aass_"BC9- PREFACE TO THE FIRST EDITION. Teiis book makes no pretense of giving to the world a new theory of the intellectual operations. Its claim to attention, if it possess any, is ground- ed on the fact that it is an attempt, not to supersede, but to embody and systematize, the best ideas which have been either promulgated on its sub- ject by speculative writers, or conformed to by accurate thinkers in their scientific inquiries. To cement together the detached fragments of a subject, never yet treat- ed as a w^hole ; to harmonize the true portions of discordant theories, by supplying the links of thought necessary to connect them, and by disentan- gling them from the errors with which they are always more or less inter- woven, must necessarily require a considerable amount of original specula- tion. To other originality than this, the present work lays no claim. In the existing state of the cultivation of the sciences, there would be a very strong presumption against any one who should imagine that he had effect- ed a revolution in the theory of the investigation of truth, or added any fundamentally new process to the practice of it. The improvement which remains to be effected in the methods of philosophizing (and the author be- lieves that they have much need of improvement) can only consist in per- forming more systematically and accurately operations with which, at least in their elementary form, the human intellect, in some one or other of its employments, is already familiar. In the portion of the work which treats of Ratiocination, the author has not deemed it necessary to enter into technical details which may be ob- tained in so perfect a shape from the existing treatises on what is termed the Logic of the Schools. In the contempt entertained by many modern philosophers for the syllogistic art, it will be seen that he by no means par- ticipates ; though the scientific theory on which its defense is usually rest- ed appears to him erroneous : and the view which he has suggested of the nature and functions of the Syllogism may, perhaps, afford the means of conciliating the principles of the art with as much as is well grounded in the doctrines and objections of its assailants. The same abstinence from details could not be observed in the First \ »k, on Names and Propositions ; because many useful principles and dis- iv PEEFACE. . yp rj A^ tinctions which were contained in the old Logic have been gradually omit- ted from the writings of its later teachers ; and it appeared desirable both to revive these, and to reform and rationahze the philosophical foundation on which they stood. The earlier chapters of this preliminary Book will consequently appear, to some readers, needlessly elementary and scholastic. But those who know in what darkness the nature of our knowledge, and of the processes by which it is obtained, is often involved by a confused apprehension of the import of the different classes of Words and Asser- tions, will not regard these discussions as either frivolous, or irrelevant to the topics considered in the later Books. On the subject of Induction, the task to be performed was that of gener- alizing the modes of investigating truth and estimating evidence, by which so many important and recondite laws of nature have, in the various sci- ences, been aggregated to the stock of human knowledge. That this is not a task free from difficulty may be presumed from the fact that even at a very recent period, eminent writers (among whom it is sufficient to name Archbishop Whately, and the author of a celebrated article on Bacon in the JEdinburgh lieview) have not scrupled to pronounce it impossible.* The author has endeavored to combat their theory in the manner in which Di- ogenes confuted the skeptical reasonings against the possibility of motion ; remembering that Diogenes's argument would have been equally conclu- sive, though his individual perambulations might not have extended be- yond the circuit of his own tub. Whatever may be the value of what the author has succeeded in effect- ing on this branch of his subject, it is a duty to acknowledge that for much of it he has been indebted to several important treatises, partly historical and partly philosophical, on the generalities and processes of physical sci- ence, which have been published within the last few years. To these trea- tises, and to their authors, he has endeavored to do justice in the body of the work. But as with one of these writers, Dr. Whewell, he has occasion fi'cquently to express differences of opinion, it is more particularly incum bent on him in this place to declare, that without the aid derived from the * In the later editions of Archbishop Whately's "Logic," he states his meaning to be, not that "rules" for the ascertainment of truths by inductive investigation can not be laid down, or that they may not be "of eminent service," but that they "must always be comparatively vague and general, and incapable of being built up into a regular demonstrative theory like that of the Syllogism." (Book iv., ch, iv., § 3.) And he observes, that to devise a system for this purpose, capable of being "brought into a scientific form," would be an achievement which "he must be more sanguine than scientific who expects." (Book iv., ch. ii., § 4.) To effect this, however, being the express object of the ])ortion of the present work which treats of Induction, the Avords in the text aie no overstatement of the difference of opinion between Arclibisiiop Whately niid me on llie subject. rKEFACIi:. V facts and ideas contained in that gentleman's "History of tlio Inductive Sciences," the corresponding portion of this work would proba}>ly not iiave been written. The concluding Book is an attempt to contribute toward the solution of a question which the decay of old opinions, and the agitation tliat disturbs European society to its inmost depths, render as important in tlie present day to the practical interests of human life, as it must at all times be to the completeness of our speculative knowledge — viz. : Whether moral and so- cial phenomena are really exceptions to the general certainty and uniformi- ty of the course of nature ; and how far the methods by which so many of the laws of the physical world have been numbered among truths irrevo- cably acquired and universally assented to, can be made instrumental to the formation of a similar body of received doctrine in moral and political science. Digitized by the Internet Archive in 2011 with funding from The Library of Congress http://www.archive.org/details/systemoflogicrat01mill PREFACE TO THE THIRD AND FOURTH EDITIONS. Several criticisms, of n, more or less controversial character, on this work, have appeared since the j^ublication of the second edition ; and Dr. Whewell has lately published a reply to those parts of it in which some of his opinions were controverted.* I have carefully reconsidered all the 23oints on which my conclusions have been assailed. But I have not to announce a change of opinion on any matter of importance. Such minor oversights as have been detected, either by myself or by my critics, I have, in general silently, corrected : but it is not to be inferred that I agree with the objections which have been made to a passage, in every instance in which I have altered or canceled it. I have often done so, merely that it might not remain a stumbling-block, when the amount of discussion necessary to place the matter in its true light would have exceeded what was suitable to the occasion. To several of the arguments which have been urged against me, I have thought it useful to reply with some degree of minuteness ; not from any taste for controversy, but because the opportunity was favorable for pla- cing my own conclusions, and the grounds of them, more clearly and com- pletely before the reader. Truth on these subjects is militant, and can only establish itself by means of conflict. The most opposite opinions can make a plausible show of evidence while each has the statement of its own case ; and it is only possible to ascertain which of them is in the right, af- ter hearing and comparing what each can say against the other, and what the other can urge in its defense. Even the criticisms from which I most dissent have been of great serv- ice to me, by showing in what places the exposition most needed to be improved, or the argument strengthened. And I should have been well pleased if the book had undergone a much greater amount of attack ; as in that case I should probably have been enabled to improve it still more than I believe I have now done. In the subsequent editions, the attempt to improve the work by addi- tions and corrections, suggested by criticism or by thought, has been con- * Now forming a chapter in his volume on "The Philosophy of DiscoA-ery." VI 1 1 PREFACE. tinned. The additions and corrections in the present (eighth) edition, wliich are not very considerable, are chiefly such as have been suggested by Professor Bain's " Logic," a book of great merit and value. Mr. Bain's view of the science is essentially the same with that taken in the present treatise, the differences of opinion being few and unimportant compared with the agreements ; and he has not only enriched the exposition by many applications and illustrative details, but has appended to it a minute and very valuable discussion of the logical principles specially applicable to each of the sciences — a task for which the encyclopedical character of his knowledge peculiarly qualified him. I have in several instances made use of his exposition to improve my own, by adopting, and occasionally by controverting, matter contained in his treatise. The longest of the additions belongs to the chapter on Causation, and is a discussion of the question how far, if at all,'the ordinary mode of stating the law of Cause and Effect requires modification to adapt it to the new doctrine of the Conservation of Force — a point still more fully and elabo- rately treated in Mr. Bain's work. CONTENTS INTRODUCTION. PAGE §1. Adefiuition at the commencement of a sub- ject must be provisional 17 2. Is logic the art and science of reasoning ?. 17 3. Or the art and science of the pursuit of truth? 18 4. Logic is concerned with inferences, not with intuitive truths 19 5. Eelation of logic to the other sciences 21 (i. Its utility, how shown 22 7. Definition of logic stated and illustrated.. 23 BOOK I. OF NAMES AND PROPOSITIONS. Chapter I. Of the NecensiUj of commencing with an Analysis of Language. § 1. Theory of names, why a necessary part of logic 26 2. First step in the analysis of Propositions. . 27 3. Names must be studied before Things — 23 CnAPTEE II. Of Xames. §1. Names are names of things, not of our ideas 29 2. Words which are not names, but parts of names 30 3. General and Singular names 32 4. Concrete and Abstract 33 5. Connotative and Non-connotative 34 6. Positive and Negative 41 7. Eelative and Absolute 42 8. Univocal and Equivocal 44 CuAPTEK III. Of the Things denoted by Xames. §1. Necessity of an enumeration of Namable Things. The Categories of Aristotle 45 2. Ambiguity of the most general names 46 3. Feelings, or states of consciousness 48 4. Feelings must be distinguished from their physical antecedents. Perceptions, what. 49 5. Volitions, an-d Actions, what 51 6. Substance and Attribute 51 7. Body 52 8. Mind 56 9. Qualities 57 10. Relations 59 11. Eesemblauce 60 12. Quantity 62 13. All attributes of bodies are grounded on states of consciousness 63 14. So also all attributes of mind 64 15. Recapitulation 64 PAGK CuAPTER IV. Of Propositions. §1. Nature and office of the copula 06 2. Affirmative and Negative propositions. ... 67 3. Simple and Complex 69 4. Universal, Particular, and Singular 71 Chapter V. Of the Import of Propositions. §1. Doctrine that a proposition is the expres- sion of a relation between two ideas 73 2. — that it is the expression of a relation be- tween the meanings of two names 75 3. — that it consists in referring something to, or excluding something from, a class. 77 4. What it really is SO 5. It asserts (or denies) a sequence, a co-exist- ence, a simple existence, a causation 81 6. — or a resemblance • 83 7. Propositions of which the terms are ab- stract 86 Chapter VI. Of Propositions merely Verbal. §1. Essential and Accidental propositions 88 2. All essential propositions are identical propositions 89 3. Individuals have no essences 91 4. Eeal propositions, how distinguished from verbal 92 5. Two modes of representing the import of a Real proposition 93 Chapter VII. Of the Nature of Classification, and the Five Piedicables. § 1. Classification, how connected with Naming 94 2. The Predicables, what 95 3. Genus and Species 95 4. Kinds have a real existence in nature 97 ■ 5. Differentia 100 6. Difierentise for general purposes, and differ- entiae for special or technical purposes... 101 7. Proprium 103 8. Accidens 104 Chapter VIII. Of Definition. § 1. A definition, what 105 2. Every name can be defined, whose meaning is susceptible of analysis 106 3. Complete, how distinguished from incom- plete definitions 107 4. — and from descriptions 103 5. What are called definitions of Things, are definitions of Xames with an implied as- sumption of the existence of Things cor- responding to them Ill 6. — even when such things do not in reality exist 116 CONTENTS. PAGE § 7. Definitions, though of names only, must be grounded on knowledge of the corre- sponding things 117 BOOK II. OF REASONING. Chapter I. Of Inference, or Reasoning, in general. 5 1. Retrospect of the preceding book 121 2. Inferences improperly so called 122 3. Inferences proper, distinguished into in- ductions and ratiocinations 125 CifAPTEE II. Of Ratiocination, or Syllogism. § 1. Analysis of the Syllogism 126 2. The dictum de omni not the foundation of reasoning, but a mere identical proposi- tion 132 3. What is the really fundamental axiom of Eatiocination 135 4. The other form of the axiom 137 CuAPTEB III. Of the Functions, and Logical Value of the Syllogism. § 1. Is the Syllogism a petitio principii ? 139 2. Insuflaciency of the common theory 139 3. All inference is from particulars to partic- ulars 141 4. General propositions are a record of such inferences, and the rules of the syllogism are rules for the interpretation of the record 146 5. The syllogism not the type of reasoning, but a test of it 148 (3. The true type, what 151 7. Relation between Induction and Deduc- tion 153 8. Objections answered 154 9. Of Formal Logic, and its relation to the Logic of Truth 156 Chapter IV, Of Trains of Reasoning, and Deduct- ive Sciences. § 1. For what purpose trains of reasoning exist. 158 2. A train of reasoning is a series of induct- ive inferences ,. 158 3. — from particulars to particulars through marks of marlis 160 4. Why there are deductive sciences 161 r>. Why other sciences still remain experi- mental 164 6. Experimental sciences may become deduct- ive by the progress of experiment 165 7. In what manner this usually takes place. . 166 iJiiAi'TKU v. Of Demonstration, and Necessary Truths. 1 1. The Theorems of geometry are necessary truths only in the sense of necessarily fol- lowing from hypotheses 168 '2. Those hypotheses are real facts with some of their circumstances exaggerated or omitted 170 ^. Some of the first principles of geometry are \ / axioms, nnd these are not hypothetical.. 171 ^y 4. —but arc (•xpcriraental truths 172 page § 5. An objection answered 174 6. Dr. Whewell's opinions on axioms exam- ined 176 Chapter VL The same Subject continued. §1. All deductive sciences are inductive 187 2. The propositions of the science of number are not verbal, but generalizations from experience 188 3. In what sense hypothetical 191 4. The characteristic property of demonstra- tive science is to be hypothetical 192 5. Definition of demonstrative evidence 193 Chapter VII. Examination of some Opinions op- ' posed to the preceding doctrines. § 1. Doctrine of the Universal Postulate 193 2. The test of inconceivability does not rep- resent the aggregate of past experience. . 195 3. — nor is implied in every process of thought 197 4. Objections answered. 201 5. Sir W. Hamilton's opinion on the Princi- ples of Contradiction and Excluded Mid- dle 204 BOOK III. OF INDUCTION. Chapter I. Preliminary Observations on Induc- tion in general. § 1. Importance of an Inductive Logic 207 2. The logic of science is also that of business and life 208 Chapter II. Of Inductions improperly so called. § 1. Inductions distinguished from verbal trans- formations 210 2. — frominductions, falsely so called,iu math- ematics 212 3. — and from descriptions 213 4. Examination of Dr. Whewell's theory of Induction 214 5. Further illustration of the preceding re- marks 221 Chapter III. Of the Ground of Induction. § 1. Axiom of the uniformity of the course of nature. 223 2. Not true in every sense. Induction per enumerationem simplicem 226 3. The question of Inductive Logic stated 227 Chapter IV. Of Laivs of Nattire. j § 1. The general regularity in nature is a tissue j of partial regularities, called laws 229 j 2. Scientific induction must be grounded on previous spontaneous inductions 231 I 3. Are there any inductions fitted to be a test j of all others ? 232 I Chapter V. Of the Law of Universal Causation. § 1. The universal law of successive phenomena is the Law of Causation 234 2. — i. e., the law that every consequent has an invariable antecedent 236 CONTENTS. XI PAGE §3. The cause of a phenomenon is the assem- bluf^e of its conditions 237 4. The distinction of agent and patient illu- sory 241 5. Case in which the effect consists in giving a property to an object 243 G. The cause is not the invariable antecedent, but the unconditional invariable anteced- ent 244 7. Can a cause be simultaneous with its ef- fect? 24T 8. Idea of a Permanent Cause, or original nat- ural agent 248 9. Uniformities of co- existence between ef- fects of different permanent causes, are not laws 251 10. Theory of the Conservation of Force 251 11. Doctrine that volition is an efficient cause, examined 255 Chapter VI. Of the Composition of Causes. §1. Two modes ofthe conjunct action of causes, the mechanical and the chemical 26G 2, The composition of causes the general rule ; the other case exceptional 268 3. Are effects proportional to their causes?. . 270 CuAPTEE VII. Of Observation and Experiment. § 1. The first step of inductive inquiry is a men- tal analysis of complex phenomena into their elements 272 2. The next is an actual separation of those elements 273 3. Advantages of experiment over observa- tion 274 4. Advantages of observation over experi- ment 276 Chapter VIII. Of the Four Methods of Experi- mental Inquiry. § 1. Method of Agreement 278 2. Method of Difference 280 3. Mutual relation of these two methods 281 4. Joint Method of Agreement and Difference. 283 5. Method of Residues 284 6. Method of Concomitant Variations 285 7. Limitations of this last method 289 Chapter IX. Miscellaneous Examples of the Four Methods. § 1. Liebig's theory of metallic poisons 292 2. Theory of induced electricity 294 3. Dr. Wells's theory of dew 296 4. Dr. Brown-Seqnard's theory of cadaveric rigidity. 301 5. Examples of the Method of Residues 305 6. Dr. Whewell's objections to tbe Four Methods 307 Chapter X. Of Plurality of Causes ; and of the Intermixture ofEffecU. § 1. One effect may have several causes 311 2. — which is the source of a characteristic imperfection of the Method of Agree- ment 311 3. Plurality of Causes, how ascertained 314 4. Concurrence of Causes which do not com- pound their effects 315 5. Difficulties of the investigation, when causes compound their effects. 317 T'AGK §6. Three modes of investigating the laws of complex effects 320 7. The method of simple observation inap- plicable 321 8. The purely experimental method inappli- cable 322 Chapter XI. Of the Deductive Method. §1. First stage; ascertainment of the laws of the separate causes by direct induction. . 325 2. Second stage; ratiocination from the sim- ple laws of the complex cases 328 3. Third stage ; verification by specific expe- rience 329 Chapter XIL Of the Explanation of Laics of Na- ture. § 1. Explanation defined 332 2. First mode of explanation, by resolving the law of a complex effect into the laws of the concurrent causes and the fact of their co-existence 332 3. Second mode ; by the detection of an in- termediate link in the sequence .332 4. Laws are always resolved into laws more general than themselves 333 5. Third mode ; the subsuraption of less gen- eral laws under a more general one 335 6. What the explanation of a law of nature amounts to 337 Chapter XIII. Miscellaneous Examj^les of the Ex- planation of Laws of Nature. § 1. The general theories of the scieuces 338 2. Examples from chemical speculations 339 3. Example from Dr. Brown- Sequard's re- searches on the nervous system 340 4. Examples of following newly -discovered laws into their complex manifestations.. 341 5. Examples of empirical generalizations, af- terward confirmed and explained deduct- ively 342 6. Example from mental science 343 T. Tendency of all the sciences to become de- ductive 344 Chapter XIV. Of the Limits to the Explanation of Laws of Nature ; and of Hypotheses. § 1. Can all the sequences in nature be resolva- ble into one law ? 345 2. Ultimate laws can not be less numerous than the distinguishable feelings of our nature 346 3. In what sense ultimate facts can be ex- plained 348 4. The proper use of scientific hypotheses.. . . 349 5. Their iudispensablenes? 353 6. The two degrees of legitimacy in hypoth- eses 355 7. Some inquiries apparently hypothetical are really inductive. 359 Chapter XV. Of Progressive Effects; and of the Continued Action of Causes. §1. How a progressive effect results from the simple continuance of the cause 361 2. — and from the progressiveness of the cause 363 3. Derivative laws generated from a single ultimate law 365 xu CONTENTS. PAGE Chapter XVI. Of Empirical Latvs. § 1. Detiiiitiou of au empirical law 366 2. Derivative laws commonly depend on col- locations 367 3. The collocations of the permanent causes are not reducible to any law 361 4. Hence empirical laws can not be relied on beyond the limits of actual experience. . . 368 5. Generalizations which rest only on the Method of Agreement can only be re- ceived as empirical laws 369 6. Sigus from which an observed uniformity of sequence may be presumed to be re- solvable 369 7. Two kinds of empirical laws 371 Chaptek XVII. Of Chance, and its Elimination. §1. The proof of empirical laws depends on the theory of chance 372 2. Chance defined and characterized 373 3. The elimination of chance 376 4. Discovery of residual phenomena by elim- inating chance 377 5. The doctrine of chances 378 Chapter XVIII. Of the Calculation of Chances. § 1. Foundation of the doctrine of chances, as taught by mathematics 379 2. The doctrine tenable 380 3. On what foundation it really rests 3S1 4. Its ultimate dependence on causation 383 5. Theorem of the doctrine of chances which relates to the cause of a given event. . . - . 385 6. How applicable to the elimination of chance 386 Chapter XIX. Of the Extension of Derivative Laws to Adjacent Cases. § 1. Derivative laws, when not casual, are al- most always contingent on collocations.. 388 2. On what grounds they can be extended to cases beyond the bounds of actual expe- rience 389 3. Those cases must be adjacent cases 390 Chapter XX. Of Analogy. § 1. Various senses of the word analogy 393 2. Nature of analogical evidence 393 3. On what circumstances its value depends. . 396 Chapter XXI. Of the Evidence of the Law of Uni- versal Causation. 5 1. The law of causality does not rest on au instinct 397 2. —but on an induction by simple enumera- tion 400 3. In what cases such induction is allowable. 402 4. The universal prevalence of the law of cau- sality, on what grounds admissible. 403 Chapter XXII. Of Uniformities of Co-existence not dependerit on Causation. 51. Uniformities of co-existence which result from laws of sequence 406 2. The properties of Kinds arc unirorniitios of co-existence 408 3. Some are derivative, others ultimate 409 4. No universal axiom of co-existence 410 5. The evidence of uniformities of co-exist- ence, how measured 411 page §6. When derivative, their evidence is that of empirical laws 412 7. So also when ultimate 413 8. The evidence stronger in proportion as the law is more general 413 9. Every distinct Kind must be examined 414 Chapter XXIII. Of Approximate Generalizations, and Prohahle Evidence. § 1. The inferences called probable, rest on ap- proximate generalizations 416 2. Approximate generalizations less useful in science than In life 416 3. In what cases they may be resorted to 417 4. In what manner proved 418 5. With what precautions employed 420 6. The two modes of combining probabilities. 421 7. How approximate generalizations may be converted Into accurate generalizations equivalent to them 423 Chapter XXIV. Of the Remaining Laws of Na- ture. §1. Propositions which assert mere existence. 425 2. Resemblance, considered as a subject of science 426 3. The axioms and theorems of mathematics comprise the principal laws of resem- blance 427 4. — and those of order In place, and rest on Induction by simple enumeration 428 5. The propositions of arithmetic affirm the modes of formation of some given num- ber 429 0. Those of algebra affirm the equivalence of different modes of formation of num- bers generally 432 7. The propositions of geometry are laws of outward nature 433 8. Why geometry Is almost entirely deduct- ive 435 9. Function of mathematical truths In the other sciences, and limits of that function. 436 Chapter XXV. Of the Grounds of Disbelief. § 1. Improbability and Impossibility 438 2. Examination of Hume's doctrine of mir- acles 438 3. The degrees of Improbability correspond to differences In the nature of the gener- alization with which an assertion con- flicts 441 4. A fact is not Incredible because the chances are against It 443 5. Are coincidences less credible than other facts ? 444 6. An opinion of Laplace examined 446 BOOK IV. OF OPERATIONS SUBSIDIARY TO IN- DUCTION. Chapter I. Of Observation and Description. §1. Observation, how far a subject of logic 449 2. A great part of what seems observation Is really inference 450 CONTENTS. XIll PAGE §3. The description of an observation affirms i more than is contained in tlie observa- | tion 452 4. — namely, an agreement amon<,' phonom- I eiia ; and the comparison of phenomena to ascertain such agreements is a prelim- inary to induction 453 CuAi'TER II. Of A bstraction, or the Formation vf Conceptions. §1. The comparison which is a preliminary to induction implies general conceptions... 455 2. — but these need not be pre-existent 456 3. A general conception, originally the result of a comparison, becomes itself the type of comparison 45S 4. What is meant by appropriate conceptions. 4.59 5. — and by clear conceptions 401 6. Farther illustration of the subject 462 CuAVTKR III. Of Xaming as Subsidiary to Induc- tion. § 1. The fundamental property of names as an instrument of thought 464 2. Names are not indispensable to induc- tion 465 ?>. In v,'hat manner subservient to it 465 4. General names noi a mere contrivance to economize the use of language 466 Chapter IV. Of the Requisites of a Philosophical Laigt(age, and the Principles of Definition. §1. First requisite of philosophical language, a steady and determinate meaning for ev- ery general name 46T 2. Names in common use have often a loose connotation 467 3. — which the logician should tix, with as little alteration as possible 469 4. Why definition is often a question not of words but of things 470 5. How the logician should deal with the transitive applications of words 472 6. Evil consequences of casting off any por- tion of the customary connotation of words 476 Chapter V. On the Natural History of the Varia- tio7is in the Meaning of Terms. §1. How circumstances originally accidental become incorporated into the meaning of words 480 2. — and sometimes become the whole mean- ing 481 3. Tendency of words to become generalized. 482 4. — and to become specialized 485 Chapter VI. The Principles of Philosophical Lan- guage farther considered. §1. Second requisite of philosophical language, a name for every important meaning 487 2. — viz., first, an accurate descriptive ter- minology 487 3. — secondly, a name for each of the more important results of scientific abstrac- tion 490 4. — thirdly, a nomenclature, or system of the names of Kinds 491 5. Peculiar nature of the connotation of names which belong to a nomenclature.. 493 I'AOK 5 0. In what cases language may, and may not, ha used mechanically 494 CuAi'TER VII. Of Classification, as Subsidiary to Induction. §1. Classification as here treated of, wherein difl'erent from the clasaificati(jn imjjlied in naming 497 2. Theory of natural groups 498 3. Are natural groups given by type, or by definition ? .501 4. Kinds are natural groups 502 5. How the names of Kinds should be con- structed 505 Chapter VIII. Of Classification by Series. §1. Natural groups should be arranged in a natural series 507 2. The arrangement should follow the de- grees of the main phenomenon 508 3. — which implies the assumption of a type species 509 4. How the divisions of the series should be determined 510 5. Zoology affords the completest type of sci- entific classification 511 BOOK V. ON FALLACIES. Cuapter I. Of Fallacies i7i General. §1. Theory of fixllacies a necessary part of logic 512 2. Casual mistakes are not fallacies 513 3. The moral sources of erroneous opinion, how related to the intellectual 513 Chapter II. Classification of Fallacies. §1. On what criteria a classification of fallacies should be grounded 515 2. The five classes of fallacies 516 3. The reference of a fallacy to one or an- other class is sometimes arbitrary 518 Chapter III. Fallacies of Simple Inspection, or A Priori Fallacies. § 1. Character of this class of fallacies 520 2. Natural prejudice of mistaking subjective laws for objective, exemplified in popular superstitions 521 3. — that things which we think of together must exist together, and that what is in- conceivable must be false 523 4. — of ascribing objective existence to ab- abstractions 52T 5. Fallacy of the Sufficient Eeason 528 6. Natural prejudice, that the difterences in nature correspond to the distinctions in language 529 7. Prejudice, that a phenomenon can not have more than one cause 532 8. — that the conditions of a phenomenon must resemble the phenomenon 533 Chapter IV. Fallacies of Observation. 51. Non-observation, and Mal-observation . 538 XIV CONTENTS, PAGK §2. Non - observation of instances, and non- observation of circumstances 53S 3. Examples of the former 539 4. — and of the latter 542 5. Mal-observation characterized and exem- plified 545 Chaptee V. Fallacies of Generalization. § 1, Character of the class 547 2. Certain kinds of generalization must al- ways be groundless 547 3. Attempts to resolve phenomena radically- different into the same 548 4. Fallacy of mistaking empirical for casual laws 549 5. Post hoc, ergo propter hoc; and the deduct- ive fallacy corresponding to it 551 6. Fallacy of False Analogies 553 7. Function of metaphors in reasoning 557 8. How fallacies of generalization grow out of bad classification 558 Chapter VI. Fallacies of Ratiocination. § 1. Introductory Remarks 559 2. Fallacies in the conversion and jequipol- lency of propositions 559 8. — in the syllogistic process 560 4. Fallacy of changing the premises 561 Chapter VII. Fallacies of Confusion. § 1. Fallacy of Ambiguous Terms 563 2. — of Petitio Priucipii 570 3. — of Ignoratio Elenchi 576 BOOK VI. ON THE LOGIC OF THE MORAL SCI- ENCES. Chapter I. Introductory Remarks. §1, The backward state of the Moral Sciences can only be remedied by applying to them the methods of Physical Science, duly ex- tended and generalized 579 2. How far this can be attempted in the pres- ent work .580 Chapter II. Of Liberty and Necessity. i 1. Are human actions subject to the law of causality ? 581 2. The doctrine commonly called Philosoph- ical Necessity, in what sense true 5S1 I 3. Inappropriatcness and pernicious efl'ect of the term Necessity 583 4. A motive not always the anticipation of a pleasure or a pain. 585 Chapter III. That there is, or may be, a Science of Human Nattire. 5 1. There may be sciences which are not exact sciences 58C 2. To what scientific type the Science of Hu- man Nature corresponds 588 Cuapteb IV. Of the Laws of Mind. 5 1. What is meant by Laws of Mind 589 2. Is there a Science of Psychology ? 590 page §3. The principal investigations of Psychology characterized 591 4. Relation of mental facts to physical con- ditions ■. 594 Chapter V. Of Ethology, or the Science of the For- mation of Character. § 1. The Empirical Laws of Human Nature 596 2. — are merely approximate generalizations. The universal laws are those of the for- mation of character 597 3. The laws of the formation of character can not be ascertained by observation and experiment 599 4. — but must be studied deductively 601 5. The principles of Ethology are the axio- mata media of mental science 603 6. Ethology characterized 604 Chapter VT. General Considerations on the Social Science. § 1. Are Social Phenomena a subject of Sci- ence ? 606 2. Of what nature the Social Science must be 607 Chapter VII. Of the Chemical or Experimental Method in the Social Science. § 1. Characters of the mode of thinking which deduces political doctrines from specific experience 608 2. In the Social Science experiments are im- possible 610 3. — the Method of Difference inapplicable. . 610 4. — and the Methods of Agreement, and of Concomitant Variations, inconclusive 611 5. The Method of Residues also inconclusive, and presupposes Deduction 612 Chapter VIII. Of the Geometrical, or Abstract Method. § 1. Characters of this mode of thinking 614 2. Examples of the Geometrical Method 615 3. The interest-philosophy of the Bentham school 616 Chapter IX. Of the Physical, or Concrete Deductive Method. § 1. The Direct and Inverse Deductive Meth- ods 619 2. Difficulties of the Direct Deductive Meth- od in the Social Science 621 3. To what extent the difierent branches of sociological speculation can be studied apart. Political Economy characterized. 623 4. Political Ethology, or the science of nation- al character 626 5. The Empirical Laws of the Social Sci- ence 628 6. The Verification of the Social Science 629 Chapter X. Of the Inverse Deductive, or Historical Method. § 1. Distinction between the general Science of Society, and special sociological inquiries. 630 2. What is meant by a State of Society? 631 3. The Progressiveness of Man and Society.. 631 4. The laws of the succession of states of so- ciety can only be ascertained by the In- verse Deductive Method 633 CONTENTS. XV V\(i K §5. Social Static?, or the science of the Co-cx- istcncea of Social Phononicnu u;}5 G. Social Dynamics, or the science of the Suc- cessions of Social Phenomena 039 7. Outlines of the Historical Method G40 S. Future j)rospects of Sociological Inquiry.. 642 CuAPTER XI. Additional Elucidations of the Sci- ence of History. §1. The subjection of historical facts to uni- form laws is verified by statistics G44 2. — does not imply the insignificance of moral causes 646 3. — nor the ineflScacy of the characters of individuals and of the acts of govern- ments 047 4. The historical importance of eminent men I'AOK and of the policy of goveriimentH illuH- trated : Or^O Chatter XII. 0/ the Logic of Practice, or A rt ; in- chulimj Morality and Policy. § 1. Morality not a Science, but an Art 052 2. IteUitiou between rules of art and the the- orems of the corresponding science or/-} 3. What is the proper function of rules of art ? G54 4. Art can not be deductive 655 5. Every Art consists of truths of Science, ar- ranged in the order suitable for some prac- tical use 655 0. Teleology, or the Doctrine of Ends G5G 7. Necessity of an ultimate standard, or first principle of Teleology 65T 8. Conclusion 659 ^^^ INTRODUCTION. § 1. There is as great diversity among authors in the modes which they have adopted of defining logic, as in their treatment of the details of it. This is what might naturally be expected on any subject on which writers have availed themselves of the same language as a means of delivering different ideas. Ethics and jurisprudence are liable to the remark in com- mon with logic. Almost every w^riter having taken a different view of some of the particulars which these branches of knowledge are usually understood to include; each has so framed his definition as to indicate beforehand his own peculiar tenets, and sometimes to beg the question in their favor. This diversity is not so much an evil to be complained of, as an inevita- ble and in some degree a proper result of the imperfect state of those sciences. It is not to be expected that there should be agreement about the definition of any thing, until there is agreement about the thing itself. To define, is to select from among all the properties of a thing, those which shall be understood to be designated and declared by its name ; and the properties must be well known to us before we can be competent to deter- mine which of them are fittest to be chosen for this purpose. According- ly, in the case of so complex an aggregation of particulars as are compre- hended in any thing which can be called a science, the definition we set out with is seldom that w^hich a more extensive knowledge of the subject shows to be the most appropriate. Until we know the particulars them- selves, we can not fix upon the most correct and compact mode of circum- scribing them by a general description. It was not until after an extensive and accurate acquaintance with the details of chemical phenomena, that it was found possible to frame a rational definition of chemistry; and the definition of the science of life and organization is still a matter of dispute. So long as the sciences are imperfect, the definitions must partake of their imperfection ; and if the former are progressive, the latter ought to be so too. As much, therefore, as is to be expected from a definition placed at the commencement of a subject, is that it should define the scope of our inquiries : and the definition which I am about to offer of the science of logic, pretends to nothing more than to be a statement of the question which I have put to myself, and which this book is an attempt to resolve. The reader is at liberty to object to it as a definition of logic; but it is at all events a correct definition of the subject of this volume. § 2. Logic has often been called the Art of Reasoning. A writer* who has done more than any other person to restore this study to the rank from which it had fallen in the estimation of the cultivated class in our own country, has adopted the above definition with an amendment ; he has de- Archbishop Whatelj. 2 18 INTRODUCTION. fined Logic to be the Science, as well as the Art, of reasoning; meaning by the former term, the analysis of th'fe mental process which takes place whenever we reason, and by the latter, the rules, grounded on that analy- sis, for conducting the process correctly. There can be no doubt as to the propriety of the emendation. A right understanding of the mental j^rocess itself, of the conditions it depends on, and the steps of which it consists, is the only basis on which a system of rules, fitted for the direction of the process, can possibly be founded. Art necessarily presupposes knowledge ; art, in any but its infant state, presupposes scientific knowledge : and if ev- ery art does not bear the name of a science, it is only because several sci- ences are often necessary to form the groundwork of a single art. So com- plicated are the conditions which govern our practical agency, that to ena- ble one thing to be done, it is often requisite to k7ioio the nature and prop- erties of many things. Logic, then, comprises the science of reasoning, as well as an art, found- ed on that science. But the word Reasoning, again, like most other scien- tific terms in popular use, abounds in ambiguities. In one of its accepta- tions, it means syllogizing ; or the mode of inference which may be called (with sufficient accuracy for the present purpose) concluding from generals to particulars. In another of its senses, to reason is simply to infer any assertion, from assertions already admitted : and in this sense induction is as much entitled to be called reasoning as the demonstrations of geometry. Writers on logic have generally preferred the former acceptation of the term : the latter, and more extensive signification is that in which I mean to use it. I do this by virtue of the right I claim for every author, to give whatever provisional definition he pleases of his own subject. But suffi- cient reasons will, I believe, unfold themselves as we advance, why this should be not only the provisional but the final definition. It involves, at all events, no arbitrary change in the meaning of the word ; for, with the general usage of the English language, the wider signification, I believe, accords better than the more restricted one. § 3. But reasoning, even in the widest sense of which the word is sus- ceptible, does not seem to comprehend all that is included, either in the best, or even in the most current, conception of the scope and province of our science. The employment of the word Logic to denote the theory of Argumentation, is derived from the Aristotelian, or, as. they are commonly termed, the scholastic, logicians. Yet even with them, in their systematic treatises. Argumentation was the subject only of the third part: the two former treated of Terms, and of Propositions ; under one or other of which heads were also included Definition and Division. By some, indeed, these previous topics were professedly introduced only on account of their con- nection with reasoning, and as a preparation for the doctrine and rules of the syllogism. Yet they were treated with greater minuteness, and dwelt on at greater length, than was i-equired for that purpose alone. More re- cent writers on logic have generally understood the term as it was employ- ed by the able author of the Port Royal Logic ; viz., as equivalent to the Art of Thinking. Nor is this acceptation confined to books, and scientific inquiries. Even in ordinary conversation, the ideas connected with the word Logic include at least precision of language, and accuracy of classifi- cation : and we perhaps oftener hear jiersons speak of a logical arrange- ment, or of exi)ressions logically defined, than of conclusions logically de- duced from premises. Again, a man is often called a great logician, or a DEFINITION ANi; J'UOVINCJK OF J.OGIC. 10 man of powerful logic, not for the accuracy of his deductions, but for the extent of his command over premises ; because the general propositions required for explaining a difficulty or refuting a sophism, copiously and promptly occur to him : because, in shoi't, his knowledge, besides being ample, is well under his command for argumentative use. Whether, there- fore, we conform to the practice of those who have made the subject their particular study, or to that of popular writers and common discourse, the province of logic will include several operations of the intellect not usually considered to fall within the meaning of the terms Reasoning and Argu- mentation. These various operations might be brought within the compass of the science, and the additional advantage be obtained of a very simple defini- tion, if, by an extension of the terra, sanctioned by high authorities, we were to define logic as the science which treats of the operations of the hu- man understanding in the pursuit of truth. For to this ultimate end, nam- ing, classification, definition, and all other operations over which logic has ever claimed jurisdiction, are essentially subsidiary. They may all be re- garded as contrivances for enabling a person to know the truths which are needful to him, and to know them at the precise moment at which they are needful. Other purposes, indeed, are also served by these operations ; for instance, that of imparting our knowledge to others. But, viewed with re- gard to this purpose, they have never been considered as within the prov- ince of the logician. The sole object of Logic is the guidance of one's own thoughts : the communication of those thoughts to others falls under the consideration of Rhetoric, in the large sense in which that art was con- ceived by the ancients ; or of the still more extensive art of Education. Logic takes cognizance of our intellectual operations only as they conduce to our own knowledge, and to our command over that knowledge for our own uses. If there were but one rational being in the universe, that being might be a perfect logician ; and the science and art of logic would be the same for that one person as for the whole human race. § 4. But, if the definition which we formerly examined included too lit- tle, that which is now suggested has the opposite fault of including too much. Truths are known to us in two ways : some are known directly, and of themselves; some through the medium of other truths. The former are the subject of Intuition, or Consciousness ;'^ the latter, of Inference. The truths known by intuition are the original premises from which all others are inferred. Our assent to the conclusion being grounded on the truth of the premises, we never could arrive at any knowledge by reasoning, unless something could be known antecedently to all reasoning. Examples of truths known to us by immediate consciousness, are our own bodily sensations and mental feelings. I know directly, and of my own knowledge, that I was vexed yesterday, or that I am hungry to-day. Examples of truths which we know only by way of inference, are occur- rences which took place while we were absent, the events recorded in his- tory, or the theorems of mathematics. The two former Ave infer from the testimony adduced, or from the traces of those past occurrences which still * I use these terms indiscriminately, because, for the purpose in view, there is no need for making any distinction between them. But metaphysicians usually restrict the name Intui- tion to the direct knowledge we are supposed to have of tilings external to our minds, and Consciousness to our knowledge of our own mental phenomena. 20 INTRODUCTION. exist ; the latter, from the premises laid down in books of geometry, under the title of definitions and axioms. Whatever we are capable of knowing must belong to the one class or to the other ; must be in the number of the primitive data, or of the conclusions which can be drawn from these. With the original data, or ultimate premises of our knowledge; with their number or nature, the mode in which they are obtained, or the tests by which they may be distinguished ; logic, in a direct way at least, has, in the sense in which I conceive the science, nothing to do. These ques- tions are partly not a subject of science at all, partly that of a very differ- ent science. Whatever is known to us by consciousness is known beyond possibility of question. What one sees or feels, whether bodily or mentally, one can not but be sure that one sees or feels. No science is required for the pur- pose of establishing such truths ; no rules of art can render our knowledge of them more certain than it is in itself. There is no logic for this portion of our knowledge. But we may fancy that we see or feel what we in reality infer. A truth, or supposed truth, which is really the result of a very rapid inference, may seem to be apprehended intuitively. It has long been agreed by thinkers of the most opposite schools, that this mistake is actually made in so familiar an instance as that of the eyesight. There is nothing of which we appear to ourselves to be more directly conscious than the distance of an object from us. Yet it has long been ascertained, that what is perceived by the eye, is at most nothing more than a variously colored surface ; that when we fancy we see distance, all we really see is certain variations of apparent size, and degrees of faintness of color; that our estimate of the object's distance from us is the result partly of a rapid inference from the muscular sensations accompanying the adjustment of the focal distance of the eye to objects unequally remote from us, and partly of a comparison (made with so much rapidity that we are unconscious of making it) between the size and color of the object as they appear at the time, and the size and color of the same or of similar objects as they appeared when close at hand, or when their degree of remoteness was known by other evidence. The per- ception of distance by the eye, which seems so like intuition, is thus, in re- ality, an inference grounded on experience ; an inference, too, which we learn to make ; and which we make with more and more correctness as our experience increases ; though in familiar cases it takes place so rapidly as to appear exactly on a par with those perceptions of sight which are really intuitive, our perceptions of color.* Of the science, therefore, which expounds the operations of the human understanding in the pursuit of truth, one essential part is the inquiry : What are the facts which are the objects of intuition or consciousness, and what arc those which we merely infer ? But this inquiry has never been considered a portion of logic. Its place is in another and a perfectly dis- tinct department of science, to which the name metaphysics more particu- larly belongs : that portion of mental philosophy which attempts to deter- mine what part of the furniture of the mind belongs to it originally, and * This important theory has of late been called in question by a writer of deserved reputa- tion, Mr. Samuel Bailey; but I do not conceive that the grounds on which it has been ad- mitted as an established doctrine for a century past, have been at all shaken by that gentle- man's objections. 1 have elsewhere said what ajjpeared to me necessary in reply to his argu- ments. (Westminster Revieiv for October. 1842; reprinted in "Dissertations and Discus- sions," vol. ii.) DEFINITION AND PJIOVINCE OF LOGIC. 21 Avhat part is constructed out of materials furnislicd to it from without. To this science appertain the great and much debated questions of the exist- ence of matter; the existence of spirit, and of a distinction between it and matter ; the reaUty of time and space, as things without the mind, and distinguishable from the objects which are said to exist in them. For in the present state of the discussion on tliese topics, it is ahnost uni- versally allowed that the existence of matter or of spirit, of space or of time, is in its nature unsusceptible of being proved ; and that if any thing is known of them, it must be by immediate intuition. To the same science belong the inquiries into the nature of Conception, Perception, Memory, and Belief ; all of which are operations of the understanding in the pursuit of truth ; but with which, as phenomena of the mind, or with the possibili- ty which may or may not exist of analyzing any of them into simpler phe- nomena, the logician as such has no concern. To this science must also be referred the following, and all analogous questions : To what extent our in- tellectual faculties and our emotions are innate — to what extent the result of association : Whether God and duty are realities, the existence of which is manifest to us a priori by the constitution of our rational faculty ; or whether our ideas of them are acquired notions, the origin of which we are able to trace and explain ; and the reality of the objects themselves a question not of consciousness or intuition, but of evidence and reasoning. The province of logic must be restricted to that portion of our knowl- edge which consists of inferences from truths previously known ; whether those antecedent data be general propositions, or particular observations and perceptions. Logic is not the science of Belief, but the science of Proof, or Evidence. In so far as belief professes to be founded on proof, the office of logic is to supply a test for ascertaining whether or not the be- lief is well grounded. With the claims which any proposition has to be- lief on the evidence of consciousness — that is, without evidence in the proper sense of the word — logic has nothing to do. § 5. By far the greatest portion of our knowledge, whether of general truths or of particular facts, being avowedly matter of inference, nearly the whole, not only of science, but of human conduct, is amenable to the au- thority of logic. To draw inferences has been said to be the great business of life. Every one has daily, hourly, and momentary need of ascertaining facts which he has not directly observed ; not from any general purpose of adding to his stock of knowledge, but because the facts themselves are of importance to his interests or to his occupations. The business of the magistrate, of the military commander, of the navigator, of the physician, of the agriculturist, is merely to judge of evidence, and to act accordingly. They all have to ascertain certain facts, in order that they may afterward apply certain rules, either devised by themselves or prescribed for their guidance by others ; and as they do this well or ill, so they discharge well or ill the duties of their several callings. It is the only occupation in which the mind never ceases to be engaged; and is the subject, not of logic, but of knowledge in general. Logic, however, is not the same thing with knowledge, though the field of logic is co-extensive with the field of knowledge. Logic is the com- mon judge and arbiter of all particular investigations. It does not under- take to find evidence, but to determine whether it has been found. Logic neither observes, nor invents, nor discovers; but judges. It is no part of the business of logic to inform the surgeon what appearances are found to 22 INTRODUCTION. accompany a violent death. This he must learn from his own experience and observation, or from that of others, his predecessors in his peculiar pursuit. But logic sits in judgment on the sufficiency of that observation and experience to justify his rules, and on the sufficiency of his rules to justify his conduct. It does not give him proofs, but teaches him what makes them proofs, and how he is to judge of them. It does not teach that any particular fact proves any other, but points out to what conditions all facts must conform, in order that they may prove other facts. To de- cide whether any given fact fulffils these conditions, or whether facts can be found which fulfill them in a given case, belongs exclusively to the par- ticular art or science, or to our knowledge of the particular subject. It is in this sense that logic is, what it was so expressively called by the schoolmen and by Bacon, ars artium; the science of science itself. All science consists of data and conclusions from those data, of proofs and what they prove : now logic points out what relations must subsist between data and whatever can be concluded from them, between proof and every thing which it can prove. If there be any such indispensable relations, and if these can be precisely determined, every particular branch of science, as well as every individual in the guidance of his conduct, is bound to con- form to those relations, under the penalty of making false inferences — of drawing conclusions which are not grounded in the realities of things. Whatever has at any time been concluded justly, whatever knowledge has been acquired otherwise than by immediate intuition, depended on the ob- servance of the laws which it is the province of logic to investigate. If the conclusions are just, and the knowledge real, those laws, whether known or not, have been observed. § 6. We need not, therefore, seek any further for a solution of the ques- tion, so often agitated, respecting the utility of logic. If a science of logic exists, or is capable of existing, it must be useful. If there be rules to which every mind consciously or unconsciously conforms in every instance in which it infers rightly, there seems little necessity for discussing whether a person is more likely to observe those rules, when he knows the rules, than when he is unacquainted with them. A science may undoubtedly be brought to a certain, not inconsiderable, stage of advancement, without the application of any other logic to it than what all persons, who are said to have a sound understanding, acquire em- pirically in the course of their studies. Mankind judged of evidence, and often correctly, before logic was a science, or they never could have made it one. And they executed great mechanical works before they understood the laws of mechanics. But there are limits both to what mechanicians can do without principles of mechanics, and to what thinkers can do without principles of logic. A few individuals, by extraordinary genius, or by the accidental acquisition of a good set of intellectual habits, may work with- out principles in the same way, or nearly the same way, in which they would have worked if they had been in possession of principles. But the bulk of mankind require either to understand the theory of what they are doing, or to have rules laid down for them by those who have understood the tluiory. In the progress of science from its easiest to its more difficult problems, each great step in advance has usually had either as its precur- sor, or as its accompaniment and necessary condition, a corresponding im- provement in the notions and principles of logic received among the most advanced thinkers. And if several of the more difficult sciences are still DEFINITION AND I'UOVINCE OF J.O(;iO. 23 in so defective a stfite ; if not only so little is proved, but disputation has not terminated even about the little which seemed to be so; the reason perhaps is, that men's logical notions have not yet acquired tlie degree of extension, or of accuracy, requisite for the estimation of the evidence prop- er to those particular de2)artments of knowledge. § 7. Logic, then, is the science of the operations of the understanding which are subservient to the estimation of evidence : both the process it- self of advancing from known truths to unknown, and all other intellectual operations in so far as auxiliary to this. It includes, therefore, the 0|)era- tion of Naming ; for language is an instrument of tliought, as well as a means of communicating our thoughts. It includes, also, Definition, and Classification. For, the use of these operations (putting all other minds than one's own out of consideration) is to serve not only for keeping our evidences and the conclusions from them permanent and readily accessible in the memory, but for so marshaling the facts which w^e may at any time be engaged in investigating, as to enable us to perceive more clearly what evidence there is, and to judge with fewer chances of error whether it be sufl&cient. These, therefore, are operations specially instrumental to the estimation of evidence, and, as such, are within the province of Logic. There are other more elementary processes, concerned in all thinking, such as Conception, Memory, and the like ; but of these it is not necessary that Logic should take any peculiar cognizance, since they have no special connection with the problem of Evidence, further than that, like all other problems addressed to the understanding, it presupposes them. Our object, then, will be, to attempt a correct analysis of the intellectual process called Reasoning or Inference, and of such other mental operations as are intended to facilitate this : as w^ell as, on the foundation of this anal- | ysis, and pari passu with it, to bring together or frame a set of rules or canons for testing the sufiiciency of any given evidence to prove any given proposition.. With respect to the first part of this undertaking, I do not attempt to decompose the mental operations in question into their ultimate elements. It is enough if the analysis as far as it goes is correct, and if it goes far enough for the practical purposes of logic considered as an art. The sep- aration of a complicated phenomenon into its component parts is not like a connected and interdependent chain of proof. If one link of an argu- ment breaks, the whole drops to the ground ; but one step toward an anal- ysis holds good and has an independent value, though wx should never be able to make a second. The results which have been obtained by analytical chemistry are not the less valuable, though it should be discovered that all wdiich w^e now call simple substances are really compounds. All other things are at any rate compounded of those elements : w^hether the ele- ments themselves admit of decomposition, is an important inquiry, but does not affect the certainty of the science up to that point. I shall, accordingly, attempt to analyze the process of inference, and the processes subordinate to inference, so far only as may be requisite for as- certaining the difference between a correct and an incorrect performance of those processes. The reason for thus limiting our design, is evident. It has been said by objectors to logic, that we do not learn to use our muscles by studying their anatomy. The fact is not quite fairly stated; for if the action of any of our muscles were vitiated by local weakness, or other physical defect, a knowledge of their anatomy might be very neces- 24 INTEODUCTION. savy for effecting a cure. But we should be justly liable to the criticism involved in this objection, were we, in a treatise on logic, to carry the anal- ysis of the reasoning process beyond the point at which any inaccuracy which may have crept into it must become visible. In learning bodily exercises (to carry on the same illustration) we do, and must, analyze the bodily motions so far as is necessary for distinguishing those which ought to be performed from those which ought not. To a similar extent, and no further, it is necessary that the logician should analyze the mental processes with which Logic is concerned. Logic has no interest in carrying the anal- ysis beyond the point at which it becomes apparent whether the operations have in any individual case been rightly or wrongly performed : in the same manner as the science of music teaches us to discriminate between musical notes, and to know the combinations of which they are susceptible, but not what number of vibrations in a second correspond to each ; which, though useful to be known, is useful for totally different purposes. The extension of Logic as a Science is determined by its necessities as an Art : whatever it does not need for its practical ends, it leaves to the larger science which may be said to correspond, not to any particular art, but to art in general ; the science which deals with the constitution of the human faculties ; and to which, in the part of our mental nature which concerns Logic, as well as in all other parts, it belongs to decide what are ultimate facts, and what are resolvable into other facts. And I believe it will be found that most of the conclusions arrived at in this work have no neces- sary connection with any particular views respecting the ulterior analysis. Logic is common ground on which the partisans of Hartley and of Reid, of Locke and of Kant, may meet and join hands. Particular and detached opinions of all these thinkers will no doubt occasionally be controverted, since all of them were logicians as well as metaphysicians ; but the field on which their principal battles have been fought, lies beyond the boundaries of our science. It can not, indeed, be pretended that logical principles can be altogether irrelevant to those more abstruse discussions ; nor is it possible but that the view we are led to take of the problem which logic proposes, must have a tendency favorable to the adoption of some one opinion, on these controverted subjects, rather than another. For metaphysics, in endeavor- ing to solve its own peculiar problem, must employ means, the validity of which falls under the cognizance of logic. It proceeds, no doubt, as far as possible, merely by a closer and more attentive interrogation of our con- sciousness, or more properly speaking, of our memory; and so far is not amenable to logic. But wherever this method is insufficient to attain the end of its inquiries, it must proceed, like other sciences, by means of evi- dence. Now, the moment this science begins to draw inferences from evi- dence, logic becomes the sovereign judge whether its inferences are well grounded, or what other inferences would be so. This, however, constitutes no nearer or other relation between logic and metaphysics, than that which exists between logic and every other science. And I can conscientiously affirm that no one proposition laid down in this work has been adopted for the sake of establishing, or with any reference to its fitness for being employed in establishing, preconceived opinions in any department of knowledge or of inquiry on which the speculative world is still undecided.* * Tlic view taken in the text, of the definition and purpose of Logic, stands in marked op- position to tliut of the school of philosophy whicli, in this country, is represented by the writ- DEFINITION AND PROVINCE OF LOGIC. 25 ings of Sir William Hamilton and of his numerous pupils. Logic, as this sfliool conceives it, is "the Science of the Formal J^aws of Tliought;" a definition framed for the express pur- pose of excluding, as irrelevant to Logic, whatever relates to Helief and Disbelief, or to the pursuit of truth as such, and restricting the science to that very limited portion of its total province, which has reference to tiie conditions, not of Truth, hut of Consistency, What I have thouglit it useful to say in op])osition to this limitation of the field of Logic, has heen said at some length in a separate work, first published in IHCi;"), and entitled "An Examina- tion of Sir William Hamilton's Philosophy, and of tlie Princii)al l'hiloso))hical Questions dis- cussed in his Writings," For the pur])oses of the present Treatise, I am content that the jus- tification of the larger extension which I give to the domain of the science, should rest on the sequel of the Treatise itself. Some remarks on the relation which the Logic of Consistency bears to the Logic of Truth, and on the place which that particular part occupies in the whole to which it belongs, will be found in the present volume (Book IL, chap, iii,, § 9). BOOK I. OF NAMES AND PROPOSITIONS. "La scolastique, qui produisit dans la logique, comme dans la morale, et dans une partie de la metaphysique, une subtilite, une pre'cision d'idees, dont Fhabitude inconnue aux anciens, a contribue plus qu'on ne croit au progves de la bonne philosophic." — Condokcet, Vie de Turgot. "To the schoolmen the vulgar languages are principally indebted for what precision and analytic subtlety they possess." — Sir W. Hamilton, Discussions in Philosophy. CHAPTER I. OF THE NECESSITY OP COMMENCING WITH AN ANALYSIS OF LANGUAGE. § 1. It is so much the established practice of writers on logic to com- mence their treatises by a few general observations (in most cases, it is true, rather meagre) on Terms and their varieties, that it will, perhaps, scarcely be required from me, in merely following the common usage, to be as particular in assigning my reasons, as it is usually expected that those should be who deviate from it. The practice, indeed, is recommended by considerations far too obvious to require a formal justification. Logic is a portion of the Art of Think- ing : Language is evidently, and by the admission of all philosophers, one of the principal instruments or helps of thought; and any imperfection in the instrument, or in the mode of employing it, is confessedly liable, still more than in almost any other art, to confuse and impede the process, and destroy all ground of confidence in the result. For a mind not previously versed in the meaning and right use of the various kinds of words, to at- tempt the study of methods of philosophizing, would be as if some one should attempt to become an astronomical observer, having never learned to adjust the focal distance of his optical instruments so as to see distinctly. Since Reasoning, or Inference, the principal subject of logic, is an opera- tion which usually takes place by means of words, and in complicated cases can take place in no other way ; those who have not a thorough insight into the signification and purposes of words, will be under chances, amount- ing almost to certainty, of reasoning or inferring incorrectly. And logi- cians have generally felt that unless, in the very first stage, they removed this source of error; unless they taught their pupil to put away the glasses which distort the object, and to use those which are adapted to his pur- pose in such a manner as to assist, not perplex, his vision ; he would not be in a condition to practice the remaining part of their disciphne with any prospect of advantage. Therefore it is that an inquiry into language, so far as is needful to guard against the errors to which it gives rise, has at all times been deemed a necessary preliminary to the study of logic. NECESSITY OF AN ANALYSIS OF NAMES. 