or to refer it to a class of things 
 previously known, and thereby to give it a common name, 
 requires the aid of a different and higher power of the 
 mind. In receiving Intuitions, the mind exerts no consciotts 
 activity whatever ; it is passively receptive of any impres- 
 sions that may be made upon it, and does not in any way 
 consciously react upon or modify those impressions. It is 
 like a mirror reflecting the objects that are held up before 
 it, perhaps giving distorted or unfaithful images of them 
 on account of the imperfections of its own surface, but hav- 
 
2 PSYCHOLOGICAL IKTBGDUCTION. 
 
 ing no power to change or in any way affect them by its 
 
 own will. 
 
 The impression made upon my mind by the portrait of a 
 friend which I am now looking at, as it hangs before me, or 
 by the sovmds to which I am listening as they are struck 
 upon a violin ; the image now present to my memory of the 
 relative whom I have recently lost ; the picture of a water- 
 fall in a wood which my imagination at this instant forms ; 
 the consciousness which I have of the present state of my 
 own mind ; — all these are Intuitions, as each one of them 
 relates to a single object, and each is immediate, — that is, 
 it does not come through the intervention of any other state 
 of mind. But what is denoted by the word man, iound, or 
 waterfall, is not an Intuition, for it does not refer to one ob- 
 ject only, but to many. Man, for instance, includes under 
 it John, Thomas, William, and many others ; and it does 
 not convey a complete image of any one of these persons, 
 but only a partial representation equally applicable to any 
 of them. John, when considered simply a» man, is not 
 regarded as he really is, that is, as possessing all his indi- 
 vidual attributes and pecuUarities, but only as having those 
 attributes which he possesses in common with all other 
 men ; he is not viewed immediately, but only through the 
 medium of what is called a Concept, or a Thought of what 
 is common to many. These words, therefore, man, sound, 
 waterfall, and all other common names, do not denote In- 
 tuitions, but Thoughts. 
 
 The Perceptive or Acquisitive faculty, through which 
 we receive Intuitions, as it is a merely passive power, or a 
 capacity of being affected in a certain way, constitutes what 
 may be called the receptimty of the mind. The Thinkina 
 or Elaborative faculty, — i. e. the Understanding, — as it 
 has no Intuitions of its own, but voluntarily reacts upon 
 and modifies those received from the Perceptive feculty 
 •comparing them with each other, and thereby combining 
 
INTUITIONS DISTINGUISHED FROM CONCEPTS. 3 
 
 them into one Thought, or disjoining them as dissimilar or 
 incompatihle, belongs to the spontaneity, or self-activity, of 
 the intellect. 
 
 In the ordinary exercise of our faculties, Intuitions are 
 so intermingled with Thoughts, so quickly pass into them, 
 and are so closely connected with them, that it is difficult 
 to illustrate the distinction between the two by giving an 
 example of an Intuition so isolated and peculiar that there 
 will be no danger of confounding it with any portion of a 
 voluntary and more complex process of mind. But a good 
 illustration may perhaps be found in the case, so frequently 
 referred to, of a person bom entu-ely blind, and subsequent- 
 ly enabled by a surgical operation, for the first time, to see. 
 Suppose that the 'first visual sensation given to such a person 
 were that of a flash of red light. This sensation, it is evi- 
 dent, would be to him entirely peculiar or sui generis. He 
 could not, at first, refer it to any class of things with which 
 he was formerly acquainted ; he could not give it a name ; 
 he could not analyze it into parts or attributes. He did 
 not will to produce or to modify it ; it comes to him, so to 
 speak, of its own accord. He could hnow it, but not recog- 
 nize it, as the presentation of an entirely new object, by 
 which his mind was involuntarily affected in a new and sur- 
 prising manner. Such, we may suppose, are the Intuitions 
 of brutes ; and the faculty of Intuitions, as the Perceptive 
 or Acquisitive faculty may be called, — a mere receptivity, 
 unmodified by any voluntary act of the patient, — is proba- 
 bly the most prominent of the few mental powers which 
 brutes possess in common with man. In respect only to 
 Intuitions produced in him by external causes, man has no 
 advantage over the lower animals. 
 
 But although all our knowledge begins in Intuitions, it 
 does not end .with them. In man, the mere receptivity of 
 mind is so soon modified by its spontaneity, — the mere In- 
 tuition so quickly passes into voluntary or consciously active 
 
4 PSYCHOLOGICAL INTRODUCTION. 
 
 T}wugU properly so called, — that we can hardly teU where 
 the one ends and the other begins. To recur to the case 
 just mentioned ; the moment the person who has now first 
 received his sight begins to consider or reflect upon the new 
 presentation that has thu5 been made to him, he probably, 
 in a certain sense, recognizes it as a new sensation, — that is, 
 he refers it to a class of feehngs with which he was former- 
 ly acquainted, as coming to him through the other senses, 
 and which, as similar in some respects, though different in 
 others, he has ranked together and called by one name, 
 " sensations " or " feehngs." Such recognition is an act of 
 Thought properly so called. It includes comparison of this 
 Intuition with others, and a conscious discrimination of 
 those respects in which it is similar to others from those in 
 which it is unlike them. The Perceptive &culty gives us 
 Intuitions of single objects, each of which is to us a distinct 
 unit, having no connection or relation with anything else ; 
 the Understanding, a higher faculty, gives us Thoughts, or 
 enables us to analyze each thing into its parts or attributes, 
 and thus to recognize its various points of resemblance and 
 difference, and so to form classes of things. The former 
 power furnishes the rude material — " the Matter," as it 
 is technically called — of our knowledge ; the latter supplies 
 " the Form," elaborating and disposing this rude material 
 in a systematic way, or according to regular laws, by throw 
 ing it into groups, so as to render it conceivable to Thought. 
 Hence the Understanding has been called tlie unifying 
 faculty, by which the many is reduced to unity. 
 
 If we look out of a window for the first time upon a 
 landscape that is entirely new to us, the momentary glance 
 gives us only an Intuition of the scene, or a confused knowl- 
 edge of it as one whole, without any distinction of parts, 
 and without recognition of any of these parts as former 
 objects of knowledge. This is because the Understanding 
 requires time to do its work. But if we dweU long enough 
 
INTUITIONS DISTINGUISHED FKOM CONCEPTS. 5 
 
 upon the scene, first, we recognize (or know over again) 
 one familiar set of objects, and call ttem trees ; then, other 
 classes of objects previously kno-\vn, and call them respec- 
 tively huildings, rocks, hills, &c. Lastly, we consider the- 
 relations of these objects and classes of objects to each 
 other and to similar objects formerly known, in respect to 
 distance, magnitude, color, &c. , and are thus enabled to 
 think the landscape as a whole. This Thought contains a 
 far more perfect knowledge than the Intuition, which was 
 all that the senses gave us at the first momentary glance. 
 
 Now, how much is imphed in the successive recognition 
 of the component parts of this knowledge as objects previ- 
 ously known, and therefore appropriately designated by a 
 familiar name ? Of course, as the landscape is supposed to 
 be now seen for the first time, we do not recognize any in- 
 dividual tree, building, or hill in it as precisely the same 
 object that we have formerly seen. We mean only that 
 we recognize it as similar to some former objects of knowl- 
 edge ; that is, having seen many objects which agreed with 
 each other as similar in many of their parts, — as possessing 
 trunks, branches, and leaves, — we have formed them into 
 one class, and called them trees. The object in the new 
 landscape is then recognized, not as famihar in itself, but as 
 belonging to a familiar class of things ; we do not recognize 
 it as an Intuition, but as a Concept, — not as this tree, but 
 as a tree. Conception is that act of the Understanding or 
 Thinking faculty whereby we unite similar objects into one 
 class by overlooking their points of difference and forming 
 their common attributes into one Concept or Thought, the 
 name of which thus becomes the common name of all the 
 individuals included in the class. Here, again, the unify- 
 ing office of the Understanding appears ; the Concept re- 
 duces the many to unity, — brings together many objects 
 into one Thought or many attributes into one subject. 
 Thus we are properly said to know many objects which we 
 
6 PSYCHOLOGICAL INTRODUCTION. 
 
 have never seen; for, through hearing or reading descrip- 
 tions of them, we have formed a right Concept of what 
 they are, and thus are enabled to recognize — i. e. know 
 them over again — and call them by their appropriate name, 
 when we do see them. But this evidently is only mediate 
 knowledge, and is more or less imperfect and inadequate, 
 depending on the scantiness or ftdness of the Concept. 
 As Mr. Mansel remarks, a Concept " is not the adequate 
 and actual representative of any single object, but an inad- 
 equate and potential representative of many." And again, 
 " it is not the sensible image of one object, but an intelligi- 
 ble relation between many." 
 
 Concepts can never come to us from without, for the ex- 
 ternal world has no Concepts. It has not even Intuitions 
 or Percepts, but only real objects, — that is, persons and 
 things, and their marks or attributes. Every real object 
 has an indefinite or countless number of such attributes ; 
 for, however long and carefully we may observe it, we can 
 never be sure that we have ascertained all its elements and 
 qualities. Carry the chemical analysis of it one step further 
 than before, or place it in new relations with other real ob- 
 jects, and it will manifest new properties or activities, the 
 existence of which was formerly unsuspected. Observation, 
 which proceeds by a series of Intuitions, can make known 
 to us an indefinite number of these attributes, but can never 
 exhaust them. Hence the knowledge which we can ac- 
 quire by Intuition, though constantly increasing in fulness 
 and complexity, can never become complete, and is sdwavs 
 attended with some uncertainty; as any conclusions that 
 we form respecting the object may be vitiated by the pres- 
 ence of a quaUty or element of whose existence we were 
 ignorant. Moreover, the hmited compass and finite powers 
 of the human mind cannot take in at once all even of those 
 attributes whose presence is perfectly known. The image 
 or representation of the object in our minds immediately 
 
INTUITIONS DISTINGUISHED FEOM CONCEPTS. 7 
 
 becomes confused, when we attempt to make it grasp too 
 much, or to comprehend, in truth, more than a very few of 
 the known attributes. Giving up the attempt at complete- 
 ness, then, we form a Concept of the object embracing 
 comparatively few of its ascertaiaed quahties, but selecting 
 those which are most distinctive and essential, in order 
 thereby more readily to discriminate it from other objects 
 of a different class. Such a Concept is certainly incomplete, 
 but it is clear in proportion to the narrowness of its dimen- 
 sions. We can more easily grasp it in thought, and con- 
 template it at once in its entireness, because it has so little 
 complexity. On the other hand, the lack of ftdness is apt 
 to render the boundaries of the Concept somewhat less dis- 
 tinct. Consequently, any object, so far as it is known only 
 mediately, or through such a Concept, is known only in a 
 few of its leading attributes ; and it may even be doubtftd 
 whether another object, which resembles it in these attri- 
 butes, but departs very widely from it in others, ought to be 
 ranked in the same class with it, and called by the same 
 name, or not. If my Concept of tree, for instance, is limit- 
 ed to these few particulars, — a vegetable organism possess- 
 ing a main trunk, hranches, and leaves, — it will be doubtful 
 whether many small plants ought to be called trees or shrubs. 
 But if I attempt to enlarge the Concept by introducing 
 more attributes, so d.s to distinguish tree fiilly from all other 
 plants, the idea becomes cumbrous and confused ; we can- 
 not so easily embrace it in a single act of thought. 
 
 "While the Percept or Intuition belongs only to the par- 
 ticular attribute or object — this one color, house, tree, or 
 stone — which has impressed it upon the mind, the Con- 
 cept refers to all the things whose common or similar at- 
 tributes or traits it conceives (^eoTV-capio'), or grasps tageiher 
 into one class and one act of mind. Thus, for example, 
 the Concept red color includes all similar red colors of any 
 object whatever ; the Concept tree refers to all trees, the 
 
8 PSYCHOLOGICAL INTBODUCTION. 
 
 Concept house to aU houses, &c. And naturaJly enough ; 
 for though the red or the white of this ohject is not the 
 identical red or white of that ohject, — is at least numeri- 
 cally different from it, and separated from it by the acci- 
 dents of place and time, the one being perceived here 
 and the other there, the one being seen now and the other 
 formerly, — yet as the two produce exactly the same im- 
 pression upon the mind, or create the same sensation, they 
 are regarded as yirtually the same color for all the purposes 
 of thought. Thus, also, though any one tree differs from 
 every other tree in many other respects besides the acci- 
 dents of place and time, yet it is common to all trees to 
 have a root, a trunk, branches, aijtd twigs. Now as the 
 Concept tree is discriminated from all other Concepts only 
 by possessing these fotir Marks or attributes, it must neces- 
 sarily apply to all trees, which are regarded as the same for 
 aU the purposes of thought. And so it is with all Concepts. 
 Hence they are also called Universals, or Greneral Idea*. 
 
 As Esser remarks, " A Concept is the representation of 
 an object through its distinctive Marks ; — that is, not 
 through those Marks which distinguish it from other objects 
 in general, but from those which come the nearest to it. 
 The distinctive Marks of an object are evidently those 
 which make it to be this object, and not some other one ; 
 i. e. they are its peevdiar and essential Marks. The com- 
 mon and unessential Marks, therefore, do not necessarily 
 belong to the Concept; if they were added to it, they 
 would not only overburden and complicate the Concept, 
 but would lessen its apphcabihty to other objects of tihe 
 same kind. Hence it is self-evident how the Concept is 
 related to the sensible Intuition. Namely, the Concept is 
 the Intuition stripped of its contingent or unessential (m- 
 dividual) attributes or Marks; and the Intuition is the 
 Concept clothed with the contingent or unessential (indi- 
 vidual) Marks." 
 
INTUITIONS DISTINGUISHED FEOM CONCEPTS. 9 
 
 A Concept may be derived from one object as well as 
 from many similar ones ; that is, it may not represent an 
 actual, but only a possible, class or plurality of things. 
 This may be illustrated by the description which a zoolo- 
 gist would give of a newly discovered animal, that was too 
 unlike those formerly known to be included in the same 
 species with any of them. Many slight pecuUarities of 
 such an animal would be passed over altogether, as unes- 
 sential either to the class to which it belonged, or to any 
 other. And of the more important Marks, which might 
 be presuned to be specific and not individual in character, 
 those only would be selected for carefiil description which 
 would serve to distinguish the new object from those which, 
 through their similarity In other respects, might be pre- 
 sumed to belong to the nearest species, or those most akin 
 to the strange specimen. The description thus formed, 
 containing possibly not more than two or three Marks, 
 would be at once a brief and clear Concept actually drawn 
 from an individual, but potentially applicable to a whole 
 .class, should other specimens of it be subsequently discov- 
 ered. In a similar manner, the mind may think any in- 
 dividual object imder a Concept consisting of a few well- 
 chosen Marks, instead of knowing it simply by an Intui- 
 tion as a confused aggregate of many parts and elements, 
 as brutes would do. We perceive only single things, for 
 such only are presented to us ; we think only actual or pos- 
 sible classes of things, for Nature does not give us classes, 
 though she furnishes U5 the resemblances of things, through 
 which we proceed to classify them. All classification is an 
 act of the mind, and is more or less arbitrary, depending 
 on our selection of the attributes or relations in reference 
 to which we classify them. 
 
 It is evident that Concepts must be much clearer repre- 
 sentations of things than the confused aggregate of Percepts 
 or Intuitions on which they are founded. With their hght 
 1* 
 
10 PSYCHOLOGICAL INTKODUCTION. 
 
 they irradiate and make clearly intelligible everything to 
 which they are referred, or with which they come together 
 into consciousness ; and thus to explicate and make clear 
 through Concepts the perceived or represented objects is, 
 says Dressier, what it is, in the strict logical acceptation of 
 the word, to think. In this sense, therefore, to think is to 
 make clear through Concepts something already otherwise 
 represented or known to consciousness. 
 
 Esser says, " To think is to designate an object through 
 a Mark or attribute, or, what is the same thing, to deter- 
 mine a subject through a predicate." According to Sir 
 William Hamilton, " Thought is the comprehension of a 
 thing imder a general notion (Concept) or attribute " ; 
 and again, "AU thought is a comparison, a recognition of 
 similarity or difference, a conjunction or disjunction ; — in 
 other words, a synthesis or analysis of its objects. In Con- 
 ception, that is, in the formation of Concepts (or general 
 notions), it compares, disjoins, or conjoins attributes ; in an 
 act of Judgment, it compares, disjoins, or conjoins Con- 
 cepts ; in Reasoning, it compares, disjoins, or conjoins Judg- 
 ments. In each step of this process, there is one essential 
 element; to think, to compare, to conjoin, or disjoin, it is 
 necessary to recognize one thing through or under another ; 
 and therefore, in defining Thought proper, we may either 
 define it as an act of comparison, or as a recognition of one 
 notion as in or under another." According to other logi- 
 cians. Thought is the reduction of complexity and plurality 
 to unity, or the bringing together of what is confused, vari- 
 ous, and manifold or multitudinous in our Intuitions into 
 the clear vmity of consciousness. 
 
 All these definitions evidently point to one thing, or in- 
 dicate what is substantially the same process. Comparison 
 is the means through which we unite what is similar, and 
 separate what is unhke or opposed ; for only through com- 
 parison do we recognize likeness or unlikeness, agreement 
 
INTUITIONS DISTINGUISHED FEOM CONCEPTS. 11 
 
 or opposition. Now we analyze, divide, and distinguish 
 only in order subsequently to bring together and combine. 
 We discriminate the various elements or attributes of ob- 
 jects through comparison of them with each other, and then 
 unite them with other objects and attributes according to 
 their similarities as ascertained by a fresh act of comparison ; 
 and this union of many things in one class, this reduction 
 of a plurahty of Intuitions under one Concept or general 
 notion, is the means through which the infinite variety and 
 multitude of natural objects are reduced to the Umited com- 
 pass of the human understanding, and made intelligible. 
 A new individual object is to us an isolated and incompre- 
 hensible thing, until we have recognized its similarity with 
 something else, and thereby assigned it to a class, or com- 
 prehended it under a Concept, and given it a common 
 name. 
 
 According to some etymologists, think comes from the 
 same root as thick* and originally signified thickening, or 
 pressing together of many into one; and this exactlj de- 
 scribes the special function of the understanding. As we 
 have already remarked, while a Percept or Intuition is a sin- 
 gle representation, limited to this one thing which excited it 
 or impressed it upon the mind, a Concept is a collective (gen- 
 eral or universal) representation of a whole class of things. 
 To make a formal definition, we may say that a Concept 
 is a representation made wp from several pa/rticular Percepts, 
 through the union of their similar elememts. It is through 
 Concepts that we think, — that is, clearly understand, com- 
 prehend, or conceive something ; for these words mean pre- 
 cisely the same thing, namely, to represent with clearer 
 consciousness what was already represented in our minds. 
 
 Besides the Percept and the Concept, the later German 
 philosophers distinguish the so-called Idea, as the pattem- 
 
 * The n in tkink is casual, ajid does not appear in the participle Sumght. 
 So in German, dick, denken, gedacM. 
 
12 PSYCHOLOGICAL INTKODUCTION. 
 
 representation, ideal Concept, or beau-ideal, by which we 
 understand such a representation as surpasses or goes be- 
 yond the perceived and the conformed to experience. The 
 Idea is that whereby we think an object in its highest possi- 
 ble perfection, and. consequently unlike anything which we 
 have actually witnessed. Hence it does not refer, like the 
 Intuition, to a single thing, nor, like the Concept, to a 
 whole class of things ; but it wholly surpasses in complete- 
 ness or perfection the object to which it is referred. Such 
 are the Ideas of the artist, moral and rehgious Ideas, &c. 
 
 The Kantians use Representations to designate the genus 
 which includes, as its several species. Percepts, Concepts, 
 and Ideas. The aggregate of the Percepts which any one 
 has had may be said to constitute his experience. 
 
 Intuitions afford the only sure means of first creating, 
 and of subsequently rectifying and enlarging, our Concepts. 
 Thus, I may have some scanty knowledge, obtained by 
 reading perhaps, of a species of plant or flower that I have 
 nevej seen. The Concept thus formed may err both by 
 excess and defect ; by excess, because it may include some 
 parts or attributes which are not pecuKar to this species, but 
 are common to it with many others ; by defect, because it 
 may not comprise enough of the attributes common to all 
 the plants ia tliis class, and peculiar to them or not belong- 
 ing to any other plants, to enable me to recognize and dis- 
 tinguish an individual of this species when I see it. It is 
 only intuitive knowledge, or that gained by direct observa- 
 tion, which can enable me to coiTect these errors. 
 
 Intuitions, then, are the only test of the reality of Con- 
 cepts ; for they alone can determine whether the Concepts 
 properly correspond to the actual objects in nature which 
 they are meant to describe. In this sense. Intuitions are 
 not only the beginning, but the basis and the source, of all 
 our knowledge. AU Concepts, however, are not meant to 
 represent actual objects ; they may be imaginary or fenci- 
 
INTUITIONS DISTINGUISHED FROM CONCEPTS. 13 
 
 fill. I can conceive a centaur or a griifin, though no such 
 animal ever lived. Yet even in this case, though the Con- 
 cept, as a whole, is unreal or imaginary, it must be made up 
 only of real parts or attributes, — that is, of such as have 
 been embraced in some preceding Intuition. I have never 
 seen a centaur ; but I have seen the head of a man and the 
 body of a horse, and I can unite, in Thought, these real parts 
 into an unreal whole. So, again, I can think or conceive 
 any combination, however fantastic, of colors that I have 
 previously spen ; but I cannot introduce into the painting, 
 even in Thought, any color that I have never seen. A 
 person bom bUnd, and remaining so, cannot conceive any 
 color whatever ; just as one who has never had the sense of 
 hearing can form no Concept of sound. Intuitions, then, 
 are the basis, not only of all Knowledge, but of aU Thought. 
 
 The perception which gives us a new Intuition may take 
 place either through the external senses, or exclusively 
 through that internal source of knowledge, sometimes called 
 an internal sense, but more properly denominated Con- 
 sciousness, by which we are made aware of the existence 
 of our own sensations, thoughts, and feelings. 
 
 Consciousness, indeed, is the universal witness which 
 testifies to the reaKty, not only of sensation and feeling, but 
 of the external perceptions which come to us through the 
 outer senses. I see a bright red color, I hear a particular 
 sound, only so far as I am conscious of that act of seeing 
 or hearing ; if I were not conscious of it, it would be to me 
 as if it were non-existent. For to know, and to know that I 
 know, are phrases that designate one indivisible act of mind ; 
 and to know that I know is a phrase which means the same 
 thing as to he consdous. Hence, though it is an act of sense 
 whereby I perceive the red color or hear the sound, it is at 
 the same time an act of consciousness ; as, otherwise, I should 
 have no knowledge either of the act of perception, or of the 
 outward phenomenon to the existence of which it testifies. 
 
14 PSYCHOLOGICAL INTRODUCTION. 
 
 I am conscious also of internal perceptions, of hnnger, 
 pain, fear, joy, etc. Still further, I am conscious of mysdf, 
 as the one being that perceives, fears, or rejoices. Every 
 act of consciousness is twofold, testifying to the existence 
 both of the subject, — that is, of the being or person who is 
 conscious, — and of the object, — that is, of the feeling, per- 
 ception, or other phenomenon of which he is conscious. 
 The very language which I am compelled to use in making 
 known the fact to another person testifies to this duality of 
 the act. Any phrase used for this purpose must contain at 
 least two terms, one expressive of the subject, and the other 
 of the object, of consciousness. Thus, in the proposition 
 " I feel hunger," the pronoun " I " denotes the person who 
 feels, and " hunger " the phenomenon which is felt. In 
 some languages, the whole may be expressed in a single 
 word, as in the Latin " esuiio " ; but the expression here is 
 elhptical, the " ego," or the subject of consciousness, being 
 always understood. The two elements can only be knoTvn 
 together, simultaneously, and in their relation to each other. 
 One is not known through the other, or in consequence of 
 the other, or after the other ; but they are known together, 
 in one act of mind. I cannot be conscious of hunger with- 
 out, at the same moment and in the same act, being con- 
 scious of mysdf as feeling the hunger. 
 
 All the phenomena, then, both of the external and intei^ 
 nal world, are presented to the mind each in its distinctive 
 or peculiar Intuition. In other words, any Intuition differs 
 from every other Intuition, at least in the relations of time 
 and space. Thus, two successive Intuitions by the same 
 person, of the same thing, are distinguishable at least in this 
 respect, that the one preceded the other, or took place at an 
 earlier time. In hke manner, — to borrow an example from 
 Mr. Mansel, — « I see lying on the table before me a num- 
 ber of shUlings of the same coinage. Examined severally, 
 the image and superscription of each is undistingnishable 
 
INTUITIONS DISTINGUISHED FROM CONCEPTS. 15 
 
 from that of its fellow ; but in viewing them side by side, 
 s(pace is a necessary condition of my perception ; and the 
 difference of locality is sufficient to make them distinct, 
 though similar, individuals." As already remarked, each 
 Intuition is of a distinct thing as perceived now and here, — 
 that is, in its own pecuHar relations both to time and space. 
 On the other hand, a Concept is freed from these relations 
 of space and time ; I can think what is denoted by the 
 word tree, without identifying it with this or that particular 
 tree, standing on a particular spot, and seen at a particular 
 time. 
 
 •As already remarked, it is the capacity of Thought prop- 
 erly so called which constitutes the immeasurable superi- 
 ority of the human over the brute mind ; but it is also true, 
 that the necessity of Thought arises from the immeasurable 
 inferiority of man's intellect to that of his Creator. If the 
 human mind were omniscient and of infinite compass, it 
 would behold all things intuitively, and would not be con- 
 ftised and overburdened by the multitude of these single 
 cognitions. But it is far otherwise ; the mind is limited 
 and imperfect, and can grasp at once but few objects, — 
 according to the common opinion, only five or six. It can 
 permanently retain in memory, so as to reproduce at will, it 
 can accurately represent in imagination, only a few of its 
 primary Intuitions. We must have recourse to the artifice 
 of Thought ; we must discard all individual attributes and 
 peculiarities, in order, through meagre Concepts, to rise to a 
 larger and clearer, though consciously imperfect, compre- 
 hension of a multitude of things. As will be shown here- 
 after, it is precisely the scantiness of the general notion in 
 respect to its import, which renders it more comprehensive 
 in respect to the number of things which it embraces ; in 
 other words, . if we would know more objects, we must 
 know each of them less perfectly. Unable to master the 
 vastness and complexity of Nature by taking in detail the 
 
16 PSYCHOLOGICAL INTRODUCTION. 
 
 objects which she offers to us, each in its separate Intuition, 
 we throw them, through discarding their differences, into 
 groups and classes. The miad can then grasp at once six 
 or seven of these groups, instead of being limited, as before, 
 to six or seven individuals. Then, by forming successively 
 groups of groups, or classes of a higher order of generaliza- 
 tion, our mental horizon is enlarged till we can take in, or 
 comprehend (corirprehendo), all the objects that we have 
 ever known. But this is like ascending a very high moun- 
 tain, whence, though we obtain a broader view, the ontlines 
 and colors of objects below are but faintly seen, and many 
 are wholly lost in the distance. 
 
 The nature of Language illustrates this process of the 
 formation of Thought. In fact, taken in its strictest sense. 
 Language is the expression of Thought only ; it has to do, 
 not with Intuitions, but with Concepts. Intuitions, from 
 their very nature, can be designated only by Proper Names ; 
 and words properly so called are Common Names. Every 
 word has a meaning, and is therefore susceptible of defi- 
 nition, or at least of explanation. But a Proper Name, 
 strictly speaking, has no meaning ; as Mr. J. S. Mill re- 
 marks, it is a sign which denotes this one thing, but which 
 connotes nothing. Like a pointing of the finger, it desig- 
 nates the individual who is meant ; but it says nothing as 
 to the nature or character of that individual. In so far, 
 indeed, as usage has limited one class of names to males, 
 and another to females, in so far the names connote sex ; 
 and precisely to this extent they cease to be Proper, and 
 become Common, Names. If, to a person who does not know 
 James, I say, " James did this," the effect is precisely the 
 same as if I had said, " A man or boy did it." If a word 
 is to express an Intuition, it must be accompanied by other 
 words, or at least be marked by emphasis or a significant 
 gesture, so as to restrict its meaning to a determmate single 
 thing ; and these hmiting words can be dispensed with only 
 
RELATIONS OF THOUGHT TO LANGUAGE. 17 
 
 ■when the context, or the custom of speech, snppUes the 
 necessary limitations. For example : " this house now be- 
 fore us," "that house on the hill," "the house in Cam- 
 bridge which I showed you yesterday," are phrases wherein 
 the general meaning of the word house is narrowed down 
 to this or that particular building, which may be known 
 through an Intuition. In other cases, the context or em- 
 phasis suffices to limit the signification of such phrases as 
 " his house," " John's house," " the house," etc., to the one 
 thing which was intended. 
 
 Dr. Reid puzzles himself in attempting to explain how it 
 comes to pass, that, whilst all the objects and events which 
 we perceive are individual or singular, all the words in a 
 language are general. But the reasons are obvious. First, 
 we cannot have countless words for the innumerable single 
 objects which we perceive, as no memory could retain 
 them : — think, for a moment, of the myriads of leaves, 
 blades of grass, insects, and other classes of things, which 
 we are constantly beholding. Secondly, these very in- 
 stances show, that, at least as far as our perceptions are 
 concerned, the similarity of objects is often as great as their 
 diversity, and even greater. Thirdly, one main purpose of 
 language being the communication of Thought to others, 
 what we need to know or to commxmicate is not so often 
 a particular fact respecting this single object, as it is a gen- 
 eral truth respecting a whole class of objects ; we do not so 
 often need to say. Avoid or seek this one thing, as. Avoid 
 or seek all of which this is. a specimen. We are more fre- 
 quently concerned, in our mental operations, with classes 
 than with individuals, though the latter alone fiirnish em- 
 ployment for our hands. Fourthly, many things are usually 
 massed together even to our perception, as individual trees 
 in a forest, and therefore can never be exhaustively desig- 
 nated by one expression. By the law of parsimony, there- 
 fore, language makes up its millions of names or designa- 
 
18 PSYCHOLOGICAL INTKODTJCTIOK. 
 
 tions out of comparatively few words, just as its thousands 
 of words are constructed out of some twenty or thirty ele- 
 mentary sounds or letters. 
 
 Language, then, deals only with groups or classes of 
 things ; and the process of classification necessarily pre- 
 cedes the formation of language. This theory explains at 
 once the most striking deficiency of the lower animals, — 
 their incapacity of using language. As they have only 
 Intuitions, the only names which they can apply or under- 
 stand are Proper Names, — the appellations of this or that 
 particular thing. These they can understand. A dog can 
 easily be taught to know the name of his master, even 
 when pronounced by another person. They can even be 
 taught to know the names of particular places and build- 
 ings, so that they can understand and obey, when they are 
 told to go to the barn, the river, or the house.* But it is 
 always the particular bam, or other object, with which they 
 have been taught to associate this sound or significant ges- 
 ture as its Proper Name. Carry the animal to a distant 
 place, near which may be a set of corresponding objects, 
 and then tell him to go to the bam or the river, and he wiU 
 not understand the order as applying to the new set of 
 objects, but wUl set off immediately for the old building or 
 placcj with whose Proper Name alone he is familiar. As 
 Kant remarks, a dog knows (kenni) his master, but does 
 not recognize him throiu/h his peculiar Marks or Attributes 
 (erkennt^, and thereby properly discriminate bim from 
 other persons. 
 
 These Intuitions, which are common to man and the 
 
 * In Mr. Lockhart's amusing account of Sir Walter Scott's first favorite 
 dog, " Camp," he says : " As the servant was laying the doth for dinner, 
 he would address the dog lying on his mat by the fire, and say, • Camp, my 
 good fellow, the Sheriff 's coming home by the ford [or by the hill],' and the 
 sick animal would immediately bestir himself to welcome his master, goiyig 
 out at the back door or the front door, according to the direction given, and ad- 
 vancing as far as ho was able." 
 
MENTAL CHAEACTEEISTICS OF BEUTES. 19 
 
 brute, and which are mere impressions passively received 
 by the miiid, may be stored up in the memory, but out of 
 consciousness, as fruits of experience ; they may be subse- 
 quently recalled to consciousness, or reproduced, either by 
 casual association or voluntary reminiscence ; and, when so 
 recalled, they may be re-presented, or pictured forth to the 
 mind, by an act of that faculty which we usually call Im- 
 agination. Brutes, as well as men, are capable of all these 
 acts of Memory, Reproduction, and Imagination, when ex- 
 ercised upon Intuitions alone; for they are aU impHed in 
 dreaming, and a dog asleep upon a rug before the fire often 
 shows, by his barking and growling, that he has vivid 
 dreams. Man can remember and reproduce Concepts or 
 Thoughts, as well as Intuitions. Imagination, whether in 
 man or the brute, is concerned only with Intuitions, as it 
 pictures forth nothing but definite images of this or that 
 particular object or event. Thoughts properly so called 
 are conceived or understood, but cannot be imagined* 
 
 Agreeably to what has been said, the mental process of 
 forming Concepts may be reduced to three steps, viz. : — 
 
 1. Comparison, whereby, among many attributes or ob- 
 jects, we determine which are similar and which are differ- 
 ent or unlike. 
 
 2. Combination or Reduction to Unity, whereby, for in- 
 stance, this, that, and the other color are recognized and 
 identified as what is usually called " one and the same " 
 shade or hue of red ; or several quadrupeds are recognized 
 as all belonging to one class called horse. 
 
 3. Alstraction,^ whereby we separate and throw aside 
 
 * If this simple distinction had been made, the old dispute between the 
 Nominalists and the Realists could never have arisen. The former clearly- 
 perceived that Concepts could not be imagined ; the Bealists knew very well 
 tliat in thinking, our thoughts were concerned with something more than 
 mere words. Both were right. 
 
 + This word, according to its etymology {ajbs-trdho, to draw off from), is 
 
20 PSYCHOLOGICAL INTEODUCTION. 
 
 — i. e. put out of Thought — the dissimilar or incongm- 
 ous attributes which, if retained, would prevent the other 
 elements from flowing together into unity. 
 
 Each of these steps evidently involves an act of Judg- 
 ment, — that is, of that ftinction of the Understanding or 
 Tliinking Faculty whereby we affirm or deny one Intuition 
 or Concept of another. Hence, we may either consider 
 Judgments as the elements of Concepts, or Concepts as 
 the elements of Judgments. Logicians generally have 
 treated of the functions of Conception or Simple Appre- 
 hension first, and those of Judgment afterwards ; and, as 
 this arrangement is in some respects more convenient, I 
 shall follow their example, though strict method would per- 
 haps require this order to be reversed. 
 
 All men are capable of comparison, and of discerning 
 those similarities on which the formation of Concepts de- 
 pends. But it does not so readily appear how many differ- 
 ent persons are naturally led to form the same Concepts, 
 according as circumstances render them familiar with simi- 
 lar classes of things. This is well explained by Dressier. 
 Before the elements which are common to the constituent 
 Intuitions can be really united into Concepts, they must be 
 excited in consciousness simultaneously, or in immediate 
 succession ; if they arose only separately, and at intervals, 
 like disjoined fragments, there would be no mutual attrac- 
 tion to draw them together. But when tlius brought be- 
 fore the mind at the same time, the synthesis of their 
 common elements into one Concept is a perfectly natural 
 process, in which we need no guidance, " as they flow to- 
 gether by a sort of spontaneous attraction for each other, 
 
 properly applied to the dissimilar elements which are put aside or aban- 
 doned, though, until recently, logicians used it to designate the process of 
 retaining and combining the similar elements. Sir W. Hamilton would say 
 that we prescind the similar which is retained, and abstract the different which 
 is thrown off. 
 
RELATIONS OF THOUGHT TO LANGUAGK 21 
 
 each of them being the object of a liveHer and clearer con- 
 sciousness than any of the dissimilar elements. For exam- 
 ple ; if I see at once, or in quick succession, six diflferent 
 trees, I perceive their similar properties — i. e. root, trunk, 
 branches, etc. — six times over, being once for each tree, 
 and thus have a hveher or stronger consciousness of them 
 than I have of those which, as dissimilar or peculiar to one 
 tree, I perceive only once. Moreover, for the very reason 
 that these common elements are similar — that is, as they 
 have fewer points of divergence or contrast — they more 
 easily coalesce and melt into one Concept." As Hamilton 
 remarks, "the qualities which by comparison are judged 
 similar are already, by this process, identified in conscious- 
 ness ; for they are only judged similar inasmuch as they 
 produce in us indiscernible effects." 
 
 But this is not aU. ^ " The Concept thus formed by an 
 abstraction of the resembhng from the non-resembling 
 quaUties of objects would again fall back into the confu- 
 sion and infinitude from which it has been called out, were 
 it not rendered permanent for consciousness by being fixed 
 and ratified in a verbal sign." Hence, Language is neces- 
 sary, not only that we may communicate our Thoughts to 
 others, but that we may permanently retain and readily 
 use these Thoughts for our own purposes. Concepts are 
 factitious units, and the particular attributes which consti- 
 tute them are somewhat arbitrarily selected, being more or 
 less numerous, and having greater or less resemblance, 
 according to circumstances. A Concept, as we have al- 
 ready remarked, cannot be pictured in Imagination; and 
 the presence of one of the real objects included under it 
 does not necessarily suggest the particular attributes out 
 of which it was formed, to the exclusion of others perhaps 
 equally prominent to the eye. Hence, a Name must be 
 given to it, which will be, of course, a Common Name for 
 .all the individuals contained under itj or the factitious 
 
22 PSYCHOLOGICAL INTEODUCTION. 
 
 aggregate will be dissolved and lost to memory almost as 
 soon as formed. The name presei-ves the unity of the 
 aggregate just as it was originally constituted, precisely as 
 a cord holds a bundle of things together, and enables us to 
 handle many objects as if they were but one. The Mem- 
 ory is then burdened with the retention only of one word, 
 which, when recalled, by the law of association will suggest 
 its meaning, instead of being urged to remember a consid- 
 erable number of attributes, which can neither be sep- 
 arately or collectively pictured in the Imagination. An 
 Intuition, on the other hand, needs not to be designated 
 by a Name, as the presence of the object immediately ex- 
 cites it anew in its original perfection, and Imagination can 
 re-present it almost as adequately and vividly as the reality. 
 But the Concept can neither be retained in mind, nor, so to 
 speak, readily manipulated in Thought, without the aid of 
 a verbal sign. 
 
 This mutual dependence of Thought and Language, 
 each bearing all the imperfections and perfections of the 
 other, has been admirably illustrated by Hamilton. 
 
 " Though, in general, we must hold that language, as 
 the product and correlative of thought, must be viewed as 
 posterior to the act of thinking itself, — on the other hand, 
 it must be admitted, that we could never have risen above 
 the very lowest degrees in the scale of thought without the 
 aid of signs. A sign is necessary to give stability to om* 
 intellectual progress, — to establish each step in our ad- 
 vance as a new starting-point for our advance to another 
 beyond. 
 
 " A country may be overrun by an armed host, but it is 
 only conquered by the establishment of fortresses. Words 
 are the fortresses of thought. They enable us to realize 
 our dominion over what we have already overrun in 
 thought, — to make every intellectual conquest the basis 
 of operations for others still beyond. Or another illustra- 
 
RELATIONS OF THOUGHT TO LANGUAGE. 23 
 
 tion : You have all heard of the process of tunnelling, of 
 tunnellmg through a sand-bank. In this operation it is im- 
 possible to succeed unless every foot — nay, almost every 
 inch — in our progress be secured by an arch of masonry, 
 before we attempt the excavation of another. Now, lan- 
 guage is to the mind precisely what the arch is to the tun- 
 nel. The power of thinking and the power of excavation 
 are not dependent on the word in the one case, on the 
 mason-work in the other ; but without these subsidiaries, 
 neither process could be carried on beyond its rudimentary 
 commencement. Though, therefore, we allow that every 
 movement forward in language must be determined by an 
 antecedent movement forward in thought, still, unless 
 thought be accompanied at each point of its evolution by 
 a corresponding evolution of language, its further develop- 
 ment is arrested. Thus it is that tho higher exertions of 
 the higher faculty of Understanding — the classification of 
 the objects presented and re-presented by the subsidiary 
 powers in the formation of a hierarchy of notions ; the con- 
 nection of these notions into judgments ; the inference of 
 one judgment from another; and, in general, all our con- 
 sciousness of the relations of the universal to the particular, 
 consequently all science strictly so denominated, and every 
 inductive knowledge of the past and future from the laws 
 of nature : not only these, but all ascent from the sphere 
 of sense to the sphere of moral and rehgious intelUgence — 
 are, as experience proves, if not altogether impossible with- 
 out a language, at least possible to a very low degree. 
 
 " Admitting even that the mind is capable of certain ele- 
 mentary Concepts without the fixation and signatm-e of 
 language, still these are but sparks which would twinkle 
 only to expire ; and it requires words to give them promi- 
 nence, and, by enabling us to collect and elaborate them 
 into new Concepts, to raise, out of what would otherwise 
 be only scattered and transitory scintillations, a vivid and 
 enduring light." 
 
24 PSYCHOLOGICAL INTRODUCTION. 
 
 But Words are not only signs and preservatives, they 
 are also substitutes, for Thoughts ; and this peculiarity of 
 Language is an excellence or defect in it, according as it is 
 or is not judiciously used. As Bishop Berkeley remarks, 
 " It is not necessary, even in the strictest reasonings, that 
 significant names which stand for ideas should, every time 
 they are used, excite in the understanding the ideas they 
 are made to stand for. In reading and discoursing, names 
 are for the most part used as letters are in algebra, in 
 which, though a particular quantity be marked by each let- 
 ter, yet, to proceed right, it is not requisite that, in every 
 step, each letter should suggest to your thoughts that par- 
 ticular quantity it was appointed to stand for." Having 
 once satisfied ourselves, by spreading out in thought all the 
 attributes which are combined in any Concept, — or, to be 
 still more careful, by having once called up in Imagination 
 a picture of some one individual possessing all these attri- 
 butes, and therefore contained in the class, — that the 
 meaning of the word, which is the Sign of that Concept 
 and the Common Name of that class, is within our power, 
 we proceed to use that word symbolically, — that is, as a 
 mere sign, and therefore with much more ease and rapidity 
 than if it were necessaiy to stop, each time it recurs, and 
 repeat the process of verifying its meaning. Hence it may 
 be said that the use of language gives us the power of 
 thinking in short-hand ; words are stenographic thoughts. 
 Moreover, this abbreviated expression of thought is a great 
 help to the memory. Having once ascertained by reflec- 
 tion the relation of various Concepts to each other, — that 
 is, having formed judgments and reasonings, and expressed 
 them in propositions, — it is a far easier and shorter method 
 to remember the few words which constitute such a propo- 
 sition, than to recall successively each of the mental pro- 
 cesses which are now embodied in it, and through wliich it 
 was first obtained. - Language is the great repository of 
 
RELATIONS OF THOUGHT TO LANGUAGE. 25 
 
 thought, not only in books, but in our own minds. The 
 algebraist easily recalls to mind a few brief formulas, which 
 enable him to perform almost mechanically long numerical 
 computations, which the mere arithmetician must slowly 
 and painfiilly think out step by step. Even when the 
 meaning of the words is not sufficiently fa miliar to enable 
 us to perform the whole process symbolically, or by the use 
 of words alone, we can often do so in part ; — that is, we 
 need only to expHcate, or spread out in our minds, that 
 particular portion of their meaning which happens to be all 
 that is necessary for the special purpose which we now have 
 in view. Thus I may not know the ftdl meaning of a tech- 
 nical term in some science, or of a certain verb in the Greek 
 language, and still be enabled to use it without error in that 
 one of its numerous apphcations with which use may have 
 made me familiar. This symbolic knowledge, as it was 
 termed by Leibnitz, bears about the same relation to the 
 full thought, of which it is the abbreviated expression, that 
 our ordinary cursive handwriting does to an ideographic 
 system, or to the picture-writing of the Mexicans. 
 
 On the other hand, it should be remembered that there 
 is peculiar danger in this use of words as a temporary sub- 
 stitute for thought. Dr. Campbell mentions it as the rea- 
 son why many persons, even among the judicious and the 
 well-informed, are sometimes led both to talk and write 
 nonsense without knowing it. When the use of words is 
 not checked by a frequent recurrence in thought to the 
 precise limitations of their meaning, even the best of us 
 are occasionally betrayed into applications of them which 
 a moment's reflection would prove to be incongruous and 
 absm-d. The ordinary safeguard against such blunders is, 
 that, having become familiar by use with certain words in 
 their ordinary relations and connections with other words, 
 anything new or peculiar in the combinations in which they 
 are sometimes found, or in which we may ourselves be 
 
26 PSYCHOLOGICAL INTRODUCTION. 
 
 tempted to, place them, at once attracts our notice, and 
 puts us upon the lookout to detect a possible absurdity. • 
 Take, for instance, the following stanza, which occurs in 
 the " Song by a Person of Quality," written by Pope to 
 ridicule this very class of blunders, as frequently committed 
 by people of feshion in their attempts to string together in 
 verse the mere coromonplaces of poetical expression : — 
 
 " Gloomy Pluto, king of terrors, 
 Armed in adamantine chains, 
 Lead me to the crystal mirrors 
 Watering soft Elysian plains." 
 
 As chains usually hind and mirrors reflect, not even the 
 smoothness of the measmre can here cause us to sUde over 
 the absurdity of supposing Pluto to be armed by the for- 
 mer, or plains watered by the latter. 
 
 To avoid such blunders, it is not enough to be able 
 merely to erpUcate in thought the meaning of each word 
 taken by itself, or separately, but the combination of words 
 must express a possible union in thought of what is ex- 
 pressed by them. Whether this can be done can be ascer- 
 tained only through the process of what Mr. Mansel calls 
 f individualizing our Concepts," — : that is, of calling up in 
 imagination a picture of some particular thing denoted by 
 the words taken together, because possessing together all the 
 attributes contained in such a imion of Concepts. It is only 
 by the feilure of the attempt to form such a mental image, 
 that we are led to perceive the absurdity of such expres- 
 sions as a bilinear fgure, an irori-gold mountain, or a water- 
 ing mirror. Hence it appears, that what is perfectly intelli- 
 gible in language, when the words are taken separately, 
 may be abgoluiely inconceivable in thought. I know what 
 each of the yvords bilinear figure means ; but such a figure 
 is inconceivable, and therefore the union of the two words 
 is absurd. 
 
 It was remarked by Burke, in his Essay on the Sublime 
 
RELATIONS OF THOUGHT TO LANGUAGE. 27 
 
 and Beautiful, that words are not only used as substitutes 
 for thoughts, but, through the laws of association, they also 
 serve to call up the same emotions which are naturally pro- 
 duced by the presence or imagination of the real objects 
 which they denote. Thus, there are many words which 
 have feehngs of awe, sorrow, or affiight so firmly associ- 
 ated with. them, by long habit, that the mere utterance of 
 them in a sermon is enough to solemnize the minds of the 
 congregation, even before the hearers have time to think of 
 what they mean. 
 
 The doctrine of the NominaKsts, then, is true to this 
 extent, — that very often, in the use of language, there is 
 nothing before the ininds either of the speakers or the 
 hearers but mere words ; and yet these words are signifi- 
 cantly and correctly used, and they answer their purpose 
 of exciting emotion and imparting knowledge. But it is 
 also often true, that, in the use of words, all the powers 
 of the Understanding, or Thinking Faculty, are in active 
 exercise ; — that we compare, combine, discriminate, judge, 
 and discern new relations before unthought of, the subsidi- 
 ary powers of the Memory and Imagination, all the while, 
 fiimishing their aid whenever needed ; and it is only by 
 such concomitant activity of the Thinking power, that we 
 can have full assurance that the words in question are cor- 
 rectly used, and the boundaries of our knowledge are en- 
 larged. Thus, in the thoughtftd use of words, we are 
 continually spreading out in our minds the attributes of / 
 which the Concepts are made up, individualizing them,/ 
 comparing them with each other, discovering new relations 
 between them, and carrying them up into higher orders of 
 generalization, or extending them to more objects. 
 
 A few remarks may be necessary in explanation of the 
 nomenclature which has been here employed. The Eng- 
 lish words thmking, thought, are commonly used, in a very 
 vague and comprehensive sense, to denote any cognitive 
 
28 PSYCHOLOGICAL INTRODUCTION. 
 
 act or object of the mind. But, as applied in Logic, they 
 are strictly limited to one well-defined class of our cogni- 
 tive functions. After the illustrations that have now been 
 given, the peculiar characteristics of Thought properly so 
 called are perhaps suificiently understood. 
 
 Hamilton justly observes, that most of the words which 
 signify operations of the mind have a triple ambiguity, for 
 they may denote either, 1. the f amity ; or, 2. the act ; or, 
 3. the product of the act. To avoid this uncertainty, the 
 Understanding is here used exclusively to denote the Fac- 
 ulty of Thinking in the narrower sense, or what Hamilton 
 calls the " Elaborative Faculty," because it elaborates, or 
 works up into Thought, the raw material which is furnished 
 to it by the Perceptive powers. Like any other faculty, 
 the Understanding at any particular time may, or may not, 
 be in exercise. Its function or peculiar office is to think ; 
 hence, thinking denotes the arf, while Thought signifies the 
 product,, of this faculty. As will be shown hereafter, 
 Thought is the generic term, for there are three species 
 of it ; viz. Concepts, Judgments, and Reasonings or Infer- 
 ences. The old logicians referred the origin of these three 
 species of Thought to as many distinct faculties, which they 
 denominated respectively Simple Apprehension, Judgment, 
 and the Discursive Faculty. Of these. Simple Apprehen- 
 sion corresponds very nearly to that sort of Thinking which 
 we now call Conception, its products being denominated 
 Concepts. In hke manner, the products of the Percep- 
 tive or Acquisitive Faculty, hitherto called Intuitions, might 
 more conveniently be termed Percepts, as we should then 
 have an English verb, perceive, to express the act of that 
 Faculty of which these are products. If it were allowable 
 to coin an EngHsh verb to express the act of intuition, an- 
 swering to the German anschav£n, analogy would direct us 
 to say intuit. The Discursive Faculty (from diacurrere, to 
 run to and fro) was so called because, in Reasoning or 
 
INTmTIONS DISTINGUISHED FROM COKCEPTS. 29 
 
 drawing Inferences, the mind runs over from one Judg- 
 ment, as the Ground or Reason, to another, as the Conse- 
 quence or Conclusion. But the whole Understanding is 
 more properly called by this name ; for, in forming Con- 
 cepts, the mind runs over the Percepts or Intuitions from 
 which they are derived, in order to separate the similar 
 elements from the unlike, and consciously to imite the for- 
 mer into one product of Thought. 
 
30 DEFmmoN of logic. 
 
 CHAPTER II. 
 
 DEFINITION OF LOGIC. 
 Divisions of the Science. — Utility of the Study. 
 
 LOGIC is the Science of the Necessary Laws of Pure 
 Thought. 
 
 The Greek word, Xoyoi;, from which Logic is derived, 
 signifies both the inward thought, and the word or outward 
 form in which this thought is expressed ; and thus includes 
 both the ratio and the oratio of the Latins. This fact, and 
 the intimate connection which, as we have already seen, 
 exists between Thought and Language, has caused some 
 writers, especially those who adopt the Nominalist theory 
 to its ftdl extent, to maintain that " Logic is entirely con- 
 versant about Language." But it is not so ; for Logic is 
 primarily and essentially conversant with Thought, and 
 only secondarily and accidentally with Language ; that is, 
 it treats of Language so far only as this is the vehicle 
 of Thought. Just the reverse is true of the science of 
 Grammar, which treats primarily of Language, and only 
 secondarily of Thought. Logic might be called the 
 Grammar of Thought. 
 
 Others have held that " the process or operation of rea- 
 soning is alone the appropriate province of Logic." But 
 this is putting the part for the whole, and is as inadequate 
 as it would be to restrict Geometry to the measurement of 
 spherical bodies, to the exclusion of lines, angles, plane sur- 
 faces, and rectilinear soHds. There are three classes of the 
 products of Thought, namely, Concepts, Judgments, and 
 
DEFINITION OF LOGIC. 81 
 
 Inferences or Reasonings, with each of which Logic is im- 
 mediately concerned, as, indeed, no one of them can be 
 adequately discussed without consideration of both the oth- 
 ers. If, on the one hand, it can be said that conception 
 and judgment are both subsidiary to the process of reason- 
 ing, so, on th§ other, judgment is the primary and essential 
 operation, of which conception and inference are only spe- 
 cial forms or complex results. 
 
 Pure, or, as it is sometimes termed, Formal Thought, is 
 the mere process of thinking, irrespective of what we are 
 thinking about. It has already been said that the Acquisi- 
 tive or Perceptive Faculty fiimishes "the Matter," while 
 the Understanding supplies "the Form," of our knowledge. 
 This distinction between Matter and Form is one of con- 
 siderable importance in the history of philosophy. The 
 former is the crude material or the stuff of which anything 
 consists, or out of which it is made ; while the latter is the 
 peculiar shape or modification given to it by the artist, 
 whereby it has become this particular tiling which it is, and 
 not something else which might have been fashioned out of 
 the same substance. Thus, wood is the Matter of the desk 
 on which I am writing, whilst the Form is that which enti- 
 tles it to be called a desk, rather than a table or a chair. 
 Vocal sound is the Matter of speech, and articulation is its 
 Form. It is evident that these are two correlative notions, 
 each of which implies the other : Matter cannot exist ex- 
 cept under some Form, and there cannot be any Form 
 except of some given Matter. But though the two cannot 
 actually be separated, the mind can consider each separately 
 through that process, called abstraction, whereby the atten- 
 tion is wholly given to the one to the exclusion of the other. 
 We may think separately of the attributes which are com- 
 mon to a whole class of Forms, disregarding altogether, for 
 the moment, the Matter of which each of them feally con- 
 sists. Borrowing algebraic symbols, the Matter in each 
 
32 DEFINITION OF LOGIC. 
 
 case may be designated by a letter of the alphabet, the pe- 
 culiar significance of which is, that it stands for any Matter 
 -whatever, and not for any one in particular. Thus, AisB, 
 is the Form of an afiirmative judgment, wherein A and B 
 stand for any two Concepts whatever. Hence, whatever is 
 true of the general formula, A is B, will be. true also of 
 any such particular instances, as Iron is mallecMe, Trees are 
 plants, &c., wherein the Form is associated with some par- 
 ticular Matter. In saying, then, that Logic is concerned 
 only with the Forms of Thought, or Pure Thought, or 
 Thought in the abstract, — for all these expressions signify 
 the same thing, — we mean only, that what is Material ia 
 Thought is extralogical, and, as logicians, we have nothing 
 to do with it ; just as the geometer has nothing to do with 
 the particular diagram on the paper before him, except so 
 far as it is a symbol, or universal Form, of all possible fig- 
 ures of the same general character. As Hamilton remarks : 
 " The objects (the Matter) of thought are infinite ; no one 
 science can embrace them all, and therefore to suppose 
 Logic conversant about the Matter of thought in general, is 
 to say that Logic is another name for the encyclopaedia — 
 the omne scibile — of human knowledge. The absurdity of 
 this supposition is apparent. But if it be impossible for 
 Logic to treat of all the objects of thought, it cannot be 
 supposed that it treats of any ; for no reason can be given 
 why it should limit its consideration to some, to the exclu- 
 sion of others. As Logic cannot, therefore, possibly include 
 all objects, and as it cannot possibly be shown why it should 
 include only some, it follows that it must exclude fi*om its 
 domain the consideration of the Matter of thought alto- 
 gether ; and as, apart fi-om the Matter of thought, there 
 only remains the Form, it follows tliat Logic, as a special 
 science of thought, must be viewed as conversant exclu- 
 sively about the Form of thought." 
 
 Again, the definition of Logic assumes that the process 
 
DIVISIONS OP THE SCIENCE. 33 
 
 of Thinking, like every other operation in nature, does not 
 take place at random, but according to certain fixed Laws 
 or invariable modes of procedure. There could be no com- 
 munication of Thought from one mind to another, if the 
 process of Thinking in all minds were not subject to the 
 same general . rules. We follow these laws for the most 
 part unconsciously, as a distinct recognition of them is not 
 by any means necessary for correct thinking ; just so, many 
 persons speak and write correctly without any knowledge 
 of the grammarian's rules. But they can be discovered 
 through analysis of their results, and the business of the 
 logician is to search them out and arrange them in order, 
 just as the grammarian's duty is to set forth those second- 
 ary laws of Thought which control the formation and the 
 use of Language. Logic, says Dr. Thomson, " like philoso- 
 phy, of which it is a part, arises from a reflection of the 
 mind upon its own processes ; a logician is not one who 
 thinks, but one who can declare how he thinks." 
 
 But here a distinction is to be made, for Logic takes cog- 
 nizance not of the contingent, but only of the necessary 
 and universal, laws of Thought. Psychology, as the science 
 of the mental phenomena in general, includes, of course, the 
 procedures of Pure Thought ; but it includes them only in 
 their contingent and phenomenal character, as actually 
 existing now and then, but not as necessarily existing at all 
 times. Logic does not consider the subsidiary processes, 
 such as Perception, Memory, and Imagination, through 
 which we collect the materials for thinking. The operations 
 of the Thinking Faculty are also contingently modified by 
 the coexistence of other powers and affections of the mind ; 
 they are obstructed by indolence, and warped by prejudice 
 and passion. Logic does not regard these accidental per- 
 versions of the Understanding, but takes into view only 
 those fundamental and absolute principles, to which all 
 Thought is necessarily subject, and which shine by their 
 
 2* • O 
 
34 DEFINITION OF LOGIC. 
 
 own light, as they cannot be transgressed except by the 
 idiot or the madman. A violation of one of these Laws is 
 not so much an error in Thinking, as a negation of Thought. 
 They are axiomatic in character ; that is, they camiot be 
 proved or deduced from higher principles, for such proof or 
 deduction would be itself an act of Thought, and therefore 
 would presuppose the validity of the very principles which it 
 was intended to guarantee. These Laws cannot be proved, 
 but they can be emuiciated and explained ; when under- 
 stood, their truth is self-evident, for they rest upon the 
 immediate testimony of consciousness. As necessary and 
 universally known, they are never consciously broken ; but 
 we may be betrayed into an apparent transgression of one 
 or more of them, through an iacautious yoking together of 
 certain words or formulas of expression, without sufficiently 
 thinking of'what they denote. Some Hibemicisms, as they 
 are termed, are of this character. The judge, who, when 
 puzzled by the ingenidty of two lawyers who were plead- 
 ing a cause before him, exclaimed in a pet, " I beheve 
 you are both right," really violated that universal Law of 
 Pure Thdught, called the Principle of Excluded Middle, 
 which declares that, of two contradictory propositions, one 
 must be true, and the other &Ise. Logic, as it proceeds 
 from axiomatic principles, and derives none of its materials 
 from experience, but considers only those laws which under- 
 he all experience and first render it possible, is a purely de- 
 monstrative science, like algebra or geometry. It treats of 
 those arguments only which are certain and in-efutable ; or 
 if it indirectly considers solne of those forms which come 
 short of perfect demonstration, such as Analogy, Impei-fect 
 Induction, and* Example, it is only for the purpose of test- 
 ing them by a reference to the standard fomis the validity 
 of which they presuppose, and which they endeavor, as it 
 were, to approximate. 
 
 Universal Logic considers the Laws of Thought in their 
 
DIVISIONS OF THE SCIENCE. 35 
 
 application, not to this or that special class of ohjects, but 
 to all objects whatsoever. This is the Logica dooms of the 
 Schoolmen, and contains the abstract theory of the science 
 in its widest sense, without any of the limitations,. that arise 
 from any special purpose or study which the thinker may 
 have in view. It corresponds to the science of Universal 
 Grammar, which treats only of those priiiciples which be- 
 long to language as such, and therefore are exemplified in 
 all languages, putting aside altogether the peculiarities of 
 Hebrew, Greek, German, or any other particular tongue. 
 On the other hand, Special Logic, or the Logica utms of 
 the Schools, is the Logic of Mathematics, or the Logic of 
 History, or of any other particular science ; consequently, 
 it involves a consideration: of the Laws of Thought so far 
 only as they are exemplified or involved in the processes 
 of this one science. Herein Logic becomes subsidiary td 
 the objects of the special inquiry which it is idtelided to 
 promote or regulate. It presupposes a knowledge of those 
 objects, and it form^ an introduction to that inquiry. 
 Hence, it is no longer' Logic considered for its own sake, 
 but it is Geometry, History, or some other science, consid- 
 ered in a logical point of view. The discussion of it is 
 therefore relegated to treatises on that science of which it 
 forms a part, and for which it is a special preparatory study. 
 Legal Logic is a part of the science of Law. Mathemati- 
 cal Logic is an introduction or an appendage to pure Math- 
 ematics. But, in what now lies before us, it is evideilt that 
 we have to do only with Universal Logic, which is one, 
 while Special Logic is multiform ; which is independent, 
 while that requires an acquaintance with other objects of 
 study and other modes of investigation ; which iS a part of 
 the Philosophy of Mind, or of Philosophy itself in its wider 
 sense, while that is a portion of a comparatively narrow 
 science. 
 
 There are certain other portions of what has usually' 
 
36 DEFINITION OF LOGIC. 
 
 been called Logic, which, though they do not properly 
 belong to the science itself, yet, as they are generally dis- 
 cussed, often at great length, in most treatises upon it, may 
 properly be defined and explained here, while a fall consid- 
 eration of them may be regarded as an appendix to the 
 body of the work. Properly speaking, Pure Logic termi- 
 nates with the consideration of the three classes of prod- 
 ucts — namely. Concepts, Judgments, and Reasonings — 
 which are the elements into which aU Thought is resolved. 
 But Thought itself is subsidiary to the attainment of knowl- 
 edge, — that is, to Science. The question remains, then, 
 after we have ftdly treated of Concepts, Judgments, and 
 Reasonings, taken separately or considered in themselves 
 alone, what use is to be made of them, taken together, 
 in the construction of Science. A full answer to this ques- 
 tion, as it would involve a study of the objects of Science, 
 — that is, of the matter of the special sciences, — evidently 
 falls outside of the province of Logic. But a partial answer 
 to it, regarding Science in its relation, not to the objects 
 known, but to the knowing mind, may be considered as a 
 natural appendage to Logic, as it embraces the conditions 
 not merely of possible, but of perfect. Thought. Such an 
 answer is usually called the Doctrine of Method, or Logi- 
 cal Methodology. Pure Logic considers only the Neces- 
 sary Laws to which all Thought must conform ; the Doc- 
 trine of Method regards those rules and principles to which 
 all Thought ought to conform in order to obtain its end, 
 which is the advancement of Science. Pure Logic treats 
 merely of the elements of Thought, while Logical Meth- 
 odology regards the proper arrangement of these elements 
 into an harmonious whole. All Method is a well-defined 
 progress towards some end ; and the end in this case is the 
 attainment of truth. Practically speaking, the Doctrine 
 of Method is a body of rules or precepts looking to the 
 proper regulation of the Thiiaking Faculty in the pursuit 
 
DIVISIONS OF THE SCIENCE. 37 
 
 of knowledge ; and, as such, it necessarily lacks the pre- 
 cision and the tlemonstrative certainty which are character- 
 istic of the principles of Pure Logic. The Laws of Pure 
 Thought are absolute ; the merits of Perfect Thought are 
 various, and attainable in different degrees, according to 
 circumstances. 
 
 Another distinction has been taken, in this science, be- 
 tween Pure and Apphed Logic, or, as Sir Wilham Hamil- 
 ton prefers to call the latter. Modified Logic. The former, 
 as we have seen, considers the Thinking Faculty alone, as 
 if it constituted the whole of the human mind, and there- 
 fore as if its Laws and Products were unaffected by any 
 collateral and disturbing influences, but were manifested in 
 precisely the same manner by different persons. It takes 
 no account of the defects and hinderances which obstruct 
 the normal action of the understanding. Modified Logic, 
 on the other hand, considers Thought as it is, and not 
 merely as it ought to be. It regards " the Causes of Error 
 and the Impediments to Truth by which man is beset in 
 the employment of his Faculties, and what are the means 
 of their removal." And yet it is a universal science, — as 
 much so as Pure Logic ; — for it does not consider the Mat- 
 ter of Thought. The obstacles and imperfections which it 
 points out are not those which arise from the objects of in- 
 quity, but from the inquiring mind. They are subjective 
 or psychological causes of error. Lord Bacon is probably 
 the first philosopher who attempted a systematic enumera- 
 tion of the causes of error. He made a quaint classification 
 of them, under the significant name of Idols, into the four 
 genera of Idols of the Tribe, or the necessary faults and 
 imperfections of the human intellect itself; Idols of the 
 Den, which arise from the special constitution, education, 
 and habits of each individual man; Idols of the Forum, 
 proceeding from the defects of the language which we are 
 obliged to employ as an instrument of Thought and a means 
 
38 DEFINITION OF LOGIC. 
 
 of communication ; and Idols of the Theatre, or the various 
 dogmas of ill-founded systems of philosophy which have 
 found their way into men's minds through tradition, negU- 
 gence, and credulity. 
 
 But Modified Logic is not properly called Logic, as it is 
 a branch of Psychology, which treats of the phenomena of 
 mind in general, and not merely of the normal action and 
 necessary laws of one special faculty, the Understanding. 
 As Modified Logic, however, is nearly allied in purpose 
 with the Doctrine of Method, both looking to the same 
 general end, — the attainment of truth through the proper 
 regulation of the Thinking Faculty, — the two may well 
 be considered together, under the general name of Applied 
 Logic, as a kind of supplement to the science properly so 
 called. Moreover, ■ the connection between Thought and 
 Language being so intimate, as we have seen, that neither 
 can exist without the other, it would be an injurious, and, 
 in fact, an impossible refinement, in a Treatise on Logic, to 
 try to avoid frequent reference to those mistakes in thinking 
 which proceed from an incautious use of words. 
 
 The utiUty of the study of Logic — at least, of ForTnal 
 Logic — has been, perhaps, more generally doubted or de- 
 nied, during the last two or three centuries, than that of 
 any other recognized science. In England especially, ever 
 since Bacon's time, but more particularly since that of 
 John Locke, the study has been as unreasonably decried as 
 it was, during an earlier period, unduly exalted. The 
 popular voice has been against it, and, tiU within the last 
 thirty years, it steadUy lost ground even in the Universities, 
 where the popular voice is n6t often heard or respected. 
 This unjust depreciation of the study was due in great part 
 to the extravagant pretensions formerly put forward in its 
 favor. An age which acknowledged Bacon and Descartes 
 to be its intellectual leaders was likely to ' scrutinize with 
 extreme jealousy the claims of a science long held forth by 
 
UTILITY OF THE STUDY. 39 
 
 its votaries as the science or art " of the right use of rea- 
 son," or " of formiag instruments for the direction of the 
 mind" ; as " the head and culminating point of philosophy," 
 « the art of thinking," " the medicine of the mind," " the 
 lighthouse of the intellect," " ars artium et scientia scientt- 
 arum, qua aperta, omnes alice aperiuntur, et qua clausa, 
 emm.es alice dauduntur." Especially was this the case, as a 
 dark shade had already been cast upon this boastfiil study 
 by the: rapid decHne and visibly approaching extinction of 
 those systems of philosophy, theology, and physical science 
 ■which acknowledged the same parentage, and had long 
 been associated with it in asserted pre-eminence and ex- 
 clusiveness. 
 
 Logic fared not much better in the hands of those, its 
 later disciples, who abated the extravagance of its preten- 
 sions, indeed, and, by throwing aside many of its technicali- 
 ties and nice distinctions, rendered its aspect less abstruse 
 and forbidding. But, stiU adhering to the opinion that its 
 main purpose was to furnish practical rules for the guid- 
 ance of the understanding in the seaarch after truth, they 
 destroyed its unity, broke down the boundaries which sepa- 
 rate it from Psychology, Grammar, and Metaphysics, and 
 encumbered it with a mass of disciplinary precepts which 
 would be out of place anywhere but in treatises on practi- 
 cal education. The authors of the excellent "Art of Think- 
 ing," which commonly passes under the name of the "Port- 
 Royal Lo^c," deemed it necessary to apologize even for 
 thei limited space which they had devoted to the special 
 doctrines of this science, on the ground that " custom has 
 introduced a sort of necessity of having at least a slight 
 knowledge of Logic " ; and they remarked, that, as the 
 heads' of chapters sufSciently indicated the topics considered 
 in them, those of exclusively logical import might be omit- 
 ted in the perusal without serious injury to what remained. 
 " When we thoi^t any matter might be of service in 
 
40 DEFINITION OF LOGIC. 
 
 forming the judgment," they added, " we never scrupled 
 to insert it, to whatever science it might belong " ; and, 
 accordingly, " in this Treatise, the reader will find many 
 things relating to Physics and Ethics, [still more, they 
 should have added, belonging to Grammar,] and almost as 
 much Metaphysics as it is necessary to know," This is 
 equivalent to denying that Logic has any claims to be con- 
 sidered as a distinct science, or that a thorough and sys- 
 tematic evolution of its principles would be of any practical 
 benefit. 
 
 The ground of these misapprehensions is entirely re- 
 moved by the view which has here been given of the 
 province and the purpose of Logic. Its boundaries are 
 clearly defined, its pretensions are moderate, and it accom- 
 pHshes all that it is intended to perform. As a Formal 
 Science, it takes no account of the Matter of Thought, 
 which is all derived from processes of observation or intui- 
 tion that He beyond its province. It is not concerned with 
 the something that is known, but only with the manner of 
 knowing it. It is not an organon of discovery, then, or a 
 means to be used for the extension of any science. It ana- 
 lyzes the Laws of Thought ; but, as these Laws are neces- 
 sary and universal, — that is, as they exist in fiiU force even 
 in the humblest and least-instructed intellect, — it does not 
 profess to teach anything absolutely new, but only to bring 
 out into distinct consciousness and scientific arrangement 
 what exists or takes place implicitly in every mind. These 
 Laws of Thought exist there in a latent or involved form ; 
 and we foUow their guidance unconsciously, just as a person 
 who has learned to speak and write only by moving in good 
 society, and following the example of others, uses language 
 in strict conformity with grammatical laws, though he is 
 unacquainted with these laws even by name. The test of 
 the validity of any doctrine in logical science is, that those 
 to whom it is now for the first time communicated imme- 
 
UTILITY OF THE STUDY. 41 
 
 diately recognize it as nothing new, except in the form of 
 statement, but as a principle to which they have always 
 conformed ever since they began to think. The purpose 
 of Logic, then, is only to teach us how we always have 
 thought, and not any new mode of thinking, or new pre- 
 cautions, through which we may avoid the errors to which 
 we were formerly hable, or by which we may discover 
 truths that were formerly unattainable. It has no counsels 
 to give, except to urge careful and uniform comphance with 
 Laws which every one admits to be authoritative and imi- 
 versal, and to which he has always intended to conform. 
 As Mr. Mansel remarks, the science advises only the better 
 performance of existing obhgations, and does not attempt 
 the imposition of new ones. "A treatise on Logic is not 
 designed primarily to give men facility in. the practice of 
 reasoning, any more than a treatise on Optics is intended 
 to improve their sight; and it would be as correct for a 
 writer on the mathematical principles of Optics to entitle 
 his work ' Optics, or the Art of improving defective Vision,' 
 as it is for a writer on the principles of Logic to adopt for 
 his title, ' Logic, or the Art of Reasoning.' " * 
 
 Indirectly, indeed, the science may be regarded as a 
 medicine of the mind.. As it brings out into clearer con- 
 sciousness the laws to which all just thinking must conform, 
 the indistinctness and confusion of thought to which we are 
 all liable are dissipated, and the errors which often follow 
 the symbolic use of language, or the substitution of words 
 for thought, are exposed and eliminated. In these respects, 
 we think rightly as soon as we have learned to think clear- 
 ly ; for the necessary forms of the understanding govern 
 without dispute, when their applicability to the case in hand 
 has become manifest. "The progress of the sciences," 
 says Hamilton, " consists, not merely in the accumulation 
 of new matter, but likewise in the detection of the relations 
 * Introduction to Aldrich'a Logic, third edition, p. Ivii. 
 
42 DEFINITION OF LOGIC. 
 
 subsisting among the materials accumulated ; and the re- 
 flective abstraction by which this is effected must not orily 
 follow the laws of Logic, but is most powerftdly cultivated 
 by the habits of logical study." As we spread out Con- 
 cepts into their constituent Intuitions, or individualize them 
 in particular Imaginations, their true relations to each are 
 intuitively perceived, and inconsequence or contradiction in 
 uniting them becomes inipossible. All this, however, is 
 but the elimination of Formal error ; the Matter of thought 
 comes from other sources ; and for the mistakes which arise 
 from Hmited observation, or imperfect induction. Logic has 
 no remedy to ofFer. It guarantees the coi^ectness neither 
 of the premises nor of the conclusion, but only the validity 
 of the inference from the former to the latter. Hence, 
 what is formally correct may be materially felse ; I may 
 reason rightly from wrong premises to a false conclusion. 
 On the other hand, as an error in the Form necessarily 
 vitiates the whole process of Thought, it may certainly be 
 said that Logic ftimishes us with a negative criterion be- 
 tween truth and falsehood. The blunders which it exposes 
 are vital, but they are not those which afe most insidious, 
 or even of the most frequent occurrence. 
 
 Truth is the agreement of a cognition with the object 
 which it is intended to represent. Now Logic, as it takes 
 no cognizance of the object, which is the Matter of Thought, 
 is evidently incompetent to determine whether such agree- 
 ment exists or not. But there is a preliminary question to 
 be settled before we come to a consideration of the object ; 
 we inquire whether the cognition agrees Avith itself, — that 
 is, whether it is Forma:lly correct. Arid this question Logic 
 is competent to determine with absolute certainty. The 
 Formal correctness of a cognition does not by any means 
 insure its Material truth ; but as Kant remarks, it is to be 
 regarded as a conditio sine qua non of such truth. 
 
 The high place which Logic once held among the proper 
 
UTILITY OF THE STUDY. 43 
 
 Studies of a University, and which within a few years it has 
 wellnigh reclaimed, is vindicated by the great value of the 
 effort which is necessary to master it, considered simply as a 
 vigorous exercise of the understanding. Indeed, its chief 
 function is disciplinary, for the effort to acquire it may be 
 said to equal or surpass in value the subsequent use to be 
 made of the acquisition. It is not of so much importance 
 to know, as it is to have strengthened and developed aU the 
 faculties in learning to know. No other study taxes so 
 severely the power of abstract thought, and hence no one 
 furnishes better preparatory training for the pursuit of aU 
 the sciences which do not consist mainly in accumulating 
 facts and registering the materials thus obtained. 
 
 Little needs to be said of the intrinsic dignity of the sub- 
 ject. " Admitting," says Heinrich Eichter, as translated by 
 Hamilton, " that this science teaches nothing new, that it 
 neither extends the boundaries of knowledge, nor unfolds 
 the mysteries which lie beyond the compass of our reflective 
 lEEtellect, and that it only investigates the immutable laws 
 to which the mind in thinking is subjected, still, inasmuch 
 as it develops the application of these laws, it bestows on 
 us, to a certain extent, a dominion over our thoughts them- 
 selves. And is it nothing to watch the secret workshop in 
 which nature fabricates cognitions and thoughts, and to 
 penetrate into the sanctuary of self-consciousness, to the end 
 that, having learnt to know ourselves, we may be qualified 
 rightly to understand all else ? Is it nothing to seize the 
 helm of thought, and to be able to turn it at our will ? For 
 through a research into the laws of thinking. Logic gives 
 ns, in a certain sense, a possession of the thoughts them- 
 selves. It is true, indeed, that the mind of man is, like the 
 universe of matter, governed by eternal laws, and follows, 
 even without consciousness, the invariable canons of its na- 
 ture. But to know and understand itself, and out of the 
 boundless chaos of phenomena presented to the senses to 
 
44 DEFINITION OF LOGIC. 
 
 form Concepts, through Concepts to reduce that chaos to 
 harmony and arrangement, and thus- to establish the domin- 
 ion of intelligence over the universe of existence, — it is 
 this alone which constitutes man's grand and distinctive 
 pre-eminence." " Our whole dignity," says Pascal, " con- 
 sists in thought." 
 
 It is also argued by Sir William Hamilton, with great 
 force, that " Logic is further useful as affording a Nomen- ^ 
 clature of the laws by which legitimate thinking is governed, 
 and of the violation of these laws, through which thought 
 becomes vicious or nuU, 
 
 " It is said, in Hudibras, — 
 
 • That all a Rhetorician's mles, 
 Serve only but to name his tools ' ; 
 
 and it may be safely confessed that this is one of the prin- 
 cipal utilities of Rhetoric. A mere knowledge of the rules 
 of Rhetoric can no more enable us to compose well, than a 
 mere knowledge of the rules of Logic can enable us to 
 think well. There is required firom nature, in both, the 
 faculty ; but this faculty must, in both departments, be cul- 
 tivated by an assiduous and also a well-directed exercise ; 
 that is, in the one, the powers of Comparison must be exer- 
 cised according to the rules of a sound Rhetoric, in the 
 other, according to the rules of a sound Logic. In so far, 
 therefore, the utility of either science is something more 
 than a mere naming of their tools. But the naming of 
 their tools, though in itself of Kttle value, is valuable as the 
 condition of an important function, which, without this, 
 could not be performed. Words do not give thoughts ; but 
 without words, thoughts could not be fixed, Umited, and 
 expressed. They are, therefore, in general, the essential 
 condition of all thinking worthy of the name. Now, what 
 is true of human thought in general, is true of Logic and 
 Rhetoric in particular. The nomenclature in these sciences 
 
UTILITY OF THE STUDY. 45 
 
 is the nomenclature of certain general analyses and distinc- 
 tions, which express to the initiated, in a single word, what 
 the uninitiated could (supposing — what is not probable — 
 tliat he could perform the relative processes) neither under- 
 stand nor express without a tedious and vague periphrasis ; 
 while, in his hands, it would assume only the appearance 
 of a particular observation, instead of a particular instance 
 of a general and acknowledged rule. To take a very sim- 
 ple example: — there is in Logic a certain sophism, or act 
 of illegal inference, by which two things are, perhaps in a 
 very concealed and circuitous manner, made to prove each 
 other. Now, the man unacquainted with Logic may per- 
 haps detect and be convinced of the fallacy ; but how will 
 he expose it ? He must enter upon a long statement and 
 explanation, and, after much labor to himself and others, he 
 probably does not make his objection clear and demonstra- 
 tive after aU. But between those acquainted with Logic, 
 the whole matter would be settled in two words. It would 
 be enough to say and show, that the inference in question 
 involved a circulus in concludendo, and the refutation is at 
 once understood and admitted. It is in like manner that 
 one lawyer will express to another the ratio decidendi of a 
 case in a single technical expression ; while their clients will 
 only perplex themselves and others in their attempts to set 
 forth the merits of their cause. Now, if Logic did nothing 
 more than estabHsh a certain number of decided and deci- 
 sive rules in reasoning, and afford us brief and precise 
 expressions by which to bring particular cases under these 
 general rules, it would confer on all who in any way employ 
 their intellect — that is, on the cultivators of every human 
 science — the most important obligation. For it is only in 
 the possession of such estabhshed rules, and of such a tech- 
 nical nomenclature, that we can accomphsh, with facOity, 
 and to an adequate extent, a criticism of any work of rea- 
 soning. Logical language is thus, to the general reasoner, 
 
46 DEFINITION OF LOGIC. 
 
 what the notation of Arithmetic, and still more of Algebra, 
 is to the mathematician. Both enable us to comprehend 
 and express, in a few significant symbols, what would other- 
 wise overpower us by their complexity ; and thus it is, that 
 nothing would contribute more to facilitate and extend the 
 faculty of reasoning, than a general acquaintance with the 
 rules and language of Logic, — an advantage extending in- 
 deed to every department of knowledge, but more especially 
 of importance to those professions which are occupied in 
 inference, and conversant with abstract matter, such as The- 
 ology and Law." 
 
THE PKIMABY AXIOMS OF PUEE THOUGHT. 47 
 
 CHAPTER III. 
 
 THE PEIMAEY AXIOMS OF PUKE THOUGHT. 
 
 HAVING defined Logic to be the Science of the Neces- 
 sary Laws of Pure Thought, our first object must be 
 to ascertain what are the Fundamental and Universal Laws, 
 here called Primary Axioms, to which all Thought, as such, 
 is subject. In the separate consideration, which wiU come 
 afterwards, of the three classes of Thoughts, — namely. 
 Concepts, Judgments, and Reasonings, — we may expect 
 to find Special Laws or Rules which are apphcable only to 
 one or two of these divisions. Such Special Rules may or 
 may not be derivative in character ; — that is, they may 
 be either immediate inferences fi-om the Primary Axioms 
 which govern all the products of the Thinking Faculty, or 
 they may be independent, as resting upon their own evi- 
 dence. Of this hereafter. But our first inquiry must be, 
 whether there are any Axioms of universal apphcabihty, 
 which underlie and govern every act and product of the 
 human Understanding ; and, if there are such, to deter- 
 mine their character and significance. 
 
 If there are such Axioms, they must be few, meagre in 
 impart, not susceptible of proof, and recognizable by all as 
 familiar truisms, which have always impHcitly directed their 
 thoughts, though perhaps, on accoimt of their very obvi- 
 ousness, they have never been explicitly stated or drawn 
 out into distinct consciousness. They must have these 
 characteristics, because they concern only the Forms of 
 Thought, or the manner of thinking irrespective of what 
 
48 THE PRIMARY AXIOMS OF PURE THOUGHT. 
 
 we are thinking about; and as these Forms themselves are 
 necessarily limited in number and narrow in significance, 
 the Axioms which underlie them all, and constitute their 
 common features, must be still fewer and poorer in import. 
 They cannot admit of proof, as their truth is presupposed 
 in every act of reasoning, and therefore no argument or 
 proof is possible unless their veracity is taken for granted. 
 They must be recognized by aU as mere truisms, because 
 they are thus self-evident, and because their truth has been 
 acknowledged and acted upon in every Form of Thought 
 which we have ever experienced. The First Principles of 
 all the sciences are avowedly thus few and meagre, as is 
 seen to be the case with the introductory axioms of Geome- 
 try and Physics. With still more reason do we expect the 
 First Principles of all Thought to possess this character, as 
 they stand in the same relation to the axioms of the special 
 sciences, that these axioms do to the most advanced theo- 
 rems which have been built upon them, or which have been 
 constructed by taking them for granted. 
 
 After this explanation, we need not be surprised to find 
 that all the Primary Axioms of Pure Thought are perhaps 
 reducible to this single principle : — All Thought must he 
 consistent with itself. If it be inconsistent, — if, direclly or 
 indirectly, it contradicts itself, — it is self-destructive, and 
 the Thought is null. Thus stated, the principle is coinci- 
 dent with that which is usually called the Law of Contra- 
 diction, though, as Hamilton remarks, it ought rather to be 
 termed the Law of Non-Contradiction. Practically speak- 
 ing, every Thought which must be rejected as formally 
 invalid — that is, which is radically vicious in Form, what- 
 ever be its Matter — offends against this principle. By 
 logicians generally, however, this prmciple has been expli- 
 cated into three general Axioms, called the Law of Identity, 
 the Law of Contradiction, and the Law of Excluded Middle. 
 The ground of this explication may be thus set forth. 
 
THE PRIMARY AXIOMS OF PURE THOUGHT. 49 
 
 The primary element of all Thought is a Judgment, 
 which aiises from a Comparison. Hence, all Thought 
 must proceed either by affirmation or denial, as these are 
 the only two possible forms of Judgment. Having com- 
 pared any two Concepts with each other, we either perceive 
 their identity, similaiity, congruence, or some other relation 
 whereby we affirm their union in one act of Thought ; or 
 we perceive the opposite relation between them, such as 
 difference, unlikeness, or incompatibihty, whereby we deny 
 one of the other. As any Concept can be compared with 
 any other, and as the Judgment which foUows such com- 
 parison must either cffirm or deny one of the other, there 
 being no third form of Judgment conceivable, we have the 
 Axiom which is usually called the Law of Excluded Third 
 or Excluded Middle, — Lex ^xclusi Tertii aut Medii. 
 Either A is B, or A is not B : if we make any Judg- 
 ment, — that is, if we think at all, — one of these two 
 must be true ; for no third form is conceivable. It has 
 been enounced in various forms : — Of two contradictory 
 judgments, one must be true; Every predicate may be 
 affirmed or denied of every subject ; Every conceivable 
 thing is either A or not-A. Of course, A and rvot-A, taken 
 together, include the universe, — the universe not only of 
 all that is actual, but of all that is conceivable ; for as nat-A 
 excludes A only and nothing else, it includes the universe 
 excepting A only. 
 
 Still further : — Not only are affirmation and negation the 
 only conceivable forms of Judgment, but, as contradictory 
 opposites, they are absolutely incompatible or mutually 
 destructive. The admission of one is tantamount to a 
 rejection of the other. If taken together, they destroy 
 each -other, and the Thought is rendered null. To express 
 this truth algebraically, A -\- not-A = 0. Here we have 
 the we]l-kno-«Ti Law of Contri^diction, more properly of 
 Non-Contradiction, qf which thp formula is, A is not not-A. 
 
50 THE PRIMARY AXIOMS OF PURE THOUGHT. 
 
 Evidently tliis Law is the principle of all logical negation 
 and discrimination. It has been variously expressed: — 
 Contradictory attributes cannot be affirmed of the same 
 subject ; What is contradictory is inconceivable. It is less 
 correctly expressed in the adage, " It is impossible for the 
 same thing to be and not to be." This is a maxim which 
 concerns the Matter of Thought, and therefore we must 
 add to it the material limitations, in the same place, at the 
 same time^ in the same imspect, &c. It is a mistake, then, to 
 maintain that the Axiom^ " Contradictory attributes cannot 
 be affirmed of the same subject," is not universally true, be- 
 cause we can form such assertions as this : A man can he 
 both young and not-yoUng, though riot at the same time. In 
 Logic, where we considef only the Form of the Thought, 
 a Judgment must be expressed by the present tense of the 
 verb to be; for what we affirm is not the past or future 
 union of two real phenomena, but the present coexistence 
 and agreement of two Concepts in the mind. Hence, the 
 lo^cal Judgment, this man is not young, is absolutely 
 incompatible with the assertion, iJiis man is young, though 
 it is compatible with the very different assertion, this, man 
 HAS BEEN young. 
 
 Once more : The formula, A is not not-A, proves, on 
 reduction, to be the exact equivalent or consequence of 
 this, A is A. Here we have the principle of affirmation 
 and agreement, as the former was that of negation and dif- 
 ference. If an object cannot be thought under contradic- 
 tory attributes, it is because it has a definite character of 
 its own, excluding one of the contradictories through in- 
 cluding the other. " The universe of conceivable objects," 
 to adopt Mr. Mansel's language, " embraces both A and 
 v/>PA ; it is only when definitely conceived as the one, that 
 an object cannot be conceived as the other. Every object 
 of thought, as such, is thus conceived by limitation and 
 difference ; as having definite characteristics by which it is 
 
THE PRIMARY AXIOMS OF PURE THOUGHT. 51 
 
 marked ofF and distinguished from all others ; as being, ia 
 short, itself, and nothing else." Here, then, we have a 
 third Primary Axiom, expressed as the Law of Identity : 
 Evertf A is A ; Every object of thought is conceived as 
 itself; Every thing is equal to itself or agrees with itself; 
 Every whole is the sum of all its parts. 
 
 Thus we have three Primary Axioms of Pure Thought, 
 — the Law of Identity, the Law of Contradiction, and the 
 Law of Excluded Middle, — all of which may be regarded as 
 explications of the single rule, that all Thought must be cortr- 
 sistemt with itself, or as corollaries from this one principle, 
 that Judgment, which is the basis of all Thought, proceeds 
 only by affirmation and denial. The mutual dependence 
 and correlation of these three Axioms may be further illus- 
 trated thus. 
 
 I can think any object only by placing it under a Con- 
 cept, or Class-notion expressed by a General Term ; and I 
 call do this only by recognizing that it possesses the attri- 
 butes which belong to this Concept and are common to all 
 the members of this Class (Law of Identity, affiimation of 
 similarity or agreement) ; by discriminating it from other 
 objects which have different attributes (Law of Contradic- 
 tion, negation of agreement) ; and both this affirmation and 
 denial proceed by the Law of Excluded Middle, which de- 
 clares, for each given attribute, that the one or the other is 
 absolutely necessary. Either it does, or does not, belong to 
 the object, and the object does or does not belong to the 
 Class. In respect to the Laws of Identity and Contradic- 
 tion, says Sir William Hamilton, " each infers the other, 
 but only through the principle of Excluded Middle ; and 
 the principle of Excluded Middle only exists through the 
 supposition of the two others. Thus, the principles of 
 Identity and Contradiction cannot move, — cannot be ap- 
 plied, — ^except through supposing the principle of Excluded 
 Middle ; and this last cannot be conceived existent except 
 
52 THE PRIMARY AXIOMS OF PURE THOUGHT. 
 
 through the supposition of the two former. They are thus 
 coordinate, but inseparable. Begin with any one, the other 
 two follow as corollaries." 
 
 Hence he symbolizes the three Axioms by a Triangle, 
 thus : — 
 
 C is either r or non-r. 
 
 These three Axioms are sufficient for all purposes of ana- 
 lytic Thought. There is, however, another large class of 
 Judgments, which are dependent in part upon a fourth Ax- 
 iom ; and, as a preliminary to the consideration of it, we 
 must explain the difi'erence between analytic and synthetic 
 Thought. Kant was the first to bring this distinction into 
 notice as one of great importance in philosophy. 
 
 In an analytic Judgment, the Predicate affirms nothing 
 which was not already, though implicitly, contained in the 
 Concept which forms the Subject. We analyze a Concept 
 into the Marks or attributes of which it consists, and then 
 predicate of it one or more of these Marks. Of course, no 
 other knowledge is requisite for forming such a Judgment 
 than is already contained in the Subject itself, as the Predi- 
 cate affirms nothing more than what is so contained. Thus, 
 if I say. Body is extended, A circle is round, An equilateral 
 triangle has three equal sides, I merely repeat, or state 
 explicitly, what is already implied in the very notion of a 
 body, a circle, and an equilateral triangle. But in the prop- 
 
THE PBIMARY AXIOMS OF PURE THOUGHT. 53 
 
 Options, Body is heavy, A circle is a particular section of a 
 cone, A triangle is a figure the three angles of which are 
 equal to two right angles, the Predicate adds something that 
 was not previously known and included in the notion of the 
 Subject. There must be some reason for such addition ; 
 otherwise, all Thought which is not merely analytical in 
 character would be arbitrary and inconsequent. Pure 
 Thought, which deals only with the Form, and not with 
 the Matter, of Thinking, does not ask what this reason is, 
 and seeks not in any way to determine its character. It 
 only demands that there should be some reason, — that the 
 connections of Thought, or those reductions to unity in 
 which aU Thinking consists, should not be merely casual or 
 capricious ; in which case, there would be no proper con- 
 nection at all. 
 
 Besides the first postulate of the Understanding, that all 
 Thought should be consistent with itself, we have, then, this 
 second deipand, in reference at least to synthetic Judg- 
 ments, that all Thought should he consequent; that is, that 
 it should never affirm or deny a union of two Concepts 
 without any ground for such affirmation or denial. The 
 sufficiency of this ground or reason is a material question, 
 with which the logician, as such, has nothing to do. Leib- 
 nitz was wrong, then, in denominating this principle that 
 of " the Sufficient Reason." The limitation is superfluous, 
 for the only reason required is one that will make the union 
 of the predicate with the subject conceivable, — not an actual 
 union of real things ; and the reason which is insufficient 
 for this end is no reason at all. This axiom, wliich is prop- 
 erly called that of Reason and Consequent, or the Condi- 
 tion and the Conditioned, is expressed in the formula, affirm 
 nothing without a ground or reason ; or, every affirmation 
 must have a ground or reason why it is affirmed. 
 
 As the former postulate was evolved into three Axioms, 
 so this one may be explicated into two, such explication. 
 
54 THE PBIMAKY AXIOMS OF PUBE THOUGHT. 
 
 beiBg, in fact, only a statement of the meaning of the words 
 employed. The first of these derivative Axioms is, that to 
 affirm the Reason or the Condition is also to affirm the Cotir 
 sequent or the Conditioned; for the Reason would not be 
 the Reason unless the Consequent followed it. The second 
 Axiom is, that to deny the Consequent is also to deny the 
 Reason; for, again, if the Consequent does not follow, the 
 Reason cannot exist, since the Reason means only that 
 which necessitates 'the Consequent, The two Axionis are 
 thus pithily stated by the old Logicians : Posita conditione 
 ponitur eonditionatum, sublato conditionato toUitur conditio ; 
 or thus : A ratione ad rationatum, a negatione rationati ad 
 negationem rationis, valet consequentia. 
 
 Observe, however, that the coBverse of these two Axi- 
 oms does not hold good. To affirm the Consequent is not 
 to affirm any given Reason, since the Consequent may have 
 followed from some other Reason ; and the same considera- 
 tion shows that it is not competent, from a denial of any 
 given Reason, to infer a denial of the Consequent. The 
 primary Axiom asserts only the necessity of some Reason 
 or other, not of any one Reason. The exphcation may be 
 thus summed up in a tabidar form : — 
 
 There must he a Ground or Reason for every cffirmaiion. 
 
 Affirming the Reason affirms also the Consequent. 
 Denying the Reason, nothing follows. 
 
 Affirming the Consequent, nothing follows. 
 Denying the Consequent denies also the Reason. 
 
 Strictly speaking, this Axiom is applicable to all analytic, 
 as well as to all synthetic Judgments, and therefore, like 
 each of the other three Axioms, it is a Universal Law of 
 Thought. But in the case of analytic Judgments this Ax- 
 iom does not need to be separately considered or enounced, 
 for the ground or reason to which it refers is contained in 
 
THE PKIMARY AXIOM? OF PURE THOUGHT. 55 
 
 the Judgment itself; we cannot ihinh the latter without the 
 former. Thus, we cannot think of body without extension; 
 and therefore, when we affii-m that hody is extended, the 
 Judgment carries its own reason or justification along with 
 it. But in synthetic Thought, as when we say th^t matter 
 i9 corr^essible, we see no reason in the Thought itself why 
 the attribute of compre^siUUty should be affirmed of it, any 
 more than ineorripreisi^ility. The Axiom of Excluded Mid- 
 dle tells us that one or the other must be so predicated, — 
 that matter must be either compressible or incompressible. 
 Anqther necessary Law of Thought — that of Reason and 
 Consequent — forbids us to predicate either of these con- 
 tradictories to the necessary exclusion of the other, without 
 a ground for such preference ; and the reason in this case 
 must bfi derived from some source exterior to the Judgment 
 itself, as no analysis of the latter will afford any such reason. 
 We may, indeed, predicate neither; we may leave the 
 f bought, so far as this pair of contradictories is concerned, 
 wholly indeterminate. But if we affirm anything of it, be- 
 yond what is already contained in it, there must be a reason, 
 express or implied, for such a^rmatipn. 
 
 With obvious propriety, analytic Judgments are also 
 called explicative, as they merely unfold, and thereby 
 bring into clearer consciousness, what we already possess. 
 By them our knowledge is cleared up and rendered exi- 
 phcit, but is not at all enlarged. Synthetic Judgments, on 
 the other hand, are properly called ampliative, as by them 
 our sum of knowledge is increased. Each of these re- 
 quires a reason, as otherwise its result would not be the 
 enlargement of knowledge, but the caprice of ignorance. 
 
 It is rightly observed by Krug, that the relation of Rea- 
 son and Consequent is something different from that of 
 Cause and Effect. It is true that Cause and Effect, so far 
 as they are conceived in tJwught, stand to each other as Rea- 
 son and Consequent. But the converse is not true ; all Rea- 
 
56 THE PEIMARY AXIOMS OF PURE THOUGHT. 
 
 sons are not Causes, and all Consequents are not Effects. 
 The two relations may be distingnished from each other as 
 being respectively what the old logicians called the ratio 
 cognoicendi and the ratio essendi. Thus, to take an exam- 
 ple, the ground being wet is the Reason why I know that it 
 has rained; this is the ratio cognoseendi, and it is evidently 
 a relation of one thought to another thought; though the 
 wetness of the ground is certainly not the Cause of the 
 rain, yet, because I know that the ground is wet, I am jus- 
 tified in thinking that- the rain has fallen. On the other 
 hand, the falling of the rain is the Cause of the ground 
 being wet ; this is the ratio esseTidi, and it is the relation 
 of one real thing, or actual occurrence, to another ; and, as 
 such, it is independent of any thought, as the one thing 
 would still cause the other, though there were no mind to 
 observe their contiection. Hence, the relation of Reason 
 and Consequent is a mere synthesis of thoughts ; the 
 thought of wetness of the ground suggests, and, so to 
 speak, justifies the thought of rain. But Cause and Effect 
 expresses an actual union of physical events, the real exist- 
 ence of the one compelling or necessitating the existence of 
 the other. 
 
 This seems the proper place to iatroduce what is called 
 " the postulate of Logic," — a precept which Logicians have 
 always assumed, and acted upon in part, but which, before 
 Sir Wilham Hamilton's time, they never distinctly enoimced, 
 or carried out consistently in all its consequences. To adopt 
 his language, — 
 
 " The only postulate of Logic which requires an articu- 
 late enouncement is the demand, that, before dealing with a 
 judgment or reasoning expressed in language, the import of 
 its terms should be fully understood ; in otlier words. Logic 
 postulates to be allowed to state explicitly in language what 
 is implicitly contained in the Thought." 
 
 This assumption is grounded upon the two fundamental 
 
THE PRIMARY AXIOMS OF PURE THOUGHT. 57 
 
 propositions already stated and explained, namely, that 
 Logic deals only with the Form, and not with the Matter, 
 of Thought; and that it is concerned primarily with the 
 Thought, and only secondarily with the accident of its ex- 
 pression. The science claims, therefore, to fill up the gaps 
 and ehsions of ordinary discourse, wherein much is sacri- 
 ficed to brevity of speech, and to pare down the complexity 
 and redundance of rhetorical expression into logical sim- 
 plicity and precision. For ordinary purposes, and for the 
 Rhetorician's use, language is a vehicle for the rapid and 
 effective communication both. of Thought and feehng; con- 
 sequently, it deals much in hints and abbreviated forms of 
 speech, taking for granted all that the reader's and hearer's 
 mind will readily supply, and aiming only to bring his fac- 
 ulties of reasoning, imagination, and emotion into play in 
 the right direction. The Logician, on the other hand, 
 seeks to express nothing but Thought; and he aims to 
 make language a perfect representative of the Thought in 
 its simplicity and entireness. His proper fiinction is to 
 point out those minute but frequently recurrent elements 
 of Thought, which, precisely because firequently recurrent, 
 are elided or passed over in ordinary discourse. Of course, 
 the expressions which he thus finds occasion to use will 
 often appear awkward and redundant, tediously minute, 
 and even tautological. But he is not responsible for their 
 rhetorical demerits ; the only question for him is, whether 
 they fully and correctly express all that is actually passing 
 in Thought. Thus, the common form of argumentation is 
 the Enthymeme, which consists of but two propositions ; 
 but its Logical fi)rm is the Syllogism, consisting of three. 
 No one but a silly pedant ever speaks or writes Syllogisms, 
 except in a treatise on Logic. But the only question is, 
 whether everybody does not ihinh Syllogisms whenever he 
 speaks or writes Enthymemes. To take another instance, 
 Hamilton's doctrine of the thoroughgoing quantification of 
 
 3* 
 
58 THE PEIMAKY AXIOMS OF PURE THOUGHT. 
 
 the predicate has been objected to for this reason, among 
 others, that the propositions which it vindicates are so awk- 
 ward and unnatural, that they seem "got up for. the purpose 
 of seeing what one can do." Perhaps so ; and yet the 
 objection is an idle one. For if there are occasions when 
 we must think affirmative Judgments with universal predi- 
 cates, and negative Judgments with particular ones, the 
 Logician's first duty is to express this fact, however awk- 
 ward and even ludicrous such expression may seem. 
 
THE DOCTKINE OF CONCEPTS. 59 
 
 CHAPTER IV. 
 
