A system of logic, ratiocinative and inductive; being a connected view of the principles of evidence and the methods of scientific investigation

Preface To The First Edition

Tus 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 grounded 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 subject by speculative writers, or conformed to by accurate thinkers in their scientific inquiries.

To cement together the detached fragments of a subject, never yet treated as a whole; to harmonize the true portions of discordant theories, by supplying the links of thought necessary to connect them, and by disentangling them from the errors with which they are always more or less interwoven, must necessarily require a considerable amount of original speculation. 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 effected 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 believes that they have much need of improvement) can only consist in performing 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 obtained 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 participates; though the scientific theory on which its defense is usually rested 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 Book, on Names and Propositions ; because many useful principles and disiv PREFACE.

tinctions which were contained in the old Logic have been gradually omitted from the writings of its later teachers; and it appeared desirable both to revive these, and to reform and rationalize 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 Assertions, 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 generalizing the modes of investigating truth and estimating evidence, by which so many important and recondite laws of nature have, in the various sciences, 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 Edinburgh Review) have not scrupled to pronounce it impossible.* The author has endeavored to combat their theory in the manner in which Diogenes confuted the skeptical reasonings against the possibility of motion ; remembering that Diogenes’s argument would have been equally conclusive, though his individual perambulations might not have extended beyond the circuit of his own tub.

Whatever may be the value of what the author has succeeded in effecting on this branch of his subject, itis 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 science, which have been published within the last few years. To these treatises, 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 frequently to express differences of opinion, it is more particularly incumbent 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 portion of the present work which treats of Induction, the words in the text are no overstatement of the difference of opinion between Archbishop Whately and me on the subject.

PREFACE, W facts and ideas contained in that gentleman’s “ History of the Inductive Sciences,” the corresponding portion of this work would probably not have been written. if

The concluding Book is an attempt to contribute toward the solution of a question which the decay of old opinions, and the agitation that disturbs European society to its inmost depths, render as important in the 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 social phenomena are really exceptions to the general certainty and uniformity 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 irrevocably acquired and universally assented to, can be made instrumental to the formation of a similar body of received doctrine in moral and political science.

Preface To The Third And Fourth Editions

SEVERAL criticisms, of a more or less controversial character, on this work, have appeared since the publication 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 points 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 placing my own conclusions, and the grounds of them, more clearly and completely 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, after 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 service 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 additions and corrections, suggested by criticism or by thought, has been con-

* Now forming a chapter in his volume on ‘‘ The Philosophy of Discovery.”

viii PREFACE.

tinued. The additions and corrections in the present (eighth) edition, which 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. TI have in several instances made use of his exposition to improye 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 elaborately treated in Mr. Bain’s work.

Introduction

PAGE

$1. A definition at the commencement of a sub-

ject must be provisional... ...2+020:.06 Is logic the art and science of reasoning ?.

Or the art and science of the pursuit of go $9

4. Logic is concerned with inferences, not

with AER TUT COI TUDE Bole taisssieiem te aint ceelele nel eyare 5. Relation of logic to the other sciences..... 6, Its utility, how shown 7. Definition of logic stated and illustrated..

Book I. Of Names And Propositions

Cuapter I. Of the Necessity of commencing with an

Analysis of Language.

§1. Theory of names, why a necessary part of HOSEN Abed anos oponnsoc nol oondoeoenoddede

2. First step in the analysis of Propositions... 3. Names must be studied before Things....

Cuarren II. Of Names.

§1. Names are names of things, not of our ideas 2. Words which are not nee but parts of INTIAL 5 ode goose aaoeCnS Ope o nO COADOCOSOO UD :

General and Singular names. Srenicobdeoarn

Concrete and Abstract............ aiaeeraiciolers

Connotative and Non-counotative.........

. Positive and Negative... ssiesssecscesees

c Relative and Absolute, <. ...00es-+cee se

8. Univocal and Aiquivocal...........e.eeees

PO 99

Cuarrer III. Of the Things denoted by Names.

§1. Necessity of an enumeration of Namable Things. The Categories of Aristotle....