27 But there is another reason, of a still more funduinental nature, why tlie import of words should be the earliest subject of the logician's considera- tion: because without it lie can not examine into the import of ]*roposi- tions. Now this is a subject which stands on the very threshold of the science of logic. The object of logic, as defined in the Introductory Chapter, is to ascer- tain how we come by that portion of our knowledge (much the greatest portion) which is not intuitive : and by what criterion we can, in matters not self-evident, distinguish between things proved and things not proved, between what is worthy and wliat is unworthy of belief. Of the various questions which present themselves to our inquiring faculties, some receive an answer from direct consciousness, others, if resolved at all, can only be resolved by means of evidence. Logic is concerned with these last. But before inquiring into the mode of resolving questions, it is necessary to in- quire what are those which offer themselves ; what questions are conceiva- ble ; what inquiries are there, to which mankind have either obtained, or been able to imagine it possible that they should obtain, an answer. This point is best ascertained by a survey and analysis of Propositions. § 2. The answer to every question which it is possible to frame, must be contained in a Pi'oposition, or Assertion. Whatever can be an object of belief, or even of disbelief, must, when put into words, assume the form of a proposition. All truth and all error lie in propositions. What, by a convenient misapplication of an abstract term, we call a Truth, means simply a True Proposition ; and errors are false propositions. To know the import of all possiljle propositions would be to know all questions which can be raised, all matters which are susceptible of being either be- lieved or disbelieved. How many kinds of inquiries can be propound- ed; how many kinds of judgments can be made; and how many kinds of propositions it is possible to frame with a meaning, are but different forms of one and the same question. Since, then, the objects of all Be- lief and of all Inquiry express themselves in propositions, a sufficient scru- tiny of Propositions and of their varieties will apprise us what questions mankind have actually asked of themselves, and what, in the nature of an- swers to those questions, they have actually thought they had grounds to believe. Now the first glance at a proposition shows that it is formed by putting- together two names. A proposition, according to the common simple defi- nition, which is sufficient for our purpose is, discourse, in lohich something is affirmed or denied of so^nething. Thus, in the proposition. Gold is yel- low, the quality yellow is affirmed of the substance gold. In the proposi- tion, Franklin was not born in England, the fact expressed by the words horn in JEnglcmd is denied of the man Franklin. Every proposition consists of three parts : the Subject, the Predicate, and the Copula. The predicate is the name denoting that which is affirmed or denied. The subject is the name denoting the person or thing which something is affirmed or denied ^of. The copula is the sign denoting that there is an affirmation or denial,* and thereby enabling the hearer or reader to distinguish a proposition from any other kind of discourse. Thus, in the proposition. The earth is round, the Predicate is the word ro?^;?ost, for examj)le, or the word box, the various senses of which it would be endless to enumerate. And the paucity of ex- isting names, in comparison with the demand for them, may often render it advisable and even necessary to retain a name in this multiplicity of ac- ceptations, distinguishing tliese so clearly as to prevent their being con- founded with one another. Such a word may be considered as -two or more names, accidentally written and spoken alike."^' § C. The fourth principal division of names, is into 2^ositive and nega- tive. Positive, as mem, tree, good; negative, as 7iot-mcm, not-tree, not-good. To every positive concrete name, a corresponding negative one might be framed. After giving a name to any one thing, or to any plurality of things, we might create a second name which should be a name of all things whatever, except that particular thing or things. These negative names are employed whenever we have occasion to speak collectively of all things other than some thing or class of things. When the positive name is con- notative, the corresponding negative name is connotative likewise ; but in a * Before quitting the subject of connotative names, it is proper to observe, that the first writer -who, in our times, has adopted from the schoolmen the word to connote, Mr. James Mill, in his Analysis of the Phenomena of the Human Mind, employs it in a signification dif- ferent from that in which it is here used. He uses the word in a sense co-extensive with its etymology, applying it to every case in which a name, while pointing directly to one tiling (which is consequently termed its signification), includes also a tacit reference to some other thing. In the case considered in the text, that of concrete general names, his language and mine are the converse of one another. Considering (very justly) the signification of the name to lie in the attribute, he speaks of the word as noting the attribute, and connoting the things possessing the attribute. And he describes abstract names as being properly concrete names with their connotation dropped ; whereas, in my view, it is the (denotation which would be said to be dropped, what was previously connoted becoming the whole signification. In adopting a phraseology at variance with that which so high an authority, and one which I am less likely than any other person to undervalue, has deliberately sanctioned, I have been influenced by the urgent necessity for a term exclusively appropriated to express the manner in which a concrete general name serves to mark the attributes which are involved in its signi- fication. This necessity can scarcely be felt in its full force by any one who has not found by experience how vain is the attempt to communicate clear ideas on the philosophy of language \^ithout such a word. It is hardly an exaggeration to say, that some of the most prevalent of the errors with which logic has been infected, and a large part of the cloudiness and confusion of ideas which have enveloped it, would, in all probability, have been avoided, if a term had been in common use to express exactly what I have signified by the term to connote. And the schoolmen, to whom we are indebted for the greater part of our logical language, gave us this also, and in this very sense. For though some of their general expressions countenance the use of the word in the more extensive and vague acceptation in which it is taken by Mr. Mill, yet when they had to define it specifically as a technical tenn, and to fix its meaning as such, with that admirable precision which always characterizes their definitions, they clearly explained that nothing was said to be connoted except forms, which ■uord may generally, in their writings, be understood as synonymous with attribtites. Now, if the word to connote, so well suited to the purpose to which they applied it, be di- verted from that purpose by being taken to fulfill another, for which it does not seem to me to be at all required ; I am unable to find any expression to replace it, but such as are commonly employed in a sense so much more general, that it would be useless attempting to associate them peculiarly with this precise idea. Such are the words, to iuA'olve, to imply, etc. By employing these, I should fail of attaining the object for which alone the name is needed, namely, to distinguish this particular kind of involving and implying from all other kinds, and to assure to it the degree of habitual attention which its importance demands. 42 NAMES AND PEOPOSITIONS. peculiar way, connoting not the presence but the absence of an attribute. Thus, not-white denotes all things whatever except white things ; and con- notes the attribute of not possessing whiteness. For the non-possession of any given attribute is also an attribute, and may receive a name as such ; and thus negative concrete names may obtain negative abstract names to correspond to them."^ Names which are positive in form are often negative in reality, and oth- ers are really positive though their form is negative. The word inconven- ient^ for example, does not express the mere absence of convenience ; it ex- presses a positive attribute — that of being the cause of discomfort or an- noyance. So the word unpleasant^ notwithstanding its negative form, does not connote the mere absence of pleasantness, but a less degree of what is signified by the word painful, which, it is hardly necessary to say, is posi- tive. Idle, on the other hand, is a word which, though positive in form, expresses nothing but what would be signified either by the phrase oiot working, or by the phrase not disposed to loork; and sober, either by not drunk or by 7iot drunken. There is a class of names called privative. A privative name is equiva- lent in its signification to a positive and a negative name taken together; being the name of something which has once had a particular attribute, or for some other reason might have been expected to have it, but which has it not. Such is the word blind, which is not equivalent to 7iot seeing, or to not capable of seeing, for it would not, except by a poetical or rhetorical figure, be applied to stocks and stones. A thing is not usually said to be blind, unless the class to which it is most familiarly referred, or to which it is referred on the particular occasion, be chiefly composed of things which can see, as in the case of a blind man, or a blind horse ; or unless it is supposed for any reason that it ought to see ; as in saying of a man, that he rushed blindly into an abyss, or of philosophers or the clergy that the greater part of them, are blind guides. The names called privative, there- fore, connote two things ; the absence of certain attributes, and the pres- ence of others, from which the presence also of the former might naturally have been expected. § v. The fifth leading division of names is into relative and absolute, or let us rather say, relative and non-relative ; for the word absolute is put upon much too hard duty in metaphysics, not to be willingly spared when its services can be dispensed with. It resembles the word cvml in the lan- guage of jurisprudence, which stands for the opposite of criminal, the op- posite of ecclesiastical, the opposite of military, the opposite of political — in short, the opposite of any positive word which wants a negative. Relative names are such as father, son; ruler, subject; like; equal'; un- like ; unequal ; longer, shorter ; cause, effect. Their characteristic property is, that they are always given in pairs. Every relative name which is pred- icated of an object, supposes another object (or objects), of which we may predicate either that same name or another relative name which is said to be the correlative of the former. Thus, when we call any person a son, we * Professor Bain {Logic, i., 5G) thinks that negative names are not names of all things whatever except those denoted hy the correlative positive name, but only for all things of some particular class : not-white, for instance, he deems not to be a name for every thing in nature except white things, but only for every colored thing other than white. In this case, however, as in all others, the test of what a name denotes is what it can be predicated of: and we can certainly predicate of a sound, or a smell, that it is not white. The affirmation and the nega- tion of the same attribute can not but divide the whole field of predication between them. NAMES. 43 suppose otlier persons who must be call('erceive, the meaning of these words is, that receiving the sensations, I intuitively believe that an external cause of those sensations exists. The laws of intuitive belief, and the conditions under which it is legitimate, are a subject which, as we have already so often remarked, belongs not to logic, but to the science of the ultimate laws of the human mind. * Philosophy of the Inductive Sciences, vol. i., p. 40. THINGS DENOTED BY NAMES. 51 To the same region of speculation belongs all that can be said respecting the distinction which the Gei-nian metapliysicians and their Fi-ench and English followers so elaborately draw between the acts of the mind and its merely passive states; between what it receives from, and what it gives to, the crude materials of its experience. I am aware that with reference to the view which those WM'iters take of the primary elements of thought and knowledge, this distinction is fundamental. But for the present purpose, which is to examine, not the original groundwork of our knowledge, but how we come by that portion of it which is not original ; the difference ])e- tween active and passive states of mind is of secondary importance. P'or us, they all are states of mind, they all are feelings ; by which, let it be said once more, I mean to imply nothing of passivity, but simply that they are psychological facts, facts which take place in the mind, and' are to be carefully distinguished from the external or physical facts with which they may be connected either as effects or as causes. § 5. Among active states of mind, there is, however, one species which merits particular attention, because it forms a principal part of the conno- tation of some important classes of names. I mean volitions, or acts of the will. When we speak of sentient beings by relative names, a large portion of the connotation of the name usually consists of the actions of those beings; actions past, present, and possible or probable future. Take, for instance, the words Sovereign and Subject. What meaning do these words convey, but that of innumerable actions, done or to be done by the sovereign and the subjects, to or in regard to one another reciprocally? So with the words physician and patient, leader and follower, tutor and pupil. In many cases the w^ords also connote actions which would be done under certain contingencies by persons other than those denoted : as the words mortgagor and mortgagee, obligor and obligee, and many other words expressive of legal relation, which connote what a court of justice w^ould do to enforce the legal obligation if not fulfilled. There are also words which connote actions previously done by persons other than those denoted either by the name itself or by its correlative ; as the word brother. From these instances, it may be seen how large a portion of the connota- tion of names consists of actions. No\v what is an action ? ISTot one thing, but a series of two things : the state of mind called a volition, followed by an effect. The volition or intention to produce the effect, is one thing; the effect produced in consequence of the intention, is another thing ; the two together constitute the action. I form the j^urpose of instantly mov- ing my arm ; that is a state of my mind : my arm (not being tied or par- alytic) moves in obedience to my purpose ; that is a physical fact, conse- quent on a state of mind. The intention, followed by the fact, or (if we prefer the expression) the fact when preceded and caused by the intention, is called the action of moving my arm. § 6. Of the first leading division of namable things, viz., Feelings or States of Consciousness, we began by recognizing three subdivisions ; Sen- sations, Thoughts, and Emotions. The first two of these we have illustrated at considerable length ; the third. Emotions, not being perplexed by similar ambiguities, does not require similar exemplification. And, finally, we have found it necessary to add to these three a fourth species, commonly known by the name Volitions. We shall now proceed to the two remaining class- es of namable things : all thinss which are reo-arded as external to the 52 NAMES AND PKOPOSITIONS. mind being considered as belonging either to the class of Substances or to that of Attributes. II. Substances. Logicians have endeavored to define Substance and Attribute ; but their definitions are not so much attempts to draw a distinction between the things themselves, as instructions what difference it is customary to make in the grammatical structure of the sentence, according as we are speak- ing of substances or of attributes. Such definitions are rather lessons of English, or of Greek, Latin, or German, than of mental philosophy. An attribute, say the school logicians, must be the attribute of something; color, for example, must be the color of something; goodness must be the goodness of something; and if this something should cease to exist, or should cease to be connected with the attribute, the existence of the attri- bute would be at an end. A substance, on the contrary, is self-existent ; in speaking about it, we need not put of after its name. A stone is not the stone of any thing ; the moon is not the moon of any thing, but simply the moon. Unless, indeed, the name which we choose to give to the substance be a relative name ; if so, it must be followed either by o/, or by some other particle, implying, as that preposition does, a reference to something else: but then the other characteristic peculiarity of an attribute would fail ; the sometliing might be destroyed, and the substance might still sub- sist. Thus, a father must be the father 0/ something, and so far resembles an attribute, in being referred to something besides himself : if there were no child, there would be no father: but this, when we look into the matter, only means that we should not call him father. The man called father might still exist though there were no child, as he existed before there was a child ; and there would be no contradiction in supposing him to exist, though the whole universe except himself were destroyed. But destroy all white substances, and where would be the attribute whiteness? White- ness, without any Avhite thing, is a contradiction in terms. This is the nearest approach to a solution of the difficulty, that will be found in the common treatises on logic. It will scarcely be thought to be a satisfactory one. If an attribute is distinguished from a substance by being the attribute of something, it seems highly necessary to understand what is meant by of • a particle which needs explanation too much itself, to be placed in front of the explanation of any thing else. And as for the self-existence of substance, it is very true that a substance may be con- ceived to exist without any other substance, but so also may an attribute without any other attribute: and we can no more imagine a substance Avithout attributes than we can imagine attributes without a substance. Metaphysicians, however, have probed the question deeper, and given an account of Substance considerably more satisfactory than this. Substances are usually distinguished as Bodies or Minds. Of each of these, philoso- phers have at length provided us with a definition which seems unexcep- tionable. § 7. A body, according to the received doctrine of modern metaphysi- cians, may be defined, the external cause to which we ascribe our sensa- tions. When I see and touch a piece of gold, I am conscious of a sensa- tion of yellow color, and sensations of hardness and weight ; and by vary- ing the mode of handling, I may add to these sensations many others com- pletely distinct from them. The sensations are all of which I am directly THINGS DENOTED BY NAMES. 53 conscious; but I consider them as produced by sornetliing not only exist- ing independently of my will, but external to my bodily organs and to my mind. This external something I call a body. It may be asked, how come we to ascribe our sensations to any exter- nal cause? And is there sufficient ground for so ascribing tliem? It is known, that there are metaphysicians who have raised a controversy on the point; maintaining that we are not warranted in referring our sensa- tions to a cause such as we understand by the word Body, or to any ex- ternal cause whatever. Though we have no concern here with this con- troversy, nor with the metaphysical niceties on which it turns, one of the best ways of showing what is meant by Substance is, to consider wliat po- sition it is necessary to take up, in order to maintain its existence against opponents. It is certain, then, that a part of our notion of a body consists of the notion of a nuniber of sensations of our own, or of other sentient beings, habitually occurring simultaneously. My conception of the table at whicli I am writing is compounded of its visible form and size, which are com- plex sensations of sight; its tangible form and size, which are complex sensations of our organs of touch and of our muscles; its weight, which is also a sensation of touch and of the muscles ; its color, which is a sensa- tion of sight; its hardness, which is a sensation of the muscles; its com- position, which is another word for all the varieties of sensation which we receive under various circumstances from the wood of which it is made, and so forth. All or most of these various sensations frequently are, and, as w^e learn by experience, always might be, experienced simultaneously, oi" in many different orders of succession at our own choice : and hence the thought of any one of them makes us think of the others, and the whole becomes mentally amalgamated into one mixed state of consciousness, which, in the language of the school of Locke and Hartley, is termed a Complex Idea. Now, there are philosophers who have argued as follows : If we con- ceive an orange to be divested of its natural color without acquiring any new one ; to lose its softness without becoming hard, its roundness without becoming square or pentagonal, or of any other regular or irregular figure whatever ; to be deprived of size, of weight, of taste, of smell ; to lose all its mechanical and all its chemical properties, and acquire no new ones ; to become, in short, invisible, intangible, imperceptible not only by all our senses, but by the senses of all other sentient beings, real or possible; nothing, say these thinkers, would remain. For of what nature, they ask, could be the residuum? and by wdiat token could it manifest its presence? To the unreflecting its existence seems to rest on the evidence of the senses. But to the senses nothing is apparent except the sensations. We know, indeed, that these sensations are bound together by some law; they do not come together at random, but according to a systematic order, which is part of the order established in the universe. When we experience one of these sensations, we usually experience the others also, or know that we have it in our power to experience them. But a fixed law of connection, making the sensations occur together, does not, say these philosophers, necessarily require what is called a substratum to support them. The con- ception of a substratum is but one of many possible forms in which that connection presents itself to our imagination ; a mode of, as it were, real- izing the idea. If there be such a substratum, suppose it at this instant miraculously annihilated, and let the sensations continue to occur in the 54 NAMES AND PROPOSITIONS. same order, and how would the substratum be missed? By what signs should we be able to discover that its existence had terminated? Should we not have as much reason to believe that it still existed as we now have? And if we should not then be warranted in believing it, how can we be so now? A body, therefore, according to these metaphysicians, is not any thing intrinsically different from the sensations which the body is said to produce in us ; it is, in short, a set of sensations, or rather, of possibilities of sensation, joined together according to a fixed law. The controversies to which these speculations have given rise, and the doctrines which have been developed in the attempt to find a conclusive answer to them, have been fruitful of important consequences to the Science of Mind. The sensations (it was answered) which we are conscious of, and which we receive, not at random, but joined together in a certain uniform manner, imply not only a law or laws of connection, but a cause external to our mind, which cause, by its own laws, determines the laws according to which the sensations are connected and experienced. The schoolmen used to call this external cause by the name we have already employed, a sub- stratum; and its attributes (as they expressed themselves) inhered, literally stuck, in it. To this substratum the name Matter is usually given in phil- osophical discussions. It was soon, however, acknowledged by all who re- flected on the subject, that the existence of matter can not be proved by ex- trinsic evidence. The answer, therefore, now usually made to Berkeley and his followers, is, that the belief is intuitive; that mankind, in all ages, have felt themselves compelled, by a necessity of their nature, to refer their sen- sations to an external cause: that even those who deny it in theory, yield to the necessity in practice, and both in speech, thought, and feeling, do, equally with the vulgar, acknowledge their sensations to be the eifects of something external to them : this knowledge, therefore, it is aflarmed, is as evidently intuitive as our knowledge of our sensations themselves is intui- tive. And here the question merges in the fundamental problem of meta- physics properly so called : to which science we leave it. But although the extreme doctrine of the Idealist metaphysicians, that objects are nothing but our sensations and the laws which connect them, has not been generally adopted by subsequent thinkers ; the point of most real importance is one on which those metaphysicians are now very gen- erally considered to have made out their case : viz., that all we know of ob- jects is the sensations which they give us, and the order of the occurrence of those sensations. Kant himself, on this point, is as explicit as Berke- ley or Locke. However firmly convinced that there exists a universe of "Things in themselves," totally distinct from the universe of phenomena, or of things as they appear to our senses ; and even when bringing into use a technical expression {N'otimenon) to denote what the thing is in it- self, as contrasted with the representation of it in our minds ; he allows that this representation (the matter of which, he says, consists of our sen- sations, though the form is given by the laws of the mind itself) is all we know of the object: and that the real nature of the Thing is, and by the constitution of our faculties ever must remain, at least in the present state of existence, an impenetrable mystery to us. " Of things absolutely or in themselves," says Sir WiUiam Hamilton,* "be they external, be they in- ternal, we know nothing, or know them only as incognizable ; and become aware of their incomprehensible existence, only as this is indirectly and * Discussions on Philosophy^ etc. Appendix I., pp. Gto, G-tl. THINGS DKNOTKD P>Y NAMKS. 55 accidentally revealed to us, through certain (|ualities related to our faculties of knowledge, and which qualities, again, we can not think as uncontlition- al, irrelative, existent in and of ourselves. All that we know is therefore phenomenal — phenomenal of the unknown.''* The same doctrine is laid down in the clearest and strongest terms by M. Cousin, whose observations on the subject are the more worthy of attention, as, in consequence of the ultra-German and ontological character of his ])hilosophy in other respects, they may be regarded as the admissions of an opponent. f There is not the slightest reason for believing that what we call the sen- sible qualities of the object are a type of any thing inherent in itself, or bear any affinity to its own nature. A cause does not, as such, resemble its effects ; an east wind is not like the feeling of cold, nor heat like the steam of boiling water. Why then should matter resemble our sensations? Why should the inmost nature of fire or water resemble the impressions made by those objects upon our senses ?J Or on what principle are we * It is to be regretted tliat Sir William Hamilton, though he often strenuously insists on this doctrine, and though, in the passage quoted, he states it with a comprehensiveness and force which leave nothing to be desired, did not consistently adhere to his own doctrine, but maintained along with it opinions with which it is utterly irreconcilable. See the third and other chapters of An Examination of Sir William Hamilton s Philosophy. t "Nous Savons qu'il existe quelque chose hors de nous, parceque nous ne pouvons expli- quer nos perceptions sans les rattacher a des causes distinctes de nous memes ; nous savons de plus que ces causes, dont nous ne connaissons pas d'ailleurs I'essence, produisent les etfets les plus variables, les plus divers, et meme les plus contraires, selon qu'elles rencontrent telle nature ou telle disposition du sujet. Mais savons-nous quelque chose de plus ? et meme, vu le caractere indetermine' des causes que nous concevons dans les corps, y a-t-il quelque chose de plus a savoir? Y a-t-il lieu de nous enque'rir si nous percevons les choses telles qu'elles sont ? Non e'videmment Je ne dis pas que le probleme est insoluble, je dis qu'il est absurde et enfenne une contradiction. Nous ne savons pas ce que ces causes sont en elles-mejnes, et la raison nous defend de chercher a le connaitre : mais il est bien evident a priori, qaelles ne sont pas en elles-memes ce quelles sont par rapport a nous, puisque la pre- sence du sujet modifie necessairement leur action. Supprimez tout sujet sentant, il est certain que ces causes agiraient encore puisqu'elles continueraient d'exister; mais elles agiraient au- trement ; elles seraient encore des qualites et des proprietes, mais qui ne ressembleraient a rien de ce que nous connaissons. Le feu ne manifesterait plus aucune des proprietes que nous lui connaissons : que serait-il ? C'est ce que nous ne saurons jamais. C'est d'ailleurs peut- etre un probleme qui ne repugne pas seulement a la nature de notre esprit, mais a I'essence meme des choses. Quand meme en effet on supprimerait par le pensee tons les sujets sentants, il faudrait encore admettre que nul corps ne manifesterait ses proprietes autrement qu'en rela- tion avec un sujet quelconque, et dans ce cas ses proprietes ne seraient encore que relatives: en sorte qu'il me parait fort raisonnable d'admettre que les propriete's determine'es des corps n'existent pas inde'pendamment d'un sujet quelconque, et que quand on demande si les pro- prietes de la matiere sont telles que nous les percevons, il faudrait voir auparavant si elles sont en tant que de'terminees, et dans quel sens il est vrai de dire qu'elles sont."' — Cours d'Histoire de la Philosophie Morale au l^me siecle, 8me le9on. X An attempt, indeed, has been made by Reid and others, to establish that although some of the properties we ascribe to objects exist only in our sensations, others exist in the things themselves, being such as can not possibly be copies of any impression upon the senses ; and they ask, from what sensations our notions of extension and figure have been derived? The gauntlet thrown down by Reid was taken up by Brown, who, applying greater powers of anal- ysis than had previously been applied to the notions of extension and figure, pointed out that the sensations from which those notions are derived, are sensations of touch, combined with sensations of a class previously too little adverted to by metaphysicians, those which have their seat in our muscular frame. His analysis, which was adopted and followed up by James 31111. has been further and greatly improved upon in Professor Bain's profound work, The Senses and the Intellect, and in the chapters on " Perception " of a work of eminent analytic power, Mr. Herbert Spencer's Principles of Psychology. On this point M. Cousin may again be cited in favor of the better doctrine. M. Cousin recognizes, in opposition to Reid, the essential subjectivity of our conceptions of what are called the primary qualities of matter, as extension, solidity, etc., equally with those of color, heat, and the remainder of the so-called secondary qualities. — Cours, ut supra, 9me le9on. 56 NAMES AND PROPOSITIONS. authorized to deduce from the effects, any thing concerning the cause, ex- cept that it is a cause adequate to produce those effects? It may, there- fore, safely be laid down as a truth both obvious in itself, and admitted by all whom it is at present necessary to take into consideration, that, of the outward world, we know and can know absolutely nothing, except the sen- sations which we experience from it.* § 8. Body having now been defined the external cause, and (according to the more reasonable opinion) the unknown external cause, to which w^e refer our sensations ; it remains to frame a definition of Mind. Nor, after the preceding observations, will this be difficult. For, as our conception of a body is that of an unknown exciting cause of sensations, so our con- ception of a mind is that of an unknown recipient or percipient, of them ; and not of them alone, but of all our other feelings. As body is under- stood to be the mysterious something which excites the mind to feel, so mind is the mysterious something which feels and thinks. It is unneces- sary to give in the case of mind, as we gave in the case of matter, a par- ticular statement of the skeptical system by which its existence as a Thing in itself, distinct from the series of what are denominated its states, is call- ed in question. But it is necessary to remark, that on the inmost nature (whatever be meant by inmost nature) of the thinking principle, as well as on the inmost nature of matter, we are, and with our faculties must al- ways remain, entirely in the dark All which we are aware of, even in our own minds, is (in the words of James Mill) a certain " thread of conscious- ness ;" a series of feelings, that is, of sensations, thoughts, emotions, and vohtions, more or less numerous and complicated. There is a something I call Myself, or, by another form of expression, ray mind, which I consider as distinct from these sensations, thoughts, etc.; a something which I con- ceive to be not the thoughts, but the being that has the thoughts, and * This doctrine, which is the most complete form of the philosophical theory known as the Relativity of Human Knowledge, has, since the recent revival in this country of an active in- terest in metaphysical speculation, been the subject of a greatly increased amount of discussion and controversy ; and dissentients have manifested themselves in considerably greater number than I had any knowledge of when the passage in the text was written. The doctrine has been attacked from two sides. Some thinkers, among whom are the late Professor Perrier, in his Institutes of Metaphysic, and Professor John Grote, in his Exploratio Philosophica, ap- pear to deny altogether the reality of Noumena, or Things in themselves — of an unknowable substratum or support for the sensations which we experience, and which, according to the theory, constitute all our knowledge of an external world. It seems to me, howevei-, that in Professor Grote's case at least, the denial of Noumena is only apparent, and that he does not essentially differ from the other class of objectors, including Mr. Bailey in his valuable Let- ters on the Philosophy of the Human Mind, and (in spite of the striking passage quoted in the text) also Sir William Hamilton, who contend for a direct knowledge by the human mind of more than the sensations — of certain attributes or properties as they exist not in us, but in the Things themselves. With the first of these opinions, that which denies Noumena, I have, as a metaphysician, no quarrel ; but, whether it be true or false, it is irrelevant to Logic. And since all the forms of language are in contradiction to it, nothing but confusion could result from its unnecessary introduction into a treatise, every essential doctrine of which could stand equally well with the opposite and accredited opinion. The other and rival doctrine, that of a direct perception or intuitive knowledge of the outward object as it is in itself, considered as distinct from the sensations we receive from it, is of far greater practical moment. But even this question, depending on the nature and laws of Intuitive Knowledge, is not within the province of Logic. For the grounds of my own opinion concerning it, I must content myself with referring to a work already mentioned — An Examination of Sir William Hamilton s Philosophy ; several chapters of which are devoted to a full discussion of the questions and theories relating to the supposed direct perception of external objects. THINGS DENOrKD BY NAMES. 57 which I can conceive as existing forever in a state of qniescence, witliout any thouo'hts at all. .l>ut what this being is, though it is myself, 1 hav(; no knowledge, other than the series of its states of consciousness. As bodies manifest themselves to me only through the sensations of which I i-egard them as the causes, so the thinking princii)le, or mind, in my own nature, makes itself known to me only by the feelings of which it is conscious. I know nothing about myself, save my capacities of feeling or being con- scious (including, of course, thinking and willing) : and were I to learn any thing new concerning my own nature, I can not with my present facul- ties conceive this new information to be any thing else, than that I have some additional capacities, as yet unknown to me, of feeling, thinking, or willing. Thus, then, as body is the unsentient cause to which w^e are naturally prompted to refer a certain portion of our feelings, so mind may be de- scribed as the sentient subject (in the scholastic sense of the term) of all feelings ; that wdiich has or feels them. But of the nature of either body or mind, further than the feelings which the former excites, and which the latter experiences, we do not, according to the best existing doctrine, know^ any thing ; and if any thing, logic has nothing to do with it, or with the manner in Avhich the knowledge is acquired. With this result we may conclude this portion of our subject, and pass to the third and only remain- ing class or division of Namable Things. III. Attributes : and, fiest, Qualities. § 9. From what has already been said of Substance, what is to be said of Attribute is easily deducible. For if we know not, and can not know^, any thing of bodies but the sensations which they excite in us or in others, those sensations must be all that we can, at bottom, mean by their attri- butes ; and the distinction which we verbally make between the properties of things and the sensations we receive from them, must originate in the convenience of discourse rather than in the nature of what is signified by the terms. Attributes are usually distributed under the three heads of Quality, Quantity, and Relation. We shall come to the two latter presently : in the fi.rst place we shall confine ourselves to the former. Let us take, then, as our example, one of wdiat are termed the sensible qualities of objects, and let that example be whiteness. When we ascribe whiteness to any substance, as, for instance, snow ; when we say that snow has the quality whiteness, w^hat do we really assert? Simply, that when snow is present to our organs, we have a particular sensation, which we are accustomed to call the sensation of white. But how do I know that snow is present? Obviously by the sensations which I derive from it, and not otherwise. I infer that the object is present, because it gives me a certain assemblage or series of sensations. And when I ascribe to it the attribute whiteness, my meaning is only, that, of the sensations composing this group or series, that w^hich I call the sensation of white color is one. This is one view which may be taken of the subject. But there is also another and a different view. It may be said, that it is true we knoic noth- ing of sensible objects, except the sensations they excite in us ; that the fact of our receiving from snow the particular sensation which is called a sensation of white, is the ground on which we ascribe to that substance the quality whiteness ; the sole proof of its possessing that quality. But be- cause one thing may be the sole evidence of the existence of another thing. 58 NAMES AND PKOPOSITIONS. it does not follow that the two are one and the same. The attribute white- ness (it may be said) is not the fact of receiving the sensation, but some- thing in the object itself; a pov^er inherent in it; something in virtue of which the object produces the sensation. And when we affirm that snow possesses the attribute whiteness, we do not merely assert that the pres- ence of snow produces in us that sensation, but that it does so through, and by reason of, that power or quality. For the purposes of logic it is not of material importance which of these opinions we adopt. The full discussion of the subject belongs to the other department of scientific inquiry, so often alluded to under the name of met- aphysics; but it may be said here, that for the doctrine of the existence of a pecuUar species of entities called qualities, I can see no foundation ex- cept in a tendency of the human mind which is the cause of many delu- sions. I mean, the disposition, wherever we meet with two names which are not precisely synonymous, to suppose that they must be the names of two different things ; whereas in reaUty they may be names of the same thing viewed in two different lights, or under different suppositions as to surrounding circumstances. Because quality and sensation can not be put indiscriminately one for the other, it is supposed that they can not both signify the same thing, namely, the impression or feeling with w^hich we are affected through our senses by the presence of an object; though there is at least no absurdity in supposing that this identical impression or feel- ing may be called a sensation when considered merely in itself, and a quali- ty when looked at in relation to any one of the numerous objects, the pres- ence of which to our organs excites in our minds that among various other sensations or feehngs. And if this be admissible as a supposition, it rests with those who contend for an entity per se called a quality, to show that their opinion is preferable, or is any thing in fact but a lingering remnant of the old doctrine of occult causes ; the very absurdity which Moliere so happily ridiculed when he made one of his pedantic physicians account for the fact that opium produces sleep by the maxim, Because it has a soporific virtue. It is evident that when the physician stated that opium has a soporific virtue, he did not account for, but merely asserted over again, the fact that it produces sleep. In like manner, when we say that snow is white because it has the quality of whiteness, we are only re-asserting in more technical language the fact that it excites in us the sensation of white. If it be said that the sensation must have some cause, I answer, its cause is the presence of the assemblage of phenomena which is termed the object. When we have asserted that as often as the object is present, and our organs in their normal state, the sensation takes place, we have stated all that we know about the matter. There is no need, after assigning a certain and intelli- gible cause, to suppose an occult cause besides, for the purpose of enabling the real cause to produce its effect. If I am asked, why does the presence of the object cause this sensation in me, I can not tell: I can only say that such is my nature, and the nature of the object ; that the fact forms a part of the constitution of things. And to this we must at last come, even after interpolating the imaginary entity. Whatever number of links the chain of causes and effects may consist of, how any one link produces the one which is next to it, remains equally inexplicable to us. It is as easy to comprehend that the object should produce the sensation directly and at once, as that it should produce the same sensation by the aid of something else called the pov^er of producing it. THINGS Di:N(rri<:i) by names. 50 But, as tlici difficulties which in:iy 1)(} felt in adopting this view of the subject can not be removed without discussions transcending tlie l)ounds of our science, I content myself with a passing indication, and shall, for tlie purposes of logic, adopt a language (compatible with either view of the na- ture of qualities. I shall say — what at least admits of no dispute — that the quality of whiteness ascribed to the object snow, is grounded on its exciting in us the sensation of white ; and adopting the language already used by the school logicians in the case of the kind of attributes called Relations, I shall term the sensation of white Iha foundation of the quality whiteness. For logical purposes the sensation is the only essential part <>i what is meant by the word ; the only part which we ever can be concerned in proving. When that is proved, the quality is proved ; if an object ex- cites a sensation, it has, of course, the power of exciting it. IV. Relations. § 10. The qualities of a body, we have said, are the attributes grounded on the sensations which the presence of that particular body to our organs excites in our minds. But when we ascribe to any object the kind of at- tribute called a Relation, the foundation of the attribute must be some- thing in which other objects are concerned besides itself and the percipient. As there may with propriety be said to be a relation between any two things to which two correlative names are or may be given, we may ex- pect to discover what constitutes a relation in general, if we enumerate the principal cases in which mankind have imposed correlative names, and ob- serve what these cases have in common. What, then, is the character which is possessed in common by states of circumstances so heterogeneous and discordant as these: one thing like another; one thing unlike another; one thing near another; one thing far from another; one thing before, after, along loith another; one thing greater, equal, less, than another ; one thing the cause of another, the effect of another; one person the master, servant, child, parent, debtor, creditor, sovereign, subject, attorney, client, of another, and so on ? Omitting, for the present, the case of Resemblance, (a relation which re- quires to be considered separately,) there seems to be one thing common to all these cases, and only one ; that in each of them there exists or occurs, or has existed or occurred, or may be expected to exist or occur, some fact or phenomenon, into which the two things which are said to be related to each other, both enter as parties concerned. This fact, or phenomenon, is what the Aristotelian logicians called the fundamentuni relationis. Thus in the relation of greater and less betw^een two magnitudes, the fundamen- tuni relationis is the fact that one of the two magnitudes could, under cer- tain conditions, be included in, without entirely filling, the space occu])ied by the other magnitude. In the relation of master and servant, the fun- dam.entum relationis is the fact that the one has undertaken, or is com- pelled, to perform certain services for the benefit and at the bidding of the other. Examples might be indefinitely multiplied ; but it is already obvi- ous that whenever two things are said to be related, there is some fact, or series of facts, into which they both enter ; jand that whenever any two things are involved in some one fact, or series of facts, we may ascribe to those two things a mutual relation grounded on the fact. Even if they have nothing in common but what is common to all things, that they are members of the universe, we call that a relation, and denominate them fellow-creatures, fellow-beings, or fellow-denizens of the universe. But in 60 NAMES AND PROPOSITIONS. proportion as the fact into which the two objects enter as parts is of a more special and pecuHar, or of a more complicated nature, so also is the relation grounded upon it. And there are as many conceivable relations as there are conceivable kinds of fact in which two things can be jointly concerned. In the same manner, therefore, as a quality is an attribute grounded on the fact that a certain sensation or sensations are produced in us by the object, so an attribute grounded on some fact into which the object enters jointly with another object, is a relation between it and that other object. But the fact in the latter case consists of the very same kind of elements as the fact in the former; namely, states of consciousness. In the case, for example, of any legal relation, as debtor and creditor, principal and agent, guardian and ward, the fundamentuwi relationis consists entirely of thoughts, feelings, and volitions (actual or contingent), either of the persons themselves or of other persons concerned in the same series of transactions ; as, for instance, the intentions which would be formed by a judge, in case a complaint were made to his tribunal of the infringement of any of the legal obligations imposed by the relation; and the acts which the judge would perform in consequence; acts being (as we have already seen) an- other word for intentions followed by an effect, and that effect being but another word for sensations, or some other feelings, occasioned either to the agent himself or to somebody else. There is no part of what the names expressive of the relation imply, that is not resolvable into states of con- sciousness ; outward objects being, no doubt, supposed throughout as the causes by which some of those states of consciousness are excited, and minds as the subjects by which all of them are experienced, but neither the external objects nor the minds making their existence known other- wise than by the states of consciousness. Cases of relation are not always so complicated as those to which we last alluded. The simplest of alt cases of relation are those expressed by the words antecedent and consequent, and by the word simultaneous. If we say, for instance, that dawn preceded sunrise, the fact in which the two things, dawn and sunrise, were jointly concerned, consisted only of the two things themselves ; no third thing entered into the fact or phenomenon at all. Unless, indeed, we choose to call the succession of the two objects a third thing; but their succession is not something added to the things themselves ; it is something involved in them. Dawn and sunrise announce themselves to our consciousness by two successive sensations. Our con- sciousness of the succession of these sensations is not a third sensation or feeling added to them; we have not first the two feelings, and then a feel- ing of their succession. To have two feehngs at all, impUes having them either successively, or else simultaneously. Sensations, or other feelings, being given, succession and simultaneousness are the two conditions, to the alternative of which they are subjected by the nature of our faculties ; and no one has been able, or needs expect, to analyze the matter any further. § 11. In a somewhat similar position are two other sorts of relations. Likeness and Unlikeness. I have two sensations; we will suppose them to be simple ones ; two sensations of white, or one sensation of white and another of black. I call the first two sensations like ; the last two unlike. What is the fact or phenomenon constituting the fundamentum of this relation ? The two sensations first, and then what we call a feeling of re- semblance, or of want of resemblance. Let us confine ourselves to the for- TIIIN(iS DKNOTKD 15Y NAMluS. fjl iiier case. Resemblance is evidently a feclinij^; a state of llie consciousiu'ss of the observer. Wliether llu^ feelinn' ol' the resemblance ot tl»e two colors be a third state of consciousness, which I liave (iftcr having the two sensa- tions of color, or whether (like the feeling of their succession) it is involved in the sensations themselves, may be a matter of discussion. J>ut in either case, tliese feelings of resemblance, and of its o})|)osite dissimilarity, are parts of our nature; and parts so far from being capable of analysis, that they are presupposed in every attempt to analyze any of our other feelings. /Likeness and unlikeness, therefore, as well as antecedence, sequence, and simultaneousness, must stand apart among relations, as things sui generis. They are attributes grounded on facts, that is, on states of consciousness, but on states which are peculiar, unresolvable, and inexplicable/ But, though likeness or unlikeness can not be resolved into any thing else, complex cases of likeness or unlikeness can be resolved into sim})ler ones. When we say of two things which consist of parts, that they are like one another, the likeness of the wholes does admit of analysis; it is compounded of likenesses between the various parts respectively, and of likeness in their arrangement. Of how vast a variety of resemblances of parts must that resemblance be composed, which induces us to say that a portrait, or a landscape, is like its original. If one person mimics another with any success, of how many simple likenesses must the general or com- plex likeness be compounded : likeness in a succession of bodily postures ; likeness in voice, or in the accents and intonations of the voice ; likeness in the choice of words, and in the thoughts or sentiments expressed, wheth- er by word, countenance, or gesture. All likeness and unlikeness of which we have any cognizance, resolve themselves into likeness and unlikeness between states of our own, or some other, mind. When we say that one body is like another, (since we know nothing of bodies but the sensations which they excite,) we mean really that there is a resemblance between the sensations excited by the two bodies, or between some portions at least of those sensations. If we say that two attributes are like one another (since we know nothing of attri- butes except the sensations or states of feeling on which they are ground- ed), we mean really that those sensations, or states of feeling, resemble each other. We may also say that two ]-elations are alike. The fact of resem- blance between relations is sometimes called analogy^ forming one of the numerous meanings of that word. The relation in which Priam stood to Hector, namely, that of father and son, resembles the relation in Avhich Philip stood to Alexander; resembles it so closely that they are called the same relation. The relation in which Cromwell stood to England resem- bles the relation in wdiich Napoleon stood to France, though not so closely as to be called the same relation. The meaning in both these instances must be, that a resemblance existed between the facts which constituted the fundamentwn relationis. This resemblance may exist in all conceivable gradations, from perfect undistinguishableness to something extremely sligTit. When we say, tliat a thought suggested to the mind of a person of genius is like a seed cast into the ground, because the former produces a multitude of other thoughts, and the latter a multitude of other seeds, this is saying that between the relation of an inventive mind to a thought contained in it, and the relation of a fertile soil to a seed contained in it, there exists a resemblance : the real resemblance being in the \j\wo fundamenta relationis, m each of which there occurs a germ, producing by its development a multitude of other 62 ' NAMES AND PKOPOSITIONS. things similar to itself. And as, whenever two objects are jointly concern- ed in a phenomenon, this constitutes a relation between those objects, so, if we suppose a second pair of objects concerned in a second phenomenon, the slightest resemblance between the two phenomena is sufficient to ad- mit of its being said that the two relations resemble ; provided, of course, the points of resemblance are found in those portions of the two phenom- ena respectively which are connoted by the relative names. While speaking of resemblance, it is necessary to take notice of an am- biguity of language, against which scarcely any one is sufficiently on his guard. Resemblance, when it exists in the highest degree of all, amount- ing to undistinguishableness, is often called identity, and the two similar things are said to be the same. I say often, not always; for we do not say that two visible objects, two persons, for instance, are the same, because they are so much alike that one might be mistaken for the other : but we constantly use this mode of expression when speaking of feelings ; as when I say that the sight of any object gives me the same sensation or emotion to-dky that it did yesterday, or the same which it gives to some other per- son. This is evidently an incorrect application of the word same; for the feeling which I had yesterday is gone, never to return ; what I have to- day is another feeling, exactly like the former, perhaps, but distinct from it ; and it is evident that two different persons can not be experiencing the same feeling, in the sense in which we say that they are both sitting at the same table. By a similar ambiguity we say, that two persons are ill of the same disease; that two persons hold the same office; not in the sense in which we say that they are engaged in the same adventure, or sailing in the same ship, but in the sense that they fill offices exactly similar, though, perhaps, in distant places. Great confusion of ideas is often produced, and many fallacies engendered, in otherwise enlightened understandings, by not being sufficiently alive to the fact (in itself not always to be avoided), that they use the same name to express ideas so different as those of iden- tity and undistinguishable resemblance. Among modern writers. Arch- bishop Whately stands almost alone in having drawn attention to this dis- tinction, and to the ambiguity connected with it. Several relations, generally called by other names, are really cases of resemblance. As, for example, equality; which is but another word for the exact resemblance commonly called identity, considered as subsisting between things in respect of their quantity. And this example forms a suitable transition to the third and last of the three heads under which, as already remarked, Attributes are commonly arranged. V. Quantity. § 12. Let us imagine two things, between which there is no difference (that is, no dissimilarity), except in quantity alone ; for instance, a gallon of water, and more than a gallon of water. A gallon of water, like any other external object, makes its presence known to us by a set of sensa- tions which it excites. Ten gallons of water are also an external object, making its presence known to us in a similar manner; and as we do not mistake ten gallons of water for a gallon of water, it is plain that the set of sensations is more or less different in the two cases. In like manner, a gallon of water, and a gallon of wine, are two external objects, making their presence known by two sets of sensations, which sensations are dif- ferent from each other. In the first case, however, we say that the differ- ence is in quantity ; in the last there is a difference in quality, while the THINGS DENOTED BY NAMES. 63 quantity of the water and of the wine is the same. What is the real dis- tinction between the two cases ? It is not within the province of Logic to analyze it ; nor to decide whether it is susceptible of analysis or not. For ns the following considerations are sufficient: It is evident that the sen- sations I receive from the gallon of watei', and those I receive from the gallon of wine, are not the same, that is, not precisely alike ; neither are they altogether unlike : they are partly similar, partly dissimilar ; and that in which they resemble is precisely that in which alone the gallon of wa- ter and the ten gallons do not resemble. That in which the gallon of wa- ter and the gallon of wine are like each other, and in which the gallon and the ten gallons of water are unlike each other, is called their quan- tity. This likeness and unlikeness I do not pretend to explain, no more than any other kind of likeness or unlikeness. But my object is to show, that when w^e say of two things that they differ in quantity, just as when we say that they differ in quality, the assertion is always grounded on a difference in the sensations which they excite. ISTobody, I presume, will say, that to see, or to lift, or to drink, ten gallons of water, does not include in itself a different set of sensations from those of seeing, lifting, or drink- ing one gallon ; or that to see or handle a foot-rule, and to see or handle a yard-measure made exactly like it, are the same sensations. I do not un- dertake to say what the difference in the sensations is. Every body knows, and nobody can tell ; no more than any one could tell what white is to a person who had never had the sensation. But the difference, so far as cognizable by our faculties, lies in the sensations. Whatever difference we say there is in the things themselves, is, in this as in all other cases, grounded, and grounded exclusively, on a difference in the sensations ex- cited by them. VI. Atteibutes Cojs^cluded. § 13. Thus, then, all the attributes of bodies which are classed under Quality or Quantity, are grounded on the sensations which we receive from those bodies, and may be defined, the powers which the bodies have of ex- citing those sensations. And the same general explanation has been found to apply to most of the attributes usually classed under the head of Rela- tion. They, too, are grounded on some fact or phenomenon into w^hich the related objects enter as parts; that fact or phenomenon having no mean- ing and no existence to us, except the series of sensations or other states of consciousness by which it makes itself known ; and the relation being simply the power or capacity which the object possesses of taking part along with the correlated object in the production of that series of sensa- tions or states of consciousness. We have been obliged, indeed, to recog- nize a somewhat different character in certain peculiar relations, those of succession and simultaneity, of likeness and unlikeness. These, not being grounded on any fact or phenomenon distinct from the related objects themselves, do not admit of the same kind of analysis. But these relations, though not, like other relations, grounded on states of consciousness, are themselves states of consciousness : resemblance is nothing but our feeling of resemblance ; succession is nothing but our feeling of succession. Or, if this be disputed (and Ave can not, without transgressing the bounds of our science, discuss it here), at least our knowledge of these relations, and even our possibility of knowledge, is confined to those which subsist be- tween sensations, or other states of consciousness ; for, though we ascribe resemblance, or succession, or simultaneity, to objects and to attributes, it 64 NAMES AND PROPOSITIONS. is always in virtue of resemblance or succession or simultaneity in the sen- sations or states of consciousness which those objects excite, and on which those attributes are grounded. § 14. In the preceding investigation we have, for the sake of simplicity, considered bodies only, and omitted minds. But what we have said, is ap- plicable, 7nutatis 7nuta7idis, to the latter. The attributes of minds, as well as those of bodies, are grounded on states of feeling or consciousness. But in the case of a mind, we have to consider its own states, as well as those which it produces in other minds. Every attribute of a mind consists either in being itself affected in a certain way, or affecting other minds in a certain way. Considered in itself, we can predicate nothing of it but the series of its own feelings. When w^e say of any mind, that it is devout, or super- stitious, or meditative, or cheerful, w^e mean that the ideas, emotions, or volitions implied in those words, form a frequently recurring part of the series of feelings, or states of consciousness, which fill up the sentient ex- istence of that mind. In addition, however, to those attributes of a mind which are grounded on its own states of feeling, attributes may also be ascribed to it, in the same manner as to a body, grounded on the feelings which it excites in other minds. A mind does not, indeed, like a body, excite sensations, but it may excite thoughts or emotions. The most important example of attri- butes ascribed on this ground, is the employment of terms expressive of approbation or blame. When, for example, we say of any character, or (in other words) of any mind, that it is admirable, we mean that the contem- plation of it excites the sentiment of admiration ; and indeed somewhat more, for the word implies that we not only feel admiration, but approve that sentiment in ourselves. In some cases, under the semblance of a sin- gle attribute, two are really predicated : one of them, a state of the mind itself; the other, a state with which other minds are affected by thinking of it. As when we say of any one that he is generous. The word gene- rosity expresses a certain state of mind, but being a term of praise, it also expresses that this state of mind excites in us another mental state, called approbation. The assertion made, therefore, is twofold, and of the follow- ing purport: Certain feelings form habitually a part of this person's sen- tient existence; and the idea of those feelings of his, excites the sentiment of approbation in ourselves or others. As we thus ascribe attributes to minds on the ground of ideas and emo- tions, so may we to bodies on similar grounds, and not solely on the ground of sensations : as in speaking of the beauty of a statue ; since this attribute is grounded on the peculiar feeling of pleasure which the statue produces in our minds ; which is not a sensation, but an emotion. VII. General Results. § 15. Our survey of the varieties of Things which have been, or which are capable of being, named — which have been, or are capable of being, either predicated of other Things, or themselves made the subject of predi- cations — is now concluded. Our enumeration commenced with Feelings. These we scrupulously dis- tinguished from the objects which excite them, and from the organs by which they are, or may be supposed to be, conveyed. Feelings are of four sorts : Sensations, Thoughts, Emotions, and Volitions. What are called Perceptions are merely a particular case of Belief, and Belief is a kind of thought. Actions are merely volitions followed by an effect. THINGS DENOTKI) BY NAMES. C5 After Feelings we proceeded to Substaiiees. These .'ire either 1 bodies or Minds. Without entering into the grounds of tlie metaphysical doid>ts which have been raised concerning the existence of Matter and Mind as ob- jective realities, we stated as sufficient for us the conclusion in which the best thinkers are now for the most part agreed, that all we can know of Matter is the sensations which it gives us, and the order of occurrence; of those sensations ; and that while the substance Body is the unknown cause of our sensations, the substance Mind is the unknown reci})ient. The only remaining class of Namable Things is Attributes; and these are of three kinds. Quality, Relation, and Quantity. Qualities, like sub- stances, are known to us no otherwise than by the sensations or otlier states of consciousness which they excite: and while, in com])liance witli common usage, we have continued to speak of them as a distinct class of Things, we showed that in predicating them no one means to predicate any thing but those sensations or states of consciousness, on which they may be said to be grounded, and by which alone they can be defined or described. Relations, except the simple cases of likeness and unlikeness, succession and simultaneity, are similarly grounded on some fact or phenomenon, that is, on some series of sensations or states of consciousness, more or less complicated. The third species of Attribute, Quantity, is also manifestly grounded on something in our sensations or states of feeling, since there is an indubitable difference in the sensations excited by a larger and a smaller bulk, or by a greater or a less degree of intensity, in any object of sense or of consciousness. All attributes, therefore, are to us nothing but either our sensations and other states of feeling, or something inextricably in- volved therein; and to this even the peculiar and simple relations just ad- verted to are not exceptions. Those peculiar relations, however, are so im- portant, and, even if they might in strictness be classed among states of consciousness, are so fundamentally distinct from any other of those states,, that it would be a vain subtlety to bring them under that common descrip- tion, and it is necessary that they should be classed apart.* As the result, therefore, of our analysis, we obtain the following as an enumeration and classification of all Namable Things : 1st. Feelings, or States of Consciousness. 2d. The Minds which experience those feelings. 3d. The Bodies, or external objects w^hich excite certain of those feelings^ together with the powers or properties whereby they excite them ; these latter (at least) being included rather in compliance with common opinion, and because their existence is taken for granted in the common language from which I can not prudently deviate, than because the recognition of such powers or properties as real existences appears to be warranted by a sound philosophy. 4th, and last. The Successions and Co-existences, the Likenesses and Un- likenesses, between feelings or states of consciousness. Those relations, when considered as subsisting between other things, exist in reality only between the states of consciousness which those things, if bodies, excite, if minds, either excite or experience. * Professor Bain (Logic, i., 49) defines attributes as "points of community among classes. ." This definition expresses well one point of view, but is liable to the objection that it applies only to the attributes of classes : though an object, unique in its kind, may be said to have at- tributes. ISIoreover, the definition is not ultimate, since the points of community themselves admit of, and require, further analysis ; and Mr. Bain does analyze them into resemblances in the sensations, or other states of consciousness excited by the object. 