 THE DOCTRINE OF CONCEPTS- 
 
 1. Their Quantity ; 2. Their Quality ; 3. Their Relation ; 4. Their Defi- 
 nition and Division. 
 
 A CONCEPT is a combination, or a reduction to unity 
 in Thought, of those elements and qualities of the 
 objects -which we are thinking of, whereby they are dis- 
 tinguished from al other objects, and especially from those 
 which, m other respects, are most similar to them.* These 
 distinguishing attributes, which are the elements of the 
 Concept, are called its Marks ; for through them the ob- 
 jects of Thought are determined, or known to be what 
 they are, and discriminated from what they are not. The 
 word, or General Term, which is the appellation of the 
 Concept, is, consequently, the Common Name of all the 
 objects that are included under it. It is a convenient use 
 of language, (though the words are sometimes applied in 
 a different manner,) to say that the word or Name connotes 
 
 * The words Conc^t and Notion, often used as synonymes, are perhaps 
 best distinguished etymolpgically ; — Concept (co;j-capere) as the grasping 
 up together of a plurality of attributes into one Thought ; Notion (noscere 
 notis, to know an object by its Marks), as the taking note of the several 
 ilarks or characteristics of an object. The meaning of Notion might, 
 perhaps, be conveniently limited to the apprehension of any single Mark 
 (nota), while Concept signifies the compreliension of all the attributes which 
 are characteristic of a certain class of things. Thus, I have a Notion of 
 each of the Marks, cold-blooded, vertebrated, animal, breathing bij means of gills, 
 and living in the water, taken singly ; and I have a Concept of them taken 
 together, as the characteristic Marks of a Fish, or of the whole class of 
 Fishes. As thus limited, Notions are a subordinate class of Concepts. 
 
60 THE DOCTRINE OF CONCEPTS. 
 
 the attributes or Marks which make up its signification,* 
 and denotes the mdividual things contained under it which 
 possess those attributes. Thus, the name Man connotes 
 Uped, two-handed, rational, animal, and denotes all indi- 
 vidual men and classes of men. 
 
 It has already been explained, that a Concept is not 
 necessarily the Thought of an actual, but only of a pos- 
 sible, class of objects; that is, its name may actually 
 denote only one thing, as, for example, the one animal, 
 just discovered, of a species hitherto unknown. Hence, 
 Esser was led to define a Concept as " the representation 
 of an (one) object through its distinguishing Marks." But 
 even in this case, the representation, in order to be a Con- 
 cept, must be a partial representation ; that is, it must 
 represent, not all the Marks, but only the distmguishing 
 Marks. Thus it becomes the representative of a possi- 
 ble class or plurality of things ; if other specimens should 
 be subsequently discovered possessing these distinguishing 
 Marks, the Concept would include them also. It is only 
 when the object is immediately preseMied before us either 
 by the Senses or the Imagination, so that we have a 
 J*resentation or Intuition of it, as one whole, with all its 
 
 • " As these qualities or modes are only identified with the thing by a 
 mental attribution, they are called attributes ; as it is only in and tlirough 
 them that we say or enounce aught of a thing, they are called predicates, 
 predicaMes, and predicaments, or categories (these words being here used in 
 their more extensive signification) ; as it is only in and through them that 
 we recognize a thing for what it is, they are called notes, signs, Tnarhs, charac- 
 ters ; finally, as it is only in and through them that we become aware that 
 a thing is possessed of a peculiar and determinate existence, they are called 
 properties, differences, determinations. As consequent on, or resulting from, 
 the existence of a thing, they have likewise obtained the name of consafuents. 
 What in reality has no qualities has no e.xistence in thought, — it is a 
 logical nonentity ; hence e connerso, the scholastic aphorism, non-entis nulla 
 sunt predicata. What, again, has no qualities attributed to it, though a^ 
 tributable, is said to be indctemiined. ; it is only a possible object of thought." 
 — Hamilton, Lectures on Logic, Am. ed., p. 55. 
 
THEIR CONTENTS. 61 
 
 attributes, that its Name is a Proper Name strictly so 
 called; for if it is present only in Thought, our repre- 
 sentation of it is necessarily partial, as not including all its 
 Marks, and its Name is then virtually Common, as the 
 designation of a possible plurality of things. Thus, if I 
 am contrasting in Thought two historical characters, as 
 Cesar and Pompey, these two names to my conception 
 become General Terms, as several individuals may each 
 possess the few Marks which, for the purposes of this 
 contrast, I attribute to those two old Romans. Gray's 
 affecting lines may be attributed to any churchyard : — 
 
 " Some mnte inglorious Milton there may rest, 
 
 Some Cromwell, guiltless of his country's blood." 
 
 Still further ; not merely may a Concept actually denote 
 only one thing, it may actually connote only one Mark. 
 But here, as before, there is a possible plurality in actual 
 unity. Thus, in the present state of ray knowledge, my 
 Notion or Concept of red color may be absolutely simple, — 
 that is, it may have but this one Mark of redness. But 
 additional acquaintance with the science of Optics would 
 teach me that this red color is an element of white light, 
 and that it has a certain degree of refrangMlity, by virtue 
 of which its 'position in the solar spectrv/m is at one end of 
 the scale. Here are three additional Marks of red color. 
 In like manner, every Concept, though actually simple, 
 must be regarded as .containing a possible plurahty of 
 Marks. I say, it must be so regarded ; for every Concept 
 must denote some existing object, — existing, that is, either 
 really or potentially ; and no such object can be conceived 
 of except as possessing a possible plurahty of Marks. 
 For every object can be conceived to be what it is, only 
 by discriminating it from several things which it is not; 
 and such discrimination is possible only through a plurality 
 of attributes. 
 
62 THE DOCTEIHE OF CONCEPTS. 
 
 This will be more evident, if we consider for a moment 
 the various kinds of Marks by which one Concept maj 
 be distinguished from another. The following enumeration 
 of them, which might be much enlarged, is taken in great 
 part from Esser. 
 
 Marks are divided, — 1. Into affirmative and neffoMve, ac- 
 cording as we know through them either what the object 
 is, or what it is not ; thus, rational is an Affirmative, im- 
 perfect a Negative, Mark of Man. 2. Into iinternal and 
 external, according as tie Mark is attributed to the object 
 either in and for itself, or on the ^ound of the relation 
 in which it stands to some other object ; thus, hiped is an 
 Internal, Father or Son an External, Mark of Man. 3. 
 Into permanefnt and transitory, according as they are al- 
 ways, or only sometimes, found in the object ; thus, metallic 
 is a Permanent, hot is a Transitory, Mark of Iron. 4. Into 
 peculiar and common, according as they belong to these 
 only, or also to other objects ; thus, right-angled is a Pe- 
 culiar, plane-figwe is a Common, Mark of a Square. 5. 
 Into essential or necessary, and accidental or contingent, 
 according as they can, or cannot, be separated from the 
 object; thus, rational is an Essential, learned an Acci- 
 dental, Mark of Man. 6. Into original or immediate, and 
 derivative or mediate, according as they are either Marks 
 of the thing itself, or only Marks of other Marks of it ; 
 thus, free-mlled is an Original, able to compute by manbers 
 a Derivative, Mark of Man, the latter being only a con- 
 sequent or Mark (£ ratimdlity. 
 
 We gain another view of the elements of a Concept 
 by dividing them into, — 1. Kinds of Existence ; 2. Quali- 
 ties, or Modes of Existence ; and 3. Relations, or Forms 
 of Intermediate Existence. 
 
 First, in order to conceive, we must conceive some- 
 thing, — i. e. some being or earistence, — which, as an object 
 of Thought, may be distinguished from other things, and 
 
THEIR CONTENTS. 63 
 
 to which qualities can be attributed. If there is no such 
 ennAUy, at the bottom of the Concept, to give it unity, the 
 Thought is null ; non-entis nulla sunt predkata. There 
 are but two kinds of Being or Existence, one of which is 
 thus necessarily presupposed in Thought; namely. Real 
 and Imaginary or Potential. One or the other must enter 
 into every Concept, not as attributed to it, but as presup- 
 posed in forming it. In other words, every Thoiight must 
 be of some real or imaginary thing. 
 
 Secondly, whatever exists must exist in some deter- 
 minate mode;; that is to say, it must have one or more 
 qualities. Being or existence, as defined above, includes 
 ■all things, both real and possible ; hence, in order to think 
 any particular thing, we must discriminate it fi-om other 
 things ; and we can do this only by attributing to it 
 Quahties, or particular modes of existence. By presup- 
 posing existence, then, we have a thing, or object of posd- 
 ble Thought.; by giving to it qualities, we have a definite 
 thing, or object of .actual Thought. The thing exists in 
 itself, per sej the quality exists only in the thing, — that 
 is, in something different from itself, per aliud, or, as the 
 lo^oians say, per aecidens. 
 
 Thirdly, a Relation exists neither in itself, per se, nor 
 in the thing as different from itself, per aliud, but between^ 
 the thing and some other, thing with which it is compared. 
 This kitermediate state of existence is the only charaoter- 
 istic feature of Relations, whereby they are distinguished 
 from other Quahties. The Relation does not merely residt 
 from a comparison and discrimination, for this is true of 
 all Qualities ; but it only exists as between one thing and 
 another, thereby necessita,ting a Thought of both. Thus, 
 the Relation of Husband and Wife exists in neither of 
 them, but between ,them,, and can be apprehended only 
 by thinking of the two together. 
 
 "Every -object," says Drobiseh, "is thought as a deter- 
 
64 THE DOCTRINE OF CONCEPTS. 
 
 minate object only through the Marks appertaining to it, 
 by means of which it is comparable, in respect to its nature, 
 with other things, and is distinguishable from them. With- 
 out these Marks, it is only an •indeterminate something, a 
 thing or being without further determination ; just as, on 
 the other hand, these Marks have no independent being in 
 and for themselves, but they can be separated only in 
 Thought from the object in which they exist. In the 
 Concept of the object, then, there is the Thought of 
 an independent but indeterminate something, united with 
 determinate, but (in themselves considered) dependent, 
 Marks ; the Concept of the object is the union of the two. 
 (Thus, my Concept of Man is a living, rational, organic 
 SOMETHING, having a mortal body and an immortal soul.') 
 The Marks are the manifold, the plurality, and the m- 
 determinate something is that which gives unity to these 
 Marks, in the Concept of an object. The Concept is com- 
 plex, therefore, and admits of separation into its elements ; 
 and this separation is called Analysis." 
 
 It is obvious enough, that the distinction between Con- 
 cept and Marks is not absolute, but relative ; they may 
 be used interchangeably. Any Concept may become the 
 Mark of some other Concept; and every Notion, which 
 may appear in one Thought as a Mark, becomes in 
 another an independent Concept. Thus, the Concept ani- 
 mM is a Mark of man; and mMal, which is a Mark of 
 iron, is itself a Concept, including under it iron, tin, 
 lead, &c. The only distinction consists in the two dif- 
 ferent uses which are made of them in Thought. If a 
 Concept is used only as a means of determining some 
 other Concept, and so without direct reference to the ob- 
 jects or things which it denotes, it is a Mark ; but if used 
 as a Class-notion of certain objects, and with only second- 
 ary reference to the attributes or qualities involved in it, 
 it is a Concept in the stricter sense. In other words, if 
 
THEIR CONTENTS. 65 
 
 used connotatively, it is called a Mark ; if used denota- 
 tively, it is called a Concept. 
 
 The only law of pure Thought applicable to the forma- 
 tion' of Concepts is the Axiom of Non-contradiction. A 
 Concept must not have contradictory Marks, as these de- 
 stroy each other, and the Thought so far becomes void or 
 null. Thus, looking only to the Form of Thought, to the 
 Concept A may be attributed the Marks B, C, D, and so 
 on without limitation; but B and not-B cannot be so 
 attributed. 
 
 Looking to the Matter of the Thought, however, a 
 further limitation arises. Considered in relation to each 
 other, Marks are either Congruent or Repugnant; the 
 former can, and the latter cannot, be attributed to the 
 same Concept. Thus, sweet and red are Congruent, as the 
 same apple may have both Marks ; but siveet and litter 
 are Repugnant, since they cannot be united in the same 
 object. If the tyro should object, that one part of it may 
 be sweet, and another part bitter, the answer is, that the 
 two parts are two different objects. Marks are said to be 
 Contradictory, when the one is a simple or direct negation 
 of the other ; as sweet and not-sweet, B and not-B. They 
 are Repugnant or Contrary, when the negation is indirect, 
 as when the one is denied, not directly, but by putting in 
 its place, or in the same Concept, another Mark with which 
 it is incompatible. The mere Form of the Marks tells 
 me whether they are Contradictory or not; but to know 
 whether they are Congruent or Repugnant, I must know 
 the Matter of the Thought, — that is, I must have re- 
 course to experience. 
 
 Again, if considered as mere Marks, or with reference 
 to their connotation only, the attributes which are imited 
 in the same object are disparate Notions, for they are 
 different without any similarity. This holds true of Con- 
 gruent, as well as of Repugnant, Marks ; thus, sweet and 
 
66 THE DOCTBINE OF CONCEPTS. 
 
 red are Disparate, for the quality of sweetness has no re- 
 semblance whatever with that of redness. On the other 
 Imnd, if considered as Concepts, or with reference to what 
 they denote, they are properly called disjunct or discrete 
 Motions, for they are only relatively different ; they have 
 at least so much in common, that they can be co-ordinated 
 under some higher Concept. Thus, sweet apples and red 
 apples are so far similar, that they both belong ^nder the 
 Class-notion apples or fruits. It is only stating the same 
 distinction in other words to say, that Disparate Notions 
 are Congruent, for they can be united in "the same Con- 
 cept ; but they do not denote any objects. On the other 
 hand, the Disjunct do denote Objects, but they are not 
 Congruent, for they cannot be united in, but axe only 
 contained under, the same Concept. 
 
 To apprehend stUl further the nature of Concepts, they 
 must be viewed in three aspects. First, if considered in 
 themselves alone, they have Quantity ; secondly, if con- 
 sidered in reference to the mind or thinking subject .in 
 which they are conceived, they have Quality ; thirdly, if 
 considered in reference to each other, they have Relation. 
 
 1. The Quantity of Concepts. 
 
 It follows from the definition which has been given, 
 that a Concept is a magnitude or Quantity, and that this 
 Quantity is twofold. First, it has a number of Marks, 
 which are reduced to unity in Thought, because they are 
 all conceived as inhering in one object or thing. This is 
 its Quantity of Intension. Secondly, it denotes a number 
 of objects, which are reduced to unity in Thought as one 
 class or species, because each of them possesses all tliese 
 Marks. This is its Quantity of Extension. Thus, the 
 Intension of bird is a winged, feathered, vertebrate, biped, 
 animal; in its Extension are contained all individual bu:ds 
 
THEIR QUANTITY. 67 
 
 and classes of birds, as eagles, vultures, hawks, pigeons, &c. 
 The plurality of objects which are denoted by the Con- 
 cept are said to constitute a Logical whole, or the whole 
 of Extension; the plurality of Marks connoted by the 
 Concept form a Metaphysical whole, or the whole of 
 Intension. 
 
 This distinction of Quantity has been expressed by Lo- 
 gicians in various ways, which are here enumerated for 
 convenience of reference, though the forms of expression 
 already given wiU be adhered to in the present work. 
 
 A Logical or Universal whole A Metaphysical or Formal whole * 
 
 has Extension, has Intension, 
 Breadth, Depth, 
 
 Sphere ; Comprehension ; 
 
 contains under it, contains in it, 
 
 denotes, connotes, 
 Objects, Marks, 
 
 Things. Attributes. 
 
 This twofold Quantity of Concepts enables us to under- 
 stand the seemingly opposite assertions, that the Subject 
 of a proposition is in the Predicate, and yet that the Predi- 
 cate is in the Subject, With reference to the Quantity 
 
 * Besides the Logical and the Metaphysical, three other sorts of wholes 
 have been distinguished by Logicians. 
 
 1. The Essential or Physical whole is that which consists of Matter and 
 Form, or substance and accident, as its essential parts. The characteristic 
 of this whole is, that, as its parts do not exist out of each other, they cannot 
 be separated except in Thought. As Burgersdyck says, "the Form per- 
 meates the Matter, and informs all its parts," so that Form and Matter are 
 inseparable. 
 
 2. The Mathematical or Integral whole, on the other hand, has parts 
 which are external to each other, so that thej can be divided asunder. 
 This is the case with geometrical figures, as the triangle, the parallelogram, 
 and with the human body and the limbs. These have partes extra partes. 
 
 3. A Collective whole, or whole of Aggregation, has its parts separate 
 and accidentally thrown together; as,.an army, a heap (f stones. 
 
68 THE DOCTRINE OF CONCEPTS. 
 
 of Intension, the Predicate is -in the Subject, inasmuch 
 as it is but one of several Marks which make up our 
 Notion of the Subject. Thus, man is animal; animal may 
 be regarded as a part of man, because it is a part of the 
 meaning of the word ; and, when taken in connection with 
 thd other parts, living, two-handed, rational, makes up the 
 whole Intension of the Concept m^n. But in respect to 
 the Quantity of Extension, man is contained imder an- 
 imal, — the Subject in the Predicate, — since he is but one 
 out of many kinds, all denoted by this one General Term, 
 or contained under this one Concept, animal. 
 
 " We find two expressions in Aristotle, both of which 
 are sometimes rendered by ' hdng in,'' — inegse. 1. imdpxfiv, 
 by which the Predicate is said to be in the Subject. This 
 
 is equivalent to KanjyopciaBai. T6 a VTrdpxft jravTi ra B ^ to 
 A Karriyopevrai Kara navT&e tou B = ^ inest omni jB (= A ig 
 
 predicated of every B = All B is A^. 2. ttvai iv, by which 
 the Subject is said to be in the Predicate. A ivriv iv Ska 
 T^ B = Omne A est B (^All A is B^. This is exactly the 
 reverse of KaTJiyopelrai. The English language is defective 
 in not having, like the Greek and Latin, a proper Copula 
 to express the relation of Intension as well as that of Ex- 
 tension. Thus the relation expreesed by imapxet and inest 
 can only be strictly rendered into English by a circum- 
 locution, ' A is a quality belonging to B.' With the ordi- 
 nary Copula, both must be translated into the language of 
 Extension." * 
 
 Besides the Concepts which are formed from individual 
 things, by abstracting their differences and uniting their 
 common or similar elements, we can, by -a perfectly similar 
 process, form Concepts of Concepts ; and then, again re- 
 peating this process, we obtain Concepts of these Concepts, 
 and so on indefinitely. In this way, we have in each case 
 
 • Manbel, Notes to Mdridt, p. 45. 
 
THEIR QUANTITY. 69 
 
 a hierarchy of Concepts, of which only the lowest in order 
 directly denotes individuals, while all the others directly 
 denote other Concepts or classes, and only indirectly denote 
 the individuals contained in those classes. Thus, spaniel, 
 terrier, hound, mastiff, &c. are Concepts of the first or 
 lowest order, each of them directly denoting certain indi- 
 vidual animals, whose common attributes haT»e become, in 
 Thought, the Marks of their class. Then, abstracting the . 
 differences of these classes, we have dog as a Concept of 
 the second order, directly denoting spaniel, terrier, &c., and 
 indirectly denoting the same individuals as before. Having 
 formed in a similar manner secondary Concepts of eat, wolf, 
 fox, hear, &c., by comparing aU of these with dag, abstracting 
 the differences and combining the similarities, we obtain the 
 tertiary Concept carnivora. Again, comparing carnivora 
 with rodents, marsupials, ruminants, &c., we have a Con- 
 cept of the next higher order, mammal, of which the Marks, 
 forming the Intension, are vertebrate, viviparous, warm-blood- 
 ed, animal, suckling its yowng. It is evident that we can 
 go on in this manner, rising through Concepts successively 
 broader and broader in generalization, till we reach the 
 limit of human Thought in the Concept tTang, entity, or 
 direct of Thought, which connotes nothing but existence 
 (real or potential), and denotes everything. 
 
 I have here intentionally taken an illustration of the log- 
 ical process of generalization from Natural History, as the 
 science in which classification is most extensive and precise, 
 though with the disadvantage of introducing here a number 
 of technical names pecuHar to that science, and with which, 
 as belonging to the- Matter of Thought, Logic has nothing 
 to do. But every word in our language, or in any language, 
 perfectly corresponds to one of these zoological technicali- 
 ties, in that it occupies a definite place in some one of the 
 countless hierarchies of Concepts which the human mind, 
 • for .various purposes, has been led to form. The greater 
 
70 THE DOCTRINE OF CONCEPTS. 
 
 part of our mental life is spent in generalizing by successive 
 steps, — that is, in forming Concepts of Concepts ; — but 
 always, except in the science of Logic, with special refer- 
 ence to the particular things denoted by these Concepts. 
 Logic, which deals only with the Form, and not the Matter, 
 of Thought, needs a set of technicaUties of its own, to de- 
 scribe these steps of generalization, and all other processes 
 of -pure Thought, with reference, not to the things which 
 they denote, but to each other and to the thinking mind. 
 This is precisely the distinction, so famous in the Scholastic 
 philosophy, between fint and seeond intmtiong, — a distinc- 
 tion which has been ignorantly ridiculed by those who did 
 not understand it, but which in itself is perfectly intelligible, 
 and is as necessary as other technical distinctions in science, 
 all of which, before they can be understood, require a 
 knowledge of the elements of the special science in which 
 they are taken. The burlesque question, utrum ehimoBra 
 bombinans in vacuo posset eomedere seeundas intentiones, is a 
 good specimen of the ftm which for a long time was heaped 
 on the study of Scholastic Logic. 
 
 A first intention or notion is a Concept, whether of a low 
 or a high order, which denotes things. Thus, in the illus- 
 tration just given, ^aniel, doff, camivor, mammal, — each 
 and all denote certain animals ; they are First Intentions. 
 On the other hand, a second intention or notion is a Concept 
 which denotes first intentions — i. e. the former Concepts — 
 in their relation, not to the things denoted, but to each other. 
 Thus, if the three lower steps in every hierarchy of Con- 
 cepts are denominated respectively, Variety, Species, Genus, 
 then these three names, applicable nof only to spaniel, dog, 
 camivor, but to every other corresponding set of three suc- 
 cessive steps of generalization, express second intentions. 
 " First Intentions," says Mr. Mansel, " as conceptions of 
 things, are predicable of tlie individuals conceived undef 
 them. Thus we may say, ' Socrates is man, animal, &c.' 
 
THEIE QUANTITY. 71 
 
 Second Intentions are not so predicable; we cannot say, 
 ' Soctates is species, genus, &c.' So, when Genus is said to 
 be predicable of Species, it is not meant that we can predi- 
 cate the one Second Intention of the other, so as to say, 
 ' Species is Genus ' ; but that the First Intention animal 
 is predicable of the First Intention man, the relation of the 
 one to the other being expressed by the Second Intentions 
 genus and species. For this reason. Logic was said to treat 
 of seeond intentions applied to first." * 
 
 It is obvious that Second Intentions are the peculiar tech- 
 ricalities of the abstract sciences of Logic and Grammar. 
 In the physical sciences, we have to deal only with Con- 
 cepts of things ; but Logic arid Grammar need Concepts 
 of our modes of thinking and speaking of things, so far as 
 these modes are related to each other. Thus, we need the 
 technical terms GenUs and Species to express the relations 
 in which the several Concepts, thatJbrm any one hierarchy 
 or series, stand to each oth^. These relations are indicat- 
 ed in the following table. 
 
 * Notes to Aldrich, p. 20. 
 
72 
 
 THE DOCTRINE OF CONCEPTS. 
 
 Second Intentions, 
 or Concepts of Coa- 
 cepta, as thought rel- 
 atively to each other. 
 
 Summum Genus. 
 
 Species or subal- 
 tern Genus. 
 
 Species or subal- 
 tern Genus. 
 
 Species or subal- 
 tern Genus. 
 
 Species or subal- 
 tern Grenus. 
 
 Infima Species. 
 
 first Intentions, 
 
 or Concepts of 
 
 things. 
 
 Thing or Entity. 
 Animal. 
 
 Mammal. 
 
 Camivor. 
 
 Dog. 
 
 Spaniel. 
 
 Intension, 
 or Marks connoted. 
 
 Existing. 
 
 Existing, organized, 
 sentient. 
 
 Existing, organized, 
 sentient, suckling 
 tlieir young. 
 
 Existing, 'organized, 
 sentient, suckling 
 their young, eat- 
 ing flesh. 
 
 Existing, organized, 
 sentient, suckling 
 their young, eat- 
 ing flesh, digiti- 
 grade quadruped, 
 &c. 
 
 Silky-haired, water- 
 dog, having all the 
 preceding Marks. 
 
 Extension, 
 or Objects denoted. 
 
 Everything. 
 
 Every Vertebrate, 
 Mollusk, Artic- 
 ulate, and Ra- 
 diate. 
 
 Every vertebrat- 
 ed animal which 
 suckles its young. 
 
 Beats,- wolves, 
 foxes, lions, 
 tigers, &c. 
 
 Mastiff, spaniels, 
 hounds, terri- 
 ers, &c. 
 
 All individual 
 
 spaniels. 
 
 Put any other, an entirely different, series of First In- 
 tentions in the place of those given in the table, — take, 
 for instance, the series Man, European, Frenchman, Paris- 
 ian, — and it is evident that the relations of these Con- 
 cepts also to each other will he correctly indicated by the 
 same Second Intentions as before. Man is now the Sum- 
 mum Genus, Parisian is the Infima Species, and the inter- 
 mediate Concepts are the Subaltern Genera or Species. 
 
 A mere inspection of the table also brings to light the 
 one law of Thought which determines the Quantity of 
 Concepts. It is, that Intension and Uxtension, the two 
 Quantities of every Concept, are always in inverse ratio to 
 each oilier. They must both be present j there must be at 
 
THEIR QUANTITY. 73 
 
 least a minimum of each ; for a Concept muse always con- 
 note something and always denote something. But if we 
 take a great number of objects, we can find but few attri- 
 butes or Marks which are common to them all, while a few 
 objects may have many common attributes, Lgoking at 
 the table, we see that, in the Summum Genus, the Inten- 
 sion is least: in the case there given, only one Mark — 
 existing — is connoted ; while the Extension is greatest, for 
 the same Concept denotes everything. Descending from 
 the Highest Genus, we see that the Intension steadily in- 
 creases through the Subaltern Genera, while the Extension 
 regularly diminishes. In the Lowest Species, the Intension 
 is at its maximum, as Spaniel connotes all the Marks of the 
 higher Genera and one or two additional Marks, and the 
 Extension is at its minimum, as there are fewer Spaniels 
 than I)ogs, still fewer than Carnivora, &c. It is only stat- 
 ing the same law in other words to say, with reference to 
 any one hierarchy or series of Concepts, that any increase 
 of the Intension produces, ipso facto, a diminution of the 
 Extension, and any diminution of the former an increase 
 of the latter. Observe, however, that it is only the origi- 
 nal and essential Marks of which we speak, when we say 
 that the number of Marks is inversely proportional to the 
 number of objects denoted. The Original Marks carry 
 their Derivatives along with them by necessary implica- 
 tion ; and therefore we do not really increase the Intension, 
 but only render it more exphcit, when we annex certain 
 Derivative attributes which were not formerly expressed — 
 perhaps not even thought — as belonging to it. Thus, the 
 Intension of triangle, as a plane figure having only three 
 sides and three angles, is not at aU enlarged by adding this 
 Mark, the sum of these three angles being equal to two right 
 angles, even though I now for the first time learn that this 
 is their sum! Though I did not, therefore, previously think 
 this Mark of the Concept, it did nevertheless belong to it 
 
74 THE DOCTRINE OF CONCEPTS. 
 
 impKcitly, or by necessary inference ; and hence its express 
 recognition does not alter either Quantity. In hke man- 
 ner, it is only the Essential Marks which determine the 
 boundaries of a Concept ; we do not enlarge the Intension 
 of man as a rational animal, by adding this Accidental 
 Mark, sometimes learned. As for the Mark capable of 
 learning, that is a Derivative from rational. 
 
 The metaphysical meaning of essence is, that internal 
 constitution of a thing which makes it what it is, — which is 
 not only the source of its attributes, but is necessary to its 
 existence. In this sense, of course, no finite mind can 
 attain to a knowledge of the Essence of any real thing 
 whatever. Passing by the disputes on this head as be- 
 yond our province, it is enough to say that Logic (which 
 has nothing to do with " real things," as they belong to 
 the Matter of Thought) considers the Essence of a Con- 
 cept to be the aggregate of its Marks, or, in other words, 
 the sum of the attributes which it connotes. Still further : — 
 Formal Logic cannot inquire into the nature of these at- 
 tributes, but designates them indifferently by letters of 
 the alphabet, as being all of the same kind. It necessarily 
 presupposes, as above stated, that only Original and Es- 
 sential attributes are used as Marks of a Concept ; and 
 hence it looks only to their number, and not to their 
 quality. Therefore, the law is universal and absolute, — 
 add ^ or subtract a single Mark, and the Extension, or 
 number of objects denoted, is thereby diminished or in- 
 creased. Essential means inseparable or necessary ; take 
 away an Essential attribute, and the Concept ceases to be 
 what it was, and becomes another Concept with a wider 
 Extension. Thus, from man as a rational animal, remove 
 the Mark of rationality, which is Essential to him, and 
 the remaining Concept is animal, which denotes all men 
 and brutes also. 
 
 Q-merification, usually called Creneralization, is the pro- 
 
THEIR QUANTITY. 75 
 
 cess of rising, through the successive abstraction of Marks, 
 from lower to higher Concepts. It is so called because the 
 lower Concept is relatively a Species, and the higher one, 
 to which we proceed, is relatively a Genus, having a wider 
 Extension. Thus, we proceed from the lower Concept 
 Mammal, which is in this relation a Species, to the higher 
 Concept Animal, which is in the same relation a Genus, 
 by throwing out the Mark mehling their young. The 
 name of this process, therefore, correctly indicates the act 
 of becoming a Grenus. 
 
 The contrary process, of descending from higher to low- 
 er Concepts through the successive assumption of Marks, 
 is called Determination, — more properly Spedfieaiion, as 
 it expresses the act of becoming a Species. It has been 
 well said, that it is the process of "thinking out objects 
 by thinking in attributes." Thus, we descend from the 
 Genus MammMlia to the Species Camivora, by throwing 
 out all herbivorous animals, through bringing in the Mark, 
 eating flesh. 
 
 It has already been observed, in treating of the Axiom 
 of Ex:cludeji' Middle and its applications, that every pair 
 of Contradictory attributes, A and nat-A, divide the uni- 
 verse between them, as one or the other must belong to 
 everything. Because a given attribute. A, can be affirmed 
 only of a certain number of objects, it must be denied of 
 all other objects ; and we may express such denial by 
 saying, all these others are Not-A. Hence we have a 
 peculiar class of Concepts, called Negative or Privative, 
 more properly Infinitated, of which the characteristic is, 
 that they denote almost everything, and connote ' next to 
 nothing,' — that is, nothing positive. Thus they afford a 
 curious illustration of the law, that the two quantities of a 
 Concept exist only in an inverse proportion to each other. 
 Logically considered, the Extension of the Concept Not-A 
 is infinite, embracing the universe of existence both real 
 
76 THE DOCTEINE OF CONCEPTS. 
 
 and potential ; for the subtraction of a finite quantity, A, 
 does not diminish infinity. Consequently, its Intension is 
 zero; for it does not connote any Mark, but only the 
 absence of the Mark, A. 
 
 Practically considered, however, or with reference to 
 the Matter of the Thought, " the universe " in such cases 
 is not thought absolutely, but relatively; it means only 
 the totality of that class of objects which we are thinking 
 of, and to which A belongs. Thus, the two Concepts 
 Frenchman and Twt^Frenehman are not thought to include 
 all things, (which, if taken strictly, they would do,) but 
 only aU mew. In like manner, not-^nale, which, if rigidly 
 construed, would denote every stock and stone, besides 
 many animals, is actually thought merely as a synonyme 
 for female, and so denotes only about one half of the ani- 
 mal kingdom. Sometimes, the name is seemingly positive, 
 but the Concept or ihougM is truly negative. Thus, 
 parallels are lines that do not meet ; therefore, as two 
 negatives destroy each other, not-parallel are lines that do 
 meet, — a really positive Concept under a Privative or 
 Infinitated form. For this reason, some writers have ar- 
 gued that infinite, i. e. not-finite, is not thought negatively, 
 but positively ; for finite, meaning limited or bounded, is a 
 restriction or negation of the magnitude which infinity 
 asserts positively. On the other hand, it is maintained 
 that the essence of Thought, as such, consists in limitation 
 or restriction ; for we cannot- think any object except by 
 distinguishing it, through its peculiar Marks, from other 
 objects ; consequently, to deny this restriction or negation, 
 is to deny that the object in question has any pecuhar 
 Marks, or that it is distinguished from other objects in any 
 manner whatever, and thereby to reduce the Thought of 
 it to zero. 
 
their quality. 77 
 
 2. The Quality of Concepts. 
 
 When considered in relation to the mind or thinking 
 subject in which they are conceived, Concepts may be 
 said to have Quality, according as they more or less 
 perfectly represent to this mind the objects which they 
 denote, and the Marks or attributes by which those objects 
 are distinguished. The three virtues of Clearness, Distinct- 
 ness, and Adequacy constitute the perfection of Thought. 
 The corresponding vices, of course, which render Thought 
 imperfect, are Obscurity, Indistinctness, and Inadequacy. 
 The Quality of a Concept depends on the degree in which 
 it possesses each of these merits or faults. 
 
 It is evident, from this account, that the QuaUty of 
 Concepts, depending on the characteristics not merely of 
 possible, but of perfect. Thought, properly belongs either 
 to the Doctrine of Method, or to what Hamilton calls 
 Modified Logic, rather than to Pure Universal Logic. As 
 the subsidiary processes of Definition and Division, however, 
 by which the Quahties of Clearness, Distinctness, and Ad- 
 equacy are obtained, are applicable to aU Concepts,, and, 
 in a certain degree, regulate their formation and use in all 
 minds, there is sufficient reason for considering the subject 
 here, instead of regarding it as a mere appendage to the 
 science, to be treated "only at the close. It is sometimes 
 convenient to depart a little fi-om a rigorously systematic 
 arrangement, more being gained than lost by the sacrifice. 
 For this reason, and even as a matter of necessity, several 
 matters properly appertaining to the Relation of Concepts 
 have been partially considered in the preceding section, 
 under the head of their Quantity. The fihation and inter- 
 dependence of the parts of a science are often such, that 
 it is impossible to give a proper explanation of any one 
 of them without presupposing some knowledge of the 
 others. 
 
78 THE DOCTEINE OF CONCEPTS. 
 
 A Concept, being the reduction of a plurality both of 
 Marks and Objects to unity, supposes the power of thinking 
 one and many both separately, and in their relation to each 
 other, or together. We think the Concept clearly as a 
 unity, when we can clearly distinguish it as one whole 
 from other unities, — that is, from other Concepts regarded 
 as wholes. We think it distinctly as a plurality, when 
 we can distinguish both the Marks and the Objects which 
 constitute it from each other. The Clearness of my 
 Concept of a given metal — iron, for instance -7— depends 
 on the fulness and precision with which I distinguish it 
 as one whole from other Concepts, especially of those 
 substances which, like the other metals, tin, copper, plati- 
 num, as nearest or most similar, would be most likely to 
 be confounded with it. The opposite of this merit is Ob- 
 scurity. On the other hand, the Distinctness of a Concept 
 depends on the fiilness and precision whereby I apprehend 
 it as a plurality, — that is, as connoting many attributes 
 or Marks, which I clearly distinguish from each other, 
 and as denoting many Objects, which also I can clearly 
 distinguish from each other. The former, or the dis- 
 tinct apprehension of the several Marks, is its Internal 
 Distinctness; the latter, the distinct apprehension of the 
 several Olg'ects contained under it, is its External Dis- 
 tinctness. The opposite of this merit is Indistinctness. 
 
 It is evident that these qualities of a perfect Concept 
 may exist in an indefinite number of degrees; and it is 
 also evident, that a Concept may be quite Clear, while 
 it is but very imperfectly Distinct. A young child may 
 have a very Clear notion of a clock, as distinguished from 
 the other objects in the room, and still have but a very 
 Indistinct apprehension of its parts, properties, and uses, 
 or of the various kinds of horological instruments all 
 denoted by this name. On the other hand, Distinctness 
 necessarily involves Clearness ; I cannot have a Distinct 
 
THEIR QUALITY. 79 
 
 apprehension of all the Marks of a Concept, without being 
 thereby enabled clearly to distinguish it as one whole from 
 other Concepts. The fact, that we may be able very 
 clearly to discriminate a whole from other wholes, or a 
 Concept from other Concepts, though we can but indis- 
 tinctly separate in thought the parts or the Marks which 
 constitute that whole or that Concept, is thus illustrated 
 by Hamilton, from the analogy of our Perceptive and 
 Representative Faculties. 
 
 " We are aU acquainted with many, say a thousand, indi- 
 ■^iduals ; that is, we recognize such and such a coimtenance 
 as the countenance of John, and as not the countenance of 
 James, Thomas, Richard, or any of the other 999. This 
 we do with a clear and certain knowledge. But the coun- 
 tenances which we thus distinguish from each other are, 
 each of them, a complement made up of a great number 
 of' separate traits or features ; and it might, at first view, 
 be supposed that, as a whole is only the sum of its parts, 
 a clear cognition of a whole countenance can only be re- 
 alized through a distinct knowledge of each of its constitu- 
 ent features. But the shghtest consideration will prove 
 that this is not the case. For how few of us are able to 
 say of any, the most familiar face, what are the particular 
 traits which go to form the general result: and yet, on 
 that account, we hesitate neither in regard to our own 
 knowledge of an individual, nor in regard to the knowl- 
 edge possessed by others. Suppose a witness be adduced 
 in a court of justice to prove the identity or non-identity 
 of a certain individual with the perpetrator of a certain 
 crime, the commission of which he had chanced to see ; — 
 would the counsel be. allowed to invalidate the credibility 
 of the witness by, first of aU, requiring him to specify the 
 various elements of which the total likeness of the accused 
 was compounded, and then by showing that, as the witness 
 either could not specify the several traits, or specified 
 
80 THE DOCTEINE OF CONCEPTS. 
 
 •what did not agree with the features of the accnsed, he 
 was therefore incompetent to prove the identity or non- 
 identity reqtured ? This would not be allowed. For the 
 court would hold that a man might have a clear perception 
 and a clear representation of a face and figure, of which, 
 however, he had not separately considered, and could not 
 separately image to himself, the constituent elements. 
 Thus, even the judicial determination of life and death 
 supposes, as real, the difference between a clear and a 
 distinct knowledge : for a distinct knowledge lies in the 
 knowledge of the constituent parts ; while a clear knowl- 
 edge is only of the constituted whole. 
 
 " Continuing our illustrations from the human counte- 
 nance ; we all have a clear knowledge of any face which 
 we have seen, but few of us have distinct knowledge even 
 of those with which we are familiar ; but the painter, who, 
 having looked upon a countenance, can retire and repro- 
 duce its likeness in detail, has necessarily both a clear and 
 a distinct knowledge of it. Now, what is thus the case 
 with perceptions and representations, is equally the case 
 with notions; We may be able clearly to discriminate one 
 oonciept from another, although the degree of consciousness 
 does not enable us distinctly to discriminate the various 
 component characters of either concept from each other.'* 
 
 Clearness and Distinctness, with their opposites, were 
 first regarded as qualities of vision merely, being applied 
 only to objects as seen, their signification being afterwards 
 extended by analogy to the other senses, and finally to 
 Thought. The distinction between them, first fully pointed 
 out by Leibnitz, was admirably illustrated by Krug, in a 
 passage which is thus paraphrased by Hamilton. 
 
 "In darkness — the complete obscurity of night — we 
 see nothing, — there is no perception, — no discrimination 
 of objects. As the Kght dawns, the obscurity diminishes, 
 the deep and uniform sensation of darkness is modified, — 
 
THEIE QUALITY. 81 
 
 we are conscious of a change, — we see something, but 
 are still unable to distinguish its features, — we know not 
 what it is. As the light increases, the outlines of wholes 
 begin to appear, but still not with a distinctness suificient 
 to allow us to perceive them completely ; but when this 
 is rendered possible, by the rising intensity of the light, 
 we are then said to see clearly. We then recognize 
 mountains, plains, houses, trees, animals, etc., that is, we 
 discriminate these objects as wholes, as unities, from each 
 other. But their parts, — the manifold of which these 
 unities are the sum, — their parts still lose themselves in 
 each other; they are still but indistinctly visible. At 
 length, when the dayhght has ftdly sprung, we are en- 
 abled likewise to discriminate their parts; we now see 
 distinctly what hes aroimd us. But stUl we see as yet 
 only the wholes which lie proximately around us, and of 
 these, only the parts which possess a certain size. The 
 more distant wholes, and the smaller parts of nearer 
 wholes, are still seen by us only in their conjoint result, 
 only as they concur in making up that whole which is for 
 us a visible minumom. Thus it is, that in the distant for- 
 est, or on the distant hUl, we perceive a green surface ; 
 but we see not the several leaves, which in the one, nor 
 the several blades of grass, which in the other, each con- 
 tributes its effect to produce that amount of impression 
 
 which our consciousness requires Clearness and 
 
 distinctness are thus only relative. For between the ex- 
 treme of obscurity and the extreme of distinctness there 
 are in vision an infinity of intermediate degrees. Now, 
 the same thing occurs in thought. For we may either be 
 conscious only of the -concept in general, or we may also 
 be conscious of its various constituent attributes, or both 
 the concept and its parts- may be lost in themselves to con- 
 sciousness, and only recognized to exist by effects which 
 indirectly evidence their existence." 
 
 4* P 
 
82 THE DOCTRINE OF CONCEPTS. 
 
 The Adequacy of a Concept depends on the number 
 and the relative importance of the Marks which constitute 
 it, considered as more or less perfectly representing the 
 objects which it denotes. A Concept may be perfectly 
 Clear and perfectly Distinct, and stUI be a very Inadequate 
 representation of the class of things for which it stands ; 
 for it may connote but two or three out of the many 
 attributes which they possess, and even these two or three 
 may be relatively insignificant, or of trifling import as com- 
 pared with several of those which are omitted. The old 
 Concept of man, happily ridiculed by Aristotle, which 
 described him as a two-legged animal without feathers, is 
 Clear, for it enables us easily to distinguish man fi-om aU 
 other animals ; and it is Distinct, for its three Marks are 
 easily distinguishable from each other ; but it is very 
 Inadequate, as it omits man's crowning and peculiar at- 
 tribute as a rational being. We may have a xery Clear 
 and Distinct Concept of an detphamt, as a qvMdrwped Uwi 
 drinks through its nostrils; obviously, however, this is a 
 very Inadequate representation of that sagacious and gi- 
 gantic brute. 
 
 The difference between the artificial system of Botany 
 invented by Linnaeus and the Natural System of Jussieu 
 illustrates very well the importance of making a proper 
 selection, and taking a sufficient number, of attributes 
 wherewith to determine the classes of things which we 
 think. Every plant may be perfectly distinguished from 
 all other plants, and easily referred to its proper class, in 
 a system founded, like that of Linnaeus, exclusively upon 
 the number, situation, and connection of its stamens and 
 pistils. Such a system furnishes an easy mode of as- 
 certaining the names of plants, just as the alphabetical 
 arrangement of words in a dictionary is the easiest way 
 of enabling one to find any word that he wants. But 
 the arrangement is artificial and arbitrary, the number 
 
THEIE QUALITY. 83 
 
 and relative situation of the stamens and pistils in a plant 
 no more determining its leading and essential character- 
 istics, than the significance and mutual relations of words 
 depend upon the position which their initial letters happen 
 to occupy in. the alphabet. In the Natural System, these 
 prominent and essential attributes of plants are made to 
 mark out the classes into which they are divided, and 
 thus the relations which actually exist between the things 
 themselves stand out with the same relative prominence 
 in the thoughts wherein they are represented to conscious- 
 ness. The Concepts here not only denote their objects, 
 but represent them in a manner which approximates, though 
 distantly, the fdlness of Intuition. 
 
 The three merits of Clearness, Distinctness, and Ade- 
 quacy, which constitute the Quality of a Concept, pre- 
 suppose a reference to some standard, which, for the very 
 reason .that it is a standard, must be independent of our 
 Thought, — that is, not subject to arbitrary change in 
 Thought. Strictly speaking, every Concept consideired 
 merely as such, or as an individual Thought in conscious- 
 ness, must have its own degree of each of these merits, 
 and cannot change this degree without becoming a dif- 
 ferent Concept from what it was. Whatever faults may 
 be imputed to it when it is compared with some standard, 
 it may still be said of it, even in its present s!ate, that 
 it connotes something and denotes something, and thus 
 has all the essential characteristics which enter into our 
 definition of a Concept. Any change to which it may 
 be subjected is not an improvement of this Concept, but 
 the substitution of another in its place, banning different 
 Marks, and therefore denoting not the same objects as 
 before. Such a change or substitution can be required 
 only through a reference in Thought to some standard, to 
 which this Concept, or the Concept as it now stands, 
 does not conform, but to which it was previously implied 
 that it ought to conform. 
 
84 THE DOCTEIHE OF CONCEPTS. 
 
 There are two standards, one of the name and the other 
 of the thing, to one or the other of which every Concept 
 which the mirid can form is, at least tacitly, referred. 
 Words, which are the names of Concepts, are the means 
 of communicating our Thought to others ; and they cannot 
 perform this office imless they have the same signification 
 to the hearer as to the speaker ; tliat is, each name must 
 call up the same Concept in the minds of both. A Con- 
 cept may he faulty, then, not as a €oneept, (for in this 
 respecti or in reference to the mere Form of Thought, 
 one Concept is as good as another,) but because it has a 
 wrong name, whereby it improperly assumes to be the same 
 Thought which is designated by that name in the minds of 
 other persons generally. Thus it is that language, among 
 its other offices^ has an important influence in the regula- 
 tion and fixation of Thought. We do not classify things 
 and form Concepts of them arbitrarily, each one according 
 to Ws own preferences ; but the necessity of maintaining 
 intercourse with other minds imposes on us a constant 
 effort to approximate our Thoughts to theirs, — that is, 
 to the Thou^ts which th^ have fixed and established 
 for general use through stamping upon them certain names. 
 The Thoughts which I attach to the words church, state, 
 government, for instance, may be as correct and proper, 
 in themSelves considered, as the connotation which you 
 attach to them ; but it is a decisive objection to my mode 
 of thinking, if I attach these old and famihar names to 
 peculiar combinations of Thought which they never before 
 designated, and to which people generally do not now 
 give these appellations. Owing to the symbolic use of 
 language, in which, as already explained, words are em- 
 ployed as temporary substitutes for Thoughts, we are 
 continually learning and using words hefore we have fully 
 learned their meaning. Gradually, by a process of in- 
 duction, we accommodate our use of iJiese words to their 
 
THEIB QUALITY. 85 
 
 established usage ; and it is while thus learning, that our 
 Thoughts are said to be wanting in Clearness, Distinctness, 
 and Adequacy. In truth, it is not our Thoughts which 
 are thus faulty, but our apprehension of other people^s 
 Thoughts, or, what is the same thing, of the meaning 
 which they attach to certain words. My own Concepts 
 of church, state, &c. are Clear and Distinct enough, unless 
 indeed I now hear these words for the first time; but I 
 cannot clearly distinguish what I imperfectly understand 
 to be your Concepts of them from certain other kindred 
 or nearly allied Thoughts ; or I have but an Indistinct 
 knowledge of the several Marks which are connoted in 
 the Concepts which you and other men have of them ; 
 or my connotation of these Marks is Inadequate, — that 
 is to say, not so fUll as other people's. 
 
 The second standard to which our Concepts are referred, 
 when they are said to be deficient in Quality, is the class 
 of things which they denote, and which they consequently 
 ought to represent as perfectly as possible. Thus, every 
 artisan, through long use, has a more Adequate, Clear, 
 and Distinct Concept of each of the tools of his trade, 
 each of the objects which he works upon, and each of the 
 processes to which these objects are subjected-, than it is 
 possible for other persons to possess who have no special 
 familiarity with the business. The Concepts which these 
 other persons have may be perfect enough for the correct 
 use of language ; that is, they may apply the technical 
 names rightly. But when compared with the fiill and 
 accurate Notions which have been acquired by experts, 
 they appear to be, as they are, very imperfect representa- 
 tions of the things themselves. 
 
 The difference between these two standards to which all 
 Concepts, in respect to their Quality or degree of perfec- 
 tion, are referred, enables us to understand the distinction 
 which logicians long ago established between nominal and 
 
86 THE DOCTRINE OF CONCEPTS. 
 
 real Definitions. This distinction has been very imperfectly 
 apprehended by many, especially by those who, unable to 
 find any other mode of distinguishing the two sorts of 
 definition, have held that a Nominal one consisted only in 
 explaining the meaning of the word by synonymes, or by 
 unfolding its etymology. Such a process would be Gram- 
 matical rather than Logical; rightly considered, it is no 
 definition at all. A Nominal Definition is the digtinct 
 explication of aU the Marki which are connoted in the name 
 of the Concept hy general consent, as evinced in the vse 
 of language. But language is imperfect, and words in 
 common use often signify much less than exact science 
 requires. A Real Definition is a distinct explication of 
 all those Marks, and those only, which a careful examination 
 of the class of things denoted by the word proves to be both 
 Original and Essential. It is obvipus that the Nominal 
 and the Real Definition of a Concept will often coincide. 
 This is usually the case with the technical terms in every 
 science, especially those of recent origin, whose connota- 
 tions are usually determined with great care before their 
 names are invented. In other cases, as already explained, 
 the two definitions may difier very widely from each other. 
 The fiirther consideration of Definition, and of Division 
 also, as the subsidiary processes by which the Quality of 
 Concepts may be improved, must be postponed till after 
 we have treated of 
 
 3. The Relations of Concepts. 
 
 The Relation of Concepts, as already remarked, is a 
 technical phrase, which is imderstood to mean their Re- 
 lations to each other only, and not to the other forms of 
 Thought, which will be considered hereafter. 
 
 A series or hierarchy of Concepts, formed by successive 
 steps of Generification, like the one given in the table on 
 
THEIK RELATIONS. 87 
 
 page 72, represents a succession of Concepts as svJbordi- 
 nated to each other in their two Quantities of Extension 
 and Intension. But the names of the Second Intentions, 
 which express the Relations of these Concepts or classes 
 to each other, are given with primary reference to the 
 Extension only. Unless express notice is given to the 
 contrary, therefore, we shall always speak only of their 
 Relation in Extension. Of any two Concepts in such a- 
 series, that one is called the Superior, Higher, or Broader, 
 which has the greater Extension, — that is, which de- 
 notes the larger number of individual objects ; it may 
 also be called the Superordinate. The other, having less 
 Extension, or denoting fewer Individuals, is called In- 
 ferior, Lower, Narrower, or Subordinate. Thus, referring 
 to the table again, animal is Superior or Superordinate to 
 mammal, which, as included under it, or denoting fewer 
 individuals, is called Inferior or Subordinate. The Supe- 
 rior, also as the more general notion, and as obtained by 
 the process of Generification or throwing out Marks, is 
 called the Genus ; while the Inferior, as more specific, and 
 obtained by the process of Specification, or thinking in 
 Marks, is called the Species. These names being merely' 
 relative, it is evident that the same Concept is, at the 
 same time, a Genus to any lower Concept, and a Species 
 to any higher one. 
 
 The Highest or Broadest Concept in such a series, 
 denoting most individuals and connoting fewest Marks, is 
 called the Summum Genus ; heilce, it is defined by logi- 
 cians to be a Grenus which cannot leeome a Species. On 
 the other hand, the lowest Concept in the series, as deinot- 
 ing the least and connoting the most, is called an Infima 
 Species. In fact, it denotes individuals only, and not any 
 classes or Species of individuals ; therefore it is defined to 
 be a Spicies which camnot become a Genus. Each interme- 
 diate Concept, as we have just said, is a Species to those 
 
88 THE DOCTKINE OF CONCEPTS. 
 
 above it, and a Genus to those below it. Its next Higher 
 neighbor is called its proximate Genus ; and its next lower 
 one might be termed a proximate Species, though this term 
 is not in frequent use. 
 
 When the name of any Higlier Concept is apphed as the 
 name of a Lower one, or of an individual, it is called its 
 abstract name, or its denomination in the ahstract ; the pecu- 
 
 ,liar or proper appellation of this lower Concept or indi- 
 vidual is called its concrete name. Thus, animal is an 
 Abstract, and man the Concrete, name of a rational animal; 
 and again, relatively, man is the Abstract, and John the 
 Concrete, appellation of the individual, this man whom we 
 are speaking of. These names obviously have reference 
 to the Intension of the Concept, the Abstract name being 
 obtained by Abstraction, that is, by throwing out Marks, 
 and the Concrete signifying all the Marks taken together 
 (oonrcresco, grown together^, or the whole Intension. 
 
 According to another and more frequent use of language, 
 an " Abstract name " has a narrower signification than the 
 one here indicated, being apphcable only to one peculiar 
 Species of Higher Concept, instead of denoting the Abstract 
 
 'use of any Higher Concept whatever. What appears only 
 as a Mark o£ the Concept in its Lower or Concrete use, is 
 itself a Higher Concept ; and if its denotation is then 
 altered, — that is, if it no longer denotes things as before, 
 but only various Idnds and degrees of that attribute which 
 the Concrete term connotes, — it is then, and then only, 
 commonly called an Abstract term. Thus, to recur to the 
 instance already given, man connoting rational animal, we 
 may take rational instead of animal as the Higher Con- 
 cept ; and then, altering its denotation, we may understand 
 it to mean, not rational beings, but various kinds and de- 
 grees of rationality. Hence, such terms as rationaHty, 
 redness, whiteness, humanity, &c. are called Abstract 
 names. According to this use, an Abstract tei-m is one 
 
THEIB RELATIONS. 
 
 89 
 
 which denotes that which, in its Concrete apphcation, it cow- 
 noted; it is a Mark or attribute considered as a thing. 
 
 The Relations thus far explained, as arising from the 
 higher or lower position of a Concept in the series or 
 hierarchy to which it belongs, are all denominated Rela- 
 tions of jSwbordination. They may be aptly symbolized by 
 a series of concentric circles, thus : — 
 
 Here, A, having the greatest 
 extent, and so containing all the 
 others under it, represents the 
 Summum Genus ; while F, as 
 least extended, and denoting 
 only individuals, not classes, 
 represents the Infima -Species. 
 Any intermediate circle, C, is a 
 subaltern Genus or Species, be- 
 ing Genus to D and Species to B. 
 If we were to use the same diagram to symbolize the 
 Relations of Intension, since the two Quantities are in 
 inverse ratio to each other, the order of the letters would 
 be reversed. F, as connoting the most Marks or having 
 the largest Intension, would be the outermost circle, and 
 A, having the least Intension, would be the innermost or 
 smallest. 
 
 In general, and for practical purposes, the terms Sum- 
 mum Genus and Infima Species ai-e applied not in an 
 absolute, but only in a relative sense ; — relative, that is, 
 not to the totahty or the smallest class of all conceivable 
 things, but to the totahty or the smallest convenient class of 
 those things only which we are now thinking of; say, all the 
 objects of some particular science. Thus, in Zoology, «m- 
 mal is considered as the Summum Genus, no notice being 
 taken of vegetables and minerals ; and what is usually 
 termed a "Variety" or " Sub- Variety " — King Charles 
 Spaniel, for instance — ^ is an Infima Species. 
 
90 THE DOCTRINE OF CONCEPTS. 
 
 Absolutely speaking, logicians maintain that Summum 
 Genus and Infima Species are both unattainable, — that 
 they are limits of classification in Thought, which we can 
 approximate, but never reach. They express this impossi- 
 bility under the form of two Laws of Thought. The first 
 of these, called ithe Law of Homogeneity, aflSrms that things 
 the most dissimilar must, in some respects, be similar or 
 homogeneous ; and consequently, any two Concepts, how 
 unlike soever, may still both be subordinated imder some 
 higher Concept. Thus, animals and vegetables, distinct as 
 they are from each other, are both contained imder the 
 higher Concept organized natural objects. And even from 
 this connotation, if we subtract the Mark organized, the re- 
 liiainder wiU be a still higher Concept, natural objects, which 
 will include minerals, as well as animals and vegetables. 
 
 On this ground, Mr. Mansel and other logicians main- 
 tain that thing or entity, connoting but one attribute, exist- 
 ence (real or imaginary), which would seem to be an 
 absolute Summum Genus, is not thinkable. They deny 
 that it is a possible object of Thought, on the ground seem- 
 ingly that it does not contain a plurality of attributes. 
 But as reasons have already been assigned (page 61) why 
 a Concept, as actually thought by us, may have only one 
 attribute or distinguishing Mark, I cannot see why ens is 
 not thinkable, as distinguished from nihil, which has not 
 even this one attribute of (real or imaginary) existence, and 
 is therefore certainly not conceivable. That it is a very 
 vague and indefinite Thought, is admitted ; this is a conse- 
 quence of its connotation being reduced to a minimum. 
 But to say, that " distinguishable from nothing " is tanta- 
 mount to affirming that it is not distinguishable at all, seems 
 to me in this connection, or for the purposes of pure 
 Thought, a mere quibble. I can certainly think a dlflTer- 
 ence — that is, a relation — between being and no-bein^, 
 though only one term of the relation is positive, and tlie 
 
THEIR RELATIONS. 91 
 
 other is merely negative. The algebraist finds a very dis- 
 tinct relation between plus a and minus a, as the presence 
 of one in place of the other afiects the results of his calcu- 
 lation very sensibly ; and both these expressions are clearly 
 distinguishable from zero. It is too much of a paradox to 
 affirm that there is no difference in Thought between some- 
 iking and nothing. 
 
 About the second principle, called the Law of Heteroge- 
 neity, there is no dispute. According to this Law, things the 
 most similar must, in some respects, be dissimilar or hetero- 
 geneous ; and consequently, any Concept, however large 
 its Intension may be, may stiU have that Intension in- 
 creased, without thereby descending to individuals. What 
 is relatively an Infima Species, or considered as such for 
 the purposes of some particular science, may be again sub- 
 divided into two or' more, and so on indefinitely. Thus, 
 King Charles Spaniel may be subdivided into such Spaniels 
 one 'year old, and those of two years or older ; into those 
 horn in Europe, and those horn in America; into those ahove, 
 and those helow, three pounds in weight, &c. Though, as 
 Mr. Mansel remarks, " as far as the Laws of Thought are 
 concerned, it is permitted to unite in an act of conception 
 all attributes which are not contradictory of each other, it 
 is impossible in practice to go beyond a very Hmited num- 
 ber. The number of attributes in the universe not logically 
 repugnant to each other is infinite ;. and the mind can there- 
 fore find no absolute limits to its downward progress in the 
 formation of subordinate notions." * 
 
 The Relation of Co-ordination exists between different 
 Species which have the same Proximate Genus ; two or 
 more Species are thus said to be Co-ordinate when each 
 excludes the other from its own Extension, but both or all 
 are included under the Extension of the same nearest 
 Higher Concept. For instance, dog, wolf, cat, lion, hear, 
 
 * Prdkgamma Logka, p. 169. 
 
92 THE DOCTRINE OF CONCEPTS. 
 
 &c. are Co-ordinate Species under the same Genus, Cwr- 
 nivora ; each excludes the other, — what is wolf is not eat, 
 — but all alike are Carnivora. As the two Quantities of a 
 Concept are in inverse ratio, and as, in reference to Ex- 
 tension, the Species is contained under the Grenus, so, in 
 reference to Intension, the Genus is contained in the Spe- 
 cies. Thus, the Intension of every Species contains the 
 Genus,' — that is, the aggregate of Marks which charac- 
 terize the Genus, — and the Specific Difference, — that is, 
 the aggregate of Marks by which this Species is distin- 
 guished both from the Genus to which it is Subordinate, 
 and from the other Species with which it is Co-ordinate. 
 Man is a rational animal: — here, animal expresses the 
 Genus to which man belongs, and rational is the Specific 
 Difference whereby man is distinguished from other Species 
 of animals. 
 
 Two things may be said to be generically different, when 
 they belong to different Genera ; gpecifieaUy different, when 
 they belong to different Species ; individually or num£ri- 
 cally different, when they do not constitute one and the 
 same reality. But as every member of the hierarchy, 
 except the highest and the lowest, may be viewed indif- 
 ferently as either Genus or Species, generic difference and 
 specific difference are only various expressions for the same 
 thing. 
 
 " Individual existences," as Krug remarks, " can only 
 be perfectly discriminated by external or internal Percep- 
 tion, and their numerical differences are endless; fcr of 
 all possible Contradictory attributes, the one or the other 
 must, on the principles of Contradiction and Excluded 
 Middle, be considered as belonging to each individual 
 thing. On the other hand, Species and Genera may be 
 perfectly discriminated by one or few characters. For 
 example, triangle is distinguished from every Genus or 
 Species of geometrical figures by the single character of 
 
THEIR DEFINITION AND DIVISION. 93 
 
 trilaterality. It is, therefore, far easier adequately to de- 
 scribe a Genua or Species than an Individual ; as, in the 
 latter case, we must select, out of the infinite multitude 
 of characters which aii Individual comprises, a few of the 
 most prominent, or those by which the thing may most 
 easily be recognized." We may describe, but cannot dejine, 
 an Individual, as there woidd be no end to the enumera- 
 tion of its peculiar attributes. In such case, the only 
 adequate definition is a view — an Intuition — of' the thing 
 itself. Omnis intuitiva notitia est definitio. 
 
 The other Relations of Concepts to each other may be 
 very briefly indicated. Concepts dre said to intersect, 
 when the Extension of one coincides in part, and only in 
 part, with the Extension of the other. Thus, Frenchman 
 and Protestant are Intersecting Concepts, for some French- 
 men are Protestants and some are not, some Protestants 
 are Frenchmen and some are not. These may be sym- 
 bolized by two circles whose circumferences cut or intersect 
 each other. Exclusive Concepts — animal and vegetahle, 
 for instance — do not coincide in any part of their Ex- 
 tension, and may therefore by symbolized by two circles 
 which he wholly apart the one from the other. Recip- 
 rocating, Convertible, or Coextensive Concepts are those 
 which have precisely the same Extension, as living being 
 and organized being, since everything which lives is or- 
 ganized. Two circles of the same diameter, and laid one 
 upon the other so as to coincide throughout, would aptly 
 represent Convertible Concepts. 
 
 4. Definition and Division. 
 
 It has already been said, that a Concept is internally 
 Distinct when we can fully enumerate and clearly distin^ 
 guish firom each other all its original and essential Marks. 
 The process through which this is accompUshed is called 
 
94 THE DOCTRINE OF CONCEPTS. 
 
 Definition. Again, a Concept is externally Distinct when 
 we can folly enumerate all its subordinate Genera and 
 Species. This process is called the Division of the Con- 
 cept. Both processes have reference to one or the other 
 of the two standards, — the name and the thing, — by 
 which it is determined whether the Concept in our minds 
 is, what it purports to be, a faithfol copy or representation 
 of what is generally designated by that name, or a foil 
 enumeration of the original and essential attributes of the 
 class of things so designated. We will first consider 
 Definition of names only, Division relating only to classes 
 of things, the object of both processes being not to de- 
 termine and render distinct the Concepts which we already 
 possess, but to substitute others for them which shall more 
 perfectly answer our purposes. The Concept to be defined 
 should be called the definieTidum, the Definition itself 
 being the definientia. 
 
 A Definition consists primarily of two parts, the Proxi- 
 mate Genus and the Specific Difference of the Concept 
 defined; for these two elements, as we have just seen, 
 make up the whole Intension of every class. Thus, 
 camivor is a flesh-eating mammal ; the word mammal here 
 denotes the Proximate Genus, and flesh-eating the Specific 
 Difference which distinguishes carnivora from other mam- 
 mals. Such a Definition, however, is incomplete, as it is 
 further necessary to define the Genus which makes a part 
 of it ; and this can be done only by considering tliis Genus 
 (mammal) as a Species, and assigning to it its own Proxi- 
 mate Genus (the next higher one in the hierarchy), ani- 
 mal, and its Specific Difference, suckling its young. We 
 proceed in this manner tUl we have reached the Summiuh 
 Genus, each Specific Difference successively taken up be- 
 ing the Mark which was abstracted in the original process 
 of Generification, and the sum of these Diflferences being, 
 therefore, the aggregate of all the Marks which make up 
 
THEIR bEFINITION A^fD DIVISION. 95 
 
 the Intension of the Concept first proposed to be defined. 
 What may be called the secondary or proper Definition, 
 then, as before stated, is the distinct explication of all the 
 Marks which are connoted in the name of the Concept. 
 Thus, having successively defined dog as oamivor, camivor 
 as mammal, mammal as animal, and animal as thing, 
 annexing . in each case the corresponding Specific Differ- 
 ence, we then sum up all these Specific Differences, and 
 thus form the proper Definition consisting solely of these 
 Differences, — that is, of all the Marks which the de- 
 finiendum connotes. Hence it appears, that though the 
 defining analysis is of the Intension only, yet it is regu- 
 lated by the Extension, as the Extension determines the 
 order in which the Intension is resolved into the Marks 
 which are its elements. 
 
 It is obvious also, that Definition by Genus and Specific 
 Difference in all its successive steps supposes a previous 
 knowledge of the whole hierarchy of Concepts through 
 which it ascends, and therefore it only explicitly enu- 
 merates the Marks which were already implicitly known. 
 The Classification here precedes, and is the means through 
 which we form, the Definition. Usually, however, we 
 proceed in the inverse order of this process : we seek first 
 for the Definition, — that is, for a knowledge of all the 
 original and essential attributes of a class of things, — as 
 a -preliminary step towards determining the Classification, 
 or assigning the class to its proper place in a hierarchy 
 of Concepts. Here, the Definition is primarily of the 
 thing, and only secondarily of the name, the problem be- 
 ing how to determine the sum of the original and essential 
 characteristics of this class of things. The following are 
 the Rules usually given by Logicians for the solution of 
 this problem, — that is, for the proper formation of Defi- 
 nitions. 
 
 1. A Definition must be adequate ; that is, it must have 
 
96 THE DOCTRINE OF CONCEPTS. 
 
 precisely the same Extension as the thing defined. If 
 not, if the Predicate defining denotes more objects than the 
 Subject defined, the Definition is too Wide ; if it denotes 
 fewer objects, it is too Narrow. Thus, when a triangle 
 is defined " a figure having three rectilinear sides," the 
 Definition is too Narrow, as there are spherical triangles 
 to which it will not apply. If we say, " water is a com- 
 pound of oxygen and hydrogen," the Definition is too 
 Wide, as it includes not only water, but something else, — 
 a deutoxide of hydrogen. When this rule is complied 
 with, the Definition and the thing defined are Reciprocat- 
 ing or Convertible Concepts; consequently, everything 
 to which the Definition applies, and nothing to which it 
 does not apply, is the thing defined. When this is the 
 case, our Concept of this class of things has become per- 
 fectly Clear, or distinguishable from all other Concepts. 
 
 2. The Definition must not be tautological ; that is, it 
 must not contain the name of the thing defined, as this 
 is precisely the word which we are bound to explain. It 
 is equally a violation of this rule to allow any of the 
 derivatives of this name, or any of its correlative notions, 
 either one of which can be explained only through the 
 other, to constitute a part of. the definition. This feult is 
 called " defining in a circle." Lexicographers often feU 
 into it unawares, as when they define a hoard to be " a thin 
 plank," and then a plank to be " a thick board " ; or when 
 they say that life is "vitality, the state of being ahve, 
 the opposite of death." 
 
 3. A Definition ought not to proceed by Negative or 
 Disjunctive attributes, when it is possible to avoid bo'th. 
 You cannot teach me what a notion is, by merely de- 
 claring what it is not, or that it is one of several things 
 without indicating which one is intended. It is no real 
 Definition to say of parallels, that they ai-e " lines which 
 do not meet," or of oxygen, tliat it is " one of the gases 
 
THEIR DEFINITION AND DIVISION. 97 
 
 fit for respiration." But convenience often requires what 
 Logicians call division by dichotomy, in which a Genus is 
 divided into, two Species having Contradictory Marks ; that 
 is, one of these Species has, and the other has not, cer- 
 tain well-defined characteristics, the latter, of course, being 
 capable only of Definition by negation. Thus Cuvier, 
 having determined with great precision the attributes of 
 Vertebrated animals, found it convenient to regard all 
 other animals as Invertebrates, that is, as not possessing 
 these attributes. 
 
 4. A Definition must be precise, — that is, it must con- 
 tain nothing, unessential or superfluous. Thus, all Deriva- 
 tive Marks should be excluded as superfluous, after their 
 Originals have been enumerated; for they are virtually 
 contained in those Marks firom which they are deducible 
 by the necessary Laws of Thought, so that the mention 
 of them only cumbers the Definition without really enlarg- 
 ing it. That a triangle is half of a parallelogromi., is no 
 proper part of the Definition of a triangle, inasmuch as 
 it is a necessary consequence of this figure having three 
 sides and three angles. Unessential attributes are also 
 superfluous ; that man is SLfeatherless biped is an accident, 
 not an essential trait, of his humanity. Give him a coat 
 of feathers, and he is still man ; but deprive him of ration- 
 ality, and he is no longer himian. 
 
 5. A Definition must be perspicuous; for we define 
 only in order to make more clear, and obscure or figurative 
 expressions do not conduce to this end, but only increase 
 the difficulty. " Tropes and figures," says Krug, " are log- 
 ical hieroglyphics: they do not indicate the thing itself, 
 but only something similar." But many expressions, origi- 
 nally metaphorical, have ceased to be so through long 
 use in their secondary meaning. Their original significa- 
 tion has become obsolete, and no longer recurs to perplex 
 us. This is the case with nearly all the words which 
 
 5 
 
98 THE DOCTKINE OF CONCEPTS. 
 
 now denote mind and its operations, though they were 
 first applied only to what is material. 
 
 Dr. Thomson takes a wider view of Definition, as in- 
 cluding any Predicate which may be " useful to mark out 
 for us more clearly the hmits of the subject defined, and 
 is therefore capable of being employed as a Definition for 
 some thinker or other." " Any of the Predicates we 
 propose to include," he continues, " though not the absolute 
 Definition, not the Genus and Difference, may be em- 
 ployed as a Definition by some particular person, and may 
 to him ftdfil the purpose of the best logical Definition 
 which can be given, "and therefore ought, if possible, 
 to be comprehended under the same head." In conformity 
 with this view, he enumerates the following six sources 
 fi-om which convenient Definitions may arise. 
 
 "i. From Resolution, when the Marks of the definitum 
 are made its definition ; as in ' a pension is an allowance 
 for past services.' It is not necessary that the Marks 
 should be completely enumerated, — that the conception 
 should be strictly adequate, — but only that the Marks 
 should suffice for the identification of the Subject, as belong- 
 ing to it all and to it alone ; so that Aristotle's Property 
 would be included in it. ii. From Composition, the reverse 
 of the last method, in which the definitum, a conception of 
 which the component Marks are enumerated, stands Subject 
 to a Definition imphcidy containing those Marks ; as, ' those 
 who encroach upon the property of others are dishonest.' 
 iii. From Division, where we define the Subject by enumer- 
 ating its Dividing Members ; as, ' Britons are those who 
 dwell in England, Scotland, or Wales.' All the judg- 
 ments called disjunctives are under this head. iv. From 
 Colligation, the exact reverse of the last ; where the Divid- 
 ing Members of a conception are enumerated in the Subject, 
 and the divided conception itself added to define them ; as, 
 ' historical, philosophical, and mathematical sciences ai-e the 
 
THEIR DEFINITION AND DIVISION. 
 
 99 
 
 sum (i. e. are all, or equal) of human knowledge.' This 
 is the form which Inductive Judgments naturally assume. 
 V. From change of Symbol, where both Subject and Predi- 
 cate are syTnboHc conceptions, the latter being given as a 
 substitute for the former on a principle of expedience only ; 
 as, ' probity is honesty.' This is the nominal definition of 
 some logic-books, vi. Prom Casual Substitution, where 
 one representatfon is put for another on a principle of 
 expedience only, as serving to recall the Marks, which 
 both possess in common, more readily to the hearer's 
 mind ; as, ' the science of politics is the best road to suc- 
 cess in life ; pleasure is the opposite of pain.' 
 " Taelb of Definition. 
 
 e 
 o 
 O 
 
 By its In- 
 tension (or 
 Harks) 
 
 By its Ex- 
 tension (or 
 Sphere) 
 
 By Acci- 
 dental Co- 
 incidence 
 
 being unfolded, = i. 
 
 being reunited, = ii. 
 being divided, = iii 
 
 Eesolution, or 
 Definition 
 proper. 
 Compositiou. 
 
 Division. 
 
 being reunited, = iv. Colligation. 
 
 of a Symbol, = v. Nominal Defi- 
 nition. 
 
 Of Notation, =5 vi. Accidental Defi- 
 nition." 
 
 As absolute Definition resolves the Intension of a Con- 
 cept into its constituent Marks, so Division resolves the 
 Extension into its constituent Genera and Species. In its 
 most general acceptation, division is the separation of any 
 whole into its parts. But Logical Division, with which 
 alone we are here concerned, is such a separation of a Lo^- 
 cal Whole only, — that is, of a class containing Under it other 
 classes, which are regarded as its parts. An individual 
 is so called (in-divido) because it cannot be (logically} 
 divided ; the process of cutting it apart is properly called 
 Partition, not Division. The Mathematical or Integral 
 whole is such an individual, an4 can be sundered into its 
 
100 THE DOCTRINE OF CONCEPTS. 
 
 parts only by Partition. The parts of an Essential or 
 Physical whole, as they interpenetrate and inform each 
 other, cannot be separated at aU except in Thought. But 
 a Logical whole is itself a creation of Thought, formed 
 out of lesser wholes of the same kind, into which it can 
 be resolved by mental analysis. 
 
 By Partition, triangle may be resolved into smaller tri- 
 angles, or into angles and sides ; the former Partition may 
 be actual, while the latter can only be ideal, — that is, it 
 is possible only in Thought. By Division, on the other 
 hand, triangle is resolved into rectilinear and curvilinear 
 triangles, or into equilateral, isoacelee, and scalene triangles, 
 as these are Species comprehended under one Genus. 
 
 The Genus to be divided is called the divisum, and 
 the constituent Species into which it is resolved are the 
 dividing members (membra dividentia~). Agreeably to the 
 nature of a hierarchy of Concepts, tlie parts which result 
 from such a'Division are in themselves wholes containing 
 other parts under them, and the dividing process repeated 
 upon these is called a Subdivision. The same Concept 
 may likewise be differently divided from different points 
 •of view, each separate analysis proceeding on what is 
 technically termed its own fundamentum divisionis, or 
 peculiar Ground of Division. Thus, man may be divided 
 geographically into European, Asiatic, American, &c. ; or, 
 in reference to color, into white, red, and black men ; or, 
 in reference to religion, into Christians, Mohammedans, and 
 Pagans; — local position, color, and religion being here 
 the successive fundamenta divisipnis. So the books in 
 a library may be arranged either according to size, as 
 fohos, quartos, octavos, &c. ; or according to the languages 
 in which they are written, as Latin, French, English, 
 &c. ; or according to the subjects of which they ti-eat, as 
 tlieological, scientific, historical, &c. Perhaps the most 
 important point in the philosophy of the Classificatory 
 
THEIR DEFINITION AND DIVISION. 101 
 
 Sciences is the right selection of a fwndamentum divisioniSy 
 or Ground of Division. i 
 
 If a Division has only two parts or members, it is called 
 a dichotomy ; and if such a Dichotomy is exhaustive, as it 
 should be, these two members are evidently Contradictories 
 of each other ; for whatever is contained in one is thereby 
 excluded from the other, and the two, taken together, 
 constitute the whole. Accordingly, these two Dividing 
 Members can always be expressed under the formula B 
 and noi^B. Thus, in dividing triangle, instead of calling 
 the two members rectilinear and ewrvilinear, it is better 
 to denominate them rectilinear and non-rectilinear. A 
 Division into three members may be called a trichotomy ; 
 into many, a polytomy. 
 
 Logicians have commonly given the following Rules for 
 the proper Division of a Concept. 
 
 1, Each Division should have but one fundamentum 
 divisionis, by which every part of the process is regulated. 
 The intervention of more than one Ground of Division 
 in the same process is the 'Logical fault which is called a 
 Cross Division. Thus, a Division of man into European, 
 American, Negro, and Pagan is faidty, because the Ground 
 of Division for the first two Dividing Members is local 
 position; for the third, it is color; and for the fourth, it 
 is religion. The consequence of this blunder is, that the 
 same individual might be contained in each of the last 
 tlu-ee Members ; — for he may be at once American, Negro, 
 and Pagan. Whatever we may select as a Ground of 
 Division, it must evidently be a Mark or attribute of the 
 Divisum, and the number of distinct forms or varieties, 
 under wliich this attribute . appears in the class of Jhings 
 to be divided, will determine the number of Dividing 
 Members. One of the Dividing Members, however, and 
 but one, may be marked only by the absence of this 
 attribute. 
 
102 THE DOCTEINE OF CONCEPTS. 
 
 2. The Mark selected as the Ground of Division should 
 be an Essential attribute of the Divisum, and one which 
 has as many Derivatives, or which determines as many 
 of its other attributes, as possible ; otherwise, the Division 
 vriU be complex and purposeless. Thus, the color of the 
 hair is an unessential attribute of man; mankind might 
 be divided into a large nimiber of classes in this respect, 
 but as very few of his physical, and none of the intellectual 
 or moral, quaUties of a man can be inferred from the feet 
 that he has red, brown, or black hair, the Division would 
 he useless.. On the other hand, a classification of men 
 according to their nationality or race, their geographical 
 position, or their rehgion, is found to be an eminently 
 fruitful one, as many of their other attributes are found 
 in invariable connection with these leading characteristics, 
 so as to be readily determined by them. The purpose 
 for which a Division is made often determines the selection 
 of its Ground. Thus, soldiers may be conveniently divided 
 into cavalry and infantry, as this distinction is one of great 
 moment in military affairs ; but to divide men in general 
 into foot and horsemen would be absurd. 
 
 3. No Dividing Member must by itself exhaust the 
 Divisum ; and the Dividing Members, taken together, 
 must exhaust, and no more than exhaust, the Divisum. 
 As the Genus and the Co-ordinate Species into which it 
 is divided stand to each other in the relation of a whole 
 to its parts, the propriety of this rule is manifest. Man 
 cannot be divided into rational and irrational, for the one 
 class of rational beings includes all men, so that neither 
 of the Dividing Members is a part, or the residt of a 
 Division, properly so called. Again, as all the parts are 
 requirra to constitute a whole, if the Co-ordinate Species, 
 taken together, do not exhaust the Genus, the Division is 
 obviously unperfect ; one or more members remain to be 
 supplied. If, on the other hand, they overlap the Genus, 
 
THEIR DEFINITION AND DIVISION. 103 
 
 there is somewhere an excess, which ought to be sub- 
 tracted and referred to another class. Crovemment cannot 
 be divided into monarchical, aristocratic, and democratic; 
 as there is a fourth class, the mixed. The old Division 
 of the science of language into Grammar, Logic, and 
 Rhetoric is redundant, as Logic is concerned with the 
 laws of thought rather than of utterance, and therefore 
 properly belongs to the science of mind. 
 
 4. The Co-ordinate Species into which a Genus is di- 
 vided must be reciprocally exclusive; that is, no one of 
 them must, in whole or in part, contain any other. In 
 order to ascertain whether this rule, the propriety of 
 which is obvious, has been complied with. Logicians apply 
 the test of Dichotomy, to which any other Division, how- 
 ever complex, may be reduced. Thus, all the Co-ordinate 
 Species, B, C, D, E, &c., of any Genus, A, may be rep- 
 resented under any one of the formulas, B and nft-B ; C and 
 not^O ; B and not-B, &c. If the Dividing Members are 
 mutually exclusive, C, D, and E will each be found under 
 not-B ; B, D, and E, under not-C; B, C, and E, under 
 not^B ; and so on. This rule is violated in a Cross Divis- 
 ion, where, as we have already seen, the same individuals 
 may appear under two or more of the Dividing Members ; 
 and also when a Member of a Subdivision is improperly 
 co-ordinated with the Members of a primary Division. 
 This last fault, however, is properly ranked under the next 
 following rule. The ten Categories of Aristotle are now 
 generally condemned as a faulty Division, because the 
 last six of them are only subdivisions of the fourth, Relation. 
 " For the Category where is the relation of a thing to 
 other things in space ; the category when is the relation 
 of a thing to other things in time ; action and passion 
 constitute a single relation, — that of agent and patient" ; 
 &c. 
 
 5. A Division must proceed step by step, in regular 
 
104 THE DOCTRINE OF CONCEPTS. 
 
 order, from proximate to remote differences, not over- 
 Jeaping any step which is properly intermediate. In other 
 words, each Species, as it appears among the Dividing 
 Members, must emerge directly from the Division of its 
 own Proximate Genus. Divigio ne fiat per mltum vel hior- 
 tum. Even the ordinary Division of all natural objects 
 into animals, vegetables, and minerals is faulty in this re- 
 spect, its three Species not being properly co-ordinate, as 
 one step has been omitted. The primary Division should 
 be by Dichotomy into organic and inorganic things, animals 
 and vegetables appearing subsequently as a subdivision of 
 the organic. 
 
THE DOCTRINE OF JUDGMENTS. 105 
 
 CHAPTER V. 
 
 THE DOCTRINE OF JUDGMENTS. 
 
 I. The Predicables and the Categories. — 2. The Quantity, Quality, and Re- 
 lation of Judgments according to the Aristotelical Doctrine. — 3. The 
 Hamiltonian Doctrine of Judgments. — 4. The Explication of Propo- 
 sitions into Judgments. 
 
 JUDGMENT is that act of mind whereby the rela- 
 tion of one Concept to another, or of an individual 
 thing to a Concept, is determined, and, as a consequence 
 of such determination, that two Concepts, or the individual 
 thing and the Concept, are reduced to unity in Thought. 
 A Judgment expressed in words is a Proposition, the 
 two terms of the Jud^ngnt being called the Subject and 
 Predicate of the Proposition. The assertions, iron is mal- 
 leable, John is brave, determine a relation of agreement 
 between the two terms involved in each, whereby these 
 two are conceived as one, and thus expressed, malleable 
 iron, brave John. On the other hand, the Judgment, 
 quadrupeds are not rational, determines the relation of 
 disagreement between the two Terms, so that one is now 
 denied to be a Mark of the other, or, what is the same 
 thing, the negative Mark,, irrational, is now attached to 
 the Concept, quadruped. 
 
 As we have already defined a Concept to be a repre- 
 sentation of one or more objects through their distinctive 
 Marks, it is evident that Judgment is the process through 
 which Concepts are formed. In fact; to judge is to recog- 
 nize a particular Mark or attribute as belonging, or not 
 
 5* 
 
 * 
 
106 THE DOCTEINE OF JUDGMENTS. 
 
 belonging, to a certain object or class of objects. The 
 Judgment is not, strictly speaking, a comparison, but it 
 is the mental act of conjoining or disjoining two things 
 which results from a previous comparison of them with 
 each other, and a. consequent recognition of their agree- 
 ment or disagreement. Hence, as Hamilton remarks, 
 "every Concept is a Judgment fixed and ratified in a 
 sign " ; and, again, " a Concept may be viewed as an 
 implicit or undeveloped. Judgment ; a Judgment as an 
 explicit and developetf' Concept." Thus, the Concept 
 man, which has the four Marks biped, two-handed, rational, 
 animal, is the combined result of four separate Judgments 
 which affirmed each of these attributes to be characteristic 
 of man. Aristotle, the Father of Logic, seems to have 
 regarded Judgments as the primary elements, out of 
 which Concepts are formed ; for his whole system is based 
 upon an analysis of Judgments. Modem writers have pre- 
 ferred, as more convenient, and at least equally correct, 
 the view which has here been taken, that Concepts are 
 the elements of Judgments. In truth, each presupposes 
 the other. If it be asked which, in the order of the 
 mind's development, comes first, the answer is, neither; 
 but a partial and confiised apprehension of a thing, which 
 is a young child's substitute for a Concept, and which is 
 first cleared up by a succession of Judgments producing 
 Concepts properly so called. Judgment is not arbitrary 
 or dependent upon the will ; I must, in Thovght, alfirm 
 the union or the separation of the two Terms, according 
 as the relation of agreement or disagreement is perceived 
 to exist between them. Hence, the Judgment is always, 
 at least subjectively, true ; the Proposition, which is only 
 the verbal affirmation, may be either true or false, accord- 
 ing as it does, or does not, agree with the mental Judgment. 
 The mere succession or coexistence of two Thoughts in 
 the mind does not constitute a Judgment. I may think 
 
THE DOCTEINE OF JUDGMENTS. 107 
 
 first of man, and then of animal ; but no Judgment takes 
 place until I affinn in Thought a perceived relation between 
 them, — until I think man is animal. Such a relation can- 
 not be perceived between them unless one is regarded as 
 an attribute or determination of the other ; — that is, one 
 must be regarded as determining, and the other as- deter- 
 mined. For if both were viewed as determining, there 
 would be nothing determined ; and both cannot be deter- 
 mined, unless there is something determining them. Hence 
 there are three ngcessary parts of a Judgment ; — first, the 
 Concept or thing determined, which is called the BuJbjeat ; 
 secondly, the determining or attributive notion, which is 
 called the Predicate ; and, thirdly, that which expresses 
 the relation of determination between the Subject and the 
 Predicate is called the Copula. The Subject and Predicate 
 are called the Terms (termini) or Extremes of the Judg- 
 ment ; and the Copula may therefore be symbolized as a 
 straight line connecting the two points'which are its Terms 
 or ends. 
 
 Though a Judgment necessarily consists of two Terms, 
 it is nevertheless a single act of mind. There is a separate 
 act of mind, whereby I perceive or conceive each of the two 
 Terms taken separately ; but it is only one act by which I 
 perceive and affirm the relation between these two Teirms, 
 and thereby unite them into one process of Thought. 
 
 When the mental Judgment comes to be expressed in 
 words as a Proposition,- each of its three parts does not 
 necessarily appear as a distinct word. The idiom of lan- 
 guage often requires or enables us to express two, or even 
 all three, of them by a single word ; but, in accordance 
 with the general Postulate of Logic, that we must be al- 
 lowed to express all that is implicitly thought, we cannot 
 deal logically with the Proposition until its form is so modi- 
 fied as to allow all the three elements to appear separately. 
 Moreover, as has been already remarked, the Copula of a 
 
108 THE DOCTRINE OF JUDGMENTS. 
 
 Judgment, since it expresses the presemb union of two 
 thoughts now before the mind, must always appear as the 
 present tense of a verb, — usually of the verb to be : is or 
 IS NOT is commonly regarded as the only distinctive expres- 
 sion of the logical Copula. Thus the Propositions, the iun 
 shines ; pluit ; cogito, ergo sum ; he came yesterday ; John 
 will arrive ; if reduced to their logical form as Judgments, 
 must be thus expressed: the sun is shining; the rain is 
 falling; I am thinking, therefore I am existing ; he is the 
 person who came yesterday ; John is he who will arrive. In 
 each of these cases, all that precedes the Copula, is or am, 
 is the Subject, and all that follows the Copula is the Predi- 
 cate.* The substantive verb, when used as a Copula, 
 
 * Hence we perceive how nnfonnded is the objection which has been ma^o 
 to the science of Formal Logic, on the ground that it does not expound the 
 whole theory of reasoning, because it furnishes no explanation of an infer- 
 ence 80 obvious as this : — 
 
 A is greater than B ; 
 
 therefore, B is less than A. 
 
 But here the Predicate is not B or A, but " greater than B " and " less than 
 A " ; the meaning of these two expressions, therefore, belongs to the Matter 
 of Thought, with which, as a logician, I have nothing more to do than with 
 the meaning of A or B taken alone. That these two expressions have a 
 correlative meaning, is a fact which belongs to the science of language rather 
 than to that of Thought. Instead of regarding one of them as an inference 
 from the other, it would be more correct to say that the two are eqmralcnt 
 statements of the same fact ; they express one relation between two Con- 
 cepts. That two lines converge from A to B is only another way of saying 
 that the same two lines diverge from B to A ; there is but one thing to be 
 said, though there are two modes of saying it. In like manner, we may say, 
 but we do not argue, that 
 
 Socrat^ is the husband of Xantippe ; 
 
 therefore, Xantippe is the wife of Socrates. 
 
 God alone is omnipotent ; 
 
 therefore, no one is omnipotent but God. 
 In such cases, the second proposition is an interpretation of the preceding 
 one, not an ihfference from it. We learn from a dictionary, not from a 
 treatise on Logic, what dififerent phrases are equivalent statements of one 
 and the same Thought. 
 
THE DOCTRINE OF JUDGMENTS. 109 
 
 never means exists ; but the idea of existence, when it is 
 jtttended to be conveyed, forms the Predicate. He is, in 
 tlie sense of he exists, is lo^cally interpreted, he is existing. 
 Fuit Ilium ; Troy is that which has been, — is that which 
 exists no longer. 
 
 Logicians generally maintain that the Copula is precisely 
 equivalent to the mathematical sign of equality. In many 
 eases, this is undoubtedly true. If the Predicate is simply 
 a definition of the Subject, or if the Proposition in any 
 manner expresses the entire equivalence of its two Terms, 
 it can then be expressed in the manner of an equation. 
 Thus, Saltpetre = nitrate of Potash ; Alexander = the son 
 of Philip. But the two Terms of a Judgment are not 
 always convertible or equivalent. What is thought and 
 expressed is always a relation between the two Terms, but 
 is not always a relation of equivalence or identity. Some- 
 times, as in a negative Judgment, it is a relation of disa- 
 greement ;. sometimes the Predicate expresses merely one 
 attribute of the Sulgect, and then the relation is that of a 
 whole to its part, since only a portion of the Subject's In- 
 tension is affirmed of the Subject. When we say, the a/pple 
 is red, we do not mean apple = red, but only that a red 
 color is one out of many attributes of the apple, — is a part 
 of its Intension. In this case^ the Copula signifies rather 
 possession, to have, than equality, to he. The form of the 
 Judgment as thought is, the apple has a red color as one of 
 its many attributes. 
 
 It is evident, then, that : there are two classes of Judg- 
 ments, properly distinguished by Dr. Thomson as Substitu- 
 tive and Attributive. In Substitutive Jud^nents, the sign 
 pf equality may be used as the Copula ; the Predicate is 
 properly identified with the Subject, or made convertible 
 with it, and. therefore every attribute of the one may also 
 be affirmed of the other. If A = B, then every- a; of A 
 is aiso a; of B; all that is true of "Alexander" is also true 
 
110 THE DOCTRINE OF JUDGMENTS. 
 
 of " the son of Philip." But if the Judgment is only At- 
 tributive, the sign of equality cannot be used ; the two 
 Terms are not convertible, and consequently it cannot be 
 inferred that they possess the same attributes. Sweetness 
 or sourness is a quality of the apple, hut not of the red 
 color which belongs to the apple. 
 
 The distinction here explained is a valid and important 
 one in respect to Judgments considered simply as such, or 
 as mere phenomena of Thought, irrespective of any use to 
 be subsequently made of them in reasoning or other mental 
 processes. In Attributive Judgments, the Predicate is 
 actually thought only connotatively, as a Mark or attribute 
 of the Subject, and not denotatively, as the name of a class 
 of things. And hence Mr. Mill is led to maintain, that 
 such Judgments never express truths of classification, and, 
 therefore, that the generally received doctrine of Predica- 
 tion, that it consists in placing something in a class or ex- 
 cluding something from a class, is entirely unfounded. 
 " When I say that snow is white," he argues, " I may and 
 ought- to be thinkitig of snow as a class ; but I am certainly 
 not thinking of white objects as a class ; I am thinking of 
 no white object whatever except snow, but only of that, and 
 of the sensation of white which it gives me." 
 
 All this is granted. At the moment of forming the Judg- 
 ment, white is not consciously before the mind as the name 
 of a class of things. We then think of it only connotatively, 
 — only as a Mark. But it is still true that we originally 
 learned the meaning of the word white not only as a Mark 
 connoting a quality, but also as a Concept denoting a class 
 of things, — namely, white objects ; otherwise, it would not 
 be, what it certainly is, a Common Name of snow, milk, 
 chalk, and many other things. And though this its deno- 
 tative meaning — its Extension — is not consciously before 
 the mind when it is used as a Mark or as a Predicate, it is 
 still there potentially, and must be brought out or expressed 
 
THE DOCTRINE OF JUDGMENTS. Ill 
 
 when we attempt to found an inference upon this Judg- 
 ment, or to employ it as one of the premises in a syllogism. 
 To borrow Mr. Mill's own instance, — : if I am in doubt 
 whether Chimborazo is snow-covered, *I may reason 
 thus : — 
 
 All mo]intains of a certain altitude, and whose summits 
 are perpetually white, are snow-covered. 
 
 But Chimborazo's lofty summit is always white, — that 
 is, it is one of this class of mountains. 
 
 Therefore, Chimborazo is snow-covered. 
 
 As already observed (p. 64), "the distinction between 
 Concepts and Marks is not absolute, but relative; they 
 may be used interchangeably." That a Concept or Com- 
 mon Name is sometimes used only as a Mark, or with no 
 conscious reference at the moment to its denotation, is 
 surely no proof that it is always so used, or even that the 
 denotative meaning, or Extension, is not potentially present 
 in this very case, so that it may be revived, if need be, 
 and an inference founded upon it. Because words are 
 sonietimes used symbolically, or without spreading out in 
 Thought all their signification, it does not follow that they 
 are always so used, or that such use of them may not be 
 checked, and kept from falHng into error, by occasionally' 
 bringing up into consciousness what they always potentially 
 signify in Thought. It follows, then, that although a Judg- 
 ment, as actually thought, may not be a truth of classification, 
 and therefi^re that the Copula may not be equivalent to the 
 mathematical sign of equahty, yet it may always be reduced 
 to the form of such a truth, and then this mathematical 
 sign fully expresses its proper form; and in reasoning, 
 such a reduction is generally necessary. Though it is not 
 true that apple ^ red, it is true that apples = some red 
 olyects ; or, as it is more commonly expressed by Conver- 
 sion, some red objecAs are apples. 
 
112 the doctrine of judgments. 
 
 1. The Pkbdicables and the Categoeies. 
 
 In his analysis of Judgments, Aristotle was led to con- 
 sider how many kinds of Predicates there are, when 
 viewed relatively to their Subjects; — in other words, to 
 determine the Second Intentions of Predicates considered 
 in relation to Subjects. Thus was formed his celebrated 
 doctrine of the Predicables, — a doctrine which was con- 
 siderably modified, but not improved, by his fbUowErs, 
 Porphyry and the Schoolmen. According to Aristotle, 
 every Judgment afiirms or denies one of four relations of 
 a Predicate to its Subject. It expresses either, — 1. the 
 Genus, i. e. the class under which it is included, as when 
 we say, man is an animal; or, 2. the Definition, which, 
 as we have seen, is the Genus and the Specific Difierence 
 taken together, and may be reduced to an enxuneration 
 of aU the essential Marks of the Subject, as, a Camivor 
 is a flesh-eating Mammal; or, 3. a Property, that is, some 
 peculiar attribute of the Subject, belonging to it univer- 
 sally, belonging to nothing else, and yet not regarded as 
 essential to it, for we could conceive of the thing without 
 it, — as polarity is a Property (proprium') of the magrvA, 
 and risibility of man; or, 4. an Accident, which is an 
 attribute that happens to belong to the Subject, but, as 
 unessential, is separable from it, as man is learned. 
 
 Two of these Predicables, namely, the Definition and 
 the Property, are convertible with the Subject, or may 
 change places with it ; and of these two, the former ex- 
 presses the whole Essence (all the essential qualities), while 
 the latter, strictly speaking, is no part of the Essence ; for 
 we can conceive of man as not having the attribute of 
 risibility, but we cannot conceive of him as deprived of 
 rationality. So, the magnet can be conceived of without 
 polarity, as its magnetic or attractive power was known 
 long before its property of pointing to the north was dis- 
 
THE PBEDICABLES AND THE CATEGORIES. 113 
 
 covered ; but its magnetic or attractive quality is essentia] 
 to our conception of it. Of the two other Predicables, 
 Genus and Accident, neither is convertible with the Sub- 
 ject ; and, again, the former expresses a part of the Essence, 
 and the latter does not. Thus we have the following 
 scheme of the Predicables : — 
 
 Definition expressing the whole Essence ) convertible 
 
 Property expressing no part of the Essence y with the Subject. 
 
 Genus expressing a part of the Essence ) inconvertible 
 
 Accident expressing no part of the Essence | with the Subject. 
 
 Porphyry and the Schoolmen modified this analysis, but 
 did not improve it, in their attempt to make it conform 
 to their philosophical doctrine of Realism. The Realists 
 maintained, that Universals or Species are not mere classes 
 of things arbitrarily formed by the mind, but are real exist- 
 ences, with perfectly w^ll-defined limits, existing in things, 
 and yet independently of them and of our conceptions 
 of them. Each Universal is the common and essential 
 element — the Essence — of all the individual things which 
 are included under it and denoted by its Name. What- 
 ever other attributes these individuals possess do not belong 
 to their Essence, but are considered as their Properties 
 or Accidents. According to this view, Species has a de- 
 terminate and fixed meaning, corresponding very nearly 
 to what we have termed the Infima Species; it was 
 absolutely the lowest class to which anything can be re- 
 ferred, and not merely the lowest relatively, as we have 
 defined it. Every Specific Difference, moreover, signifies 
 absolutely the attribute whereby a given Species is dis- 
 tinguished fi:om every other Species of the same Genus. 
 Both Species and Genus are thus supposed to be absolutely 
 determined, following the patterns or archetypes of them 
 which exist in the Divine Mind, and which presided over 
 their creation, instead of being mere creatures of om- 
 Thought, and springing from arbitrary classifications, ac- 
 
114 THE DOCTEINE OF JIJDGMENTS. 
 
 cording to which the same individual may be referred to 
 any one of several different Species, and again the same 
 Species to one Genus or another, according as it suits our 
 purpose. The Realists maintained that the hierarchy of 
 classification is not fluctuating and arbitrary, formed by 
 man for his own convenience, and therefore always chang- 
 ing to suit his ever- varying purposes ; but they held that 
 it resulted fi-om the real nature of things, as determined 
 by the Creator, and therefore is a perfect and immutable 
 copy of the Divine Thought. To adopt Mr. Mill's lan- 
 guage, "they did not admit every class which could be 
 divided into other classes to be a Genus, or every class 
 which could be included in a larger class to be a Species. 
 Animal was by them considered a Genus; and man and 
 brute, co-ordinate Species under that Genus : biped would 
 not have been admitted to be a Gtenus with reference to 
 man, but a proprium or acddens only. It was requisite, 
 according to their theory, that Genus and Species should 
 be of the Essence of the Subject. Animal was of the 
 Essence of man; biped was not. And in every classifi- 
 cation, they considered some one class as the lowest or 
 Infima Species ; man, for instance, was a lowest Species. 
 Any other divisions into which the class might be capa- 
 ble of being further broken down, as man iato white, black, 
 and red man, or into priest and layman, they did not 
 admit to be Species." They wrongly assumed, — 1. that 
 the Divine Mind classifies at all (see p. 15); 2. that it 
 would be possible for man to follow the thought of the 
 Creator so far as to copy without error such classification, 
 even if it existed ; 3. that there m no occasion, even for 
 pmrposes of human science and convenience, to distribute 
 the same individual things into different systems of clas- 
 sification, assuming various Grounds of Division, according 
 to the special ends in view. 
 
 Adopting the Realist hypothesis, the Schoolmen distin- 
 
THE PBEDICABLES AND THE CATEGORIES. 115 
 
 guished these five Predicables, — Genus, Species, Difier- 
 ence. Property, and Accident. Comparing this hst with 
 that of Aristotle, we perceive that Definition is omitted, 
 — - being resolved into its two elements. Genus and Specific 
 Difierence, both of which are admitted into this scheme, — 
 and that Species also is added. The Species here intended 
 is the Infima Species, or proximate class, and is usually de- 
 fined as being the whole Essence of the individuals of 
 which it is predicated. Difference is also taken abso- 
 lutely, being regg,rded as predicable of this class and of 
 none other, — that is, as serving to distinguish this Species, 
 not merely from the other Species in the same Genus, but 
 from all others whatever. Aristotle omitted Difference 
 from his hst, because, as he says, it is ^' of the nature of 
 Genus," or, as we should say, it is interchangeable with 
 Genus. In truth, each of the two elements of a Definition 
 is a Genus ; they are two communicant or overlapping 
 Genera. But it is more convenient to, regard one as de- 
 termined, and the other as determining, — that is, one as 
 Genus and the other as Difference. Thus, man is a ra- 
 tional animal; here are two Genera, rational beings and 
 amntal idnga,, which partially include, and partially ex- 
 clude, each other. As there are some rational beings 
 which are not animal (angds, for instance), so there are 
 some animals (brutes^ which are not rational ; but man is 
 both animal and rational, — that is, he is the common part 
 of the two overlapping Genera. He is, therefore, a rational 
 animal being, or, what is precisely the same thing, he is an 
 animoclized rational being. In the former case, animal is the 
 Genus and rational is the Specific Difference ; in the latter 
 case, this is reversed, rational 
 being the Genus and animal 
 the Difference. Thus : — 
 Let A = animal ; 
 B := rational ; 
 then, C ^ rational animal. 
 