2. Ambiguity of the most general names..... 8. Feelings, or states of consciousness.. 4, Feelings must be distinguished from their physical antecedents. hae Cas what.

sees.

18. All attributes of bodies are cee ea on

states of consciousness.... 14, So also all attributes of mind............. 15. Recapitulation......

eee ee ree eeeene a)

.

PAGE Cuarter IV. Of Propositions.

§1. Nature and office of the copula......... ee OG 2. Affirmative and Negative propositions... 67 3. Simple and Complex Bu bstateyer staletoicvers/eivars Goncee it} 4, Universal, Particular, and Singular. waetetae 71

Cuarrer V. Of the Import of Propositions.

§1, Doctrine that a proposition is the expression of a relation between two ideas.....

2, — that it is the expression of a relation between the meanings of two names..... .,

8. — that it consists in referring something to, or excluding something from, a class.

4- What itireallysisy i cteta. semettaetaee aot 5. It asserts (or denies) a sequence, a co-existence, a simple existence, a causation.....

Cuarter VI. Of Propositions merely Verbal.

§1. Essential and Accidental propositions..... 2. All essential propositions are identical

DLOPOSILLONS sis ¢ <p eiereclelo vleiarsielstere/alelsieietaiele 3. Individuals have no essences............. 4, Real propositions, how distinguished from WEE bopaondaanancoperoordasssaoang ap 5. Two modes of representing the import of a Real proposition........-. ARE GHAD DONO Ps

Cnarrer VII. Of the Nature of Classification, and the Five Predicables,

§1, Classification, how connected with Naming 94 2, The Predicables;, Whats ccjastecir cle os «mele <e 95 3. Genus and Species,..... ai caet aerate ioe nom tls) 4, Kinds have a real existence in nature..... 97 DG ELO MUA! erecoieit/ai-iaia)>sieln’e viateletalaln eleleieiaardeatets 100 6. Differentize for general purposes, and differ-

entiz for special or technical purposes... 101

8. Accidens....... BEBRECODDACude Beach pa ema 104 Cuapter VIII. Of Definition.

$1, A definition, what.......... aiaisiale steieerenres + 105

2, Every name can be defined, whose meaning is susceptible of analysis..............-. . 106 3. Complete, how distinguished from incomplete definitions........ccccesecetececcne 107 4, — and from descriptions............. Sass) 108 5. What are called definitions of Things, are definitions of Names with an implied assumption of the existence of Things corresponding to them..........+++se-+eeeee 111 6. — even when such things do not in reality OXISE 0. cpecerereqecverasnvedscescveres “eG x

PAGE

$7. Definitions, though of names only, must be grounded on knowledge of the corre- RPONGING Things... 6. 66c. stew es Spoon dltiy¢

Book II. Of Reasoning

Cnuapter I. Of Inference, or Reasoning, in general.

$1, Retrospect of the preceding book......... 121 2. Inferences improperly so called........... 122 8. Inferences proper, distinguished into in-

ductions and ratiocinations.............. 125

Cyarrrr Il. Of Ratiocination, or Syllogism.

2, The dictum de omni not the foundation of reasoning, but a mere identical proposi-

TOMY. 6 5.5 cob ote gamba deomangopcodacaan 132 3. What is the really fundamental axiom of

Ratiocination....... pro eeketerellnid atcis: inks eis lotias 135 4. The other form of the axiom.............. 137

Cuapree III. Of the Functions, and Logical Value

of the Syllogism.

§1. Is the Syllogism a petitioprincipti?....... 139 2. Insufficiency of the common theory....... 139 8, All inference is from particulars to partic-

4, General propositions are a record of such inferences, and the rules of the syllogism are rules for the interpretation of the

PECOLC NS: tetalotelsteate oltisiore ais lense iatavsiave’sisvers setters 146 5. The syllogism not the type of reasoning, UD AREC Ot OLEibsptera tetenelesa «sti menvele Sonao nets 6. The tre type,-What.ss sicasinctce sees cecees 151 7. Relation between Induction and Dedue- GRSTREA9e Giursl poh Tae le etn taitycteiw ual ova a laieie ne wlesainvare 153 8. Objections answered «.isiic.issccese noses 154 9. Of Formal Logic, and its relation to the GOV OM Deut hers cite at ekaaleeyetselelstaicelelaterete' 156

‘Cuarrer IV. Of Trains of Reasoning, and Deductive Sciences.