66 NAMES AND PEOPOSITIONS. This, until a better can be suggested, may serve as a substitute for the Categories of Aristotle considered as a classification of Existences. The practical application of it will appear when we commence the inquiry into the Import of Propositions ; in other words, when w^e inquire what it is which the mind actually believes, when it gives what is called its assent to a proposition. These four classes comprising, if the classification be correct, all ISTamable Things, these or some of them must of course compose the signification of all names : and of these, or some of them, is made up whatever we call a fact. For distinction's sake, every fact which is solely composed of feelings or states of consciousness considered as such, is often called a Psychological or Subjective fact; while every fact which is composed, either wholly or in part, of something different from these, that is, of substances and attri- butes, is called an Objective fact. We may say, then, that every objective fact is grounded on a corresponding subjective one ; and has no meaning to us (apart from the subjective fact which corresponds to it), except as a name for the unknown and inscrutable process by which that subjective or psychological fact is brought to pass. CHAPTER IV. OF PROPOSITIONS. § 1. In treating of Propositions, as already in treating of Names, some considerations of a comparatively elementary nature respecting their form and varieties must be premised, before entering upon that analysis of the import conveyed by them, which is the real subject and purpose of this preliminary book. A proposition, we have before said, is a portion of discourse in which a predicate is afiirmed or denied of a subject. A predicate and a subject are all that is necessarily required to make up a proposition : but as we can not conclude from merely seeing two names put together, that they are a predi- cate and a subject, that is, that one of them is intended to be afiirmed or denied of the other, it is necessary that there should be some mode or form of indicating that such is the intention ; some sign to distinguish a predi- cation from any other kind of discourse. This is sometimes done by a slight alteration of one of the words, called an inflection; as when we say, Fire burns ; the change of the second word from hum to hiiims showing that we mean to afiirm the predicate burn of the subject fire. But thi's function is more commonly fulfilled by the word is, when an afiirmation is intended, is not, w^hen a negation ; or by some other part of the verb to he. The word which thus serves the purpose of a sign of predication is called, as we formerly observed, the copula. It is important that there should be no indistinctness in our conception of the nature and ofiice of the copula ; for confused notions respecting it are among the causes which have spread mysticism over the field of logic, and perverted its speculations into logoma- chies. It is apt to be supposed that the copula is something more than a mere sign of predication; that it also signifies existence. In the proposition, Socrates is just, it may seem to be implied not only that the quaUty J?roposition,^^ the whole is greater than its part;" the proposition, " the Holy Ghost proceeds from the Father alone ;" the propo- sition, " kings have a divine right ;" the proposition, " the Pope is infallible." Seeing, then, that there is much less difference between hypothetical propositions and any others, than one might be led to imagine from their riiorosiTioNs. 71 form, wc iShould be at a, loss to account k)v tlio conspi(;uous |)o.sili(>n wliicli they have been selected to fill in treatises on logic, if we did not remem- ber that what they predicate of a ])roposition, namely, its beiriL? an inference from something else, is })recisely that one of its attributes with wiiicii most of all a logician is concerned. § 4. The next of the common divisions of Propositions is into Universal, Particular, Indefinite, and Singular: a distinction founded on the degree of generality in which the name, which is the subject of the proposition, is to be understood. The following are examples : All men are mortal — Universal. jSo)ne men are mortal — Particular. Man is mortal — Indefinite. tTulius Gcesar is mortal — Singular. The proposition is Singular, when the subject is an individual name. The individual name needs not be a proper name. " The Founder of Christianity was crucified," is as much a singular proposition as " Christ was crucified." When the name which is the subject of the proposition is a general name, we may intend to affirm or deny the predicate, either of all the things that the subject denotes, or only of some. When the predicate is affirmed or denied of all and each of the things denoted by the subject, the proposition is universal ; when of some undefined portion of them only, it is particular. Thus, All men are mortal ; Every man is mortal ; are uni- versal propositions. No man is immortal, is also a universal proposition, since the predicate, immortal, is denied of each and every individual de- noted by the terra man ; the negative proposition being exactly equivalent to the following. Every man is not-immortal. But " some men are wise," " some men are not wise," are particular propositions ; the predicate loise being in the one case affirmed and in the other denied not of each and ev- ery individual denoted by the term man, but only of each and every one of some portion of those individuals, without specifying what portion ; for if this were specified, the proposition would be changed either into a singu- lar proposition, or into a universal proposition with a different subject; as, for instance, " all properly instructed men are wise." There are other forms of particular propositions ; as, "J/bsi^men are imperfectly educated:" it being immaterial how large a portion of the subject the predicate is as- serted of, as long as it is left uncertain how that portion is to be distin- guished from the rest.* When the form of the expression does not clearly show whether the general name which is the subject of the proposition is meant to stand for all the individuals denoted by it, or only for some of them, the proposition is, by some logicians, called Indefinite ; but this, as Archbishop Whately ob- * Instead of Universal and Particular as applied to propositions, Professor Bain proposes {Logic, i., 81) the terras Total and Partial; reserving the former pair of terms for their in- ductive meaning, "the contrast between a general proposition and the particulars or individ- uals that we derive it from." This change in nomenclature would be attended with the further advantage, that Singular propositions, which in the Syllogism follow the same rules as Univer- sal, Avould be included along with them in the same class, that of Total predications. It is not the Subject's denoting many things or only one, that is of importance in reasoning, it is that tlie assertion is made of the whole or a part only of what the Subject denotes. The words Universal and Particular, however, are so familiar and so well understood in both the senses mentioned by Mr. Bain, that the double meaning does not produce any material inconvenience. 72 NAMES AND PROPOSITIONS. serves, is a solecism, of the same nature as ttiat committed by some gram- marians when in their list of genders they enumerate the doubtful gender. The speaker must mean to assert the proposition either as a universal or as a particular proposition, though he has failed to declare which : and it often happens that though the words do not show which of the two he in- tends, the context, or the custom of speech, supplies the deficiency. Thus, when it is affirmed that " Man is mortal," nobody doubts that the asser- tion is intended of all human beings ; and the word indicative of universal- ity is commonly omitted, only because the meaning is evident without it. In the proposition, " Wine is good," it is understood with equal readiness, though for somewhat different reasons, that the assertion is not intended to be universal, but particular.* As is observed by Professor Bain,f the chief examples of Indefinite propositions occur " with names of material, which are the subjects sometimes of universal, and at other times of partic- ular predication. 'Food is chemically constituted by carbon, oxygen, etc.,' is a proposition of universal quantity; the meaning is all food — all kinds of food. 'Food is necessary to animal life' is a case of particular quan- tity ; the meaning is some sort of food, not necessarily all sorts. ' Metal is requisite in order to strength' does not mean all kinds of metal. ' Gold will make a way,' means a portion of gold." When a general name stands for each and every individual which it is a name of, or in other words, which it denotes, it is said by logicians to be distributed^ or taken distributively. Thus, in the proposition. All men are mortal, the subject, Man, is distributed, because mortality is affirmed of each and every man. The predicate, Mortal, is not distributed, because the only mortals who are spoken of in the proposition are those who hap- pen to be men ; while the word may, for aught that appears, and in fact . does, comprehend within it an indefinite number of objects besides men. In the proposition. Some men are mortal, both the predicate and the sub- ject are undistributed. In the following, No men have wings, both the predicate and the subject are distributed. Not only is the attribute of having wings denied of the entire class Man, but that class is severed and cast out from the whole of the class Winged, and not merely from some part of that class. This phraseology, which is of great service in stating and demonstrating the rules of the syllogism, enables us to express very concisely the defini tions of a universal and a particular proposition. A universal proposition is that of which the subject is distributed; a particular proposition is that of which the subject is undistributed. There are many more distinctions among propositions than those we have here stated, some of them of considerable importance. But, for ex- plaining and illustrating these, more suitable opportunities will occur in the sequel. * It may, however, be considered as equivalent to a universal proposition with a different predicate, viz. : "All wine is good qua wine," or "is good in respect of the qualities which constitute it wine." t Logic, i., 82. IMPORT OF PROPOSITIONS. 73 CHAPTER V. OF THE IMPORT OF PROPOSITIONS. § 1. An inquiry into the nature of propositions must have one of two objects: to analyze the state of mind called Belief, or to analyze what is believed. All language recognizes a difference between a doctrine or opin- ion, and the fact of entertaining the opinion ; between assent, and what is assented to. Logic, according to the conception here formed of it, has no concern with the nature of the act of judging or believing; the consideration of that act, as a phenomenon of the mind, belongs to another science. Phi- losophers, however, from Descartes downward, and especially from the era of Leibnitz and Locke, have by no means observed this distinction ; and would have treated with great disrespect any attempt to analyze the im- port of Propositions, unless founded on an analysis of the act of Judgment. A proposition, they would have said, is but the expression in words of a Judgment. The thing expressed, not the mere verbal expression, is the important matter. When the mind assents to a proposition, it judges. Let us find out what the mind does when it judges, and we shall know what propositions mean, and not otherwise. Conformably to these views, almost all the writers on Logic in the last two centuries, whether English, German, or French, have made their the- ory of Propositions, from one end to the other, a theory of Judgments. They considered a Proposition, or a Judgment, for they used the two words indiscriminately, to consist in affirming or denying one idea of an- other. To judge, was to put two ideas together, or to bring one idea un- der another, or to compare two ideas, or to perceive the agreement or disa- greement between two ideas : and the whole doctrine of Propositions, to- gether with the theory of Reasoning (always necessarily founded on the theory of Propositions), was stated as if Ideas, or Conceptions, or whatever other term the w^riter preferred as a name for mental representations gen- erally, constituted essentially the subject-matter and substance of those op- erations. It is, of course, true, that in any case of judgment, as for instance when we judge that gold is yellow, a process takes place in our minds, of which some one or other of these theories is a partially correct account. We must have the idea of gold and the idea of yellow, and these two ideas must be brought together in our mind. But in the first place, it is evident that this is only a part of what takes place ; for we may put two ideas to- gether without any act of belief; as when we merely imagine something, such as a golden mountain ; or when we actually disbelieve : for in order even to disbelieve that Mohammed was an apostle of God, we must put the idea of Mohammed and that of an apostle of God together. To determine what it is that happens in the case of assent or dissent besides putting two ideas together, is one of the most intricate of metaphysical problems. But whatever the solution may be, we may venture to assert that it can have nothing whatever to do with the import of propositions; for this reason. 74 NAMES AND PROPOSITIONS. that propositions (except sometimes when the mind itself is the subject treated of) are not assertions respecting our ideas of things, but assertions respecting the things themselves. In order to believe that gold is yellow, I must, indeed, have the idea of gold, and the idea of yellow, and some- thing having reference to those ideas must take place in my mind ; but my belief has not reference to the ideas, it has reference to the things. What I believe, is a fact relating to the outward thing, gold, and to the impression made by that outward thing upon the human organs ; not a fact relating to my conception of gold, which would be a fact in my mental history, not a fact of external nature. It is true, that in order to believe this fact in external nature, another fact must take place in my mind, a process must be performed upon my ideas ; but so it must in every thing- else that I do. I can not dig the ground unless I have the idea of the ground, and of a spade, and of all the other things I am operating upon, and unless I put those ideas together.* But it would be a very ridiculous description of digging the ground to say that it is putting one idea into an- other. Digging is an operation which is performed upon the things them- selves, though it can not be performed unless I have in my mind the ideas of them. And in like manner, believing is an act which has for its subject the facts themselves, though a previous mental conception of the facts is an indispensable condition. When I say that fire causes heat, do I mean that my idea of fire causes my idea of heat ? No : I mean that the natural phenomenon, fire, causes the natural phenomenon, heat. When I mean to assert any thing respecting the ideas, I give them their proper name, I call them ideas : as when I say, that a child's idea of a battle is unlike the reality, or that the ideas entertained of the Deity have a great effect on the characters of mankind. The notion that what is of primary importance to the logician in a prop- osition, is the relation between the two ideas corresponding to the subject and predicate (instead of the relation between the Xwo phenomena which they respectively express), seems to me one of the most fatal errors ever introduced into the philosophy of Logic ; and the principal cause why the theory of the science has made such inconsiderable progress during the last two centuries. The treatises on Logic, and on the branches of Mental Phi- losophy connected with Logic, which have been produced since the intru- sion of this cardinal error, though sometimes written by men of extraor- dinary abilities and attainments, almost always tacitly imply a theory that the investigation of truth consists in contemplating and handling our ideas, or conceptions of things, instead of the things themselves : a doctrine tan- tamount to the assertion, that the only mode of acquiring knowledge of nature is to study it at second hand, as represented in our own minds. Meanwhile, inquiries into every kind of natural phenomena were incessant- ly establishing great and fruitful truths on most important subjects, by processes upon which these views of the nature of Judgment and Reason- ing threw no light, and in which they afforded no assistance whatever. No wonder that those who knew by practical experience how truths are ar- rived at, should deem a science futile, which consisted chiefly of such spec- * Dr. Whewell (Philosophy of Discovery^ p. 242) questions this statement, and asks, "Are we to say that a mole can not dig the ground, except he has an idea of the ground, and of the snout and paws with which he digs it?" I do not know what passes in a mole's mind, nor what amount of mental apprehension may or may not accompany his instinctive actions. But a human l)cing does not use a spade by instinct; and he certainly could not use it unless he had knowledge of a spade, and of the earth which he uses it upon. IMPORT OF PliOI'OSITlONS. 75 Illations. What lias been done for the advancement of Loiric since these doctrines came into vogue, has been done not by professed logicians, but by discoverers in the other sciences ; in whose methods of investigation many princii)les of logic, not previously thouglit of, have successively come forth into light, but wlio liave generally committed the error of sup])0sing that nothing whatever was known of the art of philosopliizing by the old logicians, because their modern interpreters have written to so little pui-- pose respecting it. We have to inquire, then, on tlie present occasion, not into Judgment, but judgments ; not into the act of believing, but into the thing believed. What is the immediate object of belief in a Proposition? What is the matter of fact signified by it? What is it to which, when I assert the proposition, I give my assent, and call upon others to give theirs ? What is that which is expressed by the form of discourse called a Proposition, and the conformity of "which to fact constitutes the truth of the proposition? § 2. One of the clearest and most consecutive thinkers wdiom this coun- try or the world has produced, I mean Hobbes, has given the following an- swer to this question. In every proposition (says he) what is signified is, the belief of the speaker that the predicate is a name of the same thing of which the subject is a name; and if it really is so, the proposition is true. Thus the proposition. All men are living beings (he would say) is true, because living being is a name of every thing of wdiich man is a name. All men are six feet high, is not true, because six feet high is not a name of every thing (though it is of some things) of which man is a name. What is stated in this theory as the definition of a true proposition, must be allowed to be a property which all true propositions possess. The sub- ject and predicate being both of them names of things, if they w^ere names of quite different things the one name could not, consistently with its sig- nification, be predicated of the other. If it be true that some men are cop- per-colored, it must be true — and the proposition does really assert — that among the individuals denoted by the name man, there are some who are also among those denoted by the name copper-colored. If it be true that all oxen ruminate, it must be true that all the individuals denoted by the name ox are also among those denoted by the name ruminating ; and who- ever asserts that all oxen ruminate, undoubtedly does assert that this rela- tion subsists between the two names. The assertion, therefore, -which, according to Hobbes, is the only one made in any proposition, really is made in every proposition : and his anal- ysis has consequently one of the requisites for being the true one. We may go a step further; it is the only analysis that is rigorously true of all propositions without exception. What he gives as the meaning of propo- sitions, is part of the meaning of all propositions, and the whole meaning of some. This, however, only shows what an extremeh' minute fragment of meaning it is quite possible to include within the logical formula of a proposition. It does not show that no proposition means more. To w^ar- rant us in putting together two words with a copula between them, it is really enough that the thing or things denoted by one of the names should be capable, without violation of usage, of being called by the other name also. If, then, this be all the meaning necessarily implied in the form of discourse called a Proposition, why do I object to it as the scientific definition of what a proposition means? Because, though the mere collocation which makes the proposition a proposition, conveys no more than this scanty amount of 76 NAMES AND PROPOSITIONS. meaning, that same collocation combined with other circumstances, that form combined with other matter^ does convey more, and the proposition in those other circumstances does assert more, than merely that relation between the two names. The only propositions of which Hobbes's principle is a sufficient account, are that limited and unimportant class in which both the predicate and the subject are proper names. For, as has already been remarked, proper names have strictly no meaning; they are mere marks for individual ob- jects : and when a proper name is predicated of another proper name, all the signification conveyed is, that both the names are marks for the same object. But this is precisely what Hobbes produces as a theory of predi- cation in general. His doctrine is a full explanation of such predications as these : Hyde was Clarendon, or, Tully is Cicero. It exhausts the mean- ing of those propositions. But it is a sadly inadequate theory of any oth- ers. That it should ever have been thought of as such', can be accounted for only by the fact, that Hobbes, in common with the other N"ominalists, bestowed little or no attention upon the connotation of words ; and sought for their meaning exclusively in what they denote: as if all names had been (what none but proper names really are) marks put upon individuals ; and as if there were no difference between a proper and a general name, except that the first denotes only one individual, and the last a greater number. It has been seen, however, that the meaning of all names, except proper names and that portion of the class of abstract names which are not conno- tative, resides in the connotation. When, therefore, we are analyzing the meaning of any proposition in which the predicate and the subject, or either of them, are connotative names, it is to the connotation of those terms that we must exclusively look, and not to what they denote^ or in the language of Hobbes (language so far correct) are names of. In asserting that the truth of a proposition depends on the conformity of import between its terms, as, for instance, that the proposition, Socrates is wise, is a true proposition, because Socrates and wise are names applicable to, or, as he expresses it, names of, the same person ; it is very remarkable that so powerful a thinker should not have asked himself the question. But how came they to be names of the same person ? Surely not because such was the intention of those who invented the words. When mankind fixed the meaning of the word wise, they were not thinking of Socrates, nor, when his parents gave him the name of Socrates, were they thinking of wisdom. The names happen to fit the same person because of a certain fact^ which fact was not known, nor in being, when the names were in- vented. If we want to know what the fact is, we shall find the clue to it in the connotation of the names. A bird or a stone, a man, or a wise man, means simply, an object having such and such attributes. The real meaning of the word man, is those at- tributes, and not Smith, Brown, and the remainder of the individuals. The word mortal^ in like manner connotes a certain attribute or attributes ; and when we say. All men are mortal, the meaning of the proposition is, that all beings which possess the one set of attributes, possess also the other. If, in our experience, the attributes connoted by man are always accompanied by the attribute connoted by mortal^ it will follow as a consequence, that the class man will be wholly included in the class mortal^ and that mortal will be a name of all things of which man is a name: but why? Those objects are brought under the name, by possessing the attributes connoted by it: but their possession of the attributes is the real condition on which IMPORT OF PROPOSITIONS. 77 the truth of the pro])ORition dopoiids ; not tlxnr Ixmiis: calk;*! l)y tho iiaino. Connotativo names do not pi-eeede, but follow, the attribut(!S which th(,'y connote. If one attribute lia})pens to be always found in conjun(;tion witli anotlier attribute, the concrete names which answer to those attributes will of course be predicable of the same subjects, and may be said, in Ilol>bes's language (in the propriety of which on this occasion I fully concur), to be two names for the same things. But the possibility of a concurrent appli- cation of the two names, is a mere consequence of the conjunction between tlie two attributes, and was, in most cases, never thought of when the names were introduced and their signification fixed. That tlie diamond is combustible, was a proposition certainly not dreamed of when the words Diamond and Combustible first received their meaning; and could not have been discovered by the most ingenious and refined analysis of the sig- nification of those words. It was found out by a very different process, namely, by exerting the senses, and learning from them, that the attribute of combustibility existed in the diamonds upon which tlie experiment was tried ; the number or character of the experiments being such, that wdiat was true of those individuals might be concluded to be true of all sub- stances "called by the name," that is, of all substances possessing the at- tributes which the name connotes. The assertion, therefore, when ana- lyzed, is, that wherever we find certain attributes, there will be found a cer- tain other attribute : which is not a question of the signification of names, but of laws of nature; the order existing among phenomena. § 3. Although Hobbes's theory of Predication has not, in the terms in which he stated it, met with a very favorable reception from subsequent thinkers, a theory virtually identical with it, and not by any means so per- spicuously expressed, luay almost be said to have taken the rank of an es- tablished opinion. The most generally received notion of Predication de- cidedly is that it consists in referring something to a class, i. e., either pla- cing an individual under a class, or placing one class under another class. Thus, the proposition, Man is mortal, asserts, according to this view of it, that the class man is included in the class mortal. "Plato is a philoso- pher," asserts that the individual Plato is one of those who compose the class philosopher. If the proposition is negative, then instead of placing something in a class, it is said to exclude something from a class. Thus, if the following be the proposition. The elephant is not carnivorous ; what is asserted (according to this theory) is, that the elephant is excluded from the class carnivorous, or is not numbered among the things comprising that class. There is no real difference, except in language, between this theory of Predication and the theory of Hobbes. For a class is absolutely noth- ing but an indefinite number of individuals denoted by a general name. The name given to them in common, is what makes them a class. To re- fer any thing to a class, therefore, is to look upon it as one of the things which are to be called by that common name. To exclude it from a class, is to say that the common name is not applicable to it. How widely these views of predication have prevailed, is evident from this, that they are the basis of the celebrated dictum de omni et nullo. When the syllogism is resolved, by all who treat of it, into an inference that what is true of a class is true of all things whatever that belong to the class ; and when this is laid down by almost all professed logicians as the ultimate principle to which all reasoning owes its validity; it is clear that in the general estimation of logicians, the propositions of which reasonings 78 NAMES AND PROPOSITIONS. ;ire composed can be the expression of nothing but the process of dividing things into classes, and referring every thing to its proper class. This theory appears to me a signal example of a logical error very often committed in logic, that of varepov Trporipoy, or explaining a thing by some- thing which presupposes it. When I say that snow is white, I may and ought to be thinking of snow as a class, because I am asserting a proposi- tion as true of all snow: 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. When, in- deed, I have judged, or assented to the propositions, that snow is white, and that several other things are also white, I gradually begin to think of white objects as a class, including snow and those other things. But this is a conception which followed, not preceded, those judgments, and there- fore can not be given as an explanation of them. Instead of explaining the effect by the cause, this doctrine explains the cause by the effect, and is, I conceive, founded on a latent misconception of the nature of classification. There is a sort of language very generally prevalent in these discussions, which seems to suppose that classification is an arrangement and grouping of definite and known individuals : that when names were imposed, man- kind took into consideration all the individual objects in the universe, dis- tributed them into parcels or lists, and gave to the objects of each list a common name, repeating this operation toties quoties until they had invent- ed all the general names of which language consists ; which having been once done, if a question subsequently arises whether a certain general name can be truly predicated of a certain particular object, we have only (as it were) to read the roll of the objects upon which that name was con- ferred, and see whether the object about which the question arises is to be found among them. The framers of language (it would seem to be sup- posed) have predetermined all the objects that are to compose each class, and we have only to refer to the record of an antecedent decision. So absurd a doctrine will be owned by nobody when thus nakedly stated; but if the commonly received explanations of classification and naming do not imply this theory, it requires to be shown how they admit of being rec- onciled with any other. General names are not marks put upon definite objects ; classes are not made by drawing a line round a given number of assignable individuals. The objects which compose any given class are perpetually fluctuating. We may frame a class without knowing the individuals, or even any of the individuals, of which it may be composed ; we may do so while believing that no such individuals exist. If by the meaning of a general name are to be understood the things which it is the name of, no general name, ex- cept by accident, has a fixed meaning at all, or ever long retains the same meaning. The only mode in which any general name has a definite mean- ing, is by being a name of an indefinite variety of things ; namely, of all things, known or unknown, past, present, or future, which possess certain definite attributes. When, by studying not the meaning of words, but the phenomena of nature, we discover that these attributes are possessed by some object not previously known to possess them (as when chemists found that the diamond was combustible), we include this new object in the class ; but it did not already belong to the class. We place the indi- vidual in the class because the proposition is true; the proposition is not true because the object is placed in the class.* * Professor Bain remarks, in qualification of the statement in the text {Logic, i., 50), that IMPORT OF TROrOSITIONS. 79 Tt will appear hereafter, in treating of reasoning, how much the theory of that intellectual process has been' vitiated by the influence of these erro- neous notions, and by the habit which they exemplify of assimilating all the operations of the human understanding which have truth for their ob- ject, to processes of mere classification and naming. Unfortunately, the minds which have been entangled in this net are precisely those which have escaped the other cardinal error commented upon in the beginning of the present chapter. Since the revolution which dislodged Aristotle from the schools, logicians may almost be divided into those who have looked upon reasoning as essentially an affair of Ideas, and those who have looked upon it as essentially an affair of Names. Although, however, Hobbes's theory of Predication, according to the well-known remark of Leibnitz, and the avowal of Hobbes himself,* renders truth and falsity completely arbitrary, with no standard but the wiU of men, it must not be concluded that either Hobbes, or any of the other thinkers who have in the main agreed with him, did in fact consider the distinction between truth and error as less real, or attached less importance to it, than other people. To suppose that they did so would argue total unacquaintance with their other speculations. But this shows how little hold their doctrine possessed over their own minds. No person, at bot- tom, ever imagined that there was nothing more in truth than propriety of expression ; than using language in conformity to a previous convention. When the inquiry was brought down from generals to a particular case, it has always been acknowledged that there is a distinction between verbal and real questions ; that some false propositions are uttered from ignorance of the meaning of words, but that in others the source of the error is a misapprehension of things ; that a person who has not the use of language at all may form propositions mentally, and that they may be untrue — that is, he may believe as matters of fact what are not really so. This last ad- mission can not be made in stronger terms than it is by Hobbes himself,f though he will not allow such erroneous belief to be called falsity, but only error. And he has himself laid down, in other places, doctrines in which the true theory of predication is by implication contained. He distinctly the word Class has two meanings; "the class definite, and the class indefinite. The class definite is an enumeration of actual individuals, as the Peers of the Realm, the oceans of the globe, the known planets. . . . The class indefinite is unenumerated. Such classes are stars, planets, gold-bearing rocks, men, poets, virtuous. ... In this last acceptation of the word, class name and general name are identical. The class name denotes an indefinite num- ber of individuals, and connotes the points of community or likeness." The theory controverted in the text, tacitly supposes all classes to be definite. I have as- sumed them to be indefinite ; because, for the purposes of Logic, definite classes, as such, are almost useless ; though often serviceable as means of abridged expression. (Vide infra, book iii., chap, ii.) * "From hence also this may be deduced, that the first truths were arbitrarily made by those that first of all imposed names upon things, or received them from the imposition of oth- ers. For it is true (for example) that man is a living creature, but it is for this reason, that it pleased men to impose both these names on the same thing." — Computation or Logic, chap, iii., sect. 8. t " Men are subject to err not only in affirming and denying, but also in perception, and in silent cogitation. . . . Tacit errors, or the errors of sense and cogitation, are made by pass- ing from one imagination to the imagination of another different thing ; or by feigning that to be past, or future, which never was, nor ever shall be ; as when by seeing the image of the sun in water, we imagine the sun itself to be there ; or by seeing swords, that there has been, or shall be, fighting, because it uses to be so for the most part ; or when from promises we feign the mind of the promiser to be such and such ; or, lastly, when from any sign we vainly imagine something to be signified which is not. And errors of this sort are common to all things that have sense." — Computation or Logic, chap, v., sect. 1. 80 NAMES AND PROPOSITIONS. says that general names are given to things on account of their attributes, and that abstract names are the names of those attributes. " Abstract is that which in any subject denotes the cause of the concrete name And these causes of names are the same with the causes of our conceptions, namely, some power of action, or affection, of the thing conceived, which some call the manner by which any thing works upon our senses, but by most men they are called accidents.''''^ It is strange that having gone so far, he should not have gone one step further, and seen that what he calls the cause of the concrete name, is in reality the meaning of it; and that when we predicate of any subject a name which is given because of an at- tribute (or, as he calls it, an accident), our object is not to affirm the name, but, by means of the name, to affirm the attribute. § 4. Let the predicate be, as we have said, a connotative term ; and to take the simplest case first, let the subject be a proper name: "The sum- mit of Chimborazo is white." The word white connotes an attribute which is possessed by the individual object designated by the words " summit of Chimborazo ;" which attribute consists in the physical fact, of its exciting in human beings the sensation which we call a sensation of white. It will be admitted that, by asserting the proposition, we wish to communicate in- formation of that physical fact, and are not thinking of the names, except as the necessary means of making that communication. The meaning of the proposition, therefore, is, that the individual thing denoted by the sub- ject, has the attributes connoted by the predicate. If we now suppose the subject also to be a connotative name, the mean- ing expressed by the proposition has advanced a step further in complica- tion. Let us first suppose the proposition to be universal, as well as affirm- ative: "All men are mortal." In this case, as in the last, what the propo- sition asserts (or expresses a belief of) is, of course, that the objects de- noted by the subject (man) possess the attributes connoted by the predi- cate (mortal). But the characteristic of this case is, that the objects are no longer individually designated. They are pointed out only by some of their attributes : they are the objects called men, that is, possessing the at- tributes connoted by the name man ; and the only thing known of them may be those attributes : indeed, as the proposition is general, and the ob- jects denoted by the subject are therefore indefinite in number, most of them are not known individually at all. The assertion, therefore, is not, as before, that the attributes which the predicate connotes are possessed by any given individual, or by any number of individuals previously known as John, Thomas, etc., but that those attnbutes are possessed by each and ev- ery individual possessing certain other attributes; that whatever has the attributes connoted by the subject, has also those connoted by the predi- cate; that the latter set of attributes constantly accompany the former set. Whatever has the attributes of man has the attribute of mortality; mortal- ity constantly accompanies the attributes of man.f * Chap, iii., sect. 3. t To the preceding statement it has been objected, that " we naturally construe the subject of a proposition in its extension, and the predicate (which therefore may be an adjective) in its intension (connotation) : and that consequently co-existence of attributes does not, any more than the opposite theory of equation of groups, correspond with the living processes of thought and language," I acknowledge the distinction here drawn, which, indeed, I had my- self hud down and exemplified a few pages back (p. 77). But though it is true that we nat- urally "construe the subject of a proposition in its extension," this extension, or in other words, the extent of the class denoted by the name, is not apprehended or indicated directly. IMPORT OK PROPOSITION'S. 81 If it be reincmbercd that every attribute is (jroanded on some fact or ])henoineiioii, either of outward sense or of inward consciousness, and tliat to possess an attribute is another pln-ase for being the cause of, or forming part of, the fact or phenomenon upon which tlie attribute is grounded ; we may add one more step to complete the analysis. The proposition whicli asserts that one attribute always accompanies another attribute, really as- serts thereby no other thing than this, that one phenomenon always accom- panies another phenomenon ; insomuch that where we find the latter, we have assurance of the existence of the former. Thus, in the proi)osition. All men are mortal, the word man connotes the attributes which we ascribe to a certain kind of living creatures, on the ground of certain ])henomena which they exhibit, and which are partly physical phenomena, namely the impressions made on our senses by their bodily form and structure, and partly mental phenomena, namely the sentient and intellectual life which they have of their own. All this is understood when we utter the word man, by any one to whom the meaning of the word is known. Now, wlien we say, Man is mortal, we mean that wherever these various physical and mental phenomena are all found, there we have assurance that the other physical and mental phenomenon, called death, will not fail to take place. The proposition does not affirm token; for the connotation of the word mortal goes no further than to the occurrence of the j^heno.menon at some time or other, leaving the particular time undecided. § 5. We have already proceeded far enough, not only to demonstrate the error of Hobbes, but to ascertain the real import of by far the most numer- ous class of propositions. The object of belief in a proposition, when it asserts any thing more than the meaning of words, is generally, as in the cases which we have examined, either the co-existence or the sequence of two phenomena. At the very commencement of our inquiry, we found that every act of belief implied two Things : we have now ascertained what, in the most frequent case, these two things are, namely, two Phenomena; in other words, two states of consciousness ; and what it is which the propo- sition affirms (or denies) to subsist between them, namely, either succession or co-existence. And this case includes innumerable instances which no one, previous to reflection, Avould think of referring to it. Take the follow- ing example : A generous person is worthy of honor. Who would expect to -recognize here a case of co-existence between phenomena? But so it is. The attribute which causes a person to be termed generous, is ascribed to him on the ground of states of his mind, and particulars of his conduct : both are phenomena: the former are facts of internal consciousness; the latter, so far as distinct from the former, are physical facts, or perceptions of the senses. Worthy of honor admits of a similar analysis. Honor, as here used, means a state of approving and admiring emotion, followed on occasion by corresponding outward acts. " Worthy of honor" connotes all this, together with our approval of the act of showing honor. All these are phenomena ; states of internal consciousness, accompanied or followed by physical facts. When we say, A generous person is worthy of honor. It is both apprehended and indicated solely through the attributes. In the ''Tiving processes of thought and language" the extension, though in this case really thought of (which in the case of the predicate it is not), is thought of only through the medium of what my acute and courteous critic terms the "intension." For further illustrations of this subject, see Examination of Sir William Hamilton's Phi- chap. xxii. 6 82 NAMES AND PROPOSITIONS. we affirm co-existence between the two complicated phenomena connoted by the two terms respectively. We affirm, that wherever and whenever the inward feelings and outward facts implied in the word generosity have place, then and there the existence and manifestation of an inward feeling, honor, would be followed in our minds by another inward feeling, approval. After the analysis, in a former chapter, of the import of names, many examples are not needed to illustrate the import of propositions. When there is any obscurity, or difficulty, it does not lie in the meaning of the proposition, but in the meaning of the names which compose it; in the extremely complicated connotation of many words; the immense multitude and prolonged series of facts which often constitute the phenomenon con- noted by a name. But where it is seen what the phenomenon is, there is seldom any difficulty in seeing that the assertion conveyed by the proposi- tion is, the co-existence of one such phenomenon with another ; or the suc- cession of one such phenomenon to another: so that where the one is found, we may calculate on finding the other, though perhaps not conversely. This, however, though the most common, is not the only meaning which propositions are ever intended to convey. In the first place, sequences and co-existences are not only asserted respecting Phenomena ; we make propo- sitions also respecting those hidden causes of phenomena, which are named substances and attributes. A substance, however, being to us nothing but either that which causes, or that which is conscious of, phenomena; and the same being true, mutatis mutandis, of attributes; no assertion can be made, at least with a meaning, concerning these unknown and unknowable en- tities, except in virtue of the Phenomena by which alone they manifest themselves to our faculties. When we say Socrates was contemporary with the Peloponnesian war, the foundation of this assertion, as of all assertions concerning substances, is an assertion concerning the phenomena which they exhibit — namely, that the series of facts by which Socrates manifested himself to mankind, and the series of mental states which constituted his sentient existence, went on simultaneously with the series of facts known by the name of the Peloponnesian war. Still, the proposition as commonly understood does not assert that alone; it asserts that the Thing in itself, the nouTnenon Socrates, was existing, and doing or experiencing those vari- ous facts during the same time. Co-existence and sequence, therefore, may be affirmed or denied not only between phenomena, but between noumena, or between a noumenon and phenomena. And both of noumena and of phenomena we may affirm simple existence. But what is a noumenon? An unknown cause. In affirming, therefore, the existence of a noumenon, we affirm causation. Here, therefore, are two additional kinds of fact, capable of being asserted in a proposition. Besides the propositions which assert Sequence or Co-existence, there are some which assert simple Exist- ence;* and others assert Causation, which, subject to the explanations * Professor Bain, in his Logic (i., 250), excludes Existence from the list, considering it as a, mere name. All propositions, he says, which predicate mere existence "are more or less ab- breviated, or elliptical: when fully expressed they fall under either co-existence or succession. When we say there exists a cons))iracy for a particular purpose, we mean that at the ])resent time a body of men have formed themselves into a society for a particular object ; which is ;i complex affirmation, resolvable into propositions of co-existence and succession (as causation). The assertion that the dodo docs not exist, points to the fact that this animal, once known in a certain place, has disappeared or become extinct; is no longer associated Avith the locality: all which may be better stated without the use of the verb 'exist.' There is a debated ques- tion — Does an ether exist? but the concrete form would be this — 'Are heat and light and IMPOUT OK IMiOl'Osri'IONS. 83 which will follow in tlic Tliinl Hook, must be considered i)rovisionally as a distinct and peculiar kind of assertion. § G. To these four kinds of matter-of-fact or assertion, must be added a fifth, Resemblance. This was a s])ecies of attribute which we found it impossible to analyze; for which no fnndmaentum, distinct from the ob- jects themselves, could be assigned. Besides propositions which assert a sequence or co-existence between two phenomena, there are therefore also propositions which assert resemblance between them; as, This color is like that color; The heat of to-day is equal to the heat of yesterday. It is true that such an assertion might with some plausibility be brought within the description of an affirmation of sequence, by considering it as an asser- tion that the simultaneous contemplation of the two colors is followed by a specific feeling termed the feeling of resemblance. But there would be nothing gained by incumbering ourselves, especially in this place, with a generalization which may be looked upon as strained. Logic does not un- dertake to analyze mental facts into their ultimate elements. Resemblance between tw^o phenomena is more intelligible in itself than any explanation could make it, and under any classification must remain specifically distinct from the ordinary cases of sequence and co-existence. It is sometimes said, that all propositions whatever, of which the pred- icate is a general name, do, in point of fact, affirm or deny resemblance. All snch propositions affirm that a thing belongs to a class ; but things being- classed together according to their resemblance, every thing is of course classed with the things which it is supposed to resemble most; and thence, it may be said, when we affirm that Gold is a metal, or that Socrates is a man, the affirmation intended is, that gold resembles other metals, and Soc- othev radiant influences propagated by an ethereal medium diffused in space ;' which is a prop- osition of causation. In like manner the question of the Existence of a Deity can not be dis- cussed in that form. It is properly a question as to the First Cause of the Universe, and as to the continued exertion of that Cause in providential superintendence." (i., 407.) Mr. Bain thinks it "fictitious and unmeaning language" to carry up the classification of Nature to one summum genus, Being, or that which Exists ; since nothing can be perceived or apprehended but by wa}^ of contrast with something else (of whicli important truth, under the name of Law of Relativity, he has been in our time the principal expounder and champion), and we have no other class to oppose to Being, or fact to contrast with Existence. I accept fully Mr. Bain's Law of Eelativity, but I do not understand by it that to enable us to apprehend or be conscious of any fact, it is necessary that we should contrast it with some other positive fact. The antithesis necessary to consciousness need not, I conceive, be an an- tithesis between two positives ; it may be between one positive and its negative, Hobbes was undoubtedly right when he said that a single sensation indefinitely prolonged would cease to be felt at all; but simple intermission, without other change, would restore it to consciousness. In order to be conscious of heat, it is not necessary that we should pass to it from cold ; it suffices that we should pass to it from a state of no sensation, or from a sensation of some other kind. The relative opposite of Being, considered as a summum genus, is Nonentity, or Nothing ; and we have, now and then, occasion to consider and discuss things merely in con- trast with Nonentity. I grant that the decision of questions of Existence usually if not always depends on a pre- vious question of either Causation or Co-existence. But Existence is nevertheless a different thing from Causation or Co-existence, and can be predicated apart from them. The meaning of the abstract name Existence, and the connotation of the concrete name Being, consist, like the meaning of all other names, in sensations or states of consciousness : their pecidiarity i> that to exist, is to excite, or be capable of exciting, ani/ sensations or states of consciousness : no matter what, but it is indispensable that there should be some. It was from overlooking this that Hegel, finding that Being is an abstraction reached by thinking away all particular attributes, arrived at the self-contradictory proposition on which he founded all his philosophy, that Being is the same as Nothing. It is really the name of Something, taken in the most comprehensive sense of the word. 84 NAMES AND PROPOSITIONS. rates other men, more nearly than they resemble the objects contained in any other of the classes co-ordinate with these. There is some slight degree of foundation for this remark, but no more than a slight degree. The arrangement of things into classes, such as the class metal, or the class man, is grounded indeed on a resemblance among the things which are placed in the same class, but not on a mere general resemblance : the resemblance it is grounded on consists in the possession by all those things, of certain common peculiarities ; and those peculiarities it is which the terms connote, and which the propositions consequently as- sert ; not the resemblance. For though when I say. Gold is a metal, I say by implication that if there be any other metals it must resemble them, yet if there were no other metals I might still assert the proposition with the same meaning as at present, namely, that gold has the various properties implied in the word metal; just as it might be said, Christians are men, even if there were no men who were not Christians. Propositions, there- fore, in which objects are referred to a class because they possess the attri- butes constituting the class, are so far from asserting nothing but resem- blance, that they do not, properly speaking, assert resemblance at all. But we remarked some time ago (and the reasons of the remark will be more fully entered into in a subsequent Book*) that there is sometimes a convenience in extending the boundaries of a class so as to include things which possess in a very inferior degree, if in any, some of the characteris- tic properties of the class — provided they resemble that class more than any other, insomuch that the general propositions which are true of the class, will be nearer to being true of those things than any other equally general propositions. For instance, there are substances called metals which have very few of the properties by which metals are commonly rec- ognized ; and almost every great family of plants or animals has a few anom- alous genera or species on its borders, which are admitted into it by a sort of courtesy, and concerning which it has been matter of discussion to w^hat family they properly belonged. Now when the class-name is predicated of any object of this description, we do, by so predicating it, affirm resem- blance and nothing more. And in order to be scrupulously correct it ought to be said, that in every case in which we predicate a general name, we af- firm, not absolutely that the object possesses the properties designated by the name, but that it either possesses those properties, or if it does not, at any rate resembles the things which do so, more than it resembles any oth- er things. In most cases, however, it is unnecessary to suppose any such alternative, the latter of the two grounds being very seldom that on which the assertion is made : and when it is, there is generally some slight differ- ence in the form of the expression, as. This species (or genus) is consider- ed, or may be ranked, as belonging to such and such a family : we should hardly say positively that it does belong to it, unless it possessed unequiv- ocally the properties of which the class-name is scientifically significant. There is still another exceptional case, in which, though the predicate is the name of a class, yet in predicating it we affirm nothing but resemblance, the class being founded not on resemblance in any given particular, but on general unanalyzable resemblance. The classes in question are those into which our simple sensations, or other simple feelings, are divided. Sensa- tions of white, for instance, are classed together, not because we can take them to pieces, and say they are alike in this, and not alike in that, but be- * Book iv., chap. vii. IMPORT OF PROPOSITIONS. 85 cause we feel them to be alike altogether, though in different degrees. When, therefore, I say. The color I saw yesterday was a white color, or, The sensation I feel is one of tightness, in both cases the attribute I affirm of the color or of the other sensation is mere resemblance — simple likeness to sensations which I have had before, and which have had those names be- stowed upon them. The names of feelings, like other concrete general names, are connotative; but they connote a mere resemblance. When predicated of any individual feeling, the information they convey is that of its likeness to the other feelings which we have been accustomed to call by the same name. Thus much may suffice in illustration of the kind of prop- ositions in which the matter-of-fact asserted (or denied) is simple Resem- blance. Existence, Co-existence, Sequence, Causation, Resemblance : one or other of these is asserted (or denied) in every proposition which is not merely verbal. This five-fold division is an exhaustive classification of matters-of- fact ; of all things that can be believed, or tendered for belief ; of all ques- tions that can be propounded, and all answers that can be returned to them. Professor Bain* distinguishes two kinds of Propositions of Co-existence. " In the one kind, account is taken of Place ; they may be described as propositions of Order in Place." In the other kind, the co-existence which is predicated is termed by Mr. Bain Co-inherence of Attributes. " This is a distinct variety of Propositions of Co-existence. Instead of an arrangement in place with numerical intervals, we have the concurrence of two or more attributes or powers in the same part or locality. A mass of gold contains, in every atom, the concurring attributes that mark the substance — weight, hardness, color, lustre, incorrosibility, etc. An animal, besides having parts situated in place, has co-inhering functions in the same parts, exerted by the very same masses and molecules of its substance. . . . The Mind, which affords no Propositions of Order in Place, has co-inhering functions. We affirm mind to contain Feeling, Will, and Thought, not in local separa- tion, but in commingling exercise. The concurring properties of minerals, of plants, and of the bodily and the mental structure of animals, are united in affirmations of co-inherence." The distinction is real and important. But, as has been seen, an Attri- bute, when it is any thing but a simple unanalyzable Resemblance between the subject and some other things, consists in causing impressions of some sort on consciousness. Consequently, the co-inherence of two attributes is but the co-existence of the two states of consciousness implied in their meaning : with the difference, however, that this co-existence is sometimes potential only, the attribute being considered as in existence, though the fact on w^hich it is grounded may not be actually, but only potentially pres- ent. Snow, for instance, is, with great convenience, said to be white even in a state of total darkness, because, though we are not now conscious of the color, we shall be conscious of it as soon as morning breaks. Co-in- herence of attributes is therefore still a case, though a complex one, of co-existence of states of consciousness ; a totally diff6rent thing, however, from Order in Place. Being a part of simultaneity, it belongs not to Place but to Time. We may therefore (and we shall sometimes find it a convenience) instead of Co-existence and Sequence, say, for greater particularity, Order in Place and Order in Time : Order in Place being a specific mode of co-existence, *io^zc, i., 103-105. 86 NAMES AND PROPOSITIONS. not necessary to be more particularly analyzed here ; while the mere fact of co-existence, whether between actual sensations, or between the potentiali- ties of causing them, known by the name of attributes, may be classed, to- gether with Sequence, under the head of Order in Time. § 7. In the foregoing inquiry into the import of propositions, we have thought it necessary to analyze directly those alone, in which the terms of the proposition (or the predicate at least) are concrete terms. But, in do- ing so, we have indirectly analyzed those in which the terms are abstract. The distinction between an abstract term and its corresponding concrete, does not turn upon any difference in what they are appointed to signify; for the real signification of a concrete general name is, as we have so often said, its connotation ; and what the concrete term connotes, forms the en- tire meaning of the abstract name. Since there is nothing in the import of an abstract name which is not in the import of the corresponding con- crete, it is natural to suppose that neither can there be any thing in the im- port of a proposition of which the terras are abstract, but what there is in some proposition which can be framed of concrete terms. And this presumption a closer examination will confirm. An abstract name is the name of an attribute, or combination of attributes. The cor- responding concrete is a name given to things, because of, and in order to express, their possessing that attribute, or that combination of attributes. When, therefore, we predicate of any thing a concrete name, the attribute is what we in reality predicate of it. But it has now been shown that in all propositions of which the predicate is a concrete name, what is really predicated is one of five things : Existence, Co-existence, Causation, Se- quence, or Resemblance. An attribute, therefore, is necessarily either an existence, a co-existence, a causation, a sequence, or a resemblance. When a proposition consists of a subject and predicate which are abstract terms, it consists of terms which must necessarily signify one or other of these things. When we predicate of any thing an abstract name, we affirm of the thing that it is one or other of these five things ; that it is a case of Existence, or of Co-existence, or of Causation, or of Sequence, or of Re- semblance. It is impossible to imagine any proposition expressed in abstract terms, which can not be transformed into a precisely equivalent proposition in which the terms are concrete ; namely, either the concrete names which connote the attributes themselves, or the names of the fundmnenta of those attributes; the facts or phenomena on which they are grounded. To il- lustrate the latter case, let us take this proposition, of which the subject only is an abstract name, " Thoughtlessness is dangerous." Thoughtless- ness is an attribute, grounded on the facts which we call thoughtless ac- tions; and the proposition is equivalent to this. Thoughtless actions are dangerous. In the next example the predicate as vv^ell as the subject are abstract names : " Whiteness is a color ;" or " The color of snow is a white- ness." These attributes being grounded on sensations, the equivalent prop- ositions in the concrete would be. The sensation of white is one of the sen- sations called those of color — The sensation of sight, caused by looking at snow, is one of the sensations called sensations of white. In these proposi- tions, as we have before seen, the matter-of-fact asserted is a Resemblance. In the following examples, the concrete terms are those which directly cor- respond to the abstract names ; connoting the attribute which these de- note. " Prudence is a virtue :" this may be rendered, " All prudent per- IMPORT OF rUOI'OSITIOX.S. 87 sons, in so far as prudent, are vii'tuous:" "Courage is deservini^ of hon- or;" thus," All courag-eous pcM-sons are deserving of honor 171 so far as they are courageous:" whicli is ecpiivalent to this — "All courageous jx'rsons deserve an addition to the honor, or a diminution of the disgrace, which would attach to them on other grounds." In order to throw still further light upon the import of j)ro])Ositions of which the terms are abstract, we will subject one of the exinnples given above to a minuter analysis. The i)roposilion we shall select is the follow- ing: "Prudence is a virtue." Let us substitute for the word virtue an equivalent but more definite expression, such as " a mental quality beneficial to society," or " a mental quality pleasing to God," or wliatever else we adopt as the definition of virtue. What the proposition asserts is a se- quence, accompanied with causation ; namely, that benefit to society, or that the approval of God, is consequent on, and caused by, prudence. Here is a sequence; but between what? We understand the consequent of the sequence, but we have yet to analyze the antecedent. Prudence is an at- tribute ; and, in connection with it, two things besides itself are to be con- sidered ; prudent persons, who are the subjects of the attribute, and pru- dential conduct, which may be called tlie foundation of it. Now is either of these the antecedent? and, first, is it meant, that the approval of God, or benefit to society, is attendant upon all prudent persons f No ; except in so far as they are prudent; for prudent persons who are scoundrels can seldom, on the whole, be beneficial to society, nor can they be acceptable to a good being. Is it upon prudential conduct^ then, that divine approbation and benefit to mankind are supposed to be invariably consequent ? Neither is this the assertion meant, when it is said that prudence is a virtue ; ex- cept with the same reservation as before, and for the same reason, namely, that prudential conduct, although in so far as it is prudential it is benefi- cial to society, may yet, by reason of some other of its qualities, be produc- tive of an injury outweighing the benefit, and deserve a displeasure exceed- ing the approbation which would be due to the prudence. Neither the substance, therefore (viz., the person), nor the phenomenon (the conduct), is an antecedent on which the other term of the sequence is universally consequent. But the proposition, " Prudence is a virtue," is a universal ju-oposition. What is it, then, upon wdiich the proposition affirms the ef- fects in question to be universally consequent? Upon that in the person, and in the conduct, wdiich causes them to be called prudent, and which is equally in them wdien the action, though prudent, is wicked ; namely, a cor- rect foresight of consequences, a just estimation of their importance to the object in view, and repression of any unreflecting impulse at variance with the deliberate purpose. These, which are states of the person's mind, are the real antecedent in the sequence, the real cause in the causation, asserted by the proposition. But these are also the real ground, or foundation, of the attribute Prudence; since wherever these states of mind exist we may predicate prudence, even before we know whether any conduct has fol- lowed. And in this manner every assertion respecting an attribute, may be transformed into an assertion exactly equivalent respecting the fact or phenomenon which is the ground of the attribute. And no case can be assigned, where that which is predicated of the fact or phenomenon, docs not belong to one or other of the five species formerly enumerated: it is either simple Existence, or it is some Sequence, Co-existence, Causation, or Resemblance. And as these five are the only things which can be aflirmed, so are they 88 NAMES AND PROPOSITIONS. the only things which can be denied. " No horses are web-footed " denies that the attributes of a horse ever co-exist with web-feet. It is scarcely necessary to apply the same analysis to Particular affirmations and nega- tions. " Some birds are web-footed," affirms that, with the attributes con- noted by hird^ the phenomenon web-feet is sometimes co-existent: "Some birds are not web-footed," asserts that there are other instances in which this co-existence does not have place. Any further explanation of a thing which, if the previous exposition has been assented to, is so obvious, may here be spared. CHAPTER VI. OF PROPOSITIONS MERELY YEEBAL. § 1. As a preparation for the inquiry which is the proper object of Logic, namely, in what manner propositions are to be proved, we have found it necessary to inquire what they contain which requires, or is sus- ceptible of, proof ; or (which is the same thing) what they assert. In the course of this preliminary investigation into the import of Propositions, we examined the opinion of the Conceptualists, that a proposition is the expression of a relation between two ideas; and the doctrine of the ex- treme Nominalists, that it is the expression of an agreement or disagree- ment between the meanings of two names. We decided that, as general theories, both of these are erroneous ; and that, though propositions may be made both respecting names and respecting ideas, neither the one nor the other are the subject-matter of Propositions considered generally. We then examined the different kinds of Propositions, and found that, with the exception of those which are merely verbal, they assert five different kinds of matters of fact, namely, Existence, Order in Place, Order in Time, Causa- tion, and Resemblance ; that in every proposition one of these five is either affirmed, or denied, of some fact or phenomenon, or of some object the un- known source of a fact or phenomenon. In distinguishing, however, the different kinds of matters of fact asserted in propositions, we reserved one class of propositions, which do not relate to any matter of fact, in the proper sense of the term at all, but to the meaning of names. Since names and their signification are entirely arbi- trary, such propositions are not, strictly speaking, susceptible of truth or falsity, but only of conformity or disconformity to usage or convention ; and all the proof they are capable of, is proof of usage; proof that the words have been employed by others in the acceptation in which the speak- er or writer desires to use them. These propositions occupy, however, a conspicuous place in philosophy; and their nature and characteristics are of as much importance in logic, as those of any of the other classes of prop- ositions previously adverted to. If all propositions respecting the signification of words were as simple and unimportant as those which served us for examples when examining Hobbes's theory of predication, viz., those of which the subject and predi- cate are proper names, and which assert only that those names have, or that they have not, been conventionally assigned to the same individual, there would be little to attract to such propositions the attention of phi- loso))hers. But the class of merely verbal propositions embraces not only much more than these, but much more than any propositions which at first VERBAL AND REAL I'KOl'OSITIONS. 