A SYSTEM OF LOGIC RATIOCINATIVE AND INDUCTIVE--VOLUME I.

BEING A CONNECTED VIEW OF THE PRINCIPLES OF EVIDENCE AND THE METHODS OF SCIENTIFIC INVESTIGATION

IN TWO VOLUMES

VOL. I.

SEVENTH EDITION

By John Stuart Mill



CONTENTS OF THE FIRST VOLUME

INTRODUCTION.
§ 1. A definition at the commencement of a subject must be provisional 1
2. Is logic the art and science of reasoning? 2
3. Or the art and science of the pursuit of truth? 3
4. Logic is concerned with inferences, not with intuitive truths 5
5. Relation of logic to the other sciences 8
6. Its utility, how shown 10
7. Definition of logic stated and illustrated 11
BOOK I.
OF NAMES AND PROPOSITIONS.
Chapter I. Of the Necessity of commencing with an Analysis of Language.
§ 1. Theory of names, why a necessary part of logic 17
2. First step in the analysis of Propositions 18
3. Names must be studied before Things 21
Chapter II. Of Names.
§ 1. Names are names of things, not of our ideas 23
2. Words which are not names, but parts of names 24
3. General and Singular names 26
4. Concrete and Abstract 29
5. Connotative and Non-connotative 31
6. Positive and Negative 42
7. Relative and Absolute 44
8. Univocal and Æquivocal 47
Chapter III. Of the Things denoted by Names.
§ 1. Necessity of an enumeration of Nameable Things. The Categories of Aristotle 49
2. Ambiguity of the most general names 51
3. Feelings, or states of consciousness 54
4. Feelings must be distinguished from their physical antecedents. Perceptions, what 56
5. Volitions, and Actions, what 58
6. Substance and Attribute 59
7. Body 61
8. Mind 67
9. Qualities 69
10. Relations 72
11. Resemblance 74
12. Quantity 78
13. All attributes of bodies are grounded on states of consciousness 79
14. So also all attributes of mind 80
15. Recapitulation 81
Chapter IV. Of Propositions.
§ 1. Nature and office of the copula 85
2. Affirmative and Negative propositions 87
3. Simple and Complex 89
4. Universal, Particular, and Singular 93
Chapter V. Of the Import of Propositions.
§ 1. Doctrine that a proposition is the expression of a relation between two ideas 96
2. Doctrine that it is the expression of a relation between the meanings of two names 99
3. Doctrine that it consists in referring something to, or excluding something from, a class 103
4. What it really is 107
5. It asserts (or denies) a sequence, a coexistence, a simple existence, a causation 110
6. —or a resemblance 112
7. Propositions of which the terms are abstract 115
Chapter VI. Of Propositions merely Verbal.
§ 1. Essential and Accidental propositions 119
2. All essential propositions are identical propositions 120
3. Individuals have no essences 124
4. Real propositions, how distinguished from verbal 126
5. Two modes of representing the import of a Real proposition 127
Chapter VII. Of the Nature of Classification, and the Five Predicables.
§ 1. Classification, how connected with Naming 129
2. The Predicables, what 131
3. Genus and Species 131
4. Kinds have a real existence in nature 134
5. Differentia 139
6. Differentiæ for general purposes, and differentiæ for special or technical purposes 141
7. Proprium 144
8. Accidens 146
Chapter VIII. Of Definition.
§ 1. A definition, what 148
2. Every name can be defined, whose meaning is susceptible of analysis 150
3. Complete, how distinguished from incomplete definitions 152
4. —and from descriptions 154
5. What are called definitions of Things, are definitions of Names with an implied assumption of the existence of Things corresponding to them 157
6. —even when such things do not in reality exist 165
7. Definitions, though of names only, must be grounded on knowledge of the corresponding Things 167
BOOK II.
OF REASONING.
Chapter I. Of Inference, or Reasoning, in general.
§ 1. Retrospect of the preceding book 175
2. Inferences improperly so called 177
3. Inferences proper, distinguished into inductions and ratiocinations 181
Chapter II. Of Ratiocination, or Syllogism.
§ 1. Analysis of the Syllogism 184
2. The dictum de omni not the foundation of reasoning, but a mere identical proposition 191
3. What is the really fundamental axiom of Ratiocination 196
4. The other form of the axiom 199
Chapter III. Of the Functions, and Logical Value, of the Syllogism.
§ 1. Is the syllogism a petitio principii? 202
2. Insufficiency of the common theory 203
3. All inference is from particulars to particulars 205
4. General propositions are a record of such inferences, and the rules of the syllogism are rules for the interpretation of the record 214
5. The syllogism not the type of reasoning, but a test of it 218
6. The true type, what 222
7. Relation between Induction and Deduction 226
8. Objections answered 227
9. Of Formal Logic, and its relation to the Logic of Truth 231
Chapter IV. Of Trains of Reasoning, and Deductive Sciences.
§ 1. For what purpose trains of reasoning exist 234
2. A train of reasoning is a series of inductive inferences 234
3. —from particulars to particulars through marks of marks 237
4. Why there are deductive sciences 240
5. Why other sciences still remain experimental 244
6. Experimental sciences may become deductive by the progress of experiment 246
7. In what manner this usually takes place 247
Chapter V. Of Demonstration, and Necessary Truths.
§ 1. The Theorems of geometry are necessary truths only in the sense of necessarily following from hypotheses 251
2. Those hypotheses are real facts with some of their circumstances exaggerated or omitted 255
3. Some of the first principles of geometry are axioms, and these are not hypothetical 256
4. —but are experimental truths 258
5. An objection answered 261
6. Dr. Whewell's opinions on axioms examined 264
Chapter VI. The same Subject continued.
§ 1. All deductive sciences are inductive 281
2. The propositions of the science of number are not verbal, but generalizations from experience 284
3. In what sense hypothetical 289
4. The characteristic property of demonstrative science is to be hypothetical 290
5. Definition of demonstrative evidence 292
Chapter VII. Examination of some Opinions opposed to the preceding doctrines.
§ 1. Doctrine of the Universal Postulate 294
2. The test of inconceivability does not represent the aggregate of past experience 296
3. —nor is implied in every process of thought 299
4. Sir W. Hamilton's opinion on the Principles of Contradiction and Excluded Middle 306
BOOK III.
OF INDUCTION.
Chapter I. Preliminary Observations on Induction in general.
§ 1. Importance of an Inductive Logic 313
2. The logic of science is also that of business and life 314
Chapter II. Of Inductions improperly so called.
§ 1. Inductions distinguished from verbal transformations 319
2. —from inductions, falsely so called, in mathematics 321
3. —and from descriptions 323
4. Examination of Dr. Whewell's theory of Induction 326
5. Further illustration of the preceding remarks 336
Chapter III. On the Ground of Induction.
§ 1. Axiom of the uniformity of the course of nature 341
2. Not true in every sense. Induction per enumerationem simplicem 346
3. The question of Inductive Logic stated 348
Chapter IV. Of Laws of Nature.
§ 1. The general regularity in nature is a tissue of partial regularities, called laws 351
2. Scientific induction must be grounded on previous spontaneous inductions 355
3. Are there any inductions fitted to be a test of all others? 357
Chapter V. Of the Law of Universal Causation.
§ 1. The universal law of successive phenomena is the Law of Causation 360
2. —i.e. the law that every consequent has an invariable antecedent 363
3. The cause of a phenomenon is the assemblage of its conditions 365
4. The distinction of agent and patient illusory 373
5. The cause is not the invariable antecedent, but the unconditional invariable antecedent 375
6. Can a cause be simultaneous with its effect? 380
7. Idea of a Permanent Cause, or original natural agent 383
8. Uniformities of coexistence between effects of different permanent causes, are not laws 386
9. Doctrine that volition is an efficient cause, examined 387
Chapter VI. Of the Composition of Causes.
§ 1. Two modes of the conjunct action of causes, the mechanical and the chemical 405
2. The composition of causes the general rule; the other case exceptional 408
3. Are effects proportional to their causes? 412
Chapter VII. Of Observation and Experiment.
§ 1. The first step of inductive inquiry is a mental analysis of complex phenomena into their elements 414
2. The next is an actual separation of those elements 416
3. Advantages of experiment over observation 417
4. Advantages of observation over experiment 420
Chapter VIII. Of the Four Methods of Experimental Inquiry.
§ 1. Method of Agreement 425
2. Method of Difference 428
3. Mutual relation of these two methods 429
4. Joint Method of Agreement and Difference 433
5. Method of Residues 436
6. Method of Concomitant Variations 437
7. Limitations of this last method 443
Chapter IX. Miscellaneous Examples of the Four Methods.
§ 1. Liebig's theory of metallic poisons 449
2. Theory of induced electricity 453
3. Dr. Wells' theory of dew 457
4. Dr. Brown-Séquard's theory of cadaveric rigidity 465
5. Examples of the Method of Residues 471
6. Dr. Whewell's objections to the Four Methods 475
Chapter X