116 THE DOCTRINE OF JUDGMENTS. 
 
 Aristotle evidently perceived, what his followers did not, 
 that there is no real distinction between Genus and Differ- 
 ence ; that both of them are, in truth. Genera ; and hence 
 that Difference, being of the nature of Genus, cannot be 
 admitted into the list of distinct Predicables. 
 
 Having ascertained the Second Intentions of Predicates, 
 which are the Predicables, Aristotle attempted to carry the 
 analysis of Judgments one step farther, by determining their 
 First Intentions, and was thus led to form his celebrated 
 list of the ten Categories or Predicaments. In other words, 
 having determined hyw many sorts of Predicates there are 
 in relation to their Subjects, he next inquired Jioto mary 
 and what particular things may be predicated of any Sub- 
 ject. Considering every Judgment as the answer to a 
 question, he sought to ascertain how many and what dif- 
 ferent questions may be asked concerning a Subject, — what 
 are the several determinations of which it is capable. The 
 inquiry evidently concerns the Matter, and not the Form, 
 of Thought, and therefore does not properly fall within the 
 province of Logic, which is exclusively occupied with Sec- 
 ond Intentions. But the Categories may be regarded as a 
 curiosity in the, history of the science, and as a monument 
 of the genius of its founder for abstract thonglit and com- 
 prehensive gerferalization. Great ingenuity has been 
 wasted upon the discussion of them by his followers. For 
 many centuries, during which the boundaries of the science 
 were not so strictly defined as they now are, the doctrine 
 of the Categories occupied a prominent place in every 
 treatise upon Logic. A very brief explanation of it will 
 answer our present wants. 
 
 The Greek verb from which category is derived properlv 
 signifies to accuse, or to affirm something of any one, and 
 hence, to predicate. But the noun has been diverted by 
 logicians from signifying affirmation or predication, and 
 applied to a list or class of things of the same kind which 
 may he predicated of any Subject. Aristotle affinns that 
 
THE PEEDICABLES AND THE CATEGORIES. 117 
 
 there are ten Categories, or classes of things that may be so 
 predicated, — namely, 1. Substance ; 2. Quantity; 3. Qual- 
 ity ; 4. Relation ; 5. Place ; 6. Time ; 7. Posture ; 8. Pos- 
 session ; 9. Action ; 10. Passion. According to a fashion 
 very common among the Scholastic logicians, of manufac- 
 turing Latin verses as aids to the memory in retaining the 
 technicalities of the, science, the several Categories are in- 
 dicated in the two following lines, though in a somewhat 
 different order from that given above, as shown by the 
 numerals prefixed. 
 
 1.23 4, 9 10 
 
 Arbor sex servos fervore refrigerat nstos ; 
 
 8 6 7 S 
 
 Ruri eras stabo, nee tunicatus ero. 
 
 The four Predicables, argues Aristotle, — " the Accident, 
 the Genus, the Property, and the Definition, — will always 
 be in one of these Categories [or classes] ; since, through 
 •these, all propositions signify either what the Subject is, or 
 how much it is, or what sort of a thing it is, or som§ one of 
 the other Categories"; as, what relation it bears to some 
 other thing, or its place, its time, its posture, what it has, 
 or does, or suffers. Adopting Aristotle's own examples of 
 predication under each of these classes, we may, for in- 
 stance, affirm of anything, — 1. under the Category of 
 Substance, that it is a mxm, a horse, or the like ; 2. mider 
 that, of Quantity, that it is two cubits long, three cubits, 
 &c. ; 3. under that of QuaHty, that it is white, grammat- 
 ical, &c. ; 4. under that of Relation, that it is double, half 
 as large, greater, &g. ; 5. imder that of Place, in the 
 Jjyceum, in the Forum, &c. ; 6. under that of Time, t/es- 
 terday, last year, &c. ; 7. under Posture, standing, seated, 
 &c. ; * 8. under Possession, having shoes or armor, &c. ; 
 
 * Many writers have interpreted Aristotle's seventh Category, KfluBm, as 
 Situation. But, as Situation is identical with Place, this interpretation makes 
 the seventh redundant and unnecessary. Besides, the examples here selected 
 prove that Aristotle here understands KeiarOai to signify Posture. 
 
118 THE DOCTRraE O^F JUDGMENTS. 
 
 9. under Action, it cuts, burns, &c. ; 10. under Passion, 
 it is cut, is burned, &c. 
 
 The purpose of Aristotle in framing his scheme of the 
 Categories, and the nature of the Categories themselves, 
 have been very differently understood by different writers, 
 ■who, in commenting upon them, seem to have had much 
 more reference to their own systems of metaphysical phi- 
 losophy than to a feir interpretation of the text of their 
 author. Thus, Kant assumes that Aristotle's intention was 
 to form a complete list of the a priori conceptions of the 
 intellect, or of the forms which the mind imposes upon 
 things by its own mode of thinking them. Under this in- 
 terpretation, he asserts very truly, that the analysis is not 
 formed upon any one principle ; that the enumeration is 
 incomplete ; that empirical notions are intruded among the 
 pure, and derivative among those which are original. 
 
 Mr. Mill supposes that the Categories are " an enumera- 
 tion of all things capable of being named, — an enumera- 
 tion by the summa genera; that is, the most extensive 
 classes into which things could be distributed ; which, 
 therefore, were so many highest Predicates, one or other 
 of which was supposed capable of being affirmed with 
 truth of every namable thing whatsoever." Taken in 
 this light, he finds, of course, that the list is both redun- 
 dant and defective ; that Relation includes Action, Passion, 
 and several others ; and that " mental states," which, in 
 Mr. Mill's opinion, are neither substances nor attributes, 
 are omitted entirely. 
 
 Sir William Hamilton's interpretation of the Categories 
 agrees very nearly with that of Mr. Mill. He finds that 
 they are an enumeration of the highest genera of Being 
 or Existence, — that is, of all things whatsoever ; and, 
 under this view, justly objects that 'Being ought first to be 
 divided by dichotomy, into absolute and rdative Being, 
 the first of which coincides with Aristotle's first Categoiy, 
 
THE PEEDICABLES AND THE CATEGORIES. 119 
 
 that of Substance, while the second includes the other 
 nine ; and that the last six may all be reduced to the 
 fourth, that of Relation. 
 
 Trendelenburg, who is followed by Mr. Mansel, main- 
 tains that the Categories are, to adopt the language of the 
 latter, " an enumeration of the different modes of naming 
 things, classified primarily according to the grammatical 
 distinctions of speech, and gained, not from the observation 
 of objects, but from the analysis of assertions." This 
 doctrine seems to be correct ; but it is obviously irrelevant, 
 for it explains only the genesis, not the nature, of the 
 Categories. To show the source of the classification, or 
 how Aristotle was led to make it, is very different from 
 explaining the nature of the things classified, and the real 
 distinctions between the several classes. 
 
 And the ground for the other criticisms falls away when 
 it is considered, that the distinction between the Form and 
 the Matter of Thought — that is, between Logic and 
 Metaphysics — is but very imperfectly preserved by Aris- 
 totle. But although much of what properly belongs to 
 Metaphysics is intruded into his treatises upon Logic, and 
 vice versa, it is never considered there primarily in its 
 metaphysical nature, but only in its logical relations. The 
 doctrine of the Categories, as conceived by him, is not 
 an attempt to enumerate the highest classes into which 
 thinffs in genenal can be distributed; for this would be a 
 purely metaphysical speculation, and, as such, open to 
 criticism on metaphysical grounds. But it is a classification 
 of things in so far only as these things are predicates, -■ — 
 that is, of things considered merely in one of their logical 
 aspects. To such a classification, metaphysical objections, 
 like those of Kant, Mill, and Hamilton, are evidently 
 irrelevant. For instance: — metaphysically, Place is in- 
 cluded under Relation, for it is the relation of a subject 
 to a fixed point in space. But, logically, these two Cate-" 
 
120 THE DOCTRINE OF JUDGMENTS. 
 
 gories are distinct , for it is one thing to assign a Subject 
 to a fixed point in space ; a second, to assign its relation to 
 another thing La quantity or quaUty ; and a third and fourth, 
 to assign its quantity and quality absolutely. Aristotle's 
 scheme or general conception of the Categories may be 
 censured, as depending on a mixture of two incongruous 
 aspects of Thought, the logical and the metaphysical ; but 
 for all that app^rs, it is as well executed as such a hybrid 
 scheme can be. 
 
 2. The Quantity, Quality, and Relation of Judg- 
 ments, ACCORDING TO THE AmSTOTELIC DoCTEINE. 
 
 The question now arises, how many things can be de- 
 termined about a Judgment considered merely as such, — 
 that is, by considering its mere Form, without reference 
 to the Matter of the Concepts which are its Terms. In 
 the first place, we may inquire concerning the number 
 of objects about which we judge, and thus determine the 
 Quantity^ or Extension, of the Judgment. Secondly, we 
 may ask what sort of a Judgment we form respecting the 
 two Terms, — that is, whether we affirm a relation of 
 agreement or of disagreement between them; we thus 
 ascertain the Quality of the Judgment, or whether it is 
 affirmative or negative. Thirdly, we may inquire respect- 
 ing the different modes in which a relation of agreement 
 or difference between the two terms may be affirmed, and 
 thus determine what is called the Relation of a Judgment. 
 In this manner are answered the three questions which 
 may be asked concerning any Judgment or Proposition 
 whatsoever, — Quanta? qualis? quce? 
 
 A fourth question has generally been asked by logicians, 
 as to the degree of certainty with which a Judgment is 
 afiumed. This was called the Modality of the Judgment, 
 being the mode or measm-e in which we hold it to be true. 
 
THEIH QUANTITY, QUALITY, AND RELATION. 121 
 
 Several degrees of it were usually distinguished, according 
 to the following formulas : — 
 Judgments are either 
 
 Pure A is B. Assertorical. 
 
 QP ^ A may be B. Contingent or Problematic. 
 
 MfiHal ) -*■ """' ** ^- Necessary. > 
 
 S A cannot be B. Impossible. ; DemonstratiTe. 
 
 ^ A can be B. Possible. 
 
 But the whole doctrine of Modality is now rightfully 
 banished from Pure Logic, as it evidently belongs not to 
 the Form, but to the Matter, of Thought. Any number 
 of Modal Propositions may be framed, all of which would 
 have as good a claim to consideration as those just specified. 
 Thus, A is rightfully B, A is justly B, A is maliciously 
 B, are as good Modals as A is possibly B, or A is certainly 
 B. In truth, since the Copula in Logic is only a sign 
 of equality, or ^e present tense of the verb to be, the 
 qualifying word must be logically regarded as a portion 
 of the Predicate ; thus, A is a possible, or a necessary B. 
 Hence it is manifest that the signs of Modality belong 
 to the Matter of the Thought, with which here we have 
 no concern. 
 
 In respect to Quantity, according to the Aristotelic 
 logicians, Judgments are either Universal or Particular. 
 A Universal Judgment is one in which the Predicate is 
 affirmed of the whole Subject taken distributively. Thus, 
 All men (i. e. each and every man) are mortal ; No quad- 
 ruped (i. e. not any one out of all quadrupeds) is rational; 
 are Universal Judgments. 
 
 A Particular Judgment is one in which the Predicate 
 is affirmed only of a part — an indefinite part — of the 
 Subject. For example: Some men (i. e. some at least, 
 some — I know not how many') are learned; Some trees are 
 not deciduous. 
 
 On the other hand, «^^ taken collectively (as, All the 
 Qreeks — i. e. the Greek nation — conqaered the Persians'), 
 •fi 
 
122 THE DOCTRINE OF JtfDGMENTS. 
 
 is the sign of a Singular or Individual Judgment, in which 
 a Predicate is affirmed of one thing, or of a class of things 
 taken as one whole. But as here also the Predicate is 
 affirmed of the whole Subject, Singular Judgments, for all 
 logical purposes, are considered as Universals. 
 
 In like manner, some certain — tome, a definite part — 
 embracing these very cases which I am thinking of and 
 no other — is the sign, not of a Particular, but of a 
 Singular Judgment, and is therefore properly ranked with 
 Universals. 
 
 " Individual names," says Mr. Mansel, " are distin- 
 guished as individua signata, expressed by a proper name, 
 as Socrates ; individua demonitrativa, by a demonstrative 
 pronoun, hie homo ; individua vaga, by an indefinite pro- 
 noun, aliquis homo, quidam homo." But he properly ob- 
 jects that this last class, the indefinites, ought to be consid- 
 ered as Particulars rather than as Singulars. " If we say 
 quidam conscionatur, quidam legit, there is no evidence that 
 the same person is spoken of in the two propositions ; while 
 Socrates, except by a mere quibble, will always designate 
 the same person. There may, indeed, be two persons of 
 the same name ; but, in this case, the name fails to accom- 
 plish the intended distinction, and we must specify, — Soc- 
 rates the son of Sophroniscus." 
 
 The logicians formerly distinguished another class of 
 Judgments as Indefinite, meaning those in which the Sub- 
 ject, having no sign or predesignation of Quantity affixed 
 to it, is not expressly declared to be either Universal, Sin- 
 gular, or Particular. Thus, Elephants are sagacious ani- 
 mals ; — Learned men are to be found at Oxford. But tliis 
 omission of the prbdesignation of Quantity is merely an 
 accident of expression, and therefore belongs only to Propo- 
 sitions, and not to Judgments, which are always thought as 
 having some one of the three specified kinds of Quantity. 
 According to the Postulate of Logic, which requires us to 
 
THEIR QUANTITY, QUALITY, AND RELATION. 123 
 
 state explicitly all tliat is implicitly thought, the two exam- 
 ples just given are logically stated thus : All elephants are 
 sagacious ; — Some learned men are found at Oxford. 
 
 An improTed classification or nomenclature of Judgments 
 in respect to Quantity is proposed by Sir Wilham Hamilton. 
 Since both Universals and Singulars have a determinate or 
 known Quantity, — namely, the whole either of a class or 
 of a unit, — he would call them Definite Judgments ; while 
 Particulars, expressing an indeterminate or unknown part 
 of a whole, should be called Indefinite. But as confiision 
 might arise from abandoning technical terms which have 
 been so long in use, we shall continue to distinguish Judg- 
 ments in respect to Quantity as either Universal or Partic- 
 ular, Singular being ranked with the fottner, and the latter 
 expressing an indefinite part. 
 
 in respect to Quality, Judgments are distinguished as 
 either Affirmative or Negative, according as they aifirm a 
 union oj? a disjunction of their two Tenns. In every real 
 Negative Judgment, the negative particle, wherever in 
 the sentence it may appear, belongs only to the Copula ; 
 dnce the question always is, whether a union of the 
 Subject and Predicate is, or is not, affirmed. Hence the 
 presence of a negative particle in the proposition is not a 
 sure sign that it is a Negative Judgment, for this particle 
 may belong in thought to one of the two Terms. Thus, 
 
 " Nil admirari prope res est una, Numici " ;* — 
 " Not to admire is all the art I know " ; — 
 '1 " :ffineas potult — non vincere Turnum " ; — 
 
 are Affirmative Judgments. This, also, is an affirma- 
 tion: 
 
 " Una sains yictis — nuUam sperare salutem." 
 
 " The only chance of preservation for the vanquished is, not to hope for 
 preservation." 
 
 Hence, by an easy artifice, a Negative Judgment may 
 be changed, in Form, to an Affirmative one of equivalent 
 
124 THE DOCTRINE OF JUDGMENTS. 
 
 meaning, by taking off the negation from the Copula, and 
 affixing it to the Predicate. Thus, X is not Y, is the 
 same as, X is not-Y; for if the universe is divided into 
 only two parts, Y and not-Y, the exclusion of X from one 
 of these parts is necessarily an inclusion of it in the other. 
 And as two negatives cancel each other, an Affirmative 
 may be made to take the Form of a Negative Judgment, 
 by negativing both the Copula and the Predicate. X is 
 Y, may be changed into, X is not not-Y. " The soul is 
 indivisible," is equivalent to " The soid is not divisible " ; 
 and " All the righteous are happy," is the same as " Not 
 any of the righteous are unhappy." We shall soon see 
 what use can be made of this artifice in the doctrine of 
 Immediate Inference. 
 
 By combining the Quantity and Quality, as there are 
 two kinds of each, we have four distinct forms of Judg- 
 ments, which are designated by the four vowels A, E, 
 I, O. To aid the memory, these distinctions have been 
 expressed in this Latin distich: — 
 
 Asserit A, negat 'E, sed nniversaliter tunbie, 
 Asserit I, negat O, sed particulariter ambo. 
 
 These lines have been thus translated into English dog- 
 gerel : — 
 
 A, it affirms of this, these, aU, 
 
 Whilst E denies of any; 
 I, it affirms, whilst O denies. 
 
 Of some (or few or many).* 
 
 Examples of these Propositional Forms, as they are 
 called, are given in the following table: — 
 
 Symbols. Examples. auality. Quantity. 
 
 A. AU animals are sentient. Affirmative. ) rr • 
 
 E. No plant is sentient. Negative. \ Umversai. 
 
 ■ I. Some men are honest. Affirmative. )-p . , 
 
 O. Some trees are not maples. Negative. | ■'^'"ticular. 
 
 * It is suggested by Hamilton, with great plansibiKty, that these font 
 letters were selected because A and I are the first two vowels in affmBo, E 
 and the two vowels in nyo. 
 
THEIR QUANTITY, QUALITY, AND RELATION. 125 
 
 Observe, however, that though the predesignation all 
 is the sign of A, a Universal Affirmative, not all is not 
 the sign of E, a Universal Negative, but is always Par- 
 ticular, and leaves the Quahty ambiguous, as it may be 
 either Affirmative or Negative. Ifat all denies univer- 
 sality, and is a direct assertion that some are not, and an 
 implied assertion that some are. Thus, Not all is gold that 
 glitters, asserts directly that some glittering things are not 
 gold, and, by implication, that some glittering things are 
 gold. "Not every one who says unto me, Lord! Lord! 
 shall enter into the kingdom of Heaven " ; — i. e. some 
 who say this shall not enter. 
 
 The predesignation some is likewise ambiguous. It may 
 mean some at least, — i. e. some, perhaps all; or it may 
 mean some at most, — i. e. some, not all. Thus, a chemist 
 might say. Some metals are dissolved hy adds, meaning 
 '■'•Perhaps all metals are thus soluble, but at any rate, some 
 are." On the other hand, he may say. Some metals are 
 malleable, meaning, some — excluding all, for he knows that 
 some metals are not malleable. In a Negative Judgment, 
 if we consider some to mean perhaps all, it is evident that 
 " Some X is not Y " may be construed " Perhaps wo X is 
 Y " ; but if some signifies not all, then some is not excludes, 
 or is inconsistent with, none — not one. The wholly indefi- 
 nite meaning, some, perhaps all, is the one generally re- 
 ceived in Logic J the other meaning is called by Sir W. 
 Hamilton semi-definite, because, by excluding all, it is so far 
 definite. Though this latter meaning has been generally 
 neglected by logicians, it leads, as we shall see hereafter, 
 to some important additional inferences, and modifies, to a 
 considerable extent, the old doctrines concerning Opposition. 
 
 Hitherto we have considered the Quantity of the Judg- 
 ment only, and we have now to consider the Quantity of 
 the two Terms as affected by the Judgment in which they 
 stand. A Term is said to be distributed when it is taken 
 
126 THE 0OCTKJNE OF JUDGMENTS. 
 
 distributively, or in the whole of its Extension, — that is, 
 when it is affected, or should be affected, by the predesig- 
 nations all, each, none, &c. ; it is not distributed when it is 
 taken only in an indefinite part of its Extension, — as 
 usually signified by the predesignations some, not all, &c. 
 The received or Aristotelic doctrine upon this matter is, 
 that the distribution of the Svijeet depends upon the Quan- 
 tity of the Judgment, thus; — in Universal Judgments, the 
 Subject is distributed, but in Particular Judgments, it is 
 not distributed. JV^ unjust aetion is expedient; — this is a 
 Universal Proposition, and its Subject is evidently dis- 
 tributed, as the meaning is, not any one out of all unjusi 
 actions is eacfedient. But in the Particular Proposition, 
 Borne men are learned, it is obvious that the Subject, men, 
 is not distributed. 
 
 On the other hand, the distribution of the Predicate 
 depends upon the Quality of the Judgment, thus ; — in 
 Negative Judgments, the Predicate is distributed, but in 
 Affirmatives, it is not distributed. This rule is evidently 
 founded upon the doctrine that all predication is classifica- 
 tion ; and consequently, that when we affirm, we thereby 
 include the Subject in the class denoted by the Predicate, 
 not meaning that the Subject cpnstitutes iAe whole of that 
 class, but only a part of it ; and that, when we deny, we 
 thereby exclude the Subject wholly, or from any part of 
 the class. Thus, when we say, " Men are animals," we 
 mean, "Men are some animals," since it is not true that 
 aU animals are men. On the other hand, when we say, 
 "No man is immortal," we mean to exclude man from 
 every part of the class of " immortal beings," so that no 
 immortal whatever can be human. And even m the case 
 of Particular Negatives, as, "Some Frenchmen are not 
 Parisians," we still mean absolute or total exclusion, — 
 that not any Parisian whatever is one of the "Some 
 Frenchmen " — say, inhabitants of Lyons — whom we were 
 speaking of. 
 
THEIR QUANTITY, QUAUTY, AND RELATION. 127 
 
 According to this doctrine, the four fiindamental Judg- 
 ments, if the statements are intended to convey the whole 
 Thought which is implied in them, must be thus ex- 
 pressed : — 
 
 A. All X are some Y. All animals are some sentient 
 beings. 
 
 E. No X is any Y. No plant is any sentient being. 
 
 I. Some X are some Y. Some men are some honest 
 persons. ' 
 
 O. Some X are not any Y. Some trees are not any ma- 
 ples. 
 
 Hence the rule for the distribution of the two Terms 
 in a Judgment may be thus briefly expressed: — In A, 
 only the Subject is distributed ; in O, only the Predicate ; 
 in I, neither ; in E, both. • 
 
 Those who maintain this doctrine are perfectly aware, 
 of course, that the Predicate is soinetimes taken universally 
 in Affirmative Judgments, as when we predicate either 
 Definition or Property; but they assert that this results 
 from considering the Matter, not the Form, of the Judg- 
 ment, and therefore is not entitled to notice in Pure Logic. 
 And they further maintain, that the Predicate is never 
 quantified particularly in a Negative Judgment. Sir W. 
 Hamilton, however, as we shall see, has denied both por- 
 tions of' the doctrine, and, by substituting for it his own 
 theory of " the thoroughgoing quantification of the Predi- 
 cate," has revolutionized the whole science of Logic. 
 
 In respect to the Relation of the Predicate to the Subject, 
 Judgments are divided into simple or absolute, and con- 
 ditional. In the former, which are technically called 
 Categorical, the Predicate is conceived as a Mark, and is 
 therefore absolutely affirmed or denied of the Subject, 
 there bemg no other ground or reason for the attribution- 
 or denial than what is contained in the Sulgect itself. All 
 
128 THE DOCTRINE OF JUDGMENTS. 
 
 Categorical Judgments are included under these two for- 
 mulas, A is B, A is not B. Conditional Judgments are 
 those in which the Predicate is affirmed or denied of the 
 Subject, not absolutely, but only under some condition 
 or prerequisite. This condition may be conceived as pri- 
 marily affecting the Subject, or the Predicate, or both; 
 and hence we have three forms of Conditional Judgments, 
 distinguished as Hypothetical, Disjunctive,, and Dilemmatic 
 or Hypothetico-Disjunctive. -Thus, in respect to Relation, 
 we have four kinds of Judgments, as distinguished in the 
 following table. 
 
 Categorical. A is B, or, A is not B. 
 
 ! Hypothetical. If A is B, A is C. 
 
 Disjunctive. A is either B or C. 
 Lhtemmatic, or 
 
 Sypothetico-Di^unctive. K A is B, then C is either D or E. 
 
 In a Categorical Judgment, Man is mortal, there is 
 evidently no ground or reason for the attribution but an 
 internal one ; the Mark of inortdlity is conceived as an 
 essential attribute of man under all circumstances or con- 
 ditions whatsoever. But in each of the other forms, the 
 attribution is conditional. In the Hypothetical Judgment, 
 If death is a transition to a happier life, then it is desirable, 
 we do not affirm absolutely that death is desirable, but 
 affirm it only under a condition affecting the Subject, 
 death. In a Disjunctive, as, Every deliberate action is either 
 good or evil, the condition evidently aftects the Predicate, 
 as neither of its two forms is affirmed absolutely, but 
 either is affirmed only on condition that the other is de- 
 nied. The Dilemmatic, as it has two conditions, the 
 one affecting the Subject and the other the Predicate, is 
 obviously a combination of the two preceding forms, and 
 is therefore properiy called the Hypotlietico°Disjunctive. 
 All Hypothetical Judgments obviously consist of two parts, 
 the first of which is called the Condition or Antecedent, 
 and the second, the Consequent; and the assertion or 
 
THEIE QUANTITY, QUALITY, AND RELATION. 129 
 
 Judgment is, that if the Condition exists, the Consequent 
 follows. 
 
 A Conditional Judgment, though seemingly complex, is 
 really simple, and expresses only a single act of Thought ; 
 it contains but one assertion. Thus, in the Hypothetical 
 just cited, we do not assert that death is a transition, or 
 that deaik is desirable ; but only, if it is a transition, then 
 it is desirable. Hence the aflSrmation is evidently single, 
 and the particles if and them, form the Copula of this 
 Judgment, as they connect its two parts together. In a 
 Disjunctive, either is and or is form the Copula, which 
 reduces an apparently complex Judgment to a simple one. 
 Sometimes where and there take the place of either, or, 
 in a Conditional Judgment; as, where fire is, there is heat ; 
 where light is, there is shadow. 
 
 In Hypotheticals, the Consequence, or tie which binds 
 together the Antecedent and the Consequent, may be 
 either mediate or immediate. It is Mediate, only when 
 there is nothing in the Terms of either of the two parts 
 which binds them together ; as when we say, 
 
 If A is B, is D. 
 
 If the air is still and ehudless, the dew wiUfall. 
 If G-od is just, sinners will he punished. 
 
 In such cases, the Consequence may be valid, but it is 
 not Immediate ; for, as there are four distinct Terms, the 
 two Parts have no common Term, and are therefore con- 
 nected only by some unknown cause, or by what is in the 
 muid, but is not expressed. The unexpressed medium, 
 which binds the two Parts together in the last case, is our 
 knowledge that G-od governs the world, and that justice 
 consists in rewarding the good and punishing sinners ; there- 
 fore, if God is just, sinners wUl be punished. 
 
 The Consequence is Immediate, when there are only 
 three Terms in the two Parts, so that, since one of these 
 
 6* I 
 
ISO THE DOCTEINE OF JUDGMENTS. 
 
 Terms is necessarily repeated, it forms an immediate con- 
 nection of the Parts with each other. In order that 
 there may be this repetition of one of the Terms, either 
 the two Parts must have the same Subject, or the same 
 Predicate, or the Predicate of the first must be the 
 Subject of the second, or the Subject of the first must 
 be the Predicate of the second. In other words, the 
 Hypothetical must appear imder one of the four following 
 formulas. 
 
 If A is B, A is C. If men do wrong, they deserve pun- 
 
 ixhnent. 
 If A is B, C is B. If metals are fusible, gold isfusMe. 
 
 K A is B, B is C. If patience he a virtue, virtue may 
 
 he painful. 
 If A is B, C is A. If happiness is mere freedom from 
 
 pain, insensibUity is happiness. 
 
 In each of these cases, the Consequence is Immediate, 
 because it results fi-om a general rule, which is presupposed 
 in the Proposition that is before us, and may be evolved 
 fi-om it without any further appeal to experience. Because 
 "all C is A," we can immediately infer that, "if A is B, 
 C is B " ; or conversely, because the latter Proposition 
 is universally true, the former can be deduced £rom it by 
 necessary implication. ^ the earth is immovable, and is 
 lighted in all parts hy the sun, the sun revolves round it; — 
 this is true so far as concerns the dependence of the one 
 Proposition upon the other, though either Proposition, 
 taken separately, is false. Hence, we do not deny a 
 Hypothetical Judgment by denying either or both of its 
 parts, but only by denying the Consequence of one fi-om 
 the other. This is usually done, in Latin, by placing the 
 negation at the begimiing. 
 
 Non si miserum foituna Sinon^n 
 Finxit, vanum etiam mendaccmque improba finget. 
 
THEIR QUANTITY, QUALITY, AND RELATION. 131 
 
 In Englisli, we may deny a Hypothetical by substituting 
 although, or some equivalent, for if in the Reason, and 
 then negativing the Consequent. 
 
 If you eat of the forUdden fruit, you shall die. 
 Although you eat, Sj-c, you shall not die. 
 
 Or the Proposition may be thus denied. 
 
 It is not true that if you eat, ^c. \ 
 
 Disjunctives are denied in the same manner. 
 
 Conditional Judgments can be reduced to Categoricals, 
 though, for logical purposes, it is more convenient to retain 
 them in the Conditional form. The Condition is equiva- 
 lent to a Hmitation, and therefore can always be expressed 
 by a limiting adjective (see page 143). In the formula, 
 If A is B, then A is O, it is not asserted that aU A is C, 
 but only those A which are B. Let d represent such A ; 
 then the equivalent Categorical formula is, dA are C. 
 To take a concrete instance: — 1^ the iron is magrietio, it 
 has the attribute of polarity ; this is equivalent to the 
 Categorical Judgment, magnetic iron is polar. Conversely, 
 if any Categorical Judgment has its Subject hmited by a 
 qualifying word, the limitation can be resolved into a 
 condition, and the Judgment thus becomes Conditional. 
 Thus, Virtumis men are happy, is equivalent to If men are 
 virtuous, they are happy. 
 
 Disjunctives are reduced in a similar manner to as many 
 Categoricals as there are disjunct members of the Predi- 
 cate. Thus, — 
 
 !AU those A which are not B are C, 
 and 
 AU those A which are not C are B ; 
 
 and if d represents the former and / the latter, we have 
 dA are 0, and fA are B. Even then, the Thought is not 
 complete until we add, dA -{• fA = all A. It amounts 
 to the same thing to say, that a Disjunctive may be first 
 
132 THE DOCTRINE OF JXJDGMENTS. 
 
 resolved into as many Hypotheticals as it has disjunct 
 members; and each of these may then be reduced, as 
 before, to a Categorical. Thus, If A is rwt B, it is C; 
 and, J^ A is not 0, it is B. Evidently, then. Disjunctives 
 are only complex Hypotheticals. 
 
 3. The Hamiltonian Doctbine of Judgments. 
 
 According to the Aristotehc doctrine, as we have seen, 
 in all AflBrmative Judgments, the Predicate is Particular, 
 while in aU Negative Judgments it is Universal. Thus 
 we have but four fundamental Judgments or Prepositional 
 Forms, which have been designated by the four vowels 
 A, E, I, and O. According to Sir WiUiam Hamilton's 
 doctrine of " the thorough-going quantification of the 
 Predicate," in both Affirmative and Negative Judgments, 
 the Predicate may be distributed or undistributed, — that 
 is, may be either Universal or Particular. This doctrine 
 gives us eight Prepositional Forms, which are thus indi- 
 cated : — A signifies that the Term to which it corresponds, 
 whether Subject or Predicate, is universal, whilst / signifies 
 that it is particular ; f* standing in the place of the 
 Copula, signifies that the Judgment is e^rmative, whilst 
 M* signifies that it is negative. Thus we have the follow- 
 ing table of Hamilton's eight fundamental Judgments, 
 those of them which are recognized under the Aristotelic 
 doctrine being also indicated, as before, by the four vowels. 
 
 Affirmatives. 
 
 Afa. All X are all Y. o. g. All copperas is aU snlphate of iron. (1.) 
 (A.) Afi. AU X are some Y. " AU whales are sonte mammals. (2.) 
 
 Ifa. Some X are all Y. " Some men are all logicisins. (3.) 
 
 (I.) Ifi. Some X are some Y. " Some quadrupeds are some amphib- 
 ious. (4.) 
 
 * These two letters are selected because they are the two first consonants 
 of affirmo and nego. 
 
THE HAAHLTONIAN ANALYSIS. 133 
 
 Negatives. 
 (E.) Ana. Not any X is any Y. e. g. Not any fish is any warm- 
 blooded. (5.) 
 Ani. Not any X is some Y. " Not any Englishman is some 
 
 Briton (Scotch). (6.) 
 
 (O.) Ina. Some X are not any Y. " Some Frenchmen are not any 
 
 Parisians. (7.) 
 
 Ini. Some X are not some Y. " Some trees (oaks) are not same 
 
 trees (maples). (8.) 
 
 The question is, whether these four Forms, "viz. Afa, Ifa, 
 Ani, and Ini, which have heen added to the list by Sir 
 W. Hamilton, are legitimate and natural Forms of Thought, 
 — whether we do not have frequent occasion to think them 
 as Judgments, though we seldom or never express them as 
 Propositions. It is admitted that the predesignations of 
 quantity, some, all, any, here italicized as belonging to the 
 Predicate, are usually elided in expression. This is the case 
 even with the old Forms, A, E, I, and O ; for language 
 aims always at brevity, and therefore usually omits all that 
 is so obvious as to be easily understood, since its expression 
 would only cumber and lengthen the sentence unnecessari- 
 ly. Thus, we usually say. Men are animah ; but nearly all 
 logicians acknowledge that the Thought, of which this is an 
 abbreviated expression, is. All men are some animals. But 
 the peculiar fiinction of Logic is to analyze, not language, 
 but Thought ; it deals, not with Propositions, but with Judg- 
 ments. Hence its necessary postulate, that we must be 
 allowed to express logically all that is contained in what 
 we think. The question is, whether we are not often 
 obliged to think Judgnients under the Forms, All are all. 
 Some are all. Not any is some, and Some are not some. 
 
 Now the evidence in favor of the first two of these 
 Forms, the affirmatives Afa and Ifa, is so strong, that the 
 only wonder is, how they could have been almost univer- 
 sally rejected by logicians for over two thousand years, 
 down to the time of Sir W. Hamilton. In the first place, 
 
134 THE DOCTEINE OF JUDGMENTS. 
 
 any process of inductive reasoning can be properly reduced 
 to logical Form only in this manner : — 
 
 X, Y, Z, &c. are B. 
 
 But X, Y, Z, &c. are (or represent) all A. 
 
 Therefoi-e, all A are B. 
 
 Here the second premise is materially false ; but with 
 this fault, as logicians, we have nothing to do. Logic does 
 not guarantee the truth of the premises, but only the validi- 
 ty of the inference from the premises to the conclusion. 
 And that this inference is valid in the preceding formula 
 may be seen by taking an instance in which neither of the 
 premises is faulty. If I am playing chess, and my king is 
 in fatal check, I must reason thus : — 
 
 I can neither move my king, nor interpose a man, nor 
 capture the attacking piece. 
 
 But these three are all the modes of obviating check. 
 
 Then I am checkmated. 
 
 Here the Predicate of the second premise is quantified 
 universally ; and men reason in this manner every day, 
 when they are reduced to a choice among a few only possi- 
 ble modes of action, and each of these modes is fatal. The 
 following example shows how we reason inductively : — 
 
 Copper, tin, lead, iron, &c. are fusible. 
 
 But copper, tin, lead, &c. are (or represent) aM metals. 
 
 Then all metals are fiisible. 
 
 As already hinted, every adequate Definition — that is, 
 every one in which the Definiendum and the Definition are 
 convertible terms — has its Predicate universally quantified 
 in Thought. To take the instance already given, All cop- 
 peras i& sulphate of iron, or, conversely. All sulphate of iron 
 is all copperas. So, also, every exhaustive Division must 
 be thought as a Judgment with a universal Predicate. 
 Thus, the geometer, having demonstrated a certain prop- 
 osition successively of equilateral, isosceles, and scalene 
 triangles, adds in ThoHght, But tAe«e are aM triangles; 
 therefore, the theorem holds good of all triangles. 
 
THE HAMILTONIAN ANALYSIS. 135 
 
 " In fact," says Hamilton, " ordinary language quantifies 
 tlie Predicate so often as this determination becomes of the 
 smallest import. This it does directly, by adding all, some, 
 or their equivalent predesignations, to the Predicate ; or it 
 accomplishes the same end indirectly, in an exceptive or 
 limitative form. 
 
 "") Directly, — as, Peter, John, James, etc. are all the 
 ^posths ; — Mercury, Venus, etc. are all the planets. 
 
 " '') But this is more frequently accomplished indirectly, 
 by tiie equ,ipollent forms oi Zdmitation or Inclusion, and 
 Exception.* 
 
 " For example, by the limitative designations, alone or 
 only, we say, God alone is good, which is equivalent to 
 saying, Crod is all good, that is, Grod is aU that is good; 
 Virtue is the only nobility, that is. Virtue is all noble, that 
 is, all that is noble. The symbols of the Catholic and 
 Protestant divisions of Christianity may afford us a logical 
 illustratiQn of the point. The Catholics say. Faith, JSbpe, 
 and Charity alone justify j that is, the three heavenly virtues 
 together are aU-justifying, that is, all that justifies ; omne 
 justifioans, justum faciens. The Protestants say. Faith 
 alone justifies ; that is, Faitfi, which they hold to comprise 
 the other two virtues, is all-justifying, that is, all that 
 justifies; omne justijioans. In either case, if we translate 
 the watchwords into logical simplicity, the predicate ap- 
 pears predesignated. 
 
 " Of animals man alone is rational; that is, Man is all 
 rational animal. What is rational is alone or only risible ; 
 that is. All rational is all risible, etc, 
 
 " I now pass on to the Exceptive Form, To take the 
 motto overhead, ^^ ' On earth there is nothing great but 
 man.' What does this mean? It means, Man — is — all 
 
 * The English Exclusive particles are, one, only, alone, exclusively, pre- 
 cisely, just, sole, sokiy, nothing, but, &c. These particles annexed to the Sub- 
 ject pre^esignate the Predicate universftllj, (>r to its whole extent. 
 
136 THE DOCTRINE OF JUDGMENTS. 
 
 earthly great. (^Hbmo — est — omne magnum terrestre.') 
 And the second clause — ' In man there is nothing great 
 but mind ' — in hke manner gives, as its logical equipollent, 
 Mtnd — is — aU humanly great, that is, all that is great in 
 man. QMens est omne magnum hwmanum.')" 
 
 The case may not seem so clear in respect to the two 
 negative Forms, Ani and Ini, in which the Predicate is 
 Particular ; for the expression of them in language is so 
 awkward and unnatural as to have provoked the remark, 
 that they seem to be got up as if for the purpose of show- 
 ing what one could do. It would certainly be accounted a 
 forced and uncouth assertion, to say that not any iron is 
 some metal, — i. e. is not lead ; or that some men (Enghsh- 
 men) are not some men (Frenchmen). Dr. Thomson ad- 
 mits that they are conceivable, but denies that they are 
 actual, cases of negative predication. He argues that 
 " such a Judgment is never actually made, because it has 
 the semblance only, and not the power, of a denial. True 
 though it is, it does not prevent oiu' making another Judg- 
 ment of the afBrmative kind from the same Terms." It 
 would be more correct to say that we can make "another 
 Proposition," instead of "another Judgment," from the 
 same Terms ; for the " some metal " in the Predicate of the 
 negative Judgment is not thought as the same "some metal" 
 in the Predicate of the afBrmative. The two assertions 
 are incompatible in Thought, though they happen to be 
 identical in expression. Thus, — 
 
 Iron is not some metal, — i. e. is not lead. 
 
 Iron is some metal, — i. e. is iron. 
 
 Englishmen are not some men, — not Frenchxaen. 
 
 Enghshmen are some men, — En^lishm&n. 
 
 In fact, the law of Division, that the Dividing Members 
 must exclude each other, compels us to think some are not 
 some, — these are not those, — these are different from those. 
 As already shown, negation is only the affirmation of dif- 
 
THE HAMILTONIAN ANALYSIS. 137 
 
 ference or exclusion ; ' A «s not B,' is equivalent to ' A is 
 not-B.' Now we never have occasion to affirm difference 
 or exclusion except for the purpose of distinguishing co- 
 ordinate Species from each other ; for if the two classes were 
 not recognized as belonging to the same Genus, — that is, 
 as similar in some respects, — it would not be necessary to 
 think or to say that they differ in certain other respects. 
 We never say, Fishes are not stars, since the two things are 
 so imlike that there is no danger of confounding them. 
 But we think and say, Oaks are not maples. Spaniels are 
 not terriers, as the classes are here thought as belonging to 
 the same proximate Genera, trees and dogs. In Thought, 
 therefore, these two Judgments are exphcated thus : Some 
 trees are not some trees ; Some dogs are not some dogs. 
 
 Even the Aristotelic doctrine admits that Unskilful are 
 some physicians is a legitimate Judgment, for it is the sim- 
 ple converse of Some physicians are unsMlful. But it 
 amounts to precisely the same thing whether we say, Un- 
 skilful are, &c., or Not (any) sMlful are some physicians. 
 Considered as Propositions, one of these may be con- 
 demned as faulty in expression ; but as Judgments, one 
 cannot be admitted and the other rejected, for they are one 
 and the same Judgment. 
 
 Again, whenever we predicate a Genus of a Species, the 
 Predicate is obviously quantified as Particular ; and some, 
 which is the predesignation of particularity, must then be 
 thought in its semi-definite sense, as some, excluding all. 
 In this sense, we cannot think that sows are, unless we also 
 think that some are not. Then, every such Judgment 
 carries with it by necessary inference, or as a part of itself, 
 another Judgment, negative in Form and with a Particular 
 Predicate. Thus the Judgment, Men are some animals , 
 (rational bipeds), is incomplete and even impossible in 
 Thought, unless we also think, Men are not some (other) ani- 
 mals (brutes). Either of these two assertions thus carrying 
 
138 THE DOOTEINE OF JUDGMENTS. 
 
 the other along with it by necesaary implication, it is more 
 natural to adopt in words the affirmative form, as the more 
 frequent and familiar one, even when the negative meaning 
 is more prominent in Thought. As Hamilton remarks, 
 " men naturally preferred to attribute positively a part of 
 one notion to another, than to deny a part." 
 
 It has already been argued, (page 110,) that although 
 the Predicate in any Judgment may be actually thought 
 only connotatively, or as a Mark, it is still potentially a 
 Concept, and as such, it denotes a class, or has Extension. 
 To predicate, therefore, is virtually to classify, or to as- 
 sign a Subject to its proper place in a class, thereby attrib- 
 uting to it aU. the Marks of that class. Now it is argued 
 by Mr. Baynes, with great force, " that when we bring an 
 object under a notion, that is, when we predicate of it 
 that it belongs to such a class, we must know that it occu- 
 pies a certain place in that class. For if we were imcer- 
 tain what place the individual object occupied in the class, 
 or whether it occupied any place at all, we should not 
 know the class, and could not therefore bring any object 
 under it ; — e. g. if I do not know whether rose comes 
 under the Concept flower, — whether it is equal to some 
 part, or the whole, or superior to it, — I cannot, of course, 
 predicate flawer of rose, since I do not know what the 
 Concept means, what it contains, and what it does not. 
 If, therefore, we understand the object at all, we must fix, 
 in Thought, the sphere which it occupies under the class to 
 which, in predication, we have assigned it. In other words, 
 if we comprehend what we utter, every notion holding the 
 place of predicate in a proposition must have a determinate 
 quantity in thought." * We cannot, for instance, predicate 
 bird successfully of pigeons, of winged and feathered bipeds, 
 and of animals, unless we know at least so much of the 
 characteristics of the class bird as to be able to think that 
 
 * Baynes's New Analytic of Logical Forms, pp. 9, 10. 
 
THK HAMILTONIAN ANALYSIS. 139 
 
 " all pigeons are some birds," " all winged and feathered 
 bipeds are all birds," and ^'some animals are all birds." 
 In like manner, we cannot exclude a Subject from a given 
 Concept or class, — as when we say. Whales are not fish, 
 unless we either think fish as cold-blooded, vertebrated ani- 
 mals, living in the water and breathing by gills, in which 
 case we think " whales are not any fish " ; or accept the 
 vulgar notion of fish as finned animals living in the water, 
 and then think " whales are not some fish," — viz. not cold- 
 blooded fish. This leads us to remark, that, in fact, any hmi- 
 tation of the predicate4 class by a limiting adjective is equiv- 
 alent to quantifying that Predicate particularly ; — e. g. 
 Pines are Tiot deciduous trees = Pines are not some trees. 
 
 These reasons, and others which wiU be mentioned when 
 we come to treat of Conversion, seem conclusive in favor 
 of Sir W. Hamilton's doctrine, that, potentially at least, 
 the Predicate is always quantified either universally or par- 
 ticularly, both in affirmative and negative Judgments. 
 
 But if each of the two Terms of a Judgment has its own 
 quantity assigned to it in Thought, then, for still stronger 
 reasons than those which have already (pp. 64, 110) been 
 assigned, the distinction between Subject and Predicate 
 ceases to be of any moment. In fact, every Judgment 
 comes from an act of comparing two quantified Terms with 
 each other ; and as the result of such comparison, we have 
 an equation, or non-equation, estabhshed between these 
 Terms, and it is completely indifferent which of them is 
 placed first. Thus, having compared two Concepts, A and 
 B, I find either that they agree, or do not agree, with each 
 other. This agreement or difference may be expressed 
 equally well in either of the following formulas : — 
 
 A is B. A is not B. 
 
 B is A. B is not A. 
 
 A and B are equal. A and B are not equal. 
 
 Convertible or equal are A and B. Unconvertible are A and B. 
 
140 THE DOCTEINE OF JITDGMENTS. 
 
 In these last two formulas, the two compared notions do 
 not stand to each other as Subject and Predicate, but are, 
 in the same proposition, either both Subjects or both Predi- 
 cates. 
 
 In common language, if the two Terms are both quanti- 
 fied universally in Thought, it is admitted to be of no 
 consequence which is placed first ; usually, that which is 
 prior or pre-eminent in Thought appears as the Subject. 
 Thus, we say either. Electricity is not the nervous fluid, or, 
 The nervous fluid is not electricity; Corpmion salt is chloride 
 of sodium, or, Chloride of sodium is common salt. 
 
 But if the two Terms differ in Quantity, the convenience 
 of language requires, in most cases (not in all*), that the 
 one which has the wider Extension should appear as the 
 Predicate, and that its Quantity, though present in Thought, 
 should be silently passed over in expression. It is more con- 
 venient that the Term which has the less Extension, as it is 
 more definite or limited in meaning, and therefore can be 
 more easily grasped in Thought, should be; placed first ; and 
 then, the Quantity of the Predicate, as it is known to be 
 greater than that of the Subject, (and it matters not how 
 much greater it is,) may be omitted in expression for the 
 sake of brevity. Metals are fusible substances is a shorter 
 and more natural expression than Some fusible svhstanees 
 are metals, though the two propositions convey precisely 
 
 * Such propositions as these, for instance, are common : — 
 
 It is disgraceful to be a slave to passion. 
 
 Twpe est obsequi tibidini. 
 
 Happy is he who is able to know the causes of things. 
 
 Felix qui potuit rerum cognoscere causas. 
 
 It is rain which has fallen. 
 
 It is foolish to listen to flatterers. 
 
 If the Term of the wider Extension must be the Predicate, we should 
 say, — To be a slave to passion is disgraceful ; He who can discover the causes 
 of things is happy ; That which has fallen is rain ; To listen to flatterers is 
 folly. 
 
EXPLICATION OF PROPOSITIONS INTO JUDGMENTS. 141 
 
 the same meaning. Hence the old logicians, having more 
 regard to Language than to Thought, maintained that the 
 former order was the only legitimate one ; they analyzed 
 this order only, and based upon it their whole system. 
 " Natural, or regular, or direct predication they held to be 
 that in which the genus is predicated of the species, the 
 species of the individual, the attribute of its subject, and, 
 in general, the extensive whole of its part; and in which, 
 therefore, the Subject notion was always of less extent than 
 the Predicate notion. Unnatural, indirect, or irregular 
 predication was the reverse of this, — that, to wit, in which 
 the species was predicated of the genus, the subject of its 
 attribute, and, in general, the extensive part of its whole."* 
 But when it is acknowledged that Logic has to do pri- 
 marily with Thought, and only secondarily with Lan- 
 guage; that each of the two Terms has its own Quantity 
 assigned to it in Thought; and that the purport of the 
 Judgment is merely to affirm the agreement or non-agree- 
 ment of these two quantified Terms, — it becomes evi- 
 dent that every proposition is logically reduced to an 
 equation, or non-equation, of two Terms, the relative posi- 
 tion of which is of no importance whatever. AU metals 
 are some fusible things, and Some fusible things are all met- 
 als, are two statements of precisely the same import. And 
 in like manner with negatives ; — Some Frenchmen are 
 not any Parisians, is the same Judgment as, Not any Pa- 
 risians are some Frenchman. 
 
 4. The Explication of Propositions into Judgments. 
 
 Strictly speakuig, as we have seen, Pure Logic deals 
 only with Judgments, and refers to the science of Lan- 
 guage for the doctrine of Propositions, or the proper ex- 
 pression of Judgments in words. But the claims of Logic 
 
 * Baynes's Analytic, p. 12. 
 
142 THE DOCTRINE OF JUDGMENTS. 
 
 to be regarded as a universal science, and its doctrine that 
 all Thought can be reduced to distinct Judgments, so that 
 the logical theory of Judgments is applicable to every 
 mental product into which Thought enters, cannot be de- 
 fended, or even properly understood, until it is clearly 
 shown how all Propositions, even the most complex in 
 character, may be reduced to simple Judgments. We 
 shall therefore consider the explication of Propositions 
 here, though the subject properly belongs to Applied 
 Logic. 
 
 Everj' pure Judgment corresponds to one of these two 
 forms, — A is B, or A is not B; and if thus expressed in 
 words, it is called a Simple Proposition. In this case, 
 neither Subject nor Predicate necessarily consists of a 
 single word ; either or both may be described in many 
 words, provided that the union of these words expresses 
 but one Judgment or a single act of Thought. Thus, Well 
 organized and skilfully administered governments are produc- 
 tive of happiness to their subjects, is a Sitnple Proposition, as 
 well as John is sick. On the other hand, several acts of 
 Thought combined in one statement constitute a Compound 
 Proposition, the plurality of which may reside either in the 
 Subject, or in the Predicate, or In both. Thus, James and 
 William are young and healthy, is a Compound Proposition, 
 which may be resolved into these four Simple ones: — 
 James is young; James is healthy; William is young; 
 William is healthy. A distinct Judgment is evidently ne- 
 cessary for each of these affirmations, whether they are 
 expressed separately, or united into one Compound Propo- 
 sition. Such a Proposition obviously may be partly true 
 and partly felse, according as all, or only some, of the Predi- 
 cates are truly affirmed of all, or only some, of the Sub- 
 jects. 
 
 But as a Simple Proposition contains only one Subject 
 and one Predicate, it would seem that it must be either 
 
EXPLICATION OF PROPOSITIONS INTO JUDGMENTS. 143 
 
 wholly true or wholly false. And so it would be, but that 
 there are many Propositions, seemingly Compound, but 
 really Simple, whose Subject or Predicate is a Complex 
 tertn, containing by implication other Judgments, that may 
 be called incidental. In these, the incidental Judgment 
 may be false, while the main Proposition may be true. In 
 those which are properly called Complex Propositions, the 
 incidental or implied Judgment may appear, either as a part 
 of the Subject or of the Predicate, with which it is joined 
 by a relative pronoun, whose oifice it is to combine several 
 Propositions into one, or only as a limiting or defining ad- 
 jective, or participle, or adjective clause. Thus, it is the 
 same thing to say, Grod, who is invisible, created the world, 
 which is visible; or. The invisible Grod created the visible 
 world. It is justly remarked by the Port Royal Logi- 
 cians, that these incidental Judgments are to be regarded 
 not so much as Propositions which we now make, but as 
 Judgments formerly made, the Predicate of which is now 
 regarded as a simple Mark or attribute of one of the 
 Terms in oUr present main Proposition. Hence it is still 
 true, that the Complex Proposition is Simple, because it 
 expresses but one Judgment made at the moment. 
 
 The incidental Judgment expressed in an additional 
 word or clause may be either explicative or limitative. It is 
 Explicative, when it is of the nature of a complete or partial 
 definition, and therefore belongs to the Term to which it is 
 annexed in the whole of its Extension. Thus, Man, who 
 is born of woman, is of few days and full of trouble ; — 
 here, the adjunct clause, bom of woman, is to be understood 
 as a definition applicable to all men. But in such a Propo- 
 rtion as this. Men who are avaricious are unhappy, the 
 rfelative clause restricts or limits the predication of linhap- 
 pineiss to some men, — to those only who are avaricious. 
 It is only these Complex Limitative Propositions which are 
 equivalent to HypotheticaJs : — thus, All iron which is mag- 
 
144 THE DOCTRINE OF JUDGMENTS. 
 
 netic is polar, has the same meaning as, Jff' iron is mag- 
 netic, it is polar. It depends upon the Matter of the 
 Thought, and can usually be determined by the context or 
 the nature of the subject, whether the adjunct word or 
 clause is to be considered as ExpHcative or Limitative. 
 
 With regard to Explicatives, it should be observed, that 
 the falsehood of the incidental does not affect the truth of 
 the principal Proposition. Thus, in the Proposition, Sar- 
 modius and Aristogeiton hilled Mipparchus, who was a 
 tyrant, or, killed the tyrant Hipparehus, the main assertion 
 would still be true, even though Hipparehus was not a 
 tyrant. If, however, there is an imphed Inference or ar- 
 gument, that the principal Proposition is true because the 
 incidental one is a correct definition, then the falsity of 
 the latter becomes a reason for doubting, not for denying, 
 the truth of the former. Thus, the Proposition, 77ie soul, 
 which is an extended substance, must occupy space, becomes 
 doubtful when the incidental affirmation, that it is extended, 
 is disproved; but it may still be true, for other reasons, 
 that the soul must have some position in space. 
 
 In respect to Limitatives, no question can arise concern- 
 ing the truth or falsity of the incidental Proposition ; for 
 its Predicate is not affirmed of the Subject to which the 
 relative refers, nor is the existence of any such Subject 
 affirmed. If I say. Judges who never do anything by 
 request or favor are worthy of praise, the only assertion is a 
 Hypothetical one. I do not affirm, that Judges never do 
 anything by request or favor, or that there are any such 
 Judges ; but only, that if there are any such, then they de- 
 serve praise. The most orthodox believer in the atoning 
 virtue of the death of Christ may still admit, that a man who 
 has never sinned, and is not sinful by nature, stands in no 
 need of an atonement. So far, indeed, as such a statement 
 contains any implication that such a human being ever 
 lived, it is false ; but if construed strictiy, it implies noth- 
 ing of the kind. 
 
EXPLICATION OF PROPOSITIONS INTO JUDGMENTS. 145 
 
 Compound Propositions are divided into those which 
 obviously contain a plurahty of Judgments, and therefore 
 do not need analysis and exposition ; and those in which 
 the plurahty is concealed, so that it is apt to escape notice. 
 The latter are called Exponibles, because they need to be 
 analyzed and explained. These are divided into Exclu- 
 sives, Exceptives, and Restrictives. 
 
 Exclusive Propositions limit the Predicate to this one 
 Subject, thereby excluding it from every other Subject. 
 Hence, every Exclusive contains two Propositions, one of 
 which affirms the Predicate of A^ and the other denies it 
 of all not-A. Thus, 
 
 (MyAuB = \^ ilf ^ is B. 
 
 I Grod is to he worshipped. 
 Crod ahne is to be worshipped = j J/b other being is to be 
 
 ' worshipped. 
 
 Hamilton, as we have seen, reduces these Compounds 
 to Simple Propositions, by showing that the Exclusive 
 particle annexed to the Subject quantifies the Predicate 
 universally ; thus : — 
 
 Only Ais B = A is all B ; 
 whence we infer immediately, by Infinitation, that 
 No not-A is B. 
 
 Sometimes the Exclusive particles only, one, sole, &c., 
 are annexed adjectively to the Predicate, and then have 
 the same meaning as all. Thus, Grod is the sole object to 
 be worshipped; — i. e. God is all that should be worshipped. 
 
 Annexed adverbially to the Copula and Predicate taken 
 together, the Exclusive particle limits the Subject to tliis 
 one Predicate, thereby excluding it from every other 
 Predicate. 
 
 Peter only plays ; i. e. he plays, and he does nothing else. 
 
 James is only a lawyer ; i. e. he is a lawyer, and nothing 
 else. 
 
146 THE DOCTRINE OF JUDGMENTS. 
 
 But, James is the only lawyer = he is all the latoyer that 
 you can find. 
 
 Exceptive Propositions state the Subject universally, yet 
 ■with a specified exception, to which it is imphed that the 
 Predicate is not attributed. These also are equivalent to 
 two Judgments, and these two, as in the case of Exclnsives 
 also, differ in QuaUty. 
 
 r (Nearly) all have disap- 
 
 AU but one have disappeared = ^ ^^^ ^^ j^^ ^^ ^,-g^ 
 
 peared. 
 
 In respect to Quantity, Exceptives are to be considered 
 as Universals. For although a part is excluded from the 
 whole of the Subject, so that the Predicate is referred 
 only to the remainder, yet this remainder constitutes a 
 whole in itself, of which the Predicate is affirmed or 
 denied. 
 
 It is obvious that an Exclusive and an Exceptive are 
 only two modes of expressing the same thing, as it is easy 
 to change them reciprocally from the one to the other ; 
 but the direct affirmation in one becomes the impUed 
 assertion in the other. A fool thinks that no method ex- 
 cept his own is right; in other words, that his own is the 
 only right method. 
 
 Restrictive Propositions are of two kinds, both of which 
 are Limitative in meaning. The first sort restricts the 
 assertion by a special clause, which determines more nar- 
 rowly the signification of the Subject or the Predicate. 
 JSthics, considered merely as a doctrine of the expedient, is 
 no longer a science of morality : — this is equivalent to 
 the two Judgments, Ethics is a science of morality, but 
 a mere doctrine of expediency is not such a science. Here 
 the Subject is the restricted Term ; but in the following 
 example, it is the Predicate. A good magistrate is merci- 
 ful to offenders, as far as the demands ofjusUoe will permit. 
 
EXPLICATION OF PROPOSITIONS INTO JUDGMENTS. 147 
 
 The second sort of Restriction is called Reduplicative, as 
 it consists in a repetition of the restricted Term. A judge, 
 as judge, ought never to receive presents ; — that is, he may- 
 receive them, like other men, on ordinary occasions, but 
 never in connection with the performance of his ofScial 
 duties. Here, also, the two Judgments into which the 
 Proposition is explicated differ in Quality. 
 
148 THE DOCTEINE OF IMMEDIATE INFEBENCE. 
 
 CHAPTER VI. 
 
 THE DOOTEINE OF IMMEDIATE INFERENCE. 
 
 1. .Squipollence or Infinitation. — 2. Conversion. — 3. Opposition and 
 Integration. 
 
 INFERENCE or Reasoning is that act of Pure Thought 
 whereby one Judgment is derived from another, or 
 from two others. The Judgment from which another is 
 deduced is called the Premise ; and that which is derived is 
 called the Conclusion. If the Conclusion is drawn directly 
 from one Premise only, without the aid either of an 
 Intuition or another Judgment, it is said to be an Immedi- 
 ate Inference. Thus, from the Premise that No quadrwped 
 is rational, I know at once, or by Immediate Inference, — 
 that is, by an act of Pure Thought, — that Uvery quadru- 
 ped is irrational, and that No rational thing is a quadruped. 
 If the Conclusion can be drawn only through the interven- 
 tion of a third Judgment, — in other words, if two Prem- 
 ises are necessary, — the result is a Mediate Inference, 
 or Syllogism. 
 
 But in either case, the act of Reasoning or Inference, 
 whether Mediate or Immediate, is simple, being one indi- 
 visible act of mind. The Premises are considered as 
 given, and their truth is taken for granted ; the Inference 
 is the act of deduction, or drawing out the Conclusion from 
 the Premises, and this act is necessarily simple. If it is 
 performed in accordance with the Laws of Pure Thought, 
 it is apodeictic or absolutely certain, as any opposite Con- 
 clusion would be Contradictory and absurd. In respect to 
 
THE DOCTRINE OF IMMEDIATE INFERENCE. 149 
 
 their Matter, both the Premises and the Conclusion may be 
 false ; and yet the Form of Inference, or the transition 
 from one to the other, may be intuitively true. Thus, the 
 Mediate Inference, 
 
 Everything material is mortal; 
 
 The Soul ig material; 
 
 Therefore the Soul is mortal; — 
 is false in each of its three Judgments. Yet its Conclusion 
 is as correctly drawn, and the Syllogism is therefore just as 
 vahd, as in the following instance, where each of the three 
 Judgments is true. 
 
 Everything material is divisible; 
 
 Gold is material ; 
 
 Therefore Gold is divisible. 
 Hence, the material truth of the Conclusion depends upon 
 the material truth of the Premises ; its formal validity is 
 the correctness of the process whereby it was deduced from 
 the Premises. Pure Logic has to do only with the latter. 
 Every correct step of Reasoning, considered simply as such, 
 or in reference to its Form, is as indisputable as one of 
 those Primary Axioms of Pure Thought on which it is 
 based, or of which it is an application. The uncertainty or 
 disputable character of much of what is improperly called 
 Reasoning lies altogether in the Premises, and is referable 
 to imperfect observation, to an improper use of words where 
 language has become a substitute for Thought, or to over- 
 hasty generalization. But the mere process of Reasoning, 
 irrespective of the data about which we reason, is the same 
 in the moral and physical, as in the purely mathematical, 
 sciences ; it is equally demonstrative in all, for it is condi- 
 tioned by the absolute laws of Pure Thought. The long- 
 est chain of argument is but a series or repetition of In- 
 ferences, whether Mediate or Immediate, in which the 
 formal validity of each step, taken by itself, is intuitively 
 perceived. 
 
150 THE DOCTRINE OF IMMEDIATE INFERENCE. 
 
 Logic, as Hamilton remarks, " is exclusively conversant 
 about Thought strictly so denominated ; and Thought 
 proper, we have seen, is the cognition of one object of 
 thought by another, in or under which it is mentally in- 
 cluded ; — in other words, Thought is the knowledge of 
 a thing through a Concept or General Notion, or of one 
 Notion through another. In Thought, all that we think 
 about is considered either as something containing, or as 
 something contained ; — in other words, every process of 
 Thought is only a cognition of the necessary relations of 
 our Concepts. This being the case, it need not move our 
 wonder that Logic, within its proper sphere, is of such 
 irrefragable certainty, that, in the midst of all the revolu- 
 tions of philosophical doctrines, it has stood, not only 
 unshattered, but unshaken. In this respect. Logic and 
 Mathematics stand alone among the sciences, and their 
 pecuhar certainty flows from the same source. Both are 
 conversant about the relations of certain a priori forms of 
 inteUigence ; — Mathematics about the necessary forms of 
 Imagination ; Logic about the necessary forms of Under- 
 standing ; — Mathematics about the relations of our repre- 
 sentations of objects, as out of each other in space and time ; 
 Logic about the relations of our Concepts of objects, as in 
 or under each other, that is, as in different relations respec- 
 tively containing and contained. Both are thus demonstra- 
 tive, or absolutely certain, sciences, only as each develops 
 what is given, — what is given as necessary, in the mind 
 itself. The laws of Logic are grounded on the mere 
 possibility of a knowledge through the Concepts of the 
 Understanding, and, through thege, we know only by com- 
 prehending the many under the one. Concerning the 
 nature of the objects delivered by the Subsidiary Faculties 
 to the Elaborative, Logic pronounces nothing, but restricts 
 its consideration to the laws according to which their 
 agreement or disagreement is affirmed." 
 
THE DOCTRINE OF IMMEDIATE INFERENCE. 151 
 
 ^'It is of itself manifest that every science must obey 
 the laws of Logic. If it does not, such pretended science 
 is not founded on reflection, and is only an irrational 
 absurdity. All Inference, evolution, concatenation, is con- 
 ducted on logical principles, — principles which are ever 
 valid, ever imperative, ever the same. But an extension of 
 any science through Logic is absolutely impossible ; for by 
 conforming to logical canons, we acquire no knowledge, 
 receive nothing new, but are only enabled to render 
 what is already obtained more intelligible, by analysis and 
 arrangement. Logic is only the negative condition of 
 truth. To attempt by a mere logical knowledge to amplify 
 a science, is an absurdity as great as if we should attempt, 
 by a knowledge of the grammatical laws of a language, to 
 discover what is written in this language, without a perusal 
 of the several writings themselves. But though Logic 
 cannot extend, cannot amplify, a science by the discovery 
 of new facts, it is not to be supposed that it does not con- 
 tribute to the progress of science. The progress of the 
 sciences consists not merely in the accumulation of new 
 matter, but likewise in the detection of the relations sub- 
 sisting among the materials accumulated ; and the reflec- 
 tive abstraction by which this is effected must not only 
 follow the laws of Logic, but is most powerfully cultivated 
 by the habits of logical study." 
 
 Aristotle has defined Inference as "a thought or propo- 
 sition in which, from something laid down and admitted, 
 something distinct from what we have laid down follows of 
 necessity." But this definition, though it describes the 
 Syllogism accurately, seems at first to be inapplicable to 
 Immediate Inference, in which, as there is only one premise, 
 and as the act of Pure Thought through which we reason 
 cannot add any new Matter (that is, any new Intuition or 
 Concept), it would appear that the Conclusion cannot con- 
 -tain anything distinct from what has already been laid .down. 
 
152 THE DOCTRINE OF IMMEDIATE INFERENCE. 
 
 And this is true ; it cannot contain any new Matter, but it 
 may represent this Matter under a new Form, so that the 
 Conclusion and the Premise will be perfectly distinct Judg- 
 ments. Thus, m the instance just given, " quadruped " 
 and " rational " are the only Terms that appear in either 
 of the two Conclusions, " irrational " being only the equiv- 
 alent of " non-rational " ; and both of these are contained 
 in the Premise. And yet the Inference is not a mere 
 repetition, but the Judgments which it involves are new 
 and distinct from what was previously laid down ; for one 
 of them is affirmative, while the Premise is negative ; and 
 the other denies a certain Mark of any " rational thing," 
 while the Premise denies a certain other Mark of any 
 " quadruped." If it be argued further, that such Conclu- 
 sions are virtually contained in the Premise, inasmuch as 
 they become evident to any one who fully apprehends it, 
 the answer is, that this is true of all Reasoning, even of 
 Syllogisms and Inductions. That a certain step is obvious 
 and easily taken, is surely no proof that it is no step at all, 
 or that we can get along without taking it. 
 
 1. JEquipollence OB Infinitation. 
 
 The first sort of Immediate Inference which we have to 
 consider is that which the Greek logicians called woSuwy«a, 
 and the Latins, ^quvpollence ; its more appropriate name 
 is Infinitation. It has already been said, that every pair 
 of Concepts, such as A and not-A, of which one is merely 
 the Contradictory or the privative of the other, divide the 
 universe between them. According to the axiom of Ex- 
 cluded Middle, either A, or its Infinitated correlative, not- 
 A, must belong to everything, and must include everything ; 
 and according to the axiom of Non-Contradiction, the pres- 
 ence of one in any given case insures the exclusion of the 
 other. Hence arise a number of Immediate Inferences, 
 
^QUIPOLLENCE OB INFINITATION. 153 
 
 some of which are of frequent occurrence in our ordinary 
 processes of thought. As akeady remarked, a negative 
 Judgment can always be changed in Form to an affirma- 
 tive, or an affirmative to a negative, simply by Infinitating 
 one of its Terms, or by dropping its Infinitation ; and the 
 result is a new Judgment, the truth of which is an Imme- 
 diate Inference from the truth of the antecedent Judgment 
 whence it was derived. Here the Inference is only an 
 application of the well-known grammatical rule, that two 
 negatives cancel each other, and thus become equivalent to 
 an affirmative. But the idiom of every language sanctions 
 a greater or smaller number of exceptions to this general 
 rule, none of which, however, are admissible in Logic, 
 where every negation must be construed rigorously. 
 
 The following memoriter lines, which I copy from Bur- 
 gersdyck, enumerate the more frequent forms of sequipol- 
 lence and of the idiomatic force of negative expressions ; 
 but of course, all of them do not hold good in this meaning 
 in any other language than the Latin. 
 
 Non omnis = quidam non ; omnis non quasi nuUus. 
 
 Non nuUus = quidam ; sed nullus non valet omnia. 
 
 Non aliquis = nullus ; non quidam non valet omnis. 
 
 Non alter = neuter ; neuter non prcMtai uterque. 
 In all cases of Immediate Inference by Infinitation, the 
 dependence of the Conclusion upon the Premise is so obvi- 
 ous, and so directly governed by the Primary Axioms of 
 Pure Thought, that no mistake is likely to arise, except 
 from a momentary doubt as to the position or the proper 
 force of the negative particle. The two following rules 
 comprehend at least all the more important cases, and 
 they hold true, I believe, without exception, for the four 
 Prepositional Forms which are recognized in the Aris- 
 totelic system. 
 
 Rule I. To change the Infinitation of the Predicate 
 (either by Infinitating it, or by dropping its Infinita- 
 7* 
 
154 THE DOCTRINE OF IMMEDIATE IKFEEENCE. 
 
 tion), change the Quality of the Judgment; — the 
 Quantity of the Judgment then remains unaltered. 
 Rule II. To change the Infinitation of the Subject, 
 convert the Judgment (i. e. make the Subject and the 
 Predicate change places with each other), and then 
 either change the Quality, or change the Infinitation 
 of the (old) Predicate also ; — here, also, the Quantity 
 of the Judgment remains unchanged. 
 The following are instances, both in the abstract and the 
 concrete, of the application of these two Rules to aU four 
 of the fundamental Judgments, A, E, I, and O, and also 
 to their Infinitated forms, here designated as A', E', I', 
 and O'. This enumeration was first made out by Mr. 
 DeMorgan. It will be seen that it contains no instance of 
 mere Conversion, as the cases under that head will be after- 
 wards separately considered. To avoid a confusing repeti- 
 tion of the negative particle Twt, words compounded with 
 the negative prefixes un and m have been adopted when- 
 ever it was practicable. For the same reason, right is used 
 for vjot-wrcmg ; brutes for not-men ; pitUegs for not-compas- 
 sionate; &c. 
 
 Peemises. Conclusions. 
 
 By Knie I. By Enle n. 
 
 A. Every X is T. =No X Is not-T. =Every not-Y b not-X. 
 
 All metals are fu- ( =No metal is infiisi- f = All infiisible things are 
 sible. "l ble. \ nnmetallic. 
 
 O. SomeXarenotY. = Some X are not-T. :=: Some not-Y are not not-X. 
 
 Some men are not < = Some men are piti- ( = Some pitiless beings are 
 
 compassionate. "5 less.* "^ not mere brutes (not-men). 
 
 E. No X is Y. = Every X is not-Y. = Every Y is notrX. 
 
 Noavaricions man (= Every avaricions ( = Every happy man is liree 
 is happy. \ man is unhappy. \ from avarice. 
 
 * Strictly speaking, or according to the mles of Logic, " not-compassion- 
 ate" has the same meaning as "pitiless," for it is the contradictory of 
 " compassionate." But in common parlance, there is a slight difference in 
 the meaning of the two words ; " not-compassionate," like most other epi- 
 thets compounded with a negative particle, means, not entire privation of the 
 quality, but only the existence of it in a very low degree. 
 
^QUIPOLLENOE OE INFINITATION. 155 
 
 I. Some X are T. =SomeXar6 not not-Y.= Some Y are not nofc-X. 
 Some wrong acts (= Some wrong acta f= Some excusable acts are 
 are excusable. | are not inexcusable. '^ not right acts. 
 
 A'. Every not-X is > „ ^ . „ 
 
 not-Y. C "=^° ^°^^ '8 ^- =ETery Y is X. 
 
 Erery unjust act j=No unjust a«t is ex- 5 =Every (truly) expedient 
 is inexpedient. | pedient. J act is just.* 
 
 O'. Some not-X are ) „ ^^ -cr r, „ 
 
 not not-Y. | = home not-X are Y. = Some Y are not X. 
 
 Some invisible things f = Some invisible (= Some tangible things are 
 are not intangible. ( things are tangible, j not visible. 
 
 E', No not-X is not -Y. = Every not-X is Y. ^ Every not-Y is X. 
 
 No mortal who-is- f= Every mortal who-) _ , , . . 
 
 nota-brute is in- \ is-not-a.brute is C =Every mortal who-is-m- 
 capableofsin. ( capable of sin. ) capabl&of-sm is a brate. 
 
 I'. Some not-X are)™ .~~ ^^c -o- -^ 
 
 .y r Somenot-Xarenot Y.= Some not-Y are not X. 
 
 Some invertebrates (= Some invertebrates (= Some wingless animals 
 are wingless. J are not winged. ^ are not vertebrates. 
 
 The Infinitation of the four additional Judgments first 
 considered by Sir W. Hamilton cannot with equal facility 
 be reduced to rule. As either Afa or Afa' is a perfect ex- 
 pression of the absolute identity of what the two Terms 
 denote, either may be deduced by Infinitation from the 
 other, and, by the same means, several other less perfect 
 expressions of the same identity may be obtained. But of 
 these less ^perfect expressions some may more properly be 
 regarded as inferences by Subaltemation. Thus, — 
 
 Afe. AUXareaU^ ( No X is not-Y ) ( Every not-Y is not-X. 
 
 .^. A,i ^ > = ^ No Yisnot-X i = <AllXareY. 
 
 Inll^Y^) (EverynotXisnot^Y) ( All Y axe X. 
 
 All extended are all divisible = All unextended are all indivisible. 
 
 On the other hand, as Ini and Ini' are indefinite expres- 
 sions of the partial disagreement of the two Terms, they 
 
 * Some writers upon the theory of morals, who have strenuously main- 
 tained that "no unjust act is expedient," have yet been very unwilling to 
 admit that "every expedient act is just." Yet the latter proposition is a 
 necessary inference from the former. 
 
156 THE DOCTRINE OF IMMEDIATE INFEEENCE. 
 
 yield no inferences by Infinitation properly so called; 
 though, if some be taken in its semi-definite sense, they 
 yield a number of unimportant inferences by what Sir W. 
 Hamilton calls Integratwn. 
 
 The following are the more common inferences by In- 
 finitation firom the two remaining pairs of these four Judg- 
 ments. In these it will be observed that the Quantity of 
 the Conclusion often differs from that of the Premise. 
 
 Ifa. Some X are all Y. = All not-X are not-T. = No T is not-X. 
 SomecnrvilinearBare f = All rectilinears are < = No circnlar is rec- 
 all circulars. \ not-circulars. \ tilinear. 
 
 Ani. No X is some Y. j = ^^ly°^^ are not > go^^Tare not-X. 
 
 No tyrants are some ( = ^"""^ ^?°, "^ "°* f = Some kings are 
 kings. j I^™ t nottyrannieal. 
 
 Ifa'. Some not-X are all ) vr tr . ^ tt- \ = Some not-X are 
 
 not-Y. | = NoX.snot-Y. | ^^^^ 
 
 Some tmsentient are ( = No sentient thing is ( = Some nnsentient 
 all inorganic. ^ inorganic. \ are not organic. 
 
 Ani'. Not any not-X is) „ -^ .— „ ..-o-_-v- 
 
 ■' ^ „ S- = Some X are not Y. = Some not-T are X. 
 
 some not-Y. J 
 
 Not any dishonest is f = Some honest are not C = Some impmdent 
 some imprudent. \ prudent. | are honest. 
 
 2. Conversion. 
 
 A Judgment is said to be converted when its Subject 
 and Predicate have been made to change places with each 
 other. Before Conversion, the Judgment is called the 
 ^ Oonvertend; after Conversion, it is the Converse. The 
 logical doctrine of Immediate Inference by Conversion 
 shows us when and why the truth of the Converse is a 
 necessary consequence of the truth of the Convertend. 
 In other words. Logic takes notice only of what is called 
 illative Conversion, in which the Convertend and the Con- 
 verse must either both be true, or both be false, together. 
 Thus, the Conversion of iVo A is £, into M B is A,i& illa- 
 tive ; we can say, 
 
CONVERSION. 157 
 
 No carnivorous animal is ruminant ; 
 
 therefore. No ruminant animal is carnivorous. 
 But the Conversion of S<yme A are not B, into Some B are 
 not A, is not illative ; because we can say, Some men are not 
 logicians, it does not follow that Some logicians are not men. 
 
 In Conversion of Judgments, the learner must remem- 
 ber that the whole Predicate must change places with the 
 whole Subject; — that is, whatever belongs to the Predi- 
 cate must be transferred to the Subject's place, and what- 
 ever relates to the Subject to the Predicate's place. For 
 example ; — Some temple is in the city, is not converted into 
 Some city is in the temple, but into Something in the city is 
 a temple. Again, — the Predicate of Every old man has 
 been a boy, is not boy, but has been a boy ; therefore, it is 
 not converted into Some hoy has been an old man, but into 
 Some one who has been a boy is an old man. To avoid mis- 
 takes of this sort, every proposition, before Conversion, — 
 or, indeed, before it is subjected to any logical treatment 
 whatever, — should be reduced to its simplest logical form, 
 — that is, to the formula A is B, or A is not B. Then no 
 error can arise, if we remember that aU which precedes the 
 Copula, is or is not, is the Subject, and that all which fol- 
 lows the Copula is Predicate. 
 
 In treating of Conversion, as well as in other portions of 
 the subject, we first consider exclusively the doctrine of the 
 AiistoteHc system, which admits only of four fdndamental 
 Judgments, and reserve for subsequent treatment the 
 Hamiltonian theory of eight Judgments. 
 
 There are three sorts of Conversion. The first is appli- 
 cable to I! and Z, Universal Negatives and Particular 
 AflSrmatives, and is called Simple Conversion, because both 
 the Quantity and the Quality of the Judgment remain un- 
 changed ; that is, E is converted into B, and I into I. If 
 it is true that No man is immortal, it follows by Immediate 
 Inference that JNb immortal is man; for if any one immor- 
 
158 THE DOCTEINE OF IMMEDIATE INFERENCE. 
 
 tal were a man, it would not be true that No man is imr 
 inortal. Likewise, if Some men are just, it follows imme- 
 diately that (Some just beings are men ; because the assertion 
 that No just being is a man, would contradict the Con- 
 vertend. By Simple Conversion, then, a Universal Nega- 
 tive passes over into a Universal Negative, and a Particular 
 Affirmative into a Partictdar Affirmative. 
 
 The second sort is Conversion per acddens, in which the 
 Quantity is changed from Universal to Particular, but the 
 Quality remains unaltered. This is applicable to A, and 
 also may be applied to E, though the latter, as we have 
 just seen, may also be converted simply. But A cannot 
 be converted simply ; because, though aU men are animals, 
 it does not follow that all animals are men. The Judgment 
 in the Convertend is, that men are included under the class 
 of animals, not that they constitute all animals ; they are 
 only some animals. Hence the Converse is, Some animals 
 are men. We have already seen that E is converted sim- 
 ply into E ; but O also is obtained by Immediate Inference 
 from B; for, if None are, it follows that Some are not. 
 Hence, the Convertend, No man is immortal, yields as its 
 Converse, not only E, No immortal is man, but O, Some 
 immortals are not men. Conversion per acddens, then, 
 changes A into I, and E into O, the Quantity in both 
 cases being diminished, but the Quality remaining un- 
 changed. 
 
 The Judgment O remains, and this cannot be converted 
 either simply or per acddens. From the Convertend, 
 Some men are not learned, we cannot infer that Some 
 learned beings are not men. Indeed, properly speaking, 
 O cannot be converted at all on the AristoteUc system ; 
 but by an artifice which is called Contraposition, the third 
 sort of Conversion, another Judgment can be inferred 
 from it, which is called its Converse, though it is prop- 
 erly the Converse of its Equipollent or Infinitated equiv- 
 
CONVERSION. 159 
 
 alent. In order to convert by Contraposition, then, first 
 infinitate the Convertend by Rule First, and then convert 
 simply. Thus, — 
 
 Convertend. Some A are wA B. Some men are not learned. 
 
 Infinitated equivalent. Some A are not-B. Some men are unteamed. 
 Converse of this. Some not-B are A. Some unlearned persons are men. 
 
 Hence I is the Converse by Contraposition of O ; and 
 in like manner, A by Contraposition yields E, the effect 
 of this sort of Conversion being to change the QuaUty of 
 the Convertend, while its Quantity remains unaltered. A 
 is thus contraponed : — 
 
 Convertend. All Ais B. All men are rationed. 
 
 Infinitated equivalent. No A is not-B. No man is irrational. 
 
 Converse of this. No not-B is A. No irrational being is a man. 
 
 No inference can be obtained from I by Contraposition ; 
 for if infinitated, I becomes O, which cannot be converted 
 except by infinitating it back again. Logicians seem to 
 have overlooked the fact that E can be contraponed into 
 I, though the inferred Judgment in this case, because its 
 Quantity is diminished, is weak and comparatively worth- 
 less. Thus, — 
 
 No A is B. No fish is warm-blooded. 
 
 Every A is not-B. Every fish is cold-blooded. 
 
 Some not-B are A Some cold-blooded animals are fishes. 
 
 The results of the three sorts of Conversion have been 
 summed up in this (nonsense) mnemonic line, in which 
 each dissyllable contains the vowel-symbol first of the Con- 
 vertend and then of its Converse ; and each pair of these 
 dissyllables is followed. by the (italicized) abbreviation of" 
 the kind of Conversion by which the two preceding infer- 
 ences have been obtained ; simp. ::= Simple : Ace. = per 
 accidens ; and Cont. = Contraposition. 
 
 Ecce tibi, simp. ; armi-geros, ace. ; ante boni, Cont. 
 
 The same thing is more briefly indicated in these two 
 Latin words. Hoc capessit, in which oc-ca signifies that O 
 and A are converted by Contraposition ; ape, A and E per 
 accidens ; essi, E and I simply. 
 
160 THE DOCTRINE OF IMMEDIATE INFERENCE. 
 
 The most striking merit of Sir W. Hamilton's system of 
 the thorough-going quantification of the Predicate is, that 
 it ahoHshes at once this whole cumbrous system of Con- 
 version in three kinds, with its attendant rules, and sub- 
 stitutes for it the universal and self-evident process of Sim- 
 ple Conversion. As it has already been demonstrated, that 
 each Term of every Judgment has its own Quantity in 
 Thought, and consequently, that the distinction of Subject 
 and Predicate may be, for most logical purposes, left en- 
 tirely out of view, every Judgment being reduced to an 
 equation, in which, of course, it makes no difference which 
 of the equated quantities is placed first. Conversion be- 
 comes at once a simple, imiform, and self-evident process. 
 As an old logician (Du Hamel, as quoted by Mr. Baynes), 
 remarks, " omnes conversionum leges pendent a cohaesione, 
 vel potius ab identitate, subjecti et aftributi ; quod si enim 
 subjectum conjungitur et identificatur, ut aiunt, cum attri- 
 buto, necesse est pariter attributum uniri et idenUJicari 
 cum subjecto." Though it is hardly necessary even for 
 the youngest learner, I give examples of the HamUtonian 
 mode of converting each of the eight Judgments. 
 
 Cmverted. Converse. 
 
 Afa. AU rational are all moral ( = Afa. All moral are all rational 
 
 beings \ beings. 
 
 Afi (A)- All lilies are (some) ira^ f := Ifa. Some fragrant things are all 
 
 grant ( lilies. 
 
 Ifa. Some plants are all trees = Afi. All trees are (some) plants. 
 
 Ifi (I). Some vicious men are rich = Ifi. Some rich men are vidons. 
 
 /.r^v -vT ^ •» ,ff = Ana. Nothidg that can move itself 
 
 Ana(E). No matter can more itselt J is matter 
 
 Ani. TSot (any) indistinct are ( = Ina. Some sounds are not indis- 
 
 some sonnds \ tinct. 
 
 Ina (O). Some virtuous men are ( = Ani. Not (any) happy are some 
 
 not happy \ virtuous men. 
 
 Ini. Some singers ore not some (s= Ini. Some musicians are not 
 
 (good) musicians 1 some singers. 
 
 Conversion per accidens, says Mr. Mansel, is so called 
 
CONVERSION. 161 
 
 because it is not a Conversion of the Universal fer se, but 
 only of tlie Particular which happens to be included in the 
 Universal. " Some B is A," is primarily the Converse of 
 " Some A is B," and only secondarilt/ of " AM A is B," or 
 because " All A " includes " Some A." Properly speak- 
 ing, then, it is no Conversion at aU, but only an Immediate 
 Inference by Subaltemation from the proper Converse. 
 This is clearly seen in the case of the Universal Negative, 
 B ; No A is B, is first converted into E, Nb B is A, whence 
 we obtain by Subaltemation O, Some B are not A. 
 
 Moreover, it is evident that, by reconvertilig the Con- 
 verse, we ought to regain the Convertend. But this can- 
 not be done after converting per accidens ; we first convert 
 A into I, and then reconvert I, not into A, but into Z. 
 For example ; — All mm are mortal, yields by accidental 
 Conversion, Some mortals are men; and this is reconverted 
 simply into Some men are mortals. 
 
 It- is fiirther argued by Hamilton, that the Aristotehe 
 doctrine applies Conversion to the naked Terms only, — 
 to the Subject and Predicate of the Convertend without 
 regard to the Quantity of either ; it thus changes aU to 
 some, and, as we have just seen, it makes the total Quan- 
 tity of the Converse inferior to that of the Convertend^ 
 But this is evidently wrong ; for the quantified Terms are 
 the Concepts which were compared in Thought in the 
 Convertend, and these only ought to appear after Conver- 
 sion, and appear unchanged. Contraposition, as we have 
 already shown, is a mediate process, the Conversion being 
 possible only through a previous Infinitation ; for the origi- 
 nal Judgment, on the AristoteHc doctrine, is not convert- 
 ible at all. But as every Judgment is certainly the result 
 of a comparison, to assert that it is inconvertible, is to 
 maintain that A can be compared with B, while, at the 
 same moment, B is not compared with A; — which is 
 absurd. Comparison is necessarily bilateral. 
 
 K 
 
162 the doctrine. of immediate infekence. 
 
 3. Opposition and Integration. 
 
 Opposition is said to exist between Judgments which 
 have the same Matter (i. e. the same naked or unquanti- 
 fied Subject and Predicate), but differ in Quantity, or in 
 QuaUty, or in both. The logical doctrine of Opposition 
 shows us what can be immediately inferred as to the truth 
 or falsity of one Judgment, from positing or sublating 
 (i. e. affirming or denying) one of its Opposites. Thus, 
 from positing E, No A is B, I can immediately infer the 
 truth of its Subaltern Opposite, O, Some A are not B, and 
 the falsity of its Contradictory Opposite, I, Some A are B ; 
 but I cannot infer, from sublating E, the truth of its Con- 
 trary Opposite, A, Ml A are B. ^ 
 
 But here the word Opposition jnust be taken in a tech- 
 nical and qualified sense. It was first apphed only to the 
 relations Between two Contraries, or two Contradictories ; 
 and this is its proper or strict meaning, as any two Buch 
 Judgments are opposed to each other, the one negativing 
 the other, and it is impossible that the two should be true 
 together. But as it was convenient for Logicians to con- 
 sider the relations of Subaltemation and Sub-Contrariety 
 under the same head with the two former, the meaning of 
 the word was extended so as to cover all the relations 
 existing between two Judgments of the same Matter, but 
 of different Form, although some of these are relations not 
 of opposition, but of congruity. 
 
 There are four sorts of Opposition. The first and most 
 perfect of these is that of Contradiction, which exists be- 
 tween two Judgments which differ from each other lath in 
 Quantity and <Quality ; that is, between A and O, and be- 
 tween E and I. This sort of Opposition is governed by 
 the Axiom of Excluded Middle, which declares that of 
 two Contradictories, — that is, of two Judgments between 
 which there is no " Middle," no intermediate Judgment, — 
 
OPPOSITION AND INTEGRATION. 163 
 
 one must be true ; and then the Axiom of Non-Contra- 
 diction adds, that the other must be false. Now, A and 
 
 are two such Judgments, and likewise B and I; so also 
 the two Singular Judgments, Socrates is wise, and Socrates 
 is not wise. Between either of these pairs, no " third " or 
 intermediate Judgment is conceivable. Hence the univer- 
 sal rule for this sort of Opposition, that Contradictories can- 
 not loth he true, and cannot both he false. Therefore, as 
 both cannot be true, if I posit (affirm) one, I immediately 
 infer that the other is sublated (denied) ; and as both can- 
 not be false, if I sublate one, the other is posited. For 
 example ; — if E is not true, that No quadrwped is rational, 
 
 1 must be true, that Some quadrwpeds are rational. 
 
 Observe that two Judgments properly contradict each 
 other only when that which is affirmed by the one is de- 
 nied by the other, — 1. in the same manner ; 2. in the same 
 respect; 3. in the same degree; and 4. at the same time. 
 Thus, to borrow some examples from Aldrich, — 1. A dead 
 body is, and is not, a man ; that is, it is a dead man, but 
 not a Uving one. 2. Zoilus is, and is not, black ; that is, 
 black-haired, but red-faced. 3. Socrates is, and is not, 
 long-haired ; that is, he is so, if you compare him with 
 Scipio, but is not so, if you compare him with Xenophon. 
 4. Nestor is, and is not, an old man, according as you 
 speak of him when in childhood, or when he was at the 
 siege of Troy. 
 
 The second sort of Opposition is that of Contrariety, 
 which exists between two Universal Judgments, that differ 
 in Quality, hui are alike in Quantity ; that is, between A 
 and E. Here the Axiom of Excluded Middle does not 
 apply ; for between A and E, there is a " Middle " or 
 intermediate Judgment, namely, I. Though it is not true, 
 either that all men are wise, or that no man is wise, it is 
 true that some men are wise. Hence both Contraries may 
 be false, so that I cannot infer the truth of one from the 
 
164 THE DOCTRINE OF IMMEDIATE INFEEENCE. 
 
 falsity of the other. On the other hand, as one of these 
 Contraries affirms what the other denies, the Axiom of 
 Non-Contradiction apphes ; both Contraries cannot be true ; 
 and, therefore, from the truth of one I can immediately 
 infer the falsity of the other. Accordingly, the rule is. 
 Contraries may he false together, hit hoik cannot he true. 
 Therefore, from positing either A or E, I can immediately 
 infer that the other is sublated ; but from sublating either, 
 I cannot infer that the other is posited. 
 
 The third sort of Opposition is that of Suh- Contrariety, 
 which exists between two Particular Judgments, that differ 
 in Quality, hut are alike in Quantity ; that is, between I 
 and O. To these, the Axiom of Excluded Middle is 
 apphcable ; for there is no third, or intermediate. Judgment 
 conceivable between Some are, and Some are not. Accord- 
 ingly, both cannot be false, but one must be true. On the 
 other hand, if I and O are considered as Propositions, that 
 is, if the Judgments are expressed in words, the Axiom of 
 Non-Contradiction does not apply to them ; for both may 
 be true. Though some men are learned, it is also true that 
 some men are not learned. But observe, that the " some 
 men " in the latter case are not the same " some men " as 
 in the former ; though expressed by the same words, they 
 are thought as different. To make the former Proposition 
 true, " some men " may be thought to be " graduates of 
 Oxford " ; to make the latter true, " some men " may 
 mean " American Indians." As Propositions, then, and 
 possibly as Judgments, the two assertions do not contradict 
 each other, but may both be true. Hence the rule, that 
 Sub-Contraries may he true together, hut cannot hoih he false. 
 Therefore, by sublating either I or O, we immediately infer 
 that the other is posited ; but by positing either, we can- 
 not infer that the other is sublated. Of course, Sub- 
 Contraries can be called " opposites " only in a qualified 
 and technical sense ; they are actually congruent, or, to 
 
OPPOSITION AND INTEGRATION. 165 
 
 adopt one of Hamilton's newly-coined words, they are 
 " compo^ible." 
 
 The fourth sort of Opposition is that of Suhalternation, 
 which exists between Judgments alike in Quality, but dif- 
 ferent in Quantity ; that is, between A and I, and between 
 E and O. Here, again, it is evident that the " Opposi- 
 tion " is merely technical, the two Judgments being not 
 merely consistent, but so nearly allied that the Particular 
 can be inferred from its Universal by the Axiom of Iden- 
 tity. Since all includes some, if we affirm A, AU A are B, 
 we thereby also aflSrm I, Some A are B ; and in Kke man- 
 ner, to posit E is also to posit O. The same Axiom com- 
 pels us to think, that sublating I Sublates A also, and 
 sublating O sublates E also. In this sort of inference, the 
 Universal may be called the Subalterwms, and the Particu- 
 lar, the Suialternate. Hence we have this rule for infer- 
 ence by Subaltemation, that if the Suhalternans is true, the 
 SubaUernate is true also ; and if the Subaltemate is false, 
 the Suhalternans is false also. 
 
 Summing up, we have the following list of Immediate 
 Inferences by Opposition. 
 
 ! If A is true, O is false, E false, and I true. 
 If E is true, Z is false, A false, and O true. 
 ( If I is false, E is true, O true, and A false. 
 ( If O is Mse, A is true, I true, and E false. 
 
 If A is false, O is true, ) , i .1 i 
 
 ^„ . „ , . \ the others unknown. 
 
 If E is false, I is true, ) 
 
 If I is true, E is false, j ^j^^ ^^^^^ unknown. 
 
 If O is true, A is false, ) 
 Hence it appears, that from the truth of a Universal or 
 the falsehood of a Particular, we may infer the character of 
 all the opposed Judgments ; but from the falsehood of a 
 Universal or truth of a Particular, we can know the char- 
 acter only of the Contradictory. 
 
166 
 
 CONSPECTUS OF THE DOCTRINE OF 
 
 JUDGMENTS, considered 
 in reference to 
 Quantity, are either Univer- 
 sal or Particular ; to 
 QuAUTY, are either Affirma- 
 tive or Negative ; to 
 Quantity and Quality, are 
 of four sorts : — 
 
 Affirmative PredesignationB of Univer- 
 salJaAgmenU. 
 
 All _ Every — Each— This — That 
 — These — Those — a Proper 
 Name. 
 
 A- Universal AffirTnatax. 
 
 e.g. All X is T. 
 
 All metals are losbrons. 
 
 IMMEDIATE INFERENCE proceeds 
 
 BY InFINITATION 
 
 of the Terms of a Judgment, or by dropping their Infini- 
 tatioh, the Judgments thus produced being, in certain 
 cases, OBqwipollent, or equivalent to those from which 
 they were derived. 
 
 BY Opposition, 
 
 or the relation that 
 exists between Judg- 
 ments which have 
 the same naked or 
 unquantified Subject 
 and Predicate, but " 
 diifer in Quantity, 
 or Quahty, or both. 
 
 Conferaiy. 
 
 Sub-Oontntiy. 
 
 Four Kinds 
 
 1. CONTRADICnOH 
 
 E exists betireen Judgments 
 which differ both in Quan- 
 tity and Quality. 
 Rule. — Contradictories can- 
 not both be true and cannot 
 both be fklse. Hence, 
 to posit A is to sublate O 
 " E " " . 1 
 to sublate A is to posit O 
 " B " " I 
 
 and conrersely, 
 
 to posit O is to Bublate A 
 
 BY Conversion, 
 
 or causing the Subject and 
 Predicate of a Judgment 
 to change places with each 
 other, but in such man- 
 ner that if the Convertend 
 is true, then the Converse 
 will be true also. 
 
 Three Kinds 
 
 1. SlMPMi, E & I, 
 
 without changing either the Quantity 
 
 or the Quality. (Ecceiibi,) 
 Convertend. No X is Y. E into 
 
 Converse. No Y is X. E. 
 
 Convertend. Some X are Y. I into 
 Converse. Some Y are X. I. 
 
JUDGMENTS AND IMMEDIATE INFERENCE. 
 
 167 
 
 Negative Predesignations of Vhiver. 
 sal Judgments. 
 
 None — Not any — Not one — Not 
 this — Not that — " Not " prefixed 
 or suffixed to a Proper Name. 
 
 Predesignations of Particular Judg- 
 ments, either Affirmative or Nega- 
 tive. 
 
 Some — Not all — or any indication 
 of an indefinite part of a whole. 
 
 E. Universal Negative. 
 
 No X is T. 
 No quadruped is rational. 
 
 I. Particular Affirmative. 
 
 Some X are T. 
 Some swans are black. 
 
 O. Particular Negative. 
 
 Some X are not T. 
 Some men are not far 
 mous. 
 
 Two Kinds of Infinitation. 
 
 Rde. — To change the Infinitation of 
 the Predicate, either by infinitating 
 it or by dropping its Infinitation, 
 change the Quality of the Judgr 
 ment; the Quantity of the Judg- 
 ment remains unaltered. 
 
 Rule. — To change the Infinitation of 
 the Subject, convert the Judgment, 
 and then either change the Quality, 
 or change the Infinitation of the 
 (old) Predicate also. Here, also, 
 the Quantity is unaltered. 
 
 OF OpposiTioisr. 
 
 2. COHTRARIBTT 
 
 exists between Universal 
 
 . .Tudgments that differ io 
 
 Quality, but are alilse in 
 
 Quantity. 
 
 Rule. — Both Contraries may 
 
 be false, but both cannot 
 
 be true. Hence, 
 
 to posit A is to sublate E 
 
 " B " " A 
 
 3. SUB-CONXRARIETT 
 
 between Particular 
 Judgments that differ in 
 Quality, but are alike in 
 Quantity. 
 Rule. — Sub-Contraries may 
 both be true, but cannot 
 both be false. Hence, 
 to sublate I is to posit O 
 " o " "I 
 
 4. SUBALTESHATION 
 
 exists between Judgments 
 alike in Quality, but differ- 
 ent in Quantity. 
 
 Rule. — If the Subaltemans 
 (the Universal) is true, the 
 Subaltemate (the Particu- 
 lar) is also true ; and if the 
 Subaltemate is false, the 
 Subaltemans is f^se also. 
 Hence, 
 
 to posit A is to posit Z 
 
 " E " " O 
 
 to sublate I is to sublate A 
 
 " o " « a 
 
 OF Conversion. (_Sbo capessit.~) 
 
 2. Pek Acoidens, a & E, 3. Bt Conteaposition, A & O. 
 
 changing the Quantity, but not the 
 
 Quality. (Armi-geros.) 
 Cmvertend. All X is Y. A into 
 
 Converse. Some Y is X. I. 
 Convertend. No X is Y. E into 
 
 Some Y is not X. O. 
 
 changing, not the Quantity, but the 
 Quality, through infinitating t]je 
 Predicate. [Anteioni.) 
 
 Convertend. All men are mortal. A- 
 
 Converse. No immortal is man. E. 
 
 Convertend. Some men are not 
 
 wliite. O- 
 
 Converse. Some not-white are men. I. 
 
168 
 
 THE DOCTEINE OF IMMEDIATE INFERENCE. 
 
 Contrary. 
 
 E 
 
 Sub-Contrarj. 
 
 That the various points in the doctrine of this sort of 
 Immediate Inference might be more easily remembered, 
 
 the old logicians contriyed, 
 not some mnemonic verses, 
 as on other occasions, but 
 the accompanying inge- 
 . nious diagram, which may 
 be called the Square of 
 Opposition. It is very 
 easy to retain the whole 
 theory in the memory, 
 when we observe the 
 proper position, upon this 
 square, of the vowels which 
 indicate the four species of Judgments. The upper line 
 belongs to the Universals, A and E ; the lower line to the 
 Particulars^ I and O ; the left hand to the Affirmatives, 
 A and I ; and the right to the Negatives, IS and O. Then 
 it is easily remembered, that the two diagonals represent 
 Contradiction, the upper line Contrariety, the lower one 
 Sub-Contrariety, and each of the two sides Subaltemation. 
 For the further convenience of learners, I have brought 
 together in the preceding Conspectus the principal techni- 
 calities and rules in the Aristotelic doctrine of Judgments 
 and Immediate Inference. 
 
 Hamilton has considerably enlarged and modified the 
 doctrine of Immediate Inference by Opposition, by intro- 
 ducing, what the logicians had hitherto neglected, the 
 semi-definite meaning of some, — that is, some at most, — 
 some excluding all and none. In the Aristotelic doctrine, 
 some was applied exclusively in its wholly indefinite mean- 
 ing, as some at least, — soms, perhaps all; — and in nega- 
 tives, some, perhaps none. Yet, as Hamilton remarks, some 
 is always thought as semi-definite when the odier Term 
 of the Judgment is Universal ; and it is only when both 
 
OPPOSITION AND INTEGRATION. 169 
 
 Terms are Particular, that the some of each is left wholly 
 indefinite. Thus, when we say, Some men are (all) hlack,^ 
 we mean to deny that all are black ; Some flowers are not 
 (any) fragrant, denies that none are fragrant. 
 