For what purpose trains of reasoning exist. 158

§1.

2. A train of reasoning is a series of induct-

nareWe fda p(orin eetra did chen Seong acnp sSeeriqnuenc oncor 160 ‘4, Why there are deductive sciences......... 161 5. Why other sciences still remain experi-

SPOT UD ert vatelsistdicletaisicis) ioe Acie ieieiselateiaieiets 164 6. Experimental sciences may become deduct-

ive by the progress of experiment........ 165 | 7. In what manner this usually takes place.. 166

CHartrr V. Of Demonstration, and Necessary Truths.

The Theorems of geometry are necessary truths only in the sense of necessarily following from hypotheses.....0......c..00+

. Those hypotheses are real facts with some

of their circumstances exaggerated or

$1.

3. Some of the first principles of geometry are axioms, and these are not hypothetical... 171 4, — but are experimental truths....... goon 4)

CONTENTS.

. An objection answered . Dr. Whewell’s opinions on axioms exam- INCA arteteisicle oil eicle pestanynie sae aS eaten 176

“The sume Subject continued. -

. All deductive sciences are inductive....... 18% . The propositions of the science of number are not verbal, but generalizations from

. In what sense hypothetical...........

. The characteristic property of demonstra-

tive science is to be hypothetical

Definition of demonstrative evidence......

Cuapter VI.

| Cuarren VII. Examination of some Opinions opposed to the preceding doctrines.

§1, Doctrine of the Universal Postulate....... 2. The test of inconceivability does not represent the aggregate of past experience. .

8. — nor is implied in every process of La We }iRe dts caraeoaT oot Neh Foo SOOO Mae SOAS

4, Objectioug answered!.. jin ccswles ss. - wac\eicr 5. Sir W. Hamilton’s opinion on the Principles of Contradiction and Excluded Mid-

BOOK IIL.

OF INDUCTION.

Cuaprrr I. Preliminary Observations on Induetion in general.

§1. Importance of an Inductive Logic......... 207 2. The logic of science is also that of business AUG fe sacri eieiteteies siatalele|eafetersielateheterabs 208

Cuarrer II. Of Inductions improperly so called.

§1. Indnctions distinguished from verbal trans-

TOLMATIONS A: ss atic shia ioe weelcioee eee 210

2. —frominductions, falsely so called,in math- OMA CSias. las otastlenin 24 Re ciswlsie eels 212 8. — and from descriptions: ...2-...2..0..... 213

4, Examination of Dr. Whewell’s theory of Induction..... dona RSNA nONS SON 5d Dah 214

5. Further illustration of the preceding re- THA TICS: § ckiscmissioeuiee memos titeatectee Perce 2a

Cnarter Ill. Of the Ground of Induction.

$1. Axiom of the uniformity of the course of TL CTLT OS <a bue.- Meee kinaite store tueha: Temi ieee teres 223°

2. Not true in every sense. Induction ‘per enumerationem simplicent...........0.+5 . 226 3. The question of Inductive Logic stated.... 227

Cnaprer IV. Of Laws of Nature.

§1. The general regularity in nature is a tissue of partial reeularities, called Jaws........ 229

2. Scientific induction must be grounded on previous spontaneous inductions...... sae 23

3. Are there any inductions fitted to be a test OPV ODWENET? aysn crateaterakies ertahatoncheletalctnteieres 232

CuartTer V... Of the Law of Universal Causation.