89 sight pr»esent tlicmselvcs as verbal ; comprcliciidiiiii; a kind of assertions which have been regarded not only as relating to things, ]>ut as having actually a more intimate relation with them than any other ])ro|)ositions whatever. The student in philosophy will ])erceive tliat I allude to tlie distinction on which so much stress was laid by tlie sclioolmen, and wliich has been retained either under the same or under other names by most metaphysicians to the present day, viz., between what were called essential, and what were called accidental, propositions, and between essential and accidental properties or attributes. § 2. Almost all metaphysicians prior to Locke, as well as many since his time, have made a great mystery of Essential Predication, and of predi- cates which are said to be of the essence of the subject. The essence of a thing, they said, was that without which the thing could neither be, nor be conceived to be. Thus, rationality was of the essence of man, because without rationality, man could not be conceived to exist. The different attributes which made up the essence of the thing were called its essential properties ; and a proposition in which any of these were predicated of it was called an Essen-tial Proposition, and was considered to go deeper into the nature of the thing, and to convey more important information respect- ing it, than any other proposition could do. All properties, not of the es- sence of the thing, were called its accidents ; were supposed to have noth- ing at all, or nothing comparatively, to do with its inmost nature; and the propositions in which any of these were predicated of it were called Acci- dental Propositions. A connection may be traced between this distinction, which originated with the schoolmen, and the well-known dogmas of sub- stantice secundm or general substances, and suhstantial forms, doctrines which under varieties of language pervaded alike the Aristotelian and the Platonic schools, and of which more of the spirit has come down to mod- ern times than might be conjectured from the disuse of the phraseology. The false views of the nature of classification and generalization which pre- vailed among the schoolmen, and of which these dogmas were the technical expression, afford the only explanation which can be given of their having misunderstood the real nature of those Essences which held so conspicuous a place in their philosophy. They said, truly, that man can not be con- ceived without rationality. But though man can not, a being may be con- ceived exactly like a man in all points except that one quality, and those others which are the conditions or consequences of it. All, therefore, whieh is really true in the assertion that man can not be conceived without ration- ality, is only, that if he had not rationality, he would not be reputed a man. There is no impossibility in conceiving the thing, nor, for aught we know, in its existing: the impossibility is in the conventions of language, which will not allow the thing, even if it exist, to be called by the name which is reserved for rational beings. Rationality, in short, is involved in the mean- ing of the word man : is one of the attributes connoted by the name. The essence of man, simply means the whole of the attributes connoted by the word ; and any one of those attributes taken singly, is an essential property of man. But these reflections, so easy to ns, would have been difficult to persons who thought, as most of the later Aristotelians did, that objects were made what they were called, that gold (for instance) was made gold, not by the possession of certain properties to which mankind have chosen to attach that name, but by participation in the nature of a general substance, called 90 NAMES AND PROPOSITIONS. gold in general, which substance, together with all the properties that be- longed to it, inhered in every individual piece of gold.* As they did not consider these universal substances to be attached to all general names, but only to some, they thought that an object borrowed only a part of its prop- erties from a universal substance, and that the rest belonged to it individu- ally : the former they called its essence, and the latter its accidents. The scholastic doctrine of essences long survived the theory on which it rested, that of the existence of real entities corresponding to general terms ; and it was reserved for Locke, at the end of the seventeenth century, to convince philosophers that the supposed essences of classes were merely the signifi- cation of their names; nor, among the signal services which his writings rendered to philosophy, was there one more needful or more valuable. Now, as the most familiar of the general names by which an object is designated usually connotes not one only, but several attributes of the ob- ject, each of which attributes separately forms also the bond of union of some class, and the meaning of some general name ; we may predicate of a name which connotes a variety of attributes, another name which connotes only one of these attributes, or some smaller number of them than all. In such cases, the universal affirmative proposition will be true ; since what- ever possesses the whole of any set of attributes, must possess any part of that same set. A proposition of this sort, however, conveys no informa- tion to any one who previously understood the whole meaning of the terms. The propositions. Every man is a corporeal being. Every man is a living creature. Every man is rational, convey no knowledge to any one who was already aware of the entire meaning of the word man, for the meaning of the word includes all this : and that every man has the attributes connoted by all these predicates, is already asserted when he is called a man. Now, of this nature are all the propositions which have been called essential. They are, in fact, identical propositions. It is true that a proposition which predicates any attribute, even though it be one implied in the name, is in most cases understood to involve a tacit assertion that there exists a thing corresponding to the name, and possess- ing the attributes connoted by it ; and this implied assertion may convey information, even to those who understood the meaning of the name. But all information of this sort, conveyed by all the essential propositions of which man can be made the subject, is included in the assertion. Men exist. And this assumption of real existence is, after all, the result of an imper- fection of language. It arises from the ambiguity of the copula, which, in addition to its proper office of a mark to show that an assertion is made, is also, as formerly remarked, a concrete word connoting existence. The act- ual existence of the subject of the proposition is therefore only apparently, not really, implied in the predication, if an essential one : we may say, A ghost is a disembodied spirit, without believing in ghosts. But an acci- dental, or non-essential, affirmation, does imply the real existence of the subject, because in the case of a non-existent subject there is nothing for the proposition to assert. Such a proposition as. The ghost of a murdered person haunts the couch of the murderer, can only have a meaning if un- derstood as implying a belief in ghosts ; for since the signification of the * The doctrines which prevented the real meaning of Essences from heing understood, had not assumed so settled a shape in the time of Aristotle and his immediate followers, as was afterward given to them by the Realists of the Middle Ages. Aristotle himself (in his Trea- tise on the Categories) expresslv denies that the 6tvTtqaL ouatat, or Substantiie Seeunda), in- here in a subject. They are only, he says, predicated of it. VERBAL AND REAL PROPOSITIONS. 91 word ghost implies nothing of tho kind, llio speaker eitlier menns notliiiig, or means to assert a thing which lie u islies to be believed to ha\e really taken place. It will be hereafter seen that when any im])ortant consequences seem to follow, as in mathematics, from an essential ])roposition, or, in otlier words, from a proposition involved in the meaning of a name, what tliey really iiow from is the tacit assumption of the real existence of the objects so named. Apart from this assumption of real existence, the class of proposi- tions in which the predicate is of the essence of the subject (that is, in which the predicate connotes the whole or part of what the subject con- notes, but nothing besides) answer no purpose but that of unfolding the whole or some part of the meaning of the name, to those who did not pre- viously know it. Accordingly, the most useful, and in strictness the only useful kind of essential propositions, are Definitions : which, to be com- plete, should unfold the whole of what is involved in the meaning of the word defined ; that is (when it is a connotative word), the whole of what it connotes. In defining a name, however, it is not usual to specify its entire connotation, but so much only as is sufiicient to mark out the objects usu- ally denoted by it from all other known objects. And sometimes a merely accidental property, not involved in the meaning of the name, answers this purpose equally well. The various kinds of definition which these distinc- tions give rise to, and the purposes to which they are respectively subserv- ient, will be minutely considered in the proper place. g 3. According to the above view of essential propositions, no proposi- tion can be reckoned such which relates to an individual by name, that is, in which the subject is a proper name. Individuals have no essences. When the schoolmen talked of the essence of an individual, they did not mean the properties implied in its name, for the names of individuals imply no properties. They regarded as of the essence of an individual, whatever was of the essence of the species in which they were accustomed to place that individual; i. e., of the class to which it was most familiarly referred, and to which, therefore, they conceived that it by nature belonged. Thus, because the proposition Man is a rational being, was an essential proposi- tion, they affirmed the same thing of the proposition, Julius Caesar is a rational being. This followed very naturally if genera and species were to be considered as entities, distinct from, but inhering in, the individuals composing them. If man was a substance inhering in each individual man, the essence of man (whatever that might mean) was naturally sup- posed to accompany it; to inhere in John Thompson, and to form the common essence of Thompson and Julius CjBsar. It might then be fairly said, that rationality, being of the essence of Man, was of the essence also of Thompson. But if Man altogether be only the individual men and a name bestowed upon them in consequence of certain common properties, what becomes of John Thompson's essence ? A fundamental error is seldom expelled from philosophy by a single vic- tory. It retreats slowly, defends every inch of ground, and often, after it has been driven from the open country, retains a footing in some remote fastness. The essences of individuals were an unmeaning figment arising from a misapprehension of the essences of classes, yet even Locke, when he extirpated the parent error, could not shake himseli free from that which was its fruit. He distinguished two sorts of essences, Keal and Xominal. His nominal essences were the essences of classes, explained nearly as we 92 NAMES AND PROPOSITIONS. have now explained them. ISTor is any thing wanting to render the third book of Locke's Essay a nearly unexceptional treatise on the connotation of names, except to free its language from the assumption of what are called Abstract Ideas, which unfortunately is involved in the phraseology, though not necessarily connected with the thoughts contained in that im- mortal Third Book.* But besides nominal essences, he admitted real es- sences, or essences of individual objects, which he supposed to be the causes of the sensible properties of those objects. We know not (said he) what these are (and this acknowledgment rendered the fiction comparatively in- nocuous) ; but if we did, we could, from them alone, demonstrate the sen- sible properties of the object, as the properties of the triangle are demon- strated from the definition of the triangle. I shall have occasion to revert to this theory in treating of Demonstration, and of the conditions under which one property of a thing admits of being demonstrated from another property. It is enough here to remark that, according to this definition, the real essence of an object has, in the progress of physics, come to be conceived as nearly equivalent, in the case of bodies, to their corpuscular structure : what it is now supposed to mean in the case of any other en- tities, I would not take upon myself to define. § 4. An essential proposition, then, is one w^hich is purely verbal; which asserts of a thing under a particular name, only what is asserted of it in the fact of calling it by that name ; and which, therefore, either gives no information, or gives it respecting the name, not the thing. Non-essential, or accidental propositions, on the contrary, may be called Real Proposi- tions, in opposition to Verbal. They predicate of a thing some fact not involved in the signification of the name by which the proposition speaks of it; some attribute not connoted by that name. Such are all proposi- tions concerning things individually designated, and all general or partic- ular propositions in which the predicate connotes any attribute not con- noted by the subject. All these, if true, add to our knowledge: they con- vey information, not already involved in the names employed. When I am told that all, or even that some objects, which have certain qualities, or which stand in certain relations, have also certain other qualities, or stand in certain other relations, I learn from this proposition a new fact ; a fact not included in my knowledge of the meaning of the words, nor even of the existence of Things answering to the signification of those words. It is this class of propositions only which are in themselves instructive, or from which any instructive propositions can be inferred. f Nothing has probably contributed more to the opinion so long prevalent of the futility of the school logic, than the circumstance that almost all the examples used in the common school books to illustrate the doctrine of * The always acute and often profound author of An Outline of Sematology (Mr. B. H. Smart) justly says, "Locke Avill be much more intelligible, if, in the majority of places, we substitute 'the knowledge of for what he calls 'the Idea of" (p. 10). Among the many criticisms on Locke's use of the word Idea, this is tlie one which, as it appears to me, most nearly hits the mark ; and I quote it for the additional reason that it precisely expresses the point of difference respecting the import of Propositions, between my view and what I have spoken of as the Conceptualist view of them. Where a Conceptualist says that a name or a proposition expresses our Idea of a thing, I should generally say (instead of our Idea) our Knowledge, or Belief, concerning the thing itself t This distinction corresponds to that which is drawn by Kant and other metaphysicians between what tliey term analytic and synthetic, judgments ; tlie former being those which can be evolved from the meaning of the terms used. VERBAL AND REAL ri{()POSITI()NS. 03 predication and tliat of llio sylloi^ism, consist of essential [)i-oposi lions. Tliey were usually taken either from tlie branches or from the main trunk of the Prcdicamental Tree, which included nothing but what was of the es- sence of the species : Onme corpus est substantia, Ornne animal est eoyyras, Omnis homo est corpus, Omnis homo est animal, Omnis homo est rationalis, and so forth. It is far from wonderful that the syllogistic art should have been thought to be of no use in assisting correct reasoning, when almost the only propositions wdiich, in the hands of its professed teachers, it was em])loyed to prove, were such as every one assented to without proof the moment he comprehended the meaning of the words ; and stood exactly on a level, in point of evidence, with the premises from which they were drawn. I have, therefore, throughout this work, avoided the employment of essential propositions as examples, except where the nature of the prin- ciple to be illustrated specifically required them. § 5. With respect to propositions which do convey information — which assert something of a Thing, under a name that does not already presup- pose what is about to be asserted ; there are two different aspects in which these, or rather such of them as are general propositions, may be consid- ered : w^e may either look at them as portions of speculative truth, or as memoranda for practical use. According as we consider propositions in one or the other of these lights, their import may be conveniently expressed in one or in the other of two formulas. According to the formula which we have hitherto employed, and which is best adapted to express the import of the proposition as a portion of our theoretical knowledge. All men are mortal, means that the attributes of man are always accompanied by the attribute mortality : No men are gods, means that the attributes of man are never accompanied by the at- tributes, or at least never by all the attributes, signified by the word god. But when the proposition is considered as a memorandum for practical use, we shall find a different mode of expressing the same meaning better adapt- ed to indicate the oflUce which the proposition performs. The practical use of a proposition is, to apprise or remind us what we have to expect, in any individual case which comes within the assertion contained in the proposi- tion. In reference to this purpose, the proposition. All men are mortal, means that the attributes of man are emdence of, are a mark of, mortality; an indication by which the presence of that attribute is made manifest. No men are gods, means that the attributes of man are a mark or evidence that some or all of the attributes understood to belong to a god are not there; that where the former are, we need not expect to find the latter. These two forms of expression are at bottom equivalent; but the one points the attention more directly to what a proposition means, the latter to the manner in which it is to be used. Now it is to be observed that Reasoning (the subject to which we are next to proceed) is a process into which propositions enter not as ultimate results, but as means to the establishment of other propositions. We may expect, therefore, that the mode of exhibiting the import of a general prop- osition which show\s it in its application to practical use, will best express the' function which propositions perform in Eeasoning. And accordingly, in the theory of Reasoning, the mode of viewing the subject which consid- ers a Proposition as asserting that one fact or phenomenon is a mark or ev- idence of another fact or phenomenon, will be found almost indispensable. For the purposes of that Theory, the best mode of defining the import of 94 NAMES AND PKOPOSITIONS. a proposition is not the mode which shows most clearly what it is in itself, but that which most distinctly suggests the manner in which it may be made available for advancing from it to other propositions. CHAPTER VII. OF THE NATURE OP CLASSIFICATION, AND THE FIVE PEEDICABLES. § 1. In examining into the nature of general propositions, we hav6 ad- verted much less than is usual with logicians to the ideas of a Class, and Classification ; ideas which, since the Reahst doctrine of General Substances went out of vogue, have formed the basis of almost every attempt at a philosophical theory of general terms and general propositions. We have considered general names as having a meaning, quite independently of their being the names of classes. That circumstance is in truth accidental, it being wholly immaterial to the signification of the name whether there are many objects, or only one, to which it happens to be applicable, or whether there be any at all. God is as much a general term to the Christian or Jew as to the Polytheist; and dragon, hippogriff, chimera, mermaid, ghost, are as much so as if real objects existed, corresponding to those names. Every name the signification of which is constituted by attributes, is po- tentially a name of an indefinite number of objects; but it needs not be actually the name of any ; and if of any, it may be the name of only one. As soon as we employ a name to connote attributes, the things, be they more or fewer, which happen to possess those attributes, are constituted ipso facto a class. But in predicating the name we predicate only the at- tributes ; and the fact of belonging to a class does not, in many cases, come into view at all. Although, however, Predication does not presuppose Classification, and though the theory of Names and of Propositions is not cleared up, but only encumbered, by intruding the idea of classification into it, there is never- theless a close connection between Classification and the employment of General Names. By every general name which we introduce, we create a class, if there be any things, real or imaginary, to compose it; that is, any Things corresponding to the signification of the name. Classes, therefore, mostly owe their existence to general language. But general language, also, though that is not the most common case, sometimes owes its exist- ence to classes. A general, which is as much as to say a significant, name, is indeed mostly introduced because we have a signification to express by it; because we need a word by means of which to predicate the attributes Avhich it connotes. 'But it is also true that a name is sometimes introduced because we have found it convenient to create a class ; because we have thought it useful for the regulation of our mental operations, that a certain group of objects should be thought of together. A naturalist, for purposes connected with his particular science, sees reason to distribute the animal or vegetable creation into certain groups rather than into any others, and he requires a name to bind, as it were, each of his groups together. It must not, however, be supposed that such names, when introduced, differ in any respect, as to their mode of signification, from other connotative names. The classes which they denote are, as much as any other classes, constituted by certain common attributes, and their names ai-e significant of those attributes, and of nothing else. The names of Cuvier's classes and CLASSIFICATION AND THE I'UIODICAIiLES. 05 orders, Plantigrades, Dlgltigradefi, etc., ai-e as much the expression of at- tributes as if tliose names had precech'd, instead of ij^rovvn out of, his clas- sification of animals. The only peculiarity of the case is, that the conven- ience of classification was here the })i-imary motive for introducing the names; while in other cases the name is introduced as a means of t)redica- tion, and the formation of a class denoted by it is only an indirect conse- quence. The principles which ought to regulate Classification, as a logical process subservient to the investigation of truth, can not be discussed to any pur- pose until a much later stage of our inquiry. But, of Classification as re- sulting from, and implied in, the fact of employing general language, we can not forbear to treat here, without leaving the theory of general names, and of their employment in predication, mutilated and formless. § 2. This portion of the theory of general language is the subject of what is termed the doctrine of the Predicables; a set of distinctions hand- ed down from Aristotle, and his follower Porphyry, many of which have taken a firm root in scientific, and some of them even in popular, phraseolo- gy. The predicables are a fivefold division of General Names, not ground- ed as usual on a difference in their meaning, that is, in the attribute which they connote, but on a difference in the kind of class which they denote. We may predicate of a thing five different varieties of class-name : A genus of the thing {yhoo). A species {elloQ). A differentia {ha(f)opa). K proprium (unuy). An accidens {avix(DEj3r}K6Q). It is to be remarked of these distinctions, that they express, not what the predicate is in its own meaning, but what relation it bears to the subject of which it happens on the particular occasion to be predicated. There are not some names which are exclusively genera, and others w^hich are ex- clusively species, or differentias ; but the same name is referred to one or another predicable, according to the subject of which it is predicated on the particular occasion. Animal, for instance, is a genus with respect to man, or John; a species with respect to Substance, or Being. Rectangu- lar is one of the Differentiae of a geometrical square; it is merely one of the Accidentia of the table at which I am writing. The words genus, spe- cies, etc., are therefore relative terms ; they are names applied to certain predicates, to ex23ress the relation between them and some given subject : a relation grounded, as we shall see, not on what the predicate connotes, but on the class which it denotes, and on the place which, in some given classi- fication, that class occupies relatively to the particular subject. § 3. Of these five names, two. Genus and Species, are not only used by naturalists in a technical acceptation not precisely agreeing with their phil- osophical meaning, but have also acquired a popular acceptation, much more general than either. In this popular sense any two classes, one of which includes the whole of the other and more, may be called a Genus and a Species. Such, for instance, are Animal and Man ; Man and Mathe- matician. Animal is a Genus; Man and Brute are its two species; or we may divide it into a greater number of species, as man, horse, dog, etc. Biped, or two-footed animal, may also be considered a genus, of which 96 NAMES AND PROPOSITIONS. man and bird are two species. Taste is a genus, of which sweet taste, sour taste, salt taste, etc., are species. Yirtue is a genus; justice, prudence, courage, fortitude, generosity, etc., are its species. The same class which is a genus with reference to the sub-classes or species included in it, may be itself a species with reference to a more comprehensive, or, as it is often called, a superior genus. Man is a species with reference to animal, but a genus with reference to the species Mathe- matician. Animal is a genus, divided into two species, man and brute ; but animal is also a species, which, with another species, vegetable, makes up the genus, organized being. Biped is a genus with reference to man and bird, but a species with respect to the superior genus, animal. Taste is a genus divided into species, but also a species of the genus sensation. Vir- tue, a genus with reference to justice, temperance, etc., is one of the species of the genus, mental quality. In this popular sense the words Genus and Species have passed into common discourse. And it should be observed that in ordinary parlance, not the name of the class, but the class itself, is said to be the genus or species; not, of course, the class in the sense of each individual of the class, but the individuals collectively, considered as an aggregate whole; the name by which the class is designated being then called not the genus or species, but the generic or specific name. And this is an admissible form of expression ; nor is it of any importance which of the two modes of speaking we adopt, provided the rest of our language is consistent with it ; but, if we call the class itself the genus, w^e must not talk of predica- ting the genus. We predicate of man the name mortal ; and by predica- ting the name, we may be said, in an intelligible sense, to predicate what the name expresses, the attribute mortality ; but in no allowable sense of the word predication do we predicate of man the class mortal. We predi- cate of him the fact of belonging to the class. By the Aristotelian logicians, the terms genus and species were used in a more restricted sense. They did not admit every class which could be divided into other classes to be a genus, or every class which could be in- cluded in a larger class to be a species. Animal was by them considered a genus ; man and brute co-ordinate species under that genus : biped, how- ever, w^ould not have been admitted to be a genus with reference to man, but a proprium or accidens 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 classi- fication they considered some one class as the lowest or infima species. Man, for instance, was a lowest species. Any further divisions into which the class might be capable of being broken down, as man into white, black, and red man, or into priest and layman, they did not admit to be species. It has been seen, however, in the preceding chapter, that the distinction between the essence of a class, and the attributes or properties which are not of its essence — a distinction which has given occasion to so much ab- struse speculation, and to which so mysterious a character was formerly, and by many writers is still, attached — amounts to nothing more than the difference between those attributes of the class which are, and those which are not, involved in the signification of the class-name. As applied to in- dividuals, the word Essence, w^e found, has no meaning, except in connec- tion with the exploded tenets of the Realists ; and what the schoolmen chose to call the essence of an individual, was simply the essence of the class to which that individual was most familiarly referred. CLASSIFICATION AND THE PKEDICABLES. 97 Is there no difference, then, save this nierely verbal one, l)etween the classes which the schoohnen admitted to be genera or sj)ecies, and tliose to whicli they refused the title? Is it an error to regard some of the differ- ences which exist among objects as diff'erences in kind (genere or specie), and others only as differences in the accidents ? Were the schoolmen riglit or wrong in giving to some of the classes into which things may be divided, the name of kinds, and considering others as secondary divisions, ground- ed on differences of a comparatively superficial nature? Examination will show that the Aristotelians did mean something by this distinction, and something important ; but which, being but indistinctly conceived, was in- adequately expressed by the phraseology of essences, and the various other modes of speech to which they had recourse. § 4. It is a fundamental principle in logic, that the power of framing classes is unlimited, as long as there is any (even the smallest) difference to found a distinction upon. Take any attribute whatever, and if some things have it, and others have not, we may ground on the attribute a division of all things into two classes ; and we actually do so, the moment we create a name which connotes the attribute. The number of possible classes, there- fore, is boundless ; and there are as many actual classes (either of real or of imaginary things) as there are general names, positive and negative to- gether. But if we contemplate any one of the classes so formed, such as the class animal or plant, or the class sulphur or phosphorus, or the class white or red, and consider in what particulars the individuals included in the class differ from those >vhich do not come within it, we find a very remarkable diversity in this respect betw^een some classes and others. There are some classes, the things contained in w^hich differ from other things only in cer- tain particulars which may be numbered, w^hile others differ in more than can be numbered, more even than w^e need ever expect to know. Some classes have little or nothing in common to characterize them by, except precisely w^hat is connoted by the name : white things, for example, are not distinguished by any common properties except whiteness ; or if they are, it is only by such as are in some way dependent on, or connected with, whiteness. But a. hundred generations have not exhausted the common properties of animals or of plants, of sulphur or of phosphorus ; nor do we suppose them to be exhaustible, but proceed to new observations and ex- periments, in the full confidence of discovering new properties which were by no means implied in those we previously knew^ While, if any one were to propose for investigation the common properties of all things which are of the same color, the same shape, or the same specific gravity, the absurd- ity would be palpable. We have no ground to believe that any such com- mon properties exist, except such as may be shown to be involved in the supposition itself, or to be derivable from it by some law of causation. It appears, therefore, that the properties, on w^hich we ground our classes, sometimes exhaust all that the class has in common, or contain it all by some mode of implication ; but in other instances we make a selection of a few^ properties from among not only a greater number, but a number inex- haustible by us, and to which as we know no bounds, they may, so far as we are concerned, be regarded as infinite. There is no impropriety in saying that, of these two classifications, the one answers to a much more radical distinction in the things themselves, than the other does. And if any one even chooses to say that the one clas- 7 98 NAMES AND PROPOSITIONS. sification is made by nature, the other by us for our convenience, he will be right ; provided he means no more than this : Where a certain apparent difference between things (though perhaps in itself of little moment) an- swers to we know not what number of other differences, pervading not only their known properties, but properties yet undiscovered, it is not op- tional but imperative to recognize this difference as the foundation of a specific distinction ; while, on the contrary, differences that are merely finite and determinate, like those designated by the words white, black, or red, may be disregarded if the purpose for which the classification is made does not require attention to those particular properties. The differences, how- ever, are made by nature, in both cases ; while the recognition of those dif- ferences as grounds of classification and of naming, is, equally in both cases, the act of man : only in the one case, the ends of language and of classifica- tion would be subverted if no notice were taken of the difference, while in the other case, the necessity of taking notice of it depends on the impor- tance or unimportance of the particular qualities in which the difference happens to consist. Now, these classes, distinguished by unknown multitudes of properties, and not solely by a few determinate ones — which are parted off from one another by an unfathomable chasm, instead of a mere ordinary ditch with a visible bottom — are the only classes which, by the Aristotelian logicians, were considered as genera or species. Differences which extended only to a certain property or properties, and there terminated, they considered as differences only in the accidents of things; but where any class differed from other things by an infinite series of differences, known and unknown, they considered the distinction as one of kind, and spoke of it as being an esseiiticd difference, which is also one of the current meanings of that vague expression at the present day. Conceiving the schoolmen to have been justified in drawing a broad line of separation between these two kinds of classes and of class-distinctions, I shall not only retain the division itself, but continue to express it in their language. According to that language, the proximate (or lowest) Kind to w?iich any individual is referrible, is called its species. Conformably to this, Isaac Newton would be said to be of the species man. There are indeed numerous sub-classes included in the class man, to which Newton also belongs ; for example. Christian, and Englishman, and Mathematician. But these, though distinct classes, are not, in our sense of the term, distinct Kinds of men. A Christian, for example, differs from other human be- ings ; but he differs only in the attribute which the word expresses, namely, belief in Christianity, and whatever else that implies, either as involved in the fact itself, or connected with it through some law of cause and effect. We should never think of inquiring what properties, unconnected with Christianity, either as cause or effect, are common to all Christians and pe- culiar to them ; w^hile in regard to all Men, physiologists are perpetually carrying on such an inquiry; nor is the answer ever likely to be completed. Man, therefore, we may call a species ; Christian, or Mathematician, we can not. Note here, that it is by no means intended to imply that there may not be different Kinds, or logical species, of man. The various races and tem- peraments, the two sexes, and even the various ages, may be differences of kind, within our meaning of the term. I do not say that they are so. For in the progress of physiology it may almost be said to be made out, that the differences which really exist between different races, sexes, etc., follow CLASSIFICATION AND THE PREDICABLES. 99 as consequences, under laws of nature, from a small number of ])rimary differences wliich can be precisely determined, and which, as th(; phrase is, account for all the rest. If this be so, these are not distinctions in kind; no more than Christian, Jew, Mussulman, and Paii^an, a difference which also carries many consequences along with it. And in this way classes are often mistaken for real Kinds, which are afterward proved not to be so. But if it turned out that the differences were not capable of being thus ac- counted for, then Caucasian, Mongolian, Negro, etc., would be really differ- ent Kinds of human beings, and entitled to be ranked as species by the logician; though not by the naturalist. For (as already noticed) the word species is used in a different signification in logic and in natural history. By the naturalist, organized beings are not usually said to be of different species, if it is supposed that they have descended from the same stock. That, however, is a sense artificially given to the w^ord, for the technical purposes of a' particular science. To the logician, if a negro and a white man differ in the same manner (however less in degree) as a horse and a camel do, that is, if their differences are inexhaustible, and not referrible to any common cause, they are different species, whether they are descended from common ancestors or not. But if their differences can all be traced to climate and habits, or to some one or a few special differences in struc- ture, they are not, in the logician's view, specifically distinct. When the infima species^ or proximate Kind, to which an individual belongs, has been ascertained, the properties common to that Kind include necessarily the whole of the common proj^erties of every other real Kind to which the individual can be referrible. Let the individual, for example, be Socrates, and the proximate Kind, man. Animal, or living creature, is also a real kind, and includes Socrates ; but, since it likewise includes man, or in other words, since all men are animals, the properties common to ani- mals form a portion of the common properties of the sub-class, man. And if there be any class which includes Socrates without including man, that class is not a real Kind. Let the class, for example, be flat-nosed; that being a class which includes Socrates, without including all men. To de- termine whether it is a real Kind, w^e must ask ourselves this question: Have all flat-nosed animals, in addition to whatever is implied in their flat noses, any common properties, other than those which are common to all animals whatever? If they had; if a flat nose were a mark or index to an indefinite number of other peculiarities, not deducible from the former by an ascertainable law, then out of the class man we might cut another class, flat-nosed man, which, according to our definition, would be a Kind. But if we could do this, man would not be, as it was assumed to be, the proxi- mate Kind. Therefore, the properties of the proximate Kind do compre- hend those (whether known or unknown) of all other Kinds to which the individual belongs; which was the point we undertook to prove. And hence, every other Kind which is predicable of the individual, will be to the proximate Kind in the relation of a genus, according to even the popu- lar acceptation of the terms genus and species ; that is, it will be a larger class, including it and more. We are now able to fix the logical meaning of these terms. Every class which is a real Kind, that is, which is distinguished from all other classes by an indeterminate multitude of properties not derivable from one an- other, is either a genus or a species. A Kind which is not divisible into other Kinds, can not be a genus, because it has no species under it; but it is itself a species, both with reference to the individuals below and to the LOFC 100 NAMES AND PROPOSITIONS. genera above (Species Prsedicabilis and Species Subjicibilis). But every Kind which admits of division hito real Kinds (as animal into mammal, bird, fish, etc., or bird into various species of birds) is a genus to all below it, a species to all genera in which it is itself included. And here we may close this part of the discussion, and pass to the three remaining predica- bles, Differentia, Proprium, and Accidens. § 5. To begin with Differentia. This word is correlative with the words genus and species, and as all admit, it signifies the attribute which distin- guishes a given species from every other species of the same genus. This is so far clear : but we may still ask, which of the distinguishing attributes it signifies. For we have seen that every Kind (and a species must be a Kind) is distinguished from other Kinds, not by any one attribute, but by an indefinite number. Man, for instance, is a species of the genus animal : Rational (or rationality, for it is of no consequence here whether we use the concrete or the abstract form) is generally assigned by logicians as the Differentia ; and doubtless this attribute serves the purpose of distinction : but it has also been remarked of man, that he is a cooking animal ; the only animal that dresses its food. This, therefore, is another of the at- tributes by which the species man is distinguished from other species of the same genus : would this attribute serve equally well for a differentia ? The Aristotelians say No; having laid it down that the differentia must, like the genus and species, be of the esse7ice of the subject. And here we lose even that vestige of a meaning grounded in the nature of the things themselves, which may be supposed to be attached to the word essence when it is said that genus and species must be of the essence of the thing. There can be no doubt that when the schoolmen talked of the essences of things as opposed to their accidents, they had confusedly in view the distinction between differences of kind, and the differences which are not of kind; they meant to intimate that genera and species must be Kinds. Their notion of the essence of a thing was a vague notion of a something which makes it what it is, i. e., which makes it the Kind of thing that it is — which causes it to have all that variety of properties which distinguish its Kind. But when the matter came to be looked at more closely, nobody could discover what caused the thing to have all those prop- erties, nor even that there was any thing which caused it to have them. Logicians, however, not liking to admit this, and being unable to detect what made the thing to be what it was, satisfied themselves with what made it to be what it was called. Of the innumerable properties, known and unknown, that are common to the class man, a portion only, and of course a very small portion, are connoted by its name ; these few, however, will naturally have been thus distinguished from the rest either for their greater obviousness, or for greater supposed importance. These prop- erties, then, which were connoted by the name, logicians seized upon, and called ihenx the essence of the species ; and not stopping there, they af- firmed them, in the case of the infiina species, to be the essence of the in- dividual too ; for it was their maxim, that the species contained the " whole essence " of the thing. Metaphysics, that fertile field of delusion propa- gated by language, does not afford a more signal instance of such delusion. On this account it was that rationality, being connoted by the name man, was allowed to be a differentia of the class ; but the peculiarity of cook- ing their food, not being connoted, was relegated to the class of accidental properties. CLASSIFICATION AND THE J'llEDICAIiLES. 101 The distinction, therefore, between Differentia, Proprium, and Aceidenn, is not grounded in the nature of things, but in the connotation of names ; and we must seek it there, if we wisli to find wliat it is. From the fact that the genus inchides tlie species, in other words (denotes more than the S])ccies, or is predicable of a greater number of individuals, it follows that the species must connote more than the genus. It must connote all the attributes which the genus connotes, or there would be nothing to prevent it from denoting individuals not included in the genus. And it must connote something besides, otherwise it would include the whole genus. Animal denotes all the individuals denoted by man, and many more. Man, therefore, must connote all that animal connotes, other- wise there might be men who are not animals ; and it must connote some- thing more than animal connotes, otherwise all animals would be men. This surplus of connotation — this which the species connotes over and above the connotation of the genus — is the Differentia, or specific differ- ence ; or, to state the same proposition in other w^ords, the Differentia is that which must be added to the connotation of the genus, to complete the connotation of the species. The word man, for instance, exclusively of what it connotes in common with animal, also connotes rationahty, and at least some approximation to that external form which we all know, but which as we have no name for it considered in itself, we are content to call the human. The Differentia, or specific difference, therefore, of man, as referred to the genus animal, is that outward form and the possession of reason. The Aristotelians said, the possession of reason, without the outward form. But if they adhered to this, they w^ould have been obliged to call the Houyhnhnms men. The question never arose, and they w^ere never called upon to decide how such a case would have affected their notion of essentiality. However this may be, they were satisfied with taking such a portion of the differentia as suf- ficed to distinguish the species from all other existing things, though by so doing they might not exhaust the connotation of the name. § 6. And here, to prevent the notion of differentia from being restricted within too narrow limits, it is necessary to remark, that a species, even as referred to the same genus, will not always have the same differentia, but a different one, according to the principle and purpose which preside over the particular classification. For example, a naturalist surveys the various kinds of animals, and looks out for the classification of them most in ac- cordance with the order in which, for zoological purposes, he considers it desirable that we should think of them. With this view he finds it advisa- ble that one of his fundamental divisions should be into Avarm-blooded and cold-blooded animals ; or into animals wdiich breathe with lungs and those which breathe with gills ; or into carnivorous, and frugivorous or graminiv- orous ; or into those which walk on the flat part and those which walk on the extremity of the foot, a distinction on which two of Cuvier's families are founded. In doing this, the naturalist creates as many new classes ; which are by no means those to which the individual animal is familiarly and spon- taneously referred ; nor should we ever think of assigning to them so prom- inent a position in our arrangement of the animal kingdom, unless for a pre- conceived purpose of scientific convenience. And to the liberty of doing this there is no limit. In the examples we have given, most of the classes are real Kinds, since each of the peculiarities is an index to a multitude of properties belonging to the class which it characterizes : but even if the 102 NAMES AND PROPOSITIONS. case were otherwise — if the other properties of those classes could all be derived, by any process known to us, from the one peculiarity on which the class is founded — even then, if these derivative properties were of primaij importance for the purposes of the naturalist, he would be warranted in founding his primary divisions on them. If, however, practical convenience is a sufficient warrant for making the main demarkations in our arrangement of objects run in lines not coin- ciding with any distinction of Kind, and so creating genera and species in the popular sense which are not genera or species in the rigorous sense at all ; d fortiori must we be warranted, when our genera and species are real genera and species, in marking the distinction between them by those of their properties which considerations of practical convenience most strong- ly recommend. If we cut a species out of a given genus — the species man, for instance, out of the genus animal — with an intention on our part that the peculiarity by which we are to be guided in the application of the name man should be rationality, then rationality is the differentia of the species man. Suppose, however, that being naturalists, we, for the pur- poses of our particular study, cut out of the genus animal the same species man, but with an intention that the distinction between man and all other species of animal should be, not rationality, but the possession of "four incisors in each jaw, tusks solitary, and erect posture." It is evident that the w^ord man, when used by us as naturalists, no longer connotes rational- ity, but connotes the three other properties specified ; for that which we have expressly in view when we impose a name, assuredly forms part of the meaning of that name. We may, therefore, lay it down as a maxim, that wherever there is a Genus, and a Species marked out from that genus / by an assignable differentia, the name of the species must be connotative, and must connote the differentia ; but the connotation may be special — not involved in the signification of the term as ordinarily used, but given to it when employed as a term of art or science. The word Man in common use, connotes rationality and a certain form, but does not connote the num- ber or character of the teeth ; in the Linnsean system it connotes the num- ber of incisor and canine teeth, but does not connote rationality nor any particular form. The word ma7i has, therefore, two different meanings; though not commonly considered as ambiguous, because it happens in both cases to c^enote the same individual objects. But a case is conceivable in which the ambiguity would become evident : we have only to imagine that some new kind of animal were discovered, having Linnseus's three char- acteristics of humanity, but not rational, or not of the human form. In ordinary parlance, these animals would not be called men ; but in natural history they must still be called so by those, if any there should be, w^ho adhere to the Linnsean classification ; and the question would arise, whether the word should continue to be used in two senses, or the classification be given up, and the technical sense of the term be abandoned along with it. Words not otherwise connotative may, in the mode just adverted to, acquire a special or technical connotation. Thus the word whiteness, as we have so often remarked, connotes nothing; it merely denotes the at- tribute corresponding to a certain sensation : but if we are making a clas- sification of colors, and desire to justify, or even merely to point out, the particular place assigned to whiteness in our arrangement, we may define it "the color produced by the mixture of all the simple rays;" and this fact, though by no means implied in the meaning of the word whiteness as ordinarily used, but only known by subsequent scientific investigation, CLASSIFICATION AND THE TREDICABLES. 103 is part of its meaning in the j)articular essay or treatise, and Ijecomes tlie differentia of the species.* Tlie differentia, therefore, of a species may be defined to })e, tliat [jart of the connotation of the si)eciiic name, whetlier ordinary or special and tecli- nical, wliich distinguislies the species in (piestion from all other species of the genus to which on the particular occasion we are referring it. § 7. Having disposed of Genus, Species, and Differentia, we shall not find much difficulty in attaining a clear concei)tion of the distinction between the other two predicables, as well as between them and the first three. In the Aristotelian phraseology. Genus and Differentia are of the essence of the subject; by which, as we have seen, is really meant that the proper- ties signified by the genus and those signified by the differentia, form part of the connotation of the name denoting the si^ecies. Proprium and Ac- cidens, on the other hand, form no part of the essence, but are predicated of the species only accidentally. Both are Accidents, in the wider sense in which the accidents of a thing are opposed to its essence ; though, in the doctrine of the Predicables, Accidens is used for one sort of accident only, Proprium being another sort. Proprium, continue the schoolmen, is pred- icated accidentally, indeed, but necessarily ; or, as they further explain it, signifies an attribute which is not indeed part of the essence, but which flows from, or is a consequence of, the essence, and is, therefore, inseparably attached to the species ; e. g., the various properties of a triangle, which, though no part of its definition, must necessarily be possessed by whatever comes under that definition. Accidens, on the contrary, has no connection whatever with the essence, but may come and go, and the species still re- main what it was before. If a species could exist without its Propria, it must be capable of existing without that on which its Propria are neces- sarily consequent, and therefore without its essence, without that which con- stitutes it a species. But an Accidens, whether separable or inseparable from the species in actual experience, may be supposed separated, without the necessity of supposing any other alteration ; or at least, without sup- posing any of the essential properties of the species to be- altered, since with them an Accidens has no connection. A Proprium, therefore, of the species, may be defined, any attribute which belongs to all the individuals included in the species, and which, though not connoted by the specific name (either ordinarily if the classification we are considering be for ordinary purposes, or specially if it be for a special purpose), yet follows from some attribute which the name either ordinarily or specially connotes. One attribute may follow from another in two ways ; and there are con- sequently two kinds of Proprium. It may follow as a conchision follows premises, or it may follow as an effect follows a cause. Thus, the attribute of having the opposite sides equal, which is not one of those connoted by the word Parallelogram, nevertheless follows from those connoted by it, namely, from having the opposite sides straight lines and parallel, and the number of sides four. The attribute, therefore, of having the opposite sides equal, is a Proprium of the class parallelogram ; and a Proprium of the first kind, which follows from the connoted attributes by way of dem- * If we allow a diiferentia to what is not really a species. For the distinction of Kinds, in the sense explained by us, not being in any way applicable to attributes, it of course follows that although attributes may be put into classes, those classes can be admitted to be genera or species only by courtesy. 104 NAMES AND PKOPOSITIONS. onstration. The attribute of being capable of understanding language, is a Proprium of the species man, since without being connoted by the word, it follows from an attribute which the word does connote, viz., from the attribute of rationality. But this is a Proprium of the second kind, which follows by way of causation. How it is that one property of a thing fol- lows, or can be inferred, from another ; under what conditions this is pos- sible, and what is the exact meaning of the phrase ; are among the ques- tions which will occupy us in the two succeeding Books. At present it needs only be said, that whether a Proprium follows by demonstration or by causation, it follows necessarily ; that is to say, its not following would be inconsistent with some law which we regard as a part of the constitu- tion either of our thinking faculty or of the universe. § 8. Under the remaining predicable, Accidens, are included all attri- butes of a thing which are neither involved in the signification of the name (whether ordinarily or as a term of art), nor have, so far as we know, any necessary connection with attributes which are so involved. They are commonly divided into Separable and Inseparable Accidents. Inseparable accidents are those which — although we know of no connection between them and the attributes constitutive of the species, and although, therefore, so far as we are aware, they might be absent without making the name in- applicable and the species a different species — are yet never in fact known to be absent. A concise mode of expressing the same meaning is, that in- separable accidents are properties which are universal to the species, but not necessary to it. Thus, blackness is an attribute of a crow, and, as far as we know, a universal one. But if we were to discover a race of white birds, in other respects resembling crows, we should not say, These are not crows ; we should say. These are white crows. Crow, therefore, does not connote blackness ; nor, from any of the attributes which it does con- note, whether as a word in popular use or as a term of art, could blackness be inferred. Not only, therefore, can we conceive a white crow, but we know of no reason why such an animal should not exist. Since, how- ever, none but black crows are known to exist, blackness, in the present state of our knowledge, ranks as an accident, but an inseparable accident, of the species crow. Separable Accidents are those which are found, in point of fact, to be sometimes absent from the species; which are not only not necessary, but not even universal. They are such as do not belong to every individual of the species, but only to some individuals ; or if to all, not at all times. Thus the color of a European is one of the separable accidents of the spe- cies man, because it is not an attribute of all human creatures. Being- born, is also (speaking in the logical sense) a separable accident of the spe- cies man, because, though an attribute of all human beings, it is so only at one particular time. A fortiori those attributes which are not constant even in the same individual, as, to be in one or in another place, to be hot or cold, sitting or walking, must be ranked as separable accidents. DEFINITION. CHAPTER VIII. OF DEFINITION. § 1. One necessjiry part of the theory of Names and of Propositions re- mains to be treated of in this place : the theory of Definitions. As being tlie most important of the class of propositions which we have character- ized as purely verbal, they have already received some notice in the chapter preceding the last. But their fuller treatment was at that time postponed, because definition is so closely connected with classification, that, until the nature of the latter process is in some measure understood, the former can not be discussed to much purpose. The simplest and most correct notion of a Definition is, a proposition declaratory of the meaning of a word ; namely, either the meaning which it bears in common acceptation, or that wdiich the speaker or writer, for the particular purposes of his discourse, intends to annex to it. The definition of a word being the proposition which enunciates its meaning, words which have no meaning are unsusceptible of definition. Proper names, therefore, can not be defined. A proper name being a mere mark put upon an individual, and of which it is the characteristic property to be destitute of meaning, its meaning can not of course be declared; though w^e may indicate by language, as we might indicate still moi-e con- veniently by pointing with the finger, upon w^hat individual ^hat particular mark has been, or is intended to be, put. It is no definition of " John Thomson " to say he is " the son of General Thomson ;" for the name John Thomson does not express this. Neither is it any definition of " John Thomson " to say he is " the man now crossing the street." These propo- sitions may serve to make know^n who is the particular man to whom the name belongs, but that may be done still more unambiguously by pointing to him, wdiich, however, has not been esteemed one of the modes of defi- nition. In the case of connotative names, the meaning, as has been so often ob- served, is the connotation ; and the definition of a connotative name, is the proposition which declares its connotation. This might be done either di- rectly or indirectly. The direct mode would be by a proposition in this form: "Man " (or whatsoever the word may be) "is a name connoting such and such attributes," or " is a name w^hich, when predicated of any thing, signifies the possession of such and such attributes by that thing." Or thus : Man is every thing which possesses such and such attributes : Man is every thing which possesses corporeity, organization, life, rationality, and certain peculiarities of external form. This form of definition is the most precise and least equivocal of any; but it is not brief enough, and is besides too technical for common discourse. The more usual mode of declaring the connotation of a name, is to predi- cate of it another name or names of known signification, which connote the same aggregation of attributes. This may be done either by predicating of the name intended to be defined, another connotative name exactly syn- onymous, as, " Man is a human being," which is not commonh' accounted a 106 NAMES AND PROPOSITIONS. definition at all ; or by predicating two or more connotative names, which make up among them the whole connotation of the name to be defined. In this last case, again, we may either compose our definition of as many con- notative names as there are attributes, each attribute being connoted by one, as, Man is a corporeal, organized, animated, rational being, shaped so and so; or we employ names which connote several of the attributes at once, as, Man is a rational animal^ shaped so and so. The definition of a name, according to this view of it, is the sum total of all the essential propositions which can be framed with that name for their subject. All propositions the truth of which is implied in the name, all those which we are made aware of by merely hearing the name, are in- cluded in the definition, if complete, and may be evolved from it without the aid of any other premises ; whether the definition expresses them in two or three words, or in a larger number. It is, therefore, not without reason that Condifiac and other writers have afiirmed a definition to be an analysis. To resolve any complex whole into the elements of which it is compounded, is the meaning of analysis : and this we do when we replace one word which connotes a set of attributes collectively, by two or more which connote the same attributes singly, or in smaller grou23S. § 2. From this, however, the question naturally arises, in what manner are we to define a name which connotes only a single attribute : for in- stance, " white," which connotes nothing but whiteness ; " rational," which connotes nothing but the possession of reason. It might seem that the meaning of such names could only be declared in two ways ; by a synony- mous term, if any such can be found ; or in the direct way already alluded to : " White is a name connoting the attribute whiteness." Let us see, however, whether the analysis of the meaning of the name, that is, the breaking down of that meaning into several parts, admits of being carried farther. Without at present deciding this question, as to the word white, it is obvious that in the case of rational some further explanation may be given of its meaning than is contained in the proposition, " Rational is that which possesses the attribute of reason ;" since the attribute reason itself admits of being defined. And here we must turn our attention to the def- initions of attributes, or rather of the names of attributes, that is, of ab- stract names. In regard to such names of attributes as are connotative, and express attributes of those attributes, there is no difficulty: like other connotative names, they are defined by declaring their connotation. Thus the word fault may be defined, " a quality productive of evil or inconvenience." Sometimes, again, the attribute to be defined is not one attribute, but a union of several : we have only, therefore, to put together the names of all the attributes taken separately, and we obtain the definition of the name which belongs to them all taken together; a definition which will corre- spond exactly to that of the corresponding concrete name. For, as we de- fine a concrete name by enumerating the attributes which it connotes, and as the attributes connoted by a concrete name form the entire signification of the corresponding abstract name, the same enumeration will serve for the definition of both. Thus, if the definition of a human being be this, " a being, corporeal, animated, rational, shaped so and so," the definition of humanity will be corporeity and animal life, combined with rationality, and with such and such a shape. When, on the other hand, the abstract name does not express a compli- DEFINITION. 