 But in the case of Subaltemation, which Hamilton pre- 
 fers to caU Restriction, if we introduce this semi-definite 
 meaning, and think some as some only — not all, instead of 
 having an Inference from the Subalternans to the Subalter- 
 nate, we find a true Opposition between them; to adopt 
 the Hamiltonian word, the two Judgments are Incom/pos- 
 sible. Thus, Some (only — not all) men are yellow, is really 
 opposed to All men are yellow, instead of being an Infer- 
 ence fi-om it ; and in like manner. Some (not all) hipeds 
 are not men, is opposed to No bipeds are men. This new 
 sort of Opposition or IncompossibiUty, as it exists between 
 two Judgments which are alike in Quality, either both 
 Affirmatives or both Negatives, while the other two sorts, 
 Contradiction and Contrariety, differ in Quality, is called 
 Inconsistency. Of course, as two Inconsistents, like any 
 other two Incompossibles or Opposites, cannot both be 
 true, the true Inference is, that by positing either A or I, 
 I! or O, the other is sublated. To express the whole doc- 
 trine of Subaltemation or Restriction in one rule; — If 
 some means some — perhips all, the Subaltemate is a direct 
 Inference from positing the Subalternans ; but if some 
 means some — not all, the Subalternans and Subalternate 
 are Opposite or Incompossible, so that, by positing either, 
 the other is sublated. 
 
 Again, it has already been shown that Sub-Contrariety 
 is properly no Opposition at all, so that both Judgments 
 may be true ; though, as both cannot be false, sublating one 
 enables us to posit the other. But if we introduce the 
 semi-definite meaning of some here also, we have a new 
 Inference fi-ogi one to the other; — fi-om the one some, 
 which is a part, to the other sonie, which is the remaining 
 
 8 
 
170 THE DOCTRINE OF IMMEDIATE INFERENCE. 
 
 part necessary to constitute the whole. This sort of Infer- 
 ence Hamilton would call Integration, as its effect is, aiiter 
 determining one part, to reconstitute the whole by bringing 
 into view the remaining part. Thus, if I know that Some 
 (not all) men are white, I can immediately infer that Some 
 (other) men are not white; and if Some poets are not philos- 
 ophers, it foUows that Some (other) poets are philosophers. 
 In such cases, though the two Judgments are different in 
 Quality, they are not opposed, but congruent ; and the 
 Inference may be not only to all others definitely, but to 
 some others indefinitely. It is valid, also, whether some 
 appears in the Subject or Predicate. Thus, from Men are 
 some animals, we immediately infer that Men are not some 
 (other) animals (say, brutes). Here, the Inference con- 
 cerns the Predicate, while in the preceding cases it con- 
 cerned the Subject. 
 
 To apply the whole doctrine of Incompossibility and In- 
 tegration, in both meanings of the word some, to the eight 
 HamUtonian Judgments, is evidently a long and complex 
 process. The following table (page 172), in which the 
 whole process is worked out, is borrowed from Sir "William 
 Hamilton, and placed here, not, of course, that it may be 
 committed to memory, but because the examination of it 
 will be a useful exercise for the learner. In explanation 
 of it, observe that the Incompossibility, or the fact that the 
 two Judgments cannot both be true, — and in some cases, 
 the Restriction (Subaltematidn) and the Integration, — 
 may be bilateral (here marked hi), as affecting both Subject 
 and Predicate ; thus, 
 
 All physical laws are all efficient causes. 
 Not any physical law is any efficient cause. 
 Or unilateral (un), as affecting either the Subject only; 
 thus. 
 
 All men are all rational. 
 
 Some men are not (any) rational. 
 
OPPOSITION AND INTEGRATION. 171 
 
 Or the Predicate only ; thus, — some in the second Judg- 
 ment being semi-definite, — 
 
 All dogs are all barking animals. 
 
 All dogs are some barking animals. 
 Or it may be unilateral cross (un. cr.), as reversing in 
 the one Judgment the relation of Genus and Species — 
 containing and contained — which exists between the 
 Terms of the other Judgment ; thus, some being semi- 
 definite, 
 
 All whites are some civilized. 
 
 Some wliites are all civilized. 
 Or bilateral cross (bi. or.'), as afiecting both Terms, but in 
 opposite relations, — as fi-om Particular to Universal in 
 the Subject, and fi-om Universal to Particular in the Predi- 
 cate ; thus, some being semi-definite. 
 
 Some blacks are all AMcans. 
 
 Not any black is some Africans. 
 Or bilateral direct (bi. di.'), as affecting both Terms, and 
 excluding any intermediate or third Judgment, both propo- 
 sitions remaining the same after conversion ; thus, 
 
 Some men are (some') irrational. 
 
 Not any man is (any) irrational. 
 
172 
 
 THE DOCTRINE OF IMMEDIATE INFERENCE. 
 
 TABLE 
 
 OF THE MCTUAL RELATIONS OF THE ElGHT PbOPOBITIOITAI, FOKMB OH 
 
 EiTHEB System of PAHxicnLABiiT. {For Generals only.) 
 
 ■s . 
 
 lit 
 
 .If 
 .Si 
 
 -rS 
 
 4 
 
 S3 
 
 MC4 
 
 is 
 8 
 
 
 i 6 
 
 °g 
 
 W .9 M 
 
 i 
 
 §1 
 
 • +3 
 
 ^^ . 
 
 
 
 
 
 6,=8 
 
 c8=g^ 
 
 
 
 fi« 
 
 ««£ 
 
 113 
 
 CQ en 09 
 
 43i 
 
 BO C 
 
 C4 CO 111 <« 1^ COI:-00 
 
 111 iT III 
 
 rH ^ pH ei CO lotoia 
 
 00 oo 
 
 1 1 
 
 op CO OD 
 
 I I i 
 
 I I 
 
 k^OD Oi>- CD 
 
 It Tit-^ 
 
 
 
 .Si 
 
 if 
 
 -3« 
 
 a c 
 o- o 
 
 o u 
 
 a a 
 
 o o 
 
 £5 
 
 
 
 
 
 h 
 
 
 s 
 
 § 
 
 § 
 
 i 
 
 ■& 
 
 §:s 
 
 ». 
 
 
 ^ 
 
 
 U 
 
 
 1 
 
 f= 
 
 i 
 
 g 
 
 ?-S 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ooo 
 
 u 
 
 O 
 
 ou 
 
 1-. ^ I 
 
 O O t 
 
 O <D 
 
 
 II I II I 
 
 
 ■a o'q S*S o*c g-- b'H S*s 
 
 ^ ^ *c ^ 'S [5 
 
 m7777 I III I III IN MM 7 
 
 q a c '3 '3 « 
 
 S5c'3'3« >S'2<2!Sqa!Bo3<B a 0! « a 
 
 <!<!<>!<5-^£ -<!<!<!<!<!<!<!-<)gSgg£aSg 
 
 3§ 
 
 ■a - 
 
 SCI 
 
 g3 
 
 153 
 
 II I II I III M I l2 IT I M lllli I Mill 
 
 Abbrbtiatiohs : Oontrar. = Contrariet ; Incons, = InconsiaterUa ; Int or Integr. = In- 
 tegration ; Eepugn. = Rtpugnantt, Contradictoriea ; Rea. or Reatr. = RestrioHon, Su»- 
 alternation ; Blanks, In I. = CompoMiblu ,- in n. ■= Wo in/erence. 
 
 ThiB Table may not be quite accurate in details. 
 
OPPOSITION AND INTEGBATION. 173 
 
 It appears from this Table, that Afi and Ina (A and O), 
 which, on the Aristotelic doctrine, are Contradictories, be- 
 come only Contraries when we admit the semi-definite 
 meaning of some ; for by sublating Ina, which denies only 
 a part (some only), we know not whether to posit Afi, 
 which affirms the whole, or Ifi, which affirms only some 
 (other) part, or Ana, which denies the whole ; since each 
 of these three is incompossible with Ina. For the same 
 reason, Ifa and Ani, which are only A and O converted, 
 are merely Contraries on this system, though Contra- 
 dictories on the other, wherein some means perhaps all. 
 Indeed, there can be no Contradiction on this system, 
 wherein whole and part negative each other, just as much 
 as cffirmation and negation. The only Contradictories are 
 those in which the distinction of whole and part does not 
 exist ; — Judgments about Singulars or Individuals, for 
 instance, and about Universals regarded as Singulars or 
 as undivided wholes. Thus, Comman salt is chloride of 
 sodium contradicts Common salt is not chloride of so- 
 diwm; for Comman salt, though reaUy a General Term, 
 is here actually thought as undivided, so that the two 
 Judgments contradict each other as directly as do these 
 two Singulars, — John is sick, John is not sick. If either 
 Judgment in one of these pairs is sublated, the other is 
 necessarily posited. 
 
 " The prepositional form i)? is consistent with all the 
 affirmatives ; Ini is not only consistent with all the nega- 
 tives, but is compossible with every other form in uni- 
 versals. It is useful only to divide a class, and is 
 opposed only by the negation of divisibiUty." 
 
 The whole scheme of Opposition upon this system may 
 be safely characteriaed as too complex to be of any prac- 
 tical use, though the learner may be profited by some 
 study of its details. 
 
174 MEDIATE INFERENCE OB SYLLOGISM. 
 
 CHAPTER VII. 
 
 THE DOCTEINE OF MEDIATE INFEEENCE : THE AEISTOTELIC 
 ANALYSIS OF SYLLOGISMS. 
 
 1. Fignre and Mood. — 2. Conditional Syllogisms. — 3. Defective and 
 Complex Syllogisms. 
 
 MEDIATE Inference is that act of Pure Thought, 
 whereby the relation of the two Terms of a pos- 
 sible Judgment to each other is ascertained by comparing 
 each of them separately with a third Term. Thus, if I 
 cannot immediately determine whether A is, or is not, B, 
 I can compare each with M. If, as the result of such com- 
 parison, it is found that A is M and B is M, then we infer 
 mediately — that is, through this relation of each to a third 
 — that A is JB. But if this comparison shows that one of 
 these Terms is, and the other is not, M, then we infer 
 mediately that A is not B. The affirmative conclusion is 
 evidently governed by the Axiom of Identity, which de- 
 clares that A is B, if it is that (M) which is the equivalent 
 of B ; or to use language more consonant with the phrase- 
 ology hitherto employed, and converting B is iff into Mis 
 B, we say that B is a Mark of A, when it is a Mark of 
 that (M) which is a Mark of A, — nota notce est nota rci 
 ipsius. The negative conclusion results from the Axiom 
 of Non-Contradiction, which declares that A is not B, when 
 it is equivalent to that (or has for a Mark that) (M), 
 which is not B ; or, what is the same thing, when it is rwi 
 equivalent to that (M) which is B. 
 
 The fundamental principle of Mediate Inference or Syl- 
 
THE ARISTOTELIC ANALYSIS. 175 
 
 logism is thus traced to those Axioms which, as we have 
 already seen, must govern all the processes of Pure 
 Thought ; or rather. Mediate Inference itself is but one of 
 the special applications of those Axioms. Instead of using 
 these Primary Axioms themselves, logicians have usually, 
 in order to demonstrate the processes of syllogistic reason- 
 ing, preferred to employ certain intermediate principles or 
 maxims, one of which we have just mentioned, — that the 
 Mark of a Mark m a Mark of the thing itself. But as these 
 maxims can be directly deduced from the original Axioms, 
 to which, indeed, they owe all their validity, it seems bet- 
 ter to test the legitimacy of each step by a reference to the 
 primary, rather than to any derivative, principle. 
 
 Thus far, A and B, in their comparison with M, have 
 been regarded simply as undivided wholes ; but it is evi- 
 dent that the same considerations will hold good if we sub- 
 stitute, for either or both of them, all, or any indefinite part, 
 of a divided Universal. Thus, if we find that Some A are 
 M, and Some B are M, we are compelled to conclude, by 
 the Axiom of Identity, that Some A are (some) B ; or, 
 taking a negative instance, if Some A are M, and Not any 
 B is M, then we infer that Some A are not (any) B. 
 Hence we see the correctness of the derivative or inter- 
 mediate principle which Sir W. Hamilton enounces as 
 " the supreme Canon of Categorical Syllogisms," — In so 
 FAE AS two Notions (Concepts or Individuals), either hoth 
 agree, or, one agreeing, the other does not agree, with a com- 
 mon third Notion, in so far these Notions do or do not 
 agree with each other. But if, by calling it " supreme," he 
 means that it is the ultimate and original Canon, his posi- 
 tion may be doubted; for it is evidently a compound 
 statement, embracing, with an unimportant change of 
 phraseology, the two Primary Axioms of Identity and 
 Non-Contradiction, and guarding, them with those limitar 
 tions under which alone are they ever applicable. 
 
176 MEDUTE INFERENCE OR SYLLOGISM. 
 
 We have seen that, though either or both of the two 
 Terms he quantified Particularly, the Syllogism still holds 
 good, — at least, -to the extent to which the two Terms 
 are quantified. But the third Term must be taken Uni- 
 versally at least once in comparing it with the other 
 Notions ; otherwise, we have no security that these others 
 are compared with the game, or " a common," third Term. 
 Though we know, for instance, that A is some M, and B 
 is some M, still we cannot conclude that A is B ; for the 
 " some M " which is A may not be the same " some M " 
 which is B. Though Some learned men are pedants, and 
 Soma learned men are wise, it does not follow that Pedarvts 
 are wise ; for two very different classes of learned persons 
 are here spoken of. Hence we have this general rule for 
 all Syllogisms, that the Middle Term must he distributed 
 (i. 6. taken Universally) in at least one of the comparisons 
 which are instituted between it and the other two Terms. 
 We say, " at least one " of the two comparisons ; for the 
 other may be quantified Particularly without injury to the 
 reasoning. Thus, if All men are mortal, and X, Y, and Z 
 are (some) mew, we may legitimately conclude that X, Y, 
 and Z are mortals ; for to whatever class these " some men " 
 belong, they are necessarily included under " all men," 
 who are declared to be mortal. 
 
 A Syllogism evidently comprises three Judgments, one 
 of which afiirms the agreement or non-agreement of its 
 two Terms with each other to be the necessary consequence 
 of two other Judgments, in which a common third Term 
 is affirmed to agree with both, or with one only, of these 
 two Terms. The main Judgment is called the Conclusimi; 
 the two subsidiary Judgments, on which it depends, are 
 termed the Premises; and the necessary connection be- 
 tween the Premises and the Conclusion — that which 
 entitles us to infer the one fi-om the other — is the Con- 
 sequence. The essence of the Syllogism, and all tliat is 
 
THE AEISTOTELIO ANALYSIS. 177 
 
 actually affinned in it, is this necessary consequence of the 
 Conclusion from the Premises. Hence the Syllogism is 
 really one, — a single and indivisible act of Thought. 
 Though apparently complex — though, in a certain sense, 
 including three Judgments — it does not afiirm either one 
 of them taken separately, but only the necessary depend- 
 ence of one upon the two others. Thus, as we have seen, 
 both Premises may be false, and the Conclusion may be 
 false ; and yet the Syllogism may be valid or correct in 
 Form, for the latter may be legitimately deduced from the 
 former. The following, for example, is a vaJid inference, 
 though each of the Propositions is false. 
 
 All men are immortal , 
 
 All bipeds are men ; 
 
 Therefore, all bipeds are immortal. 
 Hence, in order to dispute or deny a Syllogism as such, we 
 do not need to deny either of its three Judgments, but 
 only the Consequence, or the dependence of the Conclu- 
 sion upon the Premises ; in other words, a single negation 
 denies all that the Syllogism, which is but one act of 
 Thought, asserts. We say, it does not follow that A is B 
 BECAUSE A is some M and B is some M ; though possibly 
 A is B for some other reason. 
 
 In explanation of the terms employed to denote the pro- 
 cess of reasoning, the following passage is borrowed from 
 Sir William Hamilton's Lectures on Logic : " Reasoning 
 is a modification from the French raisonner (and this is a 
 derivation from the Latin ratio') and corresponds to ratio- 
 cinatio, which has, indeed, been immediately transferred 
 into our language under the form ratiocination. Ratiocina- 
 tion denotes properly the process, but improperly also the 
 product, of reasoning ; ratiocinium marks exclusively the 
 product. The original meaning of ratio was computation, 
 and from the calculation of numbers it was transferred to 
 the process of mediate comparison in general. Discourse 
 
 8* L 
 
178 MEDIATE INFEKENCE OE SYLLOGISM. 
 
 (dismrsm, BidvotaT} indicates the operation of comparison, 
 the running backwards and forwards between the char- 
 acters or notes of objects; this term may therefore be 
 properly appHed to the Elaborative Faculty in general 
 [the Understanding]. The terms discourse and diseursus 
 are, however, often, nay generally, used for the reasoning 
 process strictly considered, and discursive is even applied 
 to denote Mediate, in opposition to Intuitive [or Imme- 
 diate], judgment, as is done by Milton. • 
 
 ' Whence the soul 
 Eeason receives, and reason is her being, 
 DiscursiTe or intuitiTe ; discourse 
 Is oftest yours.' 
 
 The compound term, discourse of reason, unambiguously 
 marks its employment in this sense. 
 
 'A beast that wants discourse of reason 
 Would have mourned longer.' 
 
 Argumentation is derived from argumentari, which means 
 argumentis uti. Argument again (argumenturn) — what 
 is assumed in order to argue something — is properly the 
 middle notion in a reasoning, — that through which the 
 Conclusion is established. It is often, however, applied 
 as coextensive with argumentation. Inference or illation 
 (from infero~) indicates the carrying out into the last Prop- 
 osition what was virtually contained in the antecedent 
 Judgments. To conclude (concludere~), again, signifies the 
 act of connecting and shutting into the last Proposition the 
 two notions which stood apart in the two first. A conclu- 
 sion is usually taken, in its strict and proper signification, 
 to mean the last Proposition of a reasoning ; it is some- 
 times, however, used to express the product of the whole 
 process. To syllogize means to form Syllogisms. Syllogism 
 (crvWoyia-fio^^ seems originally, like ratio, to have denoted 
 a computation, — an adding up, — and, like the greater part 
 of the technical terms in Logic in general, was borrowed 
 
THE AEISTOTELIO ANALYSIS. 179 
 
 by Aristotle from the mathematicians. This primary 
 meaning of these two words favors the theory of those 
 philosophers who, hke Hobbes and Leidenfrost, maintain 
 that all Thought is, in fact, at bottom, only a calculation, 
 a reckoning. SvWoyicr/j.6<s may, however, be considered 
 as expressing only what the composition of the word de- 
 notes, -^ — a collecting together; for crvWoyi^eaOai comes 
 from crvXXeyeiv, which signifies to collect. Finally, in 
 Latin, a Syllogism is called collectio, and to reason, coUigere. 
 This refers to the act of collecting, in the Conclusion, the 
 two notions scattered in the Premises." 
 
 Thus the unifying office of the Understanding, to which 
 we have before adverted, is again brought to view. As a 
 Judgment is an act whereby the two notions which are its 
 Terms are brought together into one, so a Syllogism — 
 Reasoning proper — Mediate Inference — is that act of 
 Pure Thought whereby the two Judgments -s^hich are its 
 Premises are collected and summed up into one in the 
 Conclusion ; or, what is the same thing expressed in relation 
 to the Terms, whereby three notions are reduced to unity. 
 
 " Without the power of Reasoning," says Hamilton, 
 "we should have been limited in our knowledge (if 
 knowledge under such a limitation would deserve the 
 name of knowledge at all) — I say, without Reasoning, 
 we should have been limited to a knowledge of what is 
 given by Immediate Intuition; we should have been 
 unable to draw any inference from this knowledge, and 
 have been shut out from the discovery of that countless 
 multitude of truths, which, though of high, of paramount 
 importance, are not self-evident. This faculty is likewise 
 of peculiar utihty, in order to protect us in our cogitations 
 from error and falsehood, and to remove these, if*they 
 have already crept in. For every, even the most com- 
 plex, web of thought may be reduced to simple Syllo- 
 gisms ; and when this is done, their truth or felsehood, at 
 
180 MEDUTE INFERENCE OE SYLLOGISM. 
 
 least in a logical relation, flashes into view." Hence, as 
 Dr. Whately remarks, "the Syllogistic theory does not 
 profess to furnish a pecrJiar method of reasoning, but only 
 to set forth a method of analyzing that mental process which 
 must invariably take place in all correct reasoning " ; and 
 again, " a Syllogism is evidently not a peculiar kind of 
 argument, but only a pecuhar form of expression in which 
 every argument may be stated." 
 
 The power cf reasoning, of drawing Mediate Inferences, 
 like that of framing Concepts, is at once a proof of man's 
 superiority over the brutes, and of his inferiority to his 
 Creator. Brutes cannot reason, nor even form Judgments 
 respecting classes of things, their knowledge being con- 
 fined, as we have seen, to Intuitions, — to Singulars. On 
 the other hand, the Infinite Mind knows immediately or 
 intuitively the relation of one thing or class of things to an- 
 other, without being compelled to ascertain indirectly their 
 agreement or non-agreement through their relations to a 
 third or Middle Term. The power of Mediate Inference is 
 a help for an imperfect intellect ; Omniscience needs no help. 
 
 The brief view which has now been given comprises all 
 the essential principles of Mediate Inference, — that is, all 
 the rules to which all Syllogisms, whatever may be their 
 peculiarities in other respects, must conform. They may 
 be summed up as follows : — 
 
 1. A Syllogism must corUain three Terms, and no more; 
 namely, the two whose agreement or disagreement we wish 
 to ascertain, and the Third or Middle, with which each of 
 these is separately compared. If there were four Terms, 
 two of them must be intermediate, not appearing in the Con- 
 clusion ; but then the Premises would have no common Term. 
 If ^« know only that A is M and B is iV, we have no 
 means of ascertaining the relation oiA and B to each other. 
 
 2. A Sjfllogitm must contain three Judgments, and no 
 more ; namely, the two in which each of the Terms of the 
 
THE AEISTOTEUC ANALYSIS. 181 
 
 • 
 
 Conclusion is compared with the Middle Term, and that in 
 which these two are compared with each other. 
 
 3. The Middle Term must he distributed (taken univer- 
 sally) in at least one of the Premises. The necessity of 
 this Rule arises, as we have seen, from the fact that the 
 two Extremes, in order to be compared with each other, 
 must have heen separately compared with the same com- 
 mon Middle. If we consider no other kinds of Quantity 
 than all and some (Universal and Particular), the Rule as 
 here expressed is sufficient. But if we take into more 
 definite view the Quantity of some, — namely, whether it 
 does or does not exceed one half, — the Rule may be made 
 seemingly less stringent. It is enough that the quantifica- 
 tions of the Middle Term in both Premises, added together, 
 should exceed unity, — that is, exceed its possible totality 
 or its distribution in any one ; for the amount of such 
 excess over unity then constitutes a common Middle Term. 
 Something more than all the Middle Term has been men- 
 tioned in the Premises ; and both Terms in the Conclusion 
 must have this excess as a common element. If A is three 
 fourths of M, and B is one half of M, then at least one 
 fourth of M is common to A and B ; and their agreement 
 with this common term is enough to insure their agreement 
 with each other. This is called by Hamilton the ultra-total 
 quantification of the Middle Tenn. It deserves mention, but 
 as it is of very infrequent use, the Rule as first enounced 
 for the quantification of the Middle is practically sufficient. 
 
 4. One Premise at least must be affirmative ; for if both 
 Premises are negative, the Middle Term agrees with 
 neither of the two others, and therefore afibrds no ground 
 for any Inference as to their agreement or non-agreement 
 with each other. Though we know that A is not Mand 
 B is not M, we do not therebt/ know whether A is or is not 
 B. A good general is not a coward, and Pompey was not 
 a coward ; but these two assertions fiimish no reason for be- 
 
 -- lievuag that Pompey either was, or was not, a good general. 
 
182 MEDIATE INFEEENCE OK SYLLOGISM. 
 
 • 
 
 5. If either Premise is negative, the ConclvMon is nega- 
 tive ; for as one Premise, according to the preceding Rule, 
 must be affirmative, if the other Premise is negative, there 
 is a difference in the relation of the two principal Terms to 
 the Middle Term, and hence a non-agreement between the 
 two Terms themselves. 
 
 6. Neither Term must be distributed in the Conclusion if 
 it was not distributed in the Premise; for if only some is 
 premised, we cannot conclude cdl. 
 
 Logicians have usually added two other Rules, that the 
 Conclusion follows the weaker part, a Negative being re- 
 garded as weaker than an Affirmative, and a Particular as 
 weaker than a Universal ; and that no Conclusion can be 
 drawn from two Particular Premises. But both of these 
 result only from a combination of Rules 5 and 6 with 3 ; 
 hence they hardly need to be considered here, but I ap- 
 pend a demonstration of them m the note.* No syllogism 
 
 * As the two additional Roles were constructed with special reference to 
 the Aristotelic doctrine of Judgments, they can be conveniently demon- 
 strated only by bearing in mind the following maxims, which have already 
 been laid down in the exposition of that doctrine. 
 
 1. By Subaltemation, Particular Judgments are included under their 
 corresponding Universals ; that is, if A is true, I is also true ; and the 
 same holds good of E and O. 
 
 2. The Subject of a Judgment, taken univereally or particnlarly, is that 
 which renders the Judgment itself Universal or Particular. 
 
 3. The Predicate of an Affirmative Judgment is always considered as 
 Particular. 
 
 4. The Predicate of a Negative Judgment is always regarded as Univer- 
 sal, — that is, as distributed. 
 
 Now there must always be in the Premises one more Term distributed than in 
 the Conclusion ; for by Rule 3, the Middle Term (which does not appear in 
 the Conclusion) must be distributed in at least one of the Premises ; and 
 by Rule 6, if any Term is distributed which does appear in the Conclu- 
 sion, it must also be distributed in the Premises. Then it follows that no 
 Conclusion cSi be draum from two Particular Premises. For if these are I 
 and I, as neither Subject nor Predicate of I is Universal, the Middle Term 
 IS not distributed. If they are I and O, then, by Rule 5, the Conclusion is 
 
THE ARISTOTELIO ANALYSIS. 183 
 
 can be invalid which does not violate one or more of the 
 six Rules first enounced. 
 
 After the usual manner of logicians, the foregoing Rules 
 have been summed up in these mnemonic hexameters : — 
 
 Distribuas medium, nee quartus terminus adsit; 
 Utraque nee prxmissa negans, nee partieularis ; 
 Sectetur partem conclusio deteriorem, 
 Et non distribuat nisi cum prsemissa, negetre. 
 
 But the application of these rules may become a matter 
 of considerable complexity, when it is considered that, from 
 the same naked (unquantified) Terms, a great variety 
 of different Syllogisms may be formed. Each of the three 
 Terms may be either Particular or Universal ; each of the 
 three Judgments, either Affirmative or Negative ; the Judg- 
 ments may be placed in any order with respect to each 
 
 negative ; then its Predicate is distributed ; and Kule 6, taken in conjunc- 
 tion with what has just been stated respecting the number of distributed 
 Terms in the Premises, requires one of these Premises to be Universal. 
 
 Again, if either Premise is Partictdar, the Conclusion must be Particular. 
 For the Subject of a TJniversal Affirmative Conclusion must be Universal ; 
 therefore, in the Premise wherein this Subject appears, it must, by Rule 6, 
 be Universal, and the Middle Term, which is therein joined with it, must 
 consequently be Particular, since it must be the Predicate of an Affirmative 
 Judgment. Then the Middle Term, in order to be once distributed, must 
 be the Universal Subject of the other Premise. Hence, ii' the Conclusion is 
 Universal Affirmative, both Premises most be Universal. 
 
 And if the Conclusion is Universal Negative, both Premises must also be 
 Universal. Por both Terms of the Conclusion are then distributed ; and as 
 the Middle Term must also be distributed, there must be at least three 
 Terms distributed in the Premises. But this cannot be, unless both Prem- 
 ises are Universal, since both of them, by Eule 4, cannot be Negative. 
 Hence, whether the Conclusion is Affirmative or Negative, if it be Univer- 
 sal, both Premises must be Universal. Then, if either Premise is Particular, 
 the Conclusion must be Particular. 
 
 But according to Kule 5, if either Premise is Negative, the Conclusion 
 is Negative. Then, the Conclusion must follow the weaker part ; — that is, it 
 must be Particular, if either Premise is Particular, and Negative, if either 
 Premise is Negative. — Q. E. D. 
 
184 MEDIATE INFEKENCE OK SYLLOGISM. 
 
 other, and for three Judgments, six different orders of posi» 
 tion are possible ; and each of the three Terms may be 
 either Subject or Predicate in either or both of the Prem- 
 ises, the two principal Terms also assuming either place in 
 the Conclusion. The larger portion of the numerous Syl- 
 logisms thus formed, it is true, are invalid, as offending 
 against one or more of the preceding Rules. We need 
 some more succinct mode than that of severally applying 
 to each Syllogism aU these Rules, before we can be satisfied 
 that it is impeccable. Many of these Syllogistic forms, 
 moreover, are equivalents of each other ; that is, the Rea- 
 soning may be changed from one form to another, with- 
 out impairing its validity, or even changing its signification 
 in any essential respect. But of these equivalent forms 
 some are more natural and obvious than the others ; the 
 mind seeks for these by preference ; and when the process 
 of reasoning appears in one of these natural and preferred 
 forms, its validity is determined with ease and in a mo- 
 ment. The appUcation of the Rules to such cases is made 
 with the quickness of instinct, and may be reduced almost 
 to a mechanical process. 
 
 A highly ingenious, though artificial, system has been 
 contrived of classifying these numerous Syllogistic forms 
 under a few heads, throwing out at once all that are ille- 
 gitimate, immediately recognizing the remainder, and then 
 transmuting those which are valid in substance, but un- 
 natural and obscure in form, into the easy and famihar 
 types in which the mind quickly perceives their legitimacy. 
 The study of this system, a ready use of which may be 
 said to constitute the art of Syllogizing, is facilitated by a 
 series of mnemonic contrivances, many of them of mar- 
 vellous ingenuity and completeness. The notation and 
 most of the operations are of an algebraic character ; and 
 attempts have not been wanting of late years to enlarge 
 and perfect the system by a fiirther introduction of mathe- 
 
THE ARISTOTELIC ANALYSIS. 185 
 
 matical signs and processes. The failure of such an under- 
 taking is not to be wondered at, for it proceeds, as it seems 
 to me, upon a mistaken opinion as to the relative position 
 of the two sciences. Logic is not a department of mathe- 
 matics. Rather the reverse is true. Mathematics is the 
 science of pure quantity, — of reasoning about dimensions 
 and numbers in the abstract, or as unmodified by any of 
 the differences of quality by which all the objects of thought 
 are actually distinguished ; and it is, therefore, only a de- 
 partment, or a special application, of the far more compre- 
 hensive science which has for its object Reasoning itself 
 and all its subsidiary processes, and thus covers the whole 
 domain of Pure Thought. All computation is reasoning ; 
 but all reasoning is not computation, and therefore cannot 
 be carried on by the processes, or be made subject to the 
 special laws, of pure mathematics. 
 
 Syllogistic forms are classified with respect to Mood and 
 Figure, the former having regard to the value of the three 
 component Judgments, and the latter to the relative posi- 
 tion of the three Terms in these Judgments. It will be 
 convenient, then, to have a uniform mode of designating 
 these three Terms. In future, S will stand for the Sub- 
 ject, and P for the Predicate, of the Conclusion, and ilf for 
 the Middle Term. The Consequence, or what we usually 
 express by the words ther^ore, consequently, &c., will be 
 indicated by three dots placed thus .•. For example : — 
 
 Mis P; 
 
 S is M; 
 ,'. S is P. 
 To facilitate reference, the Logicians have given special 
 names to these several Terms and Jud^ents. The 
 Predicate of the Conclusion is called the Major Term, and 
 its Subject the Minor Term. The Premise in which the 
 Major is compared with the Middle Term is called the 
 Major Premise, and that in which the Minor is compared 
 
186 MEDIATE INFEEENCE OE SYLLOGISM 
 
 with the Middle, is the Minor Premise. These names 
 have reference to the Quantity of Extension only, and are 
 founded upon the received doctrine, that the natural order 
 of predication is that in which the Genus is predicated of the 
 Species, the Species of the Individual, and, generally, the 
 Extensive whole of its part. Then the more Extensive 
 Term, the Major, usually occupies, at least in Affirmative 
 Judgments, the Predicate's place. " This," says Dr. 
 Thomson, " is the natural, though not invariable, order ; 
 and it is worthy of remark, that, even in Negative Judg- 
 ments, where, from the negation, the two Terms cannot be 
 set together to determine their respective Extension, if, 
 apart from the Judgment, we know that the one is a small 
 and the other a large class, — the one a clearly determined 
 and the other a vague notion, — we naturally take the 
 small and clearly determined Concept for the Subject. 
 Thus, it is more natural to say that the Apostles are not 
 deceivers, than that No deceivers are Apostles. So that, if 
 our minds are not influenced by some previous thought to 
 give greater prominence to the wider notion, and so make 
 it the Subject," thus reversing the primary and natural 
 order, the Term of major Extension wiU always be the 
 Predicate, and that of minor Extension, the Subject. 
 
 As these names — Major, Middle, and Minor — thus 
 correctly indicate the comparative Extension of the three 
 Terms, an Affirmative Syllogism in which these Terms 
 occupy their natural place is conveniently symbolized by 
 three concentric circles, of which the outermost and largest 
 indicates the Predicate of the Conclusion, or the Major 
 Term ; the innermost and smallest, the Subject of the Con- 
 clusion, or the Minor; and the intermediate one, the 
 Middle Term. Thus : — 
 
 All mammals are viviparous ; All M are P. 
 
 All whales are mammals ; All S are M. 
 
 .-. All whales are viviparous. . . All S are P. 
 
THE AKISTOTELIC ANALYSIS. 187 
 
 Here the reasoning is, that S, which is a part of M, 
 must also be a part of P, since Jf is a part of P. We are 
 thus led to another mode of enunciating the governing 
 principle of all Syllogisms, that a part of a part is a part 
 of the whole ; or, as Leibnitz expresses it, contentum eontenti 
 est contentum continentis. This principle agrees in every 
 essential respect with the famous Dictum of Aristotle, 
 usually called the Dictum de omni et nulla, that whatever is 
 predicated (affirmed or denied) universally of any Class 
 (i. e. of any whole), may he also predicated of any part of that 
 Class. Both principles have been already recognized and 
 applied ia the doctrine of Subaltemation. The name of 
 this Dictum is derived from the two forms which it assumes 
 as applied either to affirmative or negative Conclusions ; 
 the Dictum de omni being thus expressed, Quicquid de 
 omni valet, valet etiam de quOusdam et singulis ; and the 
 Dictum de nulla being, Quicquid de nullo valet, nee de qui- 
 husdam nee de singulis valet. Both of these principles are 
 evidently of a secondary or derivative character, their af- 
 firmative and negative forms being grounded respectively 
 upon the two Axioms of Identity and Non-Contradiction ; 
 for as a whole is identical with the sum of all its parts, 
 whatever is affirmed or denied (distributively) of the 
 whole is thereby affirmed or denied of each of its parts. 
 Burgersdyck remarks, that, for the purpose of applying the 
 Dictum to Syllogisms, it may more conveniently be thus 
 expressed : Whatever Predicate is universally affirmed or 
 denied of any Middle Term, or Part is also affirmed or de- 
 nied of any S^ect which is contained under that inter- 
 mediate Term or Part. 
 
 The mode of symbolizing the mutual relations of the 
 three Terms of a Syllogism, which is appUed above to a 
 Universal Affirmative, may be extended to Negatives and 
 Particulars. The total disagreement of two Terms with 
 each other, which is expressed by a Negative Judgment, is 
 
188 MEDIATE INFERENCE OB SYLLOGISM. 
 
 properly indicated by two Circles which do not coincide in 
 any part. Thus : — 
 
 No M is P ; 
 
 AU S is M ; 
 •. No S is P. 
 
 Both the partial agreement, and the partial disagreement, 
 of two Terms, — as these are merely two aspects of one 
 
 and the same Thought, -^- 
 are properly indicated by 
 the same symbol, namely, 
 two circles which intersect. 
 Some S are M, and Some 
 S are not M, are both ex- 
 pressed by this symbol. 
 Excepting this ambiguity, 
 all Syllogisms can be adequately symbolized by some com- 
 bination of the preceding diagrams. 
 
 Hitherto we have regarded the Syllogism only as a 
 means of evincing the relation of two Terms to each other 
 through the relation of each to a common or Third Term. 
 But the Dictum as expressed by Burgersdyck indicates 
 another aspect of the Syllogism, equivalent indeed to the 
 former one, but in certain respects more convenient for 
 use. The Judgment in which " a Predicate is universally 
 affirmed or denied of any Middle Term or Part " is a Cren- 
 eral Rule ; the Judgment that a given " Subject is con- 
 tained under that intermediate Term or part," is the Sulh 
 gumption of this Subject under the condition of that Rule ; 
 and then the Conclusion following, that the given Subject is 
 governed by that Rule, is a solution of the doubt with which 
 wo commenced, whether S is, or is not, P. Every Syllogism, 
 
THE ARISTOTELIC ANALYSIS. 189 
 
 then, must consist of three Judgments, one of which must 
 be a General Rule, or, as Hamilton expresses it, a 8wmf- 
 tion ; another must be the Suhsumption of a certain Sub- 
 ject under that Rule; and the third is the Conclusion, 
 that this Subject is determined by the Rule. Thus : — 
 
 Swmption. No one who is content is miserable ; 
 
 Svimmption. Some cf the poor are content ; 
 
 CoTiclusion. Some of the poor are not miserable. 
 
 It is not difficult to prove, say the Port Royal logicians, 
 that all the Rules which we have given serve only to show 
 that the Conclusion is contained under (or embraced in the 
 Extension of) one of the Premises, which is a General 
 Rule or Sumption, and that the other Premise, the Sub- 
 sumption, shows this ; and that arguments are vicious only 
 when they fail to observe this method, and are always good 
 when it is observed. 
 
 Kant expresses the general law of the Syllogism, as thus 
 conceived, in the following formula: Whatever stands 
 under the condition of a Rule, that stands also under the 
 Rule itself. As the former view regards chiefly the three 
 Terms, so this one has primary reference to the three 
 Judgments, of which every Syllogism is composed. The 
 former view does not contradict the latter ; they are only 
 two aspects of the same thing. But what we have hitherto 
 termed the Major Premise, though it is usually the same 
 Judgment that is here called the Sumption, is not always 
 so. Thus, in the following Syllogism, (called by the 
 Logicians Disamis of the Third Figure,) the first Judg- 
 ment, as it contains the Predicate of the Conclusion, is the 
 Major Premise ; but the second Judgment is the Sumption. 
 Some wicked persons are men of high rank ; 
 All the wicked are miserable. 
 .'. Some miserable persons are men of high rank. 
 
 As. it has been demonstrated thai, from two Particulars no 
 Conebmon can he draxnm^ every Syllogism must have for a 
 
190 
 
 MEDIATE INFERENCE OK SYLLOGISM. 
 
 Premise at least one Universal Judgment ; that is, one of 
 its Premises must be a Sumption or General Rule. In the 
 First Figure, which is the only natural and obvious form 
 of reasoning, and to which all the other forms can be re- 
 duced, the Sumption is always the Major Premise, 
 
 1. Figure and Mood. 
 
 The Figure of a Syllogism depends apon the relative 
 position of its three Terms, and is determined by the posi- 
 tion of the Middle Term in the Premises. Now the Mid- 
 dle Term may be either the Subject of the Major Premise, 
 and the Predicate of the Minor, in which case we say the 
 Syllogism is of the First Figure ; or it may be the Predi- 
 cate of both, which is the Second Figure ; or it may be the 
 Subject of both, thus constituting the Third Figure ; or it 
 may be the Predicate of the Major and the Subject of the 
 Minor, thus converting the First, and giving rise to the 
 Fourth Figure. Accordingly, the four Figures are thus 
 indicated. 
 
 I. 
 
 n. 
 
 ni. 
 
 IV. 
 
 MP 
 
 PM 
 
 MP 
 
 PM 
 
 SM 
 
 SM 
 
 MS 
 
 MS 
 
 SP 
 
 .-. SP 
 
 .-. SP 
 
 .-. SP 
 
 They are also indicated in the following mnemonic 
 line: — 
 
 Sub prm ; turn prce prce ; turn sub stA ; turn prce sui. 
 
 The line should be read thus : — The Middle Term is, first, 
 /Swiject, Predicate ; then. Predicate, Predicate ; then, Sub- 
 ject, Subject; lastly, Predicate, /^MSject. 
 
 The Fourth Figure is not recognized by Aristode, but is 
 accepted, if at aU, on the supposed authority of Galen. 
 Most modem logicians reject it, not as invalid, but as un- 
 natural and unnecessary. As we have already said, the 
 
FIGURE AND MOOD. 191 
 
 natural order of predication is that in which the Genus is 
 predicated of the Species, or the more Extensive of the less 
 Extensive Term. Then it follows that the First is the 
 only natural and obvious Figure, as it is the only one 
 which observes this order throughout. Here, the Predicate 
 of the Conclusion, which is the Term of widest Extension, 
 appears as the Predicate of the Major Premise ; and the 
 Subject of the Conclusion, being the Term of least Exten- 
 sion, is the Subject of the Minor Premise, — the Middle 
 Term appearing, as it ought, intermediate between the 
 two, being of less Extension than P, and greater than S. 
 Here also, as Dr. Thomson remarks, the Conclusion in no 
 way disturbs the order of Terms which was first established 
 in the Premises ; for the Subject of the Conclusion appears 
 also as a Subject in the Premises, and the Predicate as a 
 Predicate ; — that is, no Thought which was primary be- 
 comes secondary, nor any secondary primary. Take, for 
 instance, the following Syllogism in the First Figure : — 
 
 1. No boaster deserves respect ; 
 Some heroes are (some) boasters ; 
 
 .•. Some her^s do not deserve respect. 
 
 Here, everything is in its natural place ; each Subject is of 
 less Extension than its Predicate, and the Terms preserve 
 the same relative places in the Conclusion which they 
 occupied in the Premises. 
 
 But change this Syllogism into the Second Figure, by 
 converting the Major Premise, thus : — 
 
 2. No person deserving respect is a boaster ; 
 Some heroes are (some) boasters ; 
 
 .*. Some heroes do not deserve respect. 
 
 Here, the natural order is violated in one half of the rea- 
 soning ; for the Subject of the Major is the Predicate of 
 the Conclusion, and has wider Extension than its own 
 Predicate. 
 
192 MEDIATE INFERENCE OB SYLLOGISM. 
 
 Again, change the same Syllogism into the Third Fig- 
 ure, by converting the Minor Premise, thus : — 
 
 3. No boaster deserves respect ; 
 Some boasters are (some) heroes ; 
 
 .-. Some heroes do not deserve respect. 
 Here, the other half of the reasoning appears unnatural 
 and forced. The Predicate of the Minor Premise becomes 
 the Subject of the Conclusion, and is of less Extension 
 than its own Subject. 
 
 To change this Syllogism into the Fourth Figure, we 
 must convert both Premises, thus : — 
 
 4. No person deserving respect is a boaster ; 
 Some boasters are (some) heroes ; 
 
 .•. Some heroes do not deserve respect. 
 Here, both halves of the reasoning are contorted, so that it 
 appears whoUy unnatural. Not only is the Predicate of 
 the Minor the Subject of the Conclusion and of less Extent 
 than its own Subject, but the Subject of the Major is the 
 Predicate of the Conclusion, and of greater Extent than its 
 own Predicate. The mind revolts at this perversion ; 
 striving to preserve the same order in the Conclusion 
 which it observed in the Premises, the Concluision which it 
 would naturally draw from these two Premises is this : — 
 
 No person deserving respect is (some) hero. 
 Now, this Conclusion, which is natural and obvious, is the 
 Converse of the former one, which was unnatural ; and it 
 reduces the Syllogism (changing the order of the Premises) 
 from the Fourth to the First Figure. Hence it appears, 
 that what is called the Fourth Figure is only the First 
 with a ccaiverted Conclusion ; that is, we do not actually 
 reason in the Fourth, but only in the First, and then, if 
 occasion requires, convert the Conclusion of the First. 
 The reasoning is indirect, or Mediate in a double sense; 
 the nominal Conclusion of the Fourth is actually, but ia- 
 
FIGURE AND MOOD. 193 
 
 directly, obtained by converting the Conclusion of tbe 
 First. Hence, many Logicians exclude the Fourth alto- 
 gether, and call those Syllogistic forms which would other- 
 wise fall under it " indirect Moods of the First Figure." 
 But we can also obtain, if we see fit, indirect Moods from 
 the Second or Third Figure, by converting their Conclu- 
 sions also. There is no reason, then, for giving a special 
 class of these " indirect Moods " to the First Figure, any 
 more than to the Second or Third ; that is, there is no 
 reason for considering the Moods of the so-called Fourth 
 , Figure at all. It is not only unnatural, but wholly un- 
 necessary. We need only state, that, after obtaining the 
 ordinary mediate Conclusions from either of the three Fig- 
 ures, we may, if occasion requires, obtain a- second set of 
 Conclusions im/mediately, by converting the former ones. 
 But we observe, secondly, that the natural but unex- 
 pressed Conclusion of the so-called Fourth, — 
 
 " No person deserving respect is (some) hero," — 
 is a shocking one for the Aristotelians, for it is a Negative 
 with an undistributed Predicate. They will not allow that 
 such a Judgment is possible ; but here it appears a;s actual, 
 — nay, as the only natural result of Premises to which, 
 according to the Aristotelic doctrine, only a wholly unnat- 
 ural Conclusion can be given by inventing a so-called 
 Fourth Figure, otherwise not needed, and in every respect 
 perverted and contrary to nature. Of course. Sir William 
 Hamilton, whose system expressly recognizes these Nega- 
 tive Judgments (Ani) with undistributed Predicates, has 
 taken advantage of this fact, and pressed it as an unanswer- 
 able argument against his opponents. 
 
 But to return to the Aristotelic doctrine. The reason 
 ordinarily given for awarding a decided preference to the 
 First over the other Figures is not eithibr of the two here 
 alleged, but one which immediately results from them, — 
 namely, that the Dictum ole omni et nuUo, which is held to 
 
194 
 
 MEDIATE INFERENCE OE SYLLOGISM. 
 
 be a universal principle of all reasoning, is direcdy appli- 
 cable only to the First Figure. This Dictum, which has 
 respect exclusively to the Quantity of Extension, neces- 
 sarily supposes that the order of Extension is strictly fol- 
 lowed in the Syllogism ; that is, that the Predicate in each 
 of its three Judgments should be of wider Extension than 
 the Subject. This is the case in the First Figure ; but as 
 we have seen, it is not so with the others. In the Second, 
 the Subject of the Major, and in the Third, the Subject of 
 the Minor Premise, has a wider Extension than the corre- 
 sponding Predicate. In order to show that the Dictum is 
 universally applicable, we must be able to reduce all SyUo- 
 ^sms, in whatever class they may at first be ranked, to the 
 First Figure. Now, to judge from the instance just given, 
 in which we have carried the same Syllogism successively 
 through each of the foiu: Figures, such a Reduction can be 
 very easily accompHshed. It is onljr necessary to convert 
 one or both of the Premises. Recurring for a moment to 
 the first mode of indicating the variations of Figure, — 
 
 I. 
 
 n. 
 
 in. 
 
 IV. 
 
 MP 
 
 Pli-j 
 
 MP 
 
 PM 
 
 SM 
 
 SM 
 
 MS 
 
 MS 
 
 SP 
 
 .-.SP 
 
 .-. SP 
 
 .-. SP 
 
 it is easy to see that the Second Figure is reduced to the 
 First by converting its Major Premise ; the Third, by con- 
 verting its Minor; and the Fourth, by converting both. 
 But as the order of the Premises may be transposed, as the 
 Sumption and the Major Premise do not always coincide, 
 and as the Judgment O, on the strict Aristotehc doctrine, 
 is not convertible at all, it is not always easy to tell which 
 Premise ought to be converted, and the process of Re- 
 duction practically becomes so complex and intricate, that, 
 to fecilitate it, an elaborate system and a whole set of 
 mnemonics have been contrived. These will be explained 
 hereafter. 
 
FIGURE AND MOOD. 195 
 
 ^he Aristotelic logicians appear to hesitate, or be in 
 doubt, as to the motives for reducing the three lower Fig- 
 ures to the First. At times, they speak as if the only- 
 reason for such Reduction were the one already mentioned, 
 — to reduce all Syllogistic forms to system by showing that 
 they are all controlled by one governing principle, the Dic- 
 tum de omni et nulla. The implication then is, that they 
 are vahd or coiflpetent forms of reasoning, even before such 
 Reduction ; and that they are reduced, therefore, only to 
 render them more systematic and orderly in appearance. 
 Then, again, they speaik o( proving them by this Reduction, 
 as if otherwise they were weak and needed proof, even if 
 they were not invaUd. The truth is, the reasoning under 
 either of these Figures is just as conclusive as under the 
 First. In neither case can the Conclusion be denied with- 
 out involving the denier in an absurdity, — that is, in a con- 
 tradiction of one of the' Primary Axioms of Pure Thought. 
 Nay, more ; in certain cases, it is, in one sense, more 
 natural to make inferences by the Second or Third Figm-e, 
 than by the First ; that is, the particular object which we 
 have in view in the general investigation or course of argu- 
 ment which we are pursuing, may more directly lead us to 
 the former than to the latter. Thus, when we wish to 
 exclude something from a class to which it had been 
 wrongly assigned, or to disprove something which has been 
 asserted, we are most frequently led to argue in the Second 
 Figure, since any Conclusion in this Figure must be nega- 
 ■tive; for as the Middle Term is here Predicate in both 
 Premises, it cannot be distributed unless one of the Prem- 
 ises is negative, and then, by Rule 5, the Conclusion is 
 negative. " The arguments," says Whately, " used in the 
 process called Ahsdsaio infiniti, will, in general, be the most 
 easily referred to this Figure. This phrase was applied by 
 some logicians to a series of arguments used in any inquiry 
 in which we go on excluding, one by one, certain suppo- 
 
196 MEDIATE INFERENCE OR SYLLOGISM. 
 
 sitions, or certain classes of things, from that whose real 
 nature we are seeking to ascertain." 
 
 Again, if our design is to establish exceptions to a pre- 
 tended law or rule, — that is, if we would disprove the as- 
 serted universality of the Proposition, — the Third Figure 
 will most commonly answer our purpose, for here all Con- 
 clusions must be Particular; we prove that Some are, or 
 Some are not, and thus disprove the assertion that AU are 
 not, or All are. Conclusions in the Third Figure must he 
 Particular, because both Terms of the Conclusion appear 
 as Predicates in the two Premises ; hence, if these Prem- 
 ises are both AflBrmatives, their Predicates are Particular ; 
 and if one of them is Negative, the Conclusion can only be 
 a Particular Negative, since a Universal Negative distrib- 
 utes both its Terms. 
 
 Because the two lower Figures are thus not only valid 
 in themselves, but peculiarly appropriate for certain pur- 
 poses, some logicians hold that it is unnecessary to reduce 
 them to the First Figure. Each of the three, they main- 
 tain, has its own ftmctions and its own governing principle. 
 The principle which is assigned to the Fii-st, needs but to 
 be slightly modified in order to be directly applicable to 
 the Second or the Third ; since all three are but various 
 applications of the same Axioms of Thought. Thus, if the 
 Dictum de omni et nulla be considered as the principle for 
 the First Figure, for the Second we have the Dictum de 
 diverso, — that if one Term is contained in, and another ex- 
 cluded from,, a third Term, then they are excluded from each 
 other. For the Third Figure, the principle is called the 
 Dictum de exemplo, — that two Terms which contain a com- 
 mon part partly agree; or, if one contains a part which the 
 other does not, they partly differ. 
 
 Reduction is not essential, therefore, but it is certainly 
 convenient ; the reasoning does not become more cogent by 
 being reduced to the First Figure, but it is rendered more 
 
FIGURE AND MOOD. 19T 
 
 perspicuous, more simple and natural in expression, and 
 any fallacies in it, which might otherwise escape notice, 
 become at once so obvious that they cannot avoid detection. 
 The whole theory of argumentation, moreover, is rendered 
 more systematic and elegant, when its numerous modes 
 are reduced to a very few fundamental forms, the validity 
 of which is so manifest that they do not need to be tested 
 by the application of previously determined rules. 
 
 The proper relative position of the three Judgments of 
 a Syllogism appears so obvious, on the Aristotelic doctrine, 
 that it has usually been taken for granted. If we reason 
 only in order to instruct, to convince, or to refute, — and 
 no other purpose seems to have been contemplated by the 
 old logicians, — the natural order of Thought seems to be, 
 that the Ground or Reason should precede the Conse- 
 quence ; that is, that the Premises, as their name imports, 
 should precede, and, as it were, effectuate the Conclusion. 
 And as regards the two Premises, if the reasoning is ex- 
 clusively in the Quantity of Extensic(n, the Major should 
 be placed before the Minor, the Sumption or General Rule 
 before the Subsumption. 
 
 The Mood of a Syllogism is the value of its three Judg- 
 ments considered in respect to their Quantity and Quality. 
 Since there are but four kinds of Judgments as thus viewed, 
 indicated respectively by the four vowels A, E, I, and O, 
 it is evident that three of these letters must express any 
 possible Mood. When we have ascertained its Mood and 
 Figure, the classified place afad formal value of a Syllogism 
 are determined. For instance, E I O, Fig. I., and A A I, 
 Fig. III., are thus expressed : — 
 
 Fig. I. Fio. m. 
 
 No M is P ; E 
 
 Some S are M ; I 
 
 ..Some S are not P. O 
 
 AUMareP; - A 
 All M are S ; A 
 
 .•. Some S are P. I 
 
198 MEDIATE INFEKENCE OK SYLLOGISM. 
 
 As oiily four Judgments are possible, and three are 
 necessary to constitute a Syllogism, the whole number of 
 Moods can be numerically determined. Only mxty-four 
 different arrangements can be made out of four letters 
 taken three at a time ; hence, sixty-four Moods are con- 
 ceivable. But the greater number of these are invalid, as 
 contradicting one or more of the General Rules which 
 govern, as we have seen, all forms of Mediate Inference. 
 The elimination of these invalid forms can be more easily 
 effected, if we first reduce the expression of a Mood to its 
 simplest form. 
 
 Strictly speaking, only the two letters which denote the 
 Premises need to be taken into account ; for the Quantity 
 and' Quality (and therefore the letter) of the Conclusion 
 axe determined by those of the Premises. Each Mood, 
 then, being designated by only two letters, aiid only six- 
 teen different arrangements being possible of four letters 
 taken two at a time, all conceivable Moods are contained 
 in the following list : — 
 
 1.) A A 2.) E A 3.) I A 4.) O A 
 
 AE EE IE OE 
 
 AI EI II OI 
 
 AO EO lO OO 
 
 The Rule that from two Negative Premises ru> Conehmon 
 can he drawn, excludes four from this list, namely, E E, 
 E O, O E, and O O. The Rule that no Conehmon can he 
 drawn from two Particular Premises, excludes three more, 
 namely, 1 1, I O, and O I. Finally, I E is excluded he- 
 cause its Negative Conclusion distributes the Major Term, 
 which is undistributed in I, the Major Premise; but 
 according to Rule 6, neither Term can he distributed in the 
 Conclusion, if it was not distrihvted in the Premise. We 
 may here observe, that the violation of this last Rule, in 
 *espect to the Major Term, is called illieit process of the 
 
FIGURE AND MOOD. 199 
 
 Major; in respect to the Minor Term, it is called illicit 
 process of the Minor. 
 
 These exclusions being effected, there remain but eight 
 valid Moods, namely, A A, A E, A I, A O, E A, iE I, 
 I A, and O A. Not all, even of these eight, however, 
 afford a vaUd Syllogism in each of the four Figures ; for 
 the altered position of the Middle Term may cause the 
 greater number of them to offend against the Rules which 
 forbid both an imdistributed Middle and an Illicit Process 
 whether of the Major or Minor Term. Special Rules 
 have been enounced for each of the Figures, which will 
 enable us to make the fiirther exclusions that are requisite. 
 It should be observed, that these Special Rules contain no 
 new principle, but are immediately deducible from the 
 General Rules, that have already been estabhshed for all 
 Syllogisms ; taking these General Rules in connection, how- 
 ever, with the two axioms by which the Aristotelians de- 
 termine the implicit Quantity of the Predicate ; namely, 
 that, in all Affirmative Judgments, the Predicate is Par- 
 ticular, and liiat, in all Negative Judgments, the Predicate 
 is Universal. This deduction may be left as an exercise 
 for the learner. We will here consider the Special Rules 
 under that theory which regards every Mediate Inference 
 as proceeding from the Subsumption of a particular case 
 under a General Rule or Sumption ; little more than an 
 alteration of phraseology will be needed to adapt them to 
 the theory in which we spealt only of Major and Minor 
 Premises. 
 
 The Special Rules for the First Figure are, — 
 
 1. The Sumption must be Universal ; 
 
 2. The Subsumption must be Affirmative. 
 
 These two Rules exclude I A, O A, A E, and A O. 
 There remain A A, E A, A I, and E I, as the only valid 
 Moods in this Figure ; and these are named Barlara, Cer- 
 larent, Darii, and Ferio. Observe that the three vowels 
 
200 MEDIATE INFERENCE OK SYLLOGISM. 
 
 in each of these names denote the Mood of the Syllogism 
 to which it is applied ; and the same is true of the technical 
 names which will be given to the vahd Moods in the other 
 Figures. 
 
 The Special Rules for the Second Figure are, — 
 
 1. The Sumption must be Universal ; 
 
 2. One of the Premises must be Negative, and there- 
 
 fore the Conclusion must be Negative. 
 
 These Rules exclude I A, O A, A A, and A I ; then 
 there remain as vahd in the Second Figure only the four 
 Moods which have been named Cesare, Camestres, Festino, 
 and Baroho. 
 
 The Special Rules for the Third Figure are, — 
 
 1. The Subsumption must be Affirmative ; 
 
 2. The Conclusion must be Particular. 
 
 Throwing out A E and A O under these Rules, there 
 remain for the Third Figui-e six Moods, named DarapU, 
 Disamis, Datisi, Fblapton, Bohardo, and FerUon. 
 
 The Special Rules for the Fourth Figure are, — 
 
 1. If the Sumption is Affirmative, the Subsumption 
 must be Universal. 
 
 2. If either Premise is Negative, the Sumption must be 
 Universal. 
 
 3. If the Subsumption is Affirmative, the Conclusion 
 must be Particular. 
 
 Rejecting A I, A O, and O A, as offending against 
 these Rules, there remain only five Moods, called Bra- 
 mantip, Camenes, Bimaris, Fesapo, and Fresison, as valid 
 in the Fourth Figure. 
 
 Taking the four Figures together, therefore, there are 
 nineteen vahd Moods ; but as fifteen of these can be re- 
 duced to those of the First Figure, there are only four 
 Moods which are at once vahd, natural, and perspicuous. 
 Regarding the last vowel in the names of these four (^Bar- 
 bara, Celarmt, Barii, Ferio}, we see diat these are just 
 
FIGURE AND MOOD. 201 
 
 sufficient to prove the four fundamental Judgments, A, E, 
 I, and O. 
 
 If we exclude the Fourth Figure altogether, considering 
 Bramantip, Oamenes, &c. as indirect Moods of the First, 
 there are but fourteen direct Moods. On the other hand, 
 since from every Syllogism with a Universal Conclusion 
 we can obtain, by Subalternation, a Particular Conclusion 
 also, there are five other indirect Moods, which are anony- 
 mous, making twenty-four in all. Thus, A A in the First 
 yields I, as well as A, for a Conclusion ; and from E A in 
 the Second, we may conclude not only B, but O. But 
 these anonymous Moods, besides being indirect, are prac- 
 tically useless ; since it is idle to infer some only, when the 
 Premises warrant the inference of all. 
 
 Rejecting the Fourth Figure and the indirect Moods, 
 it will be seen, from examining the last vowel in each of 
 the names, that A is proved only in one Figure and one 
 Mood ; E in two Figures and three Moods ;' I in two Fig- 
 ures and four Moods; and O in three Figures and six 
 Moods. " For this reason," says Mr. Mansel, " A is de- 
 clared by Aristotle to be the most difficult proposition to 
 establish, and the easiest to overthrow; O, the reverse. 
 And, generally, Universals are most easily overthrown, 
 Particulars more easily established." 
 
 The names of all the vahd Moods have been put to- 
 gether into the following mnemonic hexameters, which 
 deserve careful study, not only as a complete artfficial 
 system for the Reduction of aU the Moods of the subordi- 
 nate Figures to those of the First, (for which purpose the 
 names were invented,) but as a literary curiosity. They 
 have been in use in the Schools, as an aid to the mem- 
 ory, for over six centuries, their authorship being un- 
 known. Mr. DeMorgan calls them "the magic words 
 which are more ftiU of meaning than any that ever were 
 made." Sir William Hamilton says of them that " there 
 
 9* 
 
202 MEDIATE INFERENCE OK SYLLOGISM 
 
 are few htnnan inventions which disjJay a higher inge- 
 nuity." 
 
 Barbaba, Celakent, Daeii, rEKiOQUE prions. 
 Cesaeb, Camestres, FESTiifO, Baboko secnndaB. 
 Tcrtia Dahapti, Di8amis, Datisi, FBLAPTOif, 
 BoKABDO, iFEEisoN habet. Quarta insnper addit 
 Bbamantip, Camenes, Dimabib, Febapo, Febsison. 
 
 If, rejecting the Fourth Figure, we consider its contents 
 as indirect Moods of the First, instead of the first line, the 
 two following should be substituted : — 
 
 Barbara, Celabent, Dabii, Febio, BABAi,ip-<on, 
 Celanxes, Dabitis, Fapesmo, FRisESOM-orum, 
 
 the final syllables in italics being only euphonic. 
 
 As already mentioned, the three vowels in each of these 
 names indicate the Quantity and Quahty of the three Judg- 
 ments which form the Syllogism. The consonants in the 
 names belonging to the First Figure have no special mean- 
 ing ; but of those in the other Figures, every consonant 
 (except T and n, which are merely euphonic) indicates 
 some step to be taken in the process of redtuAng the Mood 
 to a Mood of the First Figure. 
 
 The initial consonant, which is either B, C, D, or F, 
 indicates that Mood of the First Figure (Barbara, Cfela- 
 rent, Darii, or Jferio) to which the Reduction brings us. 
 Thus, Cesare and Camestre& are reduced to Celarent; Fes- 
 tino, Felapton, &c^ to Ferio. The other consonants show 
 how the Reduction is made, m indicates that the Premises 
 are to be transposed ; s and p, that the Judgment indicated 
 by the vowel immediately preceding is to be converted, — 
 s, that it is to be converted mmply, while p signifies the 
 conversion per aceideng. 
 
 K, which occurs in the names of only two Moods, £a- 
 roJco and Bokardo, denotes that the Judgment indicated 
 by the preceding vowel is to be left out, another sub- 
 stituted for it, and the process to be then completed by 
 
FIGURE AND MOOD. 
 
 203 
 
 a Reduction fer impossOdle, which will be explained here- 
 after. 
 
 A few examples will sufficiently illustrate the process. 
 The name Disamis indicates the following Syllogism of 
 the Third Figure, which is to be reduced to Parii of the 
 First, by converting simply its Major Premise, transposing 
 its Premises, and then converting its Conclusion. 
 
 Disamis reduced to Dabil 
 
 Some M are P ; 
 AU M are S ; 
 .•. Some S are P. 
 
 Some wars are justifiable ; 
 All wars are inexpedient ; 
 . Some inexpedient acts are 
 justifiable. 
 
 All M are S ; 
 Some P are M ; 
 .•. Some P are S. 
 
 All wars are inexpedient ; 
 Some justifiable acts are wars ; 
 .•. Some justifiable acts are inex- 
 pedient. 
 
 Festino of the Second is reduced to Ferio of the First 
 Figure, by converting simply its Major Premise. 
 Festiho reduced to Fhrio. 
 
 No P is M ; 
 Some S are M ; 
 .-. Some S are not P. 
 
 No ruminant is solid-hoofed; 
 
 No M is P ; 
 Some S are M ; 
 .-. Some S are not P. 
 
 No solid-hoofed animal b 
 
 ruminant ; 
 Some herbivora are soUd- 
 
 hoofed ; 
 Some herbivora are not 
 
 ruminant. 
 
 Some herbivora are solid- 
 hoofed ; 
 .•. Some herbivora are not rumi- 
 nant. 
 
 Fesapo of the Fourth is reduced to Ferio of the First 
 Figure, by converting both its Premises, the Major simply, 
 and the Minor per acoidens. 
 
 Fesapo reduced to Ferio. 
 
 No P is M ; No M is P ; 
 
 All M are S ; Some S are M ; 
 
 .•. Some S are not P. .*. Some S are not P. 
 
204- MEDIATE INFERENCE OR SYLLOGISM. 
 
 No Hindoo is white ; No white is a Hindoo ; 
 
 All whites are civilized ; Some civilized are whites ; 
 
 .-. Some civilized are not Hindoos. .-. Some civilized are not 
 
 Hindoos. 
 
 BaroTco and Bokardo have been stumbling-blocks to the 
 logicians. In order to reduce either of them to the First 
 Figure, the Premise v^hich needs to be converted is O ; 
 but according to the old doctrine, O is inconvertible. To 
 overcome this difficulty, the logicians invented the awk- 
 ward, roundabout, and operose process which they called 
 Reduction per Impossibile. Through a Syllogism in Bar- 
 bara, they proved, not directly that the Conclusion in 
 Baroko and Bokardo is true, but that its Contradictory is 
 false ; now, according to the Axiom of Excluded Middle 
 (that two Contradictories cannot hoik be false), this is an 
 indirect method of proving that the Conclusion is true. 
 The process is as follows. 
 
 Of course, both Premises in every Syllogism are pre- 
 sumed to be true ; then, any Conclusion wliich contradicts 
 either one of them must be false. Now, k indicates, that, 
 instead of the Premise signified by the vowel (O) imme- 
 diately preceding, we are to substitute the Contradictoiy 
 of the Conclusion ; and as this Conclusion is O, its Contra- 
 dictory is A. But from the two Premises (A A) thus 
 obtained, we have a Conclusion which contradicts the origi- 
 nal Premise, O. Then the substituted Judgment in A 
 (which is the Contradictory of the original Conclusion) 
 must be false ; and therefore the original Conclusion itself 
 is true. This is not exactly reducing the Syllogism to the 
 First Figure, but it is indirectly proving, through the First 
 Figure, that the Conclusion of the Syllogism must be true, 
 because its Contradictory is false. 
 
 Baboko reduced to Barbara. 
 
 All P are M ; All P ai-e M ; ,^^.^^ 
 
 Some S are not M ; All S are P ; (Contradictoiy of formeTcon- 
 .'. Some S are not P. .-. All S are M. (Contradicts former Minor 
 
 Premise.) 
 
FIGURE AND MOOD. 
 
 205 
 
 All M are S ; 
 . Some S are not P. 
 
 As this Conclusion 
 
 BoKAEDO reduced to Bakbaba. 
 
 Some M are not P ; All S are P ; (Contradictory of former 
 All M are S ; ConclusioD). 
 
 . AU M arg P. (Contradicts former Major 
 Premise.) 
 
 in Barbara cannot be true, its 
 Premise, which is the Contradictory of the former Con- 
 clusion, must be false ; then the original Conclusion itself 
 is true. 
 
 All this is awkward enough. Whately and others 
 rightly remark, that these two difficult Syllogisms can be 
 reduced in a much simpler and more elegant manner, 
 through converting one of their Premises by Contrapo- 
 sition. Thus, l.et Baroho be now called FaJcoro, and let 
 Bokardo be named BoTcamok (the substitution of these two 
 names will not spoil the mnemonic hexameters) ; and let 
 K indicate Conversion- by Contraposition. 
 
 Fakoko reduced to Ferio. 
 
 All P are M ; 
 Some S are not M ; 
 .■. Some S are not P. 
 AU murders are intentional ; 
 
 Some homicides are not inten- 
 tional ; 
 . Some homicides are not mur- 
 ders. 
 
 Dokamoe reduced to 
 
 Some M are not P ; 
 All M are S ; 
 .•. Some S are not P. 
 
 by Contraposition,) .• 
 Some imprudent acts are 
 
 not vicious ; 
 All imprudent acts are foolish ; 
 
 No not-M is P ; 
 Some S are not^M ; 
 .*. Some S are not P. 
 
 No unintentional act is a 
 
 murder ; 
 Some homicides are unin- 
 tentional ; 
 .*. Some homicides are not 
 murders. 
 
 Darh. 
 All M are S ; 
 Some not-P are M ; 
 Some not-P are S ; (ori convert 
 Some S are not P. 
 AU imprudent acts are foolish; 
 
 Some not-vicious acts are 
 imprudent ; 
 
206 MEDIATE INFERENCE OE SYLLOGISM. 
 
 .-. Some foolish acts are not .•. Some not-vicious acts are 
 vicious. foolish ; 
 
 .■. Some foolish acts are not 
 vicious. 
 
 These examples show that, after Dokamok has been re- 
 duced to Darii, the Conclusion must be contraponed back 
 again, if vce vi'ould have it in its original form. 
 
 Ingenious as this whole system of Reduction is, it is 
 needlessly artificial and complex. The sole reason for re- 
 ducing Syllogisms to the First Figure, we have said, is 
 to exhibit the reasoning in its simplest and most natural 
 form, and in that in which its validity, or invalidity, is most 
 readily perceived. A few simple- Rules may be given 
 which wiU enable the learner to accomplish this object at 
 once, in whatever Figure the argumentation may originally 
 be propounded, and even vnthout knowing what this Fig- 
 ure is. 
 
 1. Every process of reasoning must consist of a Judg- 
 ment which is to be proved, and of one or two other Judg- 
 ments alleged in its support ; the former is the Conclusion, 
 the latter are the Premises. The first step is to reduce 
 each of these Judgments to its simplest logical form, — 
 that is, to a Subject and Predicate connected by the pres- 
 ent tense (affirmative or negative) of the verb to be. Care 
 must be taken to determine accurately the Quantity and 
 Quality of each of the Judgments. 
 
 2. The Middle Term is that which does not appear in 
 the Conclusion. If no such Term is found in the Prem- 
 ises, the Inference is Immediate, and must be tried by the 
 principles laid down in the preceding chapter, concerning 
 Conversion, Opposition, &c. If there is a Middle Term, 
 the Inference is Mediate ; then the Major Premise is that 
 Judgment in which this Middle Term appears connected 
 with the Predicate of the Conclusion ; the Minor Premise, 
 that in which it is connected with the Subject of the 
 
CONDITIONAL SYLLOGISMS. 207 
 
 Conclusion. If only one Premise is given in the original 
 statement, the other may be easily supplied by a moment's 
 consideration, as its two naked Terms are known, and its 
 Quantity and Quality may be inferred, through the General 
 Rules already given for all Syllogisms, from the Quantity 
 and Quality of the Conclusion and the given Premise. 
 
 3. The First Figure requires the Middle Term to be the 
 Subject of the Major, and the Predicate of the Minor, 
 Premise. If, in the Premises as determined, the Terms do 
 not already appear in this order, one or both must be cow- 
 verted, either simply, or^er accideni, or by Contraposition. 
 
 There can be no difficulty in the application of these 
 Rules, which does not arise from some ambiguity in the lan- 
 guage of the original statement ; and to resolve such am- 
 biguity is the business, not of the logician, but of the gram- 
 marian and the lexicographer. But a few cases will be 
 incidentally resolved when we come to treat of Fallacies, a 
 subject which cannot be fully considered without some- 
 times stepping out of the province of Pure Thought. 
 
 2. Conditional Syllogisms. 
 
 Thus far we have treated exclusively of the purely Cate- 
 gorical SyUogism, in which each of the component Judg- 
 ments can be reduced to one or the other of the two Cate- 
 gorical formulas, A is B, or A is not B. The reasoning in 
 this case, as we have seen, depends upon the two Axioms 
 of Identity and Non-Contradiction. We come now to 
 another class of Syllogisms, dependent upon the Axioms 
 of Reason and Consequent, and Excluded Middle. 
 
 A Conditional Syllogism is one of which the Major Prem- 
 ise, and only the Major Premise, is a Conditional Judgment, 
 There are three kinds of such Syllogisms, corresponding to 
 the three classes into which Conditional Judgments are 
 divided ; namely, the HypothMccd, the Bisjuncdive, and the 
 
208 MEDIATE INFERENCE OK SYLLOGISM. 
 
 Dilemmatic or Mypothetico-Disjunctive. The following are 
 examples of each. 
 
 Bypotheticcd. DisfuncHve. 
 
 If A is B, C is D ; A is either B or C ; 
 
 A is B ; A is B ; 
 
 .•. C is D. .•. A is not C. 
 
 Dilemmatic or Hypothetico-Disjunctive. 
 
 K A is B, C is either D or E ; 
 C is neither D nor E ; 
 .'. A is not B. 
 
 These Terms may be quantified in the Minor Premise, 
 as in Categorical Syllogisms, and the Conclusion wiLl still 
 be valid, if its proper Quantity be assigned to it according 
 to the Rules already given. Thus, if the Minor Premise 
 of the preceding Hypothetical be " All A are B," we may 
 conclude that '■'■All C are D"; but if we know only that 
 " Some A are B," we can only conclude that " Some 
 are D." We may likewise use the quantification of Sin- 
 gulars, and say, " this A," or " in certain cases, A is B " ; 
 then, " in this case," or " in the same cases," C is D. 
 
 Dr. Thomson seems to be wrong, therefore, when he 
 gives the following as an instance of a Hypothetical Syllo- 
 gism, Figure I. in which each of the three Judgments is 
 Hypothetical. 
 
 In cases where M is N, C is D. 
 
 In cases where A is B, M is N. 
 
 In cases where A is B, C is D. 
 Here, the supposed Condition, " in cases where A is B," 
 is only an awkward quantification of the Minor Premise 
 and the Conclusion, equivalent to " in certain cases" or 
 " some M is N " ; therefore, in these cases, or some, C is D. 
 The reasoning does not turn upon this phrase, " in cases 
 where A is B," as a condition, the Consequent being 
 evolved from it ; it turns upon it only as a limitation. 
 
CONDITIONAL SYLLOGISMS. 209 
 
 showing in how many cases the reasoning is applicable. 
 The reasoning does rest exclusively upon the Major 
 Premise, where the corresponding phrase, " in cases where 
 M is N," is a true condition, the Consequent being evoh'ed 
 from it, and the whole argumentation being governed by 
 the Axiom of Reason and Consequent. 
 
 This error has led Dr. Thomson into a more serious one. 
 Not perceiving that Hypothetical Reasoning is distinct in 
 kind from Categorical, being governed by a different Axiom 
 of Thought, he has overlooked the principle that, from 
 affirming the Consequent of a Reason, no Conclusion can he 
 drawn, and has presented the following as a vaUd Syllo- 
 gism : — 
 
 In cases where C is D, M is N ; 
 In cases where A is B, M is N ; 
 
 .'. In cases where A is B, C is D. 
 But here the Minor Premise only aflBrms that " M is N," 
 which is the Consequent of the hypothesis in the Major 
 Premise ; and therefore the Conclusion is illogical ; the 
 Middle Term is not distributed. This can be easily seen 
 from the following example, the Conclusion of which is 
 evidently a non sequitur. 
 
 If you whip him, the boy cries ; 
 
 If you take away his toys, the boy cries ; 
 ••. If you take away his toys, you whip him. 
 Then, in a Conditional Syllogism, it is only the Major 
 Premise which is a Conditional Judgment; for the -reason- 
 ing turns upon the relation of Reason and Consequent, and 
 this relation, being once affirmed in the Major Premise, 
 affijrds all the material requisite for the Inference. Both 
 the Minor Premise and the Conclusion must be Categorical ; 
 the Major contains all the Terms which appear in either of 
 them ; whereas, the Minor Premise of a Categorical Syllo- 
 gism contains a new Term, which did not appear in the 
 jor. If, then, both Premises, or one Premise and Con- 
 
21U MEDIATE INFERENCE 08 SYLLOGISM. 
 
 elusion, are Conditional Judgments, the reasoning is, in 
 fact. Categorical, and depends upon the Axioms of Identity 
 and Non-Contradiction. This is easily seen in the case of 
 a Disjunctive Syllogism, whose form is determined by the 
 Axiom of Excluded Middle. 
 
 Every A is either X or Y ; 
 
 But B is A ; 
 
 Then B is either X or Y. 
 Here the reasoning is evidently Categorical; the Minor 
 Premise introduces a new Term, B, not contained in the 
 Major Premise, and therefore the Conclusion is also Dis- 
 junctive. 
 
 Endeavoring to prove that, in a Disjunctive Syllogism, 
 not only the Major, but the Minor Premise or the Conclu- 
 sion, may be a Disjunctive Judgment, Dr. Thomson pre- 
 sents the following as a vahd example : — 
 C, D, and E are B ; 
 C, D, and E = A ; 
 .-. A is B. 
 This is not a Disjunctive Syllogism at all, as neither of the 
 three Judgments is Disjunctive ; the three Concepts which 
 constitute the Middle Term are not taken disjunctively, 
 but collectively ; that is, one of them does not exclude the 
 others, but requires the presence of the others, in order to 
 constitute the Predicate. They form one compound Term. 
 Thus, let C, D, and E = M, and make the substitution. 
 Then the Syllogism assumes this form, and is evidently 
 Categorical. 
 
 MisB; 
 
 M = A; 
 
 .-. A is B. 
 
 The Axiom of Reason and Consequent is explicated, as 
 
 we have seen, into these two principles ; — to affirm the 
 
 Season or the Condition is also to affirm the Ccmsequmt or 
 
 the Conditioned; and to deny the Ccmaequent is also to dmy 
 
CONDITIONAL SYLLOGISMS. 211 
 
 the Reason. The application of these principles gives us, 
 from the same Major Premise, two, and only two, valid 
 Moods of the Hypothetical Syllogism, — namely, the 
 Modus Ponens and the Modus Tollens. Thus : — 
 
 If A is B, C is D. 
 
 Modus Pohens. 
 
 Modus Tollens. 
 
 C is not D ; 
 Then A is not B. 
 
 AisB; 
 Then C is D. 
 The following are examples of these formulas : — 
 Modus Ponens. 
 If matter is essentially inert, every change in it must be 
 
 produced by mind ; 
 But matter is essentially inert ; 
 Then all changes in it are produced by mind. 
 
 Modus Tollens. 
 If the moon shines by its own light, it must always be fuU ; 
 But it is not always full ; , 
 
 Then it does not shine by its own Hght. 
 
 We have said that there are only two valid Moods, be- 
 cause, from denying the Reason, or from aiBrming the Con- 
 sequent, nothing follows. The Consequent may follow from 
 some other Reason than the particular one assigned in the 
 Major Premise ; and the original Axiom only affirms the 
 necessity of some Reason or other, not of any particular 
 one. It is true, that the Minor Premise may be quantified 
 with the predesignations all, some, or this, and correspond- 
 ing Conclusions wiU foUow. The different forms which 
 thus result may, if we please, be called Moods also. 
 
 The Major Premise, or Sumption, in either of the pre- 
 ceding examples, may be converted by Contraposition ; 
 and the result will be, that what was the Modus Tollens 
 becomes the Modus Ponens, and vice versa. These two 
 Moods are thus shown to be really one ; and this is pre- 
 cisely what we should expect, for the two principles by 
 
212 MEDIATE INFEEENCE OK SYLLOGISM. 
 
 which they are governed are only two expKcations of one 
 Axiom of Thought. Thus, the last preceding example, 
 which is now the Modus Tollem, becomes the following, if 
 we contrapone the Sumption : — 
 
 If the moon is not always full, it does not shine by its own 
 
 hght; 
 But it is not always full ; 
 Then it does not shine by its own light. 
 
 Here the Subsumption posits what is now the Reason, 
 (though both are negative in form,) and therefore the 
 Conclusion posits the Consequent. Hence the reasoning 
 has now become the Modus Ponens. 
 
 Summing up what has been said, it appears that the 
 Hypothetical Syllogism is subject to these three Special 
 Rules : — 
 
 1. It consists of three Judgments, and only three ; but in 
 these Judgments there may be more than three Terms. 
 
 2. In respect to Quantity and Quality, the Sumption 
 must always be Affirmative and Universal, while the Sub- 
 sumption may vary in either of these relations. 
 
 3. The Conclusion is regulated, both in Quantity and 
 Quality, by that member of the Sumption which is not 
 subsmned, agreeing with it in both these respects in the 
 Modus Ponens, and diflfering firom it in both m the Modus 
 ToUens. 
 
 The Sumption in the last example (after Contraposition) 
 may seem not to conform to the second of these Rules ; for 
 it appears to be Negative in Quality. But if closely ex- 
 amined, the negative particle not wiU be found to belong 
 to each of the two parts (Reason and Consequent) taken 
 separately ; while the Sumption, as a whole, affirms the 
 connection of these two negative parts witii each other. 
 
 Agreeably to what has been said, a injunctive Syllogism 
 is one of which the Major Premise is a Disjunctive Judg- 
 
CONDITIONAL SYLLOGISMS. 213 
 
 ment, while the Minor Premise and the Conelusion are Cate- 
 gorical Judgments. The Axiom of Excluded Middle, by 
 which this sort of Syllogism is governed, affirms that, of 
 two Contradictories, one must be true and the other must 
 be false. Accordingly, if the Major Premise presents 
 three or more Disjunct Members, the Axiom wiU not be 
 immediately applicable ; these three or more Members are 
 only Contraries with respect to each other, and they must 
 be reduced to two Contradictories, before we can obtain a 
 ground of inference, from positing or sublating one of them, 
 to sublating or positing the other. The number of such 
 Members can always be thus reduced by considering, for 
 the moment, two or more of them as one. After this re- 
 duction is accomplished, the Minor Premise and Conclusion 
 appear in their true character, not as Disjunctive, but as 
 Categorical Judgments. For example : — 
 
 Complete Fomaila. 
 
 A is either B, C, or D ; 
 But A is neither B nor C ; 
 Then A is D.* 
 
 Reduced Formula. 
 
 LetBorC = X. 
 A is either X or D ; 
 But A is not X '; 
 Then A is D. 
 
 This formula, as reduced, presents the universal type of 
 Disjunctive reasoning. As its two Disjunct Members are 
 Contradictories of each other, the Axiom of Excluded Mid- 
 dle authorizes us, from positing either one of them, to sub- 
 late the other. This is called the Modus ponendo tollens, 
 and it has two forms, according as we posit one or the 
 other of the two Disjunct Members. The same Axiom 
 
 * A stoiy is told to illustrate the sagacity of a dog. Following Ms 
 master by the scent, the animal came to a place where three roads met, and 
 having ascertained by his nose, at two of them, that the object of his search 
 had not taken either of the two, he immediately darted oflf by the third, with- 
 out pausing to try whether this path also was scentless. The story is un- 
 questionably a fiction ; but, if true, the dog must have reasoned by this form 
 of the Disjunctive Syllogism, in the modtis tolkndo ponens. 
 
214 MEDIATE INFERENCE OB SYLLOGISM. 
 
 permits us, from sublating either of the two, to posit the 
 other. This is called the Modus toUendo ponem, and has 
 two forms Hke the other. Hence, every Disjunctive Syllo- 
 gism affords, from the same Major Premise, two valid 
 Moods, each containing two forms. It is obvious, that the 
 remaining Term, A, of the Major Premise, may be quan- 
 tified as all or this, and the Conclusion wiU appear accord- 
 ingly as Universal or Singular. The two Moods and four 
 forms of a Disjunctive Syllogism are exhibited in the fol- 
 lowing example : — 
 
 Major Premise. Every Judgment is either Affirmative or 
 
 Negative. 
 
 MODVS PONKHDO ToLLEHS. 
 
 First form. This Judgment is Affirmative ; 
 
 Then it is not Negative. 
 Second form. This Judgment is Negative ; 
 
 Then it is not Affirmative. 
 Modus Tollendo Ponbhs. 
 First form. This Judgment is not Affirmative ; 
 
 Then it is Negative. 
 Second form. This Judgment is not Negative ; 
 
 Then it is Affirmative. 
 
 For those who are fbnd of mnemonic hexameters, Ham- 
 ilton has presented all four forms in the following verses : — 
 
 Ponendo toUens. Falleris aut fidlor ; fallor ; non fallens ergo. 
 
 PaJleris aut fallor ; ta falleris ; ergo ego nedum. 
 
 ToUendo ponens. Falleris aut fallor ; non fallor ; falleris ergo. 
 
 Falleris aut fallor ; non falleris ; ergo ego fallor. 
 
 Three Special Rules have been framed for Disjunctive 
 Syllogism, though they are so obvious that their formal 
 enouncement is hardly necessary. 
 
 1. A regular Disjunctive Syllogism must consist of 
 three Judgments only, in which, if the Major Premise 
 be reduced to its proper lo^cal form, there can be 
 
CONDITIONAL SYLLOGISMS. 215 
 
 only three Terms, all of which must appear in the Major 
 Premise. 
 
 2. The Major Premise must be Universal and Affirma- 
 tive ; the Minor Premise may be of either Quality and of 
 either Quantity. 
 
 3. The Conclusion must be of the same Quantity, but of 
 opposite Quality, with the Minor Premise. 
 
 Agreeably to what was said in treating of Disjunctive 
 Judgments, each Mood of a Disjunctive Syllogism may be 
 resolved into a Hypothetical Syllogism, and then its two 
 forms appear as the two Moods of the Hypothetical reason- 
 ing. For instance, the example last cited may be thus 
 transformed : — 
 
 If any Judgment is not Affirmative, it is Negative. 
 
 Modus Ponens. Modus Tollens. 
 
 This Judgment is not Af- This Judgment is not Neg- 
 
 fomative ; ative ; 
 
 Then it is Negative. Then it is Affirmative. 
 
 As a Dilemmatic Syllogism consists of a Hypothetical 
 and a Disjunctive combined, and as these two may be com- 
 bined in several different ways, the resulting forms are 
 numerous and complex. Most of them are really com- 
 pound, and a fall analysis would need to resolve them 
 into several simple and subordinate Syllogisms. It would 
 be tedious to ana,lyze them all, and this is not necessary, 
 as the principles already established for the Hypothetical 
 and the Disjunctive Syllogisms taken separately, still gov- 
 ern them when taken in connection ; and the learner in 
 each case may make the analysis and apply the principles 
 for himself. What follows is to be regarded only as illus- 
 trating the method to be pursued. 
 
 What has already been presented as a type of the Di- 
 lemmatic Syllogism is, in iact, only a Hypothetical dis- 
 guised, as the Disjunction is not resolved, and therefore its 
 
216 MEDIATE INFERENCE OR SYLLOGISM. 
 
 Disjunct Members, whether two or more, may be regarded 
 as a single Term. 
 
 If A is B, C is either D or E. 
 
 Modus Ponens. Modos Tollens. 
 
 But A is B ; C is neither D nor E ; 
 
 ••. C is either D or E. ••• A is not B. 
 
 In practice, however, the Disjunction is usually resolved, 
 in the Modus tollsns, by two subordinate (abridged) Syllo- 
 gisms, by which it is first separately proved that C is not JD, 
 and that O is not JE; and then the Conclusion of the com- 
 pound Modus tollens follows, that A is not B. Thus : — 
 
 If man cannot be virtuous, either he must be unable to 
 know what is right, or unable to wUl what is right. 
 
 But he is not unable to know what is right, for he is ?m- 
 telKgent; and he is not unable to will what is right, 
 for he is free. 
 
 Therefore, he can be virtuous. 
 
 Hence, the Dilemma was called by the old logicians 
 the Gornutus or horned syllogism, because, in the Sump- 
 tion, the Disjunct Members are opposed like horns to the 
 assertion of the adversary ; with these, we throw it from 
 one side to the other in the Subsumption, in order to toss 
 it altogether away in the Conclusion. 
 
 Krug remarks : " The Comutus and CroeodUinus of the 
 ancients must not be confounded with the Dilemma which 
 we are Here speaking of. The former were sophismata 
 heterozeteseos, sophisms of counter-questioning; the latter is 
 a legitimate mode of reasoning." But it may be shown 
 that the old Comutus is a legitimate Dilemma in Form, 
 and is of the type which we are now considering, the fel- 
 lacy being in the Matter. The Zdtigiosus, for instance, 
 which is one illustration of this old fellacy, may be thus 
 resolved. 
 
CONDITIONAL SYLLOGISMS. 217 
 
 Protagoras agreed for a large sum to educate Euathlus 
 as a lawyer, one half of the price to be paid down, and 
 the other half on the day when the pupil should plead and 
 gain his first cause. Some time elapsed, and Protagoras, 
 thinking that his disciple intentionally delayed the com- 
 pletion of his contract, sued him in court for the remainder 
 of the fee, and propounded this Dilemma. 
 
 If Euathlus is to be released fi:om the payment of this 
 sum, it must be either because the judgment of thia court 
 will be in his favorj or against him. 
 
 But if the judgment is in his favor, then he has pleaded 
 and gained his first cause, and the money is due me under 
 the contract. 
 
 If the judgment is against him, the money is due me 
 under the decision of the court. 
 
 Thus, both the Disjunct Members of the Consequent 
 being disproved by subordinate Syllogisms, the Conclusion 
 of the compound Modus tollens follows, that Euatyus is 
 not to be released from the payment. 
 
 The Dilemma is here correct in Form, but there is a 
 Material Fallacy in the Major Premise, since the Disjunc- 
 tion is not complete. There is a third horn to it, as Pro- 
 tagoras had no right, under the contract, to invoke the 
 judgment of the court at all, so that the judges ought to 
 have dismissed the case without a hearing. Before ajv^- 
 ment was rendered, Protagoras had no ground of action.. 
 
 Euathlus is said to have retorted upon his antagonist, by 
 propounding a Dilenima in the same Form in which it had 
 just been urged against him. " If the decision be favor- 
 able to me, I shall pay nothing under the sentence of the 
 court ; if adverse, I pay nothing in virtue of the compact, 
 because I shall not have gained my first cause." 
 
 " In siftmg a proposed Dilemma," says Krug, " we are 
 to look closely to the three following particulars : — 
 1. Whether, in the Sumption, the Consequent is a legiti- 
 !Q 
 
218 MEDIATE INFERENCE OK SYLLOGISM. 
 
 mate inference from the Antecedent; 2. Whether the 
 Disjunction in the Consequent is complete ; 3. Whether, 
 in the Subsumption, the Disjunct Members are properly 
 sublated. The following Dilemma is faulty in each of 
 these respects. 
 
 " If Philosophy be of any value, it must procure for us 
 power, riches, or honor. 
 
 " But it procures neither of them. Therefore, &c. 
 " Here, 1. the inference is wrong, as Philosophy may he 
 worth something, though it does not secure any of these 
 external advantages; 2. the Disjunction is incomplete, as 
 there are other goods, besides the three here enumerated ; 
 3. the Subsumption is false, as Philosophy has often been 
 the means of procuring these very advantages." 
 
 In another form of the Dilemma, the Sumption is a 
 Hypothetical Judgment with more than one Antecedent, 
 and the Subsimiption is a Disjunctive of which these sev- 
 eral Antecedents are the Disjunct Members. 
 
 If A is B, C is D ; and if E is F, C is D; 
 But either A is B or E is F ; 
 .-. C is D. 
 Here, the several Antecedents have the game Conse- 
 quent, and therefore the Conclusion is Categorical. If 
 they had different Consequents, the Conclusion would he 
 Disjunctive. Thus : — 
 
 If A is B, C is D ; and if E is F, G is H ; 
 But either A is B or E is F ; 
 ••• Either C is D, or G is H. 
 In this case, the Modus tollens is also valid ; if we dis- 
 junctively deny the Consequents, we may, in the Conclu- 
 sion, disjunctively deny the Antecedents. 
 
 Either C is not D, or G is not H. 
 .■. Either A is not B, or E is not F. ' 
 In the preceding case, where the Antecedents had the 
 
DEFECTIVE AND COMPLEX SYLLOGISMS. 219 
 
 same- Consequent, if we deny this one Consequent, we must 
 deny the Antecedents taken collectively, and not disjunc- 
 tively ; theh the Syllogism will be exclusively Hypotheti- 
 cal, as neither Judgment will be disjunctive. Thus : — 
 
 If A is B, C is D ; and if E is F, C is D ; 
 
 But is not D ; 
 .•. Then A is not B, and E is not F. 
 The nature of a Disjunction is, that any one of the Dis- 
 junct Members exists, or is posited, only by the non-exist- 
 ence, or sublation, of all the others. Hence, the particles, 
 eiiher — or, have a Disjunctive force; but the corresponding 
 negative particles, neither — nor, have a Conjunctive force, 
 as they denote the exclusion of both or all, and not merely 
 the exclusion of one on condition of the inclusion of aU the 
 others. A is either B or C, means that A is B only on con- 
 dition that A is not C. But A is neither B nor 0, means 
 that A is not B and is not 0. 
 
 It has been remarked, that the Modus tollens of the Di- 
 lemma, in the form in which it was here first proposed, is 
 nothing but a Negative induction. 
 
 If A is B, C is either D, E, or F ; 
 
 But C is neither D, E, nor F ; 
 
 Then A is not B. 
 This can be resolved into a Categorical Syllogism of 
 Induction. Thus : — 
 
 C is not D, is not E, and is not F ; 
 
 But these are all the possible cases of A being B ; 
 
 Then A is not B. 
 
 3. Defective and Complex Syllogisms. 
 
 It has already been mentioned, that men do not usually 
 speak or write complete Syllogisms ; nay, it is almost only 
 in treatises on Logic that we find Syllogisms completely 
 
220 • MEDIATE INFERENCE OK SYLLOGISM. 
 
 enounced, or with all their parts expressed. The abridged 
 form is preferred on all ordinary occasions, because at least 
 one of the three Judgments is so obvious, both to the 
 speaker and the hearer, that it would be a waste of time 
 and words — a sin against brevity, and even against per- 
 spicuity —r to propound it openly ; for unnecessary words 
 do not elucidate, but obscure, the Thought. We usually 
 express a single process of reasoning by two Judgments, 
 connected by an illative particle, hecause, then, therefore, 
 &c. ; sometimes only by a conjunctive particle, and. The 
 following are instances of reasoning thus enounced. 
 
 Aldebaran is a star ; therefore, it shines by its own light. 
 No avaricious person can be happy ; because he who is 
 
 never free from fear cannot be happy. 
 A liar ought not to be believed ; and this witness has been 
 
 proved to be a liar. 
 
 Such sentences as these are called Enthymemes, because 
 they are abridged statements of a process of reasoning, one 
 of the three Judgments necessary to constitute the Syllo- 
 gism being ev dv/j,co, in the mind, but not expressed. In 
 the first case, the suppressed Judgment is the Major Prem- 
 ise, — all stars shine hy their own light ; in the second, it 
 is the Minor Premise, — an avaricious person is never free 
 from fear, the Conclusion also, as is frequently the case in 
 Enthymemes, being placed first, instead of last ; in the 
 third case, the suppressed Judgment is the Conclusion, — 
 this witness ought not to he believed. 
 
 An Enthymeme, then, is not a peculiar kind of Syllo- 
 gism, but only an abridged expression of a Syllogism. Of 
 course, the doctrine of Enthymemes properly belongs, not 
 to Logic, but to Rnetoric, for it concerns expression, not 
 thought ; and it would never have been obtruded into the 
 former science but for the authority of Aristotle, who em- 
 ployed the name, indeed, in a difierent and now disused 
 
DEFECTIVE AND COMPLEX SYLLOGISMS. . 221 
 
 meaning, signiiying by it " a reasoning from signs and like- 
 lihoods." 
 
 * 
 
 Hitherto, we have treated only of the so-called Mono- 
 syllogism, — that is, of a Syllogism considered as one in- 
 dependent whole, without reference to the continuous chain 
 of reasoning, of which, in an abridged form of expression, 
 it usually constitutes a single hnk. Many truths — most 
 of the theorems in Geometry, for instance — can be 
 proved only by a Chain of Reasoning ; — that is, by a 
 connected series of Syllogisms, the several portions of 
 which are dependent upon each other. A Conclusion of 
 one may become a Premise of the next succeeding Syllo- 
 gism, and is then called, in reference to its successor, a 
 Prosyllogism ; while the latter, in reference to the one 
 which preceded it, is called an Episyllogism. A Prosyllo- 
 gism, then, is a Syllogism whose Conclusion is a Premise of 
 that which follows ; and an Episyllogism is one whose Prem- 
 ise is a Conclusion of that which p-ecedes. As, in a hierarchy 
 of Concepts, the same class-notion is at once a Genus to 
 the class below and a Species to the class above ; so, in a 
 Chain of Reasoning, the same Syllogism is at once a Pro- 
 syllogism and an Episyllogism in its opposite relations. 
 Only that which contains the primary or highest reason 
 can be exclusively called a Prosyllogism; only that which 
 enounces the last or lowest consequent, is exclusively an 
 Episyllogism. 
 
 The Syllogism constituting a Chain may be either partly 
 complete and partly abbreviated, or all equally abbreviated. 
 In the former case, the complex Syllogism which results is 
 called an Epicheirema ; in the latter, it is called a Sorites. 
 
 A Syllogism is called an Epicheirema, when,' to either or 
 both of its two Premises, there is attached a reason for its 
 support. The Premise with such a rider annexed is, in 
 fact, a Prosyllogism abbreviated, — that is, an Enthymeme 
 used to prove one of the branches of the main Syllogism. 
 Thus : — 
 
222 
 
 MEDIATK INFERENCE OR SYLLOGISM. 
 
 MisP; 
 
 S is M, because it ia N ; 
 .-. S is P. 
 
 The flesh of ruminants is good for 
 
 food; 
 These animals are ruminants, be- 
 cause they have cloven hoo& ; 
 . These animals are good for food. 
 
 Here, the Enthymeme, which is a rider of the Minor 
 Premise, may be thus exphcated into a complete Prosyllo- 
 gism. 
 
 All animals which have cloven hoofs are ruminant ; 
 These animals have cloven hoofe ; 
 .'. These animals are ruminants. 
 
 It has already been said, that every Syllogism may be 
 regarded as an application of the general and seF-evident 
 principle, that a part of a fart is a part of the whole. If, in 
 the apphcation of this principle, we do not stop at the first 
 or proximate whole, but, before drawing any expressed Con- 
 clusion, proceed step by step to remoter parts and more 
 comprehensive wholes, and, in the Conclusion, finally place 
 the smallest part under the largest whole, the complex 
 abbreviated reasoning thus formed is called a Chain-Syllo- 
 gism, or Sorites. It may be aptly symbolized by a series 
 of concentric circles. 
 
 1. AisB 
 
 2. B is C 
 
 3. C is D 
 
 4. DisE 
 Therefore, A is E. 
 
 A Sorites of this sort may be described as a series of 
 Enthymemes with suppressed Conclusions, in which the Pred- 
 icate of each is the Suby'ect of the next, and the Oonclumn 
 of the whole is formed from the first Subject and last Pred- 
 icate of the Premises. The Conclusion being thus formed. 
 
DEFECTIVE AND COMPLEX SYLLOGISMS. . 223 
 
 it is evident that there must be as many Middle Terms 
 (i. e. Terms intervening between the first Subject and last 
 Predicate, that is, again, between the smallest part and the 
 greatest whole which the reasoning connects) as there are 
 Premises minus one ; consequently, every Sorites may be 
 explicated into as many distinct Syllogisms as there are 
 Premises minus one. The first Judgment in the Sorites is 
 the only Minor Premise that is expressed ; each of the 
 other Minor Premises is the Conclusion of the separate 
 Syllogism next preceding. Hence, each of the Judgments 
 in the Sorites except the first is the Major Premise of a 
 distinct Syllogism. The preceding Sorites, for instance, 
 may be thus explicated into three Syllogisms, the correct- 
 ness of the exphcation being made very evident by a refer- 
 ence to the diagram. 
 
 I. 
 
 11. 
 
 ni. 
 
 2. B is C, 
 
 3. C is D, 
 
 4. D is E, 
 
 1. A is B ; 
 
 A is 0; 
 
 AisD; 
 
 .-. A is C. 
 
 .'. A is D. 
 