§1. The universal law ofsuccessive phenomena is the Law of Causation..... wince lic tite » 234

2. —i.e., the law that every consequent has an invariable antecedent.............0.. 236

CONTENTS. ui

PAGE The cause of a phenomenon is the assembless Ohits Conditions... section eee 287 4, The distinction of agent and patient illu- 241 5. Case in which the effect consists in giving a property to @miobjeety.. a. aestinc civic sie 6. The cause is not the invariable antecedent, but the wneonditional invariable antecedent 7. Gan a cause be simultaneous with its ef- Ges aeeaacd ED ECORI Ge ane ae cae mec 247 8. Idea of a Permanent Canse, or original nat- MUN EV ACCT iniois le reiolelalstalsfateiayais/e © iaceleSialafereteib ee 9. Uniformities of co-existence between effects of different permanent causes, are

VOD LW erarsicre eebrelb ise leiclststts civieelave etewe's tals 251 10. Theory of the Conservation of Force...... 251 11. Doctrine that volition is an efficient cause,

Cuartger VI. Of the Composition of Causes.

§1. Two modes of the conjunct action of causes, the mechanical and the chemical.........

2. The composition of causes the general rule; the other case exceptional.........

8. Are effects proportional to their causes ?..

Coapter VII. Of Observation and Experiment.

§1. The first step of inductive inquiry is a mental analysis of complex phenomena into

268 270 their clementy si aaiistercise lets item ake victolel 0 272 2. The next is an actual separation of those GIS Meet one oe ae ane aoee CCR Cee 2738 3. Advantages of experiment over observa- LORD arajataictaccarciccwiatw tips aoe ee Oi «Sate rertetemnin's 274. 4, Advantages of observation over experi- ARG Vidisteteta aiataterie areicim x otis a'areteinials\s olelNsfalssie se 276

Cuarrer VIII. Of the Four Methods of Expertmental Duquiry.

§1. Method of Agreement..............%- =cap 2..Method of Differences:.-).2 «rls. 4 eislei aes 8. Mutual relation of these two methods..... 281 4, Joint Method of Agreement and Difference. 283

5. Method of Residues. .......2 2.0.0. 0cccc00s 284 6. Method of Concomitant Variations. ....... 285 4%, Limitations of this last method..... Gorin a 289 Cuoarrrr IX. Miscellancous Examples of the Four Methods. §1. Liebig’s theory of metallic poisons.......: 292 +9. Theory ofindticed electricity........0.%.c.s 294 3. Dr. Wells’s theory of dew...../..8....0000. 296 4, Dr. Brown-Séquard’s theory of cadaveric TOK Wine HORM eanour coos condce aan atoGD 301 5. Examples of the Method of Residues...... 305 6. Dr. Whewell’s objections to the Four CTHOMS., .. 0 eee eee eee e eee e eens ghuicehan 307

Plurality of Causes; and of the Intermixture of Effects.

§1, One effect may have several causes........ 2, — which is the source of a characteristic imperfection of the Method of Agree-

POMEM bic ole) =ieisieleis Beachwood daduaguccoEdedes 311 8. Plurality of Causes, how ascertained Sreererts 314 4, Concurrence of Causes which do not com-

pound. their effects ie. cnset tte owsevstiet 315

. Difficulties of the investightion; when _ causes compound their effects............ 317

PAGE §6. Three modes of investigating the laws of

7. The method of simple observation inap-

8. The purely experimental method inappli-

Cuarren XI. Of the Dedtictive Method.

§1. First stage; ascertainment of the laws of the separate causes by direct induction.. 2. Second stage; ratiocination from the simple laws of the complex cases........ ... 328

3. Third stage; verification by specific experience

Cuarrer XII.

Of the Explanation of Laws of Nature.

$1. Explanation’ defined i. 02.5 2. t sees ees oe 2. First mode of explanation, by resolving the law of a complex effect into the laws of the concurrent causes and the fact of theinico-existemces. 4.0.1 oes lett see els 332

8. Second mode; by the detection of an intermediate link in the sequence.......... 832

4, Laws are always resolved into laws more general than’ themselves. <2 .c.25.csece.. 833 5. Third mode; the subsumption of less general laws under a more general one...... 6. What the explanation of a law of nature amounts to........... dra’ etetelele Wpteleta ee bakes ise) cw its)

2o7 oul

Cuartre XIII. Miscellaneous Examples of the E2- planation of Laws of Nature.