107 ■cation of attributes, but a single attribute, we must remember tliat evoi-y attribute is grounded on some fact or phenomenon, from vvliicli, and whicli alone, it derives its meaning. To that fact or phenomenon, called in ;i for- mer chapter the foundation of the attribute, we must, therefore, have re- course for its definition. Now, the foundation of the attribute may Ikj a phenomenon of any degree of complexity, consisting of many different parts, either co-existent or in succession. To obtain a definition of the attri- bute, we must analyze the plienomenon into these parts. Eloquence, for example, is the name of one attribute only ; but this attribute is grounded on external effects of a complicated nature, flowing from acts of tlie person to whom we ascribe the attribute; and by resolving this phenomenon of causation into its two parts, the cause and the effect, we obtain a definition of eloquence, viz. the power of influencing the feelings by speech or writing. A name, therefore, whether concrete or abstract, admits of definition, provided we are able to analyze, that is, to distinguish into parts, the attri- bute or set of attributes which constitute the meaning both of the concrete name and of the corresponding abstract: if a set of attributes, by enumer- ating them; if a single attribute, by dissecting the fact or phenomenon (whether of perception or of internal consciousness) which is the foundation of the attribute. But, further, even when the fact is one of our simple feeUngs or states of consciousness, and therefore unsusceptible of analy- sis, the names both of the object and of the attribute still admit of defini- tion ; or rather, would do so if all our simple feelings had names. White- ness may be defined, the property or power of exciting the sensation of white. A wdiite object may be defined, an object which excites the sensation of white. The only names which are unsusceptible of definition, because their meaning is unsusceptible of analysis, are the names of the simple feel- ings themselves. These are in the same condition as proper names. They are not indeed, like proper names, unmeaning ; for the words sensation of white signify, that the sensation which I so denominate resembles other sensations which I remember to have had before, and to have called by that name. But as we have no words by which to recall those former sensations, except the very word which we seek to define, or some other which, being exactly synonymous with it, requires definition as much, words can not un- fold the signification of this class of names ; and w^e are obliged to make a direct appeal to the personal experience of the individual whom Ave address. § 3. Having stated what seems to be the true idea of a Definition, I pro- ceed to examine some opinions of philosophers, and some popular concep- tions on the subject, which conflict more or less with that idea. The only adequate definition of a name is, as already remarked, one which declares the facts, and the whole of the facts, which the name involves in its signification. But with most persons the object of a definition does not embrace so much ; they look for nothing more, in a definition, than a guide to the correct use of the term — a protection against applying it in a man- ner inconsistent with custom and convention. Any thing, therefore, is to them a sufticient definition of a term, which will serve as a correct index to what the term c^enotes; though not embracing the whole, and some- times, perhaps, not even any part, of what it connotes. This gjves rise to two sorts of imperfect, or unscientific definition ; Essential but incomplete Definitions, and Accidental Definitions, or Descriptions. In the former, a connotative name is defined by a part only of its connotation ; in the latter, by something which forms no part of the connotation at all. 108 NAMES AND PROPOSITIONS. An example of the first kind of imperfect definitions is the following: Man is a rational animal. It is impossible to consider this as a complete definition of the word Man, since (as before remarked) if we adhered to it we should be obliged to call the Houyhnhnms men ; but as there happen to be no Houyhnhnms, this imperfect definition is sufl^icient to mark out and distinguish from all other things, the objects at present denoted by " man ;" all the beings actually known to exist, of whom the name is predicable. Though the word is defined by some only among the attributes which it connotes, not by all, it happens that all known objects which possess the enumerated attributes, possess also those which are omitted : so that' the field of predication which the word covers, and the employment of it which is conformable to usage, are as well indicated by the inadequate definition as by an adequate one. Such definitions, however, are always liable to be overthrown by the discovery of new objects in nature. Definitions of this kind are what logicians have had in view, when they laid down the rule, that the definition of a species should be per genus et differ entiam. Differentia being seldom taken to mean 'the whole of the peculiarities constitutive of the species, but some one of those peculiarities only, a complete definition would h^ per genus et differentias, rather than differ entiam. It would include, with the name of the superior genus, not merely soine attribute which distinguishes the species intended to be de- fined from all other species of the same genus, but all the attributes im- plied in the name of the species, which the name of the superior genus has not already implied. The assertion, however, that a definition must of necessity consist of a genus and differentiae, is not tenable. It was early remarked by logicians, that the summum genus in any classification, hav- ing no genus superior to itself, could not be defined in this manner. Yet w^e have seen that all names, except those of our elementary feelings, are susceptible of definition in the strictest sense; by setting forth in words the constituent parts of the fact or phenomenon, of which the connotation of every word is ultimately composed. § 4. Although the first kind of imperfect definition (which defines a con - notative term by a part only of what it connotes, but a part sufiicient to mark out correctly the boundaries of its denotation), has been considered by the ancients, and by logicians in general, as a complete definition ; it has always been deemed necessary that the attributes employed should really form part of the connotation ; for the rule was that the definition must be drawn from the essence of the class ; and this would not have been the case if it had been in any degree made up of attributes not connoted by the name. The second kind of imperfect definition, therefore, in which the name of a class is defined by any of its accidents — that is, by attributes which are not included in its connotation — has been rejected from the rank of genuine Definition by all logicians, and has been termed Description. This kind of imperfect definition, however, takes its rise from the same cause as the other, namely, the willingness to accept as a definition any thing which, whether it expounds the meaning of the name or not, enables us to discriminate the things denoted by the name from all othei* things, and con- sequently ^o employ the term in predication without deviating from estab- lished usage. This purpose is duly answered by stating any (no matter what) of the attributes which are common to the whole of the class, and peculiar to it; or any combination of attributes which happens to be pe- cuUar to it, though separately each of those attributes may be common to DEFINITION. 109 it with some otlier tilings. It is only necessary that the definition (or de- scription) thus fornied, should be convertible with the name vvhi(;h it pro- fesses to define; that is, should be exactly co-extensive with it, l)eing ])red- icable of every thinu!; of which it is predicable, and of nothing of which it is not predicable;' though the attributes si)ecified may have no connection with those which mankind had in view when they formed or recognized the class, and gave it a name. The following are correct definitions of Man, according to this test: Man is a mammiferous animal, having (by nature) two hands (for the human species answers to this description, and no other animal does) : Man is an animal who cooks his food : Man is a featherless biped. What would otherwise be a mere description, may be raised to the rank of a real definition by the peculiar purpose which the speaker or writer has in view. As was seen in the preceding chapter, it may, for the ends of a particular art or science, or for the more convenient statement of an author's particular doctrines, be advisaljle to give to some general name, without altering its denotation, a special connotation, diiferent from its or- dinary one. When this is done, a definition of the name by means of the attributes which make up the special connotation, though in general a mere accidental definition or description, becomes on the particular occasion and for the particular purpose a complete and genuine definition. This actual- ly occurs with respect to one of the preceding examples, " Man is a mam- miferous animal having two hands," which is the scientific definition of man, considered as one of the species in Cuvier's distribution of the animal kingdom. In cases of this sort, though the definition is still a declaration of the meaning which in the particular instance the name is appointed to convey, it can not be said that to state the meaning of the word is the purpose of the definition. The purpose is not to expound a name, but a classification. The special meaning which Cuvier assigned to the word Man (quite foreign to its ordinary meaning, though involving no change in the denotation of the word), was incidental to a plan of arranging animals into classes on a certain principle, that is, according to a certain set of distinctions. And since the definition of Man according to the ordinary connotation of the word, though it would have answered every other purpose of a definition, would not have pointed out the place which the species ought to occupy in that particular classification ; he gave the word a special connotation, that he might be able to define it by the kind of attributes on which, for reasons of scientific convenience, he had resolved to found his division of animated nature. Scientific definitions, whether they are definitions of scientific terms, or of common terms used in a scientific sense, are almost always of the kind last spoken of : their main purpose is to serve as the landmarks of scien- tific classification. And since the classifications in any science are con- tinually modified as scientific knowledge advances, the definitions in the sciences are also constantly varying. A striking instance is afforded by the words Acid and Alkali, especially the former. As experimental dis- covery advanced, the substances classed with acids have been constantly multiplying, and by a natural consequence the attributes connoted by the word have receded and become fewer. At first it connoted the attributes, of combining with an alkali to form a neutral substance (called a salt) ; being compounded of a base and oxygen ; causticity to the taste and touch ; fluidity, etc. The true analysis of muriatic acid, into chlorine and hydro- 110 NAMES AND PROPOSITIONS. gen, caused the second property, composition from a base and oxygen, to be excluded from the connotation. The same discovery fixed the attention of chemists upon hydrogen as an important element in acids; and more recent discoveries having led to the recognition of its presence in sulphuric, nitric, and many other acids, where its existence was not previously sus- pected, there is now a tendency to include the presence of this element in the connotation of the word. But carbonic acid, silica, sulphurous acid, have no hydrogen in their composition ; that property can not, therefore, be connoted by the term, unless those substances are no longer to be con- sidered acids. Causticity and fluidity have long since been excluded from the characteristics of the class, by the inclusion of silica and many other substances in it ; and the formation of neutral bodies by combination with alkalis, together with such electro-chemical peculiarities as this is supposed to imply, are now the only differentioi which form the fixed connotation of the word Acid, as a term of chemical science. What is true of the definition of any term of science, is of course true of the definition of a science itself; and accordingly (as observed in the In- troductory Chapter of this work), the definition of a science must neces- sarily be progressive and provisional. Any extension of knowledge or al- teration in the current opinions respecting the subject-matter, may lead to a change more or less extensive in the particulars included in the science ; and its composition being thus altered, it may easily happen that a different set of characteristics will be found better adapted as differentiae for defin- ing its name. In the same manner in which a special or technical definition has for its object to expound the artificial classification out of which it grows; the Aristotelian logicians seem to have imagined that it was also the business of ordinary definition to expound the ordinary, and what they deemed the natural, classification of things, namely, the division of them into Kinds ; and to show the place which each Kind occupies, as superior, collateral, or subordinate, among other Kinds. This notion would account for the rule that all definition must necessarily be jc^er genus et differ entkim, and would also explain why a single differentia was deemed sufiicient. But to ex- pound, or express in words, a distinction of Kind, has already been shown to be an impossibility: the very meaning of a Kind is, that the properties which distinguish it do not grow out of one another, and can not therefore be set forth in words, even by implication, otherwise than by enumerating them all : and all are not known, nor are ever likely to be so. It is idle, therefore, to look to this as one of the purposes of a definition : while, if it be only required that the definition of a Kind should indicate what kinds include it or are included by it, any definitions which expound the connota- tion of the names will do this : for the name of each class must necessarily connote enough of its properties to fix the boundaries of the class. If the definition, therefore, be a full statement of the connotation, it is all that a • definition can be required to be.* ' * Professor Bain, in his Logic, takes a peculiar view of Definition. He holds (i,, 71) with the present work, that "the definition in its full import, is the sum of all the properties con- noted by the name; it exhausts the meaning of a word." But he regards the meaning of a general name as including, not indeed all the common properties of the class named, but all of them that are ultimate properties, not resolvable into one another. " The enumeration of the attributes of oxygen, of gold, of man, should be an enumeration of the final (so far as can be made out), the underivable, powers or functions of each," and nothing less than this is a complete Definition (i., 75). An independent property, not derivable from other properties, even if previously unknown, yet as soon as discovered becomes, according to him, part of the DEFINITION. Ill § 5. Of the two inconiplotc and ])0]nil;ir modes of definitioM, and in wliat they differ from the complete or pliilosophical mode, enouu^li has now l^een said. We shall next examine an ancient do(;trine, once generally prevalent and still by no means exploded, wliich I regard as the source of a great [)art of the obscurity hanging over some of the most important processes of the understanding in the pursuit of truth. According to this, the deiinitions of which we have now treated are only one of two sorts into which defini- tions may be divided, viz., definitions of names, and definitions of things. The former are intended to explain the meaning of a term ; the latter, the nature of a thing; the last being incomparably the most important. This opinion was held by the ancient philosophers, and by their follow- ers, with the exception of the Nominalists ; but as the spirit of modern metapliysics, until a recent period, has been on the whole a Nominalist spirit, the notion of definitions of things has been to a certain extent in abeyance, still continuing, however, to breed confusion in logic, by its con- sequences indeed rather than by itself. Yet the doctrine in its own proper form now and then breaks out, and has appeared (among other places) where it was scarcely to be expected, in a justly admired word. Archbishop Wliately's Logic.^ In a review of that w^ork published by me in the West- meaning of the term, and should be included in the definition. "When we are told that dia- mond, which we know to be a transparent, glittering, hard, and high-priced substance, is com- posed of carbon, and is combustible, we must put these additional properties on the same level as the rest; to us they are henceforth connoted by the name"(i., 73). Consequently the propositions that diamond is composed of carbon, and that it is combustible, are regarded by Mr. Bain as merely verbal propositions. He carries this doctrine so far as to say that unless mortality can be shown to be a consequence of the ultimate laws of animal organization, mor- tality is connoted by man, and " Man is Mortal" is a merely verbal proposition. And one of the peculiarities (I think a disadvantageous peculiarity) of his able and valuable treatise, is the large number of propositions requiring proof, and learned by experience, which, in con- formity with this doctrine, he considers as not real, but verbal, propositions. The objection I have to this language is that it confounds, or at least confuses, a much more important distinction than that which it draws. The only reason for dividing Proposi- tions into real and verbal, is in order to discriminate propositions which convey information about facts, from those which do not. A proposition which affirms that an object has a given attribute, while designating the object by a name which already signifies the attribute, adds no information to that which was already possessed by all who understood the name. But when this is said, it is implied that, by the signification of a name, is meant the signification attached to it in the common usage of life. I can not think we ought to say that the meaning of a word includes matters of fact which are unknown to every person who uses the word un- less he has learned them by special study of a particular department of Nature ; or that because a few persons are aware of these matters of fact, the affirmation of them is a proposition con- veying no information. I hold that (special scientific connotation apart) a name means, or connotes, only the properties which it is a mark of in the general mind ; and that in the case of any additional pi'operties, however uniformly found to accompany these, it remains possible that a thing which did not possess the properties might still be thought entitled to the name. Ruminant, according to Mr. Bain's use of language, connotes cloven-hoofed, since the two properties are always found together, and no connection has ever been discovered between them : but ruminant does not mean cloven-hoofed ; and were an animal to be discovered which chews the cud, but has its feet undivided, I venture to say that it would still be called ruminant. * In the fuller discussion Avhich Archbishop AYhately has given to this subject in his later editions, he almost ceases to regard the definitions of names and those of things as. in any im- portant sense, distinct. He seems (9th ed., p. 115) to limit the notion of a Eeal Definition to one which "explains any thing more of the nature of the thing than is impbed in the name:'" (including under the word " implied," not only what the name connotes, but every thing which can be deduced by reasoning from the attributes connoted). Even this, as he adds, is usually called not a Definition, but a Description ; and (as it seems to me) rightly so called. A De- scription, I conceive, can only be ranked among Definitions, when taken (as in the case of the zoological definition of man) to fulfill the true office of a Definition, by declaring the connota- tion given to a word in some special use, as a term of science or art : which special couno- 112 NAMES AND PROPOSITIONS. minster Hevietc for January, 1828, and containing some opinions which I no longer entertain, I find the following observations on the question now before us ; observations with which my present view of that question is still sufficiently in accordance. " The distinction between nominal and real definitions, between defini- tions of words and what are called definitions of things, though conforma- ble to the ideas of most of the Aristotelian logicians, can not, as it appears to us, be maintained. We apprehend that no definition is ever intended to ' explain and unfold the nature of a thing.' It is some confirmation of our opinion, that none of those writers who have thought that there were defini- tions of things, have ever succeeded in discovering any criterion by which the definition of a thing can be distinguished from any other proposition relating to the thing. The definition, they say, unfolds the nature of the thing: but no definition can unfold its whole nature; and every proposi- tion in which any quality whatever is predicated of the thing, unfolds some part of its nature. The true state of the case we take to be this. All definitions are of names, and of names only ; but, in some definitions, it is clearly apparent, that nothing is intended except to explain the meaning of the word ; while in others, besides explaining the meaning of the word, it is intended to be implied that there exists a thing, corresponding to the word. Whether this be or be not implied in any given case, can not be collected from the mere form of the expression. 'A centaur is an animal with the upper parts of a man and the lower parts of a horse,' and 'A tri- angle is a rectilineal figure with three sides,' are, in form, expressions pre- cisely similar ; although in the former it is not implied that any thing, con- formable to the term, really exists, while in the latter it is ; as may be seen by substituting in both definitions, the word means for is. In the first expression, *A centaur means an animal,' etc., the sense would remain un- changed: in the second, 'A triangle means,' etc., the meaning would be al- tered, since it would be obviously impossible to deduce any of the truths of geometry from a proposition expressive only of the manner in which we intend to employ a particular sign. "There are, therefore, expressions, commonly passing for definitions, which include in themselves more than the mere explanation of the meaning of a term. But it is not correct to call an expression of this sort a peculiar kind of definition. Its difference from the other kind consists in this, that it is not a definition, but a definition and something more. The definition above given of a triangle, obviously comprises not one, but two proposi- tions, perfectly distinguishable. The one is, 'There may exist a figure, bounded by three straight lines ;' the other, ' And this figure may be termed a triangle.' The former of these propositions is not a definition at all : the tation of course would not be expressed by the proper definition of the word in its ordinary employment. Mr. De Morgan, exactly reversing the doctrine of Archbishop Whately, understands by a Real Definition one which contains less than the Nominal Definition, provided only that what it contains is sufficient for distinction. "By real definition I mean such an explanation of the word, be it the whole of the meaning or only part, as will be sufficient to separate the things contained under that word from all others. Thus the following, I believe, is a complete definition of an elephant : An animal which naturally drinks by drawing the water into its nose, and then sjjurting it into its mouth." — Formal Logic, p. 8G. Mr. De Morgan's gen- eral proposition and his example are at variance ; for the peculiar mode of drinking of the elephant certainly forms no part of the meaning of the word elephant. It could not be said, because a person happened to be ignorant of this property, that he did not know what an elephant means. DEFINITION. I 1 ;{ latter is a mere nominal dcfinitioii, or explanation of tlie use and aj>}>ii(;a- tion of a term. The first is susce])tible of truth or falsehood, and may therefore be made the foundation of a train of reasoning. The latter can neitlier be true nor false; the only character it is susceptible of is that of conformity or disconformity to the ordinary usage of language." There is a real distinction, then, between definitions of names, and what are erroneously called definitions of things ; but it is, that the latter, along with the meaning of a name, covertly asserts a matter of fact. This covert assertion is not a definition, but a postulate. The definition is a mere iden- tical proposition, which gives information only about the use of language, and from which no conclusions affecting matters of fact can possibly be drawn. The accompanying postulate, on the other hand, affirms a fact, which may lead to consequences of every degree of importance. It affirms the actual or possible existence of Things possessing the combination of attributes set forth in the definition ; and this, if true, may be foundation sufficient on which to build a whole fabric of scientific truth. We have already made, and shall often have to repeat, the remark, that the philosophers who overthrew Realism by no means got rid of the con- sequences of Realism, but retained long afterward, in their own philosophy, numerous propositions which could only have a rational meaning as part of a Realistic system. It had been handed down from Aristotle, and prob- ably from earlier times, as an obvious truth, that the science of Geometry is deduced from definitions. This, so long as a definition was considered to be a proposition "unfolding the nature of the thing," did well enough. But Hobbes followed, and rejected utterly the notion that a definition de- clares the nature of the thing, or does any thing but state the meaning of a name; yet he continued to affirm as broadly as any of his predecessors, that the apxal, principia, or original premises of mathematics, and even of all science, are definitions ; producing the singular paradox, that systems of scientific truth, nay, all truths whatever at which we arrive by reasoning, are deduced from the arbitrary conventions of mankind concerning the sig- nification of words. To save the credit of the doctrine that definitions are the premises of scientific knowledge, the proviso is sometimes added, that they are so only under a certain condition, namely, that they be framed conformably to the phenomena of nature ; that is, that they ascribe such meanings to terms as shall suit objects actually existing. But this is only an instance of the at- tempt so often made, to escape from the necessity of abandoning old lan- guage after the ideas which it expresses have been exchanged for contrary ones. From the meaning of a name (we are told) it is possible to infer physical facts, provided the name has corresponding to it an existing thing. But if this proviso be necessary, from w^hich of the two is the inference really drawn ? From the existence of a thing having the properties, or from the existence of a name meaning them ? Take, for instance, any of the definitions laid down as premises in Euclid's Elements ; the definition, let us say, of a circle. This, being analyzed, con- sists of two propositions; the one an assumption with respect to a matter of fact, the other a genuine definition. " A figure may exist, having all the points in the line which bounds it equally distant from a single point with- in it :" " Any figure possessing this property is called a circle." Let us look at one of the demonstrations which are said to depend on this defini- tion, and observe to wdiich of the two propositions contained in it the dem- onstration really appeals. " About the centre A, describe the circle B C D." 8 114 NAMES AND PROPOSITIONS. Here is an assumption that a figure, such as the definition expresses, may be described ; which is no other than the postulate, or covert assumption, involved in the so-called definition. But whether that figure be called a circle or not is quite immaterial. The purpose would be as well answered, in all respects except brevity, were we to say, "Through the point B, draw a line returning into itself, of which every point shall be at an equal dis- tance from the point A." By this the definition of a circle would be got rid of, and rendered needless ; but not the postulate implied in it ; without that the demonstration could not stand. The circle being now described, let us proceed to the consequence. " Since B C D is a circle, the radius B A is equal to the radius C A." B A is equal to C A, not because BCD is a circle, but because B C D is a figure with the radii equal. Our war- rant for assuming that such a figure about the centre A, with the radius B A, may be made to exist, is the postulate. Whether the admissibility of these postulates rests on intuition, or on proof, may be a matter of dis- pute ; but in either case they are the premises on which the theorems de- pend ; and while these are retained it would make no difference in the cer- tainty of geometrical truths, though every definition in Euclid, and every technical term therein defined, were laid aside. It is, perhaps, superfluous to dwell at so much length on what is so near- ly self-evident ; but when a distinction, obvious as it may appear, has been confounded, and by powerful intellects, it is better to say too much than too little for the purpose of rendering such mistakes impossible in future. I will, therefore detain the reader while I point out one of the absurd con- sequences flowing from the supposition that definitions, as such, are the premises in any of our reasonings, except such as relate to words only. If this supposition were true, we might argue correctly from true premises, and arrive at a false conclusion. We should only have to assume as a premise the definition of a nonentity; or rather of a name which has no entity corresponding to it. Let this, for instance, be our definition : A dragon is a serpent breathing flame. This proposition, considered only as a definition, is indisputably correct. A dragon is a serpent breathing flame : the word means that. The tacit assumption, indeed (if there were any such understood assertion), of the ex- istence of an object with properties corresponding to the definition, would, in the present instance, be false. Out of this definition we may carve the premises of the following syllogism : A dragon is a thing which breathes flame : A dragon is a serpent : From which the conclusion is, Therefore some serpent or serpents breathe flame: an unexceptionable syllogism in the first mode of the third figure, in which both premises are true and yet the conclusion false; which every logician knows to be an absurdity. The conclusion being false and the syllogism correct, the premises can not be true. But the premises, considered as parts of a definition, are true. Therefore, the premises considered as parts of a definition can not be the real ones. The real premises must be — A dragon is a really existing thing which breathes flame : A dragon is a really existing serpent : which impUed premises being false, the falsity of the conclusion presents no absurdity. If we would determine what conclusion follows from the same ostensible premises when the tacit assumption of real existence is left out, let us, ac- DEFINITION. 1 1 5 cording to the recommendation in a previous page, sul)stitute means for in. We then have — ])ragon is a word meaning a thing wliicli breathes llame : Dragon is a loord meaning a serpent: From which the conchision is, Some word orioords which mean a serpent, also mean a thing wliich breathes flame : where the conchision (as well as the premises) is true, and is the only kind of conclusion which can ever follow from a definition, namely, a proposition relating to the meaning of words. There is still another shape into w^hich we may transform this syllogism. We may suppose the middle term to be the designation neither of a thing nor of a name, but of an idea. We then have — The idea of a dragon is an idea of a thing which breathes flame : The idea of a dragon is aii idea of a serpent : Therefore, there is an idea of a serpent, which is aii idea of a thing breathing flame. Here the conclusion is true, and also the premises ; but the premises are not definitions. They are propositions affirming that an idea existing in the mind, includes certain ideal elements. The truth of the conclusion fol- lows from the existence of the psychological phenomenon called the idea of a dragon ; and therefore still from the tacit assumption of a matter of fact.^' When, as in this last syllogism, the conclusion is a proposition respecting an idea, the assumption on which it depends may be merely that of the ex- istence of an idea. But when the conclusion is a proposition concerning a Thing, the postulate involved in the definition which stands as the apparent premise, is the existence of a thing conformable to the definition, and not merely of an idea conformable to it. This assumption of real existence we always convey the impression that we intend to make, when we profess to define any name which is already known to be a name of really existing objects. On this account it is, that the assumption was not necessarily implied in the definition of a dragon, w^hile there was no doubt of its be- ing included in the definition of a circle. * In the only attempt which, so far as I know, has been made to refute the preceding argu- mentation, it is maintained that in the first form of the syllogism, A dragon is a thing whicli breathes flame, A dragon is a serpent. Therefore some serpent or serpents breathe flame, "there is just as much truth in the conchision as there is in the premises, or rather, no more in the hitter than in the former. If the general name serpent includes both real and imaginary serpents, there is no falsity in the conclusion ; if not, there is falsity in the minor premise." Let us, then, try to set out the syllogism on the hypothesis that the name serpent includes imaginary serpents. We shall find that it is now necessary to alter the predicates : for it can not be asserted that an imaginary creature breathes flame ; in predicating of it such a fact, we assert by the most positive implication that it is real, and not imaginary. The conclusion must run thus, "Some serpent or serpents either do or are imagined to breathe flame." And to prove this conclusion by the instance of dragons, the premises must be. A dragon is imagined as breathing flame. A dragon is a (real or imaginaiy) serpent : from which it undoubtedly follows, that there are serpents which are imagined to breathe flame : but the major premise is not a definition, nor part of a definition ; which is all that I am concerned to prove. Let us now examine the other assertion — that if the word serpent stands for none but real serpents, the minor premise (a dragon is a serpent) is false. This is exactly Avhat I have my- self said of the premise, considered as a statement of fact : but it is not false as part of the definition of a dragon ; and since the premises, or one of them, must be false (the conclusion being so), the real premise can not be the definition, which is true, but the statement of fact, which is false. lit) NAMES AND PKOPOSITIONS. § 6. One of the circumstances which have contributed to keep up the notion, that demonstrative truths follow from definitions rather than from the postulates implied in those definitions, is, that the postulates, even in those sciences which are considered to surpass all others in demonstrative certainty, are not always exactly true. It is not true that a circle exists, or can be described, which has all its radii exactly equal. Such accuracy is ideal only ; it is not found in nature, still less can it be realized by art. People had a difiiculty, therefore, in conceiving that the most certain of all conclusions could rest on premises which, instead of being certainly true, are certainly not true to the full extent asserted. This apparent paradox will be examined when we come to treat of Demonstration ; where we shall be able to show that as much of the postulate is true, as is required to sup- port as much as is true of the conclusion. Philosophers, however, to whom this view had not occurred, or whom it did not satisfy, have thought it in- dispensable that there should be found in definitions something more cer- tain, or at least more accurately true, than the implied postulate of the real existence of a corresponding object. And this something they flattered themselves they had found, when they laid it down that a definition is a statement and analysis not of the mere meaning of a word, nor yet of the nature of a thing, but of an idea. Thus, the proposition, "A circle is a plane figure bounded by a line all the points of which are at an equal dis- tance from a given point within it," was considered by them, not as an as- sertion that any real circle has that propei'ty (which would not be exactly true), but that we conceive a circle as having it; that our abstract idea of a circle is an idea of a figure with its radii exactly equal. Conformably to this it is said, that the subject-matter of mathematics, and of every other demonstrative science, is not things as they really exist, but abstractions of the mind. A geometrical line is a line without breadth ; but no such line exists in nature; it is a notion merely suggested to the mind by its experience of nature. The definition (it is said) is a definition of this mental line, not of any actual line : and it is only of the mental line, not of any line existing in nature, that the theorems of geometry are ac- curately true. Allowing this doctrine respecting the nature of demonstrative truth to be correct (which, in a subsequent place, I shall endeavor to prove that it is not) ; even on that supposition, the conclusions which seem to follow from a definition, do not follow from the definition as such, but from an implied postulate. Even if it be true that there is no object in nature an- swering to the definition of a line, and that the geometrical properties of lines are not true of any lines in nature, but only of the idea of a line; the definition, at all events, postulates the real existence of such an idea : it as- sumes that the mind can frame, or rather has framed, the notion of length without breadth, and without any other sensible property whatever. To me, indeed, it appears that the mind can not form any such notion ; it can not conceive length without breadth; it can only, in contemplating objects, attend to their length, exclusively of their other sensible qualities, and so determine what properties may be predicated of them in virtue of their length alone. If this be true, the postulate involved in the geometrical definition of a line, is the real existence, not of length without breadth, but merely of length, that is, of long objects. This is quite enough to support all the truths of geometry, since every property of a geometrical line is really a property of all physical objects in so far as possessing length. But even what I hold to bo the false doctrine on the subject, leaves the conclu- DEFINITION. 1 ] 7 sion tliat onr reasonings aro groiuidcHl on tlic inalters of fact ))Ostiilat('(l in definitions, and not on the deiinitions tlicniselves, entir(;ly unaffected ; and accordingly this conchision is one which I liave in common vvitli \Jv. Wlie- well, in his Philosophy of the, Inductive Sciences: tiiough, on the luiture of demonstrative truth, Dr. Wiievvell's opinions are greatly at variance with mine. And here, as in many other instances, I gladly acknowledge that his writings are eminently serviceable in clearing from confusion the initial steps in the analysis of the mental processes, even where his views respect- ing the ultimate analysis are such as (though with unfeigned respect) I can not but regard as fundamentally erroneous. § 7. Although, according to the opinion here presented, Definitions are properly of names only, and not of things, it does not follow from this that definitions are arbitrary. How to define a name, may not only be an in- quiry of considerable difficulty and intricacy, but may involve considera- tions going deep into the nature of the things which are denoted by the name. Such, for instance, are the inquiries which form the subjects of the most important of Plato's Dialogues; as, "What is rhetoric?" the topic of the Gorgias, or, "What is justice?" that of the Republic. Such, also, is the question scornfully asked by Pilate, "What is truth?" and the funda- mental question with speculative moralists in all ages, " What is virtue ?" It would be a mistake to represent these difficult and noble inquiries as having nothing in view beyond ascertaining the conventional meaning of a name. They are inquiries not so much to determine what is, as what should be, the meaning of a name ; which, like other practical questions of terminology, requires for its solution that we should enter, and sometimes enter very deeply, into the properties not merely of names but of the things named. Although the meaning of every concrete general name resides in the at- tributes which it connotes, the objects were named before the attributes ; as appears from the fact that in all languages, abstract names are mostly compounds or other derivatives of the concrete names which correspond to them. Connotative names, therefore, were, after proper names, the first which were used : and in the simpler cases, no doubt, a distinct connotation was present to the minds of those who first used the name, and was dis- tinctly intended by them to be conveyed by it. The first person who used the word white, as applied to snow or to any other object, knew, no doubt, very well what quality he intended to predicate, and had a perfectly dis- tinct conception in his mind of the attribute signified by the name. But where the resemblances and differences on which our classifications are founded are not of this palpable and easily determinable kind ; especial- ly where they consist not in any one quality but in a number of qualities, the effects of which, being blended together, are not very easily discrimi- nated, and referred each to its true source ; it often happens that names are applied to namable objects, with no distinct connotation present to the minds of those who apply them. They are only influenced by a general resemblance between the new object and all or some of the old familiar objects which they have been accustomed to call by that name. This, as we have seen, is the law which even the mind of the philosopher must fol- low, in giving names to the simple elementary feehugs of our nature : but, where the things to be named are complex wholes, a philosopher is not content with noticing a general resemblance; he examines what the resem- blance consists in : and he only gives the same name to things which re- 118 NAMES AND PROPOSITIONS. semble one another in the same definite particulars. The philosopher, therefore, habitually employs his general names with a definite connota- tion. But language was not made, and can only in some small degree be mended, by philosophers. In the minds of the real arbiters of language, general names, especially where the classes they denote can not be brought before the tribunal of the outward senses to be identified and discriminated, connote little more than a vague gross resemblance to the things which they were earliest, or have been most, accustomed to call by those names. When, for instance, ordinary persons predicate the words just or unjust of any action, noble or mean of any sentiment, expression, or demeanor, statesman or charlatan of any personage figuring in politics, do they mean to affirm of those various subjects any determinate attributes, of whatever kind ? No : they merely recognize, as they think, some likeness, more or less vague and loose, between these and some other things which they have been accustomed to denominate or to hear denominated by those ap- pellations. Language, as Sir James Mackintosh used to say of governments, " is not made, but grows." A name is not imposed at once and by previous pur- pose upon a class of objects, but is first applied to one thing, and then ex- tended by a series of transitions to another and another. By this process (as has been remarked by several writers, and illustrated with great force and clearness by Dugald Stewart in his Philosophical Essays) a name not unfrequently passes by successive links of resemblance from one object to another, until it becomes applied to things having nothing in common with the first things to which the name was given; which, however, do not, for that reason, drop the name ; so that it at last denotes a confused huddle of objects, having nothing whatever in common ; and connotes nothing, not even a vague and general resemblance. When a name has fallen into this state, in which by predicating it of any object we assert literally nothing about the object, it has become unfit for the purposes either of thought or of the communication of thought; and can only be made serviceable by stripping it of some part of its multifarious denotation, and confining it to objects possessed of some attributes in common, which it may be made to connote. Such are the inconveniences of a language which " is not made, but grows." Like the governments which are in a similar case, it may be compared to a road which is not made but has made itself: it requires con- tinual mending in order to be passable. From this it is already evident, why the question respecting the defini- tion of an abstract name is often one of so much difficulty. The question. What is justice? is, in other words. What is the attribute which mankind mean to predicate when they call an action just? To which the first an- swer is, that having come to no precise agreement on the point, they do not mean to predicate distinctly any attribute at all. Nevertheless, all be- lieve that there is some common attribute belonging to all the actions which they are in the habit of calling just. The question then must be, whether there is any such common attribute ? and, in the first place, whether man- kind agree sufficiently with one another as to the particular actions which they do or do not call just, to render the inquiry, what quality those ac- tions have in common, a possible one : if so, whether the actions really have any quality in common ; and if they have, what it is. Of these three, the first alone is an inquiry into usage and convention ; the other two are inqui- ries into matters of fact. And if the second question (whether the actions form a class at all) has been answered negatively, there remains a fourth, DEFINITION. 1 1 often move arduous than all the i-est, namely, how best to form a class arti- ficially, which tlie name may denote. And here it is fitting to remark, that the study of tlie spontaneous growth of languages is of the utmost imi)ortance to those who would logically re- model them. The classifications rudely made by established language, when retouched, as they almost all require to be, by the hands of the logician, are often themselves excellently suited to his purposes. As compared with the classifications of a philosopher, they are like the customary law of a country, which has grown up as it were spontaneously, compared with laws methodized and digested into a code : the former are a far less pei'fect in- strument than the latter; but being the result of a long, though unscien- tific, course of experience, they contain a mass of materials which may be made very usefully available in the formation of the systematic body of written law. In like manner, the established grouping of objects under a common name, even when founded only on a gross and general resemblance, is evidence, in the first piace, that the resemblance is obvious, and therefore considerable; and, in the next place, that it is a resemblance which has struck great numbers of persons during a series of j^ears and ages. Even when a name, by successive extensions, has come to be applied to things among which there does not exist this gross resemblance common to them all, still at every step in its progress we shall find such a resemblance. And these transitions of the meaning of words are often an index to real con- nections between the things denoted by them, which might otherwise escape the notice of thinkers ; of those at least who, from using a different lan- guage, or from any difference in their habitual associations, have fixed their attention in preference on some other aspect of the things. The history of philosophy abounds in examples of such oversights, committed for w^ant of perceiving the hidden link that connected together the seemingly disparate meanings of some ambiguous word.* Whenever the inquiry into the definition of the name of any real object consists of any thing else than a mere comparison of authorities, we tacit- ly assume that a meaning must be found for the name, compatible with its continuing to denote, if possible all, but at any rate the greater or the more important part, of the things of which it is commonly predicated. The in- quiry, therefore, into the definition, is an inquiry into the resemblances and differences among those things : whether there be any resemblance rinming through them all ; if not, through what portion of them such a general re- semblance can be traced : and finally, what are the common attributes, the possession of which gives to them all, or to that portion of them, the char- acter of resemblance which has led to their being classed together. When these common attributes have been ascertained and specified, the name which belongs in common to the resembling objects acquires a distinct in- * "Few people" (I have said in another place) "have reflected how great a knowledge of Things is required to enable a man to affirm that any given argument turns wholly upon words. There is, perhaps, not one of the leading terms of philosophy which is not used in almost innumerable shades of meaning, to express ideas more or less widely different from one another. Between two of these ideas a sagacious and penetrating mind will discern, as it were intuitively, an unobvious link of connection, upon which, though perhaps unable to give a logical account of it, he will found a perfectly valid argument, which his critic, not having so keen an insight into the Things, will mistake for a fallacy turning on the double meaning of a term. And the greater the genius of him who thus safely leaps over the chasm, the greater will probably be the crowing and vainglory of the mere logician, who, hobbling after him, evinces his own superior wisdom by pausing on its brink, and giving up as desper- ate his proper business of bridging it over.'' 120 NAMES AND PROPOSITIONS. stead of a vague connotation ; and by possessing this distinct connotation, becomes susceptible of definition. In giving a distinct connotation to the general name, the philosopher will endeavor to fix upon such attributes as, while they are common to all the things usually denoted by the name, are also of greatest importance in them- selves ; either directly, or from the number, the conspicuousness, or the in- teresting character, of the consequences to which they lead. He will select, as far as possible, such differentioe as lead to the greatest number of inter- esting propria. For these, rather than the more obscure and recondite qualities on which they often depend, give that general character and as- pect to a set of objects, which determine the groups into which they natu- rally fall. But to penetrate to the more hidden agreement on which these obvious and superficial agreements depend, is often one of the most diffi- cult of scientific problems. As it is among the most diflacult, so it seldom fails to be among the most important. And since upon the result of this inquiry respecting the causes of the properties of a class of things, there in- cidentally depends the question what shall be the meaning of a word ; some of the most profound and most valuable investigations which philosophy presents to us, have been introduced by, and have offered themselves under the guise of, inquiries into the definition of a name. BOOK II. OF REASONING. AiojpKTiLieviov dt TOVTOJV XsybJiiev i'lSr}, Sid rivwv, Kai Trdrf , /coi ttw^ yiverat ttuq (ryXXoytrr^tot," varfpov hk XeKTfov Trtpi ('nrodtiKtojg. IlpSrepov yap rrepi avWoy lcthov XtKTtov, f; Trtp'i c'nrocei- Ki^og, dia TO kuOoXov [xaXXov eival tov avXXoyi(7{i6v. H iiiv yap aTrooft^tg, avXXoyiajxox; rig' 6 (TvXXoyi(Tix6g dt oii Tra^, CLTTodei^ig. — Arist,, Analyt. Prior., 1. i., cap. 4. CHAPTER I. OF INFEEENCE, OR REASONING, IN GENERAL. § 1. In the preceding Book, we have been occupied not with the nature of Proof, but with the nature of Assertion : the import conveyed by a Prop- osition, whether that Proposition be true or false ; not the means by which to discriminate true from false Propositions. The proper subject, howevei", of Logic is Proof. Before we could understand what Proof is, it was nec- essary to understand what that is to which proof is appHcable; what that is which can be a subject of belief or disbelief, of affirmation or denial ; what, in short, the different kinds of Propositions assert. This preliminary inquiry we have prosecuted to a definite result. Asser- tion, in the first place, relates either to the meaning of words, or to some property of the things which words signify. Assertions respecting the meaning of words, among which definitions are the most important, hold a place, and an indispensable one, in philosophy ; but as the meaning of words is essentially arbitrary, this class of assertions are not susceptible of truth or falsity, nor therefore of proof or disproof. Assertions respecting Things, or what may be called Real Propositions, in contradistinction to verbal ones, are of various sorts. We have analyzed the import of each sort, and have ascertained the nature of the things they relate to, and the nature of what they severally assert respecting those things. We found that what- ever be the form of the proposition, and whatever its nominal subject or predicate, the real subject of every proposition is some one or more facts or phenomena of consciousness, or some one or more of the hidden causes or powers to which we ascribe those facts ; and that what is predicated or asserted, either in the affirmative or negative, of those phenomena or those powers, is always either Existence, Order in Place, Order in Time, Causa- tion, or Resemblance. This, then, is the theory of the Import of Proposi- tions, reduced to its ultimate elements : but there is another and a less ab- struse expression for it, which, though stopping short in an earlier stage of the analysis, is sufficiently scientific for many of the purposes for which such a general expression is required. This expression recognizes the com- monly received distinction between Subject and Attribute, and gives the following as the analysis of the meaning of propositions: — Every Proposi- 122 KEASONING. tion asserts, that some given subject does or does not possess some attri- bute ; or that some attribute is or is not (either in all or in some portion of the subjects in which it is met with) conjoined with some other attri- bute. We shall now for the present take our leave of this portion of our in- quiry, and proceed to the peculiar problem of the Science of Logic, name- ly, how the assertions, of which we have analyzed the import, are proved or disproved; such of them, at least, as, not being amenable to direct con- sciousness or intuition, are appropriate subjects of proof. We say of a fact or statement, that it is proved, when we believe its truth by reason of some other fact or statement from which it is said to follow. Most of the propositions, whether affirmative or negative, universal, partic- ular, or singular, which we believe, are not believed on their own evidence, but on the ground of something previously assented to, from which they are said to be inferred. To infer a proposition from a previous proposi- tion or propositions ; to give credence to it, or claim credence for it, as a conclusion from something else ; is to reason, in the most extensive sense of the term. There is a narrower sense, in which the name reasoning is confined to the form of inference which is termed ratiocination, and of which the syllogism is the general type. The reasons for not conforming to this restricted use of the term were stated in an earlier stage of our in- quiry, and additional motives will be suggested by the considerations on which we are now about to enter. § 2. In proceeding to take into consideration the cases in which infer- ences can legitimately be drawn, we shall first mention some cases in which the inference is apparent, not real ; and which require notice chiefly that they may not be confounded with cases of inference properly so called. This occurs when the proposition ostensibly inferred from another, appears on analysis to be merely a repetition of the same, or part of the same, as- sertion, which was contained in the first. All the cases mentioned in books of Logic as examples of equipollency or equivalence of propositions, are of this nature. Thus, if we were to argue. No man is incapable of reason^ for every man is rational ; or, All men are mortal, for no man is exempt from death ; it would be plain that we were not j^roving the proposition, but only appealing to another mode of wording it, which may or may not be more readily comprehensible by the hearer, or better adapted to suggest the real proof, but which contains in itself no shadow of proof. Another case is where, from a universal proposition, we affect to infer another which differs from it only in being particular : as All A is B, there- fore Some A is B : No A is B, therefore Some A is not B. This, too, is not to conclude one proposition from another, but to repeat a second time some- thing which had been asserted at first; with the difference, that we do not here repeat the whole of the previous assertion, but only an indefinite part of it. A third case is where, the antecedent having affirmed a predicate of a given subject, the consequent affirms of the same subject something already connoted by the former predicate : as, Socrates is a man, therefore Socrates is a living creature ; where all that is connoted by living creature was af- firmed of Socrates when he was asserted to be a man. If the propositions are negative, we must invert their order, thus : Socrates is not a living crea- ture, therefore he is not a man ; for if we deny the less, the greater, which includes it, is already denied by implication. These, therefore, arc not real- INFERENCE IN (iKNEUAL. 123 ly cases of inference; and yet llie trivial examples by wliicli, in manuals of Logic, the rules of the syllogism are illustrated, are often of this ill-ch(jsen kind; formal demonstrations ol conclusions to which whoever understands the terms used in the statement of the data, has already, and consciously, assented.* The most complex case of this sort of apparent inference is what is called the Conversion of propositions; which consists in turning the predicate into a subject, and the subject into a predicate, and framing out of the same terms thus reversed, another proposition, which must be true if the former is true. Thus, from the particular affirmative proposition. Some A is B, we may infer that Some B is A. From the universal negative, No A h B, we may conclude that No B is A. From the universal affirmative proposi- tion, All A is B, it can not be inferred that all B is A ; though all water is liquid, it is not implied that all liquid is water; but it is implied that some liquid is so ; and hence the proposition. All A is B, is legitimately convert- ible into Some B is A. This process, which converts a universal propo- sition into a particular, is termed conversion ^er accidens. From the prop- osition. Some A is not B, we can not even infer that some B is not A; though some men are not Englishmen, it does not follow that some English- men are not men. The only mode usually recognized of converting a par- ticular negative proposition, is in the form. Some A is not B, therefore something wdiich is not B is A ; and this is termed conversion by contra- position. In this case, however, the predicate and subject are not merely reversed, but one of them is changed. Instead of [A] and [B], the terms of the new proposition are [a thing which is not B], and [A]. The origi- nal proposition. Some A is not B, is first changed into a proposition equi- pollent with it. Some A is " a thing which is not B ;" and the proposition, being now no longer a particular negative, but a particular affirmative, ad- raits of conversion in the first mode, or as it is called, simple conversion.f In all these cases there is not really any inference; there is in the con- clusion no new truth, nothing but what was already asserted in the prem- ises, and obvious to whoever apprehends them. The fact asserted in the conclusion is either the very same fact, or part of the fact, asserted in the original proposition. This follows from our previous analysis of the Im- port of Propositions. When we say, for example, that some lawful sov- ereigns are tyrants, w^hat is the meaning of the assertion? That the attri- butes connoted by the term " lawful sovereign," and the attributes connoted by the term " tyrant," sometimes co-exist in the same individual. Now this is also precisely what we mean, when w^e say that some tyrants are lawful sovereigns ; which, therefore, is not a second proposition inferred from the first, any more than the English translation of Euclid's Elements is a col- lection of theorems different from and consequences of, those contained in the Greek original. Again, if we assert that no great general is a rash man, we mean that the attributes connoted by " great general," and those connoted by "rash," never co-exist in the same subject; wdiich is also the exact meaning which would be expressed by saying, that no rash man is a * The diflPerent cases of Eqnipollency, or "Equivalent Prepositional Forms," are set fortli with some fullness in Professor Bain's"^ Logic. One of the commonest of these changes of expression, that from affirming a proposition to denying its negative, or vice versa, Mr. Bain designates, very happily, by the name Obversion. t As Sir William Hamilton has pointed out, "Some A is not B " may also be converted in the followiug form : " No B is some A." Some men are not negroes ; therefore. No negroes are some men (e. g., Europeans). - 124 EEASONING. great general. When we say that all quadrupeds are warm-blooded, we assert, not only that the attributes connoted by " quadruped " and those connoted by " warm-blooded " sometimes co-exist, but that the former nev- er exist without the latter : now the proposition, Some warm-blooded crea- tures are quadrupeds, expresses the first half of this meaning, dropping the latter half; and therefore has been already affirmed in the antecedent prop- osition. All quadrupeds are warm-blooded. But that all warm-blooded creatures are quadrupeds, or, in other words, that the attributes connoted by " warm-blooded " never exist without those connoted by " quadruped," has not been asserted, and can not be inferred. In order to re-assert, in an inverted form, the whole of what was affirmed in the proposition. All quad- rupeds are warm-blooded, we must convert it by contraposition, thus, I^oth- ing which is not warm-blooded is a quadruped. This proposition, and the one from which it is derived, are exactly equivalent, and either of them may be substituted for the other ; for, to say that when the attributes of a quad- ruped are present, those of a warm-blooded creature are present, is to say that when the latter are absent the former are absent. In a manual for young students, it would be proper to dwell at greater length on the conversion and equipoUency of propositions. For though that can not be called reasoning or inference which is a mere re-assertion in different words of what had been asserted before, there is no more impor- tant intellectual habit, nor any the cultivation of which falls more strictly within the province of the art of logic, than that of discerning rapidly and surely the identity of an assertion when disguised under diversity of lan- guage. That important chapter in logical treatises which relates to the Op- position of Propositions, and the excellent technical language which logic provides for distinguishing the different kinds or modes of opposition, are of use chiefly for this purpose. Such considerations as these, that contrary propositions may both be false, but can not both be true ; that subcontrary propositions may both be true, but can not both be false ; that of two con- tradictory propositions one must be true and the other false ; that of two subalternate propositions the truth of the universal proves the truth of the particular, and the falsity of the particular proves the falsity of the univer- sal, but not vic^ versa ^'"^ are apt to appear, at first sight, very technical and mysterious, but when explained, seem almost too obvious to require so form- al a statement, since the same amount of explanation which is necessary to make the principles intelligible, would enable the truths which they con- vey to be apprehended in any particular case which can occur. In this respect, however, these axioms of logic are on a level with those of mathe- matics. That things which are equal to the same thing are equal to one another, is as obvious in any particular case as it is in the general state- ment : and if no such general maxim had ever been laid down, the demon- strations in Euclid would never have halted for any difficulty in stepping across the gap which this axiom at present serves to bridge over. Yet no *^^ i ^' 5!- contraries. No A IS Bj SomeAisB ) ^ . Some A is not Bj o A • , T> r contradictories. Some A is not B) No A is B) , , T . • Some A is BJ" ^^'"^ contradictories. i^^ i i' !? !- and ^° ^ ^ ^ , T,l respectively subalternate. Some A is B) Some A is not Bj ^ -' INFERENCE IN GENERAL. 125 one has ever censured writers on geometry, for j)l.'icing a list of these ele- mentary generalizations at the head of their treatises, as a first exercise to the learner of the faculty which will be recjuired in him at every step, that of apprehending a general truth. And the student of logic, in the discus- sion even of such truths as we have cited above, acquires habits of cir- cumspect interpretation of words, and of exactly measuring the length and breadth of his assertions, which are among the most indispensable condi- tions of any considerable mental attainment, and which it is one of the primary objects of logical discipline to cultivate. § 3. Having noticed, in order to exclude from the province of Reasoning or Inference properly so called, the cases in which the progression from one truth to another is only apparent, the logical consequent being a mere rep- etition of the logical antecedent ; we now pass to those which are cases of inference in the proper acceptation of the terra, those in which we set out from known truths, to arrive at others really distinct from them. Reasoning, in the extended sense in which I use the term, and in which it is synonymous with Inference, is popularly said to be of two kinds : rea- soning from particulars to generals, and reasoning from generals to partic- ulars ; the former being called Induction, the latter Ratiocination or Syllo- gism. It will presently be shown that there is a third species of reasoning, which falls under neither of these descriptions, and which, nevertheless, is not only vahd, but is the foundation of both the others. It is necessary to observe, that the expressions, reasoning from particu- lars to generals, and reasoning from generals to particulars, are recom- mended by brevity rather than by precision, and do not adequately mark, without the aid of a commentary, the distinction between Induction (in the sense now adverted to) and Ratiocination. The meaning intended by these expressions is, that Induction is inferring a proposition from propositions less general than itself, and Ratiocination is inferring a proposition from propositions equally or more general. When, from tlie observation of a number of individual instances, we ascend to a general proposition, or when, by combining a number of general propositions, we conclude from them another proposition still more general, the process, which is substantially the same in both instances, is called Induction. When from a general prop- osition, not alone (for from a single proposition nothing can be concluded which is not involved in the terms), but by combining it with other propo- sitions, we infer a proposition of the same degree of generality with itself, or a less general proposition, or a proposition merely individual, the process is Ratiocination. When, in short, the conclusion is more general than the largest of the premises, the argument is commonly called Induction ; when less general, or equally general, it is Ratiocination. As all experience begins with individual cases, and proceeds from them to generals, it might seem most conformable to the natural order of thought that Induction should be treated of before we touch upon Ratiocination. It will, however, be advantageous, in a science which aims at tracing our acquired knowledge to its sources, that the inquirer should commence with the latter rather than with the earlier stages of the process of constructing our knowledge; and should trace derivative truths backward to the truths from which they are deduced, and on which they depend for their evidence, before attempting to point out the original spring from which both ulti- mately take their rise. The advantages of this order of proceeding in the present instance will manifest themselves as we advance, in a manner su- perseding the necessity of any further justification or explanation. 126 REASONING. Of Induction, therefore, we shall say no more at present, than that it at least is, without doubt, a process of real inference. The conclusion in an induction embraces more than is contained in the premises. The principle or law collected from particular instances, the general proposition in which we embody the result of our experience, covers a much larger extent of ground than the individual experiments which form its basis. A principle ascertained by experience, is more than a mere summing up of what has been specifically observed in the individual cases which have been exam- ined ; it is a generalization grounded on those cases, and expressive of our belief, that what we there found true is true in an indefinite number of cases which we have not examined, and are never likely to examine. The nature and grounds of this inference, and the conditions necessary to make it legitimate, will be the subject of discussion in the Third Book: but that such inference really takes place is not susceptible of question. In every induction we proceed from truths which we knew, to truths which we did not know ; from facts certified by observation, to facts which we have not observed, and even to facts not capable of being now observed; future facts, for example ; but which we do not hesitate to believe on the sole evi- dence of the induction itself. Induction, then, is a real process of Reasoning or Inference. Whether, and in what sense, as much can be said of the Syllogism, remains to be de- termined by the examination into which we are about to enter. CHAPTER II. OF RATIOCINATIO]S^, OR SYLLOGISM. § 1. The analysis of the Syllogism has been so accurately and fully per- formed in the common manuals of Logic, that in the present work, which is not designed as a manual, it is sufficient to recapitulate, mevnoricie causa, the leading results of that analysis, as a foundation for the remarks to be afterward made on the functions of the Syllogism, and the place which it holds in science. To a legitimate syllogism it is essential that there should be three, and no more than three, propositions, namely, the conclusion, or proposition to be proved, and two other propositions which together prove it, and which are called the premises. It is essential that there should be three, and no more than three, terms, namely, the subject and predicate of the conclu- sion, and another called the middle term, which must be found in both premises, since it is by means of it that the other two terms are to be con- nected together. The predicate of the conclusion is called the major term of the syllogism; the subject of the conclusion is called the minor term. As there can be but three terms, the major and minor terms must each be found in one, and only one, of the premises, together with the middle term which is in them both. The premise which contains the middle term and the major term is called the major premise; that which contains the mid- dle term and the minor term is called the minor premise. Syllogisms are divided by some logicians into thvQQ figures, by others into four, according to the position of the middle term, which may either be the subject in both premises, the predicate in both, or the subject in one and the predicate in the other. The most common case is that in which RATIOCINATION, OK SYLLOGISM. 