 .'. A is M 
 
 An invahd Mood occurring anywhere in the series 
 before the last Syllogism would not only be wrong itself, 
 but, as fiimishing a Premise to its successors, woidd vitiate 
 all that follow. Hence, in a Sorites, out of all the Prem- 
 ises, only the one first expressed may be Particular ; be- 
 cause, in the First Figure, to which all the separate Syllo- 
 gisms belong, the Minor Premise may be Particular, but 
 not the Major; and all the Judgments in the Sorites, 
 except the first and the Conclusion, are Major Premises. 
 In the Sorites, also, only the last Judgment may be Nega- 
 tive ; for if any other of its Judgments were Negative, the 
 Syllogism formed fi:om the next following Judgment would 
 have a Negative Minor Premise, which the First Figure 
 does not admit. A Sorites in the Modus tollens, then, can 
 be stated only in one form ; — from denying the last Con- 
 
224 MEDIATE INFERENCE OE SYLLOGISM. 
 
 sequeiit of the last Antecedent, we go back to denying 
 this same Consequent of the first Antecedent. Thus, if 
 we say that I) is not JS, we must conclude that A is not U. 
 The three distinct Syllogisms already given are not aU 
 that may be formed from the given Sorites. Instead of be- 
 ginning with the first Judgment, and thereby finally con- 
 cluding that A is U, we may begin with the second Judg- 
 ment, first concluding that B is D, and then that B is E ; 
 and again, beginning with the third, we may conclude that 
 C is IE. Hence, fi:om a Sorites with four Premises, we 
 may form in aU six distinct Syllogisms. If tjiere were five 
 Premises, there would be ten resultant Syllogisms. " The 
 formula," says Dr. Thomson, " for ascertaining the num- 
 ber of Conclusions is this : — ■ Let the number of Premises 
 = n ; the number of terms = n -f" 1 > then the number 
 
 of Conclusions = 
 
 n(re— 1)." 
 
 1.2 
 
 Goclenius invented another form of the Sorites, to which 
 his name has been attached ; it is -the same as the conunon 
 form, except that the Premises are reversed. Referring to 
 the diagram again, it is evident that, instead of beginning 
 with the Terms of least Extension, represented by the in- 
 nermost circles, we may begin with the more Extended 
 Terms in the outer circles. Then the Subject of each 
 Judgment becomes the Predicate of the next; while, in 
 the common form, it is the Predicate of the former which 
 becomes the Subject of the latter. The Groclenian Sorites 
 is thus stated : — 
 
 DisE, 
 
 CisD, 
 
 B is C, 
 
 AisB; 
 .-. A is E. 
 
 Here, Extension is more prominent, as we start with the 
 wider Terms ; hence, this form is better suited for deduc- 
 
DEFECTIVE AND COMPLEX SYLLOGISMS. 225 
 
 tion. In the common form, Intension predominates, as 
 tlie narrower Terms come first; Induction naturally as- 
 sumes tllis Form. 
 
 " A ' pretty quarrel ' long existed amongst logicians," 
 says Dr. Thomson, " which of the two was to be c&Ued 
 progressive and which regressive. It was a mere strife 
 about words. If we are discovering truth by the inductive 
 method, the Aristoteilian form is progressive ; if we are 
 teaching truth, or tryiijg our laws upon new facts, we use 
 deduction, and the Goclenian form is progressive. In an 
 apt but famihar figure, — if I am on the ground floor, and 
 wish to fetch something that is above, my going up stairs is 
 my progress towards my object, and my coming down is a 
 regression ; if the positions of myself and j;he thing are re- 
 versed, going down would be progress, and returning up, 
 regress. The inductive truth-seeker is on the ground-flooJ' 
 of facts, and goes up to seek a law ; the deductive teacher 
 is on a higher Story, and carries his law down with him to 
 the facts. 
 
 " This will be clearer from a pair of examples. 
 
 Goclenian or descending Sorites. Aristotelian or ascending Sorites. 
 
 Sentient beings seek happiness ; Caius is a man ; 
 All finite beings are sentient ; All men are finite beings ; 
 All men are finite beings ; All finite beings are sentient ; 
 
 Caius is a man ; All sentient beings seek happi- 
 
 ness ; 
 Therefore Caius seeks happi- Therefore Caius seeks happi- 
 ness, ness." 
 
 By way of recapitulation, the chief principles and rules 
 of the Aristotelic doctrine of 'Syllogism are brought to- 
 gether in the following Conspectus. 
 
 10* 
 
226 
 
 CONSPECTUS OF THE AEISTOTELIC 
 
 Mbdiatb Inference or Syllo- 
 
 is that act of Thought whereby the 
 relation of the two-Terms of a pos- 
 sible Judgment to each other is 
 ascertained by comparing each of 
 thim separately with a Third Term. 
 
 Stllogirhb 
 
 Catxgobical, 
 
 in which each of the three Jadgments can ba 
 expressed under one or tbe#ther of these 
 two Formulaa : — 
 
 AitB; 
 
 A ia not B, 
 
 General Canon 
 
 of Categorical Syllogisms. In so far 
 as two Notions, ( Concepts or Indi- 
 viduals,) either both agree, or, one 
 agreeing, the other does not agree, 
 with a common Third Notion, in 
 so far these Notions do, or do not, 
 agree with each other. 
 
 This Canon is explicated 
 
 n. 
 
 A Syllogism must 
 contain three Terms, 
 and n^taaore. 
 
 A Syllogism most 
 contain three Judg- 
 ments, and no moie. 
 
 The Figure 
 
 of a Syllogism is determined by the 
 relative position of the Middle Term 
 in the two Premises. 
 
 LetS = 8ultjectsfthe 
 VignreL MP; 
 SM; 
 .•.SP. 
 
 The Mood 
 
 of a Syllogism is the value of its three 
 Judgments in respect to their Quan- 
 tity and Quality, as indicated in 
 each case by the four Judgments, 
 A, £, I, and O. 
 
 Valid 
 
 Pig. I. 
 
 AAA; Barbara, 
 & A E ; Ce/nrent. 
 All; Darii. 
 E I O ; Ferio. 
 
 Reduction 
 
 of the valid Moods of the three lower 
 Figures to those of the First Fig- 
 ure may be accomplished by per- 
 forming the processes indicated by 
 the following letters in the names 
 of those Moods. 
 
 B = Reduce the Mood to Barbara, 
 C = " " CelarenU 
 
 D= " " Darii. 
 
 F= " " Ferio. 
 
 General Canon 
 
 of Hypothetical Syllogisms. To affirm 
 the Reason or the Condition is to 
 affirm the Consequent ; and to deny 
 the Consequent is also to deny the 
 Reason. 
 
 This Canon pioduoes, f^om 
 
 Mqjor Premise, 
 
 Modus Ponens. 
 AlsB; 
 .-. C is D. 
 
 General Canon 
 
 of Disjunctive Syllogisms. Of two 
 Contradictories, one must be true 
 and the other must be false. 
 
 This Canon produces, fhun 
 
 Majot Premise, 
 
 Modus ponendo tollena, 
 1. AisB; 
 ... A is not C. 
 
 3. A is C ; 
 .-. A la not R. 
 
DOCTRINE OF SYLLOGISM. 
 
 227 
 
 AKB EITHER 
 
 OR Conditional, 
 
 in which the Major PremiBe, and only the Major Premise, ia a Conditional Judgment ; and 
 these are eubdivided into 
 
 Hypothetical J 
 
 Major Premise, 
 If A is B, C is D. 
 
 Disjunctive ; 
 Major Premise, 
 A is either B or G> 
 
 Dilemmatic or Hypotheti- 
 cal Disjunctive, 
 Major Premise, 
 If A is B, C is either D or E. 
 
 into these six General Bulea. 
 
 m. IV. 
 
 The Middle Term 
 must be distributed 
 in at least one of the 
 Premises. 
 
 One Premise at least 
 must be Affirmative. 
 
 V. 
 
 If either Premise is 
 Negative, the Con- 
 clusion must be Neg- 
 ative. 
 
 VI. 
 
 Neither Term must 
 be distributed in the 
 Conclusion, if it was 
 not distributed in 
 the Premise. 
 
 Conclusion ; P = Predicate of the Conclusion ; M = 
 
 Figure II. P M j f Figure in. M P ; 
 
 SM; MS} 
 
 .-.SP. .-. SP. 
 
 : Middle Term. Then, 
 
 I Figure IV. PM; 
 MS} 
 .-.SP. 
 
 Moods. 
 
 Fig. n. 
 E A £ ; Cesare. 
 A £ £* ; Canieatres. 
 E I O } Festino. 
 A O O ; Baroko (Fakoro). 
 All Negative Condusions. 
 
 Fig. in. 
 
 A A I i Darapti, 
 I A I } Disamis. 
 All; Datisi. 
 H A O -f Felapton. ^ 
 O A O ; Bokardo {Dokamok), 
 BIO. Ferison. 
 AU Particular Conclusions. 
 
 Fig. IV. 
 A A Z ; Bramantip, 
 A E E } Camenes. 
 I A I ; Dimaria. 
 E A O ; Fesapo. 
 E I O } Freaison. 
 
 m — Transpose the Premises. 
 s = Convert simply. 
 p = Convert yer accidens. 
 k = Reduce per impossibile for 
 Baroko k Bokardo ; 
 Convert by Contraposition for 
 Fakoro & Dokamok. 
 
 Barbara^ Celarent, Darii, Fertoque^ prioris ; 
 Ceffare, Camestres, Festino^ Baroko^ secundss ; 
 Tertia Daraptit Disamis, Datisi, Felapton, 
 Bokardo^ Ferison habet ; Quarta insuper addlt 
 Bramantipj Camenesj Dimaris, Fesapo, Fresiaon. 
 
 the same Premise, two valid Moods. 
 
 IfAisB, CisD. 
 
 Modus Tollens. 
 
 C is not D *, 
 ,-. A is not B. 
 
 the same Premise, two valid Moods, each having two forma. 
 
 A is either B or C. 
 
 Modus toUendo ponens. 
 
 1. A is not B ', 
 .'. A is C. 
 
 2. A is not C ; 
 .-. A is B. 
 
228 MEDIATE INFEKENCE OR SYLLOGISM. 
 
 CHAPTER VIII. 
 
 THE HAMILTONIAN DOCTRINE OF SYLLOGISMS. 
 
 SIR William Hamilton's innovations in the doctrine 
 of Syllogisms, -which had been generally received 
 up to this time, are not limited to such as are the direct 
 consequences of his theory of the thorough-going quanti- 
 fication of the Predicate. On several minor points, also, 
 he has considerahly modified the AristoteHc doctrine. 
 These changes, it is true, were probably suggested by his 
 system of quantifying the Predicate ; but they are not so 
 closely connected with it as to prevent them fi-om being 
 received, even by those logicians who, whoUy or in part, 
 reject that system. All of them deserve consideration, as 
 they involve a discussion of some incidental questions of 
 much interest, affecting the whole theory of Logic. 
 
 As to the order of enouncement, the old doctrine was, 
 that the Premises, as their name imports, should precede 
 the Conclusion. Hamilton observes that the reverse order 
 is more natural, that it more faithfully represents the 
 progress of the mind in the investigation or discovery of 
 truth, and that it effectually relieves the Syllogism fi"om 
 the imputation, which has been thrown upon it for more 
 than three centuries, of being founded upon a mere petitio 
 prindpii, or a begging of the question. " Mentally one," 
 he says, " the Categorical Syllogism, according to its order 
 of enouncement, is either Analytic, if what is inappro- 
 priately styled the ' Conclusion ' be expressed first, and 
 what are inappropriately styled the ' Premises ' be then 
 
THE HAMILTONIAN ANALYSIS. 229 
 
 stated as its reasons ; or Synthetic, if the Premises precede 
 and, as it were, effectuate the Conclusion." In the Ana- 
 lytic order, the " Conclusion " would be more properly 
 called the Qucesitum, and the "Premises" should be 
 denominated the Proofs. 
 
 Now, the Analytic order, it is argued, is the more nat- 
 ural, because the Problem or Question, which it is the 
 purpose of the Syllogism to solve or answer, and which is 
 therefore the leading thought in the mind, is propounded 
 first. When we are in doubt whether A is, or is not, B, 
 it is surely more natural to argue, Ais £, because A is 0, 
 and all is B, than to reason in the old order, placing the 
 solution of the Problem last. " In point of fact, the Ana- 
 lytic Syllogism is not only the more natural, it is even^re- 
 supposed by the Synthetic." As already stated, the Syllo- 
 gistic process in the mind is really one and undivided, con- 
 sisting only in the inference of the Conclusion from the 
 Premises. But in order to state this single process in 
 words, we must analyze it, and therefore the Conclusion, 
 which is the compound result, ought to be stated first, so 
 as to admit of analysis. It may be stated generally, that a 
 process of investigation or research, looking towards truth 
 not yet discovered, is always Analytic. The most that can 
 be said for the Synthetic method is, that it may be suc- 
 cessfully used for teaching, or proving the truth that is 
 already known. To adopt an old illustration, in order to 
 find out for ourselves how a clock is made and how it does 
 its work, we must take it to pieces ; having done this, the 
 best way to teach another person how to make a clock is 
 to take those pieces and put them tog^her again. 
 
 The common objection to the validity of the Syllogistic 
 process is, that the Conclusion is virtually contained in the 
 Premises, so that we have to assume it to be true in the 
 very propositions by which we attempt to prove it. This 
 objection is thus forcibly stated by Mr. Mill. " When we 
 say, — 
 
230 MEDIATE INFERENCE OE SYLLOGISM. 
 
 All men are mortal ; 
 
 Socrates is a man ; 
 
 Therefore, Socrates is mortal ; 
 it is unanswerably urged by the adrersaries of the Syllo- 
 gistic theory, that the proposition, ' Socrates is mortal,' is 
 presupposed in the more general assumption, ' AH men 
 are mortal ' ; that we cannot be assured of the mor- 
 tality of all men, unless we were previously certain of 
 the mortality of every individual man ; that if it be still 
 doubtful whether Socrates, or any other individual you 
 choose to name, be mortal or not, the same degree of un- 
 certainty must hang over the assertion, ' All men are 
 mortal ' ; that the general principle, instead of bejng given 
 as evidence of the particular case, cannot itself be taken 
 for true without exception, until every shadow of doubt 
 which could affect any case comprised with it is dispelled 
 by evidence aliunde ; and then, what remains for the Syl- 
 logism to prove ? that, in short, no reasoning from generals 
 to particulars can, as such, prove anything : since, from a 
 general principle, you cannot infer any particulars but those 
 which the principle itself assumes as foreknown." 
 
 But if the Syllogism be stated in the Analytic form, 
 it is obvious that this objection is inapphcable. When we 
 argue, — 
 
 Socrates is mortal. 
 Because Socrates is a man. 
 
 And all men are mortal, — 
 we do not assume the point which ought to be proved, but 
 we prove that it is right to predicate mortality of Socrates, 
 by showing that Socrates belongs to the class man, all the 
 members of which are universally admitted to be mortal. 
 We appeal to the admitted Universal truth only after we 
 have established, what is here the main point of the argu- 
 ment, the applicability of the truth to this case, — the fact 
 that Socrates is a man. Mr. Mill mistakes the compara- 
 
THE HAMILTONIAN ANALYSIS. 231 
 
 tive importance of the two Premises ; in Analytic reason- 
 ing, — in drawing an inference for the purpose of investi- 
 gation or discovery, — the proof turns chiefly upon the 
 Subsumption ; and Aristotle therefore correctly places this 
 Premise first. Thus, if I am in doubt with respect to a 
 new substance which I have found, whether it be fusible or 
 not, the doubt may be resolved by ascertaining that this 
 ^stance is a metal. Only after this fact is ascertained, 
 and then only in order to complete the thought, or to si- 
 lence cavil, I refer to the admitted truth that aU metals are 
 fusible. Men usually reason in this manner, as is shown 
 by the frequent recurrence of such Enthymemes as these : 
 This iron, is not muUeahle, for it is cast-iron ; The man is 
 dishonest, for he has taken what is not his own ; this line is 
 equal to that, for they are both radii of the same circle, &c. 
 There is certainly a mental reference in such cases to a 
 Major Premise, — to the well-known truths, that No cast- 
 iron is malleable. All radii of the same circle are equal, &c. 
 But precisely because such Premises are weU known and 
 obvious, though thought, they are not usually expressed. 
 
 The bald truisms which are usually taken as examples 
 of the Syllogistic process are unfortunately chosen, as they 
 render more plausible the imputation that this process itseF 
 is futile and needless. Any kind of reasoning appears 
 puerile, when it is applied only to establish a puerile Con- 
 clusion. Nobody wishes any proof of the fact that Soc- 
 rates was mortal. Adopt any supposition which will make 
 it appear that there was a real doubt in the case, and that 
 the point to be determined was one of some importance, 
 and the Syllogism employed loses its fi-ivolous aspect, and 
 seems grave and pertinent. Suppose that the impulsive 
 Athenians of his day had made the same mistake in rela- 
 tion to Socrates, that those of a later time committed in 
 regard to Paul and Barnabas, and had begun- to offer sac- 
 rifices to him as an inunortal being ; it would have been 
 
232 MEDIATE IKFERENCE OR SYLLOGISM. 
 
 dignified and conclusive on his part to argue witll them, as 
 the A'poStle did, by saying, " We are men of like passions 
 with you," and worship is due only unto God. The first 
 question for the inquirer or disputant is, not whether this 
 case has already been decided, and therefore included 
 under this General Rule, which is supposed to be already 
 found ; but under what Glass-notion can this case be put, 
 which shall afibrd a General Rule that wiU be applicable 
 for the solution of the doubt. The difficulty is, how to 
 find the right Rule, and not, as Mr. MUl supposes, how to 
 interprtt it when found. The astronomer proceeds in this 
 manner, when he seeks to know whether a comet, which 
 has just appeared in the heavens, wiU return at a future 
 period, or disappear forever. By determining three or 
 more points in its path, he ascertains either that its orbit is 
 an ellipse or an hyperbola; this is the Subsumption, and 
 when found, the question is really answered, for the appli- 
 cation of the Sumption — that the ellipse is a curve which 
 retuhis into itself, while the hyperbola does not — is so 
 obvious, that it is unnecessary, except for a child, to be 
 reminded of it. But though not expressed, the thought 
 without it is certainly incomplete, and the main question is 
 not answered. 
 
 Mr. Mill's doctrine is, that " we much oftener conclude 
 frorii particulars to particulars directly, than through die 
 intermediate agency of any general proposition." For .ex- 
 ample, "it is not only the village matron, who, when 
 called to a consultation upon the case of a neighbor's child, 
 pronounces on the evil and its remedy simply on the rec- 
 ollection and authority of what she accounts the similar 
 case of her Lucy." 
 
 We have already observed (page 9) that a Concept may 
 be derived fi-om one object, as well as fi-om many similar 
 ones ; that is, it may not represent an actual, but only a 
 possible, class or plurality of things. The hasty and sweep- 
 
THE HAMILTONIAN ANALYSIS. 233 
 
 ing induetions of the vulgar are of this character ; they are 
 often generalizations from a single instance. The medicine 
 which they have once successfully tried is believed by them 
 to be a panacea. The unhesitating confidence with which 
 the village matron pronounces, not merely on one case of 
 measles or whooping-cough in her neighbor's family, but 
 on every one that occurs in the village, proves that she 
 has generalized her Lucy's case. 
 
 All general truths are not learned by induction from 
 particulars. They are sometimes first obtained by Intu- 
 ition, as in the case of axioms and other necessary truths, 
 or by reasoning from the causes or conditions on which 
 they depend; and then, individual truths are proved by 
 deduction from these generals. Most of the truths of pure ' 
 mathematics are thus acquired. To borrow an example 
 from Hobbes, — because we know how a circle is gener- 
 ated, namely, by the circumduction of a body one end of 
 which is fixed, we know that all radii of the same circle 
 are equal. Most of the beautifiil applications of algebraic 
 theorems to the solution of arithmetical and geometrical 
 problems were first ascertained to be possible long after the 
 general theorems themselves were discovered. Such meta- 
 physical principles as these. Every event must have a cause. 
 All attributes presuppose a substance, Space is infinite and 
 indestructible, were not first made known to us by induc- 
 tion, and cannot be proved by that method. Yet the ob- 
 jection to the Syllogistic process, that the Major Premise 
 could not be posited if the truth of the' Conclusion were 
 not already known, has neither force nor relevancy, if it 
 be not proved that all general truths are obtained by in- 
 duction, and that the induction was so perfect that it must 
 have consciously included the very case which we are now 
 seeking to deduce from the general rule. 
 
 Hamilton's next innovation in the theory of Logic — 
 and it is one which was propounded by him at an earher 
 
234 MEDIATE INFERENCE OB SYLLOGISM. 
 
 day than his doctrme of the quantification of the Predicate 
 — was to draw attention to the fact, that reasoning does 
 not proceed, as had formerly been taught, solely in the 
 Quantity of Extension, but also in the Quantity of Inten- 
 sion, the relations of whole and part, on which he considers 
 that the whole process depends, being reversed in these 
 opposite Quantities. It has already been mentioned, that, 
 in one sense, the Predicate of every Judgment includes the 
 Subject, and therefore, as the greater or more Extensive 
 Term, it was called the Msg'or, and the Subject was desig- 
 nated as the Minor Term. As thus construed, the Judg- 
 ment, Man is an animal, means that the class Man is in- 
 cluded under, or forms a part of, the class animal. But in 
 •another sense, — that is, in the Quantity of Intension, — 
 the Subject includes the Predicate, and the relations of 
 whole and part are reversed. Interpreted Intensively, this 
 Judgment signifies that all the attributes of animal are 
 contained in or among — form a part of — the attributes of 
 man. The Subject is now the Major Term, and the Pred- 
 icate is the Minor ; and the rule being still adhered to, that 
 the Major Premise must be stated first, the order of the 
 Premises is reversed. 
 
 Hamilton gives the following example of reasoning in 
 Extension. 
 
 All responsible agents are fi'ee agents ; 
 
 But man is a responsible agent ; 
 
 Therefore, man is a fi;ee agent. 
 The Premises are stated in this order on the supposition 
 that "firee agents," as the more Extensive class, is the 
 whole or the Major Term, that " man," having the least 
 Extension, is the smallest part or the Minor Term, and 
 that the Middle Term, " responsible agent," as interme- 
 diate between the two, is made the Subject of the former, 
 as contained under it, and the Predicate of the latter, which 
 is only a part of it. In other words, man is a part of that 
 
THE HAMILTONIAN ANALYSIS. 235 
 
 Term responsible agent, which is itself a part of the Term 
 free agent ; and therefore, as a part of a part is a part of 
 the whole, man is a free agent. 
 Now reverse the Premises. 
 
 Man is a responsible agent ; 
 
 But a responsible agent is a free agent ; 
 
 Therefore, man is a free agent. 
 Here, the notion /ree agent, which was the greatest whole, 
 becomes the smallest part ; and the notion man, which was 
 the smallest part, becomes the greatest whole. " The 
 notion responsible agent remains the Middle quantity or 
 notion in both, but its relation to the two notions is re- 
 versed ; what was formerly its part being now its whole, 
 and what was formerly its whole being now its part." 
 
 Hence, in the First Figure (but not, as we shall see, in 
 the two other Figures), the order in which the two Prem- 
 ises are placed always indicates the Quantity in which we 
 are reasoning. If the Major Premise contains the Subject 
 of the Conclusion, then this Subject is the Major Term, and 
 the reasoning is in Intension. But if the Predicate of the 
 Conclusion appears in the first Premise, then this Predicate 
 is the Major quantity, and the reasoning is in Extension. 
 
 But as this indication is a faint one, and may mislead in 
 the case of the Secoild or the Third Figure, it is easy to 
 change the phraseology of the Judgments, so as to enounce 
 explicitly whether the reasoning concerns the Intensive, 
 metaphysical, whole (the whole of the Marks connoted), or 
 the Extensive, logical, whole (the whole of the Individuals 
 and Species denoted). Thus, for the latter, we may say, — 
 
 All responsible agents are included in the class of free 
 
 agents ; 
 But man is a responsible agent ; 
 Therefore, man is included in the class of free agents. 
 
 And the reasoning of Intension mav be thus stated : — 
 
236 MEDIATE INFERENCE OB SYLLOGISM. 
 
 The notion or Concept, man, includes the notion of respon- 
 sibility ; 
 But the notion of responsibility includes that of free 
 
 agency ; 
 Therefore, the notion, man, includes the notion of free- 
 agency. 
 It is the more remarkable that nearly aU the logicians 
 since Aristotle should have contemplated exclusively rea- 
 soning in Extension, as Aristotle himself seems to have 
 regarded reasoning in Intension as coextensive with the 
 former, even if not paramount to it. Hamilton has only 
 restored the doctrine of the great founder of Logic, which 
 had been strangely overlooked by nearly the whde tribe 
 of his commentators and followers. As already remarked, 
 the beiitff in a Siibyect and the beinff predicated of a Svl- 
 ject are used by Aristotle as synonymous phrases. " A 
 is predicated of all B," means AU B is A ; '■'■A is m (or 
 inheres in, inrdpyeiv) aU B," also means AU B is A. 
 The meaning evidently is, that, in the Quantity of Inten- 
 sion, the Predicate is in the Subject because it constitutes 
 a part, and only a part,- of the Intension of the Subject. 
 Animal is in man, because man has aU the attributes or 
 Marks of animal, and other attributes also. 
 
 But the relation of whole and part is not precisely the 
 same thing in the one Quantity as in the other. In Exten- 
 sion, the whole is the Genus, and the parts are the subor- 
 dinate Species ; and the first Rule for the division is, that 
 the parts, or the co-ordinate Species, mnst exclude each 
 other. But in Intension, the parts are not Species, but 
 attributes or Marks ; and these do not exclude each other. 
 Each part or attribute here interpenetrates, so to speak, 
 and informs, the whole. Black is a part of negro in the 
 sense of being only one of his attributes, since he has many 
 others, such as being long-heeled, prognathous, &c. ; but it 
 is a part which colors the whole, for the negro is black aU 
 
THE HAMILTONIAN ANALYSIS. 237 
 
 over. But if we consider the Extension, if the Genus man 
 is subdivided into the co-ordinate Species white man and 
 hlack man, these parts exclude each other; no one man 
 can belong at the same time to both Species, — can be both 
 white and black. 
 
 Hence the maxim, that a part of a part is also a part of 
 the whole, is not a universal maxim of all reasoning ; as it 
 refers only to co-exclusive parts, it is applicable only to 
 reasoning in Extension. The corresponding maxim for 
 reasoning in Intension is, that a Mark of a Mark is also a 
 Mark of the thing itself, — of the whole thing ; Tiota notce 
 est nota rd ipsius. Free agency, which is a Mark of 
 responsibility, is also a Mark of man, because responsibility 
 is a Mark of the whole man. On the other hand, reason- 
 ing Extensively, we say, men are a part or class of respon- 
 sible agents, and are, therefore, also a part'of/re« agents, 
 because responsible agents are a part oi free agents. 
 
 By not attending to this distinction, Hamilton was be- 
 trayed on one occasion into propoimding as a valid syllo- 
 gism one, which, if the language be construed literally, is 
 illogical ; and into censuring as illogical another, which, as 
 stated, is certainly irrecusable. It is . true that the error 
 consisted entirely in the use of language. As he under- 
 stood them, his approbation of the one and his censure of 
 the other are correct; but from his use of language, no 
 other person would so understand them. In his Lectures 
 on Logic, while illustrating the Special Rule of an Inten- 
 sive Syllogism (page 223, Am. ed.), that the Sumption 
 must be Affirmative, and the Subsumption Universal, he 
 states the following as a valid Syllogism : — 
 
 ' S comprehends M ; 
 M does not comprehend P ; 
 Therefore S does not comprehend P." 
 
238 MEDIATE INFERENCE OR SYLLOGISM. 
 
 If tlie language be interpreted literally, the Conclusion 
 here is illogical ; for it is evident, from the diagram which 
 we have annexed, that, though S eomprehends M, and M 
 excludes P, it may yet be true that S comprehends P. 
 
 On the same page, he censures the following as a rum 
 sequitur, though the diagram here annexed demonstrates it 
 to be valid. 
 
 S does not compre- 
 hend M ; 
 
 But M comprehends P ; 
 
 Therefore S does not 
 comprehend P. 
 
 But instead of the proposition " S comprehends M," sub- 
 stitute the meaning which was intended, that S hag Mfor 
 one of its Marks or attributes, and make the corresponding 
 change throughout, and Hamilton's verdict upon the two 
 Syllogisms becomes correct. M, though only one of the 
 attributes of S, affects or colors the whole of S ; therefore, 
 P, which is not an attribute of M, — does not affect any 
 part of M, — is not an attribute of S ; — S does not in- 
 clude P among its attributes. The Syllogism which is ap- 
 proved corresponds, in Form, to the following, which is 
 evidently vaUd. 
 
 A negro has a black skin ; 
 
 But a black skin is not an invariable sign of a brute in- 
 tellect ; 
 Therefore, a negro is not necessarily brutish in intellect. 
 
 And the Syllogism which is rejected is the following : — 
 A negro is not white ; 
 But whites are civilized ; 
 Therefore, a negro is not civilized. 
 
 In fact, the mode of symbolizing Syllogisms by circles, as 
 
THE HAMILTONIAN ANALYSIS. 239 
 
 well as the maxim, a part of a fart is also a part of the 
 whole, is inapplicable to the Intensive Syllogism ; for here 
 the " parts " are Marks or attributes ; and these are not 
 co-exclusive. They are not partes ea^a partes. 
 
 It is with some reason, then, that Mr. DeMorgan objects 
 to considering the Intension of a Concept as a quantity. 
 In the vague sense of being susceptible of more and less, it 
 is a quantity ; but so far as it is incapable of exact measure- 
 ment, it is not a quantity. " As to extent," he says, " 200 
 instances bear ar definite ratio to 100, which we can use, 
 because our instances are homogeneous. But difierent quah- 
 ties or descriptions can never be numerically summed as 
 attributes to any purpose arising out of their number. 
 Does the idea of rational animal, two descriptive terms, 
 suggest any useful idea of duplication, when compared with 
 that of animal alone ? When we say that a chair and a 
 table are more iumiture than a chair, which is true, we 
 never can cumulate them to any pmrpose, except by ex- 
 tracting some homogeneous idea, as of bulk, price, weight, 
 &c. To give equal quantitative weight to attributes, as 
 attributes, seems to me absurd ; to use them numerically 
 otherwise, is at present impossible." Perhaps this is only 
 saying that a logician's idea of quantity is not the same as 
 a mathematician's ; to the latter, it is always numerically 
 definite, or may be made so ; to the former, it is never so. 
 Perhaps, if Mr. DeMorgan had kept this fact steadUy in 
 view, a good many of his attempted innovations in Logic 
 might have appeared, even to him, irrelevant. 
 
 Hamilton has made no specific innovation in the doctrine 
 of the Figures, but his speculations upon the subject have 
 thrown a flood of light not only upon the essential nature 
 of these varieties of the Syllogism, but upon the theories 
 of former logicians in respect to them. To Aristotle, on 
 account of his peculiar method of stating a Judgment, — 
 with reference to the Intension instead of the Extension of 
 
240 MEDIATE INFEEENGE OR SYLLOGISM. 
 
 its Terms, that is, placing the Predicate first and the Sub- 
 ject last, — the Middle Term was intermediate between 
 the two others, not only in nature, but in position. Thus, 
 the following are only two different expressions of the same 
 Syllogism. 
 
 Aristotle's form. Later or common firm. 
 
 P inheres in (is predicated of) all M ; All M are P ; 
 M inheres in all S ; All S are M ; 
 
 .•. P inheres in all S. " ,*. All S are P. 
 
 Here, in Aristotle's form, P, one of the Extremes, appears 
 first, and S, the othey Extreme, comes last ; M, the Middle 
 Term, in both of its expressions, being intermediate, or 
 coming between them. In the later form, it is not so. 
 As a consequence of this mode of statement, in his defini- 
 tion of the Second Figure, Aristotle says that the Middle 
 Term is, by its position, the jint ; to us, on the contrary, 
 it is the last. In fact, in his reduction of the Second and 
 Third Figures to the First, Aristotle seems to have had in 
 view, not only the establishment of the dictum de omni et 
 nuUo as the universal principle of aU Syllogistic reasoning, 
 but the restoration of the Middle Term to its proper in- 
 termediate position. He was evidently thinking most of 
 reasoning in Intension, and his followers of what is more 
 frequent in use, though not more natural, — reasoning in 
 Extension. In the later form, if the Minor Premise is 
 stated first, the Middle Term becomes intermediate in 
 position, as in the Aristotelic formula. 
 
 In this exposition of Aristotle's mode of enouncement, 
 as contrasted with that of the later logicians, Hamilton has 
 merely followed Barth61emy St. Hilaire ; in what follows, 
 he is more original. 
 
 " When logicians," he says, " came to enoimce propo- 
 sitions and Syllogisms in common language, the Subject 
 being usually first, they had one or otHer of two difficulties 
 
THK HAMILTONIAN ANALYSIS. 241' 
 
 to encounter, and submit they must to either ; for they 
 must either displace the Middle Term from its interme- 
 diate position in the First Figure, to say nothing of rerers- 
 ing its order in the Second and Third ; or, if they kept it 
 in an intermediate position in the First Figure (in the 
 Second and Third, the Aristotelic order could not be kept), 
 it behooved them to enounce the Minor Premise first." 
 Most of the older logicians adopted the latter alternative, 
 stating the Minor Premise first in all the Figures ; and 
 this seems the more natural order, if the Syllogism is used 
 for the purpose of investigation and discovery. At a later 
 period, when instruction, disputation, and proof came to 
 be the chief purposes for which Syllogisms were formally 
 enounced, the former alternative was adopted, and the 
 Middle Term lost its proper intermediate position, the 
 Major Premise being placed first in all the Figures. 
 
 In the First Figure, according to any mode of enounce- 
 ment, the Middle Term must be the Subject of one of the 
 Extremes (the two Terms of the Conclusion), and the- 
 Predicate of the other. Hence, in this Figure, there is a 
 determinate Major and Minor Premise for reasoning in 
 either Quantity, and but one direct or proximate Conclu- 
 sion. If, in the Major Premise, the Middle Term is Predi- 
 cate to the Subject of the Conclusion, then,, in each of the 
 three Judgmemts, the Subject includes the Predicate, and the 
 reasoning is in the Quantity of Intension. If, on the con- 
 trary, in the Major Premise, the Middle Term is Subject to 
 the Predicate of the Conclusion, then, in each of the three 
 Judgments, the Predicate includes the Subject, and the reason^ 
 ing is in t^e Quantity of Extension. The relative position 
 of the two Premises is really unimportant as respects the 
 nature of the reasoning ; this depends upon the nature of 
 the Middle Term, as including, or included under, the Sub- 
 ject of the Conclusion. But following the established 
 order of logical Quantity, that j3ie greater should be placed' 
 11 p 
 
242 MEDIATE INFEEENCE OB SYLLOGISM. 
 
 first, the Middle Term as Subject, and the Predicate of 
 the Conclusion as Predicate, should be the first or Major 
 Premise for rtesoning in Extension ; and the Middle Term 
 as Predicate, with the Subject of the Conclusion as Sub- 
 ject, should be the first or Major Preaajse in Intiension. 
 Thus: — 
 
 I In Extension. In Intension. 
 
 I M is P ; S is M ; 
 
 S is M ; M is P ; 
 
 ••. S is [included under] P. .•. S is [includes] P. 
 
 Here, the relation of the Terms to each other in the 
 'Premises determines their relation to each other in the Con- 
 clusion. If, in the Premises, M is included under P, and 
 S included under M, then, in the Conclusion, S must be 
 included under P. But if, in the Premises, S includes M, 
 Mid M includes P, then, in the Conclusion, S must include 
 P. Hence, in the First Figure* there can be but one 
 direct Conclusion. 
 
 In the two other Figures, it is, not so. The Middle 
 Term is not Subject of one and Predicate of the other Ex- 
 treme, but is either, as in the Second Figure, Predicate of 
 both^ or, as in the Third, Subject of both. Consequently, 
 in each of these Figures, the Middle Term either includes 
 both the Extremes, or is included under both. As there 
 is nothing, then, to determine the rektive Quantity of the 
 twa Extremes to each other,, either may be considered as 
 Major in the Conclusion; — we may conclude either that 
 S is P, or that F is S. 
 
 Though the First Figure has but one direct or immediate 
 Conclusion, we may, by the medium of Conversion, obtain 
 &om it another Conclusion, which is then properly called 
 indirect or mediate. Thus, in the formulas just given,, hav- 
 ing concluded directly that All S is P,. we may then con- 
 dudie indirectly, or mediateily, that. Saim F is S, But in 
 
THE HAMILTONIAN ANALYSIS. 243 
 
 the other Figures, there are two indifferent Conclusions, 
 neither of which is more direct or immediate than the 
 others^ Jf A is B and G is B, we may conclude, with 
 equal propriety and directness, either that A is C, or 
 is A ; for there is nothing in the Premises to indicate 
 whether A includes, or is included under, C. And in like 
 manner in the Third Figure ; if B is A and B is 0, the 
 two Conclusions, A is and C is A, are equally compe- 
 tent and equally immediate. Of course, what has been 
 called the Fourth Figure is merely the First, with its indi- 
 rect Conclusion enounced as if it were direct or imme- 
 diate ; it is a hybrid reasoning, wiA its two Premises in 
 one Quantity, and its Conclusion in the other. Hence 
 the Fourth Figure is properly abolished. 
 
 In fact, all difference of Figure is unessential, — a mere 
 accident of form. As it is demonstrated in the Hamil- 
 tonian analysis, that a Judgment is a mere equation of its 
 two Terms,, it makes no difference which is stated first, — 
 which is Subject or which is Predicate"; A=:B and B= A 
 are the same equation. Quantify the Predicate through- 
 out, and this becomes evident. ^As all Conversion is then 
 reduced to Simple Conversion, we have only to convert 
 simply (retaining the subordination of the Terms) the 
 Major Premise of the First Figure in Extension, in order 
 to produce the Second Figure ; convert its Minor Premise, 
 and we have the Third. In Intension, this is merely re- 
 versed ; convert the Minor for the Second, and the Major 
 for the Third. 
 
 To make the Syllogistic process depend upon the mere 
 position, either of the two Terms as Subject or Predicate, 
 or of the two Premises as enounced first or second, or of 
 the Conclusion as expressed first or last, is to reduce Rea- 
 soning to a mere accident of expression, and cause it to 
 vary with the genius of different languages, or even with 
 the mental peculiarities of individuals. Reasoning is a 
 
244 MEDUTE INFERENCE OB SYLLOGISM. 
 
 process of Thought, not of language. It depends solely 
 upon the relations of inclusion and exclusion, of suhor- 
 dination and superordination, of Intension and Exten- 
 sion, existing between two Concepts and a Third ; and it 
 must be regulated by universal laws, irrespective of differ- 
 ences of language and peculiarities of mental habit. The 
 order of enouncement is a convenient, though conven- 
 tional, mode of indicating these relations to other persons, 
 and even a safeguard against confusion and error in the 
 successive elaboration of them in our own minds. But the 
 actual inference, the mental process as such, is entirely 
 independent of this order. 
 
 To show further the unessential character of variation by 
 Figure, Hamilton pointed out the manner of abohshing the 
 distinction of Subject and Predicate, and thereby reducing 
 all Mediate Inference to what he calls the Unfigured Syl- 
 logism. Any Syllogisms whatever may find adequate, 
 though awkward, expression under this form. The two fol- 
 lowing instances wOl suffice. 
 
 Fig. I. Darii, reduced to an Unfigured Syllogism. 
 All patriots are brave ; All patriots and some brave men 
 
 are equal ; 
 Some persecuted men are Some persecuted and some pa- 
 patriots ! triots are equal ; 
 ••. Some persecuted men are .•. Some persecuted and some brave 
 brave. men are equal. 
 
 Fig. n. Camestres. 
 
 All animals are sentient ; All animals and some sentient 
 
 things are equal ; 
 Nothing unorganized is Any unorganized and any sen- 
 sentient ; tient are not equal ; 
 .'.Nothing unorganized is .'.Any unorganized and any an- 
 animal. imal are not equal. 
 
 In this Unfigured Syllogism, as Hamilton remarks, " the 
 
THE HAMILTONIAN ANALYSIS. 245 
 
 dependency of Extension and Intension does not subsist, 
 and accordingly the order of the Premises is wholly arbi- 
 trary. This form has been overlooked by the logicians, 
 though equally worthy of development as any other ; in 
 fact, it affords a key to the whole mystery of Syllogism. 
 And what is curious, the Canon by which this Syllogism is 
 regulated (what may be called that of logical Analogy or 
 Proportion) has, for above five centuries, been commonly 
 stated as the one principle of reasoning, whilst the form of 
 reasoning itself, to which it properly appUes, has never been 
 generalized. This Canon, which has been often errone- 
 ously, and never adequately enounced, in rules four, three, 
 two, or one, is as follows : — In as far as two notions 
 (notions proper or individuals) either both agree, or one 
 agreeing the other does not, with a common third notion ; in 
 so far these notions do or do not agree with each other. This 
 Canon thus excludes, — 1. an undistributed Middle Term, 
 as then no common notion ; — 2. two negative Premises, 
 as then no agreement of either of the other notions there- 
 with." 
 
 A convenient, though somewhat mechanical^ rule for 
 drawing the correct Conclusion from any pair of Premises 
 is the following, which was first stated by Ploucquet, and 
 after him by Mr. De Morgan. JErase the symbols of the 
 Middle Term, the remaining symbols show the inference. 
 Ddeatur inprcemissis medius; id qiiod restat indicat conclu- 
 sionem. Thus, ia the two Syllogisms just given and re- 
 duced to the Unfigured form, strike out from the Prem- 
 ises, what I have italicized, all that relates to the Middle 
 Term, and what remains of the Premises is the Conclu- 
 sion. But it should be mentioned that this Rule, though 
 valid for all the Aristotelic moods, does not hold good, as 
 we shall see, for all the moods recognized under the Ham- 
 iltonian system. 
 
 Perhaps the most striking, and certainly the most con- 
 
246 MEDIATE INFEKENCE OK SYLLOfflSM. 
 
 Tenient, improvement wliicli Sir William Hamilton has 
 made upon the labors of former logicians, is his system of 
 •notation, — a, masterpiece of ingenuity in symhoKzation as 
 respects perspicuity, completeness, and simplicity. It is 
 valid for any system, and it manifests, at once, nearly all 
 the alterations and improvements which be has made in 
 the Aristotelic doctrine. It shows at a glance the equiv- 
 alent Syllogisms in the diflFerent Figures, the convertible 
 Syllogisms in the same Figure, and points out the two 
 meanings which can be given to every Syllogism as inter- 
 preted according to its Extension or its Intension, in refer- 
 ence to the logical or the metaphysical whole. Even as a 
 mnemonic contrivance, it is second in ingenuity and usefiil'- 
 ness only to the famous quatr^ of hexameters, which 
 contains the whole doctrine of the Reduction of the Moods 
 of the lower Figures to the first Figure. 
 
 The purpose of any system of notation is to manifest, by 
 the differences and relations of geometrical quantities (lines 
 or figures), the differences and relations of logical forms. 
 
 A Proposition or Judgment is here indicated by a straight 
 horizontal line, its two Terms or Extremes being placed at 
 the extremities of thait line, and represented, as usual, by 
 letters. 
 
 If, as in the Unfigured Syllogism, there is no distinction 
 of Subject and Predicate, this line is made of equal thick- 
 ness throughout. But if this distinction is introduced, 
 then, as it is possible to read the Judgment in two ways, 
 according to the Extension or the Intension of its Terms, 
 (the Subject, in the latter case, including the Predicate, 
 and in the former, bemg mcluded under it,) the line is 
 made wedge-shaped. Its broad end then r&presents this 
 Subject of Extension or Breadth, and the thin end, that of 
 Intension or Depth. A line gradually diminishing or in- 
 creasing from end to end aptly indicates the relation be- 
 tween two Quantities which are always co-existent, and in 
 
THE HAMILTONIAN ANALYSIS. 247 
 
 inverse ratio to each other. As the employment of letters 
 following upon each other in the same alphabet jjoight sug- 
 gest that one was invariably subordinated to th§ other, 
 instead of being its subordinate in one Quantity and its 
 superordinaite in the other, Hamilton uses for the Extremes 
 the Latin C and Greek F, each being the third letter in 
 its own alphabet ; as usual, M stands for the Middle Term. 
 Thus : — 
 
 is read, C and T are equal. 
 
 c— — r 
 
 may be read in two ways; Extensively, C is included 
 under T ; Intensively, T is included in O: — or, in the 
 usual manner, G isT, and V is 0, merely remembering, 
 without saying so, that Extension is signified in the former 
 case, and Intension in the latter. 
 
 Negation is indicated by a perpendicular stroke drawn 
 through the line, thus : ^H — . The line without this strqke 
 may be regarded as the AiErmative Copula; with the 
 stroke, as the Negative Copula. A colon (:) annexed to a 
 Term shows that it is distributed, or taken universally ; a 
 comma (,) so annexed, that it is tindistributed or Particu- 
 lar. When a Middle Term has a colon on the right, and a 
 comma on the left, it is understood that it is distributed 
 when coupled in a Judgment with the Term on the right, 
 and undistributed when coupled with the other. 
 
 A line drawn beneath or above three Terms indicates 
 the Conclusion (or the Copula of the Conclusion) deduced 
 from the two Premises which those Terms constitute. In 
 the Second and Third Figures, since there may be two 
 equally direct or immediate Conclusions, "they are repre- 
 sented by two such hnes, the one above, and the other 
 below the Premises. Thus : — 
 
 ^ This is a Syllogism in the Second 
 
 C, ■ , M : — '^j r Figure, which may be read La 
 
 — "■■■ either oiF the following ways. 
 
248 MEDIATE INFERENCE OB SYLLOGISM. 
 
 Extensivdy. Intensivdy. 
 
 Some C is some M ; All M is some T ; 
 
 Soflfe r is all M ; Some M is some C ; 
 
 .: Some T is some C; or .: Some C is some T ; or 
 
 .-. Some C is some T. .: Some F is some C. 
 
 Q , ]yj . I , . p This is a Negative Syllogian in 
 
 , , the First Figure, which may be 
 
 read in either of the following 
 ways ; but in either way, it has only one direct or imme- 
 diate Conclusion, though a Second Conclusion may be ob- 
 tained &om it'^ndirecth/, by converting simply the proper 
 or direct Conclusion. 
 
 Extensivdy. 
 
 Some M is some C ; No M is any T j 
 
 No r is any M ; Some C is some M ; 
 
 No r is some C ; or, Some C is not any T ; or, 
 
 indirectly, indirectly, 
 
 Some C is not any T. Not any T is some C. 
 
 The following diagram presents the whole Hamiltonian 
 doctrine of Figure, together with the distinction between 
 the Analytic and the Synthetic order of enonncement. 
 After the explanations which have been given, it will be 
 easily understood. 
 
 As a Judgment has been designated by a line, a Syllo- 
 gism, which is a union of three Judgments, is appropriately 
 typified by a triangle, a union of three lines, of which the 
 base represents the Conclusion, and the other two lines, 
 the Premises. As the direction of the arrows indicates, 
 we may proceed either in the usual or Synthetic order, 
 from the Premises to the Conclusion, or in the reverse 
 order, which is Analytic, from the Conclusion to the Prem- 
 ises. As there is no valid reason for always placing the 
 Major Premise first in order, the diagram shows that either 
 Premise may have precedence in this respect, so that what 
 has been called the Fourth Figure is here identified with 
 the Indirect Moods of the First. 
 
THE HAMILTONIAN ANALYSIS. 
 
 249 
 
 ^ ^ 
 
 The Unfigured Syllogism is properly represented as in- 
 cluding all the others, as any Syllogism of either Figure 
 may be easily expressed in this form. In like manner, the 
 triangle representing the First Figure is made to include 
 the two typifying respectively the Second and Third, as 
 either of the latter may be readily reduced to the former. 
 And again, the essential unity of the Syllogistic process, 
 and the unessential nature of variation by Figure, are ap- 
 propriately signified by a single triangle comprehending all 
 the varieties of form. 
 
 " The double Conclusions, both equally direct, in the 
 Second and Third Figures, are shown in the crossing of 
 two counter and corresponding hues. The Direct and 
 Indirect Conclusions in the First Figure are distinctly 
 typified by a common and by a broken line ; the broken 
 line is placed immediately under the other, and may thus 
 indicate that it represents only a reflex of — a consequence 
 ii» 
 
250 MEDIATE INFERENCE OK SYLLOGISM. 
 
 through — the other (/car dvuKKaa-tv, reflexim, per re- 
 fiexionem"). The diagram therefore can show, that the 
 Indirect Moods of the First Figure, as well as aU the Moods 
 of the Fourth, ought to he iTeduced to merely mediMe in- 
 ferences ; — that is, to Conclusions from Conclusions of the 
 conjugations or Premises of the First Figure." 
 
 If we have the two Premises, All C is some M, and All 
 Mis some F, and consider that some ilff is a Mark rf (or, 
 is included in) all 0, and gome F a Mark of all M, then 
 we are reasoning in the Quantity of Intension ; and, accord- 
 ing to the Axiom that a Mark of a Mark is also a Mark of 
 the ffiinff itsdf, the proper and direct Conclusion is, AU G is 
 some F. But if we conclude that Some F is all (7, accord- 
 ing to the Fourth Figure or the Indirect Moods of the 
 First, Some F does not appear as a Mark of aU C, but as 
 included under it, — -as a Subject of Extension ; the Prem- 
 ises, then, would be represented in one Quantity, and the 
 Conclusion in the other. " But though always coexistent, 
 and consequently alwaySj to some amount, potentially in- 
 ferring each Other, still we cannot, without the interven- 
 tion of an actual inference, at once jump from the one 
 Quantity to the other, — change, per saUum, Predicate 
 into Subject and Subject into Predicate. We must pro- 
 ceed gradatim. We cannot arbitrarily conunute the 
 Quantities, in passing from the Quassitum to the Prem- 
 ises, or in our transition from the Premises to the Con- 
 clusion. When this is appiu^htly dbne, the procedure is 
 not only unnatural, but virtually complex and mediate, 
 the mediacy being oonoeaUd hy the concedlmeM of the mental 
 inference whieh really precedet " ; — indicated by the broken 
 line in the diagtkm. 
 
 One other species of Hamiltonian notation should be 
 noticed, as it brings to light very clearly the virtual equiva- 
 lence of those Moods in the several Figures which are in- 
 dicated, in the old mnemonic hexameters, by names begin- 
 
THE HAMILTONIAU ANALYSIS. 251 
 
 ning with the same capital letter. Four stra;ight lines are 
 all that is needed for such a notation. Three of these are 
 horizontal, to represent the Terms ; and one perpendicular, 
 or the want of it, at the beginning of the comparison, to 
 express the Quality of Affirmation or Negation. " Quan- 
 tity is marked by the relative length of a terminal line 
 within, or its indefinite excursion before, the limit of com- 
 parison. This notation can represent equally totobl and 
 MftratoteZ distribution, in simple SyUo^smi and in Sorites; 
 and it shows at a glance the competence or incompetence 
 of any Conclusion." 
 
 c- 
 
 "Of these, the former, with its converse, includes Dariij 
 Dabitis, Datisi, Disamis, Ditnaris, &c. ; whilst the latter^ 
 with its converse, includes Celarent, Cesare, Celanes, Ca- 
 mestres, Cameles, &c. But of these, those which are rep- 
 resented by the same diagram are, though in different 
 Figures, formally the same Mood." "In aU the other 
 geometrical schemes hitherto proposed, whether by lines, 
 angles, triangles, squares^ or circles, the same complex 
 diagram is necessarily employed to represent an indefinite 
 plurality of Moodsi" 
 
 The apphcation of Hamilton's doctrine of the thorough- 
 going quantificatioil of the Predicate to the explication of 
 the. Syllogistic theory produces, as might have been ex- 
 pected, a great enlargement of the number of Moods. If 
 there are hut four fundamental Judgments, the number of 
 conceivable Moods that can be framed from them, by taking 
 them three and three, is siccty-four * ; excluding from these 
 
 » The computation is easily made. The four letters A, H, I, O, give 
 us four different Major Premises ; ea/!h of these may have four different 
 Minor Premises ; ^- hence there will be sixteen pairs of Premises. But 
 each of these pairs may be conceived to have four differeiit ConclnsioDS j 
 whence, 16 X * = 6* conceivable Moods. 
 
252 MEDIATE INFEEENCE OB SYLLOGISM. 
 
 the invalid Moods, as ofifending against one or more of 
 the general Rules of the Syllogistic process, there remain 
 only fourteen as valid in some one of the first three Fig- 
 ures ; — nineieen, if we admit the Fourth Figure ; — twmty- 
 fowr, if we include also the anonymous indirect Moods. 
 But under the Hamiltonian doctrine of dght fundamental 
 Judgments, we have five hundred and twelve * conceivable 
 Moods. Excluding &om these aU that offend against the 
 General Canon, (as by having an undistributed Middle, 
 two Negative Premises, or coUecting more in the Conclu- 
 sion than was distributed in the Premises,) there remain 
 thirty-six valid Moods, of which twelve are AfSrmative and 
 twenty-four Negative. On this doctrine, each Affirmative 
 Mood yields two Negative ones, as each of its Premises 
 may be successively negatived. Figure now appears in its 
 true character, as an unessential variation ; but as each of 
 these valid Moods can, if we please, be thrown into either 
 of the three Figures, there are 36 X 3 = 108 valid Moods, 
 reckoning as such all the modifications of statement of 
 which they are susceptible. But to show how trifling are 
 the changes thus effected by carrying what is really one 
 Mood through each of the three Figures, I borrow a con- 
 crete example from Mr. Baynes. 
 
 Fig. I. Fig. II. 
 
 All man is some animal ; Some animal is all man ; 
 
 Every Celt is some man ; Every Celt is some man ; 
 
 .'. Every Celt is some animal. .*. Eveiy Celt is some animaL 
 
 Fig. m. 
 
 All man is some animal ; 
 
 Some man is every Celt ; 
 
 .•. Every Celt is some animal. 
 
 * Computing as before, from eight Judgments we have eight different 
 Miyor Premises, each of which may have eight diiierent Minor Fiemises, 
 whence 8 X ^ ^ ^^ pairs of Fiemises ; and as each of these may have 
 eight different Conclusions, there are 64 X § = 312 triplets of Judgments, 
 or conceivable Syllogisms. 
 
THE HAMILTONIAN ANALYSIS. 253 
 
 Hamilton's General Canon has already been enounced 
 in the mode of statement in ■which it is directly applicable 
 to the Unfigured Syllogism. As applied to the Figured 
 Syllogism, wherein we have to consider the two counter 
 Quantities of Extension and Intension, it should be thus 
 expressed : — " What worse relation of Subject and Predi- 
 cate subsists between either of two Terms and a common 
 Third Term, with which one at least is positively [affirma- 
 tively] related, that relation subsists between the two 
 Terms themselves." As already stated, this Canon is 
 only a succinct statement of the six general Rules which 
 have been laid down as ftJfiUed in every valid case of 
 Mediate Inference ; and it is, also, only a restatement of 
 the two Primary Axioms of Pure Thought, the laws of 
 Identity and Non-Contradiction, with the necessary con- 
 ditions and hmitations which determine their application. 
 As these Rules and Axioms were found to hold good under 
 the Aristotelic doctrine of four fundamental Judgments, 
 they are also valid under the system which increases the 
 number of these Judgments to eight. No Syllogism can 
 be invalid which accords throughout with this Canon, and 
 every illegitimate process, either directly or indirectly, 
 openly or covertly, violates it. 
 
 But we must accurately determine which is the " worse 
 relation " of Subject and Predicate that can subsist be- 
 tween either of two Terms and a common Third Term. 
 When there are but four Judgments, the corresponding 
 principle, that the Conclusion follows the " weaker part," 
 admits of easy interpretation; Particular Quantity is 
 weaker than Universal, Negative Quality is weaker than 
 Affirmation. But with eight Judgments, the various de- 
 grees of better or worse, stronger or weaker, must be 
 more precisely ascertained. Always considering Negation 
 as weaker than Affirmation, we now say that the lest 
 (strongest) Quantity of Affirmation is the worst (weakest) 
 
254 MEDIATE INFEKENOE OE SYLLOGISM. 
 
 Quantity of Negation. In other words, we affirm best when 
 we affirm all, and affirm worst when we affirm only some ; on 
 the contrary, we deny best when we deny only some, and 
 deny worst when we deny all. On account of this inverse 
 relation of the two Quantities) an Affibrmative Mood with a 
 Particular Conclusion may be changed, by merely nega- 
 tiving one of its Premises, into a Negative Mood with a 
 Universal Conclusion. But though the Qiiantity is thus 
 altered from Particular to Universal, this is not a change 
 from worse to better, but from worst to worst ; for though 
 a Particular stands lowest in the scale of Affirmation, a 
 Universal stands lowest in the scale of Negation. The 
 seeming exception only confirms the rule, and proves that 
 the Canon is universally applicable. Take the following 
 instance : — 
 
 C : — , M : -^— : T Some M is all C ; 
 
 ■ , All r is all M ; 
 
 .•. Some r is all C. 
 Some blacks are all slaves ; 
 AU of African descent are all blacks ; 
 .•. Some of African descent are all slaves. 
 
 Now, if we negative this Syllo^sm by negativing die 
 Minor Premise, the Conclusion changes from Particukx to 
 Universal, thus : — 
 
 C . , TIT . I , . p Some M is all ; 
 
 " ' No r is any M ; 
 
 No r is any C. 
 
 Some blacks are all slaves ; 
 No Caucasian is any black ; 
 .*. No Caucasian is any slave. ' 
 
 This change, though from Particular to Universal, is 
 really from the worst of Affirmation to the worst of Nega- 
 tion, But such changes are infrequent, as, in the inter- 
 
THE HAMILTONIAN ANALYSIS. 255 
 
 mediate relations, the commutation is only from equal to 
 equal, and the predesignations of Quantity, in their in- 
 verse signification, remain externally the same. Oiit of 
 the twentyTfbur valid Negative Moods, only four cases are 
 found of a Particular quantification disappearing in the 
 Negative Conclusion. Hamilton gives the following ar- 
 rangement of the eight Judgments in tike order proceeding 
 from hest to worst, 
 
 Best. ^ 1. Afa. All are all. 
 
 All are some. 
 
 Some are all. 
 
 Some are some. 
 
 Some are not some. 
 
 Some are not any. 
 
 Not any is some. 
 Worst. ^ 8. Ana. Not any is any. 
 
 With these explanations, the following list of the twelve 
 valid Affirmative Moods in each of th^ three Figures, and 
 the 24 valid Negative Moods in the First Figure, all ex- 
 pressed in the Hamiltonian notation, will be found intel- 
 ligible. 
 
 In this Table, the Quantity of the Conclusion is marked 
 only in the cases already considered, wherein the Terms 
 obtain a different Quantity from that which they held in 
 the Premises; accordingly, when not marked, the quanti- 
 fication of the Premises is held as repeated in the Conclu- 
 sion. The symbol , placed beneath a Conclusion, 
 
 indicates that, when the Premises are converted, the Syllo- 
 gism remains in the same Mood ; ^><^ shows that the two 
 Moods between which it stands are convertible into each 
 other by converting their Premises. The Middle Term is 
 said to be halanced, when it is Universal in both Premises. 
 The Extremes, or Terms of the Conclusion, are balanced, 
 when both alike are distributed ; unbahmced, when one is, 
 and the other is not, distributed. Accordingly, of the 
 
256 
 
 MEDIATE INFERENCE OR SYLLOGISM. 
 
 SCHEME OF NOTATION- 
 TABLE OF SYLLO- 
 
 A. APFIRMATIVB MOODS. 
 
 Fio- 1. Fio. n. 
 
 i. C:- 
 
 :M: 
 
 ii. C,- 
 
 ;M: 
 
 m. c,- 
 
 :M, 
 
 iv. C:- 
 
 X 
 
 .,M: - 
 
 y. C- 
 
 vi. C- 
 vii. C :- 
 
 :M, 
 
 X 
 
 ■ ,M:- 
 
 :M: 
 
 L 
 
 viii. C- 
 ix. C:- 
 
 X 
 
 I :M: - 
 
 :M, 
 
 X. C:- 
 xi. C:- 
 
 xii. C ,- 
 
 X 
 
 .,M:- 
 
 :M, 
 
 -,r 
 -,r 
 
 -,r 
 ■,r 
 
 ■:r 
 
 ■:r 
 
 a 
 
 m:T 
 
 X 
 
 .,M: - 
 
 .:r C:. 
 
 :M: 
 
 ■:r 
 
 ■,r c- 
 
 :M: 
 
 ■,r 
 
 c,. 
 
 :M, 
 
 ■:r 
 
 X 
 
 ,M: 
 
 c,- 
 
 c,! 
 
 c ' 
 
 :M, 
 
 X 
 
 ,M: 
 
 :M: 
 
 X 
 
 c,. 
 
 C:. 
 
 :M: 
 
 :M, 
 
 C: 
 
 J 
 
 C: 
 
 I"" 
 
 c' 
 
 X 
 
 ,M: 
 
 ;M, 
 
 X 
 
 ,M: 
 
 -.r 
 
 ■,r 
 «,r 
 
 ■:r 
 ■:r 
 
 .:r 
 -.r 
 
 .:r 
 
 Hon — A. 1. and ii. are Ba/oneed. B. The otha mooAs an Unbalanced. Ortbeae, 
 
THE HAMILTONUN ANALYSIS. 
 
 257 
 
 FIGURED SYLLOGISM. 
 QISTIO MOODS. 
 
 A. APrlRMATIVB MOODS. 
 Fig. III. 
 
 C:- 
 
 ;M; 
 
 -:r 
 
 I :M: 
 
 C.- 
 
 :M, 
 
 -.r 
 
 X 
 
 ,M: 
 
 -r 
 
 X 
 
 c,- 
 
 C:- 
 
 c" 
 
 c'- 
 
 C:- 
 C:- 
 
 J" 
 
 c,- 
 
 i,M: 
 
 :M; 
 
 X 
 
 :M; 
 
 I :M, 
 
 -:T 
 
 X 
 
 ,,M: 
 
 I :M, 
 
 
 X 
 
 ,,M: 
 
 B. NEGATIVE MOODS. 
 ElG. I. 
 
 :M; 
 
 I aC: I —1 .M^ 
 |bC: — ,Mi 
 
 i:r 
 
 :r 
 ,r 
 ,r 
 
 i:r 
 i:r 
 
 i,r 
 i,r 
 ■,r 
 i.r 
 r 
 
 i,r 
 
 1. r 
 
 r 
 
 r 
 
 r 
 
 i:r 
 
 r 
 
 r 
 
 ■:r 
 
 r 
 
 r 
 
 i:r 
 
 r 
 
 Ul. and iT. are unbalanced in terms only, not in propositions -, the rest in both. 
 
258 MEDIATE INFERENCE OB SYLLOGISM. 
 
 Moods in the Table, numbers L and TI. are balanced as 
 respects both Terms and Propositions; in III. and IV., 
 only the Terms are unbalanced; in the remainder, both 
 Terms and Propositions are unbalanced. 
 
 " If we apply the Moods to any Matter, however ab- 
 stract, say letters, there will emerge forty-two Syllogisms ; 
 for the formal identity of the balanced Moods will then be 
 distinguished by a material diflFerence." Thus, numbers I. 
 and II., with the four Negative Moods formed from them 
 by successively negativing each of their Premises, will, 
 when thus treated, yield sis additional Syllogisms, making 
 forty-two in all. Take for instance, number I., AiErma- 
 tive ; when each of its Judgments is converted, it is still 
 in the same Mood. 
 
 Canverliag.each Judgment 
 I. All rational are all risible ; All risible are all rational ; 
 
 All men are all rational ; All rational are all men ; 
 
 .*. All men are all risible. .■. All risible are all men. 
 
 " On the contrary, if We regard the mere formal equiv- 
 alence of the Moods, these will be reduced to twenty-one 
 reasonings, — seven Affirmative and fourteen Negative." 
 For, of the unbalanced Moods, every odd number is con- 
 verted into the even number immediately following; and 
 thus, if each Mood is regarded as formally equivalent to its 
 converse, (and numbers I. and II. are so regarded in llie 
 Table,) numbers TV., VI., VIII, X., and XII. must be 
 struck out of the enumeration, and only seven valid Af- 
 fii-mative Moods remain. In like manner, in Negatives, 
 the first and second Moods (a, F) of the pair correspMid- 
 ing to the even number which was strudt out, are reduced 
 from or to th« second and first Moods (6, a) of the odd 
 number Which was retained. Five pairs being thus elim- 
 inated, CHily seven pairs — fourteen valid Negative moods 
 — remain. 
 
 Under the Aristotelic doctrine, as we have seen, 1(^- 
 
THE HAMILTOMAN ANALYSIS. '259 
 
 eians found that the six general Rules, which they had 
 enounced as governing all Mediate Inference, did not suf- 
 fice to determine which of the Moods were valid, and 
 which invalid, ik each of the four Figures. The variations 
 of Figure depend upon the relative position of the Middle 
 Term, as Suhject or Predicate to each of the two Terms 
 of the Conclusion ; and special Rules were necessary to 
 prevent these variations from conflicting with the two 
 principles which, according to the Aristotelians, determine 
 the implicit quantification of the Predicate. These prin- 
 ciples are, — 1. That in all Affirmative Judgments the 
 Predicate is Particular ; and, 2. That in all Negative Judg- 
 ments the Predicate is Universal. Now, in the Second 
 ^Figure, the Middle Term being Predicate in both PreiH" 
 ises, the logicians were compelled, in order to prevent the 
 infringement of the General Rule, that the Middle Term 
 must he distributed in at least one of the Premises, to enact 
 the Special Rule, that, in this Figure, one of the Premises, 
 and Gonsequently the Conclusion also, must be Negative. 
 But under the Hamiltonian system of the thorough-going 
 quantification of the Predicate, since the Middle Term can 
 be distributed when it j^ the Predicate of an Affirmative, 
 just as well as when it is the Predicate of a Negative 
 Judgment, this Special Rule is "both useless and false. 
 And so with all the other Special Rules for each of the 
 Figures. They are needless, because they were formed 
 only on the supposition that the Predicate coidd be but 
 partially quantified ; they are false, because the thorough- 
 going quantification of the Predicate brings to light many 
 valid forms of Syllogism which violate each of these rules. 
 
 The following demonstration of the falsity of these Spe- 
 cial Rules is borrowed in part from Mr. jBay&es's " New 
 Analytic of Logical Form's." 
 
 The Rules of the First Figure are, — 1. That the Sump- 
 tion must be Univlersal; 2. That ifche Subsumption must 
 
260 MEDIATE INFERENCE OR SYLLOGISM. 
 
 be Affirmative. Quantify the Predicate, and neither of 
 these holds good. 
 
 First Bute falsified. 
 
 Some men are some fleet-footed ; 
 
 All rational is all man ; 
 .•.Some rational is some fleet-footed. 
 Second Rale falsified. 
 
 All idealists are some philosophers ; 
 
 No sensuaUst is any idealist ; 
 -•. No sensualist is some philosopher. 
 
 The Rules of the Second Figure are, — 1. That one of 
 the Premises must be Negative ; 2. That the Sumption 
 must be Universal. Both are abrogated by a quantified 
 Predicate, thus : — 
 
 First Rule falsified. 
 
 All risible is all man ; 
 AH philosophers are some men ; 
 .•. AU philosophers are some risible. 
 
 Seamd Rule falsified. 
 
 Some mortal is all man ; 
 All rational is aU man ; 
 .". All rational is some rnGftal. 
 
 The Rules of the Third Figure are, — 1. That the Sub- 
 sumption must be Affirmative ; 2. That the Conclusion 
 must be Particular. 
 
 First Rule falsified. 
 
 All free agents are all responsible ; 
 No free agent is any brute ; 
 .•. No brute is any responsible. 
 
 Second Rule falsified. 
 
 All triangles are halves of parallelograms ; 
 All triangles are all trilaterals ; 
 .•. AU trilaterals ai-e halves of parallelograms. 
 
 All the Special Rules being thus abrogated, the unity 
 
THE HAMILTONIAN ANALYSIS. 261. 
 
 and simplicity of the Syllogistic process become manifest. 
 Hamilton's Supreme Canon, which is a mere compend of 
 the six General Rules, appears as the universal and all- 
 sufficient law of Mediate Inference, and the science of 
 Logic is freed from the encumbrance of a mass of needless 
 distinctions and superfluous details. As Figure is demon- 
 strated to be an unessential variation, all the Rules for 
 Reduction are swept away. In fact, the process of Reduc- 
 tion is so far simplified by allowing all Judgments to be 
 converted simply, that, if we still need to have recourse to 
 it in order that the reasoning may appear in its most ob- 
 vious and natural form, the requisite changes suggest them- 
 selves, and the work may be performed without the aid of 
 rules. 
 
 Some observations are necessary, however, in respect to 
 the apphcability of the different Figures to those two di- 
 rections of the reasoning process which are called Deduc- 
 tive and Inductive. This subject has been so well ex- 
 plained by Mr. Baynes, that I borrow his language. We 
 have seen that the characteristic of reasoning in Intension 
 — or Gompreheniion, as it is more frequently called — is, 
 that the Predicate is contained in the Subject ; of reason- 
 ing in Extension, that thfe Subject is contained under the 
 Predicate. " This being remembered," says Mr. Baynes, 
 " it will appear that in the Second Figure, where the Mid- 
 dle Term as Predicate contains both the Subjects under it, 
 JExtension will predominate. In the Third, where the Mid- 
 dle Term as Subject is contained under, and therefore com- 
 prehends in it both the Predicates, Comprehension will pre- 
 vail. In the First Figure, again, where the Middle Term 
 is both Subject and Predicate, Extension and Comprehen- 
 sion balance each other. The First Figure is indifferently 
 competent to either. 
 
 "Reasoning, however, proceeds not only in different 
 wholes, but in different aspects of the same whole. We, 
 
262 MEDIATE raFEEENCE OB SYLLOGISM.' 
 
 may, it is evident, regard any whole, considered as the 
 complement of its parts, in either of two ways ; for we 
 may, on the one hand, look from the whole to the parts, 
 and reason accordingly downwards; or, on the other 
 hand, look from the parts tO- the whole they constitute, 
 and reason accordingly upwards. The former of these 
 reasonings is called Deductive, the latter Inductive. De~ 
 ductive reasoning is fomided on. tiie maxim, ' What be- 
 longs to the containing whole belbnga also to the con- 
 tained parts ' ; Induction, on the contrary maxim, ' What 
 belongs to the constituent parts belongs also to the con- 
 stituted whole.'. Thus, in Deductive reasoning, the whole 
 is stated first, and what is afiSrmed of it is affirmed of the 
 parts it contains; in other words, a general law is laid 
 down, and predicated of the particular instances to which 
 it appHes. In Inductive reasoning, the parts are first stated, 
 and what is predicated of them is also predicated of the 
 whole they constitute; in other words, the particular in- 
 stances are first stated as facts, and then the law they con- 
 stitute is evolved. 
 
 " This being the nature of these counter and correlative^ 
 reasonings, it appears to us, that, though each kind is com- 
 petent in either whole (Extension or Comprehension), yet 
 the reasoning in the whole of Extension is more naturally 
 allied to the Deductive, and that in Comprehension to the 
 Inductive. For, in the whole of Extension, the reason- 
 ing proceeds from the general to the special^ — from the 
 abstract to the concrete, — from general laws to the par- 
 ticular instances which are contained under them; while 
 in that of Comprehension, on the other hand, the reasoning 
 proceeds from the special to the general, — from the con- 
 crete to the abstract, — from the particular instances to the 
 general laws, whose operation they exemphfy. 
 
 " Considering these kinds of reasoning in relatiwi to the 
 Figures, it will appear, then, that since Extension prevails 
 
THE HAMILTONIAN ANALYSIS. 263 
 
 in the Second, that will be so far more suitable for Deduc- 
 tive reasoning; and since Comprehension prevails in the 
 Third, that Figure will so far be more adapted for Induc- 
 tive reasoning ; while, since Extension and Comprehension 
 prevail equally in the First, that Figure will be equally 
 fitted for either kind of reasoning. 
 
 " The relation of the Figures to these different kinds of 
 reasoning will be best illustrated by an example. We will 
 take first the Second Figure : — 
 
 Fig. n. 
 
 Deductive Reasoning : Quantity of Extension. 
 Endowed with reason is all man. 
 European, Asiatic, African, American, are all man. 
 European, Asiatic, African, American, are endowed with reason. 
 
 " Here the reasoning is Deductive, for the law is first 
 enounced, the individual instances are next brought under 
 it, and it is then affirmed of them ; it is Extensive, for it 
 prpceeds from the wider notion through the narrower to 
 the individual. Let us now take the same Terms and treat 
 them Inductively, beginning with the individuals. The 
 rea,soning will then be in the whole of Comprehension, and 
 will naturally appear in the form of the Third Figure : — 
 
 Fig. ra. 
 Inductive Beaconing : Quantity of Comprehension. 
 European, Asiatic, African, American, are aU man. 
 European,, Asiatic, African, American, are endowed, with reason. 
 Endowed with reason is all man, 
 
 " Here the reasoning is Inductive, for, beginning with the 
 individuals in the Premises, we arrive at the law (with 
 which we started in the previous Syllogism) in the Conclu- 
 sion ; it is Oomprehensive or Jktensive, for it proceeds fi-om 
 the concrete to the abstract, from, a greater totality of attri- 
 bute to a less. In other words, in either Quantity (Exten- 
 sive or Intensive), we reason from the greatest whole ; but 
 
264 MEDIATE INFERENCE OE SYLLOGISM. 
 
 in the Quantity of Extension, the greatest whole is the most 
 abstract notion (i. e. the widest law), whereas in that of 
 Comprehension, the greatest whole is the most concrete 
 notion (i. e. the individual instance). But proceeding 
 thus from the widest law, the reasoning is necessarily- 
 Deductive, while on the other hand, proceeding from the 
 individual instance, it is as necessarily Inductive. 
 
 " We may give the same example in the First Figure, to 
 illustrate (what will now be quite obvious) that it is in- 
 differently competent to either reasoning : — 
 
 Fio. L 
 Deductive Beasoning : Quantity ofEiiension. 
 All man is endowed with reason. 
 European, Asiatic, African, American, are all man. 
 European, Asiatic, Afidcan, American, are endowed with reason. 
 
 Inductive Reasoning : Quantity of Comprehension. 
 European, Asiatic, African, American, ai-e aU man. 
 All man is endowed with reason. 
 European, Asiatic, African, American, are endowed with reason. 
 
 " The Second and Third Figures are indeed naturally 
 respectively connected with Deductive and Inductive rea- 
 soning ; for in the Second, we judge the likeness or unlike- 
 ness of two parts, as they are contained or not contained by 
 a common whole ; while in the Third, we judge the likeness 
 or unlikeness of two wholes, as they severally contain or 
 do not contain common parts." 
 
 In respect to Hypothetical and Disjunctive reasoning, 
 Hamilton has followed Kant in declaring that all Mediate 
 Inference is one, — that which has been denominated Cate- 
 gorical ; all the so-called Conditional Syllogisms are reduci- 
 ble to Immediate Inferences. Their characteristic featiu^ 
 is, that they have no Middle Term ; the agreement or dis- 
 agreement of the two Terms of the Conclusion with each 
 other is ascertained, not by comparing each of them sep- 
 arately with a third Term, which is a mediate process, but 
 
THE HAMILTONIAN ANALYSIS. 265 
 
 directly, from a single Premise, here incorrectly styled a 
 Major Premise. This Premise consists, not of two Terms 
 merely, but of two Judgments, called respectively the Ante- 
 cedent and the Consequent ; a relation of mutual depend- 
 ence is affirmed to exist between these, by virtue of which 
 the Axiom of Reason and Consequent becomes applicable 
 to the case. This Axiom, as has been shown (page 54), 
 is directly explicated into the two Laws, — 1. That to affirm 
 the Season or the Condition is also to affirm the Consequent '; 
 and, 2. That to deny the Consequent is also to deny the 
 Season. A ratione ad rationatum, a negatione rationati ad 
 negationem rationis, valet consequentia. The single Prem- 
 ise affirming that this relation of Reason and Consequent 
 exists between the Judgments which are its two parts, this 
 Axiom compels us to infer immediately, or without the aid 
 of a third Term, both that the Consequent follows when 
 the Antecedent is posited, and that the Antecedent is de- 
 nied when the Consequent is sublated. 
 
 The reduction of a Hypothetical Judgment to a Cate- 
 gorical shows very clearly the Immediacy of the reasoning 
 in what is called a Hypothetical Syllogism. Thus, Jff' A is 
 B, is B, is equivalent to 
 
 AU cases of A is B are cases of C is D. 
 Some cases of A is B are cases of ) p •„ T) 
 This case of A is B is a case of J 
 
 In such reasoning, as Kant remarks, the Premise does 
 not afford a proof of the Concliision, but a ground or man- 
 ner of proving it ; it is then only an explication of the 
 meaning of the Premise, when we say that the Consequent 
 holds good when the ground or Reason exists, and that the 
 Reason does not exist if the Consequent does not hold 
 good. Hence, this kind of reasoning may properly be 
 referred to the doctrine of Exponibles. AH the Matter 
 which we are reasoning about is embraced in the one com- 
 plex proposition that is here called the Premise ; and all 
 
 12 
 
266 MEDIATE INFERENCE OK SYLLOGISM. 
 
 that the reasoner has to do is to explicate or interpret this 
 proposition. Considered as an Exponible, the Conditional 
 Judgment, If A is B, C is D, may be interpreted in two 
 
 yj-ays, 1. as a Restrictive ; 2. as an Exclusive. The 
 
 first of these interpretations yields, by the Immediate In- 
 ference of Subaltemation, what is called the Modus ponens 
 of Conditional Reasoning ; the second yields, also Imme- 
 diately, the Modus tollens. 
 
 1. Thus, Restrictively, in aiSrming that, if A is B, is 
 B, we do not say, C is always D, but only, " All C, when 
 A is B, is D," the italicized clause being the Restriction, 
 and answering to a limiting adjective, — say, yellow : All 
 yellow is B. Then, by Subaltemation, 
 Some yellow C ) . -pv 
 ThisyeUowC \^ 
 Again, the same Judgment, If A is B, C is B, yields, by 
 the Immediate Inference of Contraposition, Jff O is not B, 
 A is not B. This is an Exclusive ; it affirms that 
 A is B only when C is D ; then, Immediately, 
 A is not B when is not B. 
 In fact, all reasoning is hypothetical ; the Syllogism, as 
 such, does not affirm its Conclusion absolutely, but only its 
 dependence on the Premises, j^ the Premises are true, 
 the Conclusion follows. Any Immediate Inference, also, 
 may be stated hypothetically. Tate that by Subaltema- 
 tion, for instance : — 
 
 All A is B ; 
 .'. Some A is B. 
 
 Stated hypothetically thus : — 
 
 If all A is B, some A is B ; 
 .•. Some A, or this A, is B. 
 
 It is unnecessary to consider separately the case of Dis- 
 junctive reasoning ; for it has already been proved (page 
 131) that Disjunctives are only complex Hypotheticals. 
 
OF FALLACIES. 267 
 
 GHAPTER IX. 
 
 OF FALLACIES. 
 
 A FALLACY is any instance of imsonnd or invalid 
 reasoning which has a deceptive appearance of cor- 
 rectness and truth. If it be such that the writer or speaker 
 is himself deceived by it, it is called a Paralogism ; if 
 framed by him for the purpose of deceiving others, while 
 he is himself aware of its unsoundness, it is a Sophism. 
 Those of the former class are what we have most to dread ; 
 for on account of the necessary dependence of Thought on 
 Language, we often commit them in our silent meditations, 
 while we are attempting to discover the truth or to dis- 
 intricate it from error. The danger is greatly enhanced 
 by the symbolic or algebraic use of Language, whereby 
 we employ words for the moment as mere signs, without 
 spreading out their signification before the mind, and thus 
 are often deceived by their ambiguity and vagueness. 
 Sophisms are comparatively of rare occurrence, as one 
 who wishes to deceive can do so more easily and eifect- 
 tially by false statements than by false reasonings. It is 
 more diffictilt to weave invalid but specious arguments, 
 knowing their incoirectness, than to reason correctly from 
 wrong premises. Formerly it was otherwise ; the great 
 use of disputation by the ancient sophists and the School- 
 men, as a logical exercise and a means of education, tended 
 to create a special art of sophistry, and has left on record a 
 multitude of logical puzzles for the amusement of later 
 times. Dexterity in framing and solving these sophisms 
 
268 OF FALLACIES. 
 
 was reckoned a scholarly accomplishment, and one of the 
 special fruits of a university education. Nowadays this 
 species of mental gymnastics has fallen into entire disre- 
 pute, as men prefer to sharpen their wits on graver matters 
 and subjects of more immediate interest. 
 
 The purpose of the doctrine of Fallacies, as it is now 
 taught, is to familiarize the mind with those instances of 
 erroneous reasoning which are most likely to lead our own 
 thoughts astray in the search after truth and the elimina- 
 tion of error. For this end, a classification of Fallacies is 
 desirahle. The earliest attempt, of which we have any 
 distinct knowledge, thus to reduce them to system, was 
 that of Aristotle ; and the chief endeavor of later logicians 
 has been to ascertain, develop, and illustrate his meaning. 
 Even the phraseology which he employed became conse- 
 crated, as it were, by long use in the Schools ; and the 
 chief dispute among modern writers has been, whether a 
 particular Fallacy is rightly designated by this or that tech- 
 nical name. A more unprofitable logomachy can hardly 
 be imagined. Our business is to teach Logic, and not to 
 write a commentary upon Aristotle. The classification 
 framed by him, though a marvellous work for the time, 
 evincing the prodigious acuteness and comprehensiveness 
 of view for which his intellect was so remarkable, must 
 still, if viewed under the hghts of modern science, be re- 
 garded as crude and imperfect. A better arrangement can 
 be effected, not by laying aside his phraseology altogether, 
 but by employing his technical terms, when they are con- 
 venient, under the conventional meaning which has long 
 been assigned to them, and by striking out many of his dis- 
 tinctions, and introducing others in their place which have 
 been suggested by later experience. The use of classifica- 
 tion, it must be remembered, is merely subsidiary; the 
 main purpose is to become familiar with the character- 
 istics of those forms of erroneous reasoning which most 
 
OF FALLACIES. 269 
 
 frequently occur in practice ; and this can be best accom- 
 plished by dividing them into species, and discriminating 
 these species from each other. 
 
 It should be observed that, strictly speaking, the consid- 
 eration of Fallacies is extralogical. We have already laid 
 down the Rules of correct or valid Inference ; any argu- 
 mentation which violates one or more of these Rules is in- 
 valid. But an open violation of one of- them, as, from its 
 very obviousness, it is not likely to deceive anybody, is not 
 usually called a Fallacy. A classification of what are prop- 
 erly denominated Fallacies would depend on an enumera- 
 tion of those circumstances which are most likely to deceive 
 us — to cover up the violation of a Rule — in the forma- 
 tion of our Judgments and Inferences ; and a disquisition 
 on these circumstances would form a valuable chapter of 
 Psychology, or in a Treatise on the practical Conduct of 
 the Understanding. The chief source of these errors is 
 the ambiguity of language, both as respects the meaning 
 of single words (cequivocatio) aud the construction of 
 sentences (amphibolia). Then the ultimate remedy for 
 them is to be found in the study of language ; it would be 
 a part of the doctrine of Hermeneutics, or the science of 
 Interpretation. But as certain prominent classes of them 
 frequently perplex and vitiate our reasonings, a description 
 of such is not entirely out of place as an appendage to the 
 science of Logic. 
 
 We observe in the first place, then, that Aristotle was 
 wrong, and his authority has misled most of the later logi- 
 cians, in forming a distinct class of the. Fallacies of language. 
 His first distinction is between those in dictione, which 
 arise merely from the improper use of words as arbitrary 
 signs of thought, and which, therefore, generally disappear 
 when the proposition is translated into another language, 
 and those extra diotionem, which are in the Thought itself, 
 whether in its Matter or its Form, and therefore adhere to 
 
270 OF FALLACIES. 
 
 the Thought, however it may be expressed. He enumer- 
 ates six classes or subdivisions of the former; but the 
 division is a faulty one, as the six can be reduced to two, 
 namely, the ambiguity of single words, or the ambiguous 
 construction of sentences. But we object generally, that 
 the erroneous use of language is of no logical import what- 
 ever, if it be not employed to hide some defect ia the rea- 
 soning. The ambiguity of words may cloak, but does not 
 constitute, the sophism. If the suspected Syllogism does 
 not contain an undistributed Middle, or four Terms instead 
 of three, or an Ilhcit Process, or some other violation of 
 logical Rule, it is a sound Inference, however faulty may 
 be the language in which it is expressed. Accordingly, it 
 wiU be found, that aU the instances given in the books to 
 illustrate the six classes of what may be briefly termed 
 Verbal Fallacies, resolve themselves, when the ambiguity 
 is detected, into logical quadrupeds, as Syllogisms with/owr 
 Terms have been derisively called, or some other form of 
 violating one or more of the Canons of Pure Logic. Take 
 the following illustration, from Mr. De Morgan, of the Fal- 
 lacy of ambiguous words, Aristotle's first subdivision. 
 
 All criminal actions ought to be punished by law ; 
 
 Prosecutions for theft are criminal actions ; 
 
 Therefore, prosecutions for theft ought to be punished by law. 
 Here the Middle Term, criminal actions, is ambiguous ; in 
 the Sumption, it means immoral deeds; in the Subsump- 
 tion, it is a technical phrase for a particular class of legal 
 proceedings. Substitute 'these definitions for the phrase 
 defined, and it is apparent that the pretended Syllogism is 
 a quadruped. 
 
 Take the following as an instance of Aristotle's second 
 subdivision, — ambiguous construction. 
 
 All that ghtters is not gold ; 
 
 Tuisel glitters ; 
 
 Then, tinsel is not gold. 
 
OF FALLACIES. 271 
 
 Here, in the Sumption, the Middle Term is apparently- 
 distributed by the predesignation all; but it is not so in 
 reality, as the negative particle ought to be construed as 
 qualifying all, and not all means some are not. But if we 
 read, Some things that glitter are not gold, the Middle is not 
 distributed in either Premise. 
 
 The class of Verbal Fallacies, then, should be abolished, 
 as all instances of invalid or erroneous reasoning, being 
 either an open or a concealed; violation of the Laws of 
 Thought, are necessarily extra dictionem, or independent of 
 language. Then the most general division of them wUl be 
 into Formal and Material Fallacies, "according as the 
 source of deception lies in the act of Thought itself, or in 
 the object upon which, or the circumstances under which, 
 it is exercised." This distinction may be well expressed 
 by saying that, in every Fallacy,, the Conclusion either 
 does, or does not, follow from the Premises. If it does not so 
 follow, it is clear that the fault is in the reasoning, and in 
 that alone ; the error concerns only the I'orm of Thought, 
 so that these alone are Logical Fallacies strictly so called. 
 If the Conclusion does follow from the Premises, we must 
 search for the deception in the Matter of the Thought ; 
 that is, we must consider what we are reasoning about, 
 and what is the Conclusion" which we wish to establish. 
 Such consideration is properly extralogical ; but as the pur- 
 pose of examining both classes of these Fallacies is the 
 same, namely, to guard the mind against error in its own 
 processes, and as the consideration of only one class of Fal- 
 lacies would very imperfectly answer this end, we subordi- 
 nate strict method to convenience, and take into view all 
 cases of defective and sophistical argumentation. While 
 considering both of these classes of Fallacies, the ambi- 
 guities of language which hide them, and which originally 
 led the reasoner astray, will incidentally come into notice, 
 and the exposure of them thus effected will be, in a prac- 
 
272 OF FALLACIES. 
 
 tical point of view, tlie most valuable result of the discn*^ 
 sion. 
 
 The subdivision of Fallacies in the Form of Thought, 
 the Conclusion being iUogically drawn, is easily effected, 
 as it must have reference to the six General Rules, which 
 are aU embodied in Hamilton's one Supreme Canon of 
 Mediate Inference. But the classification thus made is not 
 easily adhered to, as it will often be found that the same 
 Fallacy involves a violation of two or more of these Gen- 
 eral S.ules. The subject being once properly distributed 
 into parts, however, the question is of little moment 
 whether a particular case is rightly assigned to this or that 
 class, if it may fairly be placed under either. The Rules 
 most frequently violated are those which require, — 1. That 
 a Syllogism should consist of only three Terms ; 2. That 
 the Middle Term should be distributed in at least one of 
 the Premises ; 3. That neither Term can be distributed in 
 the Conclusion, if it was not taken universally in the Prem- 
 ises ; 4. That the Conclusion must be Negative, if either 
 Premise is Negative ; 5. That at least one Premise must 
 be Affirmative. Besides the five kinds of Fallacies arising 
 from violations of these Rules, two others should be men- 
 tioned, being the two invalid Moods of Hypothetical In- 
 ference : — 6. From denying the Antecedent, or, 7. From 
 affirming the Consequent, no Conclusion can be drawn. A 
 number of other classes might be framed, arising from vio- 
 lation of the various Rules of Immediate Inference, — the 
 Laws of Conversion, Opposition, Infinitation, for instance. 
 But as such errors are neither frequent nor insidious, they 
 need not be considered here. ' 
 
 1. To the class of Syllogisms which axe invalid because 
 they consist of more than three Terms may be refeiTed all 
 the cases which are usually placed under the head of anMg- 
 uous Middle. If an ambiguous word or phrase is employed 
 as the Middle Term in the Major Premise in one of its 
 
OF FALLACIES. 273 
 
 significations, and in the Minor Premise in a different sig- 
 nification, it is evident that it does not afford us any means 
 of ascertaining the relation of the Extremes to each other. 
 Having only compared A with M, and B with N, we can- 
 not tell whether A is, or is not, B. Cases of this Fallacy 
 are more numerous, and more apt to deceive, than those 
 of any other class. They are the more insidiousj because 
 terms in frequent use, and which are constantly employed 
 by the vulgar in ordinary conversation, are priecisely those 
 which are most apt to become ambiguous ; but on account 
 of their familiarity, we fancy that we are perfectly ac- 
 quainted with them, and therefore never suspect that they 
 are leading us astray. 
 
 Most political Fallacies are of this order. That very 
 common phrase, the government, means both " the system 
 of laws under which we live and the machinery by which 
 these are administered," and " the members of the ad- 
 ministration for the time being, whose duty it is to carry 
 out this system and to work this machinery " ; or it may 
 mean certain measures, or a favorite policy, of these admin- 
 istrators. Hence what Jeremy Bentham calls " the official 
 malefactor's screen"; — "Attack us, you attack the gov- 
 ernment." It may well happen that we best manifest our 
 attachment to the government in the former sense, by a 
 vehement opposition to it in the second meaning ; or, if the 
 administrators are really able and well disposed, but are 
 pursuing a mistaken policy in one respect, that we best 
 show our regard for them personally, by laboring to con- 
 vince them of their error. 
 
 Still more ambiguous is that which is so much talked and 
 written about, — the Ohwrch. How many controversies 
 might have been spared, and how many volumes remained 
 unwritten, had it been remembered that, at least in all 
 countries where a religious establishment exists supported 
 by law, " the Church " may have these six different 
 
 12* B 
 
274 OF FALLACIES. 
 
 meanings : — 1. a place of meeting for worship ; 2. all tte 
 people engaged as -worshippers ; 3. only the faithful who, in 
 in every age, since the advent of the Kedeemer, have 
 constituted the mystical Body of Christ; 4. the inferior 
 clergy by whom the ceremonies of worship are conducted ; 
 6. the superior clergy, who may be regarded as the heads 
 of the Church ; 6. rules and customs respecting the modes 
 of worship. As Bentham remarks, church is often made to 
 mean churchmen, and law to signify lawyers, by the easy 
 device of "substituting for men's proper official denom- 
 ination the name of some fictitious entity, to whom, fey 
 customary language, and hence opinion, the attribute of 
 excellence has been attached." 
 
 If it were allowable to make a new use of one of Bacon's 
 technical appellations, another large class of these sophisms 
 might be called Fallacies of the Forum. These relate 
 chiefly to money, currency, prices, interest, profits, and 
 other terms of frequent use in conunercial and financial 
 transactions. Money may mean either specie, or bank-notes, 
 or currency consisting of a mixture of these two, or credit, 
 or capital, or that portion of capital which is offered for loan. 
 An individual merchant is said to be in want of money 
 wherewith to pay his debts, when his only real lack is of 
 credit, capital, or merchandise, money serving no other 
 purpose in the affair than that of the carts by which the 
 merchandise is transported. Again, interest is usually 
 spoken of as if it were the interest of money ; whereas a 
 little reflection will satisfy any one, that money (if the 
 name be appHed, as it usually is, to specie, to bank-notes, 
 or to a combination of the two) yields neither profit nor 
 interest ; whether it is in the hands of an individual or a 
 corporation, whether in the pocket or in a safe, it is a part 
 of the owner's dead capital, and therefore he usually aims 
 to get along with the use of as little of it as possible. 
 Again, money is usually considered as the measure of 
 
OF FALLACIES. 275 
 
 wealth ; and then, by a very common metonomy, the meas- 
 ure is confounded with the thing measured. Hence the 
 following sophism, which may be said to have directed the 
 commercial legislation of all civilized countries, down, at 
 least, ^to the time of Adam Smith. 
 
 Any increase of the money in a country is an equivalent enlarge- 
 ment of its wealth. 
 
 Laws to protect native manufactures against foreign competition 
 tend to increase the money in the country. 
 
 Therefore, such laws tend to increase the nation's wealth. 
 
 But Adam Smith demonstrated that laws directed solely to 
 keeping specie at home, only tend to make the country 
 poorer ; and his arguments being at last generally admitted 
 to be conclusive, there arose the opposite Fallacy of uni- 
 versal Free Trade, which now controls the legislation of 
 England, and is gaining ground in many other quarters. 
 
 Laws which do not increase the quantity of money in the coun- 
 try are at best useless. 
 A Protective System does not increase this quantity. 
 Therefore, a Protective System is useless. 
 
 Of course, the answer to this argument is, that measures 
 which do not prevent specie from going abroad may yet 
 make the people more wealthy and prosperous, by ena^ 
 bling them, in their foreign trade, to exchange manufactures 
 for raw material, — that is, the products of skilled labor 
 for those of rude labor, — that is, again, the fniits of the 
 industry of one man for those of the industry of three or 
 four men. And it is precisely this system, — fostering the 
 growth of native manufactures and allowing the produc- 
 tion of raw material to take care of itself, — and not the 
 prevalence of the doctrine of Free Trade, which has been 
 the great source of England's prosperity. 
 
 Another frequent source of this Fallacy — the introduc- 
 tion, through the ambiguity of language, of four Terms into 
 
276 OF FALLACIES. 
 
 a Syllogism — is tlie doctrine ttat the primary or etymo- 
 lo^cal meaning of a word is its only proper signification, or 
 that it is the standard to which modem usage ought to con- 
 form. This sophism is the more frequent, as it afibrds an 
 opportunity for a httle display of erudition ; numerous 
 instances of it can he found in what is otherwise an ingeni- 
 ous and excellent work, Tooke's " Diversions of Purley." 
 Thus, right comes from rectus, and that from rego, — to 
 rule or govern ; hence an alleged confirmation of the doc- 
 trine of Hobbes, that right is only a creature of positive 
 law, another unfounded assumption being then allowed to 
 slip in, that the only kind of law is human, not divine. 
 Again, most of the words which are now significant of the 
 operations of Mind were originally applied to some of the 
 forms or changes of Matter ; and this fact has heen held to 
 coimtenance the doctrine of materialism. But that spirit 
 once signified breath, and animus, ave/j,o<;, air, does not 
 aflford even a presumption that such is their present mean- 
 ing. The secondary or usual sense of a word has often 
 travelled so iar away from its primitive application as to 
 have lost sight of it altogether, though we may be able to 
 point out the stopping-places in its long journey. 
 
 I cannot help thinking that Sir William Hamilton has 
 unconsciously glided into a Fallacy of this sort in his criti- 
 cism of Dr. Reid's definition of memory. Reid says, 
 " Memory is an immediate knowledge of things past " ; 
 meaning thereby, as it seems to me, a present knowledge 
 of the past. This, at any rate, is a very common use of 
 the word ; an action is said to be immediate which takes 
 place now, at once, or without delay. But immediate is 
 also the opposite of mediate or vicarious; we are said to 
 have an immediate knowledge of a thing when we know it 
 direcUy or in itself, in contradistinction from knowing it 
 vicariously, or through the medium of an image or repre- 
 sentation of itself. In this sense, Hamilton argues very 
 
OF FALLACIES. 277 
 
 properly that an immediate knowledge of the past is impos- 
 sible ; and Reid, I think, would have agreed with him ; 
 while Hamilton would not have denied that memory is 
 fresent knowledge, or knowledge which exists at the present 
 time. 
 
 Another source of ambiguity, which is well exposed by 
 WhateLy, is the supposition that faronymous or conjugate 
 words — as the substantive, verb, adjective, and adverb 
 formed from the same root — necessarily agree in mean- 
 ing ; whereas, they often depart widely from each other in 
 signification. Thus, what is imaginary is unreal ; but an 
 image, as formed firom wood or stone, is a reahty. To ap- 
 prehend is to lay hold of, or to come to a hnowledge of ; 
 while apprehenfision often signifies /ear, dread. 
 
 What Aristotle calls the Fallacy of Accent (he should 
 have explained it as an ambiguity which may be resolved 
 by accent) may be illustrated by the difference between 
 gal'lant and gallant! ; the former means Irave, high-spirited; 
 the latter, courteous or devoted to women. It is more diffi- 
 cult to resolve by accent the curious ambiguity of the 
 phrase, not the least, where the two meanings are opposites 
 of each other. Thus, " not the least difference " may 
 mean either " no difference at all," or, " a very consider- 
 able, perhaps the greatest, difference." In the former 
 case, the phrase is elhptical, standing for " not any, not 
 even the least, difference." The least is excluded or nega- 
 tived, as in the phrase "mo« the least," both by nothing 
 and by the greatest. 
 
 As De Morgan remarks, " a statement of what was said, 
 with the suppression of such tone as was meant to accom- 
 pany it, is the fallacia accentus. Gesture and manner often 
 make the difference between irony or sarcasm and ordi- 
 nary assertion. A person who quotes another, omitting 
 anything which serves to show the animus of the meaning ; 
 or one who without notice puts any word of the author he 
 
278 OF FALLACIES. 
 
 eites in Italics, so as to alter its emphasis; or one who 
 attempts to heighten his own assertions, so as to make 
 them imply more than he would openly say, by Italics, or 
 notes of exclamation, or otherwise, is guilty of the fcUlacia 
 aecentus." 
 
 2. The Fallacy of Undistributed Middle does not occm- 
 so frequently, and is not so insidious, as that of Ambigaoas 
 Middle. We may fall into it unawares by overlooking 
 the difference between the Collective meaning of the word 
 aZZ= " all taken together," and its Distributive meaning, 
 in which all signifies " each and every." Thus, aM the 
 Senators (taken collectively) try impeachments; all the 
 Senators (i. e. each and every Senator) are chosen by the 
 State legislatures. 
 
 All these exercises will fatigue me ; 
 This performance is one of them ; 
 Therefore, this performance will fatigue me. 
 
 Another ambiguity, which may serve to cloak this lo^cal 
 fault, is passing from the Composite to the Divisive, or from 
 the Divisive to the Composite, meaning of a proposition. 
 If we take together those members of the sentence which 
 ought to have been taken separately, it is called the soph- 
 ism of Composition ; if we take separately what is true of 
 all only when they are united, it is the sophism of Division. 
 A ludicrous instance of the latter is found in most of the 
 old text-books on Logic. 
 
 Two and three (taken compositely) are five ; 
 
 Two and three (taken divisively) are odd and even ; 
 
 Therefore, five is odd and even. 
 
 An instance of the former is what may be called the 
 
 Spendthrift's Fallacy. 
 
 All of these contemplated expenditures (taken separately) are 
 
 of trifling amount ; 
 Therefore all of them may be incurred (together) without rliin- 
 
 ing me. 
 
OF FALLACIES. 279 
 
 The lazy person reasons in the same manner, in respect 
 to the waste of an hour or two of time, or to missing this 
 or that favorable opportunity. It behooves such persons 
 to remember, that the predesignation any one is not the 
 equivalent of all taken collectively. 
 
 This is the nature of the famous old Fallacy called 
 atop6<s, a heap, whence the name Sorites applied to a differ- 
 ent and legitimate argument. Does one grain of com 
 make a heap ? No. Do two grains make a heap ? No. 
 Do three grains ? No. And in like manner, we may ask 
 a series of questions, successively adding unity to the num- 
 ber, till the respondent is at last obliged to contradict him- 
 self, and confess what he has just denied, that a single 
 grain of corn makes the only difference between what is 
 not, and what is, a heap. The same sophism was denom- 
 inated by the old logicians the Cahug, because illustrated 
 by a series of questions beginning with the inquiry, whether 
 pulling one hair out of a man's head made him bald. 
 Horace used it to ridicule the fashion of valuing ancient 
 authors simply on account of the antiquity of their pro- 
 ductions. 
 