§1. The general theories of the sciences....... 338 2, Examples from chemical speculations..... 339 3. Example from Dr. Brown-Séquard’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-

TVCL Yi siaieiats stort erate ee oe arr the» Meer. 342 6. Example from mental science............. 343 %. Tendency of all the sciences to become de-

Coarter XIV. Of the Limits to the Explanation of Laws of Nature; and of Hypotheses.

§1. Can all the sequences in nature be resolva- DlSIMEG ONE PAW. PiFo oie ti-lai=ysietwes creresisle sole oie 345

2. Ultimate laws can not be less numerous

than the distinguishable feelings of our

NL RETD ET. crests tals cits clara wialalere raitiie stare belt ees 346 3. In what sense ultimate. facts can be explained. Higemat tee Woiee halal ne cewrete pata eciee 348 4, The proper use of scientific hypotheses.... 349 5. Their indispensableness....... Belch Re 353 6. The two degrees of legitimacy in hypoth- CSCS ic cinelnieieu vcs seleic ew et atis etree ansy tee 355 7. Some inquiries apparently hypothetical are really inductive..... Got onBuddpuLOMerondac 359

Carrer 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

CMUSS preniefelciwiecralete es lott eieitlereicls\s <lalo\ele.- a(n 363 3. Derivative laws generated from a single

ultimate JAW. cece eee es Ware vnote Cv eae ane « « 365 xil PAGE Cuaprer XVI. Of Empirical Laws, §1. Definition of an empirical law...........-- 366 2. Derivative laws commonly depend on col- NOCHELONB eiple ot Fateigrsiss1nsielal tele se/ejcia doreaetayers B67

8. The collocations of the permanent causes are not reducible to any law......+-++.-+ : 4, Hence empirical laws can not be relied on beyond the limits of actual experience... . Generalizations which rest only on the Method of Agreement can only be received as empirical laws.......+..s2es- B 6. Signs from which an observed uniformity of sequence may be presumed to be re- BealyiaDlCiertctocisins «ste n myre . Two kinds of empirical laws............+. i lord it

Cuarrmr XVII. Of Chance, and its Elimination. §1. The proof of empirical laws depends on the theory of chances. 2. saccc- anne sie 872 2. Chance detined and characterized......... 873 8. The elimination of chance................ 376

4, Discovery of residual phenomena by elim- BILSON OY CHAN COs ar-tewraleieieleisty a steiner ste eiataloni eee &. Therdoctrine of chances... oc. weve nes sre 378

Cuaprrr XVIII. Of the Calculation of Chances. §1. Foundation of the doctrine of chances, as taught by mathematics.........-..6+.00. 3879 2. The doctrine tena blecs rc siatetajecieile t's ieleiclelele 380 8. On what foundation it really rests........- 381 4, Its ultimate dependence on causation..... 883 5. Theorem of the doctrine of chances which

relates to the cause of a given event...-. 385 6. How applicable to the elimination of

Cuarrrer XIX. Of the Extension of Derivative Laws to Adjacent Cases,

$1. Derivative laws, when not casual, are almost always contingent on collocations.. 3S8

2..On what grounds they can be extended to

cases beyond the bounds of actual expe- PICU CO arise eleletovielrucicrsisilosiegieeistslarsis elecieies 889 8..Those cases must be adjacent cases....... 390

Cuarrern XX. Of Analogy.

§1. Various senses of the word analogy....... 393 2. Nature of analogical evidence...'..:.:..:.. 893 3. On what circumstances its value depends.. 896

Craptmr XXI. Of the Evidence of the Law of Universal Causation.

§1. The law of causality does not rest on an LESUIM CHA. crite oieineeate este wines etter 397

3. In what cases such induction is allowable: 402 4, The universal prevalence of the law of causality, on what grounds admissible......

Cuartern XXII. Of Uniformities of Co-existence not dependent on Causation,

§1. Uniformities of co-existence which result from laws of sequence............ceecee0

2. The properties of Kinds are uniformities

8. Some are derivative, others ultimate. . S08

4. No universal axiom of co-existence.......

5. The evidence of nniformities of co-exist-

CONTENTS.

PAGE §6.-When derivative, their evidence is that of (empirical JawS,.....0.. ess seee seen cere

7. So also when ultimate.......... a afanetiee 8. The evidence strouger in proportion as the law is more general....-......++- tera fefarates

9. Every distinct Kind must be examined....

Carrer XXIII. Of Approximate Generalizations, and Probable Evidence.

§1. The inferences called probable, rest on approximate generalizations..........-.-..

2. Approximate generalizations less useful

IN BCLENCE, THAD aDEITEs or ately a caleiemieeleretes 416 3. In what cases they may be resorted to.... 417 4, In what manner proved. ...0.....c.e0e.08e 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 thems.cci. strategie oisteiesie

CuapTerR XXIV. Of the Remaining Laws of Nature.

. Propositions which assert mere existence. 425 2. Resemblance, considered as a subject of

s/BCLOMCE 2 Nenemncmieiciem eee terneeirtia oar eer cree ee 3. The axioms and theorems of mathematics comprise the principal laws of resemepiblance) Poets aeasee. 0 leteeaieee eeee 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- Lies th ober adnadrspos coop cede anne oacs on.)

6. Those of algebra affirm the equivalence of different modes of formation of numbers.ceneralliyzu>.t. ders wineean aloeteeees

7. The propositions of geometry are laws of OUEWANG. MAINO. preunaie cractisiocie re tivteteeree iets

9. Function of muthematical truths in the other sciences, and limits of that function. 486

Cnaprrr XXV. Of the Grownds of Disbelief.

3. The degrees of improbability correspond to differences in the nature of the géner-

- alization with which an assertion con-

PUGS. iciaiste o Melee a nei Rjetite eee ee Ree 441

4, A fact is not incredible because the chances ALEVATAIIIS Uber etalelscMicletetele selene erase 443

& Are coincidences less credible than other FACUS i ereys lelmictasatcrenerer state ietelee sine eeistelelserten tists 4H 6. An opinion of Laplace examined.......... 446

Book IV

OF. OPERATIONS. SUBSIDIARY TO IN- - DUCTION...

Cuartrr I. Of Observation and Description,

§1. Observation, how fara subject of logic.... 449 2. A great part of what seems observation is _ really inference... Seta e400

CC ac ara i

CONTENTS. sit

PAGE

$3. The description of an observation affirms more than is contained in the observa-

4, — namely, an agreement among phenomena; and the comparison of phenomena

to ascertain such agreements is a preliminary to induction

Cuapter Il. Of Abstraction, or the Formation of Conceptions.

§1. The comparison which is a preliminary to induction implies general conceptions...

2. — but these need not be pre-existent 3. A general conception, originally the result of a comparison, becomes itself the type GICOMIPALISOMs saa eeleis a» saver ce ciicisieldaterctete'e

4. What is meant by appropriate conceptions. 459 |

6. — and by clear conceptions..............2. 6. Farther illustration of the subject.........

Cuarrer III. Of Naming as Subsidiary to Inducrs tion.

§1. The fundamental property of names as an instrument of thought............2.0206.

3. In what manner subservient to it 465 4. General names not a mere contrivance to economize the use of language...........

Carrer IV. Of the Requisites of a Philosophical Language, and the Principles of Definition.

§1. First requisite of philosophical language, a steady and determinate meaning for ev-

LNs SOTIOLAU MAINE) cto1a afelcrelhie\eielelelsjasielele ele 0% 467 2. Names in common use have often a loose COPID Ose LOI sy tetore cyotsvelatafetate’ stele ste) o1etatataloicrsie'e 467 3. — which the logician should fix, withas little alteration as possible.............. 469 4, Why definition is often a question not of words but of things............00.+2+008 470 5. How the logician should deal with the transitive applications of words.......... 472

6. Evil consequences of casting off any portion of the customary connotation of words . 476

Cuaptrer V. On the Natural History of the Variations in the Meaning of Terms.

§1. How circumstances originally accidental become incorporated into the meaning of

OLS aes nore tolataisiote alcials,vietatelamercieteiam ileal ey « 480 2, — and sometimes become the whole mean-

ing..... OED EO SND CUODUS UCN OMNL Sedo Ga DETUO 481 3. Tendency of words to become generalized. 482 4, — and to become specialized.............. 485