127 the middle term is the subject of the innjor premise and the ])redicate of the minor. This is reckoned as the first ti<:^ure. Wiien the middle term is the predicate in both premises, the syllogism belongs to the second tigui'e ; when it is the subject in both, to the third. In the fourth figure the mid- dle term is the subject of the minor premise and the i)redicate of the major. Those writers who reckon no more than three figures, include this case in the first. Each figure is divided into moods^ according to what are called the quan- tity and quality of the propositions, that is, according as they are universal or particular, affirmative or negative. The following are examples of all the legitimate moods, that is, all those in which the conclusion correctly follows from the premises. A is the minor term, C the major, B the mid- dle term. FIRST FIGURE. AllBisC NoBisC AUBisC No B is C All A is B All A is B Some A is B Some A is B therefore therefore therefore therefore ' All A is C No A is C Some A is C Some A is not C SECOND FIGURE. NoCisB AUG is B No C is B All C is B All A is B No A is B Some A is B Some A is not B therefore therefore therefore therefore No A is C No A is C Some A is not C Some A is not C THIRD FIGURE. All B is C No B is C Some B is C All B is C Some B is not C No B is C All B is A All B is A All B is A Some B is A All B is A Some B is A therefore therefore therefore therefore therefore therefore Some A is C Some A is not C Some A is C Some A is C Some A is not C Some A is not C FOURTH FIGURE. AUG is B AUG is B Some G is B No G is B No G is B All B is A No B is A All B is A All B is A Some B isA therefore therefore therefore therefore therefore Some A is G Some A is not G Some A is G Some A is not G Some A is not G In these exemplars, or blank forms for making syllogisms, no place is assigned to singular propositions ; not, of course, because such proposi- tions are not used in ratiocination, but because, their predicate being af- firmed or denied of the whole of the subject, they are ranked, for the pur- poses of the syllogism, with universal propositions. Thus, these two syllo- gisms — All men are mortal. All men are mortal, All kings are men, Socrates is a man, therefore therefore All kings are mortal, Socrates is mortal, are arguments precisely similar, and are both ranked in the first mood of the first figure.* * Professor Bain denies the claim of Singular Propositions to be classed, for the purposes of ratiocination, with Universal ; though they come within the designation which he himself proposes as an equivalent for Universal* that of Total. He would even, to use his own ex- pression, banish them entirely from the syllogism. He takes as an example, Socrates is wise, Socrates is poor, therefore Some poor men are wise, or more properly (as he observes) "one poor man is wise." "Now, if wise, poor, and a man, are attributes belonging to the meaning of the word Socrates, there is then no march of 128 EEASONING. The reasons why syllogisms in any of the above forms are legitimate, that is, why, if the premises are true, the conclusion must inevitably be so, and why this is not the case in any other possible mood (that is, in any other combination of universal and particular, affirmative and negative propositions), any person taking interest in these inquiries may be pre- sumed to have either learned from the common-school books of the syllo- gistic logic, or to be capable of discovering for himself. The reader may, however, be referred, for every needful explanation, to Archbishop Whate- ly's Elements of Logic, where he will find stated with philosophical pre- cision, and explained with remarkable perspicuity, the whole of the com- mon doctrine of the syllogism. All valid ratiocination ; all reasoning by which, from general propositions reasoning at all. We have given in Socrates, inter alia, the facts vi^ise, poor, and a man, and we merely repeat the concurrence which is selected from the whole aggregate of properties making up the whole, Socrates. The case is one under the head 'Greater and Less Connota- tion ' in Equivalent Prepositional Forms, or Immediate Inference, "But the example in this form does not do justice to the syllogism of singulars. We must suppose both propositions to be real, the predicates being in no way involved in the subject. Thus Socrates was the master of Plato, Socrates fought at Delium, The master of Plato fought at Delium. "It may fairly be doubted whether the transitions, in this instance, are any thing more than equivalent forms. For the proposition ' Socrates was the master of Plato and fought at Delium,' compounded out of the two premises, is obviously nothing more than a grammatical abbreviation. No one can say that there is here any change of meaning, or any thing beyond a verbal modification of the original form. The next step is, ' The master of Plato fought at Delium,' which is the previous statement cut down by the omission of Socrates. It contents itself with repi'oducing a part of the meaning, or saying less than had been previously said. The full equivalent of the affirmation is, ' The master of Plato fought at Delium, and the master of Plato was Socrates:' the new form omits the last piece of information, and gives only the first. Now, we never consider that we have made a real inference, a step in advance, when we repeat less than we are entitled to say, or drop from a complex statement some por- tion not desired at the moment. Such an operation keeps strictly within the domain of equiv- alence, or Immediate Inference. In no way, therefore, can a syllogism with two singular premises be viewed as a genuine syllogistic or deductive inference." {Logic, i., 159.) The first argument, as will have been seen, rests upon the supposition that the name Soc- rates has a meaning; that man, wise, and poor, are parts of this meaning; and that by predi- cating them of Socrates we convey no information ; a view of the signification of names which, for reasons already given,* I can not admit, and which, as applied to the class of names which Socrates belongs to, is at war with Mr. Bain's own definition of a Proper Name (i., 148), "a single meaningless mark or designation appropriated to tlie thing." Such names, Mr. Bain proceeded to say, do not necessarily indicate even human beings : much less then does the name Socrates include the meaning of wise or poor. Otherwise it would follow that if Socrates had grown rich, or had lost his mental faculties by illness, he would no longer have been called Socrates. The second part of Mr. Bain's argument, in which he contends that even when the premises convey real information, the conclusion is merely the premises with a part left out, is applica- ble, if at all, as much to universal propositions as to singular. In every syllogism the con- clusion contains less than is asserted in the two premises taken together. Suppose the syllo- gism to be All bees are intelligent, All bees are insects, therefore Some insects are intelligent : one might use the same liberty taken by Mr. Bain, of joining together the two premises as if they were one — "All bees are insects and intelligent" — and might say that in omitting the middle term bees we make no real inference, but merely reproduce part of what had been pre- viously said, Mr, Bain's is really an objection to the syllogism itself, or at all events to the third figure : it has no special applicability to singular propositions, * Note to § 4 of the chapter on Definition, supra, pp. 110, 111, I RATIOC.'INATION, Oil SYLLOGISM. 129 ])revionsly fidmittcd, other i)ropositioiis cfjually oi- loss general are inferrehy, and at greater length, to his posthumous Lec- tures on Logic. In Mr. De IMorgan's volume — abounding, in its more popular parts, with valuable obsei-va- tions felicitously expressed — the principal feature of originality is an attempt to bring within strict technical rules the cases in which a conclusion can be drawn from premises of a form usually classed as particular. ]\Ir. De Morgan observes, very justly, that from the premises most Bs are Cs, most Bs are As, it may be concluded with certainty that some As are Cs, since two portions of the class B, each of them comprising more than half, must necessarily in part consist of the same individuals. Following out this line of thought, it is equally evi- dent that if we knew exactly what proportion the "most" in each of the premises bear to the entire class B, we could increase in a corresponding degree the definiteness of the conclusion. Thus if 60 per cent, of B are included in C, and 70 per cent, in A, 30 per cent, at least musr be common to both ; in other words, the number of As which are Cs, and of Cs which are As, must be at least equal to 30 per cent, of the class B. Proceeding on this conception of "numerically definite propositions," and extending it to such forms as these: — "45 Xs (or more) are each of them one of 70 Ys,'' or "45 Xs (or more) are no one of them to be found among 70 Ys," and examining what inferences admit of being drawn from the various com- binations which may be made of premises of this description, Mr. De Morgan establishes uni- versal formula3 for such inferences ; creating for that purpose not only a new technical lan- guage, but a formidable array of symbols analogous to those of algebra. Since it is undeniable that inferences, in the cases examined b}' Mr. De IMorgan, can legiti- mately be drawn, and that the ordinary theory takes no account of them, I will not say that it was not worth while to show in detail how these also could be reduced to formula; as rigor- ous as those of Aristotle. What Mr. De Morgan has done was worth doing once (perhaps more than once, as a school exercise) ; but I question if its results are worth studying and mastering for any practical purpose. The practical use of technical forms of reasoning is to bar out fallacies : but the fallacies which require to be guarded against in ratiocination properly so called, arise from the incautious use of the common forms of language ; and the logician must track the fallacy into that territory, instead of waiting for it on a territory of his own. ^^ hile he remains among propositions which have acquired the numerical precision of the Calculus of Probabilities, the enemy is left in possession of the only ground on which he can be formidable* And since the propositions (short of universal) on which a thinker has to de- 132 KEASONING. § 2. On examining, then, these two general formulae, we find that in both of them, one premise, the major, is a universal proposition; and ac- pend, either for purposes of speculation or of practice, do not, except in a few peculiar cases, admit of any numerical precision ; common reasoning can not be translated into Mr. De Morgan's forms, which therefore can not serve any purpose as a test of it. Sir William Hamilton's theory of the "quantification of the predicate " may be described as follows : "Logically" (I quote his words) "we ought to take into account the quantity, always un- derstood in thought, but usually, for manifest reasons, elided in its expression, not only of the subject, but also of the predicate of a judgment." All A is B, is equivalent to all A is some B. No A is B, to No A is any B. Some A is B, is tantamount to some A is some B. Some A is not B, to Some A is not any B. As in these forms of assertion the predicate is exactly co-extensive with the subject, they all admit of simple conversion ; and by this we obtain two additional forms — Some B is all A, and No B is some A. We may also make the assertion All A is all B, which will be true if the classes A and B are exactly co-extensive. The last three forms, though conveying real assertions, have no place in the ordinary classifi- cation of Propositions. All propositions, then, being supposed to be translated in|o this lan- guage, and written each in that one of the preceding forms which answei's to its signification, there emerges a new set of syllogistic rules, materially different from the common ones. A general view of the points of difference may be given in the words of Sir W. Hamilton {Dis- cussions, 2d ed., p. 651) : "The revocation of the two terms of a Proposition to their true relation ; a proposition be- ing always an equation of its subject and its predicate. ",The consequent reduction of the Conversion of Propositions from three species to one — that of Simple Conversion. " The reduction of all the General Laws of Categorical Syllogisms to a single Canon. "The evolution from that one canon of all the Species and varieties of Syllogisms. " The abrogation of all the Special Laws of Syllogism. "A demonstration of the exclusive possibility of Three Syllogistic Figures; and (on new grounds) the scientific and final abolition of the Fourth. "A manifestation that Figure is an unessential variation in syllogistic form; and the con- sequent absui'dity of Reducing the syllogisms of the other figures to the first. "An enouncement of one Organic Principle for each Figure. "A determination of the true number of the Legitimate Moods ; with "Their amplification in number (thirty-six); "Their numerical equality under all the figures ; and "Their relative equivalence, or virtual identity, throughout every schematic difference. "That, in the second and third figures, the extremes holding both the same relation to the middle term, there is not, as in the first, an opposition and subordination between a term ma- jor and a term mhior, mutually containing and contained, in the counter wholes of Extension and Comprehension. "Consequently, in the second and third figures, there is no determinate major and minor premises, and there are two indifferent conclusions : whereas in the first the premises are de- terminate, and there is a single proximate conclusion." This doctrine, like that of Mr. De Morgan previously noticed, is a real addition to the syl- logistic theory ; and has moreover this advantage over Mr. De Morgan's " numerically definite Syllogism," that the forms it supplies are really available as a test of the correctness of ratioc- ination ; since propositions in the common form may always have their predicates quantified, and so be made amenable to Sir W. Hamilton's rules. Considered, however, as a contribution to the Science of Logic, that is, to the analysis of the mental processes concerned in reasoning, the new doctrine appears to me, I confess, not merely superfluous, but erroneous ; since the form in which it clothes propositions does not, like the ordinary form, express what is in the mind of the speaker when he enunciates the proposition. I can not think Sir William Ham- ilton right in maintaining that the quantity of the predicate is "always understood in thought." It is implied, but is not present to the mind of the person who asserts the proposition. The quantification of the predicate, instead of being a means of bringing out more clearly the mean- ing of the proposition, actually leads the mind out of the proposition, into another order of ideas. For when we say. All men are mortal, we simply mean to affirm the attribute mor- tality of all men ; without thinking at all of the class mortal in the concrete, or troubling our- selves about whether it contains any other beings or not. It is only for some artificial pur- pose that we ever look at the proposition in the aspect in which the predicate also is thought of as a class-name, either including the subject only, or the subject and something more. (See above, p. 77, 78.) For a fuller discussion of this subject, see the twenty-second chapter of a work already re- ferred to, "An Examination of Sir William Hamilton's Philosophy." ^ KATIOCINATION, OR SYLLOGISM. J.j.j cording as tliis is affirmative or negative, the conclusion is so too. All ratiocination, therefore, starts from a (jeiieral ])roposition, principle, or as- sumption : a proposition in which \\ predicate is affirmed or denied of an entire class; that is, in which some attribute, or the negation of some attribute, is asserted of an indefinite number of objects distinguished by a common characteristic, and designated, in consequence, by a common name. The other premise is always affirmative, and asserts that something (which may be either an individual, a class, or part of a class) belongs to, or is in- cluded in, the class respecting which something was affirmed or denied in the major premise. It follows that the attribute affirmed or denied of the entire class may (if that affirmation or denial was correct) be affirmed or denied of the object or objects alleged to be included in the class: and this is precisely the assertion made in the conclusion. Whether or not the foregoing is an adequate account of the constituent parts of the syllogism, will be presently considered ; but as far as it goes it is a true account. It has accordingly been generalized, and erected into a logical maxim, on which all ratiocination is said to be founded, insomuch that to reason, and to apply the maxim, are supposed to be one and the same thing. The maxim is. That whatever can be affirmed (or denied) of a class, may be affirmed (or denied) of every thing included in the class. This axiom, supposed to be the basis of the syllogistic theory, is tei'med by logicians the dictum de oiniii et mdlo. This maxim, however, when considered as a principle of reasoning, ap- pears suited to a system of metaphysics once indeed generally received, but which for the last two centuries has been considered as finally abandoned, though there have not been wanting in our own day attempts at its revival. So long as what are termed Universals were regarded as a peculiar kind of substances, having an objective existence distinct from the individual ob jects classed under them, the dictum de omni conveyed an important mean- ing ; because it expressed the intercommunity of nature, ^vhich it was nec- essary on that theory that w^e should suppose to exist betw^een those gen- eral substances and the particular substances which w^ere subordinated to them. That every thing predicable of the universal w^as predicable of the various individuals contained under it, was then no identical proposition, but a statement of what was conceived as a fundamental law of the uni- verse. The assertion that the entire nature and properties of the substan- tia secunda formed part of the nature and properties of each of the indi- vidual substances called by the same name ; that the properties of Man, for example, were properties of all men ; was a proposition of real significance wdien man did not mean all men, but something inherent in men, and vast- ly superior to them in dignity. Now, however, when it is known that a class, a universal, a genus or species, is not an entity ^:>er se, but neither more nor less than the individual substances themselves which are placed in the class, and that there is nothing real in the matter except those objects, a common name given to them, and common attributes indicated by the name ; what, I should be glad to know, do we learn by being told, that whatever can be affirmed of a class, may be affirmed of every object con- tained in the class? The class is nothing but the objects contained in it : and the dictum de 07nni merely amounts to the identical proposition, that whatever is true of certain objects, is true of each of those objects. If all ratiocination were no more than the application of this maxim to particular cases, the syllogism would indeed be, what it has so often been declared to 134 REASONING. ^ be, solemn trifling. The dictum de omni is on a par with another truth, which in its time was also reckoned of great importance, " Whatever is, is." To give any real meaning to the dictum de omni, we must consider it not as an axiom, but as a definition; we must look upon it as intended to explain, in a circuitous and paraphrastic manner, the meaning of the word class. An error which seemed finally refuted and dislodged from thought, often needs only put on a new suit of phrases, to be welcomed back to its old quarters, and allowed to repose unquestioned for another cycle of ages. Modern philosophers have not been sparing in their contempt for the scho- lastic dogma that genera and species are a peculiar kind of substances, which general substances being the only permanent things, while the individual substances comprehended under them are in a perpetual flux, knowledge, which necessarily imports stability, can only have relation to those general substances or universals, and not to the facts or particulars included un- der them. Yet, though nominally rejected, this very doctrine, whether dis- guised under the Abstract Ideas of Locke (whose speculations, however, it has less vitiated than those of perhaps any other writer who has been in- fected with it), under the ultra-nominalism of Hobbes and Condillac, or the ontology of the later German schools, has never ceased to poison philosophy. Once accustomed to consider scientific investigation as essentially consist- ing in the study of universals, men did not drop this habit of thought when they ceased to regard universals as possessing an independent existence: and even those who went the length of considering them as mere names, could not free themselves from the notion that tlie investigation of truth consisted entirely or partly in some kind of conjuration or juggle with those names. When a philosopher adopted fully the Nominalist view of the sisrnification of oeneral lano^uao^e, retaining^ alonsj with it the dictum^ de omni as the foundation of all reasoning, two such premises fairly put to- gether were likely, if he was a consistent thinker, to land him in rather startling conclusions. Accordingly it has been seriously held, by writers of deserved celebrity, that the pi'ocess of arriving at new truths by reason- ing consists in the mere substitution of one set of arbitrary signs for an- other; a doctrine which they suppose to derive irresistible confirmation from the example of algebra. If there were any process in sorcery or necromancy more preternatural than this, I should be much surprised. The culminating point of this philosophy is the noted aphorism of Condil- lac, that a science is nothing, or scarcely any thing, but U7ie langue bien faite; in other words, that the one sufticient rule for discovering the nature and properties of objects is to name them properly : as if the reverse were not the truth, that it is impossible to name them properly except in propor- tion as we are already acquainted with their nature and properties. Can it be necessary to say, that none, not even the most trivial knowledge with respect to Things, ever was or could be originally got at by any conceivable manipulation of mere names, as such ; and that what can be learned from names, is only what somebody who used the names knew before ? Philo- sophical analysis confirms the indication of common sense, that the func- tion of names is but that of enabling us to remember and to communicate our thoughts. That they also strengthen, even to an incalculable extent, the power of thought itself, is most true : but they do this by no intrinsic and peculiar virtue ; they do it by the power inherent in an artificial mem- ory, an instrument of which few have adequately considered the immense potency. As an artificial memory, language truly is, what it has so often KATIOCINATION, OR SYLLOGISM. ITiS "oeen called, an instrument of thought; but it is one thing to be the instru- ment, and another to be the exclusive subject upon which the instrument is exercised. We think, indeed, to a considerable extent, by means of names, but what we think of, are the things called by those names ; and there can not be a greater error than to imagine that thought can be car- I'ied on with nothing in our mind but names, or that we can make the names think for us. § 3. Those who considered the dictum de omni as the foundation of the syllogism, looked upon arguments in a manner corresponding to the erro- neous view which Hobbes took of propositions. Because there are some })ropositions which are merely verbal, Hobbes, in order apparently that his definition might be rigorously universal, defined a proposition as if no propositions declared any thing except the meaning of words. If Hobbes was right; if no further account than this could be given of the import of propositions; no theory could be given but the commonly received one, of the combination of propositions in a syllogism. If the minor premise asserted nothing more than that something belongs to a class, and if the major premise asserted nothing of tliat class except that it is included in another class, the conclusion w^ould only be that what was included in the lower class is included in the higher, and the result, therefore, nothing ex- cept that the classification is consistent with itself. But we have seen that it is no sufiicient account of the meaning of a proposition, to say that it refers something to, or excludes something from, a class. Every proposi- tion which conveys real information asserts a matter of fact, dependent on the laws of nature, and not on classification. It asserts that a given object does or does not possess a given attribute; or it asserts that two attri- butes, or sets of attributes, do or do not (constantly or occasionally) co-ex- ist. Since such is the purport of all propositions which convey any real knowledge, and since ratiocination is a mode of acquiring real knowledge, any theory of ratiocination which does not recognize this import of proj^o- sitions, can not, we may be sure, be the true one. Applying this view of propositions to the two premises of a syllogism, we obtain the following results. The major premise, which, as already remarked, is always universal, asserts, that all things which have a certain attribute (or attributes) have or have not along with it, a certain other at- tribute (or attributes). The minor premise asserts that the thing or set of things which are the subject of that premise, have the first-mentioned attribute ; and the conclusion is, that they have (or that they have not), the second. Thus in our former example, All men are mortal, Socrates is a man, therefore Socrates is mortal, the subject and predicate of the major premise are connotative terms, de- noting objects and connoting attributes. The assertion in the major prem- ise is, that along with one of the two sets of attributes, we always find the other: that the attributes connoted by "man" never exist unless con- joined with the attribute called mortality. The assertion in the minor prem- ise is that the individual named Socrates possesses the former attributes; and it is concluded that he possesses also the attribute mortality. Or, if both the premises are general propositions, as 136 REASONING. All men are mortal, All kings are men, therefore All kings are mortal, the minor premise asserts that the attributes denoted by kingship only exist in conjunction with those signified by the word man. The major asserts as before, that the last-mentioned attributes are never found without the attribute of mortality. The conclusion is, that wherever the attributes of kingship are found, that of mortality is found also. If the major premise were negative, as, No men are omnipotent, it would assert, not that the attributes connoted by " man" never exist without, but that they never exist with, those connoted by " omnipotent :" from which, together with the minor premise, it is concluded, that the same incompati- bility exists between the attribute omnipotence and those constituting a king. In a similar manner we might analyze any other example of the syllogism. If we generalize this process, and look out for the principle or law in- volved in every such inference, and presupposed in every syllogism, the propositions of which are any thing more than merely verbal; we find, not the unmeaning dictimi de omni el nidlo, but a fundamental principle, or rather two principles, strikingly resembling the axioms of mathematics. The first, which is the principle of affirmative syllogisms, is, that things which co-exist with the same thing, co-exist with one another: or (still more precisely) a thing which co-exists with another thing, wdiich other co-exists with a third thing, also co-exists with that third thing. The second is the principle of negative syllogisms, and is to this effect : that a thing which co-exists with another thing, with which other a third thing does not co-ex- ist, is not co-existent with that third thing. These axioms manifestly relate to facts, and not to conventions ; and one or other of them is the ground of the legitimacy of every argument in which facts and not conventions are the matter treated of.* * Mr. Herbert Spencer {Principles of Psychology, pp. 1 25-7), though his theory of the syl- logism coincides with all that is essential of mine, thinks it a logical fallacy to present the two axioms in the text, as the regulating principles of syllogism. He charges me with falling into the error pointed out by Archbishop Whately and myself, of confounding exact Hkeness with literal identity ; and maintains, that we ought not to say tluxt Socrates possesses the same attributes which are connoted by the word Man, but only that he possesses attributes exactly like them : according to which phraseology, Socrates, and the attribute mortality, are not two things co-existing with the same thing, as the axiom asserts, but two things co- existing with two ditterent tilings. The question between Mr. Spencer and me is merely one of language ; for neither of us (if I understand Mr. Spencer's opinions rightly) believes an attribute to be a real thing, possessed of objective existence ; we believe it to be a particular mode of naming our setisations, or our expectations of sensation, when looked at in their relation to an external object which excites them. The question raised by Mr. Spencer does not, therefore, concern the properties of any really existing thing, but tlie comparative a])propriateness, for philosophical purposes, of two different modes of using a name. Considered in this point of view, the phraseology I have employed, whi(;h is that commonly used by philosophei's, seems to me to be the best. Mr. Spencer is of opinion that because Socrates and Alcibiades are not tlie same man, the attri- bute which constitutes them men should not be called the same attribute ; that because the humanity of one man and that of another express themselves to our senses not by the same individual sensations but by sensations exactly alike, humanity ought to be regarded as a dif- ferent attribute in every different man. But on this showing, the humanity even of any one man should be considered as different attributes now and half an hour hence ; for the sensa- tions by which it will then manifest itself to my organs will not be a continuation of my pres- ent sensations, but a repetition of them ; fresh sensations, not identical with, but only exactly KATIOCINATION, OR SYLLOGISM. l:{7 8 4. It rcm.'iins to trun.sliite this ox position of tlie syiloi^ism from the one into the other of the two languages in vvfiicli we foi'nierly reniarke'P*' that all propositions, and of course therefore all combinations (jf })i'oposi- tions, might be exi)resse(l. We observed that a proposition might )je con- sidered in two different liglits; as a portion of our knowledge of nature, or as a memorandum for our guidance. Under the former, or si)eculative aspect, an afHrmative general proposition is an assertion of a speculative truth, viz., that whatever has a certain attribute has a certain other attribute. Under the other aspect, it is to be regarded not as a part of our knowledge, but as an aid for our practical exigencies, by enabling us, when we see or learn that an object possesses one of the tw^o attributes, to infer that it pos- sesses the other; thus employing the first attribute as a mark or evidence of the second. Thus regarded, every syllogism comes within the following general formula : Attribute A is a mark of attribute B, The given object has the mark A, therefore The given object has the attribute B. Referred to this type, the arguments which w^e have lately cited as specimens of the syllogism, will express themselves in the following manner : The attributes of man are a mark of the attribute mortality, Socrates has the attributes of man, therefore Socrates has the attribute mortality. like the present. If every general conception, instead of being "the One in the Many," were considered to be as many different conceptions as there are things to which it is applicable, there would be no such thing as general language. A name would have no general meaning if man connoted one thing when predicated of John, and another, though closely resembling, thing when predicated of William. Accordingly a recent pamphlet asserts the impossibility of general knowledge on this precise ground. The meaning of any general name is some outward or inward phenomenon, consisting, in the last resort, of feelings ; and these feelings, if their continuity is for an instant broken, are no longer the same feelings, in the sense of individual identity. What, then, is the common something which gives a meaning to the general name ? Mr. Spencer can only say, it is the similarity of the feelings ; and I rejoin, the attribute is precisely that similarity. The names of attributes are in their ultimate analysis names for the resemblances of our sensations (or other feelings). Every general name, whether abstract or concrete, denotes or connotes one or more of those resemblances. It will not, probably, be denied, that if a hundred sensations are undistinguishably alike, their resemblance ought to be spoken of as one resemblance, and not a hundred resemblances which merely resemble one another. The things compared are many, but the something common to all of them must be conceived as one, just as the name is conceived as one, though corresponding to numerically different sensations of sound each time it is pronounced. The general term man does not connote the sensations derived once from one man, which, once gone, can no more occur again than the same flash of light- ning. It connotes the general type of the sensations derived always from all men, and the power (always thought of as one) of producing sensations of that type. And the axiom might be thus worded : Two types of sensation each of which co-exists with a third type, co-exist with another; or Two powers each of which co-exists with a third power co-exist Avith one another. ]Mr. Sjjencer has misunderstood me in another particular. He supposes that the co-exist- ence spoken of in the axiom, of two things with the same third thing, means siniultaneousnes.>- in time. The co-existence meant is that of being jointly attributes of the same subject. The attribute of being born without teeth, and the attribute of having thirty-two teeth in mature age, are in this sense co-existent, both being attributes of man, though ex vi termini never of the same man at the same time. * Supra, p. 93. 138 REASONING. And again, The attributes of man are a mark of the attribute mortality, The attributes of a king are a mark of the attributes of man, therefore The attributes of a king are a mark of the attribute mortality. And, lastly, The attributes of man are a mark of the absence of the attribute omnipotence. The attributes of a king are a mark of the attributes of man, thierefore The attributes of a king are a mark of the absence of the attribute signified by the word omnipotent (or, are evidence of the absence of that attribute). To correspond with this alteration in the form of the syllogisms, the ax- ioms on which the syllogistic process is founded must undergo a corre- sponding transformation. In this altered phraseology, both those axioms may be brought under one general expression ; namely, that whatever has any mark, has that which it is a mark of. Or, when the minor premise as well as the major is universal, we may state it thus: Whatever is a mark of any mark, is a mark of that which this last is a mark of. To trace the identity of these axioms with those previously laid down, may be left to the intelligent reader. We shall find, as we proceed, the great convenience of the phraseology into which we have last thrown them, and which is better adapted than any I am acquainted with, to express with precision and force what is aimed at, and actually accomplished, in every case of the ascertain- ment of a truth by ratiocination.* * Professor Bain {Logic, i., 157) considers the axiom (or rather axioms) liere proposed as a substitute for the dictum de omni, to possess certain advantages, but to be ' un^vorkable as a basis of the syllogism. The fVital defect consists in this, that it is ill-adapted to brmg out the difference between total and partial coincidence of terms, the observation of which is the essential precaution in syllogizing correctly. If all the terms were co-extensive, the axiom would flow on admirably ; A carries B, all B and none but B ; B carries C in the same man- ner- at once A carries C, without limitation or reserve. But in point of fact, we know that while A carries B, other things carry B also ; whence a process of limitation is required, in transferring A to C through B. A (in common with other things) carries B ; B (in common with other things) carries C ; whence A (in common with other things) carries C. The ax- iom provides no means of making this limitation ; if we were to follow A literally, we should be led to suppose A and C co-extensive : for such is the only obvious meaning of ' the attri- bute A coincides with the attribute C" , -^ A It is certainlv possible that a careless learner here and there may suppose that it A carries B it follows that B carries A. But if any one is so incautious as to commit this mistake, the very earliest lesson in the logic of inference, the Conversion of propositions, will correct it. The first of the two forms in which I have stated the axiom, is in some degree open to Mr. Bain's criticism: when B is said to co-exist with A (it must be by a lapsus calami that Mr. Bain uses the word coincide), it is possible, in the absence of warning, to suppose the meaning to be that the two things are only found together. But this misinterpretation is excluded by the other or practical, form of the maxim ; Nota notoi est nota rei ipsius. No one would be in any dinger of inferring that because a is a mark of b, h can never exist without a ; that because being in a confirmed consumption is a mark of being about to die, no one dies who is not in a consumption; that because being coal is a mark of having come out of the earth, notliing can come out of the earth except coal. Ordinary knowledge of English seems a suflicicnt protection against these mistakes, since in speaking of a mark of any thing we are never understood as implying reciprocity. ^ . . , ^ r -iKQ\ A more fundamental objection is stated by Mr. Bain in a subsequent passage (p. 158). "The axiom does not accommodate itself to the type of Deductive Reasoning as contrasted with Induction-tlie application of a general principle to a special case. Any thmg that foils to make prominent this circumstance is not adapted as a foundation for the syllogism. But FUNCTIONS AND VALUE OF THE SYLLOGISM. 139 CHAPTER III. OF THE FUNCTIONS AND LOGICAL VALUE OF THE SYLLOGISM. § 1. We have shown what is the real nature of the truths with whicli the Syllogism is conversant, in contradistinction to the more superficial manner in which tlieir import is conceived in the common theory; and what are the fundamental axioms on which its probative force or conclu- siveness depends. We have now to inquire, whether the syllogistic proc- ess, that of reasoning from generals to particulars, is, or is not, a process of inference ; a progress from the known to the unknown : a means of com- ing to a knowledge of something which we did not know before. Logicians have been remarkably unanimous in their mode of answering this question. It is universally allowed that a syllogism is vicious if there be any thing more in the conclusion than was assumed in the premises. But this is, in fact, to say, that nothing ever was, or can be, proved by syl- logism, which was not known, or assumed to be known, before. Is ratioci- nation, then, not a process of inference ? And is the syllogism, to which the word reasoning has so often been represented to be ex'clusively appro- priate, not really entitled to be called reasoning at all ? This seems an in- evitable consequence of the doctrine, admitted by all writers on the sub- ject, that a syllogism can prove no more than is involved in the premises. Yet the acknowledgment so explicitly made, has not prevented one set of writers from continuing to represent the syllogism as the correct analysis of what the mind actually performs in discovering and proving the larger half of the truths, whether of science or of daily life, which we believe; while those who have avoided this inconsistency, and followed out the gen- eral theorem respecting the logical value of the syllogism to its legitimate corollary, have been led to impute nselessness and frivolity to the syllogis- tic theory itself, on the ground of the 2^etitio 2)rinapii which they allege to be inherent in every syllogism. As I believe both these opinions to be fundamentally erroneous, I must request the attention of the reader to cer- tain considerations, without which any just appreciation of the true char- acter of the syllogism, and the functions it performs in philosophy, appears to me impossible; but which seem to have been either overlooked, or in- sufficiently adverted to, both by the defenders of the syllogistic theory and by its assailants. § 2. It must be granted that in every syllogism, considered as an though it may be proper to hmit the term Deduction to the application of a general principle to a special case, it has never been held that Ratiocination or Syllogism is subject to the same limitation; and the adoption of it would exclude a great amount of valid and conclusive syl- logistic reasoning. Moreover, if the dictum de omni makes prominent the fact of the applica- tion of a general principle to a particular case, the axiom I propose makes prominent the condition which alone makes that application a real inference. I conclude, therefore, that both forms have their value, and their place in Logic. The dictum de omni should be retained as the fundamental axiom of the logic of mere consistency, often called Formal Logic ; nor have I ever quarreled with the use of it in that character, nor proposed to banish it from treatises on Formal Logic. But the other is the proper axiom tor the logic of the pursuit of truth by way of Deduction ; and the recognition of it can alone show how it is possible that deductive reasoning can be a road to truth. 140 REASONING. argument to prove the conclusion, there is a petitio principii. When we say, All men are mortal, Socrates is a man, therefore Socrates is mortal ; it is unanswerably urged by the adversaries of the syllogistic theory, that the proposition, Socrates is mortal, is presupposed in the more general as- sumption. All men are mortal : that we can not be assured of the mortali- ty of all men, unless we are already certain of the mortality of every indi- vidual man : that if it be still doubtful whether Socrates, or any other in- dividual we choose to name, be mortal or not, the same degree of uncer- tainty must hang over the assertion. All men are mortal : that the general principle, instead of being given as evidence of the particular case, can not 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 syllogism to prove? That, in short, no reasoning from generals to particulars can, as such, prove any thing : since from a general principle we can not infer any particulars, but those which the principle itself assumes as known. This doctrine appears to me irrefragable ; and if logicians, though una- ble to dispute it, have usually exhibited a strong disposition to explain it away, this was not because they could discover any flaw in the argument itself, but because the contrary opinion seemed to rest on arguments equal- ly indisputable. In the syllogism last referred to, for example, or in any of those which we previously constructed, is it not evident that the conclu- sion may, to the person to whom the syllogism is presented, be actually and bona fide a new truth? Is it not matter of daily experience that truths previously unthought of, facts which have not been, and can not be, directly observed, are arrived at by way of general reasoning? We be- lieve that the Duke of Wellington is mortal. We do not know this by di- rect observation, so long as he is not yet dead. If we were asked how, this being the case, we know the duke to be mortal, we should probably answer. Because all men are so. Here, therefore, we arrive at the knowl- edge of a truth not (as yet) susceptible of observation, by a reasoning which admits of being exhibited in the following syllogism : All men are mortal. The Duke of Wellington is a man, therefore The Duke of Wellington is mortal. And since a large portion of our knowledge is thus acquired, logicians have persisted in representing the syllogism as a process of inference or proof; though none of them has cleared up the difficulty which arises from the inconsistency between that assertion, and the principle, that if there be any thing in the conclusion which was not already asserted in the premi- ses, the argument is vicious. For it is impossible to attach any serious scientific value to such a mere salvo, as the distinction drawn between be- ing involved by implication in the premises, and being directly asserted in them. When Archbishop Whately says* that the object of reasoning is " merely to expand and unfold the assertions wrapped up, as it were, and * Logic, p. 239 (9th ed.). FUNCTIONS AND VALUE OF THE SYLLOGISM. 141 implied in those with which we set out, utkI to brinp^ ;i person to perceive and acknowledge the full force of that which lie has admitted," he does not, I think, meet the real difficulty re(|uiring to be explained, namely, how it happens that a science, like geometry, 6Y<7i be all "wrapped up" in a few definitions and axioms. Nor does this defense of the syllogism differ much from what its assailants urge against it as an accusation, wlien they charge it with being of no use except to those who seek to press the con- sequences of an admission into which a person has been entrapped without having considered and understood its full force. When you admitted the major premise, you asserted the conclusion; but, says Archbishop Whate- ly, you asserted it by implication merely : this, however, can here only mean that you asserted it unconsciously ; that you did not know you were asserting it; but, if so, the difficulty revives in this shape — Ought you not to have known? Were you warranted in asserting the general proposi- tion without having satisfied yourself of the truth of every thing which it fairly includes? And if not, is not the syllogistic ^\% prima facie what its assailants affirm it to be, a contrivance for catching you in a trap, and hold- ing you fast in it ?* § 3. From this difficulty there appears to be but one issue. The propo- sition that the Duke of Wellington is mortal, is evidently an inference ; it is got at as a conclusion from something else ; but do we, in reality, con- clude it from the proposition, All men are mortal? I answer, no. The error committed is, I conceive, that of overlooking the distinction be- tween two parts of the process of philosophizing, the inferring part, and the registering part; and ascribing to the latter the functions of the former. The mistake is that of referring a person to his own notes for the origin of Ins knowledge. If a person is asked a question, and is at the moment una- ble to answer it, he may refresh his memory by turning to a memorandum which he carries about with him. But if he were asked, how the fact came to his knowledge, he would scarcely answer, because it was set down in his note-book : unless the book was written, like the Koran, with a quill from the wing of the angel Gabriel Assuming that the proposition, The Duke of Wellington is mortal, is immediately an inference from the proposition. All men are mortal ; whence do we derive our knowledge of that general truth? Of course from ob- servation. Now, all which man can observe are individual cases. Fi'om these all general truths must be drawn, and into these they may be again resolved ; for a general truth is but an aggregate of particular truths ; a comprehensive expression, by which an indefinite number of individual facts are affirmed or denied at once. But a general proposition is not merely a compendious form for recording and preserving in the memory a number of particular facts, all of which have been observed. Generaliza- * It is hardly necessary to say, that I am not contending for any such absurdity as that we actually "ought to have known" and considered the case of every individual man. past, pres- ent, and future, before affirming that all men are mortal : although this interpretation has been, strangely enough, put upon the preceding observations. There is no dift'erence between me and Archbishop Whately, or any other defender of the syllogism, on the practical part of the matter; I am only pointing out an inconsistency in the logical theory of it. as conceived by almost all writers. I do not say that a person who affirmed, before the Duke of "Wellington was born, that all men are mortal, knew that the Duke of AVelHngton was mortal ; but I do say that he asserted it ; and I ask for an explanation of the apparent logical fiillacy, of ad- ducing in proof of the Duke of Wellington's mortality, a general statement which presupposes it. Finding no sufficient resolution of this difficulty in any of the writers on Logic, I have attempted to supply one. 142 REASONING. tion is not a process of mere naming, it is also a process of inference. From instances which we have observed, we feel warranted in concluding, that w^hat we found true in those instances, holds in all similar ones, past, present, and future, however numerous they may be. We then, by that valuable contrivance of language which enables us to speak of many as if they were one, record all that we have observed, together with all that we infer from our observations, in one concise expression ; and have thus only one proposition, instead of an endless number, to remember or to commu- nicate. The results of many observations and inferences, and instructions for making innumerable inferences in unforeseen cases, are compressed into one short sentence. When, therefore, we conclude from the death of John and Thomas, and every other person we ever heard of in whose case the experiment had been fairly tried, that the Duke of Wellington is mortal like the rest; we may, indeed, pass through the generalization. All men are mortal, as an in- termediate stage ; but it is not in the latter half of the process, the de- scent from all men to the Duke of Wellington, that the inference resides. The inference is finished when we have asserted that all men are mortal. What remains to be performed afterward is merely deciphering our own notes. Archbishop Whately has contended that syllogizing, or reasoning from generals to particulars, is not, agreeably to the vulgar idea, a peculiar "mode of reasoning, but the philosophical analysis of the mode in which all men reason, and must do so if they reason at all. With the deference due to so high an authority, I can not help thinking that the vulgar notion is, in this case, the more correct. If, from our experience of John, Thomas, etc., who once were living, but are now dead, we are entitled to conclude that all hu- man beings are mortal, we might surely without any logical inconsequence have concluded at once from those instances, that the Duke of Wellington is mortal. The mortality of John, Thomas, and others is, after all, the w^hdle evidence we have for the mortality of the Duke of Wellington. Not one iota is added to the proof by interpolating a general proposition. Since the individual cases are all the evidence we can possess, evidence which no logical form into which we choose to throw it can make greater than it is ; and since that evidence is either sufficient in itself, or, if insuf- ficient for the one purpose, can not be sufficient for the other ; I am una- ble to see why we should be forbidden to take the shortest cut from these sufficient premises to the conclusion, and constrained to travel the " high priori road," by the arbitrary fiat of logicians. I can not perceive why it should be impossible to journey from one place to another unless we "march up a hill, and then march down again." It may be the safest road, and there may be a resting-place at the top of the hill, affording a commanding view of the surrounding country; but for the mere purpose of arriving at our journey's end, our taking that road is perfectly optional ; it is a question of time, trouble, and danger. Not only raay we reason from particulars to particulars without passing through generals, but we perpetually do so reason. All our earliest infer- ences are of this nature. From the first dawn of intelligence we draw in- ferences, but years elapse before Ave learn the use of general language. The child, who, having burned his fingers, avoids to thrust them again into the fire, has reasoned or inferred, though he has never thought of the gen- eral maxim, Fire burns. lie knows from memory that he has been burn- ed, and on this evidence believes, when he sees a candle, that if he puts his FUNCTIONS AND VALUE OF THE SYLLOGISM. 143 finger into the fl;ime of it, lie will be ])urii()(l aii^uiii. Ho l)elieves this in ev- ery cjise wliicli ]iMi)peiis to arise; but witliout looking, in each instance, be- yond the present case. lie is not generalizing; he is inferring a partic- ular from particulars. In the same way, also, brutes reason. There is no ground for attributing to any of the lower animals the use of signs, of such a nature as to render general propositions possible. But those ani- mals profit by experience, and avoid what they have found to cause them pain, in the same manner, though not always with the same skill, as a human creature. Not only the burned child, but the burned dog, dreads the fire. I believe that, in point of fact, when drawing inferences from our per- sonal experience, and not from maxims handed down to us by books or tradition, we much oftener conclude from particulars to particulars directly, than through the intermediate agency of any general proposition. We are constantly reasoning from ourselves to other people, or from one person to another, without giving ourselves the trouble to erect our observations into general maxims of human or external nature. When we conclude that some person will, on some given occasion, feel or act so and so, we sometimes judge from an enlarged consideration of the manner in which human beings in general, or persons of some particular character, are accustomed to feel and act ; but much oftener from merely recollecting the feelings and con- duct of the same person in some previous instance, or from considering how we should feel or act ourselves. It is not only the village matron, who, when called to a consultation upon the case of a neighbor's child, pro- nounces on the evil and its remedy simply on the recollection and authority of what she accounts the similar case of her Lucy. We all, where we have no definite maxims to steer by, guide ourselves in the same way : and if we have an extensive experience, and retain its impressions strongly, we may acquire in this manner a very considerable power of accurate judgment, which we may be utterly incapable of justifying or of communicating to others. Among the higher order of practical intellects there have been many of whom it was remarked how admirably they suited their means to their ends, without being able to give any sufficient reasons for what they did ; and applied, or seemed to apply, recondite principles which they were wholly unable to state. This is a natural consequence of having a mind stored with appropriate particulars, and having been long accustomed to reason at once from these to fresh particulars, without practicing the habit of stating to one's self or to others the corresponding general propositions. An old warrior, on a rapid glance at the outlines of the ground, is able at once to give the necessary orders for a skillful ari-angement of his troops ; though if he has received little theoretical instruction, and has seldom been called upon to answer to other people for his conduct, he may never have had in his mind a single general theorem respecting the relation between- ground and array. But his experience of encampments, in circumstances more or less similar, has left a number of vivid, unexpressed, ungeneralized analogies in his mind, the most appropriate of which, instantly suggesting itself, determines him to a judicious arrangement. The skill of an uneducated person in the use of weapons, or of tools, is of a precisely similar nature. The savage who executes unerringly the ex- act throw which brings down his game, or his enemy, in the manner most suited to his purpose, under the operation of all the conditions necessarily involved, the weight and form of the weapon, the direction and distance of the object, the action of the wind, etc., owes this power to a long series of 144 EEASONING. previous experiments, the results of which he certainly never framed into any verbal theorems or rules. The same thing may generally be said of any other extraordinary manual dexterity. Not long ago a Scotch manu- facturer procured from England, at a high rate of wages, a working dyer, famous for producing very fine colors, with the view of teaching to his other workmen the same skill. The workman came ; but his mode of pro- portioning the ingredients, in which lay the secret of the effects he pro- duced, was by taking them up in handfuls, while the common method was to weigh them. The manufacturer sought to make him turn his handling system into an equivalent weighing system, that the general principle of his peculiar mode of proceeding might be ascertained. This, however, the man found himself quite unable to do, and therefore could impart his skill to nobody. He had, from the individual cases of his own experience, es- tablished a connection in his mind between fine effects of color, and tactual perceptions in handling his dyeing materials ; and from these perceptions he could, in any particular case, infer the means to be employed, and the effects which would be produced, but could not put others in possession of the grounds on which he proceeded, from having never generalized them in his own mind, or expressed them in language. Almost every one knows Lord Mansfield's advice to a man of practical good sense, who, being appointed governor of a colony, had to preside in its courts of justice, without previous judicial practice or legal education. f The advice was to give his decision boldly, for it would probably be right ; but never to venture on assigning reasons, for they would almost infalhbly be wrong./ In cases like this, which are of no uncommon occurrence, it would be absurd to suppose that the bad reason was the source of the good decision. Lord Mansfield knew that if any reason were assigned it would be necessarily an afterthought, the judge being in fact guided by impressions from past experience, without the circuitous process of fram- ing general principles from them, and that if he attempted to frame any such he would assuredly fail. Lord Mansfield, however, would not have doubted that a man of equal experience who had also a mind stored with general propositions derived by legitimate induction from that experience, would have been greatly preferable as a judge, to one, however sagacious, who could not be trusted with the explanation and justification of his own judgments. The cases of men of talent performing wonderful things they know not how, are examples of the rudest and most spontaneous form of the operations of superior minds. It is a defect in them, and often a source of errors, not to have generalized as they went on ; but general- ization, though a help, the most important indeed of all helps, is not an essential. Even the scientifically instructed, who possess, in the form of general propositions, a systematic record of the results of the experience of man- kind, need not always revert to those general propositions in order to ap- ply that experience to a new case. It is justly remarked by Dugald Stew- art, that though the reasonings in mathematics depend entirely on the axioms, it is by no means necessary to our seeing the conclusiveness of the proof, that the axioms should be expressly adverted to. When it is inferred that AI^ is equal to CD because each of them is equal to EF, the most uncultivated understanding, as soon as the propositions were under- stood, would assent to the inference, without having ever heard of tlie gen- eral truth that "things which are equal to the same thing are equal to one another." This remark of Stewart, consistently followed out, goes to the FUNCTIONS AND VALUE OK 'J'lIK SYLLOCIISM. 145 root, as T conceive, of tlic ])]iiIo8()|)liy of ratiocinution ; and it is to Ije re- gretted that lie liiinself stopped sliort at a much moi-e limited apj)lication of it. lie saw that the general propositions on which a I'easoning is said to depend, may, in certain cases, be altogether omitted, without impairing its probative force. But he imagined this to be a peculiarity belojiging to axioms; and argued from it, that axioms arc not the foundations or first principles of geometry, from which all the other truths of the science are synthetically deduced (as the laws of motion and of the composition of forces in dynamics, the equal mobility of fluids in hydrostatics, the laws of reflection and refraction in optics, are the first principles of those sciences) ; but are merely necessary assumptions, self-evident indeed, and the denial of which would annihilate all demonstration, but from which, as premises, nothing can be demonstrated. In the present, as in many other instances, this thoughtful and elegant writer has perceived an important truth, but only by halves. Finding, in the case of geometrical axioms, that general names have not any talismanic virtue for conjuring new truths out of the well where they lie hid, and not seeing that this is equally true in eveiy other case of generaUzation, he contended that axioms are in their nature barren of consequences, and that the really fruitful truths, the real first principles of geometry, are the definitions; that the definition, for exam- ple, of the circle is to the properties of the circle, what the laws of equi- librium and of the pressure of the atmosphere are to the rise of the mer- cury in the Torricellian tube. Yet all that he had asserted respecting the function to which the axioms are confined in the demonstrations of geome- try, holds equally true of the definitions. Every demonstration in Euclid might be crrried on without them. This is apparent from the ordinary process of proving a proposition of geometry by means of a diagram. What assumption, in fact, do we set out from, to demonstrate by a dia- gram any of the properties of the circle? Not that in all circles the radii are equal, but only that they are so in the circle ABC. As our warrant for assuming this, we appeal, it is true, to the definition of a circle in gen- eral ; but it is only necessary that the assumption be granted in the case of the particular circle supposed. From this, which is not a general but a sin- gular proposition, combined with other propositions of a similar kind, some of which %olien generalized are called definitions, and other axioms, wx prove that a certain conclusion is true, not of all circles, but of the partic- ular circle ABC ; or at least would be so, if the facts precisely accorded w^ith our assumptions. The enunciation, as it is called, that is, the gener- al theorem which stands at the head of the demonstration, is not the propo- sition actually demonstrated. One instance only is demonstrated : but tlie process by w^hich this is done, is a process which, when we consider its nature, we perceive might be exactly copied in an indefinite number of oth- er instances ; in every instance w^hich conforms to certain conditions. The contrivance of general language furnishing us with terms which connote these conditions, we are able to assert this indefinite multitude of truths in a single expression, and this expression is the general theorem. By dropping the use of diagrams, and substituting, in the demonstrations, general phrases for the letters of the alphapet, we might prove the general theorem directly, that is, we might demonstrate all the cases at once ; and to do this we must, of course, employ as our premises, the axioms and definitions in their general form. But this only means, that if we can prove an individual conclusion by assuming an individual fact, then in whatever case we are warranted in making an exactlv similar assumption, 10 146 KEASONING. we may draw an exactly similar conclusion. The definition is a sort of notice to ourselves and others, what assumptions we think ourselves en- titled to make. And so in all cases, the general propositions, whether called definitions, axioms, or laws of nature, which we lay down at the beginning of our reasonings, are merely abridged statements, in a kind of short-hand, of the particular facts, which, as occasion arises, we either think we may proceed on as proved, or intend to assume. In any one demonstration it is enough if we assume for a particular case suitably se- lected, what by the statement of the definition or principle we announce that we intend to assume in all cases which may arise. The definition of the circle, therefore, is to one of Euclid's demonstrations, exactly what, ac- cording to Stewart, the axioms are ; that is, the demonstration does not depend on it, but yet if we deny it the demonstration fails. The proof does not rest on the general assumption, but on a similar assumption con- fined to the particular case : that case, however, being chosen as a speci- men or paradigm of the whole class of cases included in the theorem, there can be no ground for making the assumption in that case which does not exist in every other; and to deny the assumption as a general truth, is to deny the right of making it in the particular instance. There are, undoubtedly, the most ample reasons for stating both the principles and the theorems in their general form, and these will be ex- plained presently, so far as explanation is requisite. But, that unpracticed learners, even in making use of one theorem to demonstrate another, rea- son rather from particular to particular than from the general proposition, is manifest from the difficulty they find in applying a theorem to a case in which the configuration of the diagram is extremely unlike that of the dia- gram by which the original theorem was demonstrated. A difficulty which, except in cases of unusual mental power, long practice can alone re- move, and removes chiefly by rendering us familiar with all the configura- tions consistent with the general conditions of the theorem. § 4. From the considerations now adduced, the following conclusions seem to be established. All inference is from particulars to particulars: General propositions are merely registers of such inferences already made, and short formulae for making more : The major premise of a syllogism, consequently, is a formula of this description : and the conclusion is not an inference drawn from the formula, but an inference drawn according to the formula : the real logical antecedent, or premise, being the particular facts from which the general proposition was collected by induction. Those facts, and the individual instances which supplied them, may have been forgotten : but a record remains, not indeed descriptive of the facts themselves, but sliowing how those cases may be distinguished, respecting which, the facts, when known, were considered to warrant a given infer- ence. According to the indications of this record we draw our conclusion : which is, to all intents and purposes, a conclusion from the forgotten facts. For this it is essential that we should read the record correctly: and the rules of the syllogism are a set of precautions to insure our doing so. This view of the functions of the syllogism is confirmed by the consid- eration of precisely those cases which might be expected to be least favor- able to it, namely, those in which ratiocination is independent of any pre- vious induction. We have already observed that the syllogism, in the or- dinary course of our reasoning, is only the latter half of the process of traveling from premises to a conclusion. There are, however, some pecul- FUNCTIONS AND VALUE OF THE SYLLOGISM. 147 iar cases in which it is the wliole |)rocess. Particulars alone are capable of being subjected to observation; and all knowledge which is derived from observation, begins, therefore, of necessity, in particulars; but oui- knowledge may, in cases of certain descriptions, be conceived as coming to us from other sources 'than observation. It may present itself as coining from testimony, which, on the occasion and for the puri)ose in hand, is ac- cepted as of an authoritative character: and the information thus commu- nicated, may be conceived to comprise not only particular facts but general propositions, as when a scientific doctrine is accepted without examination on the authority of writers, or a theological docti'ine on that of Scripture. Or the generalization may not be, in the ordinary sense, an assertion at all, but a command ; a law, not in the philosophical, but in the moral and po- litical sense of the term : an expression of the desire of a superior, that we, or any number of other persons, shall conform our conduct to certain gen- eral instructions. So far as this asserts a fact, namely, a volition of the legislator, that fact is an individual fact, and the proposition, therefore, is not a general proposition. But the description therein contained of the conduct which it is the will of the legislator that his subjects should ob- serve, is general. The proposition asserts, not that all men are any thing, but that all men shall do something. In both these cases the generalities are the original data, and the partic- ulars are elicited from them by a process which correctly resolves itself into a series of syllogisms. The real nature, however, of the supposed de- ductive process, is evident enough. The only point to be determined is, whether the authority which declared the general proposition, intended to include this case in it; and whether the legislator intended his command to apply to the present case among others, or not. This is ascertained by examining whether the case possesses the marks by which, as those author- ities have signified, the cases which they meant to certify or to influence may be known. The object of the inquiry is to make out the witness's or the legislator's ^ intention, through the indication given by their words. This is a question, as the Germans express it, of hermeneutics. The opera- tion is not a process of inference, but a process of interpretation. In this last phrase we have obtained an expression which appears to me to characterize, more aptly than any other, the functions of the syllogism in all cases. When the premises are given by authority, the function of Reasoning is to ascertain the testimony of a witness, or the will of a legislator, by interpreting the signs in which the one has intimated his as- sertion and the other his command. In like manner, when the premises are derived from observation, the function of Reasoning is to ascertain what we (or our predecessors) formerly thought might be inferred from the observed facts, and to do this by interpreting a memorandum of ours, or of theirs. The memorandum reminds us, that from evidence, more or less carefully weighed, it formerly appeared that a certain attribute might be inferred wherever we perceive a certain mark. The proposition. All men are mortal (for instance) shows that we have had experience from which we thought it followed that the attributes connoted by the term man, are a mark of mortality. But when we conclude that the Duke of Wel- lington is mortal, we do not infer this from the memorandum, but from the former experience. All that we infer from the memorandum is our own previous belief, (or that of those who transmitted to us the proposi- tion), concerning the inferences which that lormer experience would war- rant. 148 REASONING. This view of the nature of the syllogism renders consistent and intel- ligible what otherwise remains obscure and confused in the theory of Archbishop Whately and other enlightened defenders of the syllogistic doctrine, respecting the limits to which its functions are confined. They affirm in as explicit terms as can be used, that the sole office of general reasoning is to prevent inconsistency in our opinions ; to prevent us from assenting to any thing, the truth of which would contradict something to which we had previously on good grounds given our assent. And they tell us, that the sole ground which a syllogism affords for assenting to the conclusion, is that the supposition of its being false, combined with the supposition that the premises are true, would lead to a contradiction in terms. Now this would be but a lame account of the real grounds which we have for believing the facts which we learn from reasoning, in contra- distinction to observation. The true reason why we believe that the Duke of Wellington will die, is that his fathers, and our fathers, and all other persons who were contemporary with them, have died. Those facts are the real premises of the reasoning. But we are not led to infer the conclusion from those premises, by the necessity of avoiding any verbal inconsistency. There is no contradiction in supposing that all those persons have died, and that the Duke of Wellington may, notwithstanding, live forever. But there would be a contradiction if we first, on the ground of those same premises, made a general assertion including and covering the case of the Duke of Wellington, and then refused to stand to it in the individual case. There is an inconsistency to be avoided between the memorandum we make of the inferences which may be justly drav,ai in future cases, and the inferences we actually draw in those cases when they arise. With this view we interpret our own formula, precisely as a judge interprets a law : in order that we may avoid drawing any inferences not conformable to our former intention, as a judge avoids giving any decision not conform- able to the legislator's intention. The rules for this interpretation are the rules of the syllogism : and its sole purpose is to maintain consistency be- tween the conclusions we draw in every particular case, and the previous general directions for drawing them; whether those general directions were framed by ourselves as the result of induction, or were received by us from an authority competent to give them. § 5. In the above observations it has, I think, been shown, that, though there is always a process of reasoning or inference where a syllogism is used, the syllogism is not a correct analysis of that process of reasoning or inference ; which is, on the contrary (when not a mere inference from tes- timony), an inference from particulars to particulars ; authorized by a pre- vious inference from particulars to generals, and substantially the same with it; of the nature, therefore, of Induction. But while these conclusions ap- pear to me undeniable, I must yet enter a protest, as strong as that of Arch- bishop Whately himself, against the doctrine that the syllogistic art is use- less for the purposes of reasoning. The reasoning lies in the act of gener- alization, not in interpreting the record of that act; but the syllogistic form is an indispensable collateral security for the correctness of the generaliza- tion itself. It has already been seen, that if we have a collection of particulars suffi- cient for grounding an induction, we need not frame a general proposition; we may reason at once from those particulars to other particulars. But it is to be remarked withal, that whenever, from a set of particular cases, we can legitimately draw any inference, we may legitimately make our infer- FUNCTIONS AND VALUE OF 'J'UK .SYLLOGISM. 149 ence a general one. If, from observation and experiment, we can conclude to one new case, so may we to an indefinite number. If that which lias held true in our past experience will therefore liold in time to come, it will hold not merely in some individual case, but in all cases of some given description. Every induction, therefore, which suffices to prove one inc.t, proves an indefinite multitude of facts : the experience which justifies a sin- gle prediction must be such as will suffice to bear out a general theorem. This theorem it is extremely important to ascertain and declare, in its broadest form of generality; and thus to place before our minds, in its full extent, the whole of what our evidence must prove if it proves any thing. This throwing of the whole body of possible inferences from a given set of particulars, into one general expression, operates as a security for theii* being just inferences, in more ways than one. First, the general princii>le presents a larger object to the imagination than any of the singular prop- ositions which it contains. A process of thought which leads to a com- prehensive generality, is felt as of greater importance than one which ter- minates in an insulated fact; and the mind is, even unconsciously, led to bestow greater attention upon the process, and to weigh more carefully the sufficiency of the experience appealed to, for supporting the inference grounded upon it. There is another, and a more important, advantage. In reasoning from a course of individual observations to some new and un- observed case, which we are but imperfectly acquainted with (or we should not be inquiring into it), and in which, since we are inquiring into it, we probably feel a peculiar interest; there is very little to prevent us from giving way to negligence, or to any bias which may affect our wishes or our imagination, and, under that influence, accepting insufficient evidence as sufficient. But if, instead of concluding straight to the particular case, we place before ourselves an entire class of facts — the whole contents of a general proposition, every tittle of which is legitimately inferable from our premises, if that one particular conclusion is so ; there is then a considera- ble likelihood that if the premises are insufficient, and the general inference therefore, groundless, it will comprise w^ithin it some fact or facts the re- verse of which we already know to be true ; and we shall thus discover the error in our generalization by a 7'eduetio ad im20ossihile. Thus if, during the reign of Marcus Aurelius, a subject of the Roman empire, under the bias naturally given to the imagination and expectations by the lives and characters of the Antonines, had been disposed to expect that Commodus would be a just ruler; supposing him to stop there, he might only have been undeceived by sad experience. But if he reflected that this expectation could not be justifiable unless from the same evidence he was Avarrauted in concluding some general proposition, as, for instance, that all Roman emperors are just rulers; he would immediately have thought of Nero, Domitian, and other instances, which, showing the falsity of the general conclusion, and therefore the insufficiency of the premises, would have warned him that those premises could not prove in the instance of Commodus, what they were inadequate to prove in any collection of cases in which his was included. The advantage, in judging whether any controverted inference is legiti- mate, of referring to a parallel case, is universally acknowledged. But by ascending to the general proposition, we bring under our view not one par- allel case only, but all possible parallel cases at once ; all cases to which the same set of evidentiary considerations are applicable. When, therefore, we argue from a number of known cases to another case 150 EEASONING. supposed to be analogous, it is always possible, and generally advantageous, to divert our argument into the circuitous channel of an induction from those known cases to a general proposition, and a subsequent application of that general proposition to the unknown case. This second part of the operation, which, as before observed, is essentially a process of interpreta- tion, will be resolvable into a syllogism or a series of syllogisms, the majors of which will be general propositions embracing whole classes of cases ; every one of which propositions must be true in all its extent, if the argu- ment is maintainable. If, therefore, any fact fairly coming within the range of one of these general propositions, and consequently asserted by it, is known or suspected to be other than the proposition asserts it to be, this mode of stating the argument causes us to know or to suspect that the original observations, which are the real grounds of our conclusion, are not sufficient to support it. And in proportion to the greater chance of our detecting the inconclusiveness of our evidence, will be the increased reli- ance we are entitled to place in it if no such evidence of defect shall appear. The value, therefore, of the syllogistic form, and of the rules for using it correctly, does not consist in their being the form and the rules according to which our reasonings are necessarily, or even usually, made ; but in their furnishing us with a mode in which those reasonings may always be repre- sented, and which is admirably calculated, if they are inconclusive, to bring their inconclusiveness to light. An induction from particulars to generals, followed by a syllogistic process from those generals to other particulars, is a form in which we may always state our reasonings if we please. It is not a form in which we must reason, but it is a form in which we 'may rea- son, and into which it is indispensable to throw our reasoning, when there is any doubt of its validity : though when the case is familiar and little complicated, and there is no suspicion of error, we may, and do, reason at once from the known particular cases to unknown ones.* These are the uses of syllogism, as a mode of verifying any given argu- ment. Its ulterior uses, as respects the general course of our intellectual operations, hardly require illustration, being in fact the acknowledged uses of general language. They amount substantially to this, that the induc- tions may be made once for all: a single careful interrogation of experi- ence may suffice, and the result may be registered in the form of a general proposition, which is committed to memory or to writing, and from which afterward we have only to syllogize. The particulars of our experiments may then be dismissed from the memory, in which it would be impossible to retain so great a multitude of details ; while the knowledge which those details afforded for future use, and which would otherwise be lost as soon as the observations were forgotten, or as their record became too bulky for reference, is retained in a commodious and immediately available shape by means of general language. Against this advantage is to be set the countervailing inconvenience, that inferences originally made on insufficient evidence become consecrated, and, as it were, hardened into general maxims ; and the mind cleaves to them * The language of ratiocination would, I think, be brought into closer agreement with the real nature of the process, if the general propositions employed in reasoning, instead of being in the form All men are mortal, or Every man is mortal, were expressed in the form Any man is mortal. This mode of expression, exhibiting as the type of all reasoning from expe- rience "The men A, B, C, etc., are so and so, therefoi'c any man is so and so," would much hotter manifest the true idea — that inductive reasoning is always, at bottom, inference from particulars to ])articulars, and that the whole function of general propositions in reasoning, is to vouch for the legitimacy of such inferences. FUNCTIONS AND VALUK OF TIIK .SVi>J>0(;iSM. 151 from habit, after it lias outgrown any liability to bo misled by similar falla- cious ap[)earauces if they were now for the first time presented ; but hav- ing forgotten the particulars, it does not think of revising its own former decision. An inevitable drawback, which, however considerable in itself, forms evidently but a small set-off against the immense benefits of general language. The use of the syllogism is in truth no other than the use of general propositions in reasoning. We can reason without them ; in simple and obvious cases we habitually do so; minds of great s.'igacity can do it in cases not simple and obvious, provided their experience supplies them with instances essentially similar to every combination of circumstances likely to arise. But other minds, and the same minds where they have not the same pre-eminent advantages of personal experience, are quite helpless without the aid of general propositions, wherever the case presents the smallest complication /and if we made no general propositions, few per- sons would get much beyond those simple inferences "which are di'awn by the more intelligent of the brutes. Though not necessary to reasoning, general propositions are necessary to any considerable progress in reason- ing. It is, therefore, natural and indispensable to separate the process of investigation into two parts; and obtain general formulae for determining what inferences may be drawn, before the occasion arises for drawing the inferences. The work of drawdng them is then that of applying the for- mulae ; and the rules of syllogism are a system of securities for the correct- ness of the application. § 6. To complete the series of considerations connected with the philo- sophical character of the syllogism, it is requisite to consider, since the syl- logism is not the universal type of the reasoning process, what is the real type. This resolves itself into the question, what is the nature of the mi- nor premise, and in what manner it contributes to establish the conclusion : for as to the major, we now fully understand, that the place which it nom- inally occupies in our reasonings, properly belongs to the individual facts or observations of which it expresses the general result; the major itself being no real part of the argument, but an intermediate halting-place for the mind, interposed by an artifice of language between the real premises and the conclusion, by way of a security, which it is in a most material de- gree, for the correctness of the process. The minor, however, being an in- dispensable part of the syllogistic expression of an argument, without doubt either is, or corresponds to, an equally indispensable part of the ar- gument itself, and W' e have only to inquire what part. It is perhaps worth wdiile to notice here a speculation of a philosopher to whom mental science is much indebted, but who, though a very pene- trating, was a very hasty thinker, and whose want of due circumspection rendered him fully as remarkable for what he did not see, as for what he saw\ I allude to Dr. Thomas Brown, whose theory of ratiocination is pe- culiar. He saw the 2^ctitio 2yrinci2ni which is inherent in every syllogism, if we consider the major to be itself the evidence by which the conclusion is proved, instead of being, wdiat in fact it is, an assertion of the existence of evidence sufficient to prove any conclusion of a given description. See- ing this. Dr. Brown not only failed to see the immense advantage, in point of security for correctness, which is gained by interposing this step be- tween the real evidence and the conclusion ; but he thought it incumbent on him to strike out the major altogether from the reasoning process, with- 152 REASONING. out substituting any thing else, and maintained that our reasonings consist only of the minor premise and the conclusion, Socrates is a man, therefore Socrates is mortal : thus actually suppressing, as an unnecessary step in the argument, the appeal to former experience. The absurdity of this was disguised from him by the opinion he adopted, that reasoning is merely an- alyzing our own general notions, or abstract ideas ; and that the proposi- tion, Socrates is mortal, is evolved from the proposition, Socrates is a man, simply by recognizing the notion of mortality as already contained in the notion we form of a man. After the explanations so fully entered into on the subject of proposi- tions, much further discussion can not be necessary to make the radical error of this view of ratiocination apparent. If the word man connoted mortality ; if the meaning of " mortal " were involved in the meaning of " man ;" we might, undoubtedly, evolve the conclusion from the minor alone, because the minor would have already asserted it. But if, as is in fact the case, the word man does not connote mortality, how does it appear that in the mind of every person Avho admits Socrates to be a man, the idea of man must include the idea of mortality ? Dr. Brown could not help seeing this difficulty, and in order to avoid it, was led, contrary to his intention, to re-establish, under another name, that step in the argument which corresponds to the major, by affirming the necessity oi previously perceimng the relation between the idea of man and the idea of mortal. If the reasoner has not previously perceived this relation, he will not, says Dr. Brown, infer because Socrates is a man, that Socrates is mortal. But even this admission, though amounting to a surrender of the doctrine that an argument consists of the minor and the conclusion alone, will not save the remainder of Dr. Brown's theory. The failure of assent to the argument does not take place merely because the reasoner, for want of due analysis, does not perceive that his idea of man includes the idea of mortality; it takes place, much more commonly, because in his mind that relation be- tween the two ideas has never existed. And in truth it never does exist, except as the result of experience. Consenting, for the sake of the argu- ment, to discuss the question on a supposition of which we have recog- nized the radical incorrectness, namely, that the meaning of a proposition relates to the ideas of the things spoken of, and not to the things them- selves ; I must yet observe, that the idea of man, as a universal idea, the common property of all rational creatures, can not involve any thing but what is strictly implied in the name. If any one includes in his own pri- vate idea of man, as no doubt is always the case, some other attributes, such for instance as mortality, he does so only as the consequence of experience, after having satisfied himself that all men possess that attribute : so that whatever the idea contains, in any person's mind, beyond what is included in the conventional signification of the word, has been added to it as the result of assent to a proposition ; while Dr. Brown's theory requires us to su[)pose, on the contrary, that assent to the proposition is produced by evolving, through an analytic process, this very element out of the idea. This theory, therefore, may be considered as sufficiently refuted; and the minor premise must be regarded as totally insufficient to prove the conclu- sion, except with the assistance of the major, or of that which the major represents, namely, the various singular propositions expressive of the se- ries of observations, of which the generalization called the major premise is the result. In the argument, then, which proves that Socrates is mortal, one indis- FUNCTIONS AND VALUK OF TIIK SYLLOGISM. 150 pensable part of the premises will be as follows: "My father, and my fa- ther's father, A, B, C, and an indefinite number of other persons, were mor- tal;" whieli is only an expression in different words of the observed fact that they have died. This is the major premise divested of the petitio pri7icipii, and cut down to as much as is really known l)y direct evidence. In order to connect this j)ro|)Osition with the conclusion Socrates is mor- tal, the additional link necessary is such a j)roposition as the followiiii^: "Socrates resembles my father, and my father's father, and the other indi- viduals specified." This pro])osition we assert when we say that Socrates is a man. By saying so we likewise assert in what respect lie resembles them, namely, in the attributes connoted by the word man. And we con- clude that he further resembles them in the attribute mortality. § 7. We have thus obtained what we were seeking, a universal type of the reasoning process. We find it resolvable in all cases into the follow- ing elements: Certain individuals have a given attribute; an individual or individuals resemble the former in certain other attributes ; therefore they resemble them also in the given attribute. This type of ratiocination does not claim, like the syllogism, to be conclusive from the mere form of the expression ; nor can it possibly be so. That one proposition does or does not assert the very fact which was already asserted in another, may appear from the form of the expression, that is, from a comparison of the lan- guage; but when the two propositions assert facts which are bona fide different, whether the one fact proves the other or not can never appear from the language, but must depend on other considerations. Whether, from the attributes in which Socrates resembles those men who have here- tofore died, it is allowable to infer that he resembles them also in being mortal, is a question of Induction ; and is to be decided by the principles or canons which we shall hereafter recognize as tests of the correct per- formance of that great mental operation. Meanwhile, however, it is certain, as before remarked, that if this infer- ence can be drawn as to Socrates, it can be drawn as to all others who re- semble the observed individuals in the same attributes in which he resem- bles them; that is (to express the thing concisely) of all mankind. If, therefore, the argument be admissible in the case of Socrates, we are at lib- erty, once for all, to treat the possession of the attributes of man as a mark, or satisfactory evidence, of the attribute of mortality. This we do by lay- ing down the universal proposition, All men are mortal, and interpreting this, as occasion arises, in its application to Socrates and others. By this means we establish a very convenient division of the entire logical opera- tion into two steps ; first, that of ascertaining w^hat attributes are marks of mortality ; and, secondly, whether any given individuals possess those marks. And it will generally be advisable, in our speculations on the rea- soning process, to consider this double operation as in fact taking place, and all reasoning as carried on in the form into which it must necessarily be thrown to enable us to apply to it any test of its correct performance. Although, therefore, all processes of thought in which the ultimate prem- ises are particulars, whether we conclude from particulars to a general for- mula, or from particulars to other particulars according to that formula, are equally Induction; we shall yet, conformably to usage, consider the name Induction as more peculiarly belonging to the process of establishing the general proposition, and the remaining operation, which is substantially that of interpreting the general proposition, we shall call by its usual name, 154 REASONING. Deduction. And we shall consider every process by which any thing is inferred respecting an unobserved case, as consisting of an Induction fol- lowed by a Deduction ; because, although the process needs not necessarily be carried on in this form, it is always susceptible of the form, and must be thrown into it when assurance of scientific accuracy is needed and de- sired. § 8. The theory of the syllogism laid down in the preceding pages, has obtained, among other important adhesions, three of peculiar value : those of Sir John Herschel,* Dr. Whewell,f and Mr. Bailey ;J; Sir John Herschel considering the doctrine, though not strictly " a discovery," having been anticipated by Berkeley,§ to be " one of the greatest steps which have yet been made in the philosophy of Ebgic." "When we consider" (to quote the further words of the same authority) " the inveteracy of the habits and prejudices which it has cast to the winds," there is no cause for misgiving in the fact that other thinkers, no less entitled to consideration, have formed a very different estimate of it. Their principal objection can not be bet- ter or more succinctly stated than by borrowing a sentence from Archbish- op Whately.|| "In every case where an inference is drawn from Induc- tion (unless that name is to be given to a mere random guess without any grounds at all) we must form a judgment that the instance or instances ad- duced are sufficient to authorize the conclusion ; that it is allowable to take these instances as a sample warranting an inference respecting the whole class ;" and the expression of this judgment in words (it has been said by several of my critics) is the major premise. I quite admit that the major is an affirmation of the sufficiency of the evidence on which the conclusion rests. That it is so, is the very essence of my own theory. And whoever admits that the major premise is only this, adopts the theory in its essentials. But I can not concede that this recognition of the sufficiency of the evi- dence — that is, of the correctness of the induction — is a part of the induc- tion itself; unless we ought to say that it is a part of every thing we do, to satisfy ourselves that it has been done rightly. We conclude from known instances to unknown by the impulse of the generalizing propensi- ty; and (until after a considerable amount of practice and mental disci- pline) the question of the sufficiency of the evidence is only raised by a re- trospective act, turning back upon our own footsteps, and examining wheth- er we were warranted in doing what we have provisionally done. To speak of this reflex operation as part of the original one, requiring to be expressed in words in order that the verbal formula may correctly repre- sent the psychological process, appears to me false psychology.^ We re- view our syllogistic as well as our inductive processes, and recognize that * Review of Quetelet on Probabilities, Essays, p. 367. t Philosophy of Discovery, p. 289, X Theory of Reasoning, cbap. iv., to whicb I may refer for an able statement and enforce- ment of the grounds of the doctrine. § On a recent careful reperusal of Berkeley's whole works, I have been unable to find this doctrine in them. Sir John Ilerschcl probably meant that it is implied in Berkeley's argu- ment against abstract ideas. But I can not find that Berkeley saw the implication, or had ever asked himself what bearing his argument had on tlie theory of the syllogism. Still less can I admit that the doctrine is (as has been affirmed by one of my ablest and most candid critics) " among the standing marks of what is called the empirical philosophy." II Logic, book iv., chap, i., sect. 1. ^ .See tiie important chapter on Belief, in Professor Bain's great treatise, The Emotions and the Will, pp. 581-4. FUNCTIONS AND VALUK OF Till': SYLLOGISM. ]55 they have been correctly performed; but logicians roi)Ositions as these, a a mark of b, or a and b marks of one another, c a mark of d, or c and d marks of one another, without any thini^ to connect a or b with c or d; we have a science of detached and mutually independent generalizations, such as these, that acids redden vegetable blues, and that alkalies color them green; from neither of which propositions could we, directly or indirectly, infer the other : and a science, so far as it is composed of such i)roposi- tions, is purely experimental. Chemistry, in the present state of our knowledge, has not yet thrown off this character. There are other sci- ences, however, of which the propositions are of this kind : a a mark of 5, b a mark of c, c of d, d of e, etc. In these sciences we can mount the lad- der from a to e by a process of ratiocination ; we can conclude that a is a mark of e, and that every object which has the mark a has the pi'operty e, although, perhaps, we never were able to observe a and e together, and al- though even d, our only direct mark of e, may not be perceptible in those objects, but only inferable. Or, varying the first metaphor, we may be said to get from a to e underground : the marks b, c, d, which indicate the route, must all be possessed somewhere by the objects concerning which we are inquiring ; but they are below the surface : a is the only mark that is visible, and by it we are able to trace in succession all the rest. § 6. We can now understand how an experimental may transform itself into a deductive science by the mere progress of experiment. In an experi- mental science, the inductions, as we have said, lie detached, as, a a mark of b,c 2i mark of d, e a mark of j*^, and so on : now, a new set of instances, and a consequent new induction, may at any time bridge over the interval be- tween two of these unconnected arches ; b, for example, may be ascertained to be a mark of c, which enables us thenceforth to prove deductively that « is a mark of c. Or, as sometimes happens, some comprehensive induc- tion may raise an arch high in the air, which bridges over hosts of them at once ; b, d,f, and all the rest, turning out to be marks of some one thing, or of things between which a connection has already been traced. As when Newton discovered that the motions, whether regular or apparently anomalous, of all the bodies of the solar system (each of which motions had been inferred by a separate logical operation, from separate marks), were all marks of moving round a common centre, with a centripetal force varying directly as the mass, and inversely as the square of the distance from that centre. This is the greatest example which has yet occurred of the transformation, at one stroke, of a science which was still to a great de- gree merely experimental, into a deductive science. Transformations of the same nature, but on a smaller scale, continually take place in the less advanced branches of physical knowledge, without enabling them to throw off the character of experimental sciences. Thus with regard to the two unconnected propositions before cited, namely, Acids redden vegetable blues. Alkalies make them green ; it is remarked by Liebig, that all blue coloring matters which are reddened by acids (as well as, reciprocally, all red coloring matters which are rendered blue by alka- lies) contain nitrogen : and it is quite possible that this circumstance may one day furnish a bond of connection between the two propositions in question, by showing that the antagonistic action of acids and alkalies in 166 REASONING. producing or destroying the color blue, is the result of some one, more general, law. Although this connecting of detached generalizations is so much gain, it tends but little to give a deductive character to any science as a whole ; because the new courses of observation and experiment, which thus enable us to connect together a few general truths, usually make known to us a still greater number of unconnected new ones. Hence chemistry, though similar extensions and simplifications of its generaliza- tions are continually taking place, is still in the main an experimental sci- ence; and is likely so to continue unless some comprehensive induction should be hereafter arrived at, which, like Newton's, shall connect a vast number of the smaller known inductions together, and change the whole method of the science at once. Chemistry has already one great generali- zation, which, though relating to one of the subordinate aspects of chemical phenomena, possesses within its limited sphere this comprehensive charac- ter; the princii^le of Dalton, called the atomic theory, or the doctrine of chemical equivalents : which by enabling us to a certain extent to foresee the proportions in which two substances will combine, before the experi- ment has been tried, constitutes undoubtedly a source of new chemical truths obtainable by deduction, as well as a connecting principle for all truths of the same description previously obtained by experiment. § 7. The discoveries which change the method of a science from experi- mental to deductive, mostly consist in estabhshing, either by deduction or by direct experiment, that the varieties of a particular phenomenon uni- formly accompany the varieties- of some other phenomenon better known. Thus the science of sound, which previously stood in the lowest rank of merely experimental science, became deductive when it was proved by ex- periment that every variety of sound was consequent on, and therefore a mark of, a distinct and definable variety of oscillatory motion among the particles of the transmitting medium. When this was ascertained, it fol- lowed that every relation of succession or co-existence which obtained be- tween phenomena of the more known class, obtained also between the phenomena which correspond to them in the other class. Every sound, being a mark of a particular oscillatory motion, became a mark of every thing which, by the laws of dynamics, was known to be inferable from that motion ; and every thing which by those same laws was a mark of any oscillatory motion among the particles of an elastic medium, became a mark of the corresponding sound. And thus many truths, not before suspected, concerning sound, become deducible from the known laws of the propaga- tion of motion through an elastic medium; while facts already empirically known respecting sound, become an indication of corresponding properties of vibrating bodies, previously undiscovered. But the grand agent for transforming experimental into deductive sci- ences, is the science of number. The properties of number, alone among all known phenomena, are, in the most rigorous sense, properties of all things whatever. All things are not colored, or ponderable, or even ex- tended ; but all things are numerable. And if we consider this science in its whole extent, from common arithmetic up to the calculus of variations, the truths already ascertained seem all but infinite, and admit of indefinite extension. These truths, though affirmable of all things whatever, of course apply to them only in respect of their quantity. But if it comes to be discovered that variations of quality in any class of phenomena, correspond regularly TIIAINS OF liEASOXlxN'G. IGV to variations of quantity eitlier in those same or in some otlier plienoniena ; every formula of mathematics applicable to quantities which vary in that particular manner, becomes a mark of a corresponding general truth re- specting the variations in quality which accompany them: and the sci- ence of quantity being (as far as any science can be) altogether deductive, the theory of that particular kind of qualities becomes, to this extent, de- ductive likewise. The most striking instance in point which history affords (though not an example of an experimental science rendered deductive, but of an un- paralleled extension given to the deductive process in a science which was deductive already), is the revolution in geometry which originated with Descartes, and was completed by Clairaut. These great mathematicians pointed out the importance of the fact, that to every variety of position in points, direction in lines, or form in curves or surfaces (all of which are Qualities), there corresponds a peculiar relation of quantity between either two or three rectilineal co-ordinates; insomuch that if the law were known according to which those co-ordinates vary relatively to one another, every other geometrical property of the line or surface in question, whether re- lating to quantity or quality, would be capable of being inferred. Hence it followed that every geometrical question could be solved, if the corre- sponding algebraical one could ; and geometry received an accession (act- ual or potential) of new truths, corresponding to every property of num- bers which the progress of the calculus had brought, or might in future bring, to light. In the same general manner, mechanics, astronomy, and in a less degree, every branch of natural philosophy commonly so called, have been made algebraical. The varieties of physical phenomena with which those sciences are conversant, have been found to answer to determinable varieties in the quantity of some circumstance or other; or at least to va- rieties of form or position, for which corresponding equations of quantity had already been, or were susceptible of being, discovered by geometers. In these various transformations, the propositions of the science of num- ber do but fulfill the function proper to all propositions forming a train of reasoning, viz., that of enabling us to arrive in an indirect method, by marks of marks, at such of the properties of objects as we can not direct- ly ascertain (or not so conveniently) by experiment. We travel from a given visible or tangible fact, through the truths of numbers, to the facts sought. The given fact is a mark that a certain relation subsists between the quantities of some of the elements concerned; Avhile the fact sought presupposes a certain relation between the quantities of some other ele- ments : now^, if these last quantities are dependent in some known manner upon the former, or vied versa, we can argue from the numerical relation between the one set of quantities, to determine that which subsists be- tween the other set ; the theorems of the calculus affording the intermedi- ate links. And thus one of the two physical facts becomes a mark of the other, by being a mark of a mark of a mark of it. 168 REASONING. CHAPTER V. OF DEMONSTRATION, AND NECESSARY TRUTHS. § 1. If, as laid down in the two preceding chapters, the foundation of all sciences, even deductive or demonstrative sciences, is Induction ; if every step in the ratiocinations even of geometry is an act of induction ; and if a train of reasoning is but bringing many inductions to bear upon the same subject of inquiry, and drawing a case within one induction by means of another ; wherein lies the peculiar certainty always ascribed to the sciences which are entirely, or almost entirely, deductive? Why are they called the Exact Sciences? Why are mathematical certainty, and the evidence of demonstration, common phrases to express the very highest degree of assurance attainable by reason ? Why are mathematics by al- most all philosophers, and (by some) even those branches of natural phi- losophy which, through the medium of mathematics, have been converted into deductive sciences, considered to be independent of the evidence of expierience and observation, and characterized as systems of Necessary Truth ? The answer I conceive to be, that this character of necessity, ascribed to the truths of mathematics, and (even with some reservations to be here- after made) the peculiar certainty attributed to them, is an illusion ; in or- der to sustain which, it is necessary to suppose that those truths relate to, and express the properties of, purely imaginary objects. It is acknowl- edged that the conclusions of geometry are deduced, partly at least, from the so-called Definitions, and that those definitions are assumed to be cor- rect representations, as far as they go, of the objects with which geometry is conversant. Now we have pointed out that, from a definition as such, no proposition, unless it be ouvi concerning the meaning of a word, can ever follow ; and that what apparently follows from a definition, follows in real- ity from an implied assumption that there exists a real thing conformable thereto. This assumption, in the case of the definitions of geometry, is not strictly true : there exist no real things exactly conformable to the defini- tions. There exist no points without magnitude; no lines without breadth, nor perfectly straight; no circles with all their radii exactly equal, noi- squares with all their angles perfectly right. It will perhaps be said that the assumption does not extend to the actual, but only to the possible, exist- ence of such things. I answer that, according to any test we have of possi- bility, they are not even possible. Their existence, so far as we can form any judgment, would seem to be inconsistent with the physical constitu- tion of our planet at least, if not of the universe. To get rid of this difli- culty, and at the same time to save the credit of the supposed system of necessary truth, it is customary to say that the points, lines, circles, and squares which are the subject of geometry, exist in our conceptions mere- ly, and are part of our minds ; which minds, by working on their own ma- terials, construct an a priori science, the evidence of which is purely men- tal, and has nothing whatever to do with outward experience. By how- soever high authorities this doctrine may have been sanctioned, it appears DEMONSTRATION, AND NPXESSAKY TRUTHS. ]00 to me psycholoi;-ically incorrect. TIic jjoinls, lines, circles, and squares which any one has in his niiud, are (I ai)j)relien(l) siin|)ly copies of the points, lines, circles, and squares which he has known in his experience. Our idea of a point, I apprehend to be simply our idea of the rninimurn visibile, the smallest portion of surface which we can see. A line, as de- fined by geometers, is wholly inconceivable. We can reason about a line as if it had no breadth ; because we have a powoi", which is the foundation of all the control we can exercise over the operations of our minds; tlie power, when a perception is present to our senses, or a conception to our intellects, of attending to a part only of that perception or conception, in- stead of the whole. But we can not co?iceive a line without breadth ; we can form no mental picture of such a line: all the lines which we have in our minds are lines possessing breadth. If any one doubts this, we may refer hiiu to his own experience. I much question if any one who fancies that he can conceive what is called a mathematical line, thinks so from the evidence of his consciousness : I suspect it is rather because he supposes that unless such a conception were possible, mathematics could not exist as a science : a supposition wiiich there will be no difKcuity in showing to be entirely groundless. Since, then, neither in nature, nor in the human mind, do there exist any objects exactly corresponding to the definitions of geometry, while yet that science can not be supposed to be conversant about nonentities ; nothing remains but to consider geometry as conversant with such lines, angles, and figures, as really exist; and the definitions, as they are called, must be regarded as some of our first and most obvious generalizations concerning those natural objects. The correctness of those generalizations, «6' gener- alizations, is without a flaw : the equality of all the radii of a circle is true of all circles, so far as it is true of any one : but it is not exactly true of any circle ; it is only nearly true ; so nearly that no error of any impor- tance in practice will be incurred by feigning it to be exactly true. When w^e have occasion to extend these inductions, or their consequences, to cases in which the error would be appreciable — ^^to lines of perceptible breadth or thickness, parallels which deviate sensibly from equidistance, and the like — we correct our conclusions, by combining wath them a fresh set of propositions relating to the aberration ; just as we also take in proposi- tions relating to the physical or chemical properties of the material, if those properties happen to introduce any modification into the result; which they easily may, even with respect to figure and magnitude, as in the case, for instance, of expansion by heat. So long, however, as there exists no practical necessity for attending to any of the properties of the object ex- cept its geometrical properties, or to any of the natural irregularities in those, it is convenient to neglect the consideration of the other properties and of the irregularities, and to reason as if these did not exist : according- ly, we formally announce in the definitions, that we intend to proceed on this plan. But it is an error to suppose, because we resolve to confine our attention to a certain number of the properties of an object, that we there- fore conceive, or have an idea of, the object, denuded of its other proper- ties. We are thinking, all the time, of precisely such objects as we have seen and touched, and with all the properties which naturally belong to them ; but, for scientific convenience, we feign them to be divested of all properties, except those which are material to our purpose, and in regard to which we design to consider them. The peculiar accuracy, supposed to be characteristic of the first princi- IVO REASONING. pies of geometry, thus appears to be fictitious. The assertions on which the reasonings of the science are founded, do not, any more than in other sciences, exactly correspond with the fact ; but we suppose that they do so, for the sake of tracing the consequences which follow from the suppo- sition. The opinion of Dugald Stewart respecting, the foundations of ge- ometry, is, I conceive, substantially correct ; that it is built on hypotheses ; that it owes to this alone the peculiar certainty supposed to distinguish it ; and that in any science whatever, by reasoning from a set of hypotheses, we may obtain a body of conclusions as certain as those of geometry, that is, as strictly in accordance with the hypotheses, and as irresistibly compel- ling assent, on condition that those hypotheses are true.* When, therefore, it is affirmed that the conclusions of geometry are nec- essary truths, the necessity consists in reality only in this, that they cor- rectly follow from the suppositions from which they are deduced. Those suppositions are so far from being necessary, that they are not even true ; they purposely depart, more or less widely, from the truth. The only sense in which necessity can be ascribed to the conclusions of any scientific in- vestigation, is that of legitimately following from some assumption, which, by the conditions of the inquiry, is not to be questioned. In this relation, of course, the derivative truths of every deductive science must stand to the inductions, or assumptions, on which the science is founded, and which, whether true or untrue, certain or doubtful in themselves, are always sup- posed certain for the purposes of the particular science. And therefore the conclusions of all deductive sciences were said by the ancients to be necessary propositions. We have observed already that to be predicated necessarily was characteristic of the predicable Proprium, and that a pro- prium was any property of a thing which could be deduced from its es- sence, that is, from the properties included in its definition. § 2. The important doctrine of Dugald Stev/art, which I have endeav- ored to enforce, has been contested by Dr. Whewell, both in the disserta- tion appended to his excellent MechaniGol Euclid^ and in his elaborate work on the Philosophy of the Inductive Sciences ; in which last he also replies to an article in the Edinburgh Review (ascribed to a writer of great scientific eminence), in which Stewart's opinion was defended against his former strictures. The supposed refutation of Stewart consists in proving against him (as has also been done in this work) that the premises of geometry ai'e not definitions, but assumptions of the real existence of things corresponding to those definitions. This, however, is doing little for Dr. Whewell's purpose ; for it is these very assumptions which are as- serted to be hypotheses, and which he, if he denies that geometry is founded * It is justly remarked by Professor Bain {Logic, ii., 134) that the word Hypothesis is here used in a somewhat ])eculiar sense. An hypothesis, in science, usually means a supposition not proved to be true, but surmised to be so, because if true it would account for certain known facts ; and the fni;d result of the speculation may be to prove its truth. The hypothe- ses spoken of in the text are of a different character ; they are known not to be literally true, while as much of them as is true is not hypothetical, but certain. The two cases, however, resemble in the circumstance that in both we reason, not from a truth, but from an assump- tion, and the truth therefore of the conclusions is conditional, not categorical. This suffices to justify, in point of logical propriety, Stewart's use of the term. It is of course needful to bear in mind that the hypothetical element in the definitions of geometry is the assumption that what is very nearly true is exactly so. This unreal exactitude might be called a fiction, as propeily as an hyi)()thesis ; but that a])pellation, still more than the other, would fail to point out the close relation wliich exists between the fictitious point or line and the points and lines of which we have experience. DEMONSTRATION, AND Nr:CESSARY TKL'TIIS. ]7l on hypotheses, must show to be absohite truths. All lie does, however, is to observe, that they, at any rate, are not arbitrary hypotheses; that we should not be at liberty to substitute other liypotheses for them; that not only " a delinition, to be admissible, must necessarily refer to and [igree with some conce|)tion which we can distinctly frame in our tliou^-hts," but that the straight lines, for instance, which we define, must be "those by which angles are contained, those by which triangles are bounded, tliose of which parallelism uiay be predicated, and the like.'""' And this is true; but this has never been contradicted. Those who say that the premises of geometry are hy[)otheses, are not bound to maintain them to be hypoth- eses which have no relation whatever to fact. Since an hypothesis framed for the purpose of scientitic inquiry must relate to something which has real existence (for there can be no science respecting nonentities), it fol- lows that any hypothesis we make respecting an object, to facilitate our study of it, must not involve any thing which is distinctly false, and repug- nant to its real nature: we must not ascribe to the thing any property which it has not ; our liberty extends only to slightly exaggerating some of those which it has (by assuming it to be completely wliat it really is very nearly), and suppressing others, under the indispensable obligation of restoring them whenever, and in as far as, their presence or absence would make any material difference in the truth of our conclusions. Of this na- ture, accordingly, are the first principles involved in the definitions of ge- ometry. That the hypotheses should be of this particular character, is, however, no further necessary, than inasmuch as no others could enable us to deduce conclusions which, with due corrections, would be true of real objects : and in fact, when our aim is only to illustrate truths, and not to investigate them, we ai'e not under any such restriction. We might sup- pose an imaginary animal, and work out by deduction, from tiie known laws of physiology, its natural history ; or an imaginary commonwealth, and from the elements composing it, might argue what would be its fate. And the conclusions which we might thus draw from purely arbitrary hy- potheses, might form a highly useful intellectual exercise : but as they could only teach us what would be the properties of objects which do not really exist, they would not constitute any addition to our knowledge of nature: while, on the contrary, if the hypothesis merely divests a real object of some portion of its properties, without clothing it in false ones, the conclu- sions will always express, under know^n liability to correction, actual truth. § 3. But though Dr. Whewell has not shaken Stewart's doctrine as to the hypothetical character of that portion of the first principles of geom- etry which are involved in the so-called definitions, he has, I conceive, great- ly the advantage of Stewart on another important point in the theory of geometrical reasoning ; the necessity of admitting, among those first prin- ciples, axioms as well as definitions. Some of the axioms of Euclid might, no doubt, be exhibited in the form of definitions, or might be deduced, by reasoning, from propositions similar to what are so called. Thus, if instead of the axiom. Magnitudes which can be made to coincide are equal, we in- troduce a definition, " Equal magnitudes are those which may be so ap- plied to one another as to coincide ;" the three axioms which follow (Mag- nitudes which are equal to the same are equal to one another — If equals are added to equals, the sums are equal — If equals are taken from equals, * Mechanical Euclid, pp. 149 et seqq. 172 EEASONING. the remainders are equal), may be proved by an imaginary superposition, resembling that by which the fourth proposition of the first book of Euclid is demonstrated. But though these and several others may be struck out of the list of first principles, because, though not requiring demonstration, they are susceptible of it ; there will be found in the list of axioms two or three fundamental truths, not capable of being demonstrated: among which must be reckoned the proposition that two straight lines can not inclose a space (or its equivalent. Straight lines which coincide in two points coin- cide altogether), and some property of parallel lines, other than that which constitutes their definition : one of the most suitable for the purpose being that selected by Professor Playfair : " Two straight lines which intersect each other can not both of them be parallel to a third straight line."* The axioms, as well those which are indemonstrable as those which ad- mit of being demonstrated, differ from that other class of fundamental principles which are involved in the definitions, in this, that they are true without any mixture of hypothesis. That things which are equal to the same thing are equal to one another, is as true of the lines and figures in nature, as it would be of the imaginary ones assumed in the definitions. In this respect, however, mathematics are only on a par with most other sciences. In ahnost all sciences there are some general propositions which are exactly true, while the greater part are only more or less distant ap- proximations to the truth. Thus in mechanics, the first law of motion (the continuance of a movement once impressed, until stopped or slackened by some resisting force) is true without qualification or error. The rotation of the earth in twenty-four hours, of the same length as in our time, has gone on since the first accurate observations, without the increase or dim- inution of one second in all that period. These are inductions which require no fiction to make them be received a6 accurately true : but along with them there are others, as for instance the propositions respecting the figure of the earth, which are but approximations to the truth ; and in or- der to use them for the further advancement of our knowledge, we must feign that they are exactly true, though they really want something of be- ing so. § 4. It remains to inquire, what is the ground of our belief in axioms — what is the evidence on which they rest ? I answer, they are experi- mental truths; generalizations from observation. The proposition. Two straight lines can not inclose a space — or, in other words. Two sti'aight lines which have once met, do not meet again, but continue to diverge — is an induction from the evidence of our senses. This opinion runs counter to a scientific prejudice of long standing and great strength, and there is probably no proposition enunciated in this work for which a more unfavorable reception is to be expected. It is, however, no new" opinion ; and even if it were so, would be entitled to be judged, not by its novelty, but by the strength of the arguments by which it can be supported. I consider it very fortunate that so eminent a cham- * We might, it is true, insert this property into the definition of parallel lines, framing the definition so as to rehysical sciences on the basis of the doctrine against which I now contend. Whoever is anxious that a discussion should go to the bottom of the subject, must rejoice to see the opposite side of the question worthily rei)resented. If what is said by l)r. Whewell, in support of an o})inion which he has made the foundation of a systematic work, can be shown not to be conclusive, enough will have been done, without going elsewhere in quest of stronger argu- ments and a more powerful adversary. It is not necessary to show that the truths which we call axioms are originally suggested by observation, and that wx^ should never have known that two straight lines can not inclose a space if we had never seen a straight line : thus much being admitted by Dr. Whewell, and by all, in recent times, who have taken his view of the subject. But they contend, that it is not experience which ^:>royes the axiom; but that its truth is per- ceived a priori, by the constitution of the mind itself, from the first mo- ment when the meaning of the proposition is apprehended ; and without any necessity for verifying it by repeated trials, as is requisite in the case of truths really ascertained by observation. They can not, however, but allow that the truth of the axiom, Two straight lines can not inclose a space, even if evident independently of ex- perience, is also evident from experience. Whether the axiom needs con- firmation or not, it receives confirmation in almost every instant of our lives ; since we can not look at any two straight lines which intersect one another, without seeing that from that point they continue to diverge more and more. Experimental proof crowds in upon us in such endless profu- sion, and without one instance in which there can be even a suspicion of an exception to the rule, that we should soon have stronger ground for be- lieving the axiom, even as an experimental truth, than we have for almost any of the general truths wdiich we confessedly learn from the evidence of our senses. Independently of a priori evidence, we should certainly be- lieve it with an intensity of conviction far greater than we accord to any ordinary physical truth : and this too at a time of life much earlier than that from which we date almost any part of our acquired knowledge, and much too early to admit of our retaining any recollection of the history of our intellectual operations at that period. Where then is the necessity for assuming that our recognition of these truths has a different origin from the rest of our knowledge, when its existence is perfectly accounted for by supposing its origin to be the same? when the causes which produce be- lief in all other instances, exist in this instance, and in a degree of strength as much superior to what exists in other cases, as the intensity of the be- lief itself is superior? The burden of proof lies on the advocates of the contrary opinion : it is for them to point out some fact, inconsistent with the supposition that this part of our knowledge of nature is derived from the same sources as every other part."^ * Some persons find themselves prevented from believing that the axiom. Two straight lines can not inclose a space, conld ever become known to ns through experience, by a ditiiculty which may be stated as follows : If the straight lines spoken of are those contemplated in the definition — lines absolutely without breadth and absolutely straight — that such are incapable of inclosing a space is not proved by experience, for lines such as these do not present them- selves in our experience. If, on the other hand, the lines meant are such straight lines as we do meet with in experience, lines straight enough for practical purposes, but in reality slightly zigzag, and with some, however trifling, breadth ; as applied to these lines the axiom is not 174 REASONING. This, for instance, they would be able to do, if they could prove chrono- logically that we had the conviction (at least practically) so early in infan- cy as to be anterior to those impressions on the senses, upon which, on the other theory, the conviction is founded. This, however, can not be proved: the ipoint being too far back to be within the reach of memory, and too ob- scure for external observation. The advocates of the a 2:>rlori theory are obliged to have recourse to other arguments. These are reducible to two, which I shall endeavor to state as clearly and as forcibly as possible. § 5. In the first place it is said, that if our assent to the proposition that two straight lines can not inclose a sj^ace, were derived from the senses, we could only be convinced of its truth by actual trial, that is, by seeing or feeling the straight lines ; whereas, in fact, it is seen to be true by merely tiiinking of them. That a stone thrown into water goes to the bottom, may be perceived by our senses, but mere thinking of a stone thrown into the water would never have led us to that conclusion : not so, however, with the axioms relating to straight lines : if I could be made to conceive what a straight line is, without having seen one, I should at once recognize that two such lines can not inclose a space. Intuition is " imaginary look- ing ;"* but experience must be real looking : if we see a property of straight lines to be true by merely fancying ourselves to be looking at them, the ground of our belief can not be the senses, or experience ; it must be something mental. To this argument it might be added in the case of this particular axiom (for the assertion would not be true of all axioms), that the evidence of it from actual ocular inspection is not only unnecessary, but unattainable. What says the axiom ? That two straight lines can not inclose a space ; that after having once intersected, if they are prolonged to infinity they do not meet, but continue to diverge from one another. How can this, in any single case, be proved by actual observation ? We may follow the lines to any distance we please ; but we can not follow them to infinity : for aught our senses can testify, they may, immediately beyond the farthest point to which we have traced them, begin to approach, and at last meet. Unless, therefore, we had some other proof of the impossibility than observation affords us, we should have no ground for believing the axiom at all. To these arguments, which 1 trust I can not be accused of understating, a satisfactory answer will, I conceive, be found, if we advert to one of the characteristic properties of geometrical forms — their capacity of being painted in the imagination with a distinctness equal to reality : in other words, the exact resemblance of our ideas of form to the sensations which true, for two of tliem may, and sometimes do, inclose a small portion of space. • In neither case, therefore, does experience prove the axiom. Those who employ this argument to show that geometrical axioms can not be proved by induction, show themselves unfamiliar with a common and perfectly A^alid mode of inductive proof; proof by approximation. Thougli experience furnishes us with no lines so unim- peachably straight tliat two of them are incapable of inclosing the smallest space, it presents us with gradations of lines possessing less and less either of breadth or of flexure, of which series the straight line of the definition is the ideal limit. And observation shows that just as much, and as nearly, as the straight lines of experience ajjproximate to having no breadth or flexure, so much and so nearly does the space-inclosing power of any two of them approach to zero. The inference that if they liad no breadth or flexure at all, they would inclose no space at all, is a correct inductive inference from these facts, conformable to one of the four Inductive Methods hereinafter characterized, the Method of Concomitant Variations ; of which the mathematical Doctrine of Limits presents the extreme case. * Whewell's History of Scientific Ideas, i., 140. DEMONSTRATION, AND NICCKSSAUY TRUTHS. 175 suggest tliem. This, in the first phico, ciiiiblos us to inuke (at least vvitli a little practice) mental pictures of all })0ssible combinations of lines and an- gles, which resemble the realities quite as well as any which we could make on paper; and in the next place, make those i)ictures just as fit subjects of geometrical experimentation as the realities themselves ; inasmi:ch as [)ic- tures, if sufficiently accurate, exhibit of course all the ])roperties which would be manifested by the realities at one given instant, and on simjjle inspection : and in geometry we are concerned only with such propeilies, and not with that which pictures could not exhibit, the mutual action of bodies one upon another. The foundations of geometry would therefore be laid in direct experience, even if the experiments (which in this case consist merely in attentive contemplation) were practiced solely uj)on what we call our ideas, that is, upon the diagrams in our minds, and not upon outward objects. For in all systems of experimentation we take some objects to serve as representatives of all which resemble them ; and in the present case the conditions which qualify a real object to be the rep- resentative of its class, are completely fulfilled by an object existing only in our fancy. Without denying, therefore, the possibility of satisfying our- selves that two straight lines can not inclose a space, by merely thinking of straight lines without actually looking at them ; I coutend, that we do not believe this truth on the ground of the imaginary intuition simply, but because we know that the imaginary lines exactly resemble real ones, and that we may conclude from them to real ones with quite as much certainty as we could conclude from one real line to another. The conclusion, there- fore, is still an induction from observation. And we should not be author- ized to substitute observation of the image in our mind, for observation of the reality, if we had not learned by long-continued experience that the properties of the reality are faithfully represented in the image; just as we should be scientifically warranted in describing an animal which we have never seen, from a picture made of it with a daguerreotype ; but not until we had learned by ample experience, that observation of such a pic- ture is precisely equivalent to observation of the original. These considerations also remove the objection arising from the im- possibility of ocularly following the lines in their prolongation to infinity. For though, in order actually to see that two given lines never meet, it would be necessary to follow them to infinity; yet without doing so we may know that if they ever do meet, or if, after diverging from one anoth- er, they begin again to approach, this must take place not at an infinite, but at a finite distance. Supposing, therefore, such to be the case, we can transport ourselves thither in imagination, and can frame a mental image of the appearance wdiich one or both of the lines must present at that point, which we may rely on as being precisely similar to the reality. Now, whether we fix our contemplation upon this imaginary picture, or call to mind the generalizations we have had occasion to make from former ocular observation, we learn by the evidence of experience, that a line which, after diverging from another straight line, begins to approach to it, produces the impression on our senses which we describe by the expression, '• a bent line," not by the expression, " a straight line."'^ * Dr. Whewell {Philosophy of Discovery, p. 280) thinks it unreasonable to contend that we know by experience, that our idea of a line exactly resembles a real line. ''It does not ap- pear," he says, "how we can compare our ideas with the realities, since we know the realities only by our ideas." We know the realities by our sensations. Dr. \Yhewell surely does not hold the "doctrine of perception by means of ideas," which Reid gave himself so much trou- ble to refute. 176 EEASONING. The preceding argument, which is, to my mind unanswerable, merges, however, in a still more comprehensive one, which is stated most clearly and conclusively by Professor Bain. The psychological reason why ax- ioms, and indeed many propositions not ordinarily classed as such, may be learned from the idea only without referring to the fact, is that in the proc- ess of acquiring the idea we have learned the fact. The proposition is assented to as soon as the terms are understood, because in learning to un- derstand the terms we have acquired the experience which proves the propo- sition to be true. " We required," says Mr. Bain,* " concrete experience in the first instance, to attain to the notion of whole and part ; but the notion, once arrived at, implies that the whole is greater. In fact, we could not have the notion without an experience tantamount to this conclusion When we have mastered the notion of straightness, we have also mastered that aspect of it expressed by the affirmation that two straight lines can not inclose a space. No intuitive or innate powers or perceptions are needed in such cases We can not have the full meaning of Straight- ness, without going through a comparison of straight objects among them- selves, and with their opposites, bent or crooked objects. The result of this comparison is, i7iter alia, that straightness in two lines is seen to be incompatible with inclosing a space ; the inclosure of space involves crook- edness in at least one of the lines." And similarly, in the case of every first principle,! " the same knowledge that makes it understood, suffices to verify it." The more this observation is considered the more (I am con- vinced) it will be felt to go to the very root of the controversy. § 6. The first of the two arguments in support of the theory that axioms are a, priori truths, having, I think, been sufficiently answered ; I proceed to the second, which is usually the most relied on. Axioms (it is asserted) If Dr. Whewell doubts whether we compare our ideas with the corresponding sensations, and assume that they resemble, let me ask on what evidence do we judge that a portrait of a person not present is like the original. Surely because it is like our idea, or mental image of the person, and because our idea is like the man himself. Dr. Whewell also says, that it does not appear why this resemblance of ideas to the sensa- tions of which they are copies, should be spoken of as if it were a peculiarity of one class of ideas, those of space. My reply is, that I do not so speak of it. The peculiarity I contend for is only one of degree. All our ideas of sensation of course resemble the corresponding sensations, but they do so with vei-y different degrees of exactness and of reliability. No one, I presume, can recall in imagination a color or an odor with the same distinctness and ac- c'uracy with which almost every one can mentally reproduce an image of a straight line or a triangle. To the extent, however, of their capabilities of accuracy, our recollections of colors or of odors may serve as sulyects of experimentation, as well as those of lines and spaces, and may yield conclusions which will be true of their external prototypes. A person in whom, either from natural gift or from cultivation, the impressions of color were peculiarly vivid and distinct, if asked which of two blue flowers was of the darkest tinge, though he might never have compared the two, or even looked at them together, might be able to give a confident answer on the faith of his distinct recollection of the colors ; that is, he might examine his mental pictures, and find there a ])ropcrty of the outward objects. Bnt in hardly any case except that of simple geometrical forms, could this be done by mankind generally, with a de- gree of assurance equal to that wliich is given by a contemplation of the objects themselves. Persons differ most widely in the precision of their recollection, even of forms: one person, when he has looked any one in the face for half a minute, can draw an accurate likeness of him from memory ; another may have seen him every day for six months, and hardly know whether liis nose is long or short. But every body has a perfectly distinct mental image of a straight line, a circle, or a rectangle. And every one concludes confidently from these mental images to the corresponding outward things. The truth is, that we may, and continually do, study nature in our recollections, when the objects themselves are absent ; and in the case of geometrical forms we can perfectly, but in most other cases only imperfectly, trust our recol- lections. *■ * Logic, i., 222. f Ibid., 226. DEMONSTRATION, AND NKCICSSARY TiiUTIlS. 177 are conceived by us not only as true, but as universally and necessarily true. Now, experience can not possii)ly give to any proposition this char- acter. I may have seen snow a hundred times, and may have seen that it was white, but this can not cjive me jentire assurance even that all snow is white; much less that snow must be white. "However many instances we may have observed of the truth of a i)roposition, there is nothini^ to assure us that the next case shall not be an exception to the rule. If it be strictly true that every ruminant animal yet known has cloven hoofs, we still can not be sure that some creature will not hereafter be discov- ered which has the first of these attributes, without having the other Experience must always consist of a limited number of observations; and, however numerous these may be, they can show nothing with regard to the infinite number of cases in which the experiment has not been made." Besides, Axioms are not only universal, they are also necessary. Now " ex- perience can not offer the smallest ground for the necessity of a proposi- tion. She can observe and record what has happened; but she can not find, in any case, or in any accumulation of cases, any reason for what must happen. She m.ay see objects side by side; but she can not see a reason why they must ever be side by side. She finds certain events to occur in succession ; but the succession supplies, in its occurrence, no reason for its recurrence. She contemplates external objects; but she can not detect any internal bond, which indissolubly connects the future with the past, the pos- sible with the real. To learn a proposition by experience, and to see it to be necessarily true, are two altogether different processes of thought."* And Dr. Whewell adds, " If any one does not clearly comprehend this dis- tinction of necessary and contingent truths, he will not be able to go along with us in our researches into the foundations of human knowledge ; nor, indeed, to pursue with success any speculation on the subject."f In the following passage, we are told what the distinction is, the non- recognition of which incurs this denunciation. " Necessary truths are those in which we not only learn that the proposition is true, but see that it 7nust he true; in which the negation of the ti'uth is not only false, but impossible ; in which we can not, even by an effort of imagination, or in a supposition, conceive the reverse of that which is asserted. That there are such truths can not be doubted. We may take, for example, all rela- tions of number. Three and Two added together make Five. We can not conceive it to be otherwise. We can not, by any freak of thought, imagine Three and Two to make Seven. "J Although Dr. Whewell has naturally and properly employed a variety of phrases to bring his meaning more forcibly home, he would, I presume, allow that they are all equivalent; and that what he means by a necessary truth, would be sufficiently defined, a proposition the negation of which is not only false but inconceivable. I am unable to find in any of his expres- sions, turn them what way you will, a meaning beyond this, and I do not believe he would contend that they mean any thing more. This, therefore, is the principle asserted : that propositions, the negation of which is inconceivable, or in other words, which we can not figure to ourselves as being false, must rest on evidence of a higher and more cogent description than any which experience can afford. No^v I can not but wonder that so much stress should be laid on the cir- cumstance of inconceivableness, when there is such ample experience to * History of Scientific Ideas, i., 65-67. t Ibid., i., 60. :!: Ibid,, 58, 59. 12 178 REASONING. show, that our capacity or incapacity of conceiving a thing has very little to do with the possibiHty of the thing in itself; but is in truth very much an affair of accident, and depends on the past history and habits of our own minds. There is no more generally acknowledged fact in human na- ture, than the extreme difficulty at first felt in conceiving any thing as pos- sible, which is in contradiction to long established and familiar experience ; or even to old familiar habits of thought. And this difficulty is a necessary result of the fundamental laws of the human mind. When we have often seen and thought of two things together, and have never in any one in- stance either seen or thought of them separately, there is by the primary law of association an increasing difficulty, which may in the end become insuperable, of conceiving the two things apart. This is most of all con- spicuous in uneducated persons, who are in general utterly unable to sepa- rate any two ideas which have once become firmly associated in their minds; and if persons of cultivated intellect have any advantage on the point, it is only because, having seen and heard and read more, and being more accustomed to exercise their imagination, they have experienced their sensations and thoughts in more varied combinations, and have been pre- vented from forming many of these inseparable associations. But this ad- vantage has necessarily its limits. The most practiced intellect is not ex^ empt from the universal laws of our conceptive faculty. If daily habit presents to any one for a long period two facts in combination, and if he is not led during that period either by accident or by his voluntary mental operations to think of them apart, he will probably in time become incapa- ble of doing so even by the strongest effort ; and the supposition that the two facts can be separated in nature, will at last present itself to his mind with all the characters of an inconceivable phenomenon.* There are re- markable instances of this in the history of science : instances in which the most instructed men rejected as impossible, because inconceivable, things which their posterity, by earlier practice and longer perseverance in the at- tempt, found it quite easy to conceive, and which every body now knows to be true. There was a time when men of the most cultivated intellects, and the most emancipated from the dominion of early prejudice, could not credit the existence of antipodes ; were unable to conceive, in opposition to 9ld association, the force of gravity acting upward instead of downward. The Cartesians long rejected the Newtonian doctrine of the gravitation of all bodies toward one another, on the faith of a general proposition, the re- verse of which seemed to them to be inconceivable — the proposition that a body can not act where it is not. All the cumbrous machinery of imagi- nary vortices, assumed without the smallest particle of evidence, appeared to these philosophers a more rational mode of explaining the heavenly mo- tions, than one which involved what seemed to them so great an absurdity.f * "If all mankind had spoken one language, we can not doubt that there would have been a powerful, perhaps a universal, school of philosophers, who would have believed in tlie in- herent connection between names and things, who would have taken the sound man to be the mode of agitating the air which is essentially communicative of the ideas of reason, cookery, bipedality, etc." — l)e Morgan, Forrnal Logic, p. 246. t It would be difficult to name a man more remarkable at once for the greatness and the wide range of his mental accomplishments, than Leibnitz. Yet this eminent man gave as a reason for rejecting Newton's scheme of the solar system, that God could not make a body re- volve round a distant centre, unless either by some impelling mechanism, or by miracle: " Tout ce qui n'est pas explicable," says he in a letter to the Abbe Conti, " par la nature des creatures, est mirac^uleux. II ne suffit pas de dire : Dieu a ftiit tme telle loi de nature ; done la chose est naturelle. 11 faut que la loi soit exe'cutable par Ics natures des cre'atures. !Si DEMONSTRATION, AND NKOKSSAltY TIUJI'IIS. ] 70 And they no doubt fomid it as impossible to conceive tliat a Ijody slioiild act upon the earth from the distance of the sun or moon, as we find it to conceive an end to space or time, or two straight lines inclosing a space. Newton liimself had not been able to realize the conception, or we should not have had his hypothesis of a subtle ether, the occult cause of gravita- tion ; and his writings prove, that though he deemed the ])articular nature of the intermediate agency a matter of conjecture, the necessity of some such agency appeared to him indubitable. If, tlien, it be so natural to the liuman mind, even in a high state of cul- ture, to be incapable of conceiving, and on that ground to believe impossi- ble, what is afterward not only found to be conceivable but proved to be true; what wonder if in cases where the association is still older, more con- firmed, and more familiar, and in which nothing ever occurs to shake our conviction, or even suggest to us any conception at variance with the asso- ciation, the acquired incapacity should continue, and be mistaken for a nat- ural incapacity ? It is true, our experience of the varieties in nature ena- bles us, within certain limits, to conceive other varieties analogous to them. We can conceive the sun or moon falling ; for though we never saw them fall, nor ever, perhaps, imagined them falling, we have seen so many other things fall, that we have innumerable familiar analogies to assist the con- ception ; which, after all, we should probably have some difficulty in fram- ing, were we not well accustomed to see the sun and moon move (or ap- pear to move), so that we are only called upon to conceive a slight cliange in the direction of motion, a circumstance familiar to our experience. But when experience affords no model on which to shape the new conception, how is it possible for us to form it? How, for example, can we imagine an end to space or time? We never saw any object without something beyond it, nor experienced any feeling wdthout something following it. When, therefore, we attempt to conceive the last point of space, we have the idea irresistibly raised of other points beyond it. When we try to im- agine the last instant of time, we can not help conceiving another instant after it. Nor is there any necessity to assume, as is done by a modern school of metaphysicians, a peculiar fundamental la^v of the mind to ac- count for the feeling of infinity inherent in our conceptions of space and time; that apparent infinity is sufficiently accounted for by simpler and universally acknowledged laws. Now, in the case of a geometrical axiom, such, for example, as that two straight lines can not inclose a space — a truth which is testified to us by our very earliest impressions of the external world — how is it possible (whether those external impressions be or be not the ground of our belief) that the reverse of the proposition could be otherwise than inconceivable to us? What analogy have we, w^hat similar order of facts in any other branch of our experience, to facilitate to us the conception of two straight lines inclosing a space? Nor is even this all. I have already called atten- tion to the peculiar property of our impressions of form, that the ideas or mental images exactly resemble their prototypes, and adequately represent them for the purposes of scientific observation. From this, and from the intuitive character of the observation, which in this case reduces itself to Dieu donnait cette loi, par exemple, a iin corps libre, de toiirner a rentour d"nn certain centre, il faudrait ou quil y joignit d'autres corps qui par leiir iinpulsioti I'obligeassent de rester tou- joiirs dans son orbiie circidaire, on qiiil mit un ange a ses trottsses, ou enfin il faudrait quil y concourut extraordinairement ; car natnrellement il s'ecartera par la tangente." — Works of Leibnitz, ed. Dutens. iii., 44G. 180 REASONING. simple inspection, we can not so much as call up in our imagination two straight lines, in order to attempt to conceive them inclosing a space, with- out by that very act repeating the scientific experiment which establishes the contrary. Will it really be contended that tlie inconceivableness of the thing, in such circumstances, proves any thing against the experimental or- igin of the conviction ? Is it not clear that in whichever mode our belief in the proposition may have originated, the impossibility of our conceiving the negative of it must, on either hypothesis, be the same? As, then. Dr. Whewell exhorts those who have any difficulty in recognizing the distinc- tion held by him between necessary and contingent truths, to study geom- etry — a condition which I can assure him I have conscientiously fulfilled^ I, in return, with equal confidence, exhort those who agree with him, to study the general laws of association ; being convinced that nothing more is requisite than a moderate familiarity with those laws, to dispel the illu- sion which ascribes a peculiar necessity to our earliest inductions from ex- perience, and measures the possibihty of things in themselves, by the hu- man capacity of conceiving them. I hope to be pardoned for adding, that Dr. Whewell himself has both confirmed by his testimony the effect of habitual association in giving to an experimental truth the appearance of a necessary one, and afforded a striking instance of that remarkable law in his own person. In his Philos- ophy of the Inductive Sciences he continually asserts, that propositions which not only are not self-evident, but which we know to have been dis- covered gradually, and by great efforts of genius and patience, have, when once established, appeared so self-evident that, but for historical proof, it would have been impossible to conceive that they had not been recognized from the first by all persons in a sound state of their faculties. " We now despise those who, in the Copernican controversy, could not conceive the apparent motion of the sun on the heliocentric hypothesis ; or those who, in opposition to Galileo, thought that a uniform force might be that which generated a velocity proportional to the space; or those who held there was something absurd in IsTewton's doctrine of the different refrangibility of differently colored rays; or those who imagined that when elements combine, their sensible qualities must be manifest in the compound; or those who were reluctant to give up the distinction of vegetables into herbs, shrubs, and trees. We can not help thinking that men must have been singularly dull of comprehension, to find a difficulty in admitting what is to us so plain and simple. We have a latent persuasion that we in their place should have been wiser and more clear-sighted ; that we should have taken the right side, and given our assent at once to the truth. Yet in re- ality such a persuasion is a mere delusion. The persons who, in such in- stances as the above, were on the losing side, were very far, in most cases, from being persons more prejudiced, or stupid, or narrow-minded, than the greater part of mankind now are; and the cause for which they fought was far from being a manifestly bad one, till it had been so decided by the result of the war So complete has been the victory of truth in most of these instances, that at present we can hardly imagine the struggle to have been necessary. The very essence of these triumphs is, that they lead ns to regard the views we reject as not only false hut inconceivable.''''^ This last proposition is precisely what I contend for ; and I ask no more, in order to overthrow the whole theory of its author on the nature of the * Novum Organum Renovatum^ pp. 32, 33. DEMONSTRATION, AND NKCESSAKY 'i'laJTIIS. J 81 ovidence of axioms. For what is thnt theory? 'I'hat the ti-uth of axioins can not have been learned from experience, because tiieir falsity is incon- ceivable. But Dr. Whevvell himself says, that we are continually led, by the natural progress of thought, to regard as inconceivable what our fore- fathers not only conceived but believed, nay even (he might have added) were unable to conceive the reverse of. He can not intend to justify this mode of thought : he can not mean to say, that we can be right in regard- ing as inconceivable what others have conceived, and as self-evident what to others did not appear evident at all. After so cojuplete an admis- sion that inconceivableness is an accidental thing, not inherent in the phe- nomenon itself, but dependent on the mental history of the pei'son who tries to conceive it, how can he ever call upon us to reject a proposition as impossible on no other ground than its inconceivableness? Yet he not only does so, but has unintentionally afforded some of the most remarkable examples which can be cited of the very illusion which he has Iiimself so clearly pointed out. I select as specimens, his remarks on the evidence of the three laws of motion, and of the atomic theory. With respect to the laws of motion, Dr. Whewell says : " No one can doubt that, in historical fact, these laws were collected from experience. That such is the case, is no matter of conjecture. We know the time, the persons, the circumstances, belonging to each step of each discovery."* After this testimony, to adduce evidence of the fact would be superfluous. And not only were these laws by no means intuitively evident, but some of them were originally paradoxes. The first law was especially so. That a body, once in motion, would continue forever to move in the same direc- tion with undiminished velocity unless acted upon by some new force, was a proposition which mankind found for a long time the greatest difticulty in crediting. It stood opposed to apparent experience of the most familiar kind, which taught that it was the nature of motion to abate gradually, and at last terminate of itself. Yet when once the contrary doctrine w^as firmly established, mathematicians, as Dr. Whewell observes, speedily be- gan to believe that laws, thus contradictory to first appearances, and which, even after full proof had been obtained, it had required generations to ren- der familiar to the minds of the scientific world, were under " a demonstra- ble necessity, compelling them to be such as they are and no other;" and he himself, though not venturing " absolutely to pronounce " that all these laws " can be rigorously traced to an absolute necessity in the nature of things,"f does actually so think of the law just mentioned; of which he says: "Though the discovery of the first law of motion was made, histor- ically speaking, by means of experiment, we have now attained a point of view in which we see that it might have been certainly known to be true, independently of experience."! Can there be a more striking exemplifi- cation than is here afforded, of the effect of association wdiich we have de- scribed? Philosophers, for generations, have the most extraordinary difti- culty in putting certain ideas together ; they at last succeed in doing so ; and after a sufticient repetition of the process, they first fancy a natural bond between the ideas, then experience a growing difticulty, which at last, by the continuation of the same progress, becomes an impossibility, of sev- ering them from one another. If such be fhe progress of an experimental conviction of which the date is of yesterday, and which is in opposition to first appearances, how must it fare with those which are conformable to ♦ History of Scientific Ideas, i., 264. t Ibid., i., 263. :i: Ibid., 240. 182 KEASONING. appearances familiar from the first dawn of intelligence, and of the conclu- siveness of which, from the earliest records of human thought, no skeptic has suggested even a momentary doubt ? The other instance which I shall quote is a truly astonishing one, and may be called the reductio ad ahsurdiim of the theory of inconceivableness. Speaking of the laws of chemical composition, Dr. Whewell says :* " That they could never have been clearly understood, and therefore never firmly established, without laborious and exact experiments, is certain ; but yet we may venture to say, that being once known, they possess an evidence beyond that of mere experiment. For how in fact can we conceive combi- nations^ otherioise than as definite in kind and quality f If we were to suppose each element ready to combine with any other indifferently, and indifferently in any quantity, we should have a world in which all would be confusion and indetiniteness. There would be no fixed kinds of bodies. Salts, and stones, and ores, would approach to and graduate into each other by insensible degrees. Instead of this, we know that the world consists of bodies distinguishable from each other by definite differences, capable of being classified and named, and of having general propositions asserted concerning them. And as we can not conceive a world in which this should not he the case, it would appear that we can not conceive a state of things in which the laws of the combination of elements should not be of that definite and measured kind which we have above asserted." That a philosopher of Dr. Whewell's eminence should gravely assert that we can not conceive a world in which the simple elements should com- bine in other than definite proportions; that by dint of meditating on a scientific truth, the original discoverer of which was still living, he should have rendered the association in his own mind between the idea of combi- nation and that of constant proportions so familiar and intimate as to be unable to conceive the one fact without the other; is so signal an instance of the mental law for which I am contending, that one word more in illus- tration must be superfluous. In the latest and most complete elaboration of his metaphysical system (the Philosophy of Discovery), as well as in the earlier discourse on the Fandamental Antithesis of Philosophy, reprinted as an appendix to that work, Dr. Whewell, while very candidly admitting that his language was open to misconception, disclaims having intended to say that mankind in general can noio perceive the law of definite proportions in chemical com- bination to be a necessary truth. All he meant was that philosophical chemists in a future generation may possibly see this. " Some truths may be seen by intuition, but yet the intuition of them may be a rare and a dif- ficult attainment."! And he explains that the inconceivableness which, ac- cording to his theory, is the test of axioms, " depends entirely upon the clearness of the Ideas which the axioms involve. So long as those ideas are vague and indistinct, the contrary of an axiom may be assented to, though it can not be distinctly conceived. It may be assented to, not be- cause it is possible, but because we do not see clearly what is possible. To a person who is only beginning to think geometrically, there may appear nothing absurd in the assertion that two straight lines may inclose a space. And ill the same manner, to a* person who is only beginning to think of mechanical truths, it may not appear to be absurd, that in mechanical proc- esses, lieaction should be greater or less than Action ; and so, again, to a * Hist. Scientific Ideas, ii., 25, 26. t Phil of Disc, p. 339. DEMONSTKA'IMON, AM) MCCIOSSAKY 'J^RUTIIS. 183 person who has not Ihouglil steadily about Substance, it inay not appc-ar inconceivable, that by chemical operations, we should is^ituvvnia new matter, or destroy matter which already exists.'"^ Necessary truths, therefore, are not those of which we can not conceive, but " those of whicli we can not distinctly conceive, the contrary."! . So long as our ideas are indistinct al- together, we do not know what is or is not capable of being distinctly conceived; bnt, by the ever increasing distinctness with wliich scientific men apprehend the general conceptions of science, they in time come to perceive that there are certain laws of nature, which, though historically and as a matter of fact they were learned from ex})erience, we can not, now^ that we know them, distinctly conceive to be other than they are. The account which I should give of this progress of the scientific mind is somewhat different. After a general law of nature has been ascertained, men's minds do not at first acquire a complete facility of familiai-ly repre- senting to themselves the phenomena of nature in the character which that law assigns to them. The habit which constitutes the scientific cast of mind, that of conceiving facts of all descriptions conformably to the laws which regulate them — phenomena of all descriptions according to the re- lations which have been ascertained really to exist between them; this hab- it, in the case of newly-discovered relations, comes only by degrees. So long as it is not thoroughly formed, no necessary character is ascribed to the new truth. But in time, the philosopher attains a state of mind in which his mental picture of nature spontaneously represents to him all the phenomena with which the new theory is concerned, in the exact light in which the theory regards them : all images or conceptions derived from any other theory, or from the confused view of the facts which is anterior to any theory, having entirely disappeared from his mind. The mode of representing facts which results from the theory, has now become, to his faculties, the only natural mode of conceiving them. It is a known truth, that a prolonged habit of arranging phenomena in certain groups, and ex- plaining them by means of certain principles, makes any other arrangement or explanation of these facts be felt as unnatural : and it may at last be- come as difficult to him to represent the facts to himself in any other mode, as it often was, originally, to represent them in that mode. But, further (if the theory is true, as we are supposing it to be), any other mode in which he tries, or in which he was formerly accustomed, to represent the phenomena, will be seen by him to be inconsistent with the facts that suggested the new theory — facts which now form a part of his mental picture of nature. And since a contradiction is always incon- ceivable, his imagination rejects these false theories, and declares itself in- capable of conceiving them. Their inconceivableness to him does not, how- ever, result from any thing in the theories themselves, intrinsically and a priori repugnant to the human faculties ; it results from the repugnance between them and a portion of the facts ; which facts as long as he did not know, or did not distinctly realize in his mental representations, the false theory did not appear other than conceivable; it becomes inconceiv- able, merely from the fact that contradictory elements can not be combined in the same conception. Although, then, his real reason for rejecting theo- ries at variance with the true one, is no other than that they clash with his experience, he easily falls into the belief, that he rejects them because they are inconceivable, and that he adopts the true theory because it is self-evi- dent, and does not need the evidence of experience at all. * Phil, of Disc, p. 338. t Ibid., p. 463. 184 REASONING. Thk I take to be the real and sufficient explanation of the paradoxical truth, on which so much stress is laid by Dr. Whewell, that a scientifically cultivated mind is actually, in virtue of that cultivation, unable to conceive suppositions which a common man conceives without the smallest difficul- ty. For there is nothing inconceivable in the suppositions themselves ; the impossibility is in combining them with facts inconsistent with them, as part of the same mental picture ; an obstacle of course only felt by those who know the facts, and are able to perceive the inconsistency. As far as the suppositions themselves are concerned, in the case of many of Dr. Whe- well's necessary truths the negative of the axiom is, and probably will be as long as the human race lasts, as easily conceivable as the affirmative. There is no axiom (for example) to which Dr. Whewell ascribes a more thorough character of necessity and self-evidence, than that of the inde- structibiUty of matter. That this is a true law of nature I fully admit; but I imagine there is no human being to whom the opposite supposition is inconceivable — who has any difficulty in imagining a portion of matter annihilated : inasmuch as its apparent annihilation, in no respect distin- guishable from real by our unassisted senses, takes place every time that water dries up, or fuel is consumed. Again, the law that bodies combine chemically in definite proportions is undeniably true ; but few besides Dr. Whewell have reached the point which he seems personally to have arrived at (though he only dares prophesy similar success to the multitude after the lapse of generations), that of being unable to conceive a world in which the elements are ready to combine with one another " indifferently in any quantity;" nor is it likely that we shall ever rise to this sublime height of inability, so long as all the mechanical mixtures in our planet, whether sol- id, liquid, or aeriform, exhibit to our daily observation the very phenomenon declared to be inconceivable. According to Dr. Whewell, these and similar laws of nature can not be drawn from experience, inasmuch as they are, on the contrary, assumed in the interpretation of experience. Our inability to "add to or diminish the quantity of matter in the world," is a truth which " neither is nor can be derived from experience ; for the experiments which we make to verify it presuppose its truth When men began to use the balance in chem- ical analysis, they did not prove by trial, but took for granted, as self-evi- dent^ that the weight of the whole must be found in the aggregate weight of the elements."* True, it is assumed ; but, I apprehend, no otherwise than as all experimental inquiry assumes provisionally some theory or hy- pothesis, which is to be finally held true or not, according as the experi- ments decide. The hypothesis chosen for this purpose will naturally be one which groups together some considerable number of facts already known. The proposition that the material of the world, as estimated by weight, is neither increased nor diminished by any of the processes of na- ture or art, had many appearances in its favor to begin with. It expressed truly a great number of familiar facts. There were other facts which it had the appearance of conflicting with, and w^hich made its truth, as a universal law of nature, at first doubtful. Because it was doubtful, exper- iments were devised to verify it. Men assumed its truth hypothetically, and proceeded to try whether, on more careful examination, the phenomena which ap})arently pointed to a different conclusion, would not be found to be consistent with it. This turned out to be the case: and from that time * Phil of Disc, pp. 472, 473. DEMONSTRAl'lON, AND NKCKSSARV TRL TIIS. 1S5 the doctrine took its })l;ic(^ ;is ;i univers;il truth, but as one j)i-ove(l to Ije such by experience. Tiiat the theory itself j)rece(le(l the proof of its truth — that it had to be conceived before it couhl be j)roved, and in order that it might be proved — does not imply that it was self-evident, and did not need proof. Otherwise all the true theories in the sciences are necessary and self-evident; for no one knows better than Dr. Whewell that they all began by being assumed, for the purpose of connecting them by deduc- tions with those facts of experience on which, as evidence, tliey now con- fessedly rest.* * The Quarterly Review for June, 1841, contained an article of great ability on Dr. Whe- well's two great works (since acknowledged and reprinted in Sir John Ilerschel's Essays; which maintains, on the subject of axioms, the doctrine advanced in the text, that they are generalizations from experience, and supports that opinion by a line of argument strikingly coinciding with mine. When I state that the whole of the present chapter (except the last four pages, added in the fifth edition) was written before I had seen the article (the greater part, indeed, before it was published), it is not my object to occupy the reader's attention with a matter so unimportant as the degree of originality which may or may not belong to any por- tion of my own speculations, but to obtain for an opinion which is opposed to reigning doc- trines, the recommendation derived from a striking concurrence of sentiment between two inquirers entirely independent of one another. I embrace the opportunity of citing from a writer of the extensive acquirements in physical and metaphysical knowledge and the capacity of systematic tliought which the article evinces, passages so remarkably in unison with my own views as the following : "The truths of geometry are summed up and embodied in its definitions and axioms Let us turn to the axioms, and what do we find? A string of propositions concerning mag- nitude in the abstract, which are equally true of space, time, force, number, and every other magnitude susceptible of aggregation and subdivision. Such propositions, where they are not mere definitions, as some of them are, carry their inductive origin on the face of their enunciation Those which declare that two straight lines can not inclose a space, and that tw^o straight lines which cut one another can not both be parallel to a third, are in reality the only ones which express characteristic properties of space, and these it will be worth while to consider more nearly. Now the only clear notion we can form of straightness is uniform- ity of direction, for space in its ultimate analysis is nothing but an assemblage of distances and directions. And (not to dwell on the notion of continued contemplation, i. e., mental ex- perience, as included in the very idea of uniformity ; nor on that of transfer of the contem- plating being from point to point, and of experience, during such transfer, of the homogeneity of the interval passed over) we can not even propose the proposition in an intelligible form to any one whose experience ever since he was born has not assured him of the fact. The unity of direction, or that we can not march from a given point by more than one path direct to the same object, is matter of practical experience long before it can by possibility become matter of abstract thought. We can not attempt mentally to exemplify the conditions of the assertion in an imaginary case opposed to it, without violating our habitual recollection of this experi- ence, and defacing our mental picture of space as grounded on it. What but experience, we may ask, can possibly assure us of the homogeneity of the parts of distance, time, force, and measurable aggregates in general, on which the truth of the other axioms depends ? As re- gards the latter axiom, after what has been said it must be clear that the very same course of remarks equally applies to its case, and that its truth is quite as much forced on the mind as that of the former by daily and hourly experience, including always, he it observed, in our notion of experience, that which is gained by contemplation of the inward picture ichich the mind forms to itself in any proposed case, or which it arbitrarily selects as an example — such picture, in virtue of the extreme simplicity of these primary relations, being called up by the imagination with as much vividness and clearness as cotdd be done by any external imj)ression. which is the only meaning we can attach to the ivord intuition, as applied to such relations.'' And again, of the axioms of mechanics: ''As we admit no such propositions, other than as truths inductively collected from observation, even in geometry itself, it can hardly be ex- pected that, in a science of obviously contingent relations, we should acquiesce in a contrary view\ Let us take one of these axioms and examine its evidence : for instance, that equal forces perpendicularly apphed at the opposite ends of equal arms of a straight lever will bal- ance each other. What but experience, we may ask, in the first place, can possibly inform us that a force so applied will have any tendency to turn the lever on its centre at all ? or that force can be so transmitted along a rigid hue perpendicular to its direction, as to act elsewhere in space than along its own line of action ? Surely this is so far from being self-evident that 186 REASONING. it has even a paradoxical appearance, which is only to be removed by giving our lever thick- ness, material composition, and molecular powers. Again, Ave conclude, that the two forces, being equal and applied under precisely similar circumstances, must, if they exert any effort at all to turn the lever, exert equal and opposite efforts : but what a priori reasoning can pos- sibly assure us that they do act under precisely similar circumstances ? that points which dif- fer in place are similarly circumstanced as regards the exertion of force? that universal space may not have relations to universal force — or, at all events, that the organization of the ma- terial universe may not be such as to phice that portion of space occupied by it in such rela- tions to the forces exerted in it, as may invalidate the absolute similarity of circumstances as- sumed ? Or we may argue, what have we to do with the notion of angular movement in the lever at all ? The case is one of rest, and of quiescent destruction of force by force. Now how is this destruction effected? Assuredly by the counter-pressure which supports the ful- crum. But would not this destruction equally arise, and by the same amount of counteract- ing force, if each force simply pressed its own half of the lever against the fulcrum ? And what can assure us that it is not so, except removal of one or other force, and consequent tilt- ing of the lever? The other fundamental axiom of statics, that the pressure on the point of support is the sum of the weights is merely a scientific transformation and more refined mode of stating a coarse and obvious result of universal experience, viz., that the weight of a rigid body is the same, handle it or suspend it in what position or by what point we will, and that whatever sustains it sustains its total weight. Assuredly, as Mr. Whewell justly remarks, 'No one probably ever made a trial for the purpose of showing that the pressure on the sup- port is equal to the sum of the weights.' But it is precisely because in every action of his life from earliest infancy he has been continually making the trial, and seeing it made by every other living being about him, that he never dreams of staking its result on one addi- tional attempt made with scientific accuracy. This would be as if a man should resolve to decide by experiment whether his eyes were useful for the purpose of seeing, by hermetically sealing himself up for half an hour in a metal case." On the "paradox of universal propositions obtained by experience," the same writer says : " If there be necessary and universal truths expressible in propositions of axiomatic simplicity and obviousness, and having for their subject-matter the elements of all our experience and all our knowledge, surely these are the truths which, if experience suggest to us any truths at all, it ought to suggest most readily, clearly, and unceasingly. If it were a truth, universal and necessary, that a net is spread over the whole surface of every planetary globe, we should not travel far on our own without getting entangled in its meshes, and making the necessity of some means of extrication an axiom of locomotion There is, therefore, nothing par- adoxical, but the reverse, in our being led by observation to a recognition of such truths, as general propositions, co-extensive at least with all human experience. That they pervade all the objects of experience, must insure their continual suggestion hy experience ; that they are true, must insure that consistency of suggestion, that iteration of uncontradicted assertion, which commands implicit assent, and removes all occasion of exception ; that they are simple, and admit of no misunderstanding, must secure their admission by every mind." "A truth, necessary and universal, relative to any object of our knowledge, must verify it- self in every instance where that object is before our contemplation, and if at the same time it be simple and intelligible, its verification must be obvious. The sentiment of such a truth can not, therefore, hut be present to our minds ivhenever that object is contemplated, and must therefore make a part of the mental picture or idea of that object ivhich ive may on any occa- sion summon before our imagination All propositions, therefore, become not only untrue but inconceivable, if axioms be violated in their enunciation." Another eminent mathematician had previously sanctioned by his authority the doctrine of the origin of geometrical axioms in experience. "Geometry is thus founded likewise on observation; but of a kind so familiar and obvious, that the primary notions which it fur- nishes might seem intuitive." — Sir John Leslie, quoted by Sir William Hamilton, Discourses, etc., p. 272. DEMONiSTKATlUN, AND NECEtSSAKY TJiUTllS. 187 CHAPTER VI. THE SAME SUBJECT CONTINUED. § 1. In the examination which formed the subject of the last chapter, into the nature of the evidence of those deductive sciences wliich are com- monly represented to be systems of necessary truth, we have been led to the following conclusions. The results of those sciences are indeed nec- essary, in the sense of necessarily following from certain first ])rincij)les, commonly called axioms and definitions ; that is, of being certainly true if those axioms and definitions are so; for the word necessity, even in this acceptation of it, means no more than certainty. But their claim to the character of necessity in any sense beyond this, as implying an evidence independent of and superior to observation and experience, must depend on the previous establishment of such a claim in favor of the definitions and axioms themselves. With regard to axioms, we found that, consid- ered as experimental truths, they rest on superabundant and obvious ev- idence. We inquired, w^hether, since this is the case, it be imperative to suppose any other evidence of those truths than experimental evidence, any other origin for our belief of them than an experimental origin. We de- cided, that the burden of proof lies with those who maintain the affirma- tive, and we examined, at considerable length, such arguments as they have produced. The examination having led to the rejection of those arguments, we have thought ourselves warranted in concluding that axioms are but a class, the most universal class, of inductions from experience; the simplest and easiest cases of generalization from the facts furnished to us by our senses or by our internal consciousness. While the axioms of demonstrative sciences thus appeared to be exper- imental truths, the definitions, as they are incorrectly called, in those sci- ences, were found by us to be generalizations from experience which are not even, accurately speaking, truths ; being propositions in which, while we assert of some kind of object, some property or properties which ob- servation shows to belong to it, we at the same time deny that it possesses any other properties, though in truth other properties do in every individ- ual instance accompany, and in almost all instances modify, the property thus exclusively predicated. The denial, therefore, is a mere fiction, or sup- position, made for the purpose of excluding the consideration of those mod- ifying circumstances, when their influence is of too trifling amount to be worth considering, or adjourning it, when important to a more convenient moment. From these considerations it would appear that Deductive or Demon- strative Sciences are all, without exception. Inductive Sciences ; that their evidence is that of experience; but that they are also, in virtue of the pe- culiar character of one indispensable portion of the general formulae ac- cording to which their inductions are made, Hypothetical Sciences. Their conclusions are only true on certain suppositions, which are, or ought to be, approximations to the truth, but are seldom, if ever, exactly true ; and to this hypothetical character is to be ascribed the peculiar certainty, which is supposed to be inherent in demonstration. 188 REASONING. What we have now asserted, however, can not be received as universally true of Deductive or Demonstrative Sciences, until verified by being ap- plied to the most remarkable of all those sciences, that of Numbers ; the theory of the Calculus; Arithmetic and Algebra. It is harder to believe of the doctrines of this science than of any other, either that they are not truths a priori^ but experimental truths, or that their peculiar certainty is owing to their being not absolute but only conditional truths. This, there- fore, is a case which merits examination apart ; and the more so, because on this subject we have a double set of doctrines to contend with ; that of the a priori philosophers on one side; and on the other, a theory the most opposite to theirs, which was at one time very generally received, and is still far from being altogether exploded, among metaphysicians. § 2. This theory attempts to solve the difficulty apparently inherent in the case, by representing the propositions of the science of numbers as merely verbal, and its processes as simple transformations of language, sub- stitutions of one expression for another. The proposition. Two and one is equal to three, according to these writers, is not a truth, is not the assertion of a really existing fact, but a definition of the word three; a statement that mankind have agreed to use the name three as a sign exactly equiva- lent to two and one ; to call by the former name whatever is called by the other more clumsy phrase. According to this doctrine, the longest process in algebra is but a succession of changes in terminology, by which equiva- lent expressions are substituted one for another ; a series of translations of the same fact, from one into another language ; though how, after such a series of translations, the fact itself comes out changed (as when we de- monstrate a new geometrical theorem by algebra), they have not explain- ed ; and it is a difficulty which is fatal to their theory. It must be acknowledged that there are peculiarities in the processes of arithmetic and algebra which render the theory in question very plausible, and have not unnaturally made those sciences the stronghold of Nominal- ism. The doctrine that we can discover facts, detect the hidden processes of nature, by an artful manipulation of language, is so contrary to common sense, that a person must have made some advances in philosophy to be- lieve it : men fly to so paradoxical a belief to avoid, as they think, some even greater difficulty, which the vulgar do not see. What has led many to believe that reasoning is a mere verbal process, is, that no other theory seemed reconcilable with the nature of the Science of Numbers. For we do not carry any ideas along with us when we use the symbols of arithme- tic or of algebra. In a geometrical demonstration we have a mental dia- gram, if not one on paper ; AB, AC, are present to our imagination as lines, intersecting other lines, forming an angle with one another, and the like ; but not so a and h. These may represent lines or any other magnitudes, but those magnitudes are never thought of; nothing is realized in our im- agination but a and h. The ideas which, on the particular occasion, they happen to represent, are banished from the mind during every intermediate part of the pi'ocess, between the beginning, when the premises are trans- lated from things into signs, and the end, when tlie conclusion is translated back from signs into things. Nothing, then, being in the reasoner's mind but the symbols, what can seem more inadmissible than to contend that the reasoning process has to do with any thing more ? We seem to have come to one of Bacon's Prerogative Instances; an experimentmn crucis on the nature of reasoning itself. DEMONSTRATION, AND NKOKSSAKV TliLTIIS. i^O Nevertheless, it will appear on eoiisidei-ation, that this appai'ently so de- cisive instance is no instance at all ; tliat tliere is in every step of Jin arith- metical or algebraical calcnlation a real induction, a real inference of facts from facts; and that what disguises the induction is simply its compre- hensive nature, and the consequent extreme generality of the language. All numbers must be numbers of something: there are no such things as numbers in the abstract. 7^en must mean ten bodies, or ten sounds, or ten beatings of the pulse. But though numbers must be numbers of some- thing, they may be numbers of any thing. Propositions, therefore, con- cerning numbers, have the remarkable peculiarity that they are proposi- tions concerning all things whatever; all objects, all existences of every kind, known to our experience. All things possess quantity ; consist of parts which can be numbered ; and in that character possess all the prop- erties which are called properties of numbers. That half of four is two, must be true whatever the word four represents, whether four hours, four miles, or four pounds weight. We need only conceive a thing divided into four equal parts (and all things may be conceived as so divided), to be able to predicate of it. every property of the number four, that is, every arith- metical proposition in which the number four stands on one side of the equation. Algebra extends the generalization still farther: every number represents that particular number of all things without distinction, but ev- ery algebraical symbol does more, it represents all numbers without dis- tinction. As soon as we conceive a thing divided into equal parts, without knowing into w^hat number of parts, we may call it a or cc, and apply to it, without danger of error, every algebraical formula in the books. The proposition, 2 [a -{- b) = 2 a + 2 ^, is a truth co-extensive with all nature. Since then algebraical truths are true of all things whatever, and not, like those of geometry, true of lines only or of angles only, it is no wonder that the symbols should not excite in our minds ideas of any things in particu- lar. When we demonstrate the forty-seventh proposition of Euclid, it is not necessary that the words should raise in us an image of all right-angled triangles, but only of some one right-angled triangle : so in algebra we need not, under the symbol a, picture to ourselves all things whatever, but only some one thing; why not, then, the letter itself? The mere written characters, a, b, x, y, z, serve as well for representatives of Things in general, as any more complex and apparently more concrete conception. That we are conscious of them, however, in their character of things, and not of mere signs, is evident from the fact that our whole process of reasoning is car- ried on by predicating of them the properties of things. In resolving an algebraic equation, by what rules do we proceed ? By applying at each step to a, b, and x, the proposition that equals added to equals make equals ; that equals taken from equals leave equals ; and other propositions founded on these two. These are not properties of language, or of signs as such, but of magnitudes, which is as much as to say, of all things. The infer- ences, therefore, which are successively drawn, are inferences concerning things, not symbols; though as any Things whatever will serve the turn, there is no necessity for keeping the idea of the Thing at all distinct, and consequently the process of thought may, in this case, be allowed without danger to do what all processes of thought, when they have been performed often, will do if permitted, namely, to become entirely mechanical. Hence the general language of algebra comes to be used familiarly without excit- ing ideas, as all other general language is prone to do from mere habit, though in no other case than this can it be done with complete safety. 190 REASONING. But when we look back to see from whence the probative force of the process is derived, we find that at every single step, unless we suppose our- selves to be thinking and talking of the things, and not the mere symbols, the evidence fails. There is another circumstance, which, still more tlian that which we have now mentioned, gives plausibility to the notion tliat the propositions of arithmetic and algebra are merely verbal. That is, that when considered as propositions respecting Things, they all have the appearance of being identical propositions. The assertion. Two and one is equal to three, con- sidered as an assertion respecting objects, as for instance, " Two pebbles and one pebble are equal to three pebbles," does not affirm equality be- tween two collections of pebbles, but absolute identity. It affirms that if we put one pebble to two pebbles, those very pebbles are three. Tlie ob- jects, therefore, being the very same, and the mere assertion that "objects are themselves " being insignificant, it seems but natural to consider the proposition. Two and one is equal to three, as asserting mere identity of signification between the two names. This, however, though it looks so plausible, will not bear examination. The expression " two pebbles and one pebble," and the expression " three pebbles," stand indeed for the same aggregation of objects, but they by no means stand for the same physical fact. They are names of the same ob- jects, but of those objects in two different states : though they (denote the same things, their connotation is different. Three pebbles in two separate parcels, and three pebbles in one parcel, do not make the same impression on our senses ; and the assertion that the very same pebbles may by an al- teration of place and arrangement be made to produce either the one set of sensations or the other, though a very famihar proposition, is not an iden- tical one. It is a truth known to us by early and constant experience : an inductive truth ; and such truths are the foundation of the science of Num- ber. The fundamental truths of that science all rest on the evidence of sense; they are proved by showing to our eyes and our fingers that any given number of objects — ten balls, for example — may by separation and re-arrangement exhibit to our senses all the different sets of numbers the sums of which is equal to ten. All the improved methods of teaching arithmetic to children proceed on a knowledge of this fact. All who wish to carry the child's mind along with them in learning arithmetic ; all who wish to teach numbers, and not mere ciphers — nov/ teach it through the ev- idence of the senses, in the manner we have described. We may, if we please, call the proposition, " Three is two and one," a definition of the number three, and assert that arithmetic, as it has been asserted that geometry, is a science founded on definitions. But they are definitions in the geometrical sense, not the logical ; asserting not the mean- ing of a term only, but along with it an observed matter of fact. The proposition, "A circle is a figure bounded by a line which has all its points equally distant from a point within it," is called the definition of a circle ; but the proposition from which so many consequences follow, and which is really a first principle in geometry, is, that figures answering to this de- scrii)tion exist. And thus we may call "Three is two and one "a defini- tion of three; but the calculations which depend on that proposition do not follow from the definition itself, but from an arithmetical theorem pre- supposed in it, namely, that collections of objects exist, which while they iini)ress the senses thus, °o°, may be separated into two parts, thus, o o o- Tliis proposition being granted, we term all such parcels Threes, after DEMONSTRATION, AM) NKOKSSAUV TKLTIIS. ]()[ wliich the onuiicintion of tlie ;ib()V('-nit'nlioiie(l pliysic:d fact will serve ul.so for a definition of the word Tln-ee. The Science of Niunber is tlius no exception to the conclusion we pi'e- vioiisly arrived at, that the processes even of deductive sciences are alto- gether inductive, and that their first principles are generalizations from ex- perience. It remains to be examined whether tliis science resembles geom- etry in the further circumstance, that some of its inductions are not exactly true ; and that the peculiar certainty ascribed to it, on account of which its propositions are called Necessary Truths, is fictitious and hypothetical, be- ing true in no other sense than tliat those propositions legitimately follow from the hypothesis of the truth of premises which are avowedly mere ap- proximations to truth. § 3. The inductions of arithmetic are of two sorts: first, those wliich we have just expounded, such as One and one are two. Two and one are three, etc., Avhich may be called the definitions of the various numbers, in the im- proper or geometrical sense of the word Definition ; and secondly, the tw^o following axioms : The sums of equals are equal, The differences of equals are equal. These two are sufficient; for the corresponding propositions re- specting unequals may be proved from these by a 7'eductio ad absurdmn. These axioms, and likewise the so-called definitions, are, as has already been said, results of induction; true of all objects whatever, and, as it may seem, exactly true, Avitliout the hypothetical assumption of unqualified truth where an approximation to it is all that exists. The conclusions, thei'efore, it will naturally be inferred, are exactly true, and the science of number is an exception to other demonstrative sciences in this, that the categorical certainty which is predicable of its demonstrations is independent of all hypothesis. On more accurate investigation, however, it will be found that, even in this case, there is one hypothetical element in the ratiocination. In all propositions concerning numbers, a condition is implied, without which none of them would be true ; and that condition is an assumption which may be false. The condition is, that 1 = 1 ; that all the numbers are num- bers of the same or of equal units. Let this be doubtful, and not one of the propositions of arithmetic will hold true. How^ can we know that one pound and one pound make two pounds, if one of the pounds may be troy, and the other avoirdupois? They may not make two pounds of either, or of any weight. How can we know that a forty-horse power is always equal to itself, unless we assume that all horses are of equal strength ? It is cer- tain that 1 is always equal in nmnher to 1 ; and where the mere number of objects, or of the parts of an object, without supposing them to be equiv- alent in any other respect, is all that is material, the conclusions of aiith- metic, so far as they go to that alone, are true without mixture of hypoth- esis. There are such cases in statistics ; as, for instance, an inquiry into the amount of the population of any country. It is indifferent to that in- quiry whether they are grow^n people or children, strong or weak, tall or short; the only thing we want to ascertain is their number. But when- ever, from equality or inequality of number, equality or inequality in any other respect is to be inferred, arithmetic carried into such inquiries be- comes as hypothetical a science as geometry. All units must be assumed to be equal in that other respect; and this is never accurately true, for one actual pound weight is not exactly equal to another, nor one measured mile's length to another; a nicer balance, or more accui-ate measuring instruments, would alwnvs detect some difference. 192 REASONING. What is commonly called mathematical certainty, therefore, which com- prises the twofold conception of unconditional truth and perfect accuracy, is not an attribute of all mathematical truths, but of those only which re- late to pure Number, as distinguished from Quantity in the more enlarged sense; and only so long as we abstain from supposing that the numbers are a precise index to actual quantities. The certainty usually ascribed to the conclusions of geometry, and even to those of mechanics, is nothing whatever but certainty of inference. We can have full assurance of par- ticular results under particular suppositions, but we can not have the same assurance that these suppositions are accurately true, nor that they include all the data which may exercise an influence over the result in any given instance. § 4. It appears, therefore, that the method of all Deductive Sciences is hypothetical. They proceed by tracing the consequences of certain as- sumptions ; leaving for separate consideration whether the assumptions are true or not, and if not exactly true, whether they are a sufficiently near approximation to the truth. The reason is obvious. Since it is only in questions of pure number that the assumptions are exactly true, and even there only so long as no conclusions except purely numerical ones are to be founded on them ; it must, in all other cases of deductive investigation, form a part of the inquiry, to determine how much the assumptions want of being exactly true in the case in hand. This is generally a matter of observation, to be repeated in every fresh case ; or if it has to be settled by argument instead of observation, may require in every different case different evidence, and present every degree of difficulty, from the lowest to the highest. But the other part of the process — namely, to determine what else may be concluded if we find, and in proportion as we find, the assumptions to be true — may be performed once for all, and the results held ready to be employed as the occasions turn up for use. We thus do all beforehand that can be so done, and leave the least possible work to be performed when cases arise and press for a decision. This inquiry into the inferences which can be drawn from assumptions, is what properly consti- tutes Demonstrative Science. It is of course quite as practicable to arrive at new conclusions from facts assumed, as from facts observed ; from fictitious, as from real, induc- tions. Deduction, as we have seen, consists of a series of inferences in this form — a is a mark of ^, 6 of c, c of d^ therefore a is a mark of d, which last may be a truth inaccessible to direct observation. In like manner it is allowable to say, suppose that a were a mark of h, h of c, and c of d, a would be a mark of d, which last conclusion was not thought of by those who laid down the premises. A system of propositions as complicated as geometry might be deduced from assumptions which are false; as was (lone by Ptolemy, Descartes, and others, in their attempts to explain syn- thetically the phenomena of the solar system on the supposition that the apparent motions of the heavenly bodies were the real motions, or were produced in some way more or less different from the true one. Some- times the same thing is knowingly done, for the purpose of showing the falsity of the assumption ; which is called a reductio ad absurdum. In such cases, the reasoning is as follows: a is a mark of b, and ^ of c; now if c were also a mark of d, a would be a mark of cZ; but d is known to be a mark of the absence of a ; consequently a would be a mark of its own absence, which is a contradiction ; therefore c is not a mark of d. THEORIES CONCERNING AXIOMS. 10;; § 5. It has even been hold by some writers, that y^l ratiocination rests ill the last resort on a reductio ad abmirduyn ; since tlie way to enforce as- sent to it, in case of obscurity, would be to show that if the conclusion be denied we must deny some one at least of the i)reniises, which, as they are all supposed true, would be a contradiction. And in accordance with this, many have thought that the peculiar nature of the evidence of ratiocina- tion consisted in the impossibility of admitting the premises and rejecting the conclusion without a contradiction in terms. This theory, however, is inadmissible as an explanation of the grounds on which ratiocination itself rests. If any one denies the conclusion notwithstanding his a