 " Iste qnidem veteres inter ponetur honeste, 
 Qui vel mente brevi vel toto est junior anno, 
 Utor permisBO, caudseque pilos ut equinse 
 Paulatim Telle, et demo uniim, demo etiam onnm, 
 Dum cadat elusus ratione ruentis acervi. 
 Qui redit ad fastos, et virtutem sestimat annis, 
 Miratnrque nihil nisi quod Libitina sacravit." 
 
 But while laughing at an old sophism, we may be found 
 ridiculing a modern paralogism. I have recently heard 
 this very argument gravely reproduced in a learned Acad- 
 emy, during a debate on an important question of science. 
 The answer to it is obvious; — not one alone, but one added 
 to theprevious 999, constitutes a heap. 
 
 The Fallacy of the Composite and Divisive sense is apt 
 to be repeated by the incautious in estimating the proba- 
 
280 OF FALLACIES. 
 
 bility of two events happening conjointly. Though each 
 of them, taken separately, is more Ukely than not to 
 happen, the probability of their occurrence together is 
 of a very inferior character. Thus, the probability of the 
 first being represented by ^, and that of the second by ^, 
 that of their joint occurrence is the product of these two 
 fractions, or ^, or much less than ^, which represents 
 an even chance. So we are often misled by the use of 
 the word tendency. We rightly say that a given result 
 tends to happen only when there is more than an even 
 chance of its occurrence ; if there is less than an even 
 chance, it tends not to happen. This is the form of a com- 
 mon blunder in the doctrine of means or averages. Thus, 
 all persons who have attained the age of twenty-four sur- 
 vive on an average till they are sixty-two years old. But 
 no one person, now aged twenty-four, has a right to expect 
 that this average will be exemplified in his particular case. 
 On the contrary, his chance of attaining the precise age of 
 sixty-two, no more and no less, is very much less than his 
 chance of dying at some other age. AU (collectively) tend 
 to the average ; but no one tends to the average. This is 
 no paradox ; for the average is only a compensation of 
 errors, and therefore remains the same whether the errors 
 are great or small, provided only that they are equally dis- 
 tributed on all sides of the average; and such equality of 
 distribution is the direct consequence of the fact, that no 
 one error has any tendency to be on one side of the average 
 rather than on any other side. No one tends to the aver- 
 age, but tends equally, or indifierently, to depart from it. 
 
 Mr. Darwin, in his theory of " the Origin of Species by 
 Natural Selection," is guilty of both of these forms of the 
 Fallacy. He first argues, that the specific Marks of Spe- 
 cies, both in the animal and vegetable kingdoms, tend to 
 vary, because, perhaps in one case out of ten thousand, a 
 child is born with six fingers on one hand, or a cat with 
 
OF FALLACIES. 281 
 
 blue eyes, or a flower grows out of the middle of another 
 flower. Collecting many instances of such sports of nature 
 or monstrosities, he bases his whole theory upon them, for- 
 getting that the vastly larger number of normal growths 
 and developments proves that the tendency is to non-varia- 
 tion. Then, secondly, because perhaps one out of a hun- 
 dred of these abnormal Marks is transmitted by inheritance, 
 he assumes that these freaks of nature tend to perpetuate 
 themselves in a distinct race, and thus to become perma- 
 nent Marks of distinct species. Thirdly, as either of the two 
 preceding points, taken singly, afibrds no basis whatever 
 for his doctrine, he assumes that their joint occurrence 
 is probable, because he has made out what is, in truth, a 
 very faint probability that each may separately happen. 
 But if the chance of a variation in the first instance is only 
 one out of a thousand, and that of the anomaly being 
 handed down by descent is one out of a hundred, the 
 probabiUty of a variation established by inheritance is but 
 one out of a hundred thousand. As the theory further 
 requires the cumulation of an indefinite number of such 
 variations one upon another, the formation of a new species 
 by the Darwinian process may be safely pronounced to be 
 incredible. 
 
 3. The third class of Fallacies, those which arise from a 
 violation of the Rule that neither Term must be distributed 
 in the Conclusion if it was not distributed in the Premise, 
 are frequent enough, but will deceive no one if they are 
 not ambiguously expressed. If it is the Predicate of the 
 Conclusion which is iUogically distributed, the error is 
 called an IlUcit Process of the Major Term ; if the Sub- 
 ject, an Illicit Process of the Minor Term. Of these, the 
 former is more common and insidious ; for as the Quantity 
 of the Predicate is not expressed in the ordinary use of 
 language, we are apt -to forget that, in a Negative propo- 
 sition, it is always presumed to be Universal, and in an 
 
282 OF FALLACIES. 
 
 Affirmative, if nothing be said to the contrary, it is uiually 
 Particular. In what the Aristotelians call Indefinite prop- 
 ositions, the Quantity of neither Term is expressed ; but if 
 Affirmative, both Terms are commonly understood to be 
 distributed ; for most propositions of this sort are either 
 Definitions, or statements of a general law ; and in both of 
 these cases, the Universal quantification of each Term is 
 easily supplied m thought. Thus, Falsehood is wilful decep- 
 tion, is easily and properly construed to mean, All falsehoods 
 are all wilful deceptions ; and Matter gravitates, to mean. All 
 matter is all that gravitates. But statements of a general 
 law must be carefiilly distinguished from statements of the 
 application of such a law to a particular class of cases ; 
 thus, Stones gravitate, means only, '■'■All stones are some 
 gravitating substances." 
 
 All birds are winged ; 
 The bat is not a bird ; 
 Then the bat is not winged. 
 Here, the Conclusion is logically false, for it contains an 
 Illicit Process of the Major Term. The Sumption is un- 
 derstood to mean only that " All birds are some winged 
 things " ; the bat, therefore, though not a bird, may be 
 (as here it happens actually to be) one of the other some 
 winged things, while the illogical Conclusion declares it to 
 be not (any) winged thing. 
 
 No slave has his rights ; 
 
 All slaves are persons of African descent ; 
 
 Therefore no person of Afiican descent has his rights. 
 The Illicit Process is here of the Minor Term ; for the 
 Conclusion denies of any, what the Premises authorize us 
 to deny only of some Africans. 
 
 In both these cases, the Fallacy is so obvious that it can- 
 not deceive any one who thinks clearly. But the ambigui- 
 ties of language may so cloak the deception as to render 
 its exposure difficult. Most insidious in this respect is the 
 
OF FALLACIES. 283 
 
 ambiguity between what is true absolutely, and what is 
 true only in some respect, to d7r\S)<i rj firj dirXm- From 
 this confusion of language two modes of false reasoning 
 result, the first of which is denominated by the Aristo- 
 telians the fallada a dieto secundum quid ad dictum sim- 
 plidter. It consists in inferring something as true of the 
 subject simply, or without hmitation, which is true of it only 
 in some respect. Thus, Man is immortal (in respect to his 
 soul) ; therefore, man is immortal (absolutely, both as to 
 soul and body). The second has been called the fallaeia 
 acddentis, because it confounds an accidental attribute with 
 what is essential or principally intended. But as it is the 
 exact converse of the former, it should rather be called the 
 fallaeia a dicta simplidter ad dictum secundum quid. Thus, 
 to take the converse of the former instance, Man is mortal 
 (man being here understood, as usual, to be a living or- 
 ganism) ; therefore, man is mortal (as respects his soul). 
 Aristotle gives the following illustration, which is puerile, 
 though it might well puzzle a beginner : — 
 
 Socrates is not Coriscus (in any sense) ; 
 
 But Coriscus is a man (this being one of his characteristics) ; 
 
 Therefore, Socrates is not a man. 
 
 The most difficult cases to be resolved are those in 
 which giving the name of the genus, to which the subject 
 belongs, is confounded with giving the name of its species. 
 Thus, 
 
 He who calls you a man speaks truly ; 
 He who calls you a knave calls you a man ; 
 Then he who calls you a knave speaks truly. 
 A ludicrous instance of the former mode of the Fallacy is 
 found m most of the text-books : — 
 
 "What you bought yesterday you eat to-day ; 
 But you bought raw meat yesterday ; 
 Then you eat raw meat to-day. 
 Perhaps both forms of this Fallacy are best resolved by 
 
284 OF FALLACIES. 
 
 considering that the ambiguity resides in the Copula. 
 When one thing is predicated of another, it is seldom un- 
 derstood that the Predicate is thereby entirely identified 
 with the Subject, as the proposition would then be merely 
 tautologous, A is A. But unless it is so identified, we can- 
 not afiirm of the Predicate all that might be affirmed of the 
 Subject. The logical rule as usually enounced, that no 
 Term must be distributed in the Conclusion if it was not 
 distributed in the Premises, is defective ; for it only insures 
 that the Quantity shall be the same. The seTise ought also 
 to be the same throughout, whether absolute or relative, 
 whether in one respect or in many, whether essentially or 
 accidentally. An adequate enouncement of the rule would 
 be, that no more and no less, in any respect, must be collected 
 in the Conclusion than was given out in the Premises. In 
 order to know how much was so given out, we must consider 
 the meaning of the Copula, is, in each separate case. Mr. 
 De Morgan says : " The most common uses of the verb 
 are, — 1. absolute identity, as in 'the thing he sold you 
 is the one I sold him,' — this is the dictum simpliciter ; 
 2. agreement in a certain particular or particulars under- 
 stood," dictum secundum quid, " as in ' he is a negro,' said 
 of a European in reference to his color ; 3. possession of a 
 quaUty, as in ' the rose is red ' ; 4. reference of a species to 
 its genus, as in ' man is an animal.' All these uses are 
 independent of the use of the verb alone, denoting exist- 
 ence, as in ' man is [i. e. exists].' " In most cases, these 
 meanings are not interchangeable ; and whenever they are 
 not, a Fallacy may be founded upon the difference between 
 any two of them. 
 
 But the enumeration is imperfect ; several additions may 
 be made to it, by observing, what has been already re- 
 marked in treating of Contradiction, " that two Judgments 
 properly contradict each other only when that which is 
 affirmed by the one is denied by the other, — 1. in the 
 
OF FALLACIES. 285 
 
 same respect; 2. in the same manner; 3. in the same 
 degree ; 4. at the same time." Thus, Mr. De Morgan's 
 instance of absolute identity is unhappily chosen ; for if the 
 limitation of time, is taken into account, " the horse which 
 he sold you," being ten years old, is not absolutely tl\£ %ame 
 horse which I sold him, as that was only six years old. 
 All Fallacies of this class may be easily resolved by merely 
 completing in expression what was previously only implied 
 in thought. We thereby prevent any more or less stress 
 being laid upon an accident, or upon any view of the sub- 
 ject, in the Conclusion, than was done in the Premises. 
 
 The use of wine is destructive to the health ; 
 
 Therefore its use ought to be forbidden. 
 As stated, this Enthymeme may seem indisputable ; but 
 there can be no practical application of it, unless it is under- 
 stood to mean that any use of wine is pernicious, and hence 
 that it ought always to be forbidden. This is the fallacy 
 of arguing against the Mse of a thing merely from its liabil- 
 ity to abuse. The proper caution is, that no change what- 
 ever in the Terms employed must take place during the 
 process of inference. 
 
 In ordinary language, few terms are so loosely used, or 
 so often improperly applied, as the same, all, always, &c. 
 Hence the logicians were obhged to form a separate class 
 of Fallacies, which they called those fictee universalitatis. 
 People say the same, when they mean similar ; all, when 
 they mean only mast; and always signifies to them the 
 same as frequently. They do not even mention the excuse 
 which the Psalmist alleges when conscious of his exaggera- 
 tion, — "I said in my haste, -All men are liars." It was 
 once considered a difficult question, whether a stocking, 
 which had been so much darned that not a thread of the 
 original fabric remained, was, or was not, the same stocking. 
 But it can present no diificulty to one who considers that 
 sameness or identity is an absolute term, which can neither 
 
286 OF FALLACIES. 
 
 be aifirmed nor denied except in an unqualified sense ; and 
 that all which can be truly predicated of what comes short 
 of sameness is similarity. 
 
 " We niight suppose that most persons have no idea of a 
 universal proposition ; but use the language, never intend- 
 ing all to mean more than mogt. And in the same manner, 
 principles are stated broadly and generally, which the 
 assertor is afterwards at liberty to deny, under the phrase 
 that he does not carry them so far as the instance named. 
 It would not do to avow that the principle is not always 
 true ; so it is stated to be always true, but not capable of 
 being carried more than a certain length. Are not many 
 persons imder some confusion about the meaning of the 
 word general ? In science, it always has the meaning of 
 universal; and the same in old English. Thus the Cate- 
 chism of the Church of England asserts that there are two 
 sacraments which are generally [universally] necessary to 
 salvation, — meaning, necessary for all of the genus in ques- 
 tion, be it man. Christian, member of the Church, or any 
 other. But in modem and vernacular English, general 
 means only usual, and generally means iisually." * 
 
 An opposite error, but one proceeding from the same 
 source, viz. from confounding the Universal with the Par- 
 ticular, is committed by many Americans and some Eng- 
 lishmen in respect to the word quite. Its proper meaning 
 is completely, entirely, as " quite contrary principles " ; but 
 it is often used in the sense of very, as " quite warm," 
 " quite cold," " quite recent." 
 
 The word same, in ordinary parlance, is applied to all 
 objects for which a single description will serve, or which 
 are included under one Concept. Thus we say, " This 
 writing is on the same paper with that," meaning the 
 same kind of paper ; " This erroneous reasoning is the same 
 Fallacy with the other," meaning the same kind of Fallacy. 
 
 * De Morgan's Formal Logic, p. 272. 
 
OF FALLACIES. 287 
 
 A description or Concept, as we have seen, is an imperfect 
 enumeration of the qualities of a whole class of objects ; 
 and it is only because the enumeration is imperfect that 
 many can be ranked under one class. A perfect enumera- 
 tion, if such were possible, — a list of all the qualities, — 
 would cause each Individual (if this were not a contradic- 
 tion in terms) to constitute a class by itself. 
 
 " Nothing, perhaps," says Dr. Whately, "has contributed 
 more to the error of Realism, than inattention to this ambi- 
 guity. When several persons are said to have one and the 
 same opinion, thought, or idea, many men, overlooking the 
 true, simple statement of the case, which is, that they are 
 all thinking alike [or similarly'], look for something more 
 abstruse and mystical, and imagine there must be some one 
 thing, in the primary sense, though not an Individual, 
 which is present at once in the mind of each of these per- 
 sons; and thence readily sprung Plato's theory of Ideas, 
 each of which was, according to him, one real, eternal 
 object, existing entire and complete in each of the Indi- 
 vidual objects that are known by one name.* Hence, first 
 in poetical mythology, and ultimately, perhaps, in popular 
 beUef, Fortune, Liberty, Prudence (Minerva), a Boundary 
 (Terminus), and even the Mildew of Com (Rubigo), be- 
 came personified, deified, and represented by statues; 
 somewhat according to the process which is described by 
 Swift, in his humorous manner, in speaking of Zeal, in the 
 ' Tale of a Tub,' ' how fi-om a notion it became a word, 
 and thence, in a hot summer, ripened into a tangible sub- 
 stance.' " 
 
 But Dr. Whately seems to depart Irom his own prin- 
 
 * " When abstract truth is contemplated," asks Dr. Price, " is not the 
 very object itself present to the mind ? When millions of intellects contem- 
 plate the equality of every angle in a semicircle to a right angle, have they 
 not all t}ie same object in view ? Is this object nothing ? Or is it only an 
 image or kind of shadow ? These inquiries carry our thoughts high." 
 
288 OF FALLACIES. 
 
 ciples, when he proceeds to remark, that " Sameness, in 
 the primary sense, does not even necessarily imply Simi- 
 larity ; for if we say of any man that he is greatly altered 
 since such a time, we understand, and indeed imply hy 
 the very expression, that he is one, 'person, though different 
 in several qualities ; else it would not be Ae." Surely, 
 what we mean hy Personal Identity is sameness of mh- 
 stance under great differences of phenomenal manifestation. 
 Sameness here does not imply Similarity, merely because 
 it impUes a great deal more ; — namely, absolute oneness 
 of substance, under the greatest diversity of outward ap- 
 pearance. The Person is not different at different times, 
 but his attributes and actions are. But perhaps this is 
 what Dr. Whately really means, though it is not the ob- 
 vious construction of his language. He seems to consider 
 the Person, and his outward character or manifestadon, as 
 one. 
 
 The Fallacy of over-hasty generalization is very firequent, 
 as Bentham remarks, in political reasoning. It consists in 
 attributing to an individual person or thing certain attri- 
 butes which appear in many or most others which have 
 been loosely ranked in the same class with the object in 
 question, and thereby designated by the same name. Thus, 
 a pamphlet entitled " The Crimes of Kings " was published 
 in Paris in 1792, in order to prove that Louis XVI. ought 
 to be put to death. In like manner, " The Cruelties of 
 Cathohcs " was the title of a book published in England as 
 an argument against Catholic Emancipation. Most poht- 
 ical harangues abound in argmnents of the like character ; 
 but they are evidently addressed to the passions rather 
 than the intellect, as they cannot deceive any one who is 
 cool enough to be able to think. 
 
 To the ambiguity between what is true absolutely, and 
 what is true only in some respect, may be referred the 
 famous sophism of Eubulides, called yei/So/tevos, the Liar. 
 
OF FALLACIES.* 289 
 
 According to Diogenes Laertius, Chrysippus the Stoic wrote 
 six different treatises upon this logical puzzle, and Philetas 
 of Cos studied himself to death in the vain attempt to solve 
 it. " If you say that you he, and say so truly, then you 
 do He ; but if you say so falsely, then you speak the truth. 
 In either case, therefore, the same assertion is both true 
 and false." But if any one says, " I He," his assertion is 
 not a dictum simplieiter ; for a lie is only possible seeundum 
 quid. He who lies must He about something, in some par- 
 ticular afiirmation or denial ; otherwise, his assertion is as 
 meaningless as the remark that " something is very Hke;" 
 Like what ? * If he_ means only, " I have lied in some 
 former assertion," there is no contradiction ; if he means, 
 "I He now, in saying that 'I He,' " he reaUy makes two 
 affirmations, of which the one, the oratio ohliqua, is vague 
 and meaningless, and the other, the oratio direeta, improp- 
 erly characterizes this one as a falsehood, — improperly, for 
 that which has no significance cannot be either true or 
 false. 
 
 This sophism has been stated in a different and inferior 
 form, as follows : — 
 
 " All the Cretans are liars." 
 
 But Epimenides, who says this, is himself a Cretan. 
 
 Therefore, as he is a liar, this saying is not true. 
 
 But if the saying is not true, Epimenides may have spoken the 
 
 truth. 
 Then the saying is true ; — and so on, as before. 
 
 But here the Major Premise does not support the Con- 
 clusion, unless it is construed to mean that the Cretans are 
 always Hars, — that they cannot speak the truth. And 
 even if this were true, one who is himself a Cretan could 
 not say so, for then he would speak truly, and so contra- 
 dict himself. Of a similar nature is the foUowing puzzle. 
 
 * Hansel's Notes to Aldrich, p. 145. 
 I3i s 
 
290 OF FALLACIES. 
 
 " No rule holds true without some exceptions." 
 
 But this very remark is a rule. 
 
 Then it has exceptions. 
 
 Then there are rules without exceptions. 
 Here the reasoning, as such, is correct, and the absurd- 
 ity to which it leads demonstrates what has been properly 
 called the Fallacy of mdversal seeptkigm. As Sir James 
 Mackintosh remarks, " universal scepticism involves a con- 
 tradiction in terms ; it is a belief that there can be no 
 belief." He who denies every assertion thereby denies his 
 own denial, and so contradicts himseF. The Major Pre- 
 mise in this very puzzle is such a self-contradictory asser- 
 tion ; I cannot make a true general remark, that <M general 
 remarks are false ; or, what is the same thing, that they 
 " have exceptions." 
 
 4 & 6. Little need be said to illustrate the remaining 
 classes of Fallacies, as they are of infrequent occurrence, 
 and are easy to be detected unless cloaked by some of the 
 ambiguities of language which have already been exposed. 
 Those which respect the Quality of the reasoning may well 
 be considered together. The two Rules are, that at least 
 one of the Premises must be Affirmative, and that the Con- 
 clusion must be Negative if either Premise is Negative. 
 These Rules may be violated in appearance, when they are 
 not so in reality. For instance : — 
 
 No one is rich who has not enough ; 
 
 No miser has enough ; 
 
 Therefore no miser is rich. 
 Here, both Premises are seemingly negative ; but they 
 are not really so, for the negation of having enough is a 
 part of the Predicate, and therefore does not affect the 
 Quality; of the Judgment, which depends on the Copula. 
 Instead of not having enough, substitute tlie equivalent 
 phrase, wanting more, and the seeming incorrectness is 
 removed. 
 
OF FALLACIES. 291 
 
 No one who wants more is rich ; 
 Every miser wants more ; 
 Therefore no miser is rich. 
 
 As has been shown in treating of Exponibles, the -Ex- 
 clusive proposition, " None but Whites are civilized," is 
 reaUy complex ; it contains one direct assertion, respecting 
 aU non-Whites, that they are not civilized, and one imphe.d 
 assertion, that some Whites are civilized. Then the follow- 
 ing syllogism is valid, though each of its three Judgments 
 appears to be negative. 
 
 None but Whites are civilized ; = No non-White is civilized ; 
 The Hindoos are not Whites ; = The Hindoos are non- Whites ; 
 The Hindoos are not civilized. 
 
 Two ludicrous instances, which have often been repeated 
 in the books, are enough to illustrate the Fallacy which 
 arises from a violation of the fifth Rule, though both of 
 them can be referred also to one of the other classes which 
 have been already considered. 
 
 Nothing is heavier -than platinum ; 
 Feathers are heavier than nothing ; 
 Therefore, feathers are heavier than platinum. 
 
 This sophism cannot puzzle even a beginner, and is of 
 the same character in the following. 
 
 No cat has two tails ; 
 
 Every cat has one tail more than no cat ; 
 
 Therefore, every cat has thi-ee tails. 
 
 ' The Fallacy plurium interrogationum, as it was called, 
 may be brought under this head by being referred to the 
 ambiguous construction of sentences. It is a mere trick, 
 which consists in asking two or more questions as if they 
 were one; then the respondent is entrapped whether he 
 answers in the Affirmative or the Negative, as either will 
 be inappropriate to one or the other of the two interroga- 
 tories. Of course, the Fallacy is solved by dividing the 
 
292 OF FALLACIES. 
 
 questions and answering them separately. The standard 
 illustration is asking a man " whether he has ceased beating 
 his father." Lawyers are often guilty of this sophism 
 while examining a witness in court, by insisting that he 
 shall give what they call " a categorical answer " ; — that 
 is, that he shall say either Yes or No. But to the question 
 as they propound it, either Yes or No will be a false 
 answer. A question often involves a real duplicity under 
 a seeming unity, as the uncertainty may regard, not the 
 meaning, but the extension, of the Terms employed ; and the 
 same ambiguity may lurk in a categorical proposition, or in 
 the answer to an interrogatory. The distinction between 
 Contraries and Contradictories, and the relation between 
 Sub-Contraries, must be kept in view. He who denies, 
 that all are lost, does not thereby deny that some, perhaps 
 many, even aU hut one, have perished. Some are not may 
 mean perhaps all are not, or some certainly are. To assert 
 or deny a particular motive for an action, is stiU to leave the 
 question undecided as to the concurrence of many motives, 
 and to say nothing about their comparative strength. 
 Most of our actions procfeed from a mixture of motives, 
 and the agent himself may not be able to say which was 
 the principal. Men easily deceive themselves in this 
 respect, as their memory, their vanity, or even their re- 
 morse, may mislead them ; and the mistake is especially 
 frequent when conscientious or religious motives are in 
 question. 
 
 Those who made it their business to invent logical puz- 
 zles, and to entrap an opponent in disputation, often secured 
 their Premises beforehand, by requiring their interlocutor 
 to answer a series of questions. Socrates was a great mas- 
 ter of this eristic art ; but though it may feirly and profita- 
 bly be employed in the communications of a teacher with 
 his pupils, a free use of it may reduce an opponent to silence 
 without convincing him. In Plato's Dialogues, Socrates 
 
OF FALLACIES. 293 
 
 often appears in no better light than a satirical disputant 
 qTiibbling about the meaning of words. The following 
 instance of the Fallacy plurium interrogationum, which 1 
 borrow from Fries, would not puzzle any one if it were not 
 stated in the form of questions and answers. 
 Is it not true that you must have lost that which you once had, 
 
 but which you have no longer ? Yes. 
 Did you not have ten counters when you commenced the game ? 
 
 Yes. 
 Have you ten counters now ? No. 
 Then you have lost ten counters. 
 
 But he still had eight, having lost only two; to deny 
 possession of the whole is not necessarily to deny that you 
 have a part. But if obliged to answer simply Yes or No, 
 the respondent could not avail himself of this distinction. 
 
 6 & 7. From Dr. Whately's convenient collection of 
 " examples for the exercise of learners," to which I have 
 been indebted for several of the preceding illustrations, I 
 borrow the following instances of violation of the Canons 
 of hypothetical reasoning. 
 
 If penal laws against Papists were enforced, they would be ag- 
 grieved ; 
 But they are not enforced ; 
 Therefore, the Papists are not aggrieved. 
 
 Though this argument was often gravely repeated in 
 Parliament, and elsewhere, during the debates on Cathohc 
 Emancipation, it is, of course, entirely invalid by the rules 
 of Logic ; for from denying the Antecedent in a Hypo- 
 thetical Judgment, no Conclusion follows, since the Conse- 
 quent may still be true from some other reason than the 
 one here specified. In this case, though the penal laws 
 were not enforced, the Catholics had a right to feel ag- 
 grieved that these laws should be permitted to remain in 
 the statute-book, as this was an insult to them personally, 
 and to their faith. 
 
294 OF FALLACIES. 
 
 We ought to give one day in seven to religious duties, if the 
 
 Fourth Commandment is obligatory on us ; 
 But we are bound to set apart one day in seven for religion ; 
 Therefore, the Fourth Commandment is obligatory on us. 
 
 The Canon here violated is, that from affirming the 
 Consequent no Conclusion can be drawn, since the Conse- 
 quent may have resulted from some other reason than that 
 specified in the Antecedent. A little "attempt is here made 
 to cloak the Fallacy, by inverting the natural position of 
 the Antecedent and the Consequent in the Major Premise. 
 
 We pass now to a consideration of those fallacious rea- 
 sonings which are correct in Form, since the Conclusion is 
 logically drawn, but are faulty in Matter, either from some 
 error or undue assumption in the Premises, or some mis- 
 take as to the point to which the argumentation ought to 
 be directed. An exhaustive classification of Material Fal- 
 lacies is not to be expected, as they are numerous and 
 varied in form, and derive their characteristics chiefly from 
 the particular Matter of the special sciences which first 
 suggested them. The only proper classes of them which 
 have been separately considered by logicians are those 
 which, ever since Aristotle's time, have been technically 
 designated as the petitio principii, the ignoratio elencM, and 
 the norircausa pro causa ; to which may be added several 
 miscellaneous sophisms of so puzzling a character that the 
 old logicians called them the Inexplicables. 
 
 1. The vulgar equivalent for petitio principii is legging 
 the question; and the common explanation of it is, that it 
 consists in assuming, in the course of the argument, the 
 very point which ought to be proved. Its most deceptive 
 application is what is called reasoning in a circle^ in which 
 Premises are first assumed, and subsequently proved" by 
 means of the very Conclusions which they had been used 
 to establish. This error is more difficult of detection in 
 proportion as the circle is more extended, or as more Syl- 
 
OF FALLACIES. 295 
 
 logisms are employed before the reasoner Comes round to 
 the very point that he started from. As Krug remarks, 
 " to the Circle there are properly required two probations, 
 which are so reciprocally related that the Antecedent in 
 the one is proved by its own Consequent in the other. 
 The proposition A is true because the proposition B is 
 true ; and the proposition B is true because the proposition 
 A is true. A Circle so palpable as this would, indeed, be 
 committed by no one. The vice is usually concealed by 
 the interpolation of intermediate propositions, or by a 
 change in the expression." "Thus," says Hamilton, "Pla^ 
 to, in his Phcedo, demonstrates the immortality of the soul 
 from its simplicity ; and, in the RepvMic, he demonstrates 
 its simphcity from its immortality." Theologians, also, 
 sometimes faU into this error, by first proving the authority 
 of the Church from the testimony of the Scriptures, and 
 then seeking to establish the authenticity of the Scriptures 
 by the testimony of the Church ; and the Fallacy escapes 
 notice, because one branch of it is found, perhaps, in a 
 polemic tract on Church government, and the other half in 
 a treatise on the Evidences. 
 
 Strictly speaking, aU valid reasoning proceeds ex con- 
 cessis. Two Premises must be assumed, or taken for 
 granted ; and these two, taken in conjunction, necessarily 
 involve the Conclusion. Thus much must be conceded to 
 those who claim that every Syllogism presupposes the truth 
 of what it is brought forward to establish. But then it is 
 presumed that there is no undue assumption ; — that the 
 two Premises, which we now posit, either have been al- 
 ready proved, or that they are universally admitted truths, 
 or that they have just been conceded, pro hac vice, by the 
 opponent. As Mr. Mansel remarks, " the petitio prindpii is 
 a material, not a formal Fallacy, and consists in assuming, 
 in demonstration, a non-axiomatic principle as axiomatic, 
 or in dialectic disputation, a non-probable principle as prob- 
 
296 OF FALLACIES. 
 
 able." It consists not in mere assumption, then, for that 
 is necessary, but in undue assumption. That branch of it 
 which is called reasoning in a circle is, from the nature of 
 the case, not a vice which can be committed in a single 
 Syllogism, but only in a series of Syllogisms constituting a 
 chain of proof. That which vitiates a single Syllogism is 
 reasoning from Premises, one, if not both, of which either 
 is in more need of proof than the very proposition which 
 we seek to prove by it, or it is that proposition itself 
 only veiled in other words, or it assumes two Terms to 
 be mere equivalents of each other, when they really have 
 not the same meaning. We must not reason like the 
 physician in Molidre, who accounts for opium producing 
 sleep by saying that it has a soporific virtue. The argu- 
 ment that locomotion is not an attribute of all animals, since 
 sponges cannot change their place, contains the undue as- 
 sumption that sponges are animals. Indeed, the Fallacy 
 in this case becomes obvious when the argument is expK- 
 cated into a regular Syllogism. And this is usually so in 
 what is popularly called begging the question ; the argument 
 is stated as an Enthymeme, and the suppressed Premise is 
 that which contains the undue assumption. 
 
 A petitio principii is involved in every case of reasoning 
 wliich depends upon an Imperfect Disjunction, though such 
 cases might also be properly referred to other kinds of 
 Fallacy. A Disjunction must be assumed to be perfect, or 
 the Dilemma which is founded upon it is obviously invahd. 
 Of this character is the famous sophism of Diodorus Cro- 
 nus, which professes to demonstrate the impossibility of 
 motion, and which has probably occasioned more discus- 
 sion than any other logical puzzle on record. It occupies 
 a high place among those which were formerly called the 
 Inexplicables. Dr. Whately seems tacitly to admit that it 
 is insoluble ; for, though he justly criticises an attempted 
 explanation of it by Aldrich, he proposes notliing to take 
 its place. The sophism may be thus stated. 
 
OF FALLACIES. 297 
 
 If motion is possible, a body must move either in the place where 
 
 it is, or in a place where it is not. 
 But a body cannot move in the place where it is ; and of course, 
 
 it cannot move where it is not. 
 Therefore, motion is impossible. 
 
 It is hazardous to differ froln Mr. Mansel upon any logi- 
 cal question ; but the solution of this sophism which he has 
 adopted and improved seems to me unsatisfactory. He 
 says, " The true solution is, that the disjunctive premise is 
 false. ' The place vfhere a body is,' is contradictory of 
 ' the place where a body is not ' ; as ' Englishmen ' is -con- 
 tradictory of ' not-Enghshmen ' ; but ' moving in the place 
 where it is,' is no more contradictory of ' moving in the 
 place where it is not,' than ' an army composed of English- 
 men ' is contradictory of ' an army composed of not-Eng- 
 lishmen.' As it would be felse to say, ' Every army must 
 be composed of Englishmen or not-Englishmen,' to the ex- 
 clusion of the third possibility of a mixed force, so it is 
 false to say, ' Every body must move in the place where 
 it is, or in the place where it is not,' to the exclusion of 
 the third possibility of moving partly in the one and partly 
 in the other. This solution is substantially given by 
 Hobbes." * 
 
 Hobbes even gives a diagram to prove that a body — 
 quantulumcunque sit, however small it may be — " cannot, 
 aU at once, so leave the whole of its former place that a 
 part of it shall not he in that portion which is common to 
 the two places, namely, the one which is left and the other 
 which is reached." But the difficulty cannot be thus 
 evaded. A part of a body cannot be in two places at once, 
 any more than the whole. For suppose that which moves 
 to be a mathematical point, as in the geometer's conception 
 of the generation of a line. Such a point, of course, being 
 indivisible, cannot be " partly in the one and partly in the 
 
 * Hansel's Notes to Aldridi, p. 144. 
 13* 
 
298 OF FALLACIES. 
 
 Other " place. A whole cannot move unless every point in 
 it moves also. Every individual must be, as Mr. Mansel 
 acknowledges, either an Englishman or a not-Englishman. 
 Reduce the army to a single soldier, and the difficulty of 
 moving him, according to this sophism, is still insuperable. 
 
 The following solution, I believe, has not before ap- 
 peared in print. The Major Premise of the sophism is not 
 true except with a proviso or limitation, which is improperly 
 suppressed ; so that the Fallacy may properly be referred 
 to the class a dido secundum quid ad dictum gimpliciter. 
 " A moving body, at any one indivisible moment, must be 
 either where it is, or where it is not." When the proviso 
 here italicized is expressed, the proposition is true, the 
 reasoning is sound, and the conclusion is correct. J5j any 
 one indivisible moment, motion is impossible ; for motion re- 
 quires time as well as . space. The Axiom of Excluded 
 Middle, that a thing must be, or not be,' in a certain place, 
 does apply to a body ; \mi it does not apply to a moving 
 body, and this is what covers up the Fallacy. For in order 
 to be moving, it must, at the second indivisible instant, be 
 where it was not at the first instant. . Hence, we do not 
 violate the Axiom when we deny the Major Premise as 
 originally stated ; for " a moving body " is that which has 
 been where it now is not. The difference of tense (time) 
 makes it possible for the same thipg to be and not to be. 
 The law of Excluded Middle itself, as we have seen, is true 
 only when the qualification at the same time is understood. 
 
 A solution which is substantially similar to the one here 
 given is proposed by Mr. De Morgan. Movement is 
 change, and so requires two places ; a body is not moved in 
 a place, hnt from one place to another. 
 
 2. Ignoratio elenchi is what we should now call answer- 
 ing to the wrong point. It is proving something which 
 does not really controvert your antagonist's position, though 
 it is assumed to do so. An Elenchus is a Syllogism which 
 
OF FALLACIES. 299 
 
 will confute the argument of your opponent ; and ignoratio 
 elenohi is ignorance of what wiU so confute him, — igno- 
 rance of the fact that your Conclusion, even if it were 
 established, would not contradict his Conclusion. This 
 error in reasoning is so common, that special' precautions 
 have, in some cases, been adopted in order to obviate it. 
 Thus, in Law, the only object of what is called special 
 pleading is, to ascertain the precise point at issue, or to 
 prevent irrelevancy of evidence and argument by binding 
 both parties in the suit to address themselves . to what is 
 really the sole point in controversy. A Dem/urrer has been 
 happily explained to be equivalent to the remark, " Well, 
 what of that?" .Even granting the facts stated in the 
 declaration to be true, it may be insisted that these facts 
 give the plaintiff no ground of action ; and hence, that it 
 was an ignoratio elenohi to state them at all. 
 
 As the Port Royal logicians remark, the, passions of men 
 afford the reason why this sophism is so common in con- 
 troversy. " We dispute with warmth, and often without 
 understanding one another. Passion or bad faith leads us 
 to attribute to our adversary that which is very far from 
 his meaning, in order to carry on the contest with greater 
 advantage; or to impute to him consequences which we 
 imagine may be derived from his doctrine, although he 
 disavows and denies them. All this may be reduced to 
 this kind of sophism, which an honest and good man ought 
 to avoid above all things." 
 
 Logicians have distinguished and described certain kinds 
 of argument which are valid, and may fairly enough be 
 used, provided that it is clearly seen and admitted that they 
 have no bearing upon the main question. The Fallacy 
 consists in referring such arguments to a wrong Conclusion, 
 in urging them as if they established the real point of con- 
 troversy, whereas they actually tend only to direct censure 
 or laughter against those who hold the opposite opinion, or 
 
300 OF FALLACIES. 
 
 to some other equally irrelevant object. Let the reasoning 
 which tends directly to prove the main point at issue he 
 called the argummMi/m ad rem. Then the argumenium ad 
 hominem is that which convicts your opponent of inconsis- 
 tency, ignorance, bad faith, or illogical reasoning. Any or 
 all these charges may be well founded, but they are aside 
 from the purpose ; for the doctrine which is in dispute may 
 be well founded, though its supporter is deficient in ah, the 
 quahties of a good reasoner. The argumerdum ad vere- 
 cundiam appeals to our reverence for some high authority, 
 or some venerable institution, as a means of silencing an 
 opponent, but not of convincing him that he is mistaken 
 in opinion. The argumentwm ad populum is a similar 
 appeal to the passions or prejudices of common people ; it 
 is a fair inference that proper arguments are wanting, when 
 such appeals are permitted. 
 
 To these must be added the argumentum ad ignorantiam, 
 which is asserting that your own position is correct, unless 
 your opponent can show some valid reason to the con- 
 trary. This mistake is often committed with reference to 
 alleged occurrences which appear to us strange and improb- 
 able, or which we may even believe to be impossible. The 
 Fallacy consists in denying that the thing is so, merely be- 
 cause we do not know how it is so. But if this reasoning 
 were correct, we ought to deny that the human will has 
 any control over a single movement of our animal organ- 
 ism, or even that the grass grows ; for, certainly, no one 
 can tell how a mere vohtion moves the arm, or how the 
 green herb in the spring-time absorbs inorganic matter and 
 assimilates it to itself. But our ignorance of one thing, the 
 modus operandi, is no disproof of a very different thing, the 
 opus operatum. The king of Siam was illogical in denying 
 that water could become ice, merely because, within his 
 experience, a liquid had never become solid. The incon- 
 ceivable is no sure indication of the impossible. Sir Wil- 
 
OF FALLACIES. 301 
 
 liam Hamilton even undertakes to show, that all which is 
 conceivable in thought lies between two extremes, both of 
 which are inconceivable, but of which, as they are contra- 
 dictories of each qther, one must be true. 
 
 But lest this exposition should seem to favor credulity 
 and superstition, it should be observed, that the paralogism 
 here exposed is usually met by a counter argument just as 
 untenable as the one which it is brought forward to con- 
 fute. Because neither I nor you know how a certain 
 phenomenon is produced, I am not justified in arbitrarily 
 assigning it to a certain cause, whether natural or super- 
 natural, and then calling upon you to accept this explana- 
 tion for want of a better. This also would be an appeal 
 to ignorance, — an attempt to found knowledge upon ig- 
 norance. To take an instance fi*om the reputed wonders 
 of animal magnetism ; — perhaps I do not know how the 
 table tips ; but you are not therefore to assume that spirits 
 from the other world are tipping it. It is an ignoratio 
 elenchi to argue, that your hypothesis must be well founded 
 because I aln not able to invent a better. Your business 
 is to support your own Conclusion by vahd reasoning, not 
 to rest it merely on my inabihty to prove the opposite. 
 
 This Fallacy pervades aU the speculations of those whom 
 Dr. Whewell calls the uniformitarian school of geologists. 
 They argue that the geological phenomena now visible, 
 many of which are of stupendous magnitude, can be ac- 
 counted for by the ordinary working of physical causes 
 now in operation, if we only assign a sufficient lapse of time 
 for the cumulation of their results. It is unnecessary, they 
 say, to suppose that there was any cataclasm, any violent 
 disruption of what is the usual course of nature in our own 
 days, in order to account for the elevation of vast mountain 
 chains, the sinking of continents, or the dislocation of strata 
 many mUes in thickness ; the same causes, which are now 
 altering the level of a continent at the rate of an inch in a 
 
302 OF FALLACIES. 
 
 century, can have piled up the Andes or the Himalayas, if 
 you give them time enough. Perhaps so ; and yet it may 
 be questioned which is the more violent supposition, the 
 sudden and irresistible outbreak of a power whose opera- 
 tions, at least on so grand a scale, have never since been 
 witnessed, or the undisturbed lapse of those countless mil- 
 lions of ages on which the imaginations of geologists love to 
 dwell. But this is not the real question. Their ignoratia 
 elenchi consists in multiplying proofs that slow-working 
 causes might have effected all these stupendous results; 
 and -then jumping at the Conclusion that these causes 
 did so produce them. They propound this Dilemma : — 
 Accept this solution of the problem, or propose a better 
 one. We may logically decline to do either. An ingeni- 
 ous mechanic, witnessing for the first time the uniform 
 motion of the hands over the dial-plate of a clock, if chal- 
 lenged to explain, without inspecting the works, how this 
 equable and long-continued motion could be produced, 
 might easily invent a combination of springs, wheels, and 
 pinions, which would be adequate .for the purpose ; but it 
 would be extravagant for him to assume that the machin- 
 ery thus invented by himself was an exact copy of the 
 works which he had not been allowed to examine. He 
 could only say, the results in question might he brought 
 about by my apparatus; but I cannot tell how they are 
 actually produced. Science does not rest on hypothesis, 
 and is not content with possible explanations of phenomena. 
 The well-known rule in controversy, that the burden of 
 proof rests on him who maintains the affirmative, because 
 it is difficult, or impossible, to prove a negative, rests on 
 the considerations here alleged. In order to prove a nega- 
 tive, it must be demonstrated that not one out of many 
 different contingencies admits the positive. Thus a survey 
 of the whole field is necessary, and the exclusion of the 
 opposite hypothesis from every point in it must be made 
 
OF FALLACIES. 803 
 
 certain. On the other hand, the proof of the positive is 
 established at a single point; no wide range of search is 
 requisite. To borrow an illustration, it is easy to demon- 
 strate that the book is in the room ; we have only to pro- 
 duce it. But to prove that it is not there, " it must be 
 made certain, first, that every book in the room has been 
 found and examined, secondly, that it has been correctly 
 examined. No one, in fact, can prove more than that he 
 cannot find the book ; whether the book be there or not, is 
 another question, to be settled by our opinion of the vigi- 
 lance and competency of the searcher." The geologists 
 say their opponents cannot find any proof that the ordinary 
 working of Nature's laws could vat, in an indefinite lapse 
 of years, produce the effects in question. What is that to 
 the purpose ? Our inability to find a needle in a hay-mow 
 is no proof that the needle is not there. 
 
 Indirectly, indeed, many negatives are established by a 
 single positive ; it is thus that an accused person in court 
 makes a triumphant defence by proving what the lawyers 
 call an alibi ; direct testimony that he was in Manchester, 
 on the night in question, is an indirect demonstration that 
 ?ie was not in any part of Birmingham, where the crime 
 must have been committed. Here, the testimony required 
 is positive in character, though it tends indirectly to a nega- 
 tive restrtt ; hence, it is easily obtained. Sometimes, in- 
 deed, when there are but few possible cases, so that the 
 field for search is very limited, we may be required to 
 prove a negative directly. This is the nature of the ge- 
 ometer's demonstration per impossibile, as it is called. Fail- 
 ing to obtain direct proof that the angle A is equal to the 
 angle B, we remember that only three suppositions are pos- 
 sible ; and then, by demonstrating that it cannot be either 
 greater or less, we indirectly prove that it must be equal. 
 In like manner, after it has been proved that the accused 
 person committed a homicide, it is a pregumptim in law 
 
304 OF FALLACIES. 
 
 that the act was done "with malice prepense"; in other 
 words, the law pats upon the accused the burden of proof 
 that he did not do it maliciously. But this seemingly harsh 
 presumption of law rests, as Mr. De Morgan remarks, upon 
 the fact, that there are so few alternatives to the supposi- 
 tion of wUful murder ; in order to disprove malice, the 
 accused is only required to make out either mishap, insan- 
 ity, or heat of blood. He is not put to hunting for a needle 
 in a hay-mow, under penalty of being hanged if he fails ; 
 but, out of four possible cases, he is obliged to disprove the 
 single fatal supposition by direct evidence that his case is 
 some one of the three others. 
 
 Most rhetorical artifices may be referred to the class of 
 the ignoratio elenchi. Thus, says Dr. Whately, " when 
 the occasion or object in question is not such as calls for, or 
 as is likely to excite in those particular readers or hearers, 
 the emotions required, it is a common rhetorical artifice to 
 turn their attention to some object which wiU call forth 
 these feelings ; and when they are too much excited to be 
 capable of judging calmly, it will not be difficult to turn 
 their passions, once roused, in the direction required, and 
 to make them view the case before them in a very different 
 light. When the metal is heated, it may easily be moulded 
 into the desired form. Thus, vehement indignation against 
 some crime may be directed against a person who has not 
 been proved guilty of it ; and vague declamations against 
 corruption, oppression, &c., or against the mischiefe of 
 anarchy, with high-flown panegyrics on Uberty, rights of 
 man, &c., or on social order, justice, the constitution, law, 
 religion, &c., will gradually lead the hearers to take for 
 granted, without proof, that the measure proposed will lead 
 to these evils, or to these advantages ; and it will in con- 
 sequence become the object of groundless abhorrence or 
 admiration." 
 
 Under this class of Fallacies also may be ranked the 
 
OF FALLACIES. 305 
 
 error of adopting an argument which proves either too little 
 or too much. In one of these cases, however, the error is 
 by no means so serious as in the other. The reasoning 
 which proves too little may be good as far as it goes ; it 
 conduces to the end in view, and, taken in conjunction 
 with another argument also partial in its effect, it may 
 establish the whole doctrine in question. But the argu- 
 ment which proves too much is invalid throughout ; JFalsus 
 in una, falsus in omnibus, is a sonnd logical maxim. If 
 any portion of the Conclusion is evidently false, the rea- 
 soning which led to it, considered in itself alone, must 
 be essentially and altogether vicious ; since from correct 
 premises, and by valid inference, no error whatever can 
 possibly be deduced. 
 
 When the main purpose is to disprove a particular doc- 
 trine, it is not enough to refiite one or more arguments 
 that have been alleged in its support ; this is merely con- 
 futing your opponent, and not the proposition which he 
 maintains, and which may be supported by better reasons 
 than he has been able to adduce. In like manner, to state 
 objections, though they may be perfectly valid ones, to a 
 specific plan of action, is insufficient to prove that this plan 
 ought to be rejected ; for it may well be that some action 
 is unavoidable, and yet that strong objections may be urged 
 against every mode of action that can be devised. When 
 the Necessitarian says that the doctrine of the freedom of 
 the human will is inconceivable. Sir William Hamilton 
 justly replies, that the argument proves too httle ; for it is 
 at least equally inconceivable that the will should rwt be 
 free. Unbelievers, says Dr. Whately, " may find numer- 
 ous objections against various parts of Scripture, to some 
 of which no satisfactory answer can be given ; and the 
 incautious hearer is apt, while his attention is fixed on 
 these, to forget that there are infinitely more and stronger 
 objections against the supposition that the Christian religion 
 
306 OF FALLACIES. 
 
 is of hwman origin ; and that, where we cannot answer all 
 objections, we are bound in reason and in candor to adopt 
 the hypothesis which labors under the least." 
 
 3. A full illustration of the Fallacy, non eauBa pro causa, 
 would carry us too far into the domain of the physical 
 sciences, and therefore would be more in place as a chapter 
 of Applied Logic. Only the more frequent and obvious 
 errors of this class can be noticed here. Prominent among 
 these are the common blunders of reasoning post hoc, ergo 
 propter hoc; of mistaking physical laws for efficient causes; 
 and of applying the doctrine of the Necessitarian or Fatalist 
 as a motive of action, or rather of inaction, in our ordinary 
 concerns. 
 
 An invariable antecedent is a sign, but often it is indis- 
 putably not a cause, of the phenomenon which it precedes. 
 As that which leads the mind to expect a certain event, it 
 may be regarded as a causa cognoscendi ; but this is very 
 different from the causa essendi, which is the ordinary sig- 
 nification of the word cause. Cicero states this distinction 
 very clearly : — Causa autem ea est qme id efficit cujus est 
 causa. Non sic causa intelligi debet, vi, quod cuigue ante- 
 cedat, id ei causa sit, sed quod cuique effi,cienter antecedat. 
 In this sense, deliberation is certainly not the cause of the 
 action which foUows it, nor is one beat of the pulse the 
 cause of the subsequent beats. In fact, two successive 
 states of the same substance are seldom regarded even by 
 the vulgar as cause and effect. But since we necessarily 
 think a cause as immediately preceding its effect, or as 
 simultaneous with it, the mind is prone, especially in tlie 
 case of obscure and anomalous phenomena, of which the 
 true cause cannot easily be discovered, to consider any an- 
 tecedent event as such a cause. This is the origin of the 
 belief in omens, and many other superstitions of the vulgar. 
 An accidental conjunction in time between some private 
 or public calamity, and the appearance of a meteor or a 
 
OF FALLACIES. 307 
 
 comet, or the occurrence of an earthquake, is regarded as 
 indicating a causal union of the two events. The science 
 of medicine, at least in that branch of it which is called 
 therapeutics, is little else than an apphcation of the maxim, 
 Post hoc, ergo propter hoc. The wisest physician cannot 
 tell, in any one case, whether the recovery of the patient 
 took place because he swallowed the drugs, or in spite of 
 them, or whether they were powerless in respect either to 
 good or evil. A harsh application of this fallacious rule 
 consists in judging the wisdom of a man's conduct by its 
 consequences, or the uprightness of his intentions by the 
 immediate results of his action upon the happiness or 
 misery of those around him. A brave and able com- 
 mander is not always successful in battle, and a consci- 
 entious and kind-hearted man may be compelled by a 
 sense of duty to inflict sufiering and death. Practical 
 men, as they are called, who profess to be guided only by 
 experience, and to rely upon facts instead of theories, are 
 especially liable to this class of errors. In their eyes, the 
 disorders and other evils which follow some long-delayed 
 reform are attributable to the reform itself, and not to its 
 undue postponement. 
 
 Forming an induction from too small a class of cases, 
 and disregarding negative instances, are the frequent 
 source of this confusion' between an antecedent phenome- 
 non and an efficient cause. The most common of all the 
 superstitions of the -vulgar, the belief that Friday is an 
 unlucky day for beginning any new enterprise, may be 
 traced to this origin. And it should not be forgotten, that 
 the prognostications of evil thus formed very often bring 
 about their own fulfilment ; fearful and dispirited men 
 can make little effectual effort to avert danger. The 
 belief in the hereditaiy transmission of diseases of mind 
 and body, at least in the unreasonable extent to which it 
 new prevails, is formed in this manner, and tends in this 
 
308 OF FALLACIES. 
 
 way to veiify itself. Gout and ' insanity run in families 
 where a perpetual apprehension of them exists, and where, 
 perchance, habits of life are actually transmitted from 
 father to son which are likely to induce and foster such 
 diseases. But even in these cases, a careftJ enumeration 
 might satisfy one that, of all who are within the unlucky 
 circle, at least as many escape the dreaded calamity as 
 those who suffer from it. Were it otherwise, indeed, the 
 circle would continue to enlarge itself in successive gener- 
 ations, till few could hope to escape the hereditary taint. 
 As Dr. Johnson remarks, the one prophetic dream which 
 comes to pass is remembered and spoken of, while the 
 ninety and nine which fail of accomplishment are for- 
 gotten. 
 
 " In minds not habituated to accurate thinking," says 
 Mr. Mill, " there is often a confiised notion that the gen- 
 eral laws are the causes of the partial ones ; that the law 
 of general gravitation, for example, causes the phenomenon 
 of the fall of bodies to the earth. But to assert this would 
 be a misuse of the word cause; terrestrial gravity is not 
 an effect of general gravitation, but a ca^e of it ; that is, 
 one kind of the particular instances in which that general 
 law obtains." A Law of Nature is only a general fact, or, 
 rather, a general statement comprehending under it many 
 similar individual facts. Hence, such a Law does not ac- 
 count for., or explain, the phenomena of Nature ; it only 
 describes them. Thus, it is not a Law of Hydrostatics 
 which causes water to remain at the same level in the two 
 arms of a bent tube ; but the fact that water stands at this 
 level is ranked among many other facts, which are com- 
 prehended imder the general statement called a Law of 
 Hydrostatics. 
 
 The process of Thought by which we pas's from a Phys- 
 ical Law to an individual case happening under it is one 
 of Deduction, and is therefore governed by the dictum de 
 
OF FALLACIES. 309 
 
 omni. Because all bodies tend to fall towards the common 
 centre of gravity, therefore this body thus tends to fall. 
 Hence, the statement of the Law is that which makes us 
 belike that ^e individual event will happen ; and this, by 
 a very natural confusion of Thought, is mistaken for the 
 cause which makes the event happen. But the relation in 
 the former case is that between Premises and Conclusion ; 
 in the latter, between Cause and Effect ; the former is a 
 law of Thought, the latter is a law of things ; the one is 
 the causa cognoscendi, the other, the causa essendi. 
 
 The Fallacy here exposed is one of much interest, as it 
 is that which lies at the bottom of every scheme of Materi- 
 alism, — every attempt to account for the origin of species, 
 and the general phenomena of the universe, without bring- 
 ing in any other agency than that of mere Physical Laws, 
 or what it was once the fashion to call " Second Causes." 
 Such a theory is not only insufficient, or unsupported by 
 the requisite evidence ; it is founded upon a mere confusion 
 of Thought, and is illogical and absurd. There is no such 
 thing as the agency or action of a Law ; except as a figure 
 of speech, we might as well predicate locomotion of an idea, 
 or speak of bilateral triangles. " Second Causes " are no 
 causes at all ; they are mere fictions of the intellect, and 
 exist only in Thought. A cause in the proper sense of the 
 word, that is, an efficient cause, as original and direct in its 
 action, must be a First cause ; that through which its ac- 
 tion is transmitted is not a cause, but a portion of the 
 effect, — as it does not act, but is acted upon. 
 
 The Ignava Ratio, or do-nothing argument, is a falla- 
 cious application of the Necessitarian theory. According 
 to this theory, all occurrences whatever have their environ- 
 ment of circumstances, with which they stand in neces- 
 sary and fixed relations by an absolute law ; and the state 
 of the universe at any one moment, in all its parts, from 
 the creation of a world to the stirring of an aspen-leaf, could 
 
310 OF FALLACIES. 
 
 not possibly have been different from what is. Every oc- 
 currence has its cause, of which it is the necessary result, 
 and to which it is necessarily proportioned, even in the 
 minutest respects. Every event, of course, js surroifhded 
 by other events, and must be considered as being at the 
 same time both antecedent and consequent, — as necessa- 
 rily resulting from those which preceded it, and neces- 
 sarily followed by those which come after it, — and thus 
 as forming one link in an adamantine chain which extends 
 from eternity to eternity. As Mr. Mill himself, an en- 
 lightened and consistent advocate of this theory, remarks, 
 " there is no Thing produced, no event happening, in the 
 known universe, which is not connected by a uniformity, 
 or invariable sequence, with some one or more of the 
 phenomena which preceded it ; insomuch that it will hap- 
 pen again as often as these phenomena occur again, and 
 as no other phenomenon having the character of a counter- 
 acting cause shall coexist. These antecedent phenomena, 
 again, were connected in a similar manner with some that 
 preceded them ; and so on, until we reach, as the ultimate 
 step attainable by us, either the properties of some one 
 primeval cause, or the conjunction of several. The state 
 of the whole universe at any instant we beheve to be the 
 consequent of its state at the previous iastant ; insomuch 
 that one who knew all the agents which exist at the pres- 
 ent moment, their collocation in space, and their properties, 
 — in other words, the laws of their agency, — could pre- 
 dict the whole subsequent history of the universe, at least 
 unless some new volition of a power capable of controlling 
 the universe should supervene."* 
 
 The conftitation of this astounding theory is the business 
 of the metaphysician or the theologian ; we have no con- 
 cern with it here, except to point out the Fallacy of re- 
 garding it as justifying inaction, or as, demonstrating the 
 
 • Mill's Ijogk, 3d ed.. Vol. I. p. 358. 
 
OF FALLACIES. 311 
 
 hopelessness of any endeavor on our part to control the 
 course of natural events. The Ignava Ratio is thus stated 
 by Cicero, in the form of an argument against taking any 
 measures for the restoration of one's health. 
 
 If it is fated that you shall recover from the present disease, then 
 you will recover whether you call in a physician or not. 
 If it is fated that you shall not recover, then, with or with- 
 out a physician, you will not recover. 
 
 But either the one or the other of these two contradictories is 
 fated. 
 
 Therefore, it will be of no use to call in a doctor. 
 
 As Cicero remarks, if this reasoning were correc,t, our 
 whole life would be reduced to a state of hopeless inactiv- 
 ity ; as it would prove the inutility of any endeavor to 
 bring about a desirable result, or to avert a threatened 
 calamity. The Turks, who are fatalists, so understand it, 
 and reduce it to practice by refusing to take any precau- 
 tions against a pestilence, or to remove a lighted match 
 from its dangerous proximity to a powder-magazine. But 
 they only show thereby that they are incapable of follow- 
 ing out correctly the logical consequences of their own doc- 
 trine. Calling in medical aid fiirnishes a new antecedent, 
 and thus presents a new case for the determination of Fate. 
 It may also be fated that I should send for a physician, and, 
 with his aid, that I should recover ; or it may be fated that 
 he should not be called in, and, as a consequence of this 
 neglect, and not as a necessary result of the disease alone, 
 that I should die. Fate is only a concurrence of causes 
 and an assemblage of conditions ; supply a new cause, take 
 away one of the necessary conditions, and the result will 
 be different, though it will still be a fated or necessary 
 result. Zeno aptly confuted this Fallacy, when he was 
 whipping a slave, who called out, in excuse for his fault, 
 that it was fated for him to steal ; " And so it is for me to 
 whip you," was the reply. 
 
312 OF FALLACIES. 
 
 Most of the sophisms once called Inexplicable have been 
 already resolved in treating of the different classes of Fal- 
 lacies to which they were respectively referred. It is only 
 necessary to consider here the famous argmnent, called the 
 Achilles, proposed by Zeno the Eleatic, as Mr. Mansel says, 
 " to support the leading tenet of Parmenides, of the unity 
 of all things, by showing that the identity of rest and mo- 
 tion is a necessary result from the contrary opinion." It 
 might more aptly be adduced to prove that extension is not 
 infinitely divisible, for if it were so, according to this argu- 
 ment, motion would be impossible. The sophism is thus 
 stated. 
 
 The swiftest runner can never overtake the slowest, if 
 the latter has ever so little the start. Suppose, for instance, 
 that Achilles runs ten times as fast as a tortoise, and that 
 the tortoise is one mUe in advance at the outset. While 
 Achnies is traversing this mile, the tortoise has advanced 
 -jlj^th of a mile farther ; before his pursuer has passed over 
 this j^th, the tortoise has advanced j^th, and then, again, 
 ■j-gViftli) ^nd so on forever, always being some fraction, 
 however small, of a mile in advance. 
 
 Dr. Whately seems to have been entirely puzzled by 
 this sophism, as he does not attempt a solution of it, but 
 merely remarks that it "furnishes a confirmation of the 
 utility of an acquaintance with the Syllogistic form, in 
 which form the pretended demonstration cannot possibly 
 be expressed." But this confession, as Mr. Mansel ob- 
 serves, " is in fact a surrender of the Syllogistic criterion, 
 as a means of discriminating between sound and unsound 
 reasoning. On the contrary, nothing is easier than to ex- 
 hibit the reasoning in a Syllogism, and to show thereby 
 that the fallacy does not lie in the Form, but the Matter. 
 Thus, representing the whole space to be traversed by a, 
 
 'Any space equal to — + j^ -f- y^, &c is infinite (being the 
 sum of an infinite series). 
 
OF FALLACIES. 313 
 
 'The space to be passed before Achilles overtakes the tortoise is 
 
 equal to this sum. 
 ' Therefore, it is infinite.' 
 
 " The whole logical mystery of this famous Fallacy lies 
 in this, that the major premise is false. The sum of an 
 infinite series may be, and in this case is, finite. This 
 premise is equally false, whether space is, or is not, divis- 
 ible ad injinitum.'" * 
 
 Fries remarks that the sophistry is here covered up by 
 the mode of stating the problem. The question really 
 asked is, when wiU Achilles have passed over the particular 
 extent of ground which the tortoise, at any one moment, has 
 already left behind him; and this question, on account of 
 the infinite divisibility of space and time, may be repeated 
 ad infinitum. The true question, at what point will Achil- 
 les overtake the tortoise, is not allowed to come into view. 
 The space between the two parties, however small, is, in 
 thought, though not in reality, infinitely divisible ; and the 
 series of constantly diminishing terms into which it is 
 mentally broken up, though infinite in number, is finite in 
 amount, the sum of the series being equal, of course, only 
 to the small space originally divided. Any finite quantity 
 may be broken up into an infinite number of terms, if these 
 terms become infinitely small. The confusion of thought 
 consists in mistaking the sum of the terms of such a de- 
 scending series, composed of infinitesimals, for the sum of 
 an infinite series the terms of which are not infinitely small. 
 It is only this latter sum which is necessarily an infinite 
 quantity. 
 
 * Hansel's Notes to AMrich, pp. 141, 142. 
 
 14 
 
814 APPLIED LOGIC. 
 
 CHAPTER X. 
 
 APPLIED LOGIC. 
 
 APPLIED Logic, as it will be here understood, includes 
 both what has usually been called the Doctrine of 
 Method, and what Sir William Hamilton terms Modified 
 Logic. Its object is the proper regulation of the Thinking 
 Faculty, not only in forming individual cognitions, but in 
 the more complex processes required for the construction 
 and advancement of Science. Pure Logic, as we have 
 seen, is concerned only with the Forms of Thought ; it 
 considers these as given, or already formed, and regards 
 only the necessary and fdndamental laws, emanating from 
 the mind itself, which have concurred in their formation 
 and which regulate their use. Applied Logic has regard 
 also to the Matter of Thought, — to the infinitely numer- 
 ous and diversified objects of cognition which Nature fur- 
 nishes us, — and considers by what general processes these 
 are brought within the grasp of mind, or are made intelli- 
 gible, or, what is the same thing, are put under the Forms 
 of Thought. The laws which govern these processes are 
 not universal and necessary, as in the former case, but are 
 contingent and varied, depending, in part, on the diverse 
 and multiform characteristics of the objects of cognition, 
 and, in part, on the powers and limitations of the human 
 mind itself. To avoid tlie vagueness and perplexity which 
 result from attempting to grasp too much, Applied Logic 
 treats directly only of the latter, — that is, of the fonnation 
 of Science so fiir as this depends on the nature of the human 
 
APPLIED LOGIC. 315 
 
 intellect, leaving to the special sciences the duty of adapt- 
 ing their own procedures to the nature of the pecuUar 
 objects of study with which they are immediately con- 
 cerned. 
 
 This division, however, like many others in Science, can- 
 not be always accurately preserved. The processes through 
 which the mind acts can be exemplified only in their appli- 
 cation to various classes of objects, and as varying some- 
 what with the nature of those objects. The practical dis- 
 tinction will be, that Applied Logic regards the pecuharities 
 of what we are thinking about only so far as these illustrate, 
 and in some measure direct, the processes of thinking. It 
 considers primarily how the mind acts, and only secondarily 
 what it is acting upon. 
 
 Science is a body of truths relating to any well-defined 
 object or class of objects, so arranged as to be easily com- 
 prehended and retained, and conveniently used. The mer- 
 its at which it aims are Completeness, Thoroughness, and 
 Method. Its objects are the numberless things which Na^ 
 ture fiimishes us for study. 
 
 What we call Nature is an assemblage of objects and a 
 succession of events. The mind, on account of the limita- 
 tion of its faculties, and the endless number and variety of 
 these obgects and events, cannot grasp and consider them 
 all at once. Neither can it undertake to study successively 
 each individual thing by itself ; for a lifetime might be so 
 spent, before we could obtain even a small fi-action of the 
 knowledge which is reqidsite for the proper guidance of life. 
 The first necessity, then, which is imposed upon us by the 
 constitution of the mind itself, is to break up the infinite 
 •wealth of Nature into groups and classes of things, with 
 reference to their resemblances and afiinities, and thus to 
 enlarge the grasp of our mental faculties, even at the ex- 
 pense of sacrificing the minuteness of information which 
 can be acquired only by studying objects in detail. The 
 
316 APPLIED LOGIC. 
 
 first efforts in the pursuit of knowledge, then, must be 
 directed to the business of Classification. Perhaps it will 
 be found in the sequel, that Classification is not only the 
 begmning, but the culmmation and the end, of human 
 knowledge. 
 
 We will first consider the mental processes through which 
 we gain a knowledge of real Objects, — that is, of Objects 
 which coexist in space, leaving for subsequent inquiry the 
 question, how far these processes must be modified in con- 
 structing a science of Events which succeed each other in 
 time. 
 
 It has already been remarked, that the beginning of all 
 knowledge is in single acts of the Perceptive or Acquisitive 
 Faculty, which operates either through the external senses, 
 thus constituting External Perception, or through that no- 
 tice which the mind takes of what is passing within itself, 
 this being denominated Consciousness, or Internal Percep- 
 tion. In either case, one indivisible act of the Perceptive 
 Faculty gives us to know only one phenomenon. A suc- 
 cession of such acts relating to one Object fiu:nishes a num- 
 ber of cognitions of the quahties or attributes of that Ob- 
 ject ; and these quahties we unite together, and bind up 
 into one whole, through the conception, which the mind 
 furnishes, of Substance, or that in which the qualities inhere. 
 Thus, suppose the Object presented is an apple ; the eye 
 tells me that it is red; the touch, that it is spherical and 
 moderately hard ; the muscular sense, that it has weight ; 
 the taste, that it is subacid, &c. ; and these qualities I unite 
 into one whole by the conception of one stibstance in which 
 they aU inhere, and call the aggregate tlius formed apple. 
 The reason why just these quahties, and no others, are 
 united into the whole is, that they all are, or may be, 
 received at one time, under the same circumstances, and 
 appear to proceed fi-om one Object, as they are referred by 
 me to one definite locality in space. 
 
APPLIED LOGIC. 31T 
 
 Take another instance from Internal Perception. I am 
 conscious, either at once or in succession, of joy or pain, of 
 a thought, reminiscence, or vohtion, of a sensation of hun- 
 ger, coldness, &c. ; and these separate Intuitions I put 
 together into one whole through the Intuition, which enters 
 into each of them, that they are rrnne, or that they all be- 
 long to the one person which I call ntyself. Here, the Intui- 
 tion of Self is the unifying principle, or that through which 
 the aggregation of majiy into one is accomplished, just as, 
 in the former case, it was the conception of Svhstance. 
 
 Manifestly, then, the first step towards the formation of 
 science is a Synthesis, a putting together of the Matter of 
 several Intuitions into that one whole which we call an 
 Individual Object. This Object itself, though called an In- 
 dividual, as if it were one thing, has in truth only a virtual 
 unity ; it is really complex, consisting of many parts and 
 many qualities, which were at first separately perceived ; 
 but having often been perceived together, or in combina- 
 tion, they become so firmly united that the perception of a 
 few, perhaps of only one, of its parts or qualities immedi- 
 ately calls up the imagination of all the others, that is, of 
 the whole. Thus, I am said to perceive the apple, when, 
 in fact, I perceive only its shape and color ; but this shape 
 and color immediately suggest all its other qualities, and 
 the complex Intuition thus formed, partly perceived and 
 partly imagined, is what is called, though improperly, 8 
 single perception of one thing. The wholes thus formed 
 are of all degrees of complexity, either having as many 
 parts, qualities, and uses as a house or an intricate machine, 
 or as few as a spot of purple cloud in the sky. They may 
 be either real or factitious, the conception and belief of 
 actual existence being one of the parts or elements of the 
 former, but not of the latter. Each of these wholes is, or 
 might be, designated by a Proper Name, belonging to this 
 one thing and to nothing else. 
 
B18 APPLIED LOGIC. 
 
 But as the number of such Objects and Names would be 
 endless, we seek, as has been said, to bring them within 
 the grasp of the mind by throwing them into groups and 
 classes. The first step of the process directed to this end 
 is the reverse of the former one ; we muSt now begin by- 
 Analysis. The many complex whales, called Indiyidual 
 Objects, which we have previously formed by a procedure 
 so easy and so frequently repeated that we are almost un- 
 conscious of it, must now be resolved into their constituent 
 parts and properties, in order that, by an abstraction of 
 their dissimilar elements and restrictmg the attention to 
 those which are similar, classes may be formed, all the 
 members of which have some like or equivalent attributes. 
 The process of Classification, then, is an Analysis immedi- 
 ately followed by a Synthesis into groups, this Synthesis 
 being directed by the Comparative or Elaborative Faculty 
 of the mind, the chief function of which is the perception 
 of relations, and especially the relations of likeness and 
 unlikeness. Having formed one set of classes, called the 
 Infimse Species, because they are composed of Individuals 
 only, we then proceed, in an exactly similar way, to group 
 these groups into Genera ; and so on, erecting a hierarchy 
 of Concepts, until we at least approximate a Summum 
 Genus, or that thought which embraces all conceivable 
 things. The highest generalization usually attempted is 
 ftiat which arranges all existence, whether actual or poten- 
 tial, under the three heads, Man, the Universe, and God 
 who is Absolute Being and Absolute Cause. 
 
 Evidently, then, the universal procedure of Science is 
 an Analysis followed by a Synthesis, the result of the 
 whole being a more or less complete Classification. All 
 the problems which Science has to solve may be reduced 
 to these two questions : What Classes ought to be formed ? 
 and. Does this or that Object possess the special attribute or 
 attributes which entitle it to be ranked under a certain 
 
APPLIED LOGIC. 319 
 
 Class ? Isolated cognitions — the knowledge, for instance, 
 that this particular attribute does, or does not, belong to 
 this particular thing — are not entitled to be called Sci- 
 ence, until they are arranged in some Class, or subsumed 
 under some comprehensive Law. 
 
 There is a confusion in the application of the terms Anal- 
 ysis and Synthesis, which may be best resolved by bor- 
 rowing a passage from Sir Wilham Hamilton. " It is 
 manifest, in general, from the meaning of the words, that 
 the term Analysis can only be applied to the separation of 
 a whole into its parts ; and that the term Synthesis can 
 only be applied to the collection of parts into a whole. So 
 far, no ambiguity is possible, — no room is left for abuse. 
 But there are different kinds of whole and parts ; some of 
 the wholes, Uke the whole of Comprehension (called also 
 the MetaphydcaT), and the whole of Extension (called also 
 the Logical), are in the inverse ratio of each other; so 
 that what in the one is a part, is necessarily in the other a 
 whole. It is evident, then, that the counter processes of 
 Analysis and Synthesis, as appUed to these counter wholes 
 and parts, should fall into one, or correspond ; inasmuch as 
 each in the one quantity should be diametrically opposite to 
 itself in the other. Thus, Analysis, as applied to Compre- 
 hension, is the reverse process of Analysis as applied to 
 Extension, but a corresponding process with Synthesis ; 
 and viae versa. Now, should it happen that the existence 
 and opposition of the two quantities are not considered, — 
 that men, viewing the whole of Extension or the whole of 
 Comprehension, each to the exclusion of the other, must 
 define Analysis and Synthesis with reference to that sin- 
 gle quantity which they exclusively take into account ; — 
 on this supposition, I say, it is manifest that, if different 
 philosophers regard different wholes or quantities, we may 
 have the terms Analysis and Synthesis absolutely used by 
 different philosophers in a contrary or reverse sense. And 
 
32Q APPLIED LOGIC. 
 
 this has actually happened. The ancients, in general, 
 looking only to the whole of Extension, use the terms 
 Analysis and Synthesis simply to denote a division of the 
 Genus into Species, — of the Species into Individuals ; the 
 moderns, on the other hand, in general, looking only at the 
 whole of Comprehension, employ these terms to express a 
 resolution of the Individual into its various attributes." 
 
 The words analytic and synthetic, Hamilton ftirther ob- 
 serves, "are, like most of our logical terms, taken from 
 Geometry " ; and the appUcations of them in this science 
 are thus admirably illustrated by Dr. W he well. In discur- 
 sive processes of reasoning, he remarks, " we obtain our 
 conclusions, not by looking at our conceptions steadily 
 in one view, which is intuition, but by passing from one 
 view to another, like those who run from place to place 
 (jdiscurms'). Thus, a straight line may be, at the same 
 time, a side of a triangle and a radius of a circle ; and in 
 the first proposition of Euclid, a line is considered first in 
 one of these relations, and then in the other, and thus the 
 sides of a certain triangle are proved to be equal. And by 
 this ' discourse of reason,' as by our older writers it was 
 termed, we set forth from those axioms which we perceive 
 by intuition, travel securely over a vast and varied region, 
 and become possessed of a copious store of mathematical 
 truths." In such geometrical reasoning, he continues, " we 
 introduce at every step some new consideration ; and it is 
 by combining all these considerations that we arrive at the 
 conclusion, that is, the demonstration of the proposition. 
 Each step tends to tlie final result, by exhibiting some part 
 of the figure under a new relation. To what we have 
 already proved, is added something more ; and hence this 
 process is called Synthesis, or putting together. The proof 
 flows on, receiving at every turn new contributions from 
 different quarters; hke a river fed and augmented by 
 many tributary streams. And each of these tributaries 
 
APPLIED LOGIC. 321 
 
 flows from some definition or axiom as its fountain, or is 
 itself formed by the union of smaller rivulets which have 
 sources of this kind. " In descending along its course, the 
 synthetical proof gathers all these accessions into one com- 
 mon trunk, the proposition finally proved. 
 
 " But we may proceed in a difierent manner. We may 
 begin from the formed river, and ascend to its sources. 
 We may take the proposition of which we require a proof, 
 and may examine what the supposition of its truth imphes. 
 If this be true, then something else may be seen to be 
 true ; and from this, something else, and so on. We may 
 often, in this way, discover of what simpler propositions our 
 theorem or solution is compounded, and may resolve these 
 in succession, till we come to some proposition which is 
 obvious. This is geometrical Analysis. Having succeeded 
 in this analytical process, we may invert it ; and may de- 
 scend again, from the limple and known propositions, to the 
 proof of a theorem, or the solution of a problem, which was 
 our starting-place." * 
 
 We have said that an Individual Object, as thought, is a 
 Synthesis of parts and attributes. But it is not an arbi- 
 trary Synthesis, — not a putting together of any elements 
 whatever, such as mere caprice may have induced us to 
 select. Imaginary Objects, it is true, may be thus bmlt up 
 at pleasure ; mere fancy may construct a centaur, a griffin, 
 or any other imaginative creation, recognizing it at the mo- 
 ment to be unreal. But if actual existence is one of the 
 elements of the combination, that is, ilP Ifoe Object thus 
 thought is understood to be a real Object, our conception of 
 it must be a Synthesis of such parts and properties only as 
 we know it actually possesses. Truth may be defined to 
 be the conformity of our mental representations to the 
 things which they are intended to represent ; and in Ap- 
 plied Logic, where we are concerned not only with the 
 
 * Philosophy of the Inductive Sciences, Vol. I. p. 144. * 
 
 14* • n 
 
322 APPLIED LOGIC. 
 
 Form, but with the Matter, of Thought, truth is the chief 
 object in view, — the first requisite of Science. The Syn- 
 thesis in thought is true only when' it corresponds to the 
 combination which exists in nature. 
 
 In like manner, the Classification which is to serve the 
 purposes of Science cannot be arbitrary. In the construc- 
 tion of Science, the first, and perhaps the most diificult, 
 question which we have to answer is, What classes ought 
 to be formed. " The power of framing classes," says Mr. 
 Mill, " is unlimited, as long as there is any (even the 
 smallest) diiference to found a distinction upon. Take 
 any attribute whatever, and if some things have it and 
 others have it not, we may groimd upon this attribute a 
 division of all things into two classes ; and we actually do 
 so, the moment we create a name which connotes the 
 attribute"; — as the class of white things, and that of 
 things not-white. " The number of possible classes, there- 
 fore, is boundless ; and there are as many actual classes 
 (either of real or imaginary things) as there are general 
 names, positive and negative together." 
 
 The relations and connections of the various attributes 
 with each other must guide us in selecting those upon 
 which the Classification is to be founded. The purpose of 
 the arrangement is, that all the individual objects included 
 in any one class shall have as many common or similar 
 elements as possible ; — that they shall resemble each other 
 in numerous and important respects. Now it is found that 
 certain attributed always carry along with them, or are 
 constantly found in company with, many other attributes ; 
 — not merely those which are necessarily thus connected 
 as derivative from them by necessary inference, but many 
 others, of which we can only say that nature always puts 
 them together. On the other hand, certain attributes 
 have no such regular companionship, but are found indif- 
 ferently in connection with entirely diflfei-ent sets of ele- 
 
APPLIED LOGIC. 323 
 
 ments. Among inorganic bodies, for example, the metallic 
 property is an instance of the former class ; among animals, 
 the possession of a vertebrated column or backbone. There 
 is good reason, then, for forming a, class of Metals, and a 
 class of Vertebrates, because we are- sure that each of these 
 classes will have many common properties, besides the sin- 
 gle one from which their name is derived. On the con- 
 trary, the same color or the same magnitude is not found in 
 constant companionship with many other qualities, so that 
 it would be comparatively useless to form a class of white 
 objects, or a class of animals three feet high. Such classes 
 would be found to include the most dissimilar and hetero- 
 geneous members. 
 
 It is evident even from these few examples, that the 
 quality selected as a principle of Classification is not usu- 
 ally an obvious or conspicuous trait. The casual observer 
 would generally think that it was small and insignificant. 
 Thus, the Botanist, disregarding the size, shape, and color 
 of trunk, branches, and leaves, founds an important classi- 
 fication of plants upon the minute and rudimentary cotyle- 
 dons, or seed-coverings. All the Monocotyledons are En- 
 dogens, and therefore have in common all the numerous 
 traits of that great tribe or family ; while the Dicotyledons 
 are all.Exogens. On the other hand, the number and 
 relative position of the stamens and pistils, on which Lin- 
 naeus founded his artificial system, are not found to be 
 invariably joined with any important features in the organ- 
 ization of the vegetable kingdom. It should be observed, 
 however, that classifications are framed for difierent uses ; 
 and the peculiar nature of the purpose in view may justify 
 an arrangement that would be otherwise indefensible. 
 Thus, the alphabetical order is the only convenient one for 
 a dictionary ; but only such classifications of words are 
 properly scientific as are found in Logic and Grammar. 
 
 In order to carry on the Classification, and erect a hie- 
 
B2A APPLIED LOGIC. 
 
 rarchy of Concepts of many ascending steps, it is absolutely 
 essential that the Infima Species, or class first formed, 
 should embrace only those individuals which have, at least, 
 several common attributes. There must be, at least, as 
 many of these attributes as wiU furnish a Specific Differ- 
 ence for each step iu the ascending scale. 
 
 Passing now. fi:om the science of coexistent objects to 
 that of events which succeed one another in time, we come 
 upon a totally different principle of connection. In the 
 former case, it was the Concept of substance ; in the pres- 
 ent one, it is that of causation. It belongs to Metaphysics 
 rather than to Logic to explain the peculiar nature of the 
 relation of Cause and Effect. Here it is enough to say, 
 that the connection between them is conceived to be abso- 
 lute or necessary ; where the Cause exists, the Efiect mu^ 
 follow, and the presence of the Effect is inconceivable un- 
 less the Cause immediately precedes it. But causation, as 
 well as substance, is incognizable through the perceptions of 
 sense. In the outward world, at least, we never can per- 
 ceive the n£xus, the bond of union which compels tlie Effect 
 to follow. We believe that it exists, and that the connec- 
 tion is a necessary one ; but we are compelled to infer its 
 existence from the invariableness of the sequence in time 
 between the two events. If heat is applied to wax, the 
 wax always melts ; if poison in sufficient quantity is taken 
 into the stomach, the man invariably dies. Hence we are 
 led to believe that the heat causes the melting, and the 
 poison causes the death ; or, in other words, that the sub- 
 sequent event is the necessary result of some power or force 
 in the antecedent, which, though it cannot be perceived by 
 us, inevitably produces this phenomenon. If heat be a true 
 Cause, the melting of the wax must follow ; but as fex as 
 our experience, and, if human testimony may be beUeved, 
 as far as all human experience has gone, the melting always 
 does follow; therefore, the heat is the Cause. On such 
 
APPLIED LOGIC. 825 
 
 reasoning as tliis, all our evidence of physical causation — 
 i. e. of Causation in the material universe — depends. But 
 it is obvious that the reasoning is illogical and the evidence 
 is insufficient. Human experience is limited; it extends 
 only to a certain number of cases, — no matter to how- 
 many, as the number is certainly finite. Any number of 
 instances of actual measurement ■would never satisfy the 
 geometer that the three angles of a triangle must equal two 
 right angles. It is conceivable — nay, the case has actu- 
 ally happened — that, after one himdred millions of favor- 
 able instances occurring in uninterrupted succession, the 
 hundred-miUion-and-first instance should be an exception, 
 or one of an opposite character. Mr. Babbage tells us that 
 his Calculating Machine may be so adjusted that, when put 
 in regular motion by the descent of a weight, it will pre- 
 sent to the eye successively the series of natural numbers, 
 1, 2, 3, 4, 5, &c. ; that, if we should have patience and time 
 to watch it long enough, we should find that it would 
 present this series in one unbroken chain fi:om 1 up to 
 100,000,000, each term exceeding its antecedent by unity. 
 Now an induction extending successively to 100,000,000 
 terms, without a single inconformable instance being dis- 
 covered, would be regarded by most persons as equivalent 
 to a demonstration that the law of the series was universal 
 or absolute. But in fact, the next number presented, 
 after 100,000,001, instead of being 100,000,002 would be 
 100,010,002, and the next term would be 100,030,003. 
 Human experience, then, as it is limited to a finite number 
 of cases, can never estabUsh an absolute law, or prove that 
 a certain result is necessary. As the very idea of Efficient 
 Causation involves that of the necessary consequence of the 
 Efiect, it follows that the range of human experience in 
 the material universe does not extend to the discovery of 
 Causes properly so called. 
 
 In all the Physical Sciences, then, causation should be 
 
826 APPLIED LOGIC. 
 
 understobd to mean only constant conjunction in time. We 
 cannot even declare that this conjunction - is absolutely 
 invariable ; all that can be said iSj that it has been invari- 
 able so far as human observation has extended, and we 
 may firmly believe that no instance will ever be found to 
 the contrary. But this is not a wecMSa^y belief ;. its con- 
 tradictory neither violates any Law of Thoughtj nor any of 
 the primitive and ineradicable laws of htunan belief. The 
 assumed invariability of what are called " the laws of na- 
 ture " rests upon no foundation whatever but uniform ex- 
 perience, and is absolutely certain, therefore, only to the 
 extent of that experience. That a Law of Nature may here- 
 after be violated, or be altogether changed, is not merely 
 conceivable; we say as much as that of any Judgment 
 which does not contradict one of the Axioms of Pure 
 Thought. Such a violation or change must be pronounced 
 to be possible, though not probable. Our only reason, for 
 instance, for believing that sugar always will be soluble in 
 water, and that powdered chalk, under the same circum- 
 stances, wiU always be insoluble, is, that, though a vast 
 number of experiments have been tried, we have not, as 
 yet, known or heard of one instance to the contrary. 
 
 But in the strict meaning of the word cause, — that is, 
 efficient cause, — what is called the Law of Causation is 
 absolute ; it is, in the strictest meaning of the term, impos- 
 sible that any event should take place without a true 
 Cause. I do not say that lihe contradictory of this Law 
 would violate any Axiom of Pure Thought ; for as we are 
 now concerned, not with the Form, but with the Matter, 
 of Thought, these Axioms are inapplicable. But it may 
 be said that the Law of Causation is held to be inviolable 
 by what I have here called " the primitive and ineradicable 
 laws of human belief." It is, for instance, just as impos- 
 sible for us to believe that an event should take place with- 
 out a Cause, as it is to believe that any particular space 
 
APPLIED LOGIC. 327 
 
 should be annihilated, or that what I am now conscious of 
 does not really exist as a mental phenomenon. He who 
 can believe that space has hmits or boundaries beyond 
 which there is no space, or that he himself does not exist 
 as a thinking being, may also beheve that a physical event 
 can take place without a Cause ; no sane person is capable 
 of crediting either of these propositions. 
 
 The distinction here established would seem to authorize 
 some change of the phraseology usually employed in Phys- 
 ical Science. What has hitherto been denominated, not 
 only by physicists, but by people generally, a cause, might 
 more properly be called a constant condition, of the phe- 
 nomenon. What the physical inquirer is really in search of, 
 when he is inquiring after what he calls the cause of any 
 event, is a constant antecedent of it, which, being discovered, 
 will ever afterwards enable him, should not the sequence 
 of antecedent and consequent be altered, (and of this he 
 justly entertains no fears whatever,) to predict the recur- 
 rence of the phenomenon. To him, the Law of Causa- 
 tion, to adopt Mr. J. S. Mill's language, means only this : 
 ^' For every event, there exists some combination of events, 
 some given concurrence of circumstances, positive and neg- 
 ative, the occurrence of which will always be followed by 
 that phenomenon." Under this view, the so-called Laws 
 of Nature might more properly be denominated General 
 Facts, as the word " law " generally implies what is abso- 
 lute or necessary. But as any sweeping change of scien- 
 tific phraseology is hardly to be expected, the language 
 heretofore in use must continue to be employed, though 
 under protest from those who understand the impropriety 
 of its application. There may be Laws of Nature which 
 are absolutely invariable ; but it is certain that none such 
 have been, or ever can be, discovered. Human science is 
 merely able to establish certain General Facts, which are 
 indisputably true only to the extent of our experience. 
 
328 APPLIED LOGIC. 
 
 We shall hereafter examine some of the reasons which 
 have caused a higher degree of certainty and generahly 
 to be attributed to these Facts than they actually deserve. 
 
 It is manifest from what has been said, that Science is 
 made up of two sorts of cognitions, — those in which the 
 objects are given as contingent phenomena, and those in 
 which the objects are given as necessary facts or laws. 
 The former are called empirical, as they are derived from 
 experience, and are true only to the extent of that experi- 
 ence. Their origin is also said to be a poBterwri, because 
 they are subsequent to experience. The latter are said to 
 be a priori in origin, for although first manifested on occa- 
 sion of experience, they are truly prior to it ; for if they 
 had not previously existed, as native to the mind and in- 
 wrought into its very constitution, experience itself would 
 not have been possible. We have already had examples 
 of such, in our notions of substance, cause, space, time, &c. 
 These may be expressed, as here, each by a single term 
 which is significant of one act of the mind, — an indivisible 
 Intuition or Thought ; or they may be resolved into one 
 or more Judgments, as statements of necessary laws. Thus, 
 the cognition of substance may be resolved into this Law, 
 that every real attribute or quality presupposes some sub- 
 stance in which it inheres. Cause, as already mentioned, 
 furnishes the universal and absolute Law of Causation, that 
 every physical event or change must have a cause. The In- 
 tuition of space yields many necessary Judgments, thus: 
 Every physical object must exist in space; Space is inde- 
 structible, even in Thought, as a whole, or in any of its parts; 
 Space is boundless; &c. The notion of Time also is re- 
 solved into several necessary laws, thus : Every event must 
 take place at some determinate point in time ; Time necessa- 
 rily flows on in one continuous lapse ; Time is boundless 
 both before and after, or, as the Schoolmen say, both a 
 parte ante and a parte post ; &c. 
 
APPLIED LOGIC. 32& 
 
 These necessary Laws must be regarded as mere ex- 
 plications of their respective a priori cognitions ; they are 
 not inferences from such cognitions, but are involved in 
 them, so that it is impossible, to have a fiill and adequate 
 conception of the one — that is, to fully understand the 
 meaning of the term — without the other. In neither 
 form, as one conception nor as a judgment, can they be de- 
 rived from experience ; for experience can only teU me of 
 what is true in certain cases, — namely, those cases which 
 I or other persons have actually witnessed ; while these 
 Laws are known to be absolutely true for all cases past, 
 present, and future. AH the maxims of experience are 
 reversible in thought; that is, I can conceive that their 
 opposites or contraries should be true ; — I can conceive, 
 for instance, that fire should not bum, that water should 
 not drown, that stones should fall upward? instead of down- 
 wards, that " when the brains were out, the man should 
 not die." But these necessary cognitions a priori are not 
 reversible in thought ; I cannot conceive that an attribute 
 should exist without a substance, or that space should be 
 annihilated, or have limits affixed to it, or that a physical 
 event should take place without a Cause. Moreover, as 
 has been said, these cognitions are prerequisites of experi- 
 ence, without which experience itself would not be possible. 
 As no body can exist without space, no quality without a 
 substance, I could not have my first experience of either, 
 — that is, I could not know body to be body, or quality to 
 be quality, — unless these cognitions were already present 
 to the mind, although then first drawn out and made dis- 
 tinct to consciousness. As the capacity of being exploded 
 must be conceived to exist in the gunpowder before the 
 actual explosion can take place, although this capacity was 
 latent up to that moment, so the cognition of space must 
 have been in the mind before we could have a conception 
 of body, and the cognition of time, before we could have 
 that of an event, since every event must be m time. 
 
3S0 APPLIED LOGIC. 
 
 And yet these cognitions are not, like the Axioms which 
 we formerly considered, mere Laws of thowgM ; for they are 
 necessarily apprehended as actual and immutahle Laws of 
 real -t^m^is. It is true, that tl(^ attribution of these Laws to 
 actual phenomena is an act of thought ; so is aU cognition, 
 whether of external events and things, or of abstract uni- 
 versal principles. Berkeley and other Idealists, then, who 
 hold that what we call external realities exist only in 
 the mind, may consistency maintain that these a priori 
 cognitions are merely necessities of thinking thus and so. 
 But the Realist, who believes in the objective validity of 
 our external perceptions, who holds that things are what 
 they seem to be, cannot consistently deny the objective 
 reahty of those Forms and Laws without which any external 
 existence would be impossible, — which are, in fact, neces- 
 sary conditions of the reality of such existence. Hence I 
 cannot but regard Kant's elaborate attempt to reduce these 
 cognitions to mere Laws of Thought as inconsistent with his 
 own doctrine. He affirms that we have no knowledge of 
 external realities, and are, therefore, incompetent to pro- 
 nounce whether they do, or do not, possess certain attri- 
 butes ; and yet he declares that " things in themselves " 
 have a real existence apart from our thoughts. He admits 
 the distinction between noumena and phenomena, between 
 things as they are and things as they appear, and asserts 
 the reality of the former, though they are wholly incogniza- 
 ble to our minds. But if they are absolutely incognizable, 
 how does he know that they do not exist under the Laws of 
 space, time, and Cause ; and if they are real, how can they 
 exist except under those Laws which are the conditions of 
 all reality ? To deny the objective validity of these Laws 
 is to contradict the primitive testimony of consciousness, 
 and to cut awaj'- the foundations of all philosophy, whether 
 dogmatic, critical, or sceptical, by impeaching the correct- 
 ness of those principles and arguments by which the sceptic 
 
APPLIED LOGIC. 331 
 
 himself attempts to show the reasonableness of his doubts. 
 I have no better and no other reason for affirming that two 
 straight lines cannot enclose a space, than for pronouncing 
 that space itself exists in some other manner than as a 
 mere law of the perceptive faculty. The doctrine of the 
 Idealists is at least intelligible ; for I can imagine the an- 
 nihilation or non-existence of objects in space ; but the 
 non-existence of space itself is literally unthinkable. It is 
 a mere paradox to assert the reaUty of the objects, whose 
 existence is contingent, and deny that of space, which 
 exists by necessity. And the argument is worse than the 
 doctrine which it is offered to support ; since the only rea- 
 son alleged for believing space and time to be imreal, is the 
 impossibihty of thinking that they are unreal. 
 
 In conformity with what has been said, it might seem 
 that the doctrine of the formation of Science would prop- 
 erly fall into two great divisions ; the one relating to the 
 acquisition of contingent knowledge by means of expe- 
 rience, and the other to the attainment of necessary 
 knowledge by the development and application of those 
 primitive truths which are revealed to us in the very con- 
 stitution of our minds. Andj in a certain sense, this divis- 
 ion exists. Geometry and Arithmetic, as the sciences of 
 continuous and discrete quantity, are apphed most directly, 
 and in their purest form, to the conceptions of space and 
 time, in which these two modes of quantity are most 
 clearly manifested, not being modified or confused by the 
 presence of other attributes. The lapse of time cannot be ' 
 conceived or expressed except by the idea of number, or 
 discrete quantity ; and the extent of space, in like manner, 
 is necessarily conceived as continuous quantity. And in 
 both cases, our conception of pure quantity is most distinct, 
 because there are so few other attributes of space and time 
 with which it might become confused. But these two 
 sciences are not restricted to the consideration of pure 
 
332 APPLIED LOGIC. 
 
 space and time, and do not exhaust our conceptions of 
 them. They relate to space and time only so far as 
 these are magnitudes, or things to be measured ; and they 
 relate to everything else, so far forth as any other thing is 
 susceptible of measurement. Mathematics itself is the 
 science of relative magnitude. Thus, Algebra, which is 
 the highest form of mathematical generalization, * is the 
 science of pure magnitude, or quantity in the abstract, and 
 thus includes both Geometry and- Arithmetic, since its 
 principles and formulas are alike and indiscriminately ap- 
 plicable both to space and time. Thus the expression for 
 the square of the sum of two quantities, (a + 6)^ ^c?-\- 
 2ah -\-}?, holds true alike for continuous and discrete 
 quantity, for space and time ; since it is equally an expres- 
 sion of the truth, that the square erected upon the sum of 
 two lines may always be resolved into two smaller squares 
 and two rectangles, corresponding to the formula ; and also 
 of that which is only another aspect of the same truth, 
 viz. that the arithmetical expression for the square of the 
 sum of two numbers may be resolved in precisely the same 
 manner. 
 
 It does not appear, then, that what are called the de- 
 monstrative sciences owe their attribute of logical certainty 
 to the peculiar nature of the subjects about which they are 
 conversant. It is not because space and time are at once 
 necessary conceptions of the intellect and immutable laws 
 of real things, that the mathematician is able to bmld tip 
 his vast fabric of pure truths, which are absolutely certain 
 and are independent of any verification by experience. 
 The science of pure quantity, which seems to me the only 
 proper definition of mathematics, is also the science of real 
 things, but so far only as these are affected by quantity 
 and thus subject to measurement, and so far only as this 
 measurement is executed with that ideal precision and 
 accuracy which are presupposed in every mathematical 
 
APPLIED LOGIC. 333 
 
 investigation. The necessary and a 'priori cognitions of 
 the human mind do not constitute a department of science 
 by themselves, but are interwoven with the empirical ele- 
 ments of our knowledge. Their office is not constitutive, 
 but regulative. They determine the limits of the under- 
 standing, prescribe its functions, and regulate its belief. 
 Whatever is apprehended under the relations of Quantity, 
 is subject to the immutable laws of Quantity. Whatever is 
 known as an event or change, is governed by the necessary 
 laws of Causality and Time. Attributes or qualities are 
 apprehended under the law of Substance, which determines 
 the mode of their existence. It is only by abstraction, or 
 disjoining in thought what cannot be separated in reality, 
 that a separate science can be created of necessary cog- 
 nitions a priori, as in that branch of Metaphysics which is 
 called Ontology. 
 
 Going back to the physicist's conception of Cause, that 
 is. Invariable Antecedence, we observe that the method of 
 distinguishing invariable sequences from accidental ones is 
 by analysis. Every event has many antecedents and a 
 crowd of concomitant circumstances. We seek to ascertain 
 which of these are necessary conditions of the phenomenon 
 by analyzing them ; that is, by trying the experiment over 
 again, leaving out each time one or more of the attendant 
 circumstances ; if the same result still follows, the circum- 
 stances thus left out are not the causes which we are in 
 seaVch of, but were only accidental concomitants, that did 
 not at all affect the issue. Proceeding in this manner, 
 step by step, we come at last to some of the original ante- 
 cedents, which being omitted, the event no longer takes 
 place. Then, in common parlance, we are said to have 
 discovered the cause of the phenomenon ; strictly speak- 
 ing, it is only, so far as we know, its invariable antecedent, 
 or a condition of its existence, — perhaps only a condition 
 of our knowing that it exists. The whole method is ten- 
 
334 APPLIED LOGIC. 
 
 tative, and is evidently exposed to error, as it is only an 
 application of that fallacious mode of reasoning which has 
 been exposed as the sophism pod hoc, ergo propter hoc. 
 Hence, the conclusion is not held to be established for the 
 purposes of science, until the experiment has been tried, or 
 the observation repeated, under every possible variety of 
 circumstances. But a large experience, especially if con- 
 firmed by some analogy between this phenomenon and 
 others that are known to follow similar antecedents, may 
 estabUsh the conclusion beyond all reasonable doubt. 
 
 As our knowledge of the phenomena of succession in- 
 creases, the Concepts which we form of individual objects 
 and classes of objects become larger and more complex. 
 Our conception of any corporeal thing must include not 
 only those obvious qualities, such as shape, color, specific 
 gravity, texture, &c., which it manifests on nearly aU 
 occasions, but the changes to which these are subject when 
 it is larought in contact with other substances under differ- 
 ent circumstances, and also those changes in other bodies 
 of which its presence may be a constant antecedent. 
 " The ideas," says John Locke, " that make up our com- 
 plex notions of corporeal substances are of these three 
 sorts. First, the ideas of the primary qualities of things, 
 which are discovered by our senses, and are in them even 
 when we perceive them not ; such are the bulk, figure, 
 number, situation, and motions of the parts of bodies, which 
 are really in them, whether we take notice of them or "no. 
 Secondly, the sensible secondary qualities, which, depend- 
 ing on these, are nothing but the powers those substances 
 have to produce several ideas in us by our senses ; which 
 ideas are not in the thmgs themselves, otherwise than as 
 anything is in its Cause. Thirdly, the aptness we consider 
 in any substance to give or receive such alterations of 
 primary qualities as that the substance so altered should 
 produce in us different ideas from what it did before ; these 
 
APPLIED LOGIC. 335 
 
 are called active and passive powers ; all which powers, so 
 far as we have any notice or notion of them, terminate 
 only in sensible simple ideas. For whatever alteration a 
 loadstone has the power to make in the minute particles of 
 iron, we should have no notion of any power it had at all 
 to operate on iron, did not its sensible motion discover it ; 
 and I doubt not but there are a thousand changes, that 
 bodies we daily handle have a power to cause in one 
 another, which we never suspect, because they never ap- 
 pear in sensible effects." 
 
 " Powers therefore justly make a great part of our com- 
 plex ideas of substances. He that will examine his com- 
 plex idea of gold, will find several of its ideas that make it 
 up to be only powers ; as the power of being melted, but 
 of not spending itself in the fire, of being dissolved in aqua 
 regia, are ideas as necessary to make up our complex idea 
 of gold, as its color and weight ; which, if duly considered, 
 are also nothing but different powers. For to speak truly, 
 yellowness is not actually in gold, but is a power in gold 
 to produce that idea in us by our eyes, when placed in a 
 due light ; and the heat which we cannot leave out of our 
 idea of the sun is no more really in the sun, than the 
 -white color it introduces into wax. These are both equally 
 powers in the sun, operating, by the motion and figure of 
 its sensible parts, so on a man, as to make him have the 
 idea of heat, and so on wax, as to make it capable to pro- 
 duce in a man the idea of white." * 
 
 A fourth class of the elements that form our Concepts of 
 individual objects consists of the Relations in which these 
 objects stand to other things. These, of course, are num- 
 berless, and therefore are a great source of the indistinctness 
 and imperfection of this sort of knowledge. Every object 
 may be compared with every other object in nature, and 
 with every Concept which the mind has previously formed ; 
 
 • Essay on Buman Understanding, Book n. Chap. 23, §§ 9 and 10. 
 
336 APPLIED LOGIC. 
 
 and of the countless Relations thus brought to our notice, 
 many are essential to an adequate knowledge of the related 
 object. Most of Aristotle's Categories are an imperfect 
 attempt to classify these Relations, and place them under 
 their summa genera. Some of them, such as those of 
 Quantitj', Place, and Time, are definite and admit of accu- 
 rate determination ; as such, they are the objects of the 
 Exact Sciences. Others, like those of Quality, Posture, 
 and Modes of Being, Doing, and Suffering, are wholly 
 indeterminate, at least in this respect, that their various 
 sorts and degrees are shaded into each other imperceptibly, 
 or without any natural lines of demarcation. These, of 
 course, can be grouped into classes only in some rough 
 and arbitrary way, the divisions not being marked out by 
 nature. As our knowledge of them is thus vague and 
 incomplete, our conclusions or inferences concerning them 
 must be uncertain, and the Sciences under which they fidl 
 may be said to be occupied with Contingent Matter. 
 
 In Applied Logic, the test of the adequacy of a Concept 
 is its more or less complete enumeration of the essential 
 qualities of the real thing, or class of things, which it de- 
 notes^. Any attempt to ascertain and enumerate all of 
 these empirically, or by successive observations and experi- 
 ments, is hopeless ; a lifetime would not suffice to accumu- 
 late more than a small fraction of such knowledge of a 
 single object. Thus, its active and passive powers, as 
 they are termed, or, more properly, the fixed Relations of 
 antecedence and consequence which subsist between the 
 changes affecting it and those affecting all other substances, 
 could be ascertained only by placing it in juxtaposition with 
 every other thing singly, and with every conceivable com- 
 bination of other things. Apply heat or water to some one 
 substance taken separately, and only two or three series of 
 changes would be observed, such as its greater or less fusi- 
 bility, solubility, absorption of heat or fluid, capability of 
 
APPLIED LOGIC. 337 
 
 being oxidized, &c. But apply the same agents to it in 
 combination with one or more other substances, and series 
 of very different phenomena may be manifested. By rea- 
 son of the endless number and variety of such possible 
 observations and experiments, the results of them in a vast 
 majority of cases being individual truths of no special inter- 
 est or importance, no one can think of engaging in them by 
 detail, or with a view of exhausting the round of possible 
 inquiry and trial ; and hence our knowledge must always 
 fall infinitely short of the truth of things. The most im^ 
 portant single facts of this character now known to man 
 were accidentally discovered ; they are the fruits, not of 
 study and research, but of mere chance. Hence we sel- 
 dom know the history of such discoveries, or the person 
 who made them. Centuries after the attractive power of 
 magnetic iron had been known, some one, we know not 
 who, happened to observe its polarity, or quality of point- 
 ing constantly to the north ; and the result was the inven- 
 tion of the mariner's compass. The ancients were familiar 
 with the obvious quaUties of nitre, sulphur, and charcoal ; 
 but some obscure alchemist, some time in the fourteenth 
 century, happened to mix them together in the right pro- 
 portions, and the explosion which enliied taught the world 
 the secret of gunpowder. The art of printing was hit 
 upon by a similar lucky chance. Yet " these three tilings," 
 says Lord Bacon, " to wit. Printing, Gunpowder, and the 
 Mariner's Compass, have changed the whole face and state 
 of things throughout the world ; the first in Uterature, the 
 second in warfare, the third in navigation ; whence have 
 followed innumerable changes ; insomuch that no empire, 
 no sect, no star, seems to have exerted greater power and 
 influence in human affairs than these mechanical discov- 
 eries." 
 
 But as much the greater number of casual observations 
 of individual things reveal only unimportant relations and 
 
 15 V 
 
338 APPLIED LOGIC. 
 
 sqiualities, thei-e is no encouragement to pursue and record 
 them methodically, in the hope of hitting at last upon 
 some one of interest and value. Yet Lord Bacon, misled 
 by a few brilliant examples, such as those just cited, seems 
 to have required, as the first step towards carrying out his 
 new system of inductive research, a "Natural and Experi- 
 mental History, sufficient and good, as the foundation of 
 all." This " History " was to be a comiplete record of 
 individual observations and experiments, omitting nothing 
 on account of its seeming triviality and obviousness, to be 
 subsequently digested into " Tables and Arrangements of 
 Instances, in such method and order that the understand- 
 ing may be able to deal with them." * Upon this vast 
 store of crude material, towards furnishing which he him- 
 self made a respectable beginning in his Ehtoria Naturalis 
 et Experkmntalis ad eondendam Philosophiam, and his iSh/l- 
 va Si/lvarum, or a Natural History, all the subsequent pro- 
 cesses of his Inductive Method were to be expended. 
 " Since there is so great a number and army of particu- 
 lars," he observes, " and that army so scattered and dis- 
 persed as to distract and confound the understanding, little 
 is to be hoped for from the skirmishings and slight attacks 
 and desultory movements of the intellect, imless aU the 
 particulars which pertain to the subject of inquiiy shall, 
 by means of Tables of Discovery, apt, well arranged, and 
 as it were animate, be drawn up and marshalled ; and the 
 mind be set to work upon the helps duly prepared and 
 digested whicli these Tables supply." f 
 
 Bacon failed to observe that the minds of all men natu- 
 rally and inevitably proceed in great part by this method, as 
 is evinced by the construction of language. As we have 
 «een, all words properly so called are only the Grenei-al 
 Names of the groups and classes into which we marshal 
 and digest our individual observations; — yet with this 
 
 * Nomm Orgamm, Book II. Aph. x. f Id. Book I. Aph. <rfi. 
 
APPLIED LOGIC. 339 
 
 improvement upon the system that Bacon recommends, 
 that the Concepts thus framed include only the original 
 and essential attributes, the others being left out as of no 
 account, and needlessly burdening the memory by their 
 vast number. If experiment or casual observation should 
 hereafter determine that one of these omitted elements is 
 really of interest and importance, it ■will then henceforward 
 constitute an integral part of the Concept. Every one's 
 notion of the maffnet now includes its attribute oi polarity. 
 
 Derivative attributes, it has been mentioned, are not 
 expressly included in the Intension of a Concept, because 
 they are implied and virtually contained in their primaries. 
 Thus, the numberless properties of every geometric figure 
 are reduced, in the Concept which bears the Name of that 
 figure, to the two or three qualities, constituting its Defini- 
 tion, from which they may all be derived by necessary infer- 
 ence a priori, or without the aid ;of actual observation and 
 experiment. Down 'to the time of the Baconian reform in 
 the processes of physical science, it seems to have been 
 imagined that individual substances or bodies, like geo- 
 metric figures, had each its one or two essential properties, 
 which being known, all the others could be imunediately 
 deduced from them by a purely logical process, without 
 any aid from experience. This, in fact, was the meaning of 
 the word essence, that internal constitution of a body which 
 makes it what it is, or from which all its attributes neces- 
 sarily flow. Change the essence of the body, then, and you 
 thereby change all its properties. To the eye of Omni- 
 science, doubtless, there is such an essence ; but it must 
 ever remain unknown to man's finite capacities, on account 
 of the endless number of unknown attributes with which 
 it is intermingled. Those qualities alone appear to us 
 essential which are known to be constantly associated with 
 a few others, either because these others can be deduced 
 from them by necessary inference, or because they have 
 
340 APPLIED LOGIC. 
 
 always been found together in a large experience. In the 
 latter case, of course, the conclusion is contingent or un- 
 certain, being necessarily true only to the extent of our 
 previous observation. In the former case, the conclusion 
 is absolute, if, by the hypothesis, aU other qualities are 
 excluded from the Concept except those which are cer- 
 tainly known. In geometry, for instance, the Concept or 
 definition of any solid body includes only its shape and 
 magnitude, and supposes that these are accurately deter- 
 mined; abstraction is made of all its other qualities, be- 
 cause these are not susceptible of perfect determination, 
 and we know only from experience how far they associated 
 with each other. 
 
 If the Matter of Thought, then, includes real existences, 
 or such objects and events as are actually presented to us 
 in nature, our conclusions respecting them, being derived 
 only from experience, must always be subject to doubt. 
 As we know them only imperfectly, our inferences respect- 
 ing them can never be logically certain. But if the Con- 
 cepts are limited to imaginary objects, consisting only of a 
 few perfectly determinate qualities, our conclusions respect- 
 ing them will be absolute, though they will be applicable 
 only in the realm of pure abstractions. Bacon was right, 
 then, in maintaining that the Physical Sciences, so far as 
 they extend to the knowledge of real objects, are dependent 
 solely upon observation and experiment. " Man, being 
 the servant and interpreter of Nature, can do and under- 
 stand so much only as he has observed, either in fact or in 
 thought, of the course of Nature ; beyond this, he cannot 
 understand or do anything." 
 
 We can now see what are the preliminary classifications 
 upon the formation of which all Science depends, and can 
 point out the principles which regulate this formation. 
 
 1. We form closes of real things or Natural Objects, 
 arranging them according to the similarity of their attri- 
 
APPLIED LOGIC. 841 
 
 butes, and selecting by preference, as the basis of the clas- 
 sification, those qualities which are invariably found con- 
 joined with the greatest number of other uniform qualities ; 
 as the presence of one of these constant elements enables 
 us to infer, in anticipation of experience, that it wiU be 
 found in conjunction with those others. The science of 
 Natural History, in its various departments, consists exclu- 
 sively of such classifications, together with such descriptions 
 and definitions as are subsidiary to them. 
 
 2. We classify the qualities themselves, according to 
 their similarities, irrespective of the real objects in which 
 they inhere. Thus, we form classes of colors, sounds, 
 shape, and dimension, degrees of consistency, specific grav- 
 ity, &c. Sometimes a single set of these arrangements is 
 found important enough to be made the basis of a distinct 
 science, as in the case of Acoustics and Optics ; more fre- 
 quently, several sets of them are grouped together for 
 scientific consideration, as is the case with the chemical 
 quaUties of substances. 
 
 3. We classify events according to the uniformity of 
 their succession in time. These, if regarded as mere se- 
 quences of phenomena, may be referred to the subsequent 
 head of Relations ; if regarded as the active or passive 
 powers of bodies, they may be placed under the preceding 
 head of Qualities. A constant order of succession is often 
 erroneously supposed to be a necessary sequence, because 
 the mind superadds in such cases its pure conception of the 
 necessary relations of Cause andEfiect; and hence sciences 
 based upon such classifications are improperly termed 
 sciences of causation. Several departments of Physics, 
 such as the sciences of Mechanics and Hydrostatics, and 
 some divisions of the moral sciences, such as Pohtics and 
 Civil History, are made up chiefly of classifications of this 
 sort. • 
 
 4. We classify the relations of things, irrespective of the 
 
342 APPLIED LOGIC. 
 
 other Qualities and differences'of the things related. Thus, 
 Geography is, in the main, a classification of the Relation* 
 of the dififerent portions of the earth's surface to each other ; 
 Astronomy takes a simOar view of the Relations between 
 the different members of the sokr and stellar systems. A 
 large portion of the sciences of Law and Politics has regard 
 to the different Relations which subsist between human 
 beings, such as those of husband and wife, parent and 
 child, rulers and subjects, countrymen and aliens, &c. 
 The mind takes special cognizance only of a very few of 
 the countless Relations which comparison and reflection 
 bring to light. We select those only which happen' to be 
 of special interest to us, through the guidance which they 
 afford for our future conduct, the wonder and curiosity 
 which they excite, or the bearing which they may have in 
 any way upon our welfare. 
 
 It is not meant that each one of the Classes and Sciences 
 which we fonn consists exclusively of one or the other of 
 the four species here enumerated. Indeed, the division 
 itself is a very imperfect one, for the Dividing Members, 
 as we have intimated, do not exclude each other ; a Ccm- 
 cept of Real Things includes a view of their Qualities, their 
 active and passive Powers, and their Relations ; and the 
 two latter may be comprised under the name of Qualities. 
 But these four, sometimes separately and sometimes in 
 combination, are the elements which we group together 
 into classes, out of which those higher classes, or hierar- 
 chies of Concepts, which we call Sciences, are subsequently 
 erected. In every case, the classifying principle is simi- 
 larity, or unifonnity of succession, those Objects and QuaU- 
 ties being united which resemble each other in certain 
 respects, and those events being reduced to the same head 
 which uniformly foUow one another under amilar circum- 
 stances. The educatioii of every human being consists in 
 the gradual acquisition of a large stock of these elementary 
 
APPLIED LOGIC. 343 
 
 Concepts, whicli axe taught to him in learning the use of 
 his mother-toHtgue, while exercising at the same time his 
 powers of observation and reflection. 
 
 The advancement of Science depends on the success of 
 the attempts which man is constantly making to enlarge 
 and improve the classifications which are the bases of these 
 Concepts. By detecting hitherto- unobserved simUaritiea 
 and conjunctions in time, we extend the generalizations 
 and reduce the ntmiber of classes^ thereby bringing the 
 infinitude of objects and events which nature offers us 
 more nearly within the grasp of thc' human intellect. 
 Sometimes the principle itself or the Ground of Division, 
 which determines the classification of a whole set of phe- 
 nomena, is altered ; as we find a greater number of the 
 attributes of these phenomena to be in constant companion- 
 ship with some one or more traits hitherto disregarded as 
 of Httle account, a differently constituted hierarchy of Con- 
 cepts, founded upon these traits, is adopted. This may be 
 called an improvement in the Meliod, rather than an 
 actual enlargement of the domain, of Science. Thus the 
 Natural System was substituted for the Linnsean classifica- 
 tion of plants, and an improvement almost equally exten- 
 sive was made by Cuvier in the arrangement of the ani- 
 mal kingdom. But most of the questions and problems 
 which Science encounters in its progress relate to suc- 
 cessive improvements and extensions of the classification 
 which, in all its main features, was long since farmed, and 
 not to the substitution of an entirely different one in its 
 place. The fixedness of language, which stereotypes, as it 
 were, the names and phraseology appropriated to the old 
 division, is a great obstacle to the introduction of a new 
 one, which would require a new set of words. The prin- 
 cipal object of the researches of Science is to determine 
 whether this or that object, or class of objects, has the 
 special characteristics which entitle it to be placed in a 
 
344 APPLIED LOGIC. 
 
 certain class, and therefore to be called by the name of 
 that class. For instance : — Is the lightning to be placed 
 in the class of electrical phenomena? Can the revolution 
 of the planets be reduced to the phenomena of falling 
 bodies ? Is light the undulatory movement of an ether ? 
 Are the processes of digestion and assimilation reducible 
 to the ordinary action of chemical affinities ? Ought the 
 relation of a motive to a volition to be classed with the 
 relations of cause and effect, or with those of mere ante- 
 cedence and consequence ? 
 
 Such questions relate, for the most part, not to some one 
 object or event, but to whole classes of phenomena, and 
 therefore presuppose a classification already formed. Some- 
 times, indeed, one particular phenomenon of an anomalous 
 character may now be obsei-ved for the first time; and 
 then the purpose of the inquiry is, to refer it to its proper 
 class, and call it by its right name. But such inquiries be- 
 long usually to the education of a child, who has not yet 
 acquired the amount of knowledge long since possessed by 
 his elders, and embodied by them in language through the 
 appropriation of names to the different Concepts. But 
 Science advances almost exclusively by the resolution of 
 problems which concern whole classes of objects, and a 
 single phenomenon is observed and experimented upon 
 only as a typical specimen of its class, and therefore, as 
 leading to conclusions which affect all that are called by 
 the same name. Thus, Ftankhn experimented with his 
 kite upon a particular thunder-cloud, but only because this 
 one represented to his mind the whole class of meteoro- 
 logical phenomena whose characteristics he was investi- 
 gating. This, indeed, is the difference between the intel- 
 lect of a common man and that of a philosopher. The 
 latter flies at once to generalities ; the former wonders at 
 the individual case, and seldom goes beyond it. 
 
 " From the moment an isolated fact is discovered," says 
 
APPLIED LOGIC. 345 
 
 Hamilton, " we endeavor to refer it to other facts which it 
 resembles. Until this be accomplished, we do not view it 
 as understood. This is the case, for example, with sulphur,, 
 which, in a certain degree of temperature, melts like other 
 bodies ; but at a higher degree of heat, instead of evapo- 
 rating, again consolidates." Another example may be 
 taken from the General Fact, which some will call a Law 
 of Nature, that all bodies give out heat on passing from a 
 gaseous to a liquid, or from a Hquid to a solid, state ; in 
 other words, that contraction of bulk is attended or occa- 
 sioned by loss of heat, and expansion of bulk by addition 
 or absorption of heat. Yet clay is known to contract from 
 the application of heat ; and though water contracts in btdk 
 when it is cooling down to as low a temperature as 40°, yet 
 as it falls below that point it expands again, and in the 
 act of congelation there is a sudden and considerable in- 
 crease of bulk. Our natural love of unity, or disposition 
 to reduce corresponding phenomena to one class or Law, 
 does not allow us to rest in the consideration that such 
 cases are anomalous, or isolated exceptions. We seek 
 either for a new expression of the Law, which shall cover 
 also these apparent exceptions, or for the discovery of 
 some attribute of these now isolated cases which shall 
 harmonize them with the Law as already expressed. When 
 the facts are thus generalized, or brought together under 
 one Concept and name, " our discontent is quieted," Ham- 
 ilton continues, " and we consider the generality itself as 
 tantamount to an explanation. Why does this apple fall 
 to the ground ? Because all bodies gravitate towards each 
 other. Arrived at this General Fact, we inquire no more, 
 although ignorant now, as previously, of the cause of gravi- 
 tation ; for gravitation is nothing more than a name for a 
 General Fact, the why of which we know not. A mystery, 
 if recognized as universal, would no longer appear myste- 
 rious." 
 
 15* 
 
346 APPLIED LOGIC. 
 
 We now see how it is that the successive discoveries, 
 and consequent enlarged and improved generalizations, of 
 Science are embodied, as fest as they are made, in lan- 
 guage, so that we learn them through the simple mode of 
 gradually acquiring the use of our mother tongue. This is 
 done to some extent by the actual introduction of new 
 words and names, these being necessary to designate the 
 new groups and Concepts which the improved classification 
 requires. But it is effected stUl more largely by modifying 
 and enlarging the connotation of words already in use. 
 For a time, these new elements of phraseology are in cur- 
 rent use only among a small circle of scientific inquirers, 
 whose labors have made them necessary. But gradually 
 they creep out into the ordinary dialect of the market, the 
 parlor, and the newspaper, and are naturaUzed there, and 
 taught to. children as fast as children learn to speak. How 
 much more knowledge is -now necessarily acquired in learn- 
 ing the use of the English language, than was gained from 
 such learning only one or two centuries ago I 
 
 The same considerations of interest and convenience, of 
 immediate relation to the curiosity or the physical wants 
 of men, which determine us to classify and name some 
 of our individual observations and experiences, to the ex- 
 clusion of many others, also guide us in the selection of 
 those groups of Concepts which we enlarge, develop, and 
 methodize into distinct Sciences. As many objects and 
 events do not need to be classified because they are not 
 worth remembrance, so the classification of many others 
 needs not to be extended beyond the first and most ele- 
 mentary stage, because a Science elaborated out of them 
 would neither interest us nor minister to our necessities. 
 We do not chronicle petty occurrences, we do not study 
 out and subsequently generalize the insignificant relations 
 of unimportant objects to each other. But as circum- 
 stances change and knowledge is enlarged, what formerly 
 
APPLIED LOGIC. 347 
 
 seemed trivial often assumes a new dignity and interest, 
 or is unexpectedly found to be subservient to some gr^at 
 purpose. A new Science, or department of Science, is thus 
 formed, perhaps to be carried up by subsequent diseoyeries 
 and generalizations higher than any of those formerly cul- 
 tivated. How many new departments of study and re- 
 search have thus been, opened within the last few genera- 
 tions ! The Sciences of Geology, Ethnology, Comparative 
 PliUology, and Political Economy are hardly more than a 
 century old. The modems know more than the ancients, 
 not so much because they know the same things more per- 
 fectly, as because their investigations are extended over a 
 larger range of objects. 
 
 Hence it is easy to see why the numerous attempts that 
 have been made to classify the Sciences, and thereby to 
 reduce them into one complete and orderly, system of 
 human knowledge, have not been more successful. The 
 Sciences have not been formed on any predetermined and 
 systematic plan, with a view of covering the whole ground 
 of inquiry ; but they have grown by a natural and irregular 
 development, corresponding both to the ever increasing 
 wants and stimulated curiosity of those who prosecute 
 them, to the different aptitudes of the various classes of 
 objects to be digested into system and divided by obvious 
 lines of demarcation, and especially to the facihty with 
 which our conclusions respecting these objects may be 
 drawn without the aid of observation and experience. 
 Such a survey of all that is possible to be known, com- 
 pared with all that is actually known, as Bacon attempted 
 to make in liis treatise on the " Advancement of the Sci- 
 ences," must always disclose, as it did to him, many lacunce, 
 or gaps which it is necessary to fill, before man can be said 
 even to have entered upon aU the avenues which lead to 
 truth. Divisions of the Sciences, like those which have 
 heen devised by Bacon, Locke, Ampere, Comte, Wilson, 
 
348 APPLIED LOGIC. 
 
 and others, must always be imperfect, or, if they approxi- 
 mate completeness, must always indicate at least as many 
 blanks as there are departments already occupied. Whether 
 we try to distribute the various branches of knowledge, as 
 Bacon did, according to the different faculties of the mind 
 which they respectively call into play; or, with Locke, 
 according to the several ends in view ; or, with Descartes, 
 as followed by Comte, according to the order of their de- 
 velopment, as determined by their degrees of simplicity ; — 
 some Sciences will appear redundant, others as defective, 
 and many as having an equally good title to be ranked 
 under two or three different heads. 
 
 As one of the best specimens of these attempts at 
 classification, we may take Dr. Thomson's account of the 
 arrangement proposed by Comte, on the basis of Descartes's 
 aphorism, that knowledge should advance from the simpler 
 to the more complex phenomena. 
 
 " Mathematics,' or the science of quantities, is at once the 
 most simple in its elements and the most general in its ap- 
 plication, entering, more or less, into all the sciences of Na- 
 ture, and constituting almost the whole of that which comes 
 next it in the order of dependence. Astronomy, or the 
 science of the heavenly bodies, is the application of mathe- 
 matical truths to the laws of matter and motion ; matter 
 and the motions of material bodies being the new concep- 
 tions 'which belong to this science. Physics, being the 
 science, or rather group of sciences, which is conversant 
 with the general laws of the world, so far as they relate to 
 beings without life or organization, would come next ; and 
 it imports, in addition to the conceptions of Astronomy, 
 those of light, of heat, of sound, of electricity, of magnetism, 
 and many others. Chemistry would rank next, which is 
 the science of the decomposition and combinations of the 
 various substances that compose and surround the earth. 
 Next in order of complexity would rank Physiology, founded 
 
APPLIED LOGIC. • 349 
 
 on the additional conception of vegetable and animal life. 
 To this would succeed Anthropology, or the science of 
 man's nature ; and to this, Social Science, which ascertains 
 the laws that govern men when combined in cities and na- 
 tions. Each of these departments may be divided into 
 many branches ; as Physics into Acoustics, Optics, Elec- 
 tricity, and the like ; or Social Science into Morals, Poh-: 
 tics, Political Economy, Law, and the Uke. 
 
 " On comparing scientific works, differences in the mode 
 of teaching the same subject become apparent. In one, 
 the pure theory of Astronomy is presented ; in another, the 
 striking features of its historical progress as a science, with 
 speculations on the historical sequence of the phenomena 
 themselves ; in a third, the practical appHcations of which 
 the Science admits in respect to the comfort and progress of 
 mankind. This threefold mode of treatment runs through 
 all the Sciences, and in a table of them might well be ex- 
 pressed. The classification would thus embody all that is 
 valuable of another system of classes, that according to the 
 purpose towards which the Science was directed. 
 
 " A classification which advances on Descartes's principle, 
 from the more simple to the more complex subjects, which 
 commences from the notions of extension and quantity, 
 and proceeds through material things up to living, intelli- 
 gent, and moral agents, ought to coincide with the order 
 in which the sciences themselves have reached maturity. 
 And this it certainly does. Mathematics had made good 
 its ground when Astronomy was yet in its infancy ; Physics 
 began to obtain a sure footing later than either ; whilst the 
 Sciences which relate to Life are still very immature ; and 
 some of the main problems of Social Science are yet mat- 
 ter of controversy even in our own days." 
 
 It is an obvious imperfection of this scheme, that it takes 
 no notice of the numerous branches of that Science, Natu- 
 ral History, wliich, as it depends solely upon observation, 
 
350 
 
 APPUED LOGIC. 
 
 and thus gives us our first knowledge of all the ohjects of 
 study, would seem to constitute the basis of all the other 
 Sciences. In explanation of this defect, Comte remarks, 
 " we must distinguish between the two classes of Natural 
 Science ; — :- the abstract or general, which have for their 
 object the discovery of the Laws which regulate phenomena 
 in all conceivable cases ; and the concrete, particular, or 
 descriptive, which are sometimes called Natural Sciences 
 in a restricted sense, whose fimction it is to apply these 
 Laws to the actual history of existing beings. The first 
 are fundamental ; and our business is with them alone, as 
 the second are derived, and, however important, not rising 
 into the rank of our subjects of contemplation. We shall 
 treat of Physiology, but not of Botany and Zoology, which 
 are derived from it. We shall treat of Chemistry, but not 
 of Mineralogy, which is secondary to it." But this remark 
 is inconsistent with the previous assertion, that this order 
 of classification " coincides with the order in which the 
 Sciences themselves have reached maturity." In the order 
 of time, certainly. Zoology and Botany had been cultivated 
 to a considerable extent before men had obtained more 
 than the crudest notions of the physiological processes of 
 animal and vegetable life ; just as Civil History, the basis 
 of another department, had been very fully treated before it 
 first suggested the idea of Social Science. In what may 
 be called the logical order, or the order of ideas, however, 
 it is true that the Sciences which embody principles and 
 general results take precedence of those which afiford only 
 the material of knowledge. 
 
DEMONSTRATIVE REASONING. 351 
 
 CHAPTER XI. 
 
 DEMONSTRATIVE REASONING AND DEDUCTIVE EVIDENCE. 
 
 WE have already said, that the principal object of the 
 researches of Science is, to determine whether this 
 or that object, or class of objects, has the special character- 
 istics which entitle it to be placed in a certain class, and 
 called by a certain name. 
 
 Most of such questionsj if they relate only to one thing, 
 or to a very few things, are answered directly, and with- 
 out difficulty, by observation or intuition. We answer one 
 of them, in fact, whenever we perceive any object and call 
 it by its appropriate Common Name. For instance ; — this 
 thing which I now hold in my hand I call a 'pen, a ro»e, or 
 an apple, because I perceive that it has the attributes which 
 are the Marks connoted by that name. In hke manner, I 
 pronounce the animals now before me to be dogs, horses, or 
 cows, according as I recognize their distinctive qualities. 
 
 "Writers like Dr. Brown, Mr. J. S. Mill, and Mr. Bailey, 
 who have laboriously attempted to restrict the range and 
 depreciate the utility of the Syllogistic process, have seem- 
 ingly failed to notice the fact, that we must reason syllogis- 
 tically whenever we use language with any perception of 
 its meaning, — that is, when we call anything by its appro- 
 priate name. If I had not already spread out before my 
 mind the Marks which constitute the Intension of the 
 Concept apple, or rose, I could not designate the object 
 now presented to me by that appellation. This process of 
 reasoning, which we are performing almost every moment 
 
362 
 
 DEMONSTRATIVE REASONING 
 
 of our lives, and therefore so quickly and easily that its 
 several steps are taken almost unconsciously, is thus spread 
 out into the formal process. 
 
 The Concept or Class-notion apple has, as Marks, a 
 nearly spherical shape, a red color, a moderate hardness, 
 and a certain smell ; 
 
 This object has all these Marks ; 
 
 Therefore, this object is an apple. 
 
 This is what Hamilton calls Reasoning in Intension, for, 
 in each of the Premises, the Predicate is contained in the 
 Subject. Moreover, the Reasoning is not only logical, — 
 i. e. vaUd in Form, but it is also Demonstrative, — i. e. abso- 
 lutely certain in respect to its Matter. It is Demonstrative, 
 because the Major Term, which is here the Subject of the 
 Major Premise, is a Concept or Class-notion, which, being 
 a mere creation of the mind, cannot have any other Marks 
 or quaUties than those which we voluntarily attribute to it. 
 As we know by Intuition, that the object has all the Marks 
 which we included in the Concept, it is certain that it 
 should be designated by the name of that Concept, — that 
 is, that it should be included under its Extension. 
 
 On the other hand, if the Reasoning is made to concern, 
 not a mere Concept in the mind, but a class of real things, 
 which, as we have seen, always have an unknown and un- 
 knowable number of quahties and relations, then I cannot 
 be sure that the object in question possesses all these quali- 
 ties, but can only doubtfully infer that it has all, because I 
 know that it possesses some, of the more important of them. 
 An element of uncertainty is introduced ; the Reasoning 
 ceases to be Demonstrative, and becomes merely Probable 
 or contingent. For instance; — if, in the Major Premise 
 of the preceding Syllogism, we say, not " the Concept or 
 Class -notion apple," but " AU apples" — i. e. All the 
 actual objects which we have been accustomed to call ap- 
 ples — " have a nearly spherical shape, a red color, a mod- 
 
AND DEDUCTIVE EVIDENOE. 353 
 
 erate hardness, and a certain smell " ; then, though " this 
 object has all these Marks," I cannot be sure that "it is an 
 apple." It may be only a wax counterfeit, and the decep- 
 tion would instantly be detected by the taste, which quahty 
 was not included in the enumeration. The Reasoning is 
 still vahd in Form, but the Major Premise is false ; it cov- 
 ers up the Fallacy jictoe universalitatis. In order to be 
 sure that an object is properly ranked under a given class, 
 we must be certain- that it contains all the original and 
 essential qualities of the objects denoted by the class-name ; 
 and this certainty, in the case of real things, is unattain- 
 able. In our conception, we may arbitrarily restrict the 
 meaning of the word apple, so as to exclude the quality of 
 taste; and in this sense, the wax counterfeit is properly 
 called an apple. But in speaking to others, the word 
 would be understood to signify all the qualities possessed 
 by the real things, viz. this sort of fiuit ; and in this mean- 
 ing, the wax substitute is not an apple. ' 
 
 We can now see why the Reasonings of the mathema- 
 tician are Demonstrative, whUe those of the zoologist, the 
 botanist, and other naturalists who deal only with real 
 things, are merely Probable or contingent. The Form is 
 always the same ; Reasoning, as such, must always be 
 Syllogistic ; and when the rales of Pure Logic are duly 
 observed, the Consequence, or the mere deduction of the 
 Conclusion from the Premises, must be absolutely cer- 
 tain. The difference, then, concerns the Premises only, 
 the truth of which, as we have seen, is not guaranteed by 
 the principles of Logic. The universal rule, that the Mid- 
 dle Term must always be distributed, requires that the 
 predesignation all, or none, should appear in at least one 
 of the Premises. Now, our knowledge of real things is 
 derived solely from experience ; and experience, as has 
 been mentioned, must be restricted, from its very nature, 
 to a limited number of examples. In respect to real ob- 
 
354 DEMOHSTEATIVE KEASONING 
 
 jects and events, it can never extend either to the indu- 
 sion or the exclusion of all; it can never pronounce with 
 certainty either upon all, or none. Only with reference to 
 a certain class arbitrarily formed by the Understanding, — 
 to the very things which I am now thinking oi, or which 
 I have actually observed, and to none others,-^ to the 
 things which are included under this Definition, and to 
 these only, — can the finite nnderstandiBg of man, so fe,r 
 as it is enlightened only by experience, safely pronounce 
 upon all or none. Without such Umitations, naturaUste, 
 and all others who seek to educe Science from mere expe- 
 rience, can never speak of all or noTie, without falUng into 
 the Fallacy fictoe universalitatis. 
 
 The mathematician deals only with certain Concepts of 
 Quantity, whether continuous or discrete, which are pre- 
 cisely liinited and determined by the Definitions that he 
 employs. The propositions which he establishes do not 
 concern circular objects and triangular objects, which are 
 real things, but circles and triangles, which are imaginary 
 things as conceived by the Understanding, and which are 
 restricted by their Definitions to the possession of those 
 quahties only which Thought voluntarily attributes to 
 them. Hence, the conclusions which the mathematician 
 forms respecting them are not liable to be vitiated by the 
 intrusion of any unexpected and counteracting elements. 
 Any theorem, therefore, which is proved of one, must hold 
 good of all; any property which cannot belong to one, can 
 be possessed by none, of the class thus defined. The same 
 measure of certainty which the student of nature obtains 
 by Intuition respecting a single real object, the mathe- 
 matician acquires respecting a whole class of imaginary 
 objects, because the latter has the assurance, which the for- 
 mer can never attain, that the single object, which he is 
 contemplating in Thought, is a perfect representative of its 
 whole class ; he has this assurance, because the whole class 
 
AND DEDUCTIVE EVIDENCE. 355 
 
 exists only in Thought, and are therefore all actually before 
 him, or present to consciousness. For example; this bit 
 of iron, I find by direct observation, melts at a certain 
 temperature ; but it may well happen that another piece 
 of iron, quite shnilar to it in external appearance, may be 
 fusible only at a much higher temperature, owing to the 
 unsuspected presence with it of a little more, or a little less, 
 carbon in composition. But if the angles at the basis of 
 this triangle are equal to each other, I know that a corre- 
 sponding equality must exist in the case of every other 
 figure which conforms to the Definition of an isosceles 
 triangle ; for that Definition excludes every xiisturbing ele- 
 ment. The conclusion in this latter case, then, is Univer- 
 sal, while in the former, it can be only Singular or Par- 
 ticular. 
 
 Conclusions which are demonstratively certain and abso- 
 lutely universal can be obtained only when we are reason- 
 ing about abstract conceptions. In the case of natural 
 objects and events, which can be hnawn only through ex- 
 perience, we approximate universality and certainty in rea- 
 soning only by the aid of Induction, and Analogy. The 
 lack of certainty is a consequence of the lack of univer- 
 sality. No douht affects the few instances which I am 
 now actually observing, or which are present to sense or 
 consciousness. Of these, I am as certain as of any conclu- 
 sions in arithmetic or geometry. The doubt comes in only 
 when I attempt to extend the conclusion from some, which 
 I have examined, to all others, of which I know nothing, 
 except from testimony. Induction, or Analogy. And this 
 doubt is inevitable ; no matter how many cases have been 
 examined, experience can never extend to all. The fact 
 that all matter gravitates, or has weight, is a truth which 
 rests upon as large a testimony from experience as has ever 
 been collected. Yet the chemist will readily admit that it 
 is not only conceivable, but we may almost say prohahU, 
 
356 DEMONSTRATIVE KEASONING 
 
 that some of the imponderable agents, as they are called, — 
 heat, light, electricity, &c., — may at last be found to be 
 material ; and the astronomer has not yet proved entirely 
 to his satisfaction, that the law of gravitation is universal 
 throughout the stellar system. From the nature of the case, 
 he would say, the fact does not admit of absolute proof. 
 
 It appears, then, that the range of Deductive reasoning 
 and Demonstrative proof is not confined to pure Mathe- 
 matics. Whenever the objects about which we reason are 
 pure Concepts, or mere creations of the intellect, strictly 
 limited by Definition, and thus guarded against reference 
 to things actually existent in Nature, our conclusions re- 
 specting them, if obtained in strict uniformity with logical 
 rules, are as absolute as the truths of the multiplication- 
 table. But Mathematics, it must be admitted, afibrd vastly 
 the larger number of conclusions of this class ; in no other 
 science is Demonstrative reasoning either carried so far, or 
 so fruitful in results. This peculiarity seems to be due 
 to the nature of those Concepts, quantity, space, and num- 
 ber, with which the mathematician deals. Two of these, 
 quwniity and number, are imiversal attributes, as they belong 
 to all things, both to objects of sense and consciousness ; and 
 the third, space or extension, is an attribute of all external 
 things. They are suggested to us on a greater variety of 
 occasions than any other qualities, and thus are more fre- 
 quent objects of contemplation, and more fully determined. 
 " Propositions concerning numbers," as Mr. MiU observes, 
 " have this remarkable peculiarity, that they are proposi- 
 tions concerning all things whatever, — all objects, all ex- 
 istences of every kind, known to our experience. All 
 things possess quantity ; consist of parts which can be num- 
 bered ; and, in that character, possess all the properties 
 which are called properties of numbers." 
 
 Again, the various modes, properties, and relations of 
 quantity, space, and nurriber admit of being more accurately 
 
AND DEDUCTIVE EVIDENCE. 357 
 
 defined and clearly determined than those of any other 
 class of ideas ; they are separable from each other by lines 
 of demarcation that cannot be overlooked or mistaken. 
 Differences of degree, with which we are chiefly concerned 
 in the case of all other qualities, are not by any means so 
 definite, as they are shaded into each other by impercep- 
 tible gradations ; their minute differences are inappreciable 
 either by the senses or by the understanding. But the 
 difference between two quantities, whether of number or 
 extension, may be reduced as low as we please, and still 
 remain as distinct to our apprehension as if it were world- 
 wide. 
 
 But the chief pecuHarity of these three Concepts, which 
 causes them to afford so broad and fruitful a field for De- 
 monstrative reasoning, is the measureless variety of accu- 
 rately determinable relations in which all their modes stand 
 to each other. Any one quantity stands in a perfectly con- 
 ceivable ratio — whether it can be exactly expressed in 
 numbers or not — to every other quantity, and also has a 
 countless number of peculiar relations in which it stands to 
 many at once. Attempt to enumerate, for instance, the 
 properties of the number 9 ; — that it is the square of 3, 
 the square-root of 81, the double of 4|^, the half of 18, 
 &c., — and we soon abandon the undertaking in despair. 
 And when we come to think of the relations of these rela- 
 tions, as in the doctrine of proportions, it becomes evident 
 that the properties of quantity are too great to be num- 
 bered. The field of investigation is infinite. 
 
 These innumerable and perfectly definite relations, which 
 subsist between distinct quantities, furnish an inexhaustible 
 number of Middle Terms, through which we obtain, by 
 Mediate Inference, such Conclusions as are not apparent at 
 a glance, or by direct Intuition. When the geometer, for 
 instance, cannot determine directly the distance firom one 
 point to another, he constructs a triangle, the base of which. 
 
358 DEMONSTRATIVE REASONING 
 
 with its adjacent angles, as accessible, can be easily meas- 
 ured ; and he can then deduce the required distance, or 
 the height of the triangle, from the known relations which 
 exist between it and the quantities which he has thus di- 
 rectly determined. In like manner, the value of one or 
 more unknown quantities, symbolically represented in an 
 algebraic equation, is deduced from some of the ^ven rela- 
 tions which subsist between them and the known quan- 
 tities, with which they are taken in connection. Indeed, 
 the pecuhar function -of algebraic science is to determine 
 general relations between different groups and classes of 
 magnitudes, these general ratios, proportions, and analyses 
 being subsequently applied by the geometer and the arith- 
 metician to the solution oi parHcular problems. The mere 
 construction of a geometrical diagram enables us to see the 
 use which is made of one or two hnown relations between 
 several quantities, as means of determining indirectly other 
 relations between them which cannot be directly meas- 
 ured. The diagram is only a means of making clear to 
 our apprehension the fact, that the same straight hne, or 
 length already determined, is at once the base of a triangle, 
 the radius of a circle, the side of a square, &c ; then this 
 line may be used as a Middle Term, or means of proving 
 ■syllogistically what the other properties and dimensions, 
 hitherto unascertained, of this triangle, circle, and square 
 mast be. Thus to ascertain a new property of a former 
 object of Thought is to advance a step in the classifications 
 wliich the mind is continually forming, enabling us to refer 
 this object, perhaps hitherto anomalous, to its proper class. 
 The diagram, indeed, is a Singular instance ; but what it 
 enables us to discover is a General Truth ; for, as already 
 remarked, we know that this one instance is a perfect rep- 
 resentative of its whole class, since that class exists only in 
 our Thought, and is therefore perfectly known. The little 
 triangle which I am contemplating as drawn on paper cor- 
 
AND DEDTJCTrVE EVIDENCE. 359 
 
 responds perfectly, in all particulars that can be essential for 
 the Reasoning, to the magnificent one, having as its base 
 hne the diameter of the earth's orbit, which the astrono- 
 mer, when he would determine the distance of a fixed star, 
 imagines to be erected in the heavens. 
 
 These considerations appear to me to evince very clearly, 
 that the pecnHar cogency and iruitfiilness of mathematical 
 reasoning do not arise, as Kant maintains, fi-om the fact 
 that it concerns nothing but Space and Time, and that 
 Space and Time exist only in our minds. The sole object 
 of this sort of reasoning seems to be quantity in its various 
 forms ; and reasoning would be equally Demonstrative, if 
 it related to any other single attribute of things considered 
 abstractly, or as we conceive it apart fi-om all other proper- 
 ties with which it is united in the actual constitution of 
 things. The fact that Quantity is a universal attribute, be- 
 -loHging to all objects of Thought whatever, explains the 
 broad scope and general applicability of mathematical rea- 
 soning ; while its peculiar fi?uitfulness, or the vast number 
 of truths which it brings to light, appears to proceed from 
 the countless number and definite character of the relations 
 which subsist between different quantities. No other attri- 
 bute presents itself so universally, or in modes at once so 
 numerous and so distinct, capable alike of indefinite aug- 
 mentation and diminution. The field is boundless, and we 
 advance over any portion of it with the precision and cer- 
 tainty in eveiy movement which admit neither error nor 
 doubt. 
 
 The views which have now been presented enable us to 
 refiite the doctrine^ originally proposed, as Mr. Stewart 
 thinks, by Leibnitz, that the certainty of mathematical 
 reasoning depends upon the fact, that all the evidence on 
 which it is supported may be resolved, m the last analysis, 
 into the perception of iiemtity ; — "the innumerable vari- 
 ■ety' of propositions which have been discovered, or which 
 
360 DEMONSTRATIVE REASONING 
 
 remain to be discovered in the science, being only diversi- 
 fied expressions of the simple formula, a = a." It is true 
 that this theory correctly presents the form, not only of 
 mathematical reasoning, but of all reasoning whatever ; 
 for we have shown that every Affirmative Judgment, in a 
 certain sense, or with reference to the denotation of the 
 Concepts which it concerns, is an equation of its two 
 Terms. The formula, A is B, to which all conceivable 
 Affirmative Judgments may be reduced, is resolvable, in 
 this seme, as B equals A, into A^A. But the peculiar 
 cogency of mathematical evidence cannot be explained by 
 the possession of an attribute which does not distinguish it 
 from Moral Reasoning. In reference to the connotation 
 of its Terms, a Judgment does not express an equation, 
 but the inclusion of an object in a class, and the conse- 
 quent possession by that object of the peculiar attributes 
 of that class. In this sense, the signification is, not that 
 the Subject equals the Predicate, but that it possesses one 
 or more of the attributes of the Predicate, or possesses the 
 Predicate itself as one of its own attributes. The doctrine 
 which we are considering owes its plausibility to a con- 
 fusion of the significance of these two very different words, 
 identity and equivalence. When the geometer proves the 
 area of a circle to be equal to that of a triangle having the 
 circumference for its base and the radius for its altitude, 
 he certainly does not mean that it is idenUcal with such a 
 triangle, but only that it is equivalent to it in a single re- 
 spect, — viz. in magnitude; they are not identical, for, in 
 shape, they are wholly unlike. Take even a simpler case, 
 which seems more nearly resolvable into an expression of 
 identity : 4 = 2 + 2. Even here, the meaning is not that 
 the two members of the equation are identical, but only 
 that the Concept or group four is equivalent in one respect 
 — viz. the possession of an equal number of units — to 
 the two groups two and two. It is plain that one group 
 
AND DEDUCTIVE EVIDENCE. 361 
 
 cannot be identical with two groups, or that two distinct 
 acts of the mind, each conceiving or grasping together two 
 units, cannot be literally the same thing as one mental act 
 conceiving four. 
 
 Tlie essential distinction between Pure and Applied 
 Mathematics consists in this, that, in the former, our 
 thoughts never go beyond the conception of pure quan- 
 tity, or magnitude in the abstract, considered in either of 
 its two modes, space or number ; while in the latter, .the 
 additional qualities of weight, attraction, impenetrahHitif, 
 elasticity, density, and many others, are brought in, not 
 merely as they are conceived in the mind> but as they 
 actually exist, or are manifested, in real things. These 
 qualities also, so far as they are viewed in the former light, 
 that is, abstractly, as mere Concepts strictly limited "by 
 Definition, may be reasoned about demonstratively ; though 
 it is only in respect to their quantity that the reasoning will 
 have any wide range, or be fi^uitful in conclusions, since 
 they have not the numerous and distinctly conceived relar 
 tions which subsist between the innumerable degrees of 
 Quantity. But if viewed as actual qualities of real things, 
 our knowledge of them is derived merely fii-om experience, 
 and must therefore be subject to all the hmitations and im- 
 perfections of knowledge so derived. No Judgments con- 
 cerning them can be absolute or universal ; they are objects 
 only of Probable Reasoning. Previous to experience, we 
 could not attribute weight to any material substance, much 
 less to all such substances; that every particle of matter 
 should attract, would seem no more probable than that it 
 should repel, every other particle. This is the source of 
 Dr. Whewell's error ; because weight, attraction, impener 
 trability, &c. can be conceived abstractly, and therefore 
 be strictly limited by Definitions, and so reasoned about 
 demonstratively, he maintains that the Physical Laws of 
 Motion are necessary truths, and " capable pf demonstra- 
 
 16 
 
862 DEMONSTRATIVE REASONING 
 
 tion, like the truths of Geometry." So they are, if viewed 
 as mere Concepts, not necessarily having anything cor- 
 responding to them in the outward universe. But if re- 
 garded as Physical Laws, expressing the actual phenom- 
 ena of real things, they are mere educts from experience, 
 can be reasoned about only Inductively, and rest solely 
 upon Probable evidence. 
 
 Deduction is not a happily chosen word to indicate the 
 characteristic feature of reasoning from Universals to Par- 
 ticulars, as contradistinguished from Induction, whereby we 
 reason from Particulars to Generals. In the Syllogism 
 which expresses the Form of the latter process, the Con- 
 clusion is as much a deduction from the Premises, as in 
 the former case. We may speak of a Law, or general rule, 
 as deduced from several individual facts, with just as much 
 propriety as of facts as deduced from the Law. In either 
 ease, the Conclusion may be said to depend upon the Prem- 
 ises in this sense, that the latter authorize us to proceed to 
 the former. But it is a mere figure of speech, and not a 
 very happy one, to speak of the Conclusion as so involved 
 in the Premises, that the one can be drawn out of, or de- 
 duced, from the other. The process is rather an ea^lica- 
 tion of what was previously in the mind, whereby two acts 
 of Tbonght are brought into harmony with each other. 
 The Subsumption either includes one or more individuals 
 in a class, or excludes them from it; and the Conclusion 
 then states explicitly what is virtually or implicitly thought 
 in that act of inclusion or exclusion. The process of rea- 
 soning is not so much a mode of evolving a new truth, as 
 it is of establishing or proving an old one, by showing how 
 much was admitted in the concession of the two Premises 
 taken together, or what follows fiom. the act of bringing 
 them into hannony. The Conclusion is not authorized by 
 either of them taken singly. 
 
 Hence it is a Stpl graver mistake, and one which has 
 
AND DEDUCTIVE EVIDENCE. 363 
 
 giTen rise to much misunderstanding, to speak of the Con- 
 clusion as deduced from owe of its antecedents, from the 
 Major Premise only. A Sumption or General Rule is a 
 necessary part of every Syllogism ; but it does not by any 
 means follow, that this Rule alone implicitly contains all 
 the particular Conclusions which are ordinarily said to be 
 drawn out of it. The Conclusion is drawn in accordance 
 with the Rule, and the latter may, in one sense, be said to 
 afford a proof of the former, inasmuch as it evinces that 
 the Conclusion, if the truth of the Minor Premise or Suh- 
 svmption is granted, cannot be denied without overthrow- 
 ing a general principle the truth of which is presupposed, 
 as resting upon the evidence either of Intuition, or of a 
 Primary Law of Thought, or of previous Demonstration. 
 In one sort of Immediate Inference, that of Subalterna- 
 tion, the Premise may be rightly viewed as containing the 
 Conclusion, as a whole contains one of its parts, and the 
 latter may therefore be held to be deduced from the for- 
 mer. But the relation between the Subaltemans and the 
 Subalternate is very different from that which subsists be- 
 tween the Sumption and the Conclusion in a case of Mediate 
 Inference. In the latter case, the gist of the reasoning 
 does not depend upoii any Maxim or First Principle, but 
 upon the discovery of a Middle Term, with which both 
 Terms of the Conclusion are separately compared. This 
 Middle Term is the name of a Class, and the new truth 
 which is developed by the reasoning consists in the Sub- 
 sumption of the Subject of the Conclusion into that Class, 
 and the consequent discovery that it possesses all the attri- 
 butes or properties which are connoted by its Name. For 
 example : — the geometer, wishing to ascertain the size of 
 a certain angle, finds that it is one of the angles of an equi- 
 lateral triangle ; this is the Subsumption, and when it is 
 accomplished, the discovery is really made and the problem 
 solved, for the Conclusion that the angle measures 60° im- 
 
364 DEMONSTRATIVE EEASONING 
 
 mediately follows, in accordance with the General Truths 
 already demonstrated, that the three angles of an equilat- 
 eral triangle are equal to each other, and that their sum is 
 180°. But no manipulation, no analysis, of these Truths 
 previously demonstrated would enable him to evolve from 
 them, without the aid of the classification given in the 
 Minor Premise, the measure of this particular angle. 
 When the Sumption, instead of being, as in this case, a 
 General Theorem previously demonstrated, happens to be 
 
 one of those Maxims which are called Axioms in Geome- 
 
 » 
 
 try, it is still more evident that it is a meagre and barren 
 Rule, from which no fruitful and significant Conclusion 
 can properly be deduced. 
 
 I accept, then, to its Ml extent, the doctrine originally 
 propounded by John Locke, and adopted and defended in 
 our own day by Dugald Stewart, that the Axioms of Ge- 
 ometry, and the other very general maxims which are 
 usually considered as First Principles in our researches, 
 " are not the foundations on which any of the Sciences are 
 built, nor at all useftil in helping men forward to the dis- 
 covery of unknown truths." If Reasoning were an organon 
 of discovery, a means for the advancement of truth, its char- 
 acteristic feature would appear in the Subsumption, which 
 places the Subject of inquiry, hitherto anomalous, or of 
 uncertain classification, under a Concept, or, what is the 
 same thing, in a class, the attributes of which are known ; 
 and the proof that it possesses one or more of the attributes 
 of that class then appears by citing the General Rule, 
 which is the Major Premise. In other words, each of the 
 two Premises in a Syllogism has its own appropriate ftinc- 
 tion ; the Minor announces a discovery, a new truth, which 
 is always a truth of classification, and the Major cites an 
 Axiom, or some other general rule, previously well known, 
 which proves some consequence of this new truth, or en- 
 ables us to acquiesce, with more or less confidence, in the 
 
AND DEDUCTIVE EVIDENCE. 365 
 
 announcement of this consequence. If the Major is an 
 Axiom properly so called, or a truth previously demon- 
 strated, — in either case, having absolute universality and 
 certainty, — then the Conclusion, if the Subsumption is 
 correct, is demonstrated ; but if it is merely a general rule 
 obtained by Induction or Analogy, the Conclusion is merely 
 probable. 
 
 The correctness of this analysis wiU appear, I think, 
 from an examination of either of the following Syllogisms. 
 
 1. All electricity may be silently drawn off from any charged 
 
 body, by bringing near to it a sharp-pointed rod. 
 Lightning is electricity. 
 .*. Lightning may be so discharged. 
 
 2. The nervous fluid will not travel along a tied nerve. 
 Electricity will travel along a tied nerve. 
 
 .*. Electricity is not the nervous fluid. 
 
 3. AU alternate angles made by one straight line cutting two 
 
 parallel lines are equal. 
 ABC and B C E are alternate angles. 
 .•.ABC and B C E are equal. 
 
 4. Things which are equal to the same thing are equal to each 
 
 other. 
 A B and B C are each equal to C D. 
 .-. A B and B C are equal. 
 
 5. Happiness is desirable. 
 Virtue is happiness. 
 
 .*. Virtue is desirable. 
 
 It is evident that no one of the General Rules which 
 form the Major Premises of these Syllogisms can be " at 
 all useftd in helping men forward to the discovery of un- 
 known truths." The real discovery is announced in the 
 Minor Premise, and the connection of the two Premises in 
 one act of reasoning is the means of proving the Conclu- 
 sion, and of assuming it into its proper place under the 
 General Rule. It does not appear, then, that Reasoning 
 
366 DEMONSTRATIVE SEASONING 
 
 as such, or as an act of Pure Thought, is a means fw the 
 advancement of knowledge. This doctrine, indeed, feUo^re 
 immediately from the principles that have heen already 
 laid down. Reasoning as such is one of the processes of 
 pure Thought which determine the Form, but not the Mat- 
 ter, of our knowledge. The Matter of Thought is ob- 
 tained by Intuition, — by observation through the senses or 
 through consciousness. "The fiict or truth thus discovered 
 is announced in the Subsumption, not as first made known 
 by it, or as deduced from what was previously known, but 
 in order to be proved through the Reasoning process ; that 
 is, to he hrought into harmony with our p-evious Jatowledge 
 as stated in the Major Premise, and that the same conse- 
 quences may he attribided to it which are already known to 
 follow from all the cases included under that general state- 
 ment. 
 
 . Accordingly, what Hamilton remarks of the whole doc- 
 trine of Logic may be applied to the theory of Reasoning, 
 which is but one of the departments of this science. We 
 cite again, in reference to onfi of the parts, what has been 
 already quoted in reference to the whole. "An extension 
 of any science through [pure Reasoning] is absolutely im- 
 possible ; for, by conforming to the logical canons, we ac- 
 quire no knowledge, — receive noising new, but are ««ily 
 enabled to render what is already obtained more intelligi- 
 ble by analysis and arrangement. [Reasoning] is only the 
 negative condition of truth. To attempt by mere [Reason- 
 ing] to amplify a science, is an absurdity as great as if we 
 should attempt, by a knowledge of the grammatical laws of 
 a language, to discover what is written in this language, 
 without a perusal of the several writings themselves. But 
 though [Reasoning] cannot extend, cannot amplify, a sci- 
 ence by the discovery of new &cts, it is not to be supposed 
 that it does not contribute to the progress of science. ' The 
 progress of the sciences consists not merely iji the accumu- 
 
AND DEDUCTIVE EVIDENCE. 367 
 
 Lation of new matter, but likewise in the detection of the 
 relations subsisting among the materials accumulated ; and 
 the reflective abstraction by which this is effected " must 
 follow the laws of Reasoning. 
 
 "We are now prepared to understand and appreciate 
 Locke's doctrine, which has been accepted and ably sup- 
 ported by Mr. Bailey and Mr. J. S. Mill, that " the imme- 
 diate object of all our reasoning and knowledge is nothing 
 but particulars." Locke argues that " the perception of 
 the agreement or disagreement of our particular ideas ia 
 the whole and utmost of all our knowledge. Universality 
 is but accidental to it, and consists only in this, that the 
 particular ideas about which it is are such as more than 
 one particular thing can correspond with and be repre- 
 sented by. But the perception of the agreement or dis- 
 agreement of any two . ideas is equally clear and certain, 
 whether either, or both, or neither, of those ideas be capa- 
 ble of representing more real beings than one, or no."* 
 Mr. Mill says : " We much oftener conclude from particu- 
 lars to particulars directly, than through the intermediate 
 agency of, any general proposition. We are constantly 
 reasoning from ourselves to other people, or from one per- 
 son to another, without giving ourselves the trouble to 
 erect our observations into general maxims of himian or 
 external nature." f 
 
 The only question here concerns the proper use of words. 
 The process of comparing one individual object or event 
 with another, and thereby ascertaining some relation be- 
 tween them, is unquestionably the first step to knowledge, 
 and the only means of enlarging our stock of knowledge. 
 But the particular fact thus learned is a fact of observation, 
 not of reasoning. Certainly 1 do not need to reason, nor, 
 in the strict and technical sense, to think, in order to per- 
 
 • Essay on Human Understandirlg, Book IV. Chap. IT, § 8. 
 t System af Logic, Book TL Chap. 3, § 3. 
 
368 DEMONSTRATIVE REASONING 
 
 ceive that John is taller than William. A brute perceives 
 this faet as well as I do, and acts upon it, as in distinguish- 
 ing his master. Even if we carry the process one step 
 further, and form a Judgment, by subsuming the individual 
 object of intuition under a class, through perceiving that it 
 affects our senses just as some other objects ranked under 
 that class have done, still we are engaged only in enlarging 
 and generalizing our knowledge, and not in reasoning prop- 
 erly so called. But when we take one step more, and pro- 
 ceed to attribute certain qualities to that individual thing, 
 which are not now directly perceived in it, but are sup- 
 posed to exist in it, because we have noticed them in other 
 objects of the same class, we are properly said to reason ; 
 the act is one of Mediate Inference. But this act does not 
 properly enlarge our knowledge, but only expUcates it, by 
 bringing out explicitly into Thought what was already vir- 
 tually contained in it. By putting an object into a class, 
 we have already virtually attributed to it all the quahties 
 which belong to that class. 
 
 This doctrine is not inconsistent with what has already 
 been maintained, that an act of Reasoning is necessary to 
 enable us to call anything by its appropriate Common 
 Name. Mere observation cannot teach us what is the 
 proper appellation of any object which is now for the first 
 time perceived ; its name is not stamped upon it, — is not 
 one of its qualities directly perceptible either by sense or 
 consciousness. But by the joint action -of our faculties of 
 perception and comparison, we are made aware that the 
 new object resembles a certain class of previously known 
 objects in all the particulars which are connoted by the 
 name of that class, and therefore, that the object may be 
 properly subsumed into that class, and called by its name. 
 
 The doctrine of Locke and Mill, then, appears true to 
 this extent; — that we certainly compare one mdividual 
 thing with another, and only by such comparison can dis- 
 
AND DEDUCTIVE EVIDENCE. 869 
 
 coveries be made and knowledge advanced. . But that sim- 
 ple comparison, and the consequent perception of a relation 
 of likeness or unlikeness, is not an act of reasoning. We 
 do not, in the technical sense of the term, " conclude from 
 particulars to particulars." Before this particular discov- 
 ery can be made available for the purposes of Science, — 
 before it can be brought into union and harmony with our 
 previous stock of knowledge, an act of Pure Thought 
 — -of Mediate Inference, or Reasoning properly so called 
 — is necessary. We must become aware that at least one 
 of the two Individuals which were compared together is a 
 typical specimen or representative of a whole Class, and 
 the correspotlding Conclusion must be reached, that the 
 other Individual possesses some one or more of the essen- 
 tial attributes of that Class. To advance to this Conclu- 
 sion is, in one sense, an unimportant step ; for it contains 
 nothing new, — it does not increase our knowledge. Hav- 
 ing learned the individual fact, that " A and B are both 
 equal to C," we do not really make any progress, except in 
 the way of systematizing our knowledge, when we add the 
 very obvious corollary, that "they are equal to each other," 
 since this is but one instance under the General Rule, that 
 " all which are equal to the same thing are equal to each 
 other." But in another respect, this step is far from being 
 unimportant. Though we have already virtually attributed 
 all the qualities of the class to the individual when we have 
 included that individual in the class, so that the technical 
 Conclusion only draws out explicitly what was already im- 
 plicitly thought, a new act of classification is thus com- 
 pleted, and the memory is disburdened of particulars by an 
 act of arranging and harmonizing our knowledge. First 
 to bring out into distinct consciousness the truths which 
 are already, so to speak, within our reach, but in a con- 
 fused and undeveloped state, and then to place them under 
 their appropriate heads or classes in a methodized system 
 
'370 DEMONSTRATIVE REASONING 
 
 of knowledge, is the peculiar office of Beaaonihgi The 
 Conclusion, when once drawn, is obvious enough ; other- 
 wise it could not be said to be demonstratively proved. 
 But far the greater part of our knowledge exists in this 
 half latent senu^developed state ; only by aa act of Rea- 
 soning can it be drawn forth, proved, and made available 
 for use in further inquiry. In respect to utility, it matters 
 little whether our stores are positively enlarged, or our 
 previous acquisitions are devejpped, systematized, and ren- 
 dered more efficient. I believe that no new trudi was 
 ever discovered by a direct process of pure Reasoning; 
 and, on the other hand, that, without the aids and appli- 
 ances furnished by such Reasoning, no progress beyond 
 the most elementary steps of Science would have been 
 practicable. Good observers discover new &cts, but good 
 xeasoners do most to educate and instruct mankind. 
 
 Of course, the fact of observation on which the Reason- 
 ing is based, and which it is die office of the Reasoning to 
 develop, is not necessarily one perceptible by sense. The 
 mere thinker, who, by some lucky chance or by dint of 
 patient reflection, hits upon some relation, hitherto unob- 
 served, between two abstract ideas, is just as much a dis- 
 coverer, as the chemist who first finds that a metal is the 
 basis of an alkali; otherwise, no progress could be made 
 in pure mathematics or any other abstract science. The 
 naked fact^that the square upon the hypothenuse of a 
 right-angled triangle is equal to the sum of the squares 
 on the two other sides, was observed and known long be- 
 fore Pythagoras first succeeded in proving it, by showing, 
 through a series of Middle Terms, that it is really involved 
 in and harmonizes with some elementary principles, the 
 whole compass and meaning of which had not before been 
 duly developed. The fact was first made known by reflec- 
 tive observation, — perhaps by sensible experiment; but it 
 did not become a step in the progress of Science till it had 
 
AND DEDUCTIVE EVIDENCE. 371 
 
 been proved, or subsumed under some broader principles, 
 and thus assigned its due place in a system of knowledge, 
 by an act of pure Reasoning. 
 
 To those who have ftdly considered the doctrine which 
 was laid down at the commencement, that Logic is not an 
 organon for the discovery of truth, and that it is exclu- 
 sively concerned with the Form, and not the Matter, of 
 Thought, this discussion may seem to have been needlessly 
 prolonged. But it has sqtlong been supposed that the 
 admission of the inapplicability of the Syllogistic process 
 to the discovery of truth was tantamount to a confession 
 of the entire inutility of the science, that it seemed worth 
 while, even at the expense of some repetition, to prove 
 that this supposition was wholly groundless, and to show 
 precisely what is the utility of the ends to which mere 
 Reasoning is subservient. When Mr. Locke says, " I am 
 apt to thiak that he who should employ all the force of his 
 reason only in brandishing of Syllogisms wiU discover very 
 little of that mass of knowledge which lies concealed in the 
 secret recesses of nature," we have a right to answer, in 
 the words of an acute logician, Mr. J. Walker, of Dubhn, 
 that " he expresses himself with needless caution. Such a 
 man will certainly not discover any of it. And if any im- 
 agined that the mere brandishing of Syllogisms could in- 
 crease their knowledge, as some of the Schoolmen seemed 
 to think, tJiey were indeed very absurd." But to those 
 who consider how hmited the range of human knowledge 
 would be, if it were confined to isolated facts of observation 
 resulting from the comparison of one individual thing with 
 another, having no cotmection with each other, often seem- 
 ingly at variance, not systematized, not summed up into 
 general truths, and hence incapable of communication by 
 language, it wiU be evident that, without the capacity and 
 the constant exercise of Reasoning, mankind would have 
 advanced but little beyond the condition of the brutes. 
 
3T2' DEMONSTRATIVE REASONING 
 
 It may be useful to enumerate the different classes of 
 Genelral Rules which are the Major Premises of all Syllo- 
 gisms, and, as such, are not so much the First Principles 
 whence all our Conclusions are derived, as they are the 
 Ultimate Truths in which all Reasoning terminates, 
 
 1. The first of these classes consists of the Primary 
 Laws of Pure Thought, and those secondary or derivative 
 maxims into which, in different sciences and for different 
 purposes, these Primary Laws%re explicated. In Logic, 
 as we have seen, both the supreme Canons of Mediate In- 
 ference, such as the Dictum de omni et nvMo, and the spe- 
 cial Rules of various sorts of Syllogisms, are all resolvable, 
 in the last analysis, into these Laws of Thought. In like 
 manner, the Axioms properly so called of Geometry, that 
 "if equals are added to equals, the wholes are equal," "if 
 equals are subtracted from equals, the remainders are 
 equal," &c., are only varied expressions, explications, or 
 immediate consequences, of the Laws of Identity and Non- 
 contradiction. 
 
 2. The foregoing maxims are merely analytic or explica- 
 tive. The next class consists of synthetic or ampUative 
 Judgments. These are necessary intuitions of pure rea- 
 son, or universal truths known a priori, as resulting from 
 the constitution of the mind itself. Such are the Judgments, 
 that every event must have a cause, that space is infinite, 
 that substance underhes all material attributes, &c. With 
 these I am inclined to rank what have been called Axioms 
 — more properly. Assumptions — of geometrical science, 
 as they are propositions which- the geometer must assume 
 to be true, though they cannot be demonstrated ; for ex- 
 ample, — two straight lines cannot enclose a space ; a 
 straight line is the shortest distance between two points ; 
 two straight lines cut by a third line at equal angles, if 
 produced, will never meet. 
 
 3. We also reason demonstratively from Definitions, that 
 
AND DEDUCTIVE EVIDENCE. 873 
 
 is, from explications of the Intension of any Concepts which 
 we see fit to frame. Of course, such Judgments are purely 
 analytic, and if they contain no unfounded assumption, 
 that the signification thus assigned to the Names of the 
 Concepts is that which is usually afiixed to them in the 
 common use of language, or that the Marks enumerated 
 are all the original and essential quahties of the real things 
 which these Names denote, the Conclusions at which we 
 arrive must be demonstratively certain. 
 
 4. The laws, or positive precepts, which emanate from 
 any suificient authority, whether human or divine. These 
 are not Judgments, tut commands, and, as they are to be 
 obeyed at all hazards, and on all occasions, the only ques- 
 tion which can arise respecting them concerns their inter- 
 pretation. Of this nature are the injunctions of conscience, 
 the laws of the land, and the commands of God, as made 
 known in his revealed word. Apart from any doubt which 
 may arise concerning the signification of the terms in which 
 they are expressed, any Conclusion legitimately deduced 
 from such commands must be absolutely valid, since uni- 
 versality is of the very nature of law. 
 
 5. Universal propositions previously demonstrated. 
 
 6. Truths of generalization, based upon observation and 
 Induction or Analogy. These are true only to the extent 
 of our experience, which, as we have seen, never extends 
 to all or none. Consequently, these propositions rest only 
 upon probable evidence ; and though such evidence be suf- 
 ficient for moral certainty, they are not available for Dem- 
 onstration strictly so called. We may assume them to 
 be universally true, and upon such assumptions may rest 
 perfectly valid syllogisms ; but the Conclusion in such 
 cases will have no other or higher certainty than belongs 
 to the Major Premise. 
 
 It should be observed, however, that, when we thus 
 speak of merely probable evidence, the epithet is used only 
 
374 DEMONSTEATIVE REASONING 
 
 in its technical sense, and it is not meant that we have 
 necessarily less confidence in it than in mathematical Dem- 
 onstration. " The word prdbahle, when thus used," says 
 Dugald Stewart, "does not imply any defidehxy in the 
 proof, but only marks the peculiar nature of that proof as 
 contradistinguished from another species of evidence. It 
 is opposed, not to what is certain, but to what admits of 
 being demonstrated after the manner of mathematicians. 
 This differs widely from th© meaning annexed to the same 
 word in popular diseom-se ; according to which, whatever 
 event is said to be probable is understood to be expected 
 whh some degree of doubt." Perhaps the clearest distinc- 
 tion between Demonstrative and Probable evidence consists 
 in the fact, that the former does not admit of degrees^ as a 
 proposition is either demonstrated absolutely, or not at aU ; 
 while the latter may exist in any degree, from the faintest 
 shade of probabUity up to moral certainty. 
 
 This seems the proper place for the explanation of 
 the technical terms, or Second Intentions of Judgments, 
 that are used in the construction of Science. Most of 
 these, however, are of infrequent occurrence, except in the 
 mathematical sciences. All propositions are either Theo- 
 fetical or Practical; — the former are purely speculative, 
 the truths which they enounce being merely objects of con- 
 telbplaticMi by the mind, as having no reference to action 
 or conduct ; the latter have regard to something which is 
 to be done or omitted, to some performance or mode of 
 procedure. Propositions are also said to be demonstrable, 
 if they require or admit of proof; they are indemenstrable, 
 if, they are self-evident, or intuitively known. 
 
 An indemonstrable judgment, if theoretical, is called an 
 Axiom; if practical, it is styled a Postulate. A demon- 
 strable judgment, or one which is announced as needing 
 proof, if theoretical, is called a Theorem; if practical, it is 
 a Problem. A Thesis coincides very nearly with a Theo- 
 
AND DEDUCTIVE EVIDENCB. 375 
 
 rem ; it is a judgment proposed for discussion and proof. 
 A CoroUary is a truth announced as an immediate conse- 
 quence or collateral result of another judgment that has 
 just been proved, and therefore as not needing any sepa- 
 rate proof for itself. A Judgment which does not properly 
 belong to the science in which it appears, but is borrowed 
 from some other, is called a Lemma; one which merely 
 illustrates the science,- but is not an integral part of it, is a 
 SchoUon. An BypotheBis is a judgment not known to be 
 true, bioit accepted for the time as a provisional explanation 
 of some phenomena, and as liable to be modified or rejected 
 altogether on the production of further evidence. A The^ 
 0?^, soraetimes incorrectly used as a synonyme ior Bypoihe- 
 sis, is a comprehensive and methodical arrangement of 
 some large group of phenomena under, their supposed 
 Causes and Laws, offered as at least a provisional account 
 of them and mode of reducing them to system. " Theories 
 rum vireii" says Bacon, ?' ard,a et quasi se mutw) sustinente 
 pariiwm adaptationey qud quasiin orhem cohoerent, firm^Tin 
 tur." 
 
376 INDUCTION AND ANALOGY. 
 
 CHAPTEE XII. 
 
 INDUCTION AND ANALOGY. 
 
 ANY act of Reasoning strictly so called presupposes the 
 universality of its Sumption or Major Premise. If I 
 am not absolutely certain that all A are B, then, though 
 the Subsumption that C is A be undoubtedly true, I can- 
 not be sure that C is B. 
 
 Now it has been repeatedly proved, that universal Judg- 
 ments cannot be derived from mere experience, which is 
 competent to pronounce upon some, or many, but never 
 upon all, or none. But as we cannot have any knowledge 
 of real things, or actual existences, except by means of 
 experience, it follows that such things are not objects of 
 Reasoning in the proper sense of the term, — that is, 
 of Demonstrative Reasoning, in which the Conclusion is 
 accepted with absolute certainty. From the enumeralion 
 which has just been made, it appears that, with the unim- 
 portant exceptions of legal precepts and a few truths known 
 a priori, all Major Premises must be either mere analytic 
 judgments obtained by explicating our own abstract con- 
 ceptions, or general rules that are true only to the extent 
 of our experience. We may assume such rules to be uni- 
 versally true, and the Reasoning will then become perfect 
 or Demonstrative in Form; but as the Conclusion can 
 never be purged from the shade of uncertainty thrown 
 upon it by the imperfect evidence of the universality of 
 its Major Premise, such Reasoning is rightly considered as 
 merely probable or contingent. We may suppose, also, that 
 
INDUCTION AND ANALOGY. 377 
 
 the real existences perfectly correspond to the abstract con- 
 ceptions that we have formed of them, and, in this way, 
 may seem to obtain absolute Conclusions about matters of 
 fact. This is commonly said to be reasoning from hypoth- 
 eses ; but just so far as such reasoning is Demonstrative, it 
 concerns only the Concept, which cannot be more than an 
 imperfect representation of the reality. 
 
 For illustration, I borrow from Mr. Bailey's " Theory 
 of Reasoning," page 2, the following examples of Probable 
 or- contingent Reasoning. 
 
 1. " I am walking, I will suppose, on the sea-shore, and, perceiv- 
 
 ing a quantity of sea-weed lying on the beach, while the 
 water is at the moment a quarter of a mile from it, I con- 
 clude that the tide has ebbed, and left the weed where I 
 perceive it lying." 
 
 2. "I notice the print of a small foot on the sand, and I feel 
 
 pretty sure that it was made by a child." 
 
 Each of these instances may be resolved into the Form 
 of perfect or Demonstrative Reasoning, and it will then be 
 seen that the uncertainty which attaches to the Conclusion 
 arises solely from the doubt, which experience, however 
 often repeated, is incompetent to remove, as to the abso- 
 lute universality of the Major Premise. 
 
 1. All sea-weed found within the space usually covered by the 
 
 sea at high water must have been left there by the ebbing 
 of the tide ; 
 This bunch of sea-weed was so found ; therefore, &c. 
 
 2. No small foot-shaped imprint on the sand can have been left 
 
 by anything else than the foot of a child ; 
 This is a small foot-shaped imprint on the sand ; therefore, &c. 
 
 " In these several cases," says Mr. Bailey, " my mind is 
 determined by the sight of present phenomena, conjoined 
 with knowledge previously acquired, to believe something 
 which I do not actually perceive through the organs of 
 
378 INDUCTION AND ANALOGY. 
 
 sense ; — something past, something future, or something 
 distant ; or, in other words, to believe that some event has 
 happened, will happen, or is happening, although beyond 
 the sphere of my observation." In short, it is an attempt 
 to make the Thinking faculty do the work of the Percep- 
 tive faculty ; to gain a knowledge of an external fact by a 
 mere process of Thought, instead of acquiring it by obser- 
 vation through the senses. Such an attempt can have but 
 imperfect success ; its result is not properly denominated 
 knowledge, but belief, or opinion. The inference is rightly 
 said to rest upon Tuoral, or probable, evidence. 
 
 It is contended by some, that the mind actually rests 
 such inferences upon the amount of evidence which has 
 really been collected, though conscious that it is incom- 
 plete, and does not go through the Form of assuming a 
 Major Premise which is absolutely universal, and which, 
 if we were only sure that it was well founded, would ren- 
 der the Conclusion certain. Thus, to recur to one of the 
 instances just cited, Mr. Bailey argues, that the Premise 
 from which the mind actually draws the inference is what 
 he terms the Collective Fact, viz. that, in all the cases which 
 I have ever observed or heard of, all sea-weed so found has 
 been left by the tide, — and not the General Law, an- 
 nounced without this limitation, *hich affirms as much ab- 
 solutely of aU sea-weed so found. He maintains that the 
 General Law itself, just as much as the particular case in 
 question, is an inference from the Collective Fact. To 
 rest the inference respecting the individual case upon the 
 General Law, does not make the Conclusion a whit more 
 probable, than to rest it upon the Collective Fact on which 
 this General Law itself is founded. 
 
 Perhaps the question is one which does not merit much 
 discussion. Obviously it matters not whether tlie mind, in 
 seeking for competent proof of this particulai* inference, 
 proceeds by throwing what evidence it possesses into the 
 
INDUCTION AND ANALOGY. 879 
 
 ^orm, of perfect or Demonstrative reasoning, through the 
 assumption of a Major Premise which is not free from 
 doubt ; or whether it forbears any undue assumption in the 
 Premises, and adopts a process of inference which is con- 
 fessedly imperfect even in Form. Taking a doubtftil asser- 
 tion for a Premise, it thus preserves the Form of valid 
 reasoning. 
 
 AU men are fallible ; 
 
 The author of this book is a man ; 
 
 Therefore the author of this book is fallible. 
 
 Restrict thB statement in the Major Premise, so that it 
 shall express iio more than what is known to be true, and 
 tlie Reasoning thus becomes invalid through an undistrib- 
 uted Middle. 
 
 All men, so far as observation has extended, have been fallible ; 
 T?herefore this author is fallible. 
 
 As a fact, however, I believe the first of these forms is 
 much more frequently in Use. For proof in any particular 
 case, we usually refer to a Law of Nature, the universal- 
 ity of which is expressed with as little hesitation as if it 
 were a Law of Thought. The usual form of Enthymeme 
 employed is the following:^ — This bit of iron will melt, 
 because all iron is ftisible ; This water will boil at 212°, 
 because water always boils at that temperature ; These 
 men must die, for all human beings are mortal. In truth, 
 with the exception of those who have made a special study 
 of the theory of Reasoning, nobody thinks of restricting 
 the universaKty of such statements by the qualifying clause, 
 " so far as has been observed," or " according to all known 
 experience." And it is not mere carelessness in the use 
 of language, or the proneness to exaggeration which has 
 already been pointed, out for censure, that causes such 
 statements to be made without their proper limitations. 
 Very few are conscious, even after reflection, that there 
 
380 INDUCTION AND ANALOGY. 
 
 is any exaggeration in the case ; and there is none, except 
 what is implied by adopting the Form, without the sub- 
 stance, of Demonstrative Reasoning. 
 
 Induction and Analogy are the two processes of thought 
 by which we endeavor to make our Judgments about whole 
 classes of real objects, or actual existences, approximate the 
 absolute certainty and universality of our Judgments about 
 abstract conceptions. Hence they are, what Pure Reason- 
 ing is not, organa for the discovery of truth and the ax;tual 
 advancement of knowledge. But just so far as they are 
 means to these ends, they lose the character of Pure or 
 Demonstrative Reasoning; the Syllogisms to which they 
 are reducible are faulty either in Matter, as having a 
 Major Premise the universality of which -is merely •prdbor- 
 hie, or in Form, as containing an undistributed Middle. 
 The question whether they are entitled to be called Bea- 
 soning is hardly worth discussing here, as it concerns only 
 the use of words. Logical or Demonstrative Reasoning 
 they are not; but they may be denominated Probable 
 Reasoning, or Philosophical Presumptions. 
 
 It should be mentioned, however, that what may be 
 termed Logical Induction, the plena env/merabio "of the 
 logicians, which deduces a General Rule from what is 
 known to be true of every individual in the class, belongs 
 to Pure Reasoning strictly so called. Conclusions drawn 
 from such Premises as the following, are Demonstrative or 
 absolutely certain ; but these only generalize our knowl- 
 edge, or alter its expression; they do not enlarge it. 
 Mercury, Venus, the Earth, &c are all the Planets. 
 Peter, James, John, Matthew, &c are all the Apostles. 
 
 This mode of Reasoning has already been analyzed ; but 
 it is not what is understood by Induction in the processes 
 of Science. Logical Induction concludes from each one to 
 all; Induction properly so called concerns the Matter of 
 Thou^t, and concludes fit)m some to oM, 
 
INDUCTION AND ANALOGY. 381 
 
 The difference between Induction and Analogy has been 
 clearly stated and illustrated by Kant. In order to enlarge 
 our knowledge beyond the bounds of experience, we niust 
 either conclude from many things to all others of the same 
 Species, which is Induction ; or we must conclude from 
 the known agreement of twx) things in several qualities, 
 that they agree also in Home other quahty which, is not 
 directly known. In our progress from the Particular to 
 the General, Induction proceeds upon the principle, that 
 vihaA c&rtairdy belongs to many Individuals of the same kind, 
 also probably belongs to all the other Individuals of that hind; 
 the principle of Analpgy.is, that, if two things agree in many 
 respects, they probably agree also in some other respect. Be- 
 cause some one quality exists in many things, therefore it 
 exists in all of the same kind ; this is Induction. Because 
 many qualities in this are the same as in that, therefore one 
 other quality in this resembles that ; this is Analogy. In 
 other words. Induction concludes from one in many to the 
 others, by way of Extension ; Analogy, from many in one 
 to the others, by way of Intension. 
 
 The following are instances of Induction : — 
 
 1. In many cases in which water has been analyzed, it 
 has been found to consist solely of oxygen and hydrogen ; 
 therefore, all water is made up from these two elements. 
 
 2. Very many animals have Hbeen examined, and these, 
 without a single exception^ have been found to possess a 
 nervous system ; therefore, all animals have a nervous 
 system. 
 
 3. Most bodies expand in bulk, if heated; therefore, 
 heat always produces expansion, if it be not counteracted 
 by some other cause. 
 
 The following are instances of Analogy : — 
 1. The planets Venus and Mars resemble' the earth in 
 many respects, as in size, density, time of rotation on the 
 axis, distance from the sun, receiving light arid heat from 
 
382 INDUCTION AND ANALOGY. 
 
 it, &c. ; therefore, they probably resemble it in one other 
 respect, in being inhabited by living beings. 
 
 2. Fossil skeletons that are found in the rocks bear a 
 close resemblance in very many respects to the skeletons 
 which, as we know, once belonged to recently living ani- 
 mals ; therefore, they resemble them in one other respect, 
 in that these fossils are the remains of animals which were 
 formerly living upon the earth, 
 
 3. In many respects, as in complexity of parts, nice ad- 
 justment and mutual dependence of these parts one upon 
 another, dehcacy of finish, symmetry, and adaptation to 
 many useftd ends, the human hand resembles some inge- 
 nious machines, which we know to have been contrived and 
 fashioned by the exercise of mind ; therefore the hand was 
 so contrived and fashioned. 
 
 4. The argument of Origen and Bishop Butler is, that 
 if the Scriptures and the constitution of Nature are ahke in 
 this respect, that they proceeded from the same Author, 
 we may well expect to find the same difficulties in the for- 
 mer as are found in the latter. 
 
 It is plain that what is here called Analogy is the same 
 mental process which is described and analyzed by Aris- 
 totle as " reasoning from Example." He gives the follow- 
 ing as an instance of this sort of argument. If we would 
 prove that it is not expedient for the Athenians to make 
 war upon the Thebane, who are their neighbors, we may 
 reason from the analogous case, that the war against the 
 Phoceans, who were their neighbors, was fatal to the The- 
 bans. He says that Example is not founded, like Syllo- 
 gism, upon the relation of the whole to its parts, nor, like 
 Induction, upon the relation of the parts to the whole, but 
 upon the relation of one part to another, because the one 
 is more perfectly known than that other. The Aristotelic 
 Induction proceeds from aU the individual cases, while Ex- 
 ample is founded only upon some cS them, perhaps, as 
 above, upon a single instance. 
 
INDUCTION AND ANALOGY. 383 
 
 Comparatively little need be said of Analogy, as the Con- 
 clusions to which it leads are evidently not Demonstrative, 
 but merely Probable. Strictly speaking, there is no proof 
 whatever, because two things resemble each other, how- 
 ever nearly, or in however many respects, that the resem- 
 blance extends to a single point other than what has been 
 actually observed. The existence of one quality, it is true, 
 may be necessarily implied in that of another, either by the 
 Laws of Thought, or by the a priori laws of the human 
 mind ; as one geometrical property of a body may be de- 
 duced from another, or as its divisibility may be inferred 
 from its extension. This is Demonstrative Reasoning, but it 
 is merely explicating our knowledge, and not directly add- 
 ing to it ; and certainly it is not reasoning from Analogy, 
 which proceeds from similarity in some respects to similar- 
 ity in one other, or in many others. Analogical conclu- 
 sions may have any degree of probabiHty, varying from a 
 merely permissible hypothesis up to what may fairly he 
 called moral certainty. Because this kind of inference is 
 often greatly abused, for some degree of resemblance may 
 often be detected between two things apparently most dis- 
 similar, ^ skUl in such detection, when the inference is 
 ludicrously improbable, constituting wit, — I am inclined 
 to think that the force of which it is susceptible is generally 
 underrated. Shght Analogies are worth nothing, except 
 to show that the coexistence of two or more qualities is 
 barely possible, no belief whatever being justly created that 
 it is probable. On the other hand, the Analogy may be 
 so perfect that the Conclusion founded upon it may be ac- 
 cepted with as ftiU faith as if it rested upon an extensive 
 and cautious Induction, with which, indeed, it is frequently 
 confounded. 
 
 To recur to the instances just cited. The supposition 
 "that the other planets are inhabited rests upon an Analogy 
 which is so faint and imperfect, that it does not afford sufS- 
 
384 IN&UCtlON AND ANALOGY. 
 
 cient ground for making up any opinion on the subject, 
 either for or against the hypothesis. The resemblance is 
 but slight, even in the few particulars that are cited ; and 
 we have no evidence that there is any similarity whatever 
 in a vast number of other respects, many of which are 
 essential to the existence of life under any of the forms 
 with which we are acquainted. On the other hand, the 
 Analogy between the skeletons that exist only in a fossil 
 state, and those of animals now living, is so broad and per- 
 fect, that a man's sanity or sincerity Would be questioned 
 who should affect to doubt that the former also once walked 
 the earth or swam in the seas. These fossils do not differ 
 more from the extant types than many of the latter do 
 frflin each other, while in the numberless points of Analogy 
 the resemblance is perfect. And the conclusion in the 
 third case, founded upon the Analogy between the human 
 hand and a contrivance of man's device, is still more indis- 
 putable. If, without the aid of mind, without foresight or 
 design, the mere fortuitous concourse of atoms, in the lapse 
 of a past eternity, could have formed a livirui tree, fish, or 
 elephant, then, we say, that same rudderless and purpose- 
 less crowd of primeval atoms, in the lapse of a past eter- 
 nity, could have formed, what is much easier, a fossil tree, 
 fish, or elephant. We are here pointing out the analogous 
 character of two arguments, each founded upon Analogy, 
 but pointing to different Conclusions ; and we find the re- 
 semblance between them so perfect, that it is impossible to 
 maintain the validity of the Conclusion in the former case, 
 and deny it in the latter. 
 
 The definition which is ordinarily given of Analogy, that 
 it means proportion, or a similarity of relations, does not 
 differ from the one here propounded. Thus, it is said, 
 when we affirm the relation of the fins of a fish to the 
 water to be the same [similar] to that of the wings of a 
 bird to the air, that we are judging from Analogy. So we 
 
INDUCTION AND ANALOGY. 385 
 
 are ; we are pointing out what is perhaps an unexpected 
 resemblance amid apparent diversity. However unlike 
 fins are to wings, we still pronounce that they agree in this, 
 the adaptation of the former to the animal's motion through 
 the water being very similar to the fitness of the latter to 
 efiect motion through the air. From this equality of fit- 
 ness for corresponding purposes, we reason analogically that, 
 if one was contrived by intelhgence, the other was also. 
 
 Induction, says Mr. Mill, " may be summarily defined as 
 Generalization fii'om Experience. It consists in inferring 
 fi"om some individual instances in which a phenomenon is 
 observed to occur, that it occurs in all instances of a cer- 
 tain class ; namely, in all which resemble the former in 
 what are regarded as the material circumstances." This 
 last qualification is an important one, and has not received 
 sufficient notice fi-om those who have speculated upon the 
 theory of Induction. The process would be invalid and 
 nugatory, if we did not presuppose the correctness of the pre- 
 ceding Classifications that have been formed of the objects of 
 Science. A conclusion from some to all would not hold, 
 would not have even the slightest shade of probability, if it 
 were applied to a Class formed of the objects now contained 
 in this room, or of those embraced within my present field 
 of vision, or of things having no common attribute except 
 that they are of the same color, or the same size. But 
 such a conclusion becomes extremely probable, even mor- 
 ally certain, when applied to a Class, like that of metals 
 or stars, having many common characteristics which are 
 definite and peculiar, Thus, having ascertained of only 
 two metals, iron and copper, that they are conductors of 
 electricity, it would be ^ tolerably safe Induction, that 
 all metals are such conductors. Having found that one 
 thunder-cloud was electrical, Franklin at once safely leaped 
 to the conclusion, that all such clouds had that property. 
 T7g have already seen that the Classifications fqrmed of the 
 
 17 T 
 
386 INDUCTION AND ANALOGY. 
 
 innumerable objects of thought cannot be arbitrary, but 
 must be framed to embrace as many common or similar 
 elements as possible. The numberless properties of a 
 geometric figure can be deduced by necessary inference 
 from the one or two leading properties of it which are 
 selected to form its Definition. And the hope always is, 
 in forming a Classification of real objects or events in Na- 
 ture, to hit upon some attribute as the basis of the arrange- 
 ment with which all the other qualities of it are connected 
 by some necessary, though to us invisible, tie. 
 
 This appears to afibrd the solution of a problem which 
 has puzzled many inquirers ; — how it is, that we often 
 safely frame an Induction from a single instance, while, in 
 other cases, the conclusion is precarious, though supported 
 by a multitude of affirmative examples. Thus, the chem- 
 ist, having discovered a new metal, ascertains by a single 
 experiment its specific gravity, degree of hardness, tough- 
 ness, &c., and then safely concludes that every other speci- 
 men of the metal, which may afterwards be obtained, will 
 be found to possess these qualities in the same degree. On 
 the other hand, a multitude of instances of recovery from a 
 specific disease after the administration of a particular dmg 
 are insufficient to establish the universal efiicacy of the med- 
 icine in what appear to be similar cases. In Meteorology, 
 also, and in the several branches of Natural History, though 
 the Induction may be very extensive, and conducted with 
 all possible caution, the general conclusions have only that 
 low degree of probabUity which is indicated by calling 
 them empirical laws. The reason of this difference evi- 
 dently is, that the Classifications in the science of Chemistry 
 approach very nearly to perfection, the qualities determina- 
 ble by chemical analysis being definite, strongly marked, 
 and constant in their forms of combination with each other ; 
 while Medicine, Meteorology, and Natural History are, 
 and probably must ever remain, sciences very imperfect in 
 
INDUCTION AND ANALOGY. 887 
 
 Classification, as the objects with which they are concerned 
 have an indefinite multitude of ill-determined attributes, 
 shaded into each other by imperceptible degrees, and com- 
 bined in the most irregular manner. The lines, and even 
 the principles, of division of the objects of these sciences are 
 •merely provisional, and are frequently changed, so as to 
 adapt them to the progress of observation, or in the hope 
 of hitting upon some qualities which may be found in more 
 constant relations with the other leading properties than 
 those which have hitherto formed the basis of the Classifica- 
 tion. Of course, the Induction becomes extremely preca- 
 rious, when we are not sure that the instances over which 
 it extends agree with each other in all material circum- 
 stances. 
 
 It is evident, moreover, that the smaller the Class is, or 
 the nearer that it comes to an Infima Species, the stronger 
 is our assurance that, in reference to this Class, the conclu- 
 sion from some to all will hold good. The Induction is 
 safer, for instance, from some to all lumps of iron, than 
 from some to all metals ; and it is still more certain in ref- 
 erence to all specimens of one kind of iron, wrought or 
 malleable, than with respect to all sorts of that metal. As 
 the Extension and Intension of the Class-name are in in- 
 verse ratio to each other, that is, as the number of attri- 
 butes connoted is greater in proportion as the number of 
 objects denoted is less, the similarity of the members of the 
 Class to each other is increased as the number of those 
 members is diminished ; and the greater the similarity, the 
 safer the Induction, because it is then more probable that 
 the resemblance extends to the material or essential cir- 
 cumstances. As the Intension is greater, the Induction is 
 founded upon a larger number of qualities, that is, upon a 
 more perfect resemblance ; and as the Extension is less, 
 the Induction extends to fewer- objects, and is therefore 
 more likely to be well founded. The gap between some 
 
888 INDUCTION AND ANALOGY. 
 
 and all is not so great, when even all denot-es only a few. 
 We cannot safely reason, from the process of treatment 
 ■which has been effectual in one case of fever, to the effi- 
 cien'cy of the same treatment in any other instance, merely 
 because the symptoms of no one fever-stricken patient have 
 anything more than a general resemblance to those of an- 
 other ; and the internal peculiarities of the malady, of 
 which the outward symptoms are only the faint and easily 
 mistakable indications, are still more unlike. 
 
 Thus much, however, is certain, that if the Classification 
 is correct, if the cases brought together are really parallel 
 in all the essential circumstances, — and we must presup- 
 pose as much as this before we can reason from Induction 
 at all, — then we firmly believe, and assume it even as an 
 axiomatic truth, that " the course of nature is uniform," 
 that "natural events are governed by constant general 
 laws," that "what has been will be," and that "what has 
 been even in one instance has been in all other instances." 
 These are only different modes of expressing one and the 
 same Universal Truth, — one invincible conviction of the 
 human mind. This Truth is the ultimate Major Premise, 
 upon which all reasoning from Induction depends, or which 
 is taken for granted in all such reasoning. The simplest 
 and most indisputable case of such reasoning depends upon 
 this Maxim, just as much as the latest and broadest general 
 conclusion that has been propounded in physical science, 
 though this conclusion may be so questionable that it is 
 propounded only as an hypothesis. I could not be sure, for 
 instance, that the identical piece of coin now in my hand 
 stiU possesses the same weight, malleability, hardness, pu- 
 rity, &c., which I ascertained from actual observation that 
 it had only five minutes ago, if it were not for this irresisti- 
 ble belief in the uniformity of nature's laws. Whatever 
 doubts may perplex or weaken the inference from some to 
 all, these doubts do not concern the Primary Truth upon 
 
INDUCTION AND ANALOGY. 389 
 
 which all such inferences are based, but relate solely to the 
 correctness of the Classification over which the inference 
 extends. Is it certain that we have classified rightly ? 
 that the cases brought together are really parallel in all 
 essential respects ? If so, one instance is just as good to 
 base an Induction upon as ten thousand ; for we have an 
 irresistible conviction that, as the law thus operates in one 
 case, it must so operate in all. What is the ground of our 
 assumption of this General Truth ? How came we to be 
 convinced thus absolutely that nature's course is uniform? 
 He who can answer this question has solved the great 
 problem in the philosophy of Induction. 
 
 Dr. Reid, Mr. Stewart, and most of the other Scotch 
 philosophers, attempt to resolve our assumption of this 
 Maxim into an ultimate fact, into an original and instinc- 
 tive law of the human mind. Experience is constantly 
 tending to confirm it, but they hold that we believe in it 
 previously to all experience. They do not identify it with 
 the principle of Causation, — with the law that every event 
 must have a Cause, — but maintain that it is a distinct and 
 independent Axiom. Dr. Brown even goes so far as to at- 
 tempt to resolve the law of Causality itself into this Axiom. 
 He asserts that we are obliged to refer every event, every 
 beginning to be, to some Cause, because we have an instinc- 
 tive anticipation of the uniformity of nature's laws. My 
 own opinion, as will be seen hereafter, is exactly the re- 
 verse of Brown's thebry. It seems to me that our irre- 
 sistible conviction of the truth of this Maxim, that nature's 
 course is uniform, is resolvable into our necessary belief 
 of the law of CausaUty ; that the latter is the primitive 
 judgment a priori, -and the former is secondary and de- 
 rivative ; that a process of Thought, an act of Reasoning, 
 if not an appeal to experience, always precedes, and is 
 used to confirm or prove, our assertion that nature's course 
 is uniform, while we affirm at once, antecedently to all ex- 
 
890 INDUCTION AND ANALOGY. 
 
 perience, and without any attempt at proof, that every 
 event must have a Cause. 
 
 But however this may be, the doctrine in which Brown 
 agrees with Reid and Stewart, that we have an instinctive 
 and a priori conviction that nature's laws are imchange- 
 able, appears plainly indefensible. Entia non sunt mvl- 
 tiplicanda prceter neoesdtatem ; it is a cardinal maxim in 
 philosophy, that no principle can be admitted as an ulti- 
 mate fact until it is clearly shown that it cannot be ex- 
 plained as derivative. Indirectly, therefore, this doctrine 
 is refuted by the proof, which wiU subsequently be at- 
 tempted, that this principle is resolvable into the law of 
 Causahty. But still further : — any conviction, which is a 
 priori in its origin and character, must be universal, neces- 
 sary, and immediate. Now without going so far as Comte 
 and Mill, who maintain, with respect to this principle, that 
 " far firom being the first Induction we make, it is one of 
 the last," that "it was only acquired gradually, and ex- 
 tended itself, as observation advanced, from one order of 
 phenomena to another," and that "there are cases, in 
 which we reckon with the most unfailing confidence upon 
 uniformity, and other cases in which we do not count upon 
 it at all"; — without adopting these assertions, I say, it 
 may safely be pronounced, that we do not accept this prin- 
 ciple at first, or in all cases, unless it is justified by some 
 reflection or experience ; that is, imtil we have satisfied 
 ourselves that it is a necessary consequence of some intui- 
 tive and imperative belief, or have verified it by subsequent 
 observations. Tlu-ough the law of the Association of Ideas, 
 it is true, the recurrence of any phenomenon suggests all 
 the circumstances by which it was originally accompanied ; 
 it may even incline us to believe that these circumstances, 
 also, will recur in the same order as before. Even the dog 
 cowers at the sight of the whip which has once or twice 
 been used to punish him. But this is very far fi^om an 
 
INDUCTION AND ANALOGY. 391 
 
 immediate and necessary conviction that any of these for- 
 mer concomitants must so recur. We stop to analyze the 
 case and make distinctions ; we separate the conjunctions 
 that are believed to be invariable from those that are 
 merely casual, and accept the former only because we 
 recognize one of the events either as a Cause, or what is 
 believed to be the regular concomitant of a -Cause, of the 
 other. 
 
 " Every person's consciousness," says Mr. Mill, "assures 
 him that he does not always expect uniformity in the course 
 of events ; he does not always beUeve that the unknown 
 will be similar to the known, that the future will resemble 
 the past. Nobody believes that the succession of rain and 
 fine weather will be the same in every future year as in 
 the present. Nobody expects to have the same dreams 
 repeated every night. On the contrary, everybody men- 
 tions it as something extraordinary, if the course of nature 
 is constant, and resembles itself, in these particulars. To 
 look for constancy where constancy is not to be expected, 
 as, for instance, that a day which has once brought good 
 fortune will always be a fortunate day, is justly accounted 
 superstition. The course of nature, in truth, is not only 
 uniform, it is also infinitely capricious. Some phenomena 
 are always seen to recur in the very same combinations in 
 which we met with them at first ; others seem altogether 
 capricious." 
 
 On the other hand, the doctrine of Comte and Mill, that 
 our conviction of the uniformity of nature's laws, which is 
 the ground or principle upon which all Induction rests, is 
 it-self, obtained by Induction, appears to be an evident beg- 
 ging of the question. How can any mental operation be 
 used as a «ieans of discovering and verifying a principle 
 which must be taken for granted before that operation it- 
 self can be performed ? To obtain a number of Conclusions 
 by adopting a certain Maxim as a Major Premise, and then 
 
392 INDUCTION AND ANALOGY. 
 
 to use those very Conclusions as a means of proving that 
 Maxim, is evidently reasoning in a circle. Mr. Mill is per- 
 fectly aware of this objection to his doctrine, and frankly 
 states it in the strongest terms. " Can we prove a prop- 
 osition," he asks, " by an argument which takes it for 
 granted ? And if not so proved, on what e\'idence does it 
 rest?" 
 
 But though aware of the objection, it does not appear 
 that Mr. Mill has been successful in his endeavors to ob- 
 viate it. He rather augments the difBculty, by admitting 
 that the Maxim " was not, of course, derived from rigid 
 Induction, but from the loose and uncertain mode of Induc- 
 tion per enumerationem simplicem." Then the Premise 
 rests upon legs satisfactory evidence than the Conclusion, 
 and yet the latter is based exclusively upon the former. 
 Is not this a contradiction ? How can the superstructure 
 be more stable than the very foundation on which it rests ? 
 
 Induction by simple enumeration " consists in ascribing 
 the character of general truths to all propositions which are 
 true in every instance that we happen to know of." Thus, 
 we say that "All ruminating animals divide the hoof," 
 merely because no instance to the contrary has, as yet, 
 been discovered. But " to Europeans, not many years 
 ago, the proposition, 'All swans are white,' appeared an 
 equally unequivocal instance of uniformity in the course 
 of nature. Further experience has proved that they were 
 mistaken." Then the presumption in favor of what is still 
 the accepted rule, in the present state of our knowledge, 
 that all ruminating animals divide the hoof, would not be 
 held to outweigh the testimony of one unimpeachable wit- 
 ness, who should declare that, in some hitherto imperfectly 
 explored region, he had discovered a solid-hoofed ruminat- 
 ing animal. How can the evidence of these merely pro- 
 visional truths, which are liable to be overturned at any 
 moment, be the same with that which supports the validity 
 
INDUCTION AND ANALOGY. 893 
 
 of the Maxim upon which the most rigorous Inductions de- 
 pend ? 
 
 Mr. Mill answers, that even this precarious Induction, 
 that something is universally true because we have never 
 known any instance to the contrary, may become a valid 
 ground of behef when it is preceded by the assurance, that, 
 " if there were in nature any instances to the contrary, we 
 should have known of them." An empirical law, he argues, 
 " of which the truth is exemplified at every moment of 
 time, and in every variety of place or circumstance, has an 
 evidence which surpasses that of the most rigid Induction, 
 even if the foundation of scientific Induction were not itself 
 l^id, as we have seen that it is, in a generalization of this 
 very description." As to the admissions made in the pas- 
 sage which has just been quoted fi-om Mr. Mill, that we do 
 " not always expect uniformity in the course of events," 
 and that " the course of nature, in truth, is not only uni- 
 form, it is also infinitely capricious," it is claimed that the 
 progress of Inductive Science has already explained away 
 these apparent exceptions. This progress has been so 
 great, it is argued, that we now know directly that the 
 Maxim holds good of far the greater number of phenom- 
 ena, " the utmost that can be said being that of some we 
 cannot positively, fi:om direct evidence, afiirm its truth ; 
 while phenomenon after phenomenon, as they become bet- 
 ter known to us, is constantly passing fi:om the latter class 
 into the former ; and in all cases in which that transition 
 has not yet taken place, the absence of direct proof is ac- 
 counted for by the rarity or the obscurity of the phenomena, 
 or our deficient means of observing them, or the logical dif- 
 ficulties arising from the complication of the circumstances 
 in which they occur." 
 
 But even when the doctrine is thus limited and ex- 
 plained, it does not appear to be reheved firom the two fiin- 
 damental objections which have been urged against it, first, 
 
 17* 
 
394 INDUCTION AND ANALOGY. 
 
 that it founds the principle of Induction upon Induction 
 itself, which is reasoning in a circle, and secondly, that it 
 bases a stronger conviction upon a weaker one, a higher 
 probability upon a lower one. Granted, if you wiU, that 
 Induction itself, a rude Induction, gradually lead» us to be- 
 lieve in rigorous scientific Induction ; this may explain the 
 genesis of the phenomenon, or how it was that we were 
 first led to employ this organon of discovery. But before 
 we can accept the finiit of the Induction with the strong 
 and unhesitating conviction which we now accord to any 
 well-established Law of Nature, we must not only know 
 how we were first induced to believe that such a Law 
 exists, but we must find some valid principle which may 
 fairly be accounted a proof of its existence. Certainly such 
 proof cannot be obtained by reasoning in a circle. Mill 
 and Comte would have us believe, that our invincible con- 
 viction of the universality of the Law of Gravitation rests 
 upon no firmer basis than the opinion, which, indeed, is 
 daily gaining ground, and which the progress of mere Phys- 
 ical Science evidently tends to confirm, that everything in 
 nature is subject to law, so that it takes place by a phys- 
 ical necessity, and might be predicted with unerring con- 
 fidence, if we had a perfect knowledge of its antecedents. 
 " Every event has some invariable and unconditional ante- 
 cedent " ; — if we hesitate to admit this proposition in all its 
 generality, Mr. Mill thinks we cannot consistently believe 
 that all matter gravitates, that oxygen is necessary for the 
 support of animal life, or even that fire wiU burn and water 
 drown. We maintain that the latter propositions are in- 
 contestable, while the former, the principle of the univer- 
 sality of law, is' merely a hypothetical conclusion, though 
 an extremely probable one. Accordingly, to base the lat- 
 ter upon the former is to make the superstructure stronger 
 than its own foundation. Mr. Mill himself is compelled to 
 admit, with respect to one very large class of phenomena. 
 
INDUCTION AND ANALOGY. 395 
 
 those of the human will, that at least one half of the specu- 
 lative world, even in our own day, do not believe in the 
 universality of law, or that every event is necessarily de- 
 termined by its antecedents. And with regard even to 
 physical events, a large and increasing number of philos- 
 ophers, among whom are ranked Bishop Berkeley, Dr. 
 Samuel Clarke, and Dugald Stewart, hold that none of 
 them are subject to law, in the sense of being absolutely 
 determined by their physical antecedents, but are the re- 
 sults of volition, which is fi'ee to modify them at any mo- 
 ment. But without adopting this theory, he is a bold 
 advocate of the perfectibility of Physical Science who will 
 maintain that the probabihty of ultimately discovering that 
 phenomena still so apparently irregular and inconstant as 
 those of the weather, of health and disease, the countless 
 peculiarities of individual plants and animals, and the 
 equally numerous idiosyncrasies of human intellect and 
 character, are subject to fixed and definite laws, is so great, 
 that we may safely rest upon it all our confidence in the 
 physical laws that have already been established ; — that 
 this probability is the measure and the test of all the cer- 
 tainty that has hitherto been obtained in Physical Science. 
 
 Let us examine, then, the only remaining theory, which 
 is, that the ultimate Ground of Induction is the Law of 
 CausaKty, or the judgment that every event must have a 
 Cause, — not merely a constant physical antecedent, but an 
 efficient Cause. It is only necessary to show, that the Law 
 of Causality is readily and naturally explicated into the 
 Maxim that nature's course is uniform, so that the abso- 
 lute and imperative conviction, which belongs to the for- 
 mer as an a priori cognition of the human mind, is trans- 
 ferred, by an easy association of ideas, to the latter, though 
 not logically belonging to it. 
 
 Take the simplest case of Induction, by which we are 
 led to expect that any physical object will always continue 
 
396 INDUCTION AND ANALOGY. 
 
 to manifest the same qualities that have hitherto been ob- 
 served in it, unless it is exposed to some new inflaences, or 
 a new antecedent is brought in. Here the assumption evi- 
 dently is, that the qualities of the same thing are perma- 
 nent, unless some Cause intervenes to change them ; and 
 this assumption is logically certain, for it is an Immediate 
 Inference from the Law of Causality, that no change what- 
 ever can take place in anything without a Cause. The 
 coin mugt retain the same attributes which it was recently 
 observed to possess, if there has not been some Caitse of al- 
 teration. This proviso is the source of doubt which must 
 always arise when an unquestionable abstract truth is ap- 
 plied to real objects or actual events. We never can be 
 sure that such a Cause of change has not intervened ; but 
 we are morally certain that it has not, if there has been no 
 apparent alteration of the circumstances of the case, no 
 seeming exposure to new influences. To this extent, then, 
 we can safely reason from the past to the ftiture, or from 
 some to all, when satisfied that the Classification is correct, 
 — that is, that no new occurrence or Efficient Cause has 
 destroyed the resemblance of the observed instances to the 
 expected ones, or of some to the others. 
 
 The next sort of Induction, though a little more compli- 
 cated, is easily resolved into the same Law of Causality. It 
 has already been shown that among the other properties 
 of any particular substance must be ranked its active and 
 passive powers, that is, the changes in other bodies of 
 which its proximity has been a constant antecedent, or the 
 changes to which it is itself subject when brought into re- 
 lation with other substances under different circumstances. 
 These active and passive powers, regarded as mere se- 
 quences of phenomena, may properly be reduced to the 
 preceding head of qualities ; they form, as we have seen, 
 one class of the attributes of every substance, and, as such, 
 enter into the Intension of the Concept which denotes that 
 
INDUCTION AND ANALOGY. 397 
 
 substance. In truth, what are called secondary qualities 
 are only the powers which bodies possess to excite certain 
 sensations in us, when brought into relation with our or- 
 gans of sense. And in like manner, the capacity of gold 
 to be melted on the application of a sufficient degree of 
 heat is an integral part of our complex notion of this sub- 
 stance. Powers being nothing but qualities, then, the Law 
 of Causahty is applicable just as in the former case ; these 
 powers must be fixed or constant in their operation, if a 
 new Cause has not supervened to alter them. The general 
 maxim is one of absolute certainty, but in its application to 
 a given case we never can be sure that the proviso in it 
 has been rigidly fulfilled. This doubt must always remain, 
 and is usually more serious, and less capable of being re- 
 duced by further observation and experiment, as regards 
 the powers, than with respect to the other qualities, of bod- 
 ies. The circumstances to be observed in order to prevent 
 the intrusion of a new antecedent are more numerous and 
 complex ; we cannot so easily be assured that the cases are 
 strictly parallel. The unexpected, presence of a httle more 
 or less carbon may have diminished the ftisibihty of the 
 metal ; if a large mass of iron be near, the action of the 
 magnetic needle is disturbed. 
 
 Still further; — it is now known that the merely physi- 
 cal antecedents and other circumstances are not the Effi- 
 cient Cause of the phenomenon, but are beheved to be its 
 regular concomitants only because their presence, thus far, 
 has been invariably followed by the effect. Accordingly, 
 whatever assurance we may possess that the outward cir- 
 cumstances are unchanged, it is still possible that the real 
 Cause may be so far modified that the expected result will 
 no longer be produced. The doubt which thus rests upon 
 the case cannot be dispelled by any precautions whatsoever. 
 The cases may be strictly parallel in every visible respect, 
 as tested by the nicest observations ; but if the physical 
 
S98 INDUCTION AND ANALOGY. 
 
 antecedent was only the occasion, and not the Cause, the 
 phenomenon may not be repeated, as it is always possible 
 that the true Cause may now for the first time exist under 
 different combinations. To recur to the illustration taken 
 from Mr. Babbage's machine ; — though, in countless in- 
 stances, each number presented has been greater than its 
 immediate predecessor by unity, yet as this constant pre- 
 cursor was not the true Cause which determined the num- 
 ber that was to come after it, it is always conceivable that 
 the next presentation should be of an entirely novel char- 
 acter. 
 
 We can now see why it is that the Maxim which is the 
 Ground of Induction, and on the assumption of which the 
 validity of all our reasoning about real objects and actual 
 events depends, appears so unquestionably true that. we 
 regard it as an Axiom. To say that nature's course is 
 uniform, and that all events are subject to law, is only to 
 assert our intuitive conviction, that every phenomenon must 
 have an Efficient Cause, that, while the Cause remains 
 the same, the effect must he constant and proportional to it, 
 and hence, that, whenever the true Cause is discovered, we 
 are enabled to predict unerringly the recurrence of the 
 effect. The relation between a true Cause — that is, an 
 efficient Cause — and its effect, is radically unlike that be- 
 tween a physical antecedent and its physical consequent. 
 No absolute conviction, no law of the human mind, mani- 
 festing itself anterior to all experience, and tliereby first 
 rendering experience possible, asserts any connection be- 
 tween antecedent and consequent like that which exists 
 between Cause and effect. The relation between the two 
 former, that of mere succession in time, is contingent, rest- 
 ing solely upon experience, and liable to be overturned at 
 any moment by subsequent experience ; between the two 
 latter, it is a Causal relation, and, as such, is absolute and 
 imchangeable, for it is irreversible even in thought. What 
 
INDlJCTION AND ANALOGY. 399 
 
 do we mean when, as a ground of reasoning from some to 
 all, we assert that nature acts uniformly, or that all phys- 
 ical events are subject to law ? Not, surely, that a given 
 antecedent must always be followed by that particular phe- 
 nomenon which, according to all experience thus far, has 
 been its invariable consequent. This is the only conclu- 
 sion which mere Induction aims to establish ; but it is not 
 competent to serve as the Ground of Induction itself, or as 
 that Premise which must be taken for granted before rea- 
 soning by Induction is possible. But we mean only that 
 the sequence in question is necessary, if the antecedent is 
 the Efficient Cause (or the invariable concomitant, sign, or 
 precursor of such Cause) of the consequent. We mean 
 only to assert the existence of an irreversible law, and not 
 necessarily that such law has already been discovered. 
 Comte and all his followers will tell us that no event, how- 
 ever extraordinary and unexpected, is to l)e deemed a 
 miracle, — that is, a violation of law, — because the pre- 
 sumption is, that ftirther research will either reveal a new 
 law, or an improved expression of an old one, under which 
 the occurrence, however strange and marvellous, may nat- 
 urally be subsumed. He will say, — to adopt a well-worn 
 illustration, — that the conversion of water into a solid was 
 a miracle to the King of Siam ; but with our larger expe- 
 rience, it is no miracle to us, for we have even discovered 
 the law, — that is, the constant antecedent, — under which 
 the formation of ice takes place. What is this but to assert 
 that our conviction of the universality and permanence of 
 law, so far from being derived from experience, so far from 
 resting on that very process of Induction of which it is the 
 sole support, is strong enough to contradict all experience, 
 and to maintain its place as an Axiom, though contradicted 
 by the largest and most cautious Induction which human 
 science has ever framed ? Not even the resurrection of a 
 dead man, says the Positivist, would be a violation of 
 
400 INDUCTION AND ANALOGY. 
 
 law ; — then his conviction of the permanence of nature's 
 laws overrides all the evidence, of experience, and contra- 
 dicts the whole tenor of modem Inductive science. 
 
 What is called physical necessity is nothing but a convic- 
 tion that the relation of an Efficient Cause to its effect is 
 unalterable, coupled with the assumption, which is a natural 
 one, but still illogical, either that the particular antecedent 
 or concomitant phenomenon is itself the Cause, or is so 
 closely connected with it that its presence must always be 
 followed by the recurrence of the effect. The only ground 
 of this assumption is the invariability of the succession in 
 time, or the fact that, so far as our experience, or as all 
 human experience, has extended, the one phenomenon has 
 always been the immediate consequent of the other. That 
 this ground is insufficient to justify us in calling the succes- 
 sion a necessary one has already been abundantly proved. 
 The Positivists, in their desire to eliminate the notion of 
 cause altogether, although they are compelled to retain the 
 word and all the associations connected with it, refuse to 
 attribute the phenomenon to any single antecedent. The 
 invariable sequence, they say, exists between a consequent 
 and the sum of its several antecedents, all of which must 
 concur before we can be sure of the presence of the effect. 
 In other words, what they call a catise is only an assem- 
 blage of the conditions, all of which must be ftdfiUed before 
 the phenomenon can be reproduced. " The real Cause," 
 says Mr. Mill, " is the whole of these antecedents ; and we 
 have, philosophically speaking, no right to give the name 
 of cause to one of them, exclusively of the others." And 
 again, " the Cause is the sum total of the Conditions, posi- 
 tive and negative, taken together ; the whole of the con- 
 tingencies of every description, which, being reahzed, the 
 consequent invariably follows." Among tliese " negative " 
 conditions, or rather, as the sum of them, he ranks " the 
 absence of preventing or counteracting Causes." In con- 
 
INDUCTION AND ANALOGY. 401 
 
 formity with this view, the distinction between agent and 
 patient, between something which acts and some other 
 thing which is acted upon, is formally abolished, as it is 
 denied that there is any action in the case. An inevitable 
 corollary of this doctrine is, that there is no 'power or ^- 
 dmcy in any one of the antecedents the exertion of which 
 necessarily creates the effect. Yet the denial of any such 
 causal agency entirely refutes the hypothesis that there 
 is any necessary connection between the two events, and 
 leaves their union merely a contingent one, hable to be 
 dissolved or contradicted by subsequent experience. By 
 rejecting the doctrine of Efficient Causation, the Positivist 
 theory throws away all evidence of the permanence and 
 universality of nature's laws. 
 
 This conclusion will appear still more obvious when it is 
 demonstrated, as can very easily be done, that every pro- 
 cess of Inductive Reasoning, however rigidly conducted, 
 and however verified by subsequent observations, is still re- 
 solvable, in the last analysis, into the despised " Induction 
 by simple enumeration," which Lord Bacon calls mera pal- 
 patio, or groping in the dark. The best evidence which 
 physical science has been able to collect in support of the 
 most generally recognized Laws of Nature amounts only to 
 this, that they are found to be true in every instance that 
 we happen to know of. Mr. Mill admits that Induction 
 necessarily commences with this very imperfect evidence ; 
 and he should have added, that it also proceeds and ends 
 with it, finding no other or stronger basis on which to rest 
 its conclusions. 
 
 Nearly all the additional evidence which the advance- 
 ment of science procures for those conclusions which were 
 at first avowedly accepted as inferences from Induction by 
 simple enumeration, (perhaps fr'om an enumeration only of 
 a few instances, or even from a single case,) arises either 
 from extended observation and experiment, from an im- 
 
402 INDUCTION AND ANALOGY. 
 
 proved classification of the objects about which we reason, 
 or from what Dr. Whewell calls, by a happily invented 
 phrase, the consilience of several Inductions. The process 
 of Induction, when considered as an operation of mind, or 
 asa sort of inference, is essentially one and the same, and 
 perfectly determinate in character. There are not several 
 kinds of it, though there are various degrees of caution, 
 precision, and thoroughness with which it is carried out. 
 It is always employed with reference to a class of objects, 
 qualities, or events, whether that class be well or iU formed, 
 that is, whether the members of it do, or do not, agree 
 with each other in aU material respects ; and it always pro- 
 ceeds from some to all of that class, whether the conclusion 
 thus formed does, or does not, coincide or harmonize with 
 other conclusions obtained by a perfectly similar process, 
 though from other data, and with a difiFerent purpose in 
 view. The village matron, undertaking to prescribe for 
 the illness of her neighbor's child from what she judges to 
 be the similar cases that have happened in her own family, 
 and Sir Humphry Davy, anticipating that his mode of 
 analyzing potash into the oxide of a new metal would not 
 only hold good of all other lumps of potash besides the 
 very one he was experimenting upon, but would be found 
 practicable, and would lead to similar results, in the case 
 of other alkalis and earths, are both alike reasoning from 
 Induction by simple enumeration. The only difference is, 
 that the diseases which affect the human frame are very 
 numerous, and, as they have but few recognizable symp- 
 toms, can be but imperfectly classified at best, and a village 
 matron would probably classify them very ill, so that her 
 inference from some to all would be wrong ; while the 
 alkalis are few in number, and have determinable and 
 strongly marked common quahties, so that the correspond- 
 ing inference in their case was entirely safe. 
 
 Attempts have been made at various times to frame what 
 
INDUCTION AND ANALOGY. 403 
 
 may be called a " Logic of Induction," or a fuU analysis 
 and description of the operations by which we proceed to 
 the discovery of physical laws. Lord Bacon, who made 
 tbe earliest and most remarkable endeavor of this sort, 
 hoped to furnish a method of scientific investigation which 
 should be so complete and accurate as to constitute an or- 
 ganon of discovery, and reduce all intellects to a level, 
 making success in the search after truth a matter merely 
 of time and labor. Taught by experience that discoveries 
 cannot be thus made by rule, but are generally the results 
 of a tentative process many times repeated, and a happy 
 combination of circumstances, the later followers of Lord 
 Bacon have attempted merely to analyze and describe the 
 process by which discoveries have been made, without hop- 
 ing to indicate any sure method of adding to their number. 
 But even this endeavor, though aided by all the lights of 
 modern physical science, and prosecuted by such eminent 
 thinkers as Sir John Herschel, Dr. Whewell, and Mr. J. 
 S. Mill, has had but very hmited success. The results do 
 not agree ; though the same compound phenomena are pre- 
 sented for examination, they are analyzed by these three in- 
 quirers into very different elements and processes of thought. 
 These theorists do not even hold the same opinion as to 
 the nature of the process which they have to separate into 
 its elements, or, in other words, as to what constitutes Iut 
 duction. Dr. Whewell, fearful of resting the whole cer- 
 tainty of physical science upon so narrow and unstable a 
 basis as reasoning in respect merely to all the cases that we 
 happen to know of, boldly restricts the name of Induction 
 to what seems to be a mere generalization of the facts 
 already observed, but as now seen imder a new light be- 
 cause succinctly comprehended in one general formula; 
 and appears to lose sight altogether of the necessity, if 
 science is to fiilfil its office of anticipation and prediction, 
 of extending the generalization to all the objects and events 
 
404 INDUCTION AND ANALOGY. 
 
 of a given class, whether they have yet been observed or 
 not. Mr. J. S. Mill, who has more confidence in the pre- 
 cautions and the means of verification by which men of 
 science test and confirm the rude Inductions of the vulgar, 
 justly asserts that Dr. Whewell's mere " Colligation of 
 Facts," far fi-om being the type of Induction generally, 
 "is not Induction at all," but only a new description of 
 the phenomena. He undertakes to analyze and reduce to 
 system these precautions and means of subsequent verifi- 
 cation, and to show that, when they are duly observed 
 and practised, scientific Induction differs in kind, and not 
 merely in degree, from Induction by simple enumeration, 
 and, though based merely on experience, establishes its 
 conclusions with the highest certainty of which the human 
 mind is capable. But experience, fi-om its very nature, 
 cannot extend beyond a limited nmnber of cases ; and as 
 even the most cautious and rigorous Induction avowedly 
 has no other foundation than experience, either the abso- 
 lute universahty of the Laws of Nature is not scientifically 
 established, or it must be deduced fi-om a priori considera- 
 tions respecting the relation of an Efficient Cause to its 
 effects. The consilience of several Inductions merely ex- 
 tends the enumeration to a larger number of cases ; but 
 any such extension, of course, cannot include future in- 
 stances, nor in any way enlarge the domain of possible ex- 
 perience. In fact, most of the scientific processes, which 
 are ably analyzed by Mr. Mill, have reference to the use of 
 Induction as an organon of discovery, and not as a medium 
 of proof ; they point out the inferences which we ought to 
 make, but they do not render any more stable the founda- 
 tion by which all such inferences are supported. And any 
 improvements in the modes of observation, or in the classi- 
 fication of the things observed, are merely preparatory to 
 the process of Induction, and do not in any way affect the 
 essential nature of that process. 
 
INDUCTION AND ANALOGY. 405 
 
 Putting aside the terminology invented by Dr. Whewell, 
 and also that recommended by Mr. Mill, as not even their 
 authority has sufficed to bring either into common use, it 
 may be said that there are but three phrases generally em- 
 ployed to designate those results of Induction which con- 
 stitute the highest generalizations of science. These are 
 a G-eneral Fact, a Law of Nature, and a Cauge, this last 
 being now usually understood to mean nothing more than 
 an Invariable Antecedent. Unfortunately, even these three 
 phrases are so wavering and uncertain in their significa- 
 tion, that they are often employed as synonymes, while 
 hardly any scientific person is consistent in the use which 
 he makes of them, and no two writers upon the philosophy 
 of the physical sciences agree with each other in the at- 
 tempt to hmit and define their meaning. 
 
 The first of the number, a General Fact, though em- 
 ployed with somewhat more precision and consistency than 
 the other two, is yet of narrow and indeterminate range, 
 and is grudgingly used, because it is modest in pretension, 
 and does not feed the pride of science, or gratify the van- 
 ity of the inquirer into the secrets of nature. It coincides 
 with what Mr. Mill calls an Empirical Law, or the result 
 of' an Induction by simple enumeration. Thus, it is prop- 
 erly a General Fact that all horned .animals are ruminant, 
 that all quadrupeds are viviparous, that every living thing 
 is produced from an egg, that opium and alcohol intoxicate, 
 &c. But the phrafee is sparingly used, because we are not 
 content simply to point out a new characteristic of a whole 
 class of objects, or to form a new class of facts by tracing 
 their hitherto unsuspected agreement with each other, so 
 far as our observation has extended, in some latent attri- 
 bute; We aspire to the much higher praise of determin- 
 ing a new " Law of Nature," which must hold true on all 
 occasions, whether observed or not, and the discovery of 
 which is therefore equivalent to a revelation of another of 
 
406 INDUCTION AND ANALOGY. 
 
 the immutable purjioses of the Almighty. The General 
 Fact is admitted to be true only so far as our observation 
 has extended, or at any rate to afford comparatively but a 
 shght presumption that it will be found to hold good in 
 cases as yet unobserved. But as already remarked, the 
 narrower and the more definite the class, the stronger is 
 ■ this presumption. Thus, that every antelope is ruminant, 
 is a far more probable conclusion than that all homed ani- 
 mals are ruminant; we admit very readily that all the 
 mammalia are produced from eggs, but not so readily that 
 the whole animal kingdom are thus produced. 
 
 A Law of Nature, in its more definite signification, is 
 employed to designate a group or series of General Facts, 
 relating to the same subject or class of subjects, and difier- 
 ing from each other by some mode of proportional varia- 
 tion, so that the place of every member of the series may 
 be easily deduced irom one numerical formida. Such are 
 Kepler's laws of the planetary motions, the law of definite, 
 reciprocal, and multiple proportions in Chemistry, and of 
 phyllotaxis in Botany. The General Facts may be known, 
 long before their relation to each other, or their law of 
 proportional variation, is discovered. Thus, the General 
 Fact that the leaves of the apple-tree are disposed in cycles 
 of fives, and so that the spiral hne connecting their points 
 of insertion passes twice round the stem for each cycle, 
 their arrangement being thus conveniently denoted by the 
 fraction |, was ascertained, and a corresponding General 
 Fact for many other species of plants was equally well 
 known, before the " Law " was discovered, that the result- 
 ing fractions fall into a series, any one of which has for its 
 numerator the sum of the two preceding numerators, and 
 for its denominator the sum of the two preceding denomi- 
 nators. So, also, the General Facts in Optics, that the 
 angle of refraction, measured from the perpendicular to 
 the surface of any medium heavier than air, is always less 
 
INDUCTION AND ANALOGY. 407 
 
 than the angle of incidence, and is not proportional to it, 
 were commonly known, and even Tables had been labori- 
 ously formed, giving experimental measures of refraction 
 for the various angles of incidence, and for different media, 
 many centuries before Snell, in 1621, superseded the use 
 of many of these Tables by discovering the simple Law 
 of Nature, that the ratio of the sines of the angles of 
 incidence and those of refraction is constant for the 
 same medium. Every measurement of refraction as for- 
 merly given in those Tables was a General Fact, includ- 
 ing every case of a ray of hght falling upon the given 
 medium at the given angle ; and this Fact was obtained, 
 of course, by reasoning Inductively, that as the refraction 
 for this angle of incidence and this medium had been ac- 
 tually observe^ to be of this magnitude in some cases, 
 (namely, in all that had bfeen observed,) it would be 
 found of the same magnitude in all such cases. Snell's 
 discovery of the " Law " took the place of an immense 
 number of such Facts, by summing them all up in one 
 general proposition or formula, thereby rendering any de- 
 tailed mention of them unnecessary. 
 
 Such a discovery as this by Snell is what Dr. Whewell, 
 by a happily selected phrase, calls a " Colligation of Facts " ; 
 and the process by which it is arrived at — the method, if 
 there be one, of making such a discovery — is what he de- 
 nominates Induction. Mr. Mill very properly objects, that 
 it is not Induction at all. It is an act of generalization, 
 founded on direct intuition of the relations which the cases 
 actually before us bear to each other, and not professing to 
 extend beyond these cases. Consequently, it does not en- 
 large our knowledge, as Induction always does, but only 
 grasps up together into one Concept the knowledge which 
 we already possessed ; and it accomplishes this through 
 perceiving that this group of General Facts, instead of 
 being entirely heterogeneous, as they at first appeared, 
 
408 INDUCTION AND ANALOGY. 
 
 are really linked together by some common relation, the 
 expression of which reduces them to unity in the Under- 
 standing, and so renders them more easy to be remem- 
 bered and more convenient to be used. 
 
 It is true, as Mr. Mill remarks, that a real act of Induc- 
 tion usually goes along with the Colligation, as subsidiary 
 to it. In this case, Snell not only took for granted the 
 previous Inductions, which, as we have seen, are expressed 
 in the separate General Facts that he grouped together in 
 his formula, but also, having ascertained by actual observa- 
 tion that this formula held true for refi^ction in some media, 
 he reasoned Inductively that it would hold true for aU 
 media, or, in other words, that it was the universal Law 
 of refraction. 
 
 It ought also to be remarked, that the discovery of the 
 Law which colligates the General Facts does not change 
 the nature of the evidence on which those Facts depends, 
 or raise them out of the rank of Probable, into that of De- 
 monstrative, judgments. These Facts are still nothing but 
 truths of Induction, just as much after the discovery of the 
 Law as they were before it. The discovery, it is true, 
 laakes the previous Inductions somewhat more probable 
 than they were before ; but it does not by any means de- 
 monstrate them. The degree of probability is increased 
 through the discovered consili&nce of the Inductions, as this 
 consilience amoimts to increasing the basis of enumera- 
 tion on which each of them rests. A number of conclu- 
 sions affecting a group of kindred subjects are mutually 
 strengthened, when it is found that the separate Induction 
 leading to each one of them harmonizes in one respect, 
 or in several respects, with the Inductions leading to all 
 the others ; for such harmony is precisely what we expect, 
 in view of the Maxim on which all Inductive reasoning 
 depends, that nature's course is uniform. Each Induction 
 stands more firmly, when it not only rests on its own foun- 
 
INDUCTION AND AKALOGY. 409 
 
 dation, but is indirectly supported by the foundations of it? 
 neighbors. 
 
 According to the view here given, a Law of Nature is a 
 generalization of the second order ; in some respects, it 
 bears the same relation to General Facts, that a General 
 Fact bears to Individual Facts. I say "in some respects" ; 
 for this statement does not convey the whole truth. A 
 Law of Nature is not a mere truth of classification ; it is 
 not merely a Genus of which the several General Facts are 
 the Species. If it were, then the tabulated measures of 
 refraction, or any other mere collection of General Facts 
 relating to the same class of subjects, might be called a 
 Law. But it is not so ; a Law may be contained in such 
 a Table, but it is concealed there, and when discovered, 
 the Table itself becomes useless. The discovery, as I have 
 said, consists in a perception of the truth, that the group 
 of General Facts falls naturally into a series, in which the 
 place or power of any term is easily deduced fropi a single 
 brief formula. The effort of mind by which such a dis- 
 covery is made is rather an Intuition, or a happy conjec- 
 ture, than an Induction. The kind of conviction which 
 attends the discovery, when made, is not mere probability, 
 but certainty. With reference to the General Facts actu- 
 ally before us, we hnow that the Law is there, for we see it 
 just as soon as we have learned where to look for it. But 
 the universality of the Law, the extension of it to all other 
 General Facts, not now observed, of the same class, is the 
 result of an Induction ; and the establishment of the Law 
 also takes for granted the vahdity of the preceding Induc- 
 tions on which each separate General Fact depends. Here, 
 as elsewhere, whenever we attempt to extend our knowl- 
 edge beyond what is actually observed, our only guide is 
 Induction by simple enumeration. 
 
 The process, of hunting for a Law of Nature amid a 
 group of General Facts is essentialljjr tentative, resembling 
 
 18 
 
410 INDUCTION AND ANALOGY. 
 
 an attempt to find the meaning of a riddle ; we try one 
 guess after another, and at last stumble upon the right one 
 ■when we least expected it. Success is usually obtained, 
 not by trying to extend the survey, or to contemplate the 
 largest possible number of cases, but by restricting the 
 field of search to a few well-chosen instances, and attempt- 
 ing to find a pattern or construction which these few will 
 precisely fit. To take an example from a quarter where 
 we should least expect to find one, — from pure mathe- 
 matics ; Newton discovered the Binomial Theorem, which 
 is a true Law of Nature according to our definition, prob- 
 ably by simple inspection of a few of the lower powers of 
 binomials, the law of the exponents being obvious enough, 
 and that of the coefiieients offering but little difficulty to 
 his marvellous insight. He certainly discovered and used 
 the Theorem long before he endeavored to demonstrate it, 
 or to trace it to its true mathematical principles. There 
 is reason«to beUeve that not a few of the general theorems 
 of the higher mathematics have been discovered in a pre- 
 cisely similar manner. 
 
 Why the Law should be suddenly revealed to a single 
 happy glance, when it had previously escaped the most 
 laborious research, is a curious problem, which perhaps 
 admits of no complete solution, though the process may 
 be elucidated in a few particulars. The essential charac- 
 teristic of such a Law is a series proceeding by some uni- 
 form gradation, the relation between two or more consecu- 
 tive terms in any part of it being the same as that existing 
 between the coi'responding terms in any other part. This 
 relation may be simple or complex, recondite or obvious. 
 Each term may be an increment of its predecessor by the 
 addition of a constant quantity, or may be a simple multi- 
 ple of it, or may be related to it through some of tlie peri- 
 odic magnitudes connected with a varying angle, such as 
 the sine, tangent, secant, &c. ; or the law of progression 
 
INDUCTION AND ANALOGY. 4ll 
 
 may be coveted up, ds it were, by a constant quantity 
 added to each of the terms ; or the numbers, as we have 
 them, may be the complex results of t'W'o or more indepen- 
 dent series multiplied into each other, in which case there 
 are two or more independent Laws to be discovered. Two 
 difficulties, then, are to be overcome, either one of which 
 would seem to be insuperable if the other had not been 
 previously mastered ; we must pfopetly arrange the terms 
 of the series before the LaW of it can be discovered, but a 
 knowledge of the Law is indispensable before we can with 
 certainty make such an artangement. In a contest with 
 60 many and so serious difficulties, it is not surprising that 
 success at last should often Seem attributable quite as much 
 to accident, as to sagacity and dogged perseverance. 
 
 Kepler has furnished an instructive narrative of his suc- 
 cessive attempts to reduce to Law the astronomical obser- 
 vations of Tycho, constructing many formulae by hypothesis, 
 finding that one after another Would hot fit, and, after each 
 disappointment, trying again with unwearied patience. At 
 last, his perseverance was rewarded with the discovery of 
 the great Laws which deservedly bear his name, as they 
 are the foundations of the whole modern science of astron- 
 omy, for they sum up ill three sentences all recorded as- 
 tronomical observations. He also attempted, in a similar 
 way, to detect the Law concealed in the measured angles 
 of relfraction, by comparing them with the angles of inci- 
 dence through a variety of constructions by triangles, conic 
 sections, &Ci ; but all without success. Where he failed, 
 Snell succeeded, twenty years later, merely by turning his 
 attention from the direct measures of the angles to the ratio 
 of their sines. The law was then manifest at a glance. 
 Such instances are needed to remind us, that the well- 
 known fable of Columbus and the egg is not a caricature, 
 but a faithful representation, of many of the greatest dis- 
 coteries in science. What Dr. Whewell happily calls 
 
412 INDUCTION AND ANALOGY. 
 
 " the ex-pogt-facto obviousness of discoveries, is a delusion 
 to which we are liable with regard to many of the most 
 important discoveries." 
 
 The validity of a Law of Nature thus discovered, as it 
 were, by a happy casualty, is regarded as sufficiently estab- 
 lished by comparison with but very few of the observed 
 data from which it was educed. Thus, Dalton's magnifi- 
 cent generalization, coextensive with all matter, and now 
 verified by almost countless analyses, that chemical ele- 
 ments combine only in definite, reciprocal, and multiple 
 proportions, was first suggested to him during his examina- 
 tion of only two compounds ; " and was asserted gener- 
 ally," says Dr. Whewell, " on the strength of a few facts, 
 being, as it were, irresistibly recommended by the tJear- 
 ness and simplicity which the notion possessed." What is 
 the ground of this bold anticipation of the universality of a 
 Law as yet verified only by a very few examples, when, in 
 the case of a General Fact, as already shown, a very ex- 
 tensive Liduction may stiU leave us in doubt whether the 
 supposed truth may not be contradicted by the next in- 
 stance that arises ? In general terms, the answer is obvi- 
 ous. Simple uniformities, such as are comprehended in a 
 General Fact, may be merely accidental ; to recur to an 
 instance already cited, all ruminating animals now known 
 divide the hoof ; but as the number of such animals is not 
 very great, this simple coincidence of two properties may 
 be as casual as the experience of an individual obseryer 
 who has never happened to see a squint-eyed person that 
 had not also brown hair. But complex uniformities, such 
 as are mai-shalled into the symmetrical series called Laws 
 of Nature, and thus expressed in one formula, cannot be 
 regarded as accidental. As the nmnber of individual facts 
 comprehended in one of these series is very great, it is in- 
 credible that mere chance should throw even a portion of 
 them into symmetrical groups, bearing a constant ratio to 
 
INDUCTION AND ANALOGY. 413 
 
 each other. Hence, if we can detect but a portion, even a 
 fragment, of such a series, we feel assured that it will prove 
 to be continuous, that the Law will not change, that the 
 uniformity will be carried out to the end. Only the action 
 of a permanent and unvarying Cause, it is assumed, could 
 so harmonize results. Nay, so strong is our assurance of 
 the universality of the principle thus discovered, though it 
 seems as yet very imperfectly verified, that, when an anom- 
 alous or inconformable instance actually arises, we seek at 
 once for the means of eliminating it, or explaining it away, 
 instead of allowing it to wrest the inchoate discovery out 
 of our grasp and send us to the work of research again. 
 We class the exception immediately among those apparent 
 exceptions which really confirm the rule ; — just as we 
 now see that the rising of a balloon in the atmosphere does 
 not contradict, but actually verifies, the Law of gravita- 
 tion. 
 
 We come, then, to the conception of a physical Cause, as 
 indicating the third or highest stage in the generalizations 
 of science, and therefore as bearing the same relation to a 
 Law of Nature,' that such a Law bears to a General Fact. 
 As thus understood, a Cause is simply a higher Law, un- 
 der which several inferior Laws are subsumed ; it appears 
 as the original principle, of which these lower Laws are 
 the derivatives by immediate and necessary consequence. 
 Thus, the theory of gravitation, or the doctrine that every 
 body attracts every other body with a force which is di- 
 rectly as its mass and inversely as the square of its dis- 
 tance, is the statement of a universal principle, under which 
 not only Kepler's Laws of the planetary motions, but the 
 Laws of falling bodies, of the equiUbrium of fluids, &c., are 
 subsumed in this sense ; — that if we take for granted the 
 existence of the force or physical Cause, termed Gravity, 
 which this theory assumes, then these inferior Laws may 
 all be deduced from it by Demonstrative Reasoning. That 
 
414 INPUCTION AND ANALOGY. 
 
 sneh Deduction k possible, is the only proof we have that 
 such a force or Cause exists. The hypothetical force, for it 
 is nothing more, represents the inferior Laws that are sub- 
 sumed under it, merely because it is an expression of them 
 in a single formula. It may well happen that two or more 
 such formulas may be devised, differing essentially from 
 each other, yet answering equally well all the conditions 
 of the case, as the given Laws may logically be deduced 
 from either of them. For instance : — all, or the greater 
 part, of the Laws of vision and light may be explained with 
 equal precision and accuracy either on the doctrine of emis- 
 sion, or on the undulatory thecny. Two such hypotheses 
 correspond to two very dissimilar engines, which different 
 mechanics might invent, in order to cause the ha^ds of a 
 clock to make the required movements over the dial-plaste, 
 or the little balls in an orrery to coimterfeit the motions of 
 the solar system. It is no more necessary to suppose that 
 such an attractive force as Gravity, or such a luminiferous 
 ether as the undulatory theory treats of, actually exists, 
 than it is to believe that a set c^ wheels stud pinions, like 
 that which moves an orrery, really produces the motion of 
 the planets. All that the theory does for us is to represmt 
 the phenoniena correctly; no one who imderstands the 
 subject supposes that the hypQthstical force or Cause, which 
 is merely a convenient supposition for the theorist, actually 
 j^diiees those phenomena. 
 
 It is evident that such Onuses as we are now speaking 
 of are merely the highest generalizations of Physical Sci- 
 ence, and that the invention of them — for they are rather 
 invented than discovered — affords not the slightest addi- 
 tional evidence of the universality of those Laws of Nature 
 which they represent, or which are subsumed under them. 
 The proof, indeed, proceeds in the opposite direction ; the 
 only evidence we have that the right Cause has been as- 
 signed is, that it correctly represents the Laws which are 
 
INDUCTION AND ANALOGY. 415 
 
 pl^iced under it. When it is demonstrated that the Law- 
 may be deduced from such a Cause, the real course of the 
 argument is, from the admitted validity of the Conclusion 
 to infer the soundness of the Premise. Gravity does not 
 cause heavy bodies to fall to the ground, nor does it bind 
 the planets to their orbits ; but Gravity is rightly consid- 
 ered as a " physical Cause," in the technical sense of that 
 phrase, because its hypothetical existence enables us cor- 
 rectly to represent in a single formula the phenomena of 
 falling bodies and of the planetary motions. 
 
 The higher generalizations, then, depend exclusively, for 
 proof of their correctness, on the validity of those which are 
 next below them. When the proper Law of Nature is 
 provisionally assumed, certain conseq^uences can be demon- 
 strated to follow which agree with the General Facts that 
 were previously established on Inductive evidence ; when 
 the proper physical Caiise is assumed, we can Ip^cally 
 make certain Deductions from it which b^^rmonize with the 
 Laws of Nature which this Cause was inven,te(i to express. 
 Neither the Law nor the Cause brings any additional evi- 
 dence of its own, but both alike depend for proof, in the 
 last analysis, on the validity of the Induction by simple 
 enumeration by which we first collected their common 
 basis, the General Facts. The process of verifying both 
 consists in enlarging the Induction, but not in altering its 
 character ; both the Law and the Cause being assumed to 
 be universally true, we make further Deductions from 
 them, and still find these to coincide with the observed 
 Facts. In other words, we first reason Inductively from 
 some to aU, and then, assuming provisionally that the prin- 
 ciple holds true of all, we reason from it Deductively to 
 oiheir some, and find that these also are confirmed by obser- 
 vation, so that they reflect evidence upon the Law or fhe 
 Cause of which they are the logical consequences. Turn 
 the matter as we may, Induction b^ simple enumeration is 
 
416 INDUCTION AND ANALOGY. 
 
 still the basis of the whole procedure, and the discovery or 
 invention of Laws of Nature, or physical Causes, only sup- 
 plies names and formulas of expression for the successive 
 steps of generalization, as we form one after another the 
 proper hierarchy of Concepts. 
 
 We can now see more plainly than before the correct- 
 ness of the doctrine already advanced, that the strong and 
 unhesitating belief which we accord to any well-established 
 Law of Nature, and which we indicate by saying that an 
 event happening under it takes place by a physical neces- 
 sity, is not due to the strength of the Induction through 
 which the Law was discovered, but to our absolute a priori 
 conviction of the fixedness of the relation which connects 
 every effect with its efficient Cause. The Law is discovered 
 by Induction ; but it is proved by a different process, — by 
 bringing it under a necessary a priori conception of the 
 htmian mind, that of Efficient Cause, and thereby subject- 
 ing it to the principle of Causahty, that every event must 
 have a Cause, and must be proportional to that Cause. 
 
 In speaking of the use which is sometimes made of In- 
 ductive reasoning in pure mathematics, as in the case of 
 Newton's discovery of the Binomial Theorem, Mr. Mill 
 maintains that the process of thought in such cases is not 
 an Induction properly so called, but is governed by certain 
 '''■a priori considerations (which might be exhibited in the 
 form of demonstration), that the mode of formation of the 
 subsequent terms, each from that which preceded it, must 
 be similar to the formation of the terms which have been 
 already calculated." But it was certainly Inductive in this 
 respect, that the observed regular formation of the first few 
 terms of the series originally led Newton to anticipate that 
 all the other terms must be formed in the same manner, 
 and to act upon this anticipation, — that is, confidently to 
 use the Theorem for a long time, — without giving himself 
 the trouble to work out a demonstration of it. Undoubt- 
 
INDUCTION AND ANALOGY. 417 
 
 edly he had a strong belief that such a demonstration was 
 practicable ; and this belief prompted him to acquiesce with 
 greater confidence in the result of the Induction. For this 
 very reason, this instance appears to be a typical and in- 
 structive case of Inductive reasoning. Pure Induction is 
 exclusively an organon of discovery, a clew for anticipating 
 fects not yet observed and truths not yet proved. The 
 Ground of the Induction, that is, the proof, if it may be 
 called such, or the source of the confidence with which we 
 accept its conclusions, is an indistinct assurance, derived 
 from a priori considerations, that the results might be de- 
 monstrated, if we were acquainted with all the circumstances 
 of the case. Newton's assurance was founded on his indis- 
 tinct anticipation of the truth, that the formation of the co- 
 efficients of the series must depend in some manner on the 
 laws of the permutation and combination of numbers, — 
 an anticipation which he did not stop to work out and 
 verify. The physicist's assurance is based primarily, as 
 we have seen, on his necessary conviction that every event 
 or change must have an efficient Cause, a truth which 
 is readily explicated into the maxim that Nature's course 
 is uniform ; and secondarily, upon his belief that the pro- 
 portional variation of the successive terms in such a se- 
 ries as is called a Law of Nature is another consequence 
 of the axiomatic principle of Causality, that effects must be 
 proportional to their Causes. The physicist's anticipation 
 cannot be verified, because, in the physical universe. Effi- 
 cient Causes lie beyond the reach of human insight. We 
 can discover nothing but Invariable Antecedents. But so 
 strong is the bias which leads us to identify an Invariable 
 Antecedent with an Efiicient Cause, that the phraseology 
 of Causation is stiU employed throughout our investigations, 
 though it has been demonstrated over and over again, that 
 constancy of sequence is no certain indication of causal 
 efficiency. We still speak of physical Causes, of agents 
 
 18* AA 
 
418 INDUCTION AND ANALOGY. 
 
 and their action, o{ forces and powers, although it is now 
 admitted on all hands that we mean nothing by such 
 language, when employed with reference to the material 
 universe, except "constant relations of succession or of 
 similarity." The very persistency of this inappropriate 
 phraseology indicates quite clearly the source of our con- 
 viction that Nature's course is uniform, and her Laws un- 
 changeable, except by Him whose infinite wisdom first 
 established them, and whose unvarying purposes and modes 
 of action they express. 
 
SO0ECES OF EVIDENCE AND CAUSES Q¥ EKEOB. 4X9 
 
 CHAPTER XIII. 
 
 THE SOURCES OF EVIDENCE AND THE CAUSES OF EEKOE. 
 
 INTUITION is not only the source in which all our 
 knowleclge originates, but it is the universal basis of 
 certainty, or the sole ground of the confidence with which 
 we accept any facts or truths as known. What we directly 
 or immediately perceive, whether by the ex,ternal senses 
 or by consciousness, that we kftow. What is not thus di- 
 rectly perceived is entitled to be called knowledge only in a 
 secondary or derivative sense ; properly spegiing, it is only 
 an inference from our knowledge, and however legitimate 
 this Inference may be, it is worth nothing if the truth of 
 one or more Intuitions, on which it depends, be not previ- 
 ously taken for granted. Take even Demonstrative Refi- 
 soning, for instance, in which it is rightly said that the 
 Conclusion is a necessary inference from the Premises. 
 Still, before we can accept this Conclusion as certain, we 
 must assume that both the Premises are true. Now, what- 
 ever be the nature of the Major Premise, the Subsumption 
 must express, either directly or indirectly, a truth of Intui- 
 tion. We can knowingly assert that a given object pos- 
 sesses a certain attribute, or bears a certain relation of like- 
 ness or unlikeness to some other object, only through our 
 direct perception of this fact either by sense or conscious- 
 ness ; and such an assertion must enter into every act of 
 Reasoning, as one of the grounds on which the Conclusion 
 rests. Any Reasoning, then, by which we might attempt 
 to doubt or deny the validity of our Intuitions, would be 
 
420 THE SOUECES OF EVIDENCE 
 
 self-destructive ; for in such Reasoning, the truthftdness of 
 our Intuitive faculties must be presupposed, or taken for 
 granted. We should, by such scepticism, deny the legiti- 
 macy of our Own denial. 
 
 Intuition, therefore, is the highest source of evidence, 
 and the ultimate foundation of all certainty. If we can- 
 not accept, as absolutely true, what we immediately per- 
 ceive, or are conscious of, then we can know nothing ; we 
 caimot even know that we do not know. But before we 
 place this absolute reliance upon Intuition or Perception, 
 we must carefiiUy distinguish what it is that we really per- 
 ceive, or, in other words, what that is of which we have 
 an Intuition. In ordinary mental action. Inferences are so 
 quickly and habitually drawn from Intuitions, and thereby 
 so closely blended with them, acts of comparison and gen- 
 eralization also entering into the compound result, that it 
 becomes extremely difficult to separate the pure Matter of 
 Intuition, of which we are absolutely certain, from the 
 heterogeneous ingredients which are thus united with it, 
 and of which we are not by any means equally sure. 
 Hence it is often said that our senses deceive us, when 
 the truth is, that we are mistaken only in the Inferences 
 which we have incorrectly drawn from the data actually 
 furnished by the senses. Thus we are often deceived into 
 accepting a counterfeit as a good coin ; but the mental act 
 which thus leads us into a mistaken belief is really com- 
 pound, embracing an act of memory, one of generahza- 
 tion, and one of Reasoning. The little object placed in 
 our hands for examination is perceived to have a certain 
 color, weight, shape, stamp, &c. ; and it is impossible that 
 these qualities should be, to us, in any respect different fi-om 
 what they are perceived to be. But when we proceed to 
 compare these qualities with others which we rememher to 
 have perceived at some other time in good coins, and to 
 ijjfer frota their similarity that this supposed coin is not a 
 
AND THE CAUSES OF ERROR. 421 
 
 counterfeit, it is evident that we are exposed to many 
 sources of error. Even if we go so far only as to desig- 
 nate one of these quahties by its Common Name, — to say, 
 for instance, that this coin is yellow, — we go beyond the 
 Intuition, and, so far, become liable to mistake ; it may well 
 be that we have but an imperfect recollection and imagi- 
 nation of the color which is usually so called, and therefore 
 may be mistaken in supposing that this color is so similar 
 to it as to merit the same name. In like manner, any 
 other comparison, as of the weight, shape, or stamp, as it 
 requires either memory, if both objects be not actually be- 
 fore us, or a decision as to the degree of similarity, if they 
 are both present to sense, must involve an element of un- 
 certainty. 
 
 The question has been raised, whether external objects 
 are directly perceived by us as external, or whether their 
 externality is an Inference subsequently drawn from this 
 perception as combined with others, and as governed by 
 the necessary and a priori convictions of the mind. In 
 other words, is the externality of the object, or the .fact 
 that it is something different from myself, that it is not-me, 
 a constituent part of the Intuition, or only an Inference 
 from it? If the former supposition be true, then I hnow 
 that the external world exists, and any Reasoning upon the 
 case, either for or against this knowledge, is superfluous, 
 and even illogical ; for as Reasoning must involve and de- 
 pend upon Intuition, it cannot contradict Intuition. But 
 if the latter supposition be correct, then the reahty of the 
 outward universe is not, strictly speaking, known, but only 
 inferred through an act of the understanding, which, as it 
 purports to relate to real objects, and not to a mere con- 
 ception of the mind, certainly may be a mistaken One. 
 
 The question is an important one, but the full discussion 
 of it belongs to Metaphysics, and not to Logic. We can 
 t)nly consider here the nature and the relevancy of the evi- 
 
422 THE, SOURCES OF EVIDENCE 
 
 dence adduced, regarded as illustrating the general laws of 
 evidence. Thus much, I think, must be admitted, that 
 the mind, in its adult state, is immediately conscious of tlie 
 affections of its own bodily organism as «t(cA, — that is, as 
 affections of the body, which is foreign to itself, or a part 
 of the not-me ; for we localize these affections, or refer tliem 
 instantly, and without an act of reasoning, to the affected 
 parts. Thus, I am immediately conscious of a pain, not 
 merely as a pain, but as a pain in the foot, in the hand, or 
 in the head, the Intuition extending to the locality, just as 
 much as to the severity, of the affection. But it is said 
 that the pain, being a sensation, can exist only in the .sen- 
 tient mind, and not in the unsentient m9,tter of the body. 
 Very true ; but the question then arises. Where is the mind? 
 You have no right to confine it to a certain part of the 
 body, — to the brain, for instance. I say, that the mind is 
 wherever it feels; for its feeling — its state of consciousness 
 — is the only evidence that we have of its existence. It 
 is present, at least, to the whole nervous organism. As we 
 certainly feel at the tips of our fingers, it is little more than 
 tautology to assert, that that which feels is existent at the 
 tips of the fingers. It is admitted that this doctrine of the 
 ubiquity of the mind to the body is incomprehensible ; we 
 cannot see how it is that the thinking being should be " all 
 ill every part" of its extended nervous organism. In like 
 manner, many physical facts, especially those of electricity 
 and magnetism, and whatever involves the action of what 
 are called Polar Forces, are inconceivable ; but this is no 
 reason for doubting their reality, when they are evidenced 
 by Intuition. But if the mind immediately localizes its 
 sensations, if it perceives that the pain is here, and not 
 there, then it is immediately conscious of its own body as 
 extended, and therefore of space and externality. 
 
 This is a mere outline of Sir William Hamilton's doc- 
 trine of our immediate perception, or consciousness, of the 
 
AND THE CAUSES OF EEEOE. 423 
 
 ,?xternal world. It appears to disprove very satisfactorily 
 Kant's counter assertion, that space is wholly subjective, 
 r— a mere law of our perceptive faculty, which imposes 
 the modes of its own being upon the constitution of the 
 objects which it perceives. But while the Hamiltonian 
 doctrine seems to hold good of the adult mind, it is not so 
 clear that it would apply to the perceptions of an infant. 
 It -may be questioned whether, at the dawn of our exist- 
 ence, our sensations are distinctly referred to outward 
 things, or that the perceptions by which they are accom- 
 panied appear to be ^.nything else than states of our own 
 consciousness. An infant's world, it may be suspected, 
 Ijes eU'tirely within himself; and if so, the subsequent 
 reference , of these perceptions to external realities must 
 be produced, or aided, by experience and an g,ct of Reason- 
 ing, and the knowledge or belief thus gained is no longer 
 exclusively Intuitive, 
 
 Passing over this metaphysicsil question, however, it is to 
 be observed that Memory, as a source of evidence, stands 
 next in extent and importance to Intuition. In many cases, 
 the two are so closely interwoven with each other, as we 
 have just seen, that facts are often loosely said to be Intui- 
 tively known, when we have no better evidence of their 
 existence than is afforded by Memory. Intuition, as such, 
 is always present, relating only to what exists now and 
 Jiere; past Intuitions can be now known to us only by an 
 iet of remembrance ; and as the strength of a chain is the 
 strength of its weakest link, that which we did know Intui- 
 tively, can be now accepted only on the strength of our be- 
 lief that we remember rightly. In like manner, when we 
 are judging of Individual Objects by comparison, or are 
 ascertaining their relations to each other, or to a class of 
 cognate Objects, the results of thd observation will not be 
 Intuitively certain, unless all the related objects are pres- 
 ent, at pne and the sapie nioment, either to sense or con- 
 
424 THE SOURCES OF EVIDENCE 
 
 sciousness ; if all are not thus present, then, to the extent 
 of this deficiency, objects actually observed must be com- 
 pared with those which are merely remembered. More- 
 over, as Locke and Dugald Stewart have remarked, even 
 in mathematical demonstration, we have not, at every step, 
 the immediate evidence of Intuition, but only that of 
 Memory. The whole science of geometry hangs together 
 by a continued chain of Intuitive judgments ; but in the 
 case of any advanced theorem, it is not to be supposed that 
 we can carry in mind, as simultaneously present to con- 
 sciousness, aU the truths, previously established, which must 
 concur in order to support this particular demonstration. 
 In by far the greater number of instances, we trust entirely 
 to judgments resting on the evidence of Memory. At the 
 close, before we can accept the Conclusion as demonstrated, 
 we must remember the whole chain so perfectly as to be 
 sure that nothing has been left out; we must recollect not 
 only that we have proved, but how we proved, each point. 
 Practically, then, the truths of geometry, and all other 
 Conclusions dependent on a chain of Demonstrative Rea- 
 soning consisting of more than two or three links, must be 
 accepted on the evidence of Memory quite as much as on 
 that of Intuition. Of course, the Inductive Sciences, in- 
 cluding, as they do, a vast collection of fects, are dependent, 
 to a still greater extent, upon this source of evidence. 
 
 But the edifice of Science, when it is thus shown to be 
 largely dependent upon individual recollections, would seem 
 to rest on a very insecure basis. The defects of Memory, 
 as every one is aware, are both numerous and grave. It 
 is capricious, it often fails us when we most need its aid, 
 and it exists in very different degrees in different persons. 
 We might be tempted, at the first glance, to pronounce 'it 
 one of the most imtrustworthy of all our facilities. But on 
 closer observation, it will appear that the faults with which 
 it is chargeable are not so serious as we might at first sup- 
 
AND THE CAUSES OF EEEOE. 425 
 
 pose, and, especially, that they do not much diminish its 
 useftilness, or the confidence which we place in it, as an 
 indispensable means for the progress of Science. In the 
 first place, its faults are rather negative than positive in 
 character ; we often forget, but we are very seldom mis- 
 taken in what we think that we distinctly remember. In 
 truth, a remembrance, seemingly clear and distinct, of 
 what we have but recently observed, especially if the phe- 
 nomenon be of a simple and definite character, must be 
 placed next to Intuition as a ground of certainty. The 
 distinction between a pure Intuition now present to the 
 mind, and a distinct recollection of a very recent one, ex- 
 perienced perhaps within the last hour, is theoretical rather 
 than practical. In the ordinary conduct of life, no one 
 would think of maintaining that the former was more trust- 
 worthy than the latter. Our judicial tribunals, in grave 
 matters involving pi'operty and life, will not allow the clear 
 and distinct recollections of a witness, though extending 
 over a much longer period, to be even called in question. 
 Still, the theoretical distinction exists ; Intuition, as the 
 basis of Demonstration, has absolute or logical certainty, 
 and does not admit of degrees ; while Memory is confess- 
 edly subject to error, and therefore is a source only of 
 probable evidence, though, in its highest degree, it amounts 
 to what is called moral certainty. 
 
 And here another distinction must be drawn. We must 
 distinguish, as Hamilton has done, between the simple fact 
 that we do remember, or think that we remember, a cer- 
 tain phenomenon, and the truthfulness of this act of re- 
 membrance, or our belief in the former actual existence of 
 that phenomenon. The former is matter of du-ect Intui- 
 tion, and therefore does not admit of doubt ; the latter rests 
 merely upon probable evidence, and may be a mistaken be- 
 lief. Memory may be compared to a witness giving testi- 
 mony in a court of justice ; the judge and jury cannot 
 
426 THE SOURCES OF EVIDENCE 
 
 doubt that he does testify to this or that occurrence, fpr 
 they have sensible — that is, Intuitive — evidence of the 
 fact ; but they may well doubt whether he testLSes truh/, — 
 whether the occurence in question ever took place. It is 
 only in this last respect, the correctness of the representa- 
 tion of what we remember, that the faculty of Memory is 
 said to be a source of merely probable evidence. 
 
 It is to be observed that the art of writing is a most val- 
 uable auxiliary to the faculty of Memory, inasmuch as a 
 proper use of it may obviate, in great part, the uncertainty 
 that would otherwise attach to this source of evidence. 
 Remembrance is more perfect, that is, more clear and dis- 
 tinct, and thus more trustworthy, according as the Intui- 
 tions which it preserves and stores up are more recent. 
 But a written record of the observations, taken at the 
 time when they were made, or as soon afterwards as might 
 be, keeps the evidence as perfect as it would be if Mem- 
 ory were not liable to be impaired by the lapse of time. 
 The possession of such a record may enable even ftiture 
 generations to accept the evidence of the occurrence with 
 as ftdl confidence as if it had been observed by their con- 
 t^piporaries only a few days, or a few hours, before. Of 
 course, the age and genuineness of the document must first 
 be proved, just as we must first establish, on satisfactory 
 grounds, the veracity and competency of the witnesses who 
 testify to contemporary events which we have not ourselves 
 observed. But this being done, and it is generally about 
 as easy to do in the one case as in the other, the evidence 
 remains as perfect after the lapse of centuries as it was at 
 the time when the record was made. Time is thus de- 
 prived of its power to wipe out by degrees the recollection 
 of events. Many facts in history, though of very old date, 
 must be admitted to be now as firmly established as if they 
 had taken place within the lifetime of the present genera- 
 tion. Thus, the fact that a deed of privileges, called the 
 
AND THE CAUSES OF EEBOB. 427 
 
 (xreat Charter, was granted by King John to the English 
 people, Jnne 6, 1215, is even now as firmly established as 
 that of the passage of the Reform Bill in 1832 ; and the 
 precise nature and extent of the franchises granted are as 
 fully known in the formei* case as in the latter, for in both 
 cases the original parchment rolls, on which these title- 
 deeds of freedom were first engrossed, and attested by the 
 seals and signatures of those who were parties to them, are 
 yet extant. 
 
 We dwell upon this point as one of some importance, be- 
 cause it has been wrongly maintained, in reference to what 
 may be called the historical part of Christianity, that as the 
 mere lapse of time slowly, kut surely, wears away all his- 
 torical evidence, the great /aeis on which our religious faith 
 depends must become subject in future centuries to so 
 much uncertainty as to be whoUy unworthy of credit. 
 The proper answer to this assertion is, that nothing less 
 than a general conflagration, which should burn up aU the 
 written and printed records now in existence, could make 
 these facts, to any appreciable extent, less certain thousands 
 of years hence, than they are at the present day. Miracles 
 were needed for the first estabhshment of Christianity ; buj; 
 only the ordinary course of God's providence is necessary 
 to preserve its blessings to any number of future genera- 
 tions. 
 
 The two faculties of Intuition and Memory are the 
 sources only of our individual experience. But the ex- 
 perience of an individual — what I have myself observed 
 and remembered, or reduced to writing — is extremely 
 limited, when compared with the vast fund of information 
 that is opened to us by accepting the experience of our fel- 
 low-men, and combining it with our own. Not merely in 
 our labors for the advancement of Science, but in the or- 
 dinary management of our every-day concerns, we are 
 obliged to depend upon the Testimony and the Authority 
 
428 THE SOURCES OF EVIDENCE 
 
 of others. Science grows by a combination of the labors 
 of many minds and a long succession of generations. The 
 lifetime of an individual might be- spent in a vain endeavor 
 to review, and verify by personal observation, all the data 
 which support the conclusions in but one of its depart- 
 ments. Many of them, from the nature of the case, can- 
 not be so verified ; the occurrences of former times, and 
 even those in our own day that took place under a pecu- 
 liar combination of circumstances, such as may never be 
 repeated, must be received on the Testimony of others, or 
 be left entirely out of account, together with all the con- 
 clusions that are founded upon them. We must contin- 
 ually accept on trust what otHfers have observed, and even 
 the Inferences that they have drawn, without pretending 
 to verify them for ourselves, or we must sit down ia igno- 
 rance. And this remark is apphcable not merely to the 
 Inductive, but also to the Exact Sciences. In astronomi- 
 cal calculations, for example, very few of the data rest 
 upon the evidence of our own senses, and we compute by 
 the aid of a book of logarithms, the accuracy of which, at 
 the present day, no one thinks of verifying by independent 
 calculation. 
 
 Testimony and Authority ought to be sharply distin- 
 guished from each other, though they are often loosely used 
 as synonymous. Properly speaking, we accept Testimony 
 as to matters of fact, and yield to Authority in matters of 
 opinion. Our confidence in the former depends mainly on 
 our opinion of the veracity of our informant ; in the latter 
 case, we rely chiefly on the soundness of his judgment, the 
 accuracy of his habits of reasoning, and the largeness of 
 his information. We disbelieve Testimony, we reject Au- 
 thority. The reason why these two sources of belief are 
 so frequently confounded is, that the provinces of observa- 
 tion and of reasoning are not kept sufficiently distinct ; 
 the certainty of the Intuition is improperly extended to the 
 
AND THE CAUSES. OF EREOK. 429 
 
 Inference which is drawn friDm it, and drawn so quickly 
 and easily that it is mistaken for a part of the observation 
 itself. When Dr. CuUen remarked, with as much truth 
 as point, that " there are more false facts than there are 
 false theories in the world," he did not mean to impugn 
 the general disposition of men to tell the truth. He al- 
 luded to what are generally supposed to be facts, and 
 which go by that name, but are really nothing but loose 
 compounds of matters of opinion with those of observa- 
 tion. Probably what he had in mind was the insufficiency 
 of the evidence on which the members of his own profes- 
 sion, that of Medicine, are often obliged to act. Thus, it 
 is said that a patient is in a Consumption ; this, if true, 
 would be a fact ; but the only known fact is, that certain 
 symptoms were manifested from which it was inferred, 
 perhaps wrongly, that the case was one of Consumption. 
 Again, it is announced as a fact, that the use of a certain 
 medicine cured the disease ; when the truth is, that the 
 dose was administered, and the man got well, perhaps in 
 spite of the medicine. Men are so prone to confound their 
 own crude conjectures with what they have actually seen 
 or heard, that very few, except those who have been care- 
 fully trained to scientific habits of mind, can be trusted to 
 report their own observations, until they have undergone 
 a severe cross-examination. They do not intend to de- 
 ceive others, but they have effectually deceived them- 
 selves. The reputed sciences of Phrenology and Animal 
 Magnetism rested exclusively, in the opinion of their ad- 
 mirers, on a basis of observed facts, and hence were to be 
 maintained, in spite of the arguments with which they 
 were assailed, because facts are admitted to be a better 
 test of truth than reasoning. But it became evident on 
 severe scrutiny, that this basis was made up, for the most 
 part, out of what Dr. Cullen calls " false facts." 
 
 On account of this frequent confusion of two very dis- 
 
430 THE SOUECES OF EVIDENCE 
 
 similar things, it is commonly sdd, and with good reason, 
 that before accepting Testimony, we ought to have satis- 
 factory proof both of the veracity and the competency of 
 the witness. But if people generally could be trusted to 
 separate their Inferences from their observations, and to 
 report the latter unmixed, it would evidently be enough 
 to have assurance only upon the former point. In respect 
 only to their quahty or certainty, though not with regard 
 to their extent or comprehensiveness, one man's Intuitions 
 are as good as another's. The one, indeed, may see more 
 than the other, because he knows where to look and what 
 to observe. He will therefore have more to report, or, at 
 any rate, more that is pertinent and useful. But the Tes- 
 timony of the other, as far as it goes, will be equally valid 
 and trustworthy, for it is equally a report of what has actu- 
 ally been observed, and the Intuitive faculty cannot de- 
 ceive. The only doubt, then, which can properly affect 
 the reception of Testimony, or the admission of other peo- 
 ple's experience as at least of equal value with our own, is 
 that ■which regards the disposition of the witness to tell the 
 truth. Doubts respecting his competency as an observer 
 can be settled by sifting the report itself, better than by 
 inquiring into the abilities of him who made it. 
 
 The proper distinction to be made is, that the claims of 
 Testimony to be accepted depend upon the evidence which 
 is offered as to the Veracity of the witness, while those of 
 Authority rest upon the proofs which we possess of the 
 Competency of the person whose opinions we are invited 
 to follow. The rules for forming an estimate either of the 
 Veracity of an observer or the Competency of a judge are 
 too obvious to need mention here, except in very general 
 terms. " In regard to the honesty of a witness," says 
 Esser, as translated by Hamilton, " this, though often 
 admitting of the highest probability, never admits of abso- 
 lute certainty; for though, in many cases, we may know 
 
AND THE CAUSES OF ERROR. 431 
 
 enough of the general character of the witness to rely with 
 perfect confidence on his Veracitj, in no case can we look 
 into the heart, and observe the influence which motives 
 have actually had upon his volitions. We are, however, 
 compelled, in many of the most important concerns of our 
 existence, to depend on the Testimony, and consequently 
 to confide in the sincerity, of others. But, from the moral 
 constitution of human nature, we are warranted in presum- 
 ing on the honesty of a witness ; and this presumption is 
 enhanced in proportion as the following circumstances con- 
 cur in its confirmation. In the first place, a witness is pre- 
 sumed to be veracious in this case, in proportion as his love 
 of truth is already established from others. In the second 
 place, a witness is to be presumed veracious, in proportion 
 as he has fewer and weaker motives to falsify his Testi- 
 mony. In the third place, a witness is to be presumed 
 veracious, in proportion to the likelihood of contradiction 
 which his Testimony would encounter, if he deviated from 
 the truth." 
 
 In respect to the Cotapetency of the person to whose 
 Authority we are requested to defer, the only important 
 principle which needs to be here laid down is contained in 
 the old adage, Ouique credendum est in sud arte, — Trust 
 each person in his own specialty. Eminence in one depart- 
 ment of science, far from being an indication of superior 
 power of judgment and reasoning in other departments, 
 is often a disqualification for forming a correct opinion in 
 them. The mind is prone to carry over the special forms 
 and processes which are appropriate to one science into 
 others, where they are out of place, and lead only to error. 
 To adopt Bacon's expressive metaphor, it imports into a 
 new sphere of research the rust and tarnish contracted in 
 the workshop wherein it has chiefly labored. A distin- 
 guished mathematician, other things being equal, is not so 
 competent to form an opinion upon some disputed point in 
 
432 THE SOURCES OF EVIDENCE 
 
 the moral sciences, as one who is conversant with ques- 
 tions of this sort, though he has never gained distinction 
 in them, and may be ignorant of the first principles of 
 Algebra and the Calculus. " The merit of a mathemati- 
 cal invention," as Hamilton justly remarks, " consists in 
 the amoim.t of thought which it supersedes"; and hence 
 it is matter of common remark, that those who are most 
 capable of making such inventions, and profiting by them, 
 are least fitted for reasoning by Induction and Analogy. 
 Consequently, " Mathematics afford us no assistance either 
 in conquering the difficulties, or in avoiding the dangers, 
 which we encounter in the great field of probabilities 
 wherein we live and move." 
 
 Hume's celebrated argument against the credibility of 
 miracles is a fallacy which results fi:om losing sight of the 
 distinction between Testimony and Authority, between 
 Veracity and Competency. He argues, that it is contrary 
 to all experience that a Law of Nature should be broken, 
 but it is not contrary to experience that human testimony 
 should be false ; and therefore wa ought to believe that 
 any amount of Testimony is false, in preference to admit- 
 ting the occurrence of a miracle, as this would be a viola- 
 tion of Law. We answer, that the miraculous character 
 of an event is not a matter of Intuition, but of Inference ; 
 hence, it is not to be decided by Testimony, but by Rea- 
 soning fi-om the probabUities of the case, the only question 
 being whether, in view of all the circumstances, the Con- 
 clusion is competent that the occurrence was supernatural. 
 The Testimony relates only to the happening of the event 
 considered merely as an external phenomenon ; the ques- 
 tion respecting the nature of this event, whether it is, or is 
 not, a violation of Physical Law, whether it is an effect 
 of this or that Efficient Cause, cannot be determined by 
 Intuition and Testimony, but is a matter for Judgment 
 founded on Reasoning, in view of all the circumstances of 
 
AND THE CAUSES OF EEROK. 433 
 
 the case. If doubtful of our own Competency to form a 
 correct opinion on this point, we may defer to the Author- 
 ity of another, who is familiar with the kind of Reasoning 
 by which such questions are settled. Now we have abun- 
 dant evidence from experience, that no event whatever, 
 regarded simply as an external phenomenon, can be so 
 strange and marvellous that sufficient Testimony will not 
 convince us of tte reality of its occurrence. To the con- 
 temporaries of our Saviour, not even bringing a dead man 
 to life would have appeared so incredible as the transmis- 
 sion of a written message five thousand miles, without 
 error, within a minute of time. Yet this feat has been 
 accomplished by the Magnetic Telegraph. Why do we 
 decide, then, that the raising of Lazarus was, and the 
 transmission of intelhgence by telegraph is not, a mira- 
 cle? Evidently not by Intuition, but by reasoning from 
 the very different circumstances of the two cases. The 
 /aei, that the eyes of the blind were opened, or a storm was 
 reduced to a calm, or the dead were raised, is established 
 by Intuition and Testimony, which have established many- 
 other facts quite as wonderful ; the charaeter of this fact, 
 whether miraculous or not, is to be settled in a very dif- 
 ferent manner. We say, then, that Hume's argument, 
 which is based exclusively upon an appeal to experience 
 and Testimony, is totally inapplicable to the question re- 
 specting the credibility of a miracle. Testimony has noth- 
 ing to do with the correct inference of a Conclusion from 
 its Premises. 
 
 We can touch only very briefly on the Critidsm of re- 
 corded Testimony, and of writings in general. As we must 
 avail ourselves, in the construction of Science, of the ex- 
 perience of former generations, in respect to which the 
 Testimony of eye- and ear-witnesses is no longer directly 
 accessible, we are obliged to consider the credibility of 
 this Testimony as aflected by the channels oF traasnaiasion 
 
 19 BB 
 
434 THE SOURCES OF EVIDENCE 
 
 through which it has been passed. There are but two such 
 channels, Tradition and Ancient Writings. The former 
 of these may be left out of account ; for if the lapse of time 
 has been considerable, the probability that the Testimony, 
 if transmitted merely by word of mouth, has been mate- 
 rially altered or falsified, is so great, that the report can be 
 received only with extreme caution. But it has already 
 been mentioned, that the invention of the art of writing has 
 rendered it possible for the experience of a former genera- 
 tion to be handed down, through an indefinite lapse of cen- 
 turies, in as perfect a state as that in which it was first 
 communicated to those who were the contemporaries of 
 the events narrated. This is possible, we say ; the ques- 
 tion whether it has been actually so transmitted is what we 
 have to consider in the Criticism of Ancient Writings. 
 
 When a document purporting to be the recorded Testi- 
 mony of certain individuals of a former generation is pre- 
 sented to us, we have first to inquire whether it is actually 
 the handwriting, or the composition as taken down by dic- 
 tation, or a faithful report, made at the time, of the sub- 
 stance of the evidence of the individuals whose names it 
 bears, or to whom it is attributed. The establishment of 
 either of these three points is the proof of what is called 
 the Genuineness of the writing. It is comparatively un- 
 important which of the three is proved, as either of them 
 gives us assurance that the document is a &ithfiil record 
 of the Testimony of the persons whose evidence is to be 
 weighed. Thus, even if we were sure that the Testimony 
 of the Evangelists was originally written out by their own 
 hands, we certainly do not possess their autograph copies ; 
 still, the Gospels are Genuine, if we have sufficient evi- 
 dence that they are feithful records, made at the time, (or 
 correct transcripts of such records,) of what the Evange- 
 lists said. 
 
 But a second question must be answered before we can 
 
AND THE CAUSES OF ERROR. 435 
 
 accept the evidence furnished by the document. We must 
 be satisfied, not only that the Testimony is Genuine, — that 
 it was actually given by those fi:om whom it purports to 
 come, but that it is Authentic, — that this Testimony is 
 a true and faithful narrative of what actually happened. 
 Proofs of the Genuineness of the writing amount, at the 
 utmost, only to bringing the witnesses into court and estab- 
 lishing their identity ; proofs of the Authenticity must be 
 found by sifting their evidence, and applying to it all the 
 tests and means of verification which we possess, in order 
 to ascertain whether they are telling the truth. If not 
 Genuine, the document is said to be Spurious; if not 
 Authentic, it is false. 
 
 As most of the tests and proofs of the Genuineness and 
 Authenticity of a writing are such as readily suggest them- 
 selves to the inquirer, it as unnecessary to consider them 
 here at any length. Generally, they may be divided into 
 two classes, called respectively the External and the Inter- 
 nal Evidences of the point to be proved. The External 
 Evidences of Genuineness are to be found either in other 
 and admitted writings of the supposed author, or in the 
 works of writers who were either his contemporaries, or 
 nearly of the same antiquity ; and the evidence is either 
 direct, if the disputed writing is therein explicitly attributed 
 to hun, or indirect, if these works quote as his production' 
 passages which are found in the document. This indirect 
 testimony has the greater force, for on account of its casual 
 or incidental chara,cter there is less reason to suspect that it 
 has been forged. The External Evidences of the Authen- 
 ticity of the writing, considered as a narrative of facts, are 
 too numerous to mention. They are found in allusions to 
 the same facts, or to incidents obviously connected with 
 them, by contemporary authors ; in customs, traditions, and 
 institutions, which have come down to later times, and the 
 origin of which cannot be accounted for, except on the sup- 
 
436 THE SOURCES OF EVI0ENCK 
 
 position that the reported events actually took place; in 
 coins, medals, and inscriptions, belonging to the same age, 
 or one immediately subsequent, and connected by equally 
 close relations with the alleged facts; in the notoriety 
 ■vybich such incidents must have obtained,, the interest which 
 must have been felt in them, and the consequent probabil- 
 ity that falsifications and forgeries respecting them would' 
 never have been attempted, or would have been detected 
 and disproved at the time. 
 
 Of the Internal Evidence, it has been justly remarked, 
 tjiat it is weak to establish either Genuineness or Autben- 
 tjcity,! but powerful to disprove both. As Hamilton remarks, 
 " We can easily conceive that an able and learned forger 
 may accommodate his fabrications both to all the general 
 circumstances of time, place, people, and language under 
 -^hich it is supposed to have been written, and even to all 
 the particular circumstances of the style, habit of thought, 
 personal relations, &c. of the supposed author." On the 
 other hand, a single anachronism, well made out, in respect 
 either to events, institutions, customs,, or even the use of 
 language, is. as fatal to the document's claim to antiquity, as 
 a well-fistablished alibi is to the success of a criminal prose- 
 cution. Bentley's Dissertation upon the Epistles of PhaJa- 
 ris. might have been limited to pointing out two or three of 
 the numerous anachronisms which he detected in tbem, if 
 his only object in writing it had been to prove that these 
 alleged Epistles were an impudent forgery. In respect to 
 the Authenticity of a narrative, it is to be observed, that 
 thp credibility of certain, facts is one thing, and tlie proof 
 of thqir actual occurrence is another. For estabUshing the 
 former,. Internal Evidence is suiEcient ; for the latter, it is 
 powerless, being entirely inapplicable. By saying that a 
 narrative of certain events bears with it Internal Evidence 
 of its, truth,, we mean only that the events are possible, — 
 that they are consistent with each other, — that they har- 
 
AND THE CAUSES OF EEROE. 437 
 
 monize witli what we know from other sources concerning 
 the men of that country and that age, — that they are con- 
 formable to the ordinary course of things. All this may be 
 true of an avowed fiction. Some of Shakespeare's plays, 
 most of Scott's novels, have as much Internal Evidence of 
 truth as any testimony given in a court of justice. They 
 may have even more ; for it is a common proverb that truth 
 is often stranger than fiction. If we disregard all extrane- 
 ous circumstances, and look only at the face of the narra- 
 tive, Robuison Crusoe appears as true a story as Cook's 
 Voyages, and Richaxdson the novelist is as faithful an his- 
 torian as Hume. 
 
 As the evidence from the several sources that have now 
 been mentioned may be of various degrees of strength, and 
 as opinion is often drawn in opposite directions by conflict- 
 ing testimony, we are naturally led to inquire whether 
 there is any measure of probability, or any means of accu- 
 rately estimating the amount of belief which ought to be 
 accorded under different circumstances. This brings us at 
 once to the Theory of Probabilities, or, as the mathemati- 
 cians sometimes call it, the Doctrine of Chances. Only 
 the outlines, or first principles, of the subject can be con- 
 sidered here, as the details are exclusively mathematical, 
 and so do not come within our province. 
 
 It is first to be observed, that, in the calculation of 
 Chances, as in every other department of pure mathe- 
 matics, since the reasoning employed is Demonstrative in 
 character, the correctness of the results obtained depends 
 upon the truth of certain assumptions made in the outset ; 
 and the applicability of one of these results to any given 
 case, or actual instance, turns upon the answer to the ques- 
 tion whether this instance is exactly comprehended within 
 the Definition of the Concept upon which the whole calcu- 
 lation is based. Thus, in calculatmg the probability of any 
 one out of a given number of events, it is assumed that all 
 
4^8 THf, SOURCES OF EVIDENCE 
 
 the events considered are equally possible, ^- that no one 
 has; any advantage, which would render it more likely to 
 happen than the others. Practically, this supposition is 
 never fulfilled. In illustrating their conclusions, the mathe- 
 maticians have shown much ingenuity in selecting cases 
 where the chances would seem to be equally balanced ; but 
 it is easy to show that, they have never entirely succeeded. 
 Their fe,vorite case is that of putting a number of balls, 
 equal in size, but different in color, into an urn, and then 
 oonaiderii^ the probabihty of a blindfolded person drawing 
 one of a certain color after a given number of trials. But 
 suppose the number of balls is considerable, that, all the 
 white ones are- first thrown in together, and then all the 
 blat^ ones ; in such case, the chance of drawing a black 
 ball at the first trial is obviously much greater than that of 
 at white one. A dozen, other suppositious might be made, 
 depending on the size and shape of the urn, and the manner 
 of throwing in the balls, any one of which would be fatal to 
 a; piscise agreement of the actual with the calculated result. 
 Another favorite case is that of throwing up a half-penny, 
 tO' determine whether it wiU give head or tail; but here it 
 is. assumed that the two sides of the coin just balance each 
 other, which,, on account of the different imprints that they 
 bear, is never the case. Even in the better chosen illus- 
 trations, then, the calculated result will be only an approx- 
 imation to the truth. In ordinary cases. in which the Doc- 
 trine of Chances is applied, as in gambliog, it will be but a 
 mde approximation; most * what are called games of 
 chance are, at least in some faint degree, games of skiU ; 
 and ID the long run, though not necessarily in a few trials, 
 skill will tell. 
 
 In most cases of the practical application of the Doctrine 
 of Chances, the existence of numerous causes of error is, 
 admitted ; but as we know nothing of the character of these, 
 causeS] and. do not see any reason, why more of them should 
 
AND THE CAUSES OF EERGE. 439 
 
 operate on one side than on the other, it is assumed that, in 
 the long run, they will compensate each other, so that the 
 result will agree with the. calculation. But this is only the 
 argument ad ignorantiam, the fallacy of which has already 
 been, noticed ; Because we- do not know any reason why there 
 should not be as many and as heavy errors on one side as 
 on the other, it; does not follow that there is no such rea- 
 son. It was for a long time supposed, that the arithmetical 
 mean of several distinct observations of the same astrono.- 
 mical phenomenon would afford the nearest approximation 
 to a correct result, as there was no known reason why dif- 
 ferent observers should not err as- much on one side as on 
 the other. But- it is now known that each observer has a 
 constant tendency, distinctly appreciable in amount, to err 
 in one direction ; and if allowance is not made for this 
 "personal equation," as it is called, the arithmetical mean 
 is not the- nearest attainable approximation to the truth. 
 
 What is called "the Method of Least Squares " has been 
 adopted as a mode of finding the most probable result, since 
 it was ascertained that the arithmetical mean is not the best 
 mean of a number of observed quantities. This Method 
 proceeds upon the assumption that all errors are not equally 
 probable, but that small errors are more probable than large 
 ones. An easy corollary from this assumption is, that the 
 most probable conclusion can be obtained by making, not 
 the errors themselves, but the sum of the squares of these 
 errors, of the smallest possible amount. To borrow an in- 
 stance from Dr. Whewell : — Let the observed numbers be 
 4, 12, 14 ; and suppose it known that these numbers must 
 be erroneous, as they ought to form an arithmetical pro- 
 gression.. The question is, what arithmetical progression 
 do they most probably,, represent. The following table 
 shows that, there are three such progressions which approx- 
 imate the observed series, and also indicates which one of 
 thein, according to the Method of Least Squares^ is the 
 most probable. 
 
440 THE SOURCES OF EVIDENCE 
 
 _ Sums of Sums of sqnarei 
 
 *'"■'>"■ errors. of errors. 
 
 Observed Series 4, 12, 14 
 
 1st Progression 4, 9, 14 0, 3, 3 9 
 
 2d « 6, 10, 14 2, 2, 4 8 
 
 3d « 5, 10, 15 1, 2, 1 4 6 
 
 We here see, although the first progression gives the 
 least sum of errors, the third shows the least sum of the 
 squares of the errors; and therefore,- according to this 
 Method, the third is the most probable of the three. 
 
 These remarks were necessary in order to obviate the 
 inference which too many are inchned to draw, that, be- 
 cause the calculations in the Doctrine of Chances are made 
 on strict mathematical principles, the calculated probability 
 of an event, in any actual application of this Doctrine, 
 must therefore be mathematically exact and absolutely 
 certain. On the contrary, in any such application of the 
 principles, the result is only a rough approximation to the 
 truth. 
 
 It is also important to remember, that the application of 
 the Theory of Probabilities only shows us what we ought 
 to expect, or what, as rational beings, we are bound to be- 
 lieve, and does not reveal any Cause or Law that actually 
 determines the occurrence. To speak technically, the cal- 
 culated probability is subjective, and not objective ; it re- 
 veals what may be called a law of thought, but not a law 
 of things. " The subject-matter of calculations in the 
 Theory of Probabilities," says Professor Donkin, " is quaTii- 
 tity of belief. In every problem, a certain number of hy- 
 potheses are presented to the mind, along with a certain 
 quantity of information relating to them ; the question is, — 
 In what way ought belief to be distributed among them ? " 
 The calculation of the chances does not assume to increase 
 this " quantity of information," or to reveal any new data 
 on which our judgment ought to be based ; but only how 
 we ought to judge and to act on the data that we already 
 
AND THE CAUSES OF EEROE. 441 
 
 possess. The doctrine does not even assure us that the 
 calculated result will be verified at the first trial,, or at any 
 subsequent trial; but it only shows- us how we ought to 
 expect the actual results to be distributed in the course of 
 an infinite number of trials. The calculation does not re- 
 late merely to future events, the occurrence of which is 
 still contingent ; it may be applied also to the past, to de- 
 termine the probability that the event did, or did not, take 
 place. In eases of the latter sort,, it is sufiiciently obvious 
 that the application of the Theory of Probabilities does not 
 in any wise affect the event itself, which is already irrev- 
 ocably determined either one way or the other ; but only 
 assimies, in our ignorance of what the actual result has 
 been,, to determine what we ought to believe respecting it, 
 
 Keeping this distinction in mind, yre can explain the 
 seeming paradox,, that an event should be sure to happen 
 at the first trial,- though the chances were indefinitely great 
 against its occurrence. Put into an urn any number of 
 balls numbered consecutively firom one upwards, — say 
 1,000. Of course, there are 999 chances to 1 against a 
 blindfolded person drawing, at the first trial, the particular 
 ball marked with any one of these numbers ; and yet some 
 one ball so marked must be drawn. But this is no viola- 
 tion of the law regulating what we ought to expect ; for 
 we ought not to expect any particular number to come at 
 the first trial, though we are certain that some — we know 
 not what — number must so come. 
 
 It is assumed in the Doctrine of Chances, that the va- 
 rious degrees of belief may be represented by numbers. 
 An impossible event, as it has no probability whatever in 
 its favor, is appropriately represented by zero. An event 
 which is sure to happen, as the expectation of its occur- 
 rence is not broken or divided by any chance of failure, 
 might be represented by any integral number; its most 
 convenient, because the simplest,, symbol is uniiy. Then 
 
 19* 
 
442 THE SOUECES OF EVIDENCE 
 
 all the degrees of probability between impossibility and 
 certainty will be denoted by the fractions that may be in- 
 terpolated between and 1. 
 
 The first principle of the Doctrine of Chances is, that 
 the probahility of an uncertain event is represented hy the 
 number of chances favorable to its occurrence, divided by the 
 total number of chances whether favorable or unfavorable. 
 Thus, as a pack contains 52 cards, divided into four equal 
 suits, into 12 pictured and 40 plain cards, and into 26 red 
 and 26 black cards, the chance of drawing a heart at the 
 first trial is -5^ or ^ ; of a pictured card, ^| or ^ ; of a red 
 card, |-| or J. This last case represents an event which is 
 entirely uncertain, the chances being equal for and against 
 its occurrence. We may get rid of the fractional form by 
 expressing the probabiUty of an event in that mode which 
 is called " the odds " ; that is, we may take the numerator 
 to express the chances for, and the difiference between the 
 numerator and the denominator to signify the chances 
 against, the occurrence. This rule is an immediate corol- 
 lary from the first principle as just stated, since the numer- 
 ator gives the number of favorable chances, and the de- 
 nominator the total number of them both favorable and 
 unfavorable. Thus, the chance of drawing a pictured card 
 is represented fractionally, as above, by ^, or by the odds 
 as 3 to 10 ; of a red card, as -H, or 26 to 26, — even 
 chance. 
 
 The improbability of an occurrence is denoted by the 
 complement of the fraction which expresses its probability ; 
 that is, the odds are reversed. Thus, as there are six faces 
 to a die, all of which are supposed to be equally likely to 
 come uppermost, the probability of throwing sic is ^ or 1 
 to 5 ; the improbability of it is 1 — e =^ 6' or 5 to 1. The 
 reason of this rule is obvious ; the improbability of one 
 event must be the sum of the probabilities of all the other 
 possible occurrences ; and as the total of all tlie chances. 
 
AND THE CAUSES OF EEEOR. 443 
 
 •which represents what is sure to happen, is unity, the sum 
 of the probabilities of all the others is found by subtract- 
 ing the probabihty of this one from unity. Thus, some 
 one of the six faces must come uppermost ; this certainty 
 is denoted as 1. Then, as the probabihty of a six is \, the 
 chance of some one out of the other five faces, (in other 
 ■words, the improhahility of a six,) is 1 — ^ = f • As each 
 of the five other faces has a probability of ^, the sum of 
 their chances, or the improbabiHty of the remaining one, is 
 evidently |. 
 
 The probabiliti/ of a compound event — that is, of two 
 independent uncertainties happening conjointly — is ascer- 
 tained hy multiplying the separate chances of the two to- 
 gether. Thus, the chance of throwing six with one die 
 being \, and of throwing the same with another die being 
 ^, the chance of obtaining sixes at once with the two dice 
 is ^ X |- = -gig . This rule, again, is a direct corollary from 
 the first principle as already enounced ; for as the number 
 of possible throws with two dice is 6 X 6 =36, (since 
 each face of the one might be combined with either of the 
 six faces of the other,) and as only one of these is favor- 
 able, the odds are evidently as 1 to 35. To take another 
 instance : — the chance of drawing a pictured card out of 
 a pack being ^, and of a red card, |-, the probability of 
 having a red pictured card is -3^ X ^ = ^ or -§^, as there 
 are six red pictured cards out of the 52 in the pack. 
 
 According to this rule, the chance of drawing a red card 
 four times in succession, the card being replaced after each 
 trial, so that the number in the pack shall always be 52, 
 
 will be J X i X i X J = t'e' o^ °"V 1 *° ^^- ^"■t g^™" 
 blers often deceive themselves in respect to the application 
 of this riole. As it is so unlikely that a red card will turn 
 up several times in succession, they imagine that, after it 
 has thrice thus turned up, the chance of obtaining a black 
 card at the fourth trial is much greater than it was at first. 
 
444 THE SOURCES OF EVIDENCE 
 
 But it is not so ; if the card drawn is always immediately 
 replaced, tlie probability c£ drawing a black card after we 
 have drawn a red one at three, or even at a thousand, suc- 
 cessive trials, is precisely what it was before the first ex- 
 periment, — namely, ^. The number of cards being always 
 the same, 26 red and 26 black, the probability of obtaining 
 a red one is always the same, whatever previous erperiments 
 may have been made with the same pack. The three ex- 
 periments already tried have reduced so many uncertainties 
 to certainties, — that is, have thrown them out of the cal- 
 culation in the Doctrine of Chances, which deals only with 
 uncertain events. Before any trial was made, the chance 
 of a red card turning up four times in succession was only 
 -jlj, each of the four results being then uncertain ; after 
 three trials, but one event is stUl an uncertainty, and the 
 probability of its occurrence is J. We see, then, the folly 
 of the gambler's expectation that his luck must soon turn, 
 because he has had a long series of ill-luck. But all his 
 past trials having been reduced to certainties, his chance 
 of good fortune is now precisely what it was when he be- 
 gan. His only chance of success, after he has had a long 
 series of misfortunes, is to stop playing altogether; and this 
 is also the best thing he can do, if fortune has smiled upon 
 him. 
 
 The development of these principles must be left to the 
 mathematician ; but a fLu-ther caution in respect to the 
 application to be made of them by the gambler may be 
 borrowed from BufFon. " If two men," he asks, " were to 
 determine to play for their whole property, what would be 
 the effect of this agreement ? The one would only double 
 his fortune, and the other reduce his to naught. What 
 proportion is there between the loss and the gain ? The 
 same that there is between all and nothing. The gain of 
 the one is but a moderate sum ; the loss of the other is 
 numerically infinite, and morally so great that tiie labor of 
 
AND THE CAUSES OF EEROE. 445 
 
 his whole hfe may not, perhaps, suffice to restore his prop- 
 erty." But the fascination of gamhhng is so great, and 
 the hahit of it, when once formed, is so incontrollable, that 
 every one who even begins to play may be regarded as 
 staking his whole fortune upon the issue, and thus as volun- 
 tarily subjecting himself to these tremendous odds. 
 
 The principal intellectual Causes of Error have been al- 
 ready indirectly considered, inasmuch as they consist in any 
 violation of the rules and methods which have been laid 
 down for the attainment of truth. But the moral Causes 
 which bhnd our perceptions, warp our judgments, and lead 
 us to accept illusions in the place of truths, deserve some 
 separate notice. Most of these are modifications or conse- 
 quences of self-love, or rather of that short-sighted selfish- 
 ness which has more regard for present ease and enjoyment, 
 however trifling, than for future good, however great, if 
 the latter be attainable only by eifort and self-denial. Such 
 are prejudices, pride, undue desires, precipitancy, and sloth. 
 All of these are faults of character rather than of intellect ; 
 yet they are more frequent sources of delusion, and more 
 formidable obstacles to our mental progress, than can be 
 found in the original weakness and limited range of our 
 faculties, or in the insufficiency of the aids and incitements 
 which nature furnishes for the pursuit of truth. We ap- 
 proach the study of a subject, not as prepared to accept any 
 conclusions to which our researches might naturally lead, 
 but with minds stuffed with preconceived opinions, which 
 pride prevents us from relinquishing after they have been 
 once avowed, or with a bias in favor of some startling con- 
 sequences of the inquiry, the announcement of which may 
 feed our vanity or establish our reputation. Pride also 
 leads us astray, by inducing us to over-estimate the extent 
 and importance of the acquisitions that we have already 
 made, or to adopt too easily the conclusion that the investi- 
 gation has reached its limit, and that we already know as 
 
446 THE SOUECES OF EVIDENCE 
 
 much as is capable of being known. I know of no error 
 whicb is more fatal to progress than the idea that there is 
 no progress to be made, — of no opinion which is more det- 
 rimental to improvement than the beHef that no improve- 
 ment is possible. It is true that a low estimate of the ex- 
 tent of our knowledge does not amount to the Christian 
 virtue of humility in the largest sense. It may be, it fre- 
 quently is, accompanied with a very lofty opinion of the 
 extent of our powers, or the excellence of our natural en- 
 dowments. But a conceit of ability, bad as it is, is not so 
 injurious to progress as a conceit of knowledge. The one 
 encourages a person to study, by leading him to believe that 
 he can grapple with any subject ; the other disposes him to 
 sit down in idleness, under the belief that he has already 
 mastered that subject. Seneca says, Multos. potuisse ad 
 sapientiam pervenire, niin putassent ae pervenisse, — Many 
 might have obtained wisdom, if they had not supposed that 
 they had already got it. 
 
 Moderation in our personal desires, and that earnestness 
 of inquiring purpose which leads not so- much to an abne- 
 gation as to the entire forgetftdness of self, are more im- 
 portant elements of success in the pursuit of truth than is 
 commonly supposed. The brilliant results of Dr. Frank- 
 lin's scientific career seem attributable, in a great degree, 
 to his generous disregard of his own fame and standing in 
 the eyes of the public. A lively curiosity, an eye quick at 
 observation, great sagacity in detecting the more occult re- 
 lations of facts and bearings of experiments, and a mind of 
 incessant and intense activity, were not the only means 
 that enabled him to accompUsh so much in science. His 
 attention was not diverted from the object of investigation 
 by any regard for what the world might think of the im- 
 portance of that object, or of his own merit in obtaining it. 
 The necessary experiments were instituted, not to convince 
 others, but to satisfy himself. The most brilliant results at 
 
AND THE CAUSES OF EEROE. 447 
 
 whicli he arrived were communicated only in private let- 
 ters to a few friends, to whom he left the care of publishing 
 them or not, as they saw fit. His theories sat loosely upon 
 him, and he modified or abandoned them, when flirther ob- 
 servations made it necessary, without dreading the charge 
 of inconsistency, and without shame at confessing a mis- 
 take. He was never seduced, by the accidental brilliancy 
 or novelty of one object of inquiry, to pay more attention 
 to it than to another, apparently of a more homely charac- 
 ter, but really of equal interest to a phUpsophical mind. 
 He studied the meaiis of remedying smoky chimneys with 
 as much ardor and industry as he showed in penetrating 
 the secrets of the clouds, and robbing the thunderbolt of its 
 terrors. He formed theories of the earth, and projects for 
 cleaning and lighting the streets of Philadelphia, with equal 
 zeaJ ; and having communicated the former in a private 
 letter to a friend, and urged upon his feUow-citizens the 
 adoption of the latter, he dismissed both from his mind, and 
 pursued with fresh interest a whoUy different set of inves- 
 tigations. 
 
 The most frequent cause of failure in any pursuit is the 
 lack of earnestness. Habit may impart a kind of mechan- 
 ical facihty in the performance of a given task ; but there 
 will be little vigor or energy in the work, if the feelings 
 be not deeply interested in it, so that the result shall be 
 awaited with eager expectation or trembling anxiety. Long- 
 continued labor easily degenerates into mere routine ; and 
 then, even though the specific object, in view should be ob- 
 tained, — though a science should be learned or a liveli- 
 hood got, — there wUl be no strain of the faculties, and 
 consequently no development of them, — no correction of 
 errors, and. therefore no discipUne of mind., This is the 
 secret of the great force displayed, and the large results 
 that are often accomplished, by those who are opprobri- 
 ously termed "men of one idea," — persons who have con- 
 
448 THE SOURCES OF EVIDENCE 
 
 centrated their attention upon one object, and who pursue 
 it, regardless of everything else, with all the strength and 
 the bitterness of fanaticism. Half an hour of strenuous 
 exertion is worth a week of mechanical and desultory la- 
 bor. Too often we dawdle over the business of hfe, instead 
 of taking it up with eagerness, and prosecuting it to the end 
 as a work of love. There is all the difference in the world 
 between an active mind and a passive one ; between ear- 
 nestly hunting after truth, and only swallowing knowledge 
 inertly, as it is poured into the memoiy by a teacher or a 
 book, and just as quickly washed out again. We are made 
 what we are, experts or dolts, much more by our acquired 
 habits than by success or failure in the attainment of knowl- 
 edge. Aim not so much to be learned, as to be able to 
 learn ; one truly wise man is worth a hundred erudite ped- 
 ants. The study of Logic itself will do httle to cultivate 
 our power of reasoning, or to improve our habits of thought, 
 except indirectly, by the effort which is necessary for the 
 mastery of its principles, and by the endeavor to verify or 
 correct them in the course of our subsequent researches. 
 What we really need to attain is Logical power, and a 
 knowledge of the science of Logic is useful so far only 
 as it is conducive to such attainment. 
 
 Among the occasions for the use of this power, that to 
 which the gravest responsibiHty is attached is the formation 
 of our opinions. Properly speaking, we must all begin life 
 without any opinions which we can call our own by any 
 better right than that of passive inheritance or unconscious 
 inoculation. We have probably imbibed most of them just 
 as we took the measles or the whooping-cough in infancy, 
 fi'om accidental contact vrith others. We are Whig, Dem- 
 ocrat, or Republican, conservative or radical, — we go to 
 the Episcopal, Presbyterian, or Congregationahst chm-ch, — 
 simply because parents and fiiends thought so, or did so, 
 formerly. Now, in one respect, this is aU right and just as 
 
AND THE CAUSES OF ERROR. 449 
 
 it should be. It is fortunate, both for ourselves and the 
 world, that we begin life with a set of provisional opinions 
 already formed, not by us, but for us. This vis inertice of 
 opinion, this tendency of the human mind to move in the 
 ruts where others have preceded it, is the great conserva- 
 tive principle of society, all that keeps us from intellectual 
 and social anarchy. Without it, all the wise men who 
 have been before us would have lived in vain, and society 
 would drift along helplessly, without keel or rudder. If 
 we were not willing to accept opinions before we are able 
 to form them for ourselves, — ay, and to cling to them 
 with the fondness which early association imparts, — half of 
 the time we should act at random, and the other half ex- 
 travagantly and foohshly. 
 
 But we cannot pass through life merely as docile chil- 
 dren ; and our first duty as men — at any rate, as educated 
 and thinking men — is to begin the great work of fashion- 
 ing our own creeds in politics, religion, philosophy, and so- 
 cial economy. When we have attained our majority, we 
 have become as accountable for our opinions as for our con- 
 duct. A wise man, however, might hesitate before going 
 as far as Descartes, who urges us to begin by doubting 
 everything ; his advice is, to take up every question, as it 
 were, de novo, with a determination not to accept any an- 
 swer to it the correctness of which is not made out by evi- 
 dence satisfactory to our own minds, and ehcited by our own 
 inquiries. A safer course, as it seems to me, is to begin, 
 not by discarding all our previous opinions, but by examin- 
 ing the foundations on which they rest. There is just as 
 much of prejudice and rashness in presuming that they are 
 all false, as in behoving, previous to inquiry, that they are 
 all true. Do not ask. Why may it not be otherwise ? but 
 rather. Why is it so ? The presumption is in favor of the 
 received doctrines in any science, until good reasons are 
 made to appear for doubting or denying them. But the 
 
450 SOUECES OF EVIDENCE AND CAUSES OF EEEOB. 
 
 duty of inquiry, in order to ascertain whether there are 
 such reasons, is one which always exists, and which opens 
 the largest and fairest field for the exercise and develop- 
 ment of our powers of thought. Only by such exercise 
 can we hope to perfect our knowledge of the principles of 
 Logic, and to make that knowledge of use to ourselves and 
 others. " We employ reason," said the Port-Royalist logi- 
 cians, " as an instrument for acquiring the sciences, whereas 
 we ought to use the sciences as a means of perfecting our 
 reason, correctness of judgment and accuracy of thought 
 being infinitely more valuable than all the speculative 
 knowledge which we can obtain fi-om the best-estabUshed 
 sciences. Wise men, therefore, ought to engage in the 
 study of the sciences only so far as they conduce to this 
 end, and to make them only the training-ground, and 
 not the field for the regular employment, of their mental 
 powers." 
 
 THE END. 
 
 Cambridge : Stereotyped and Printed by Welch, Bigelow, & Co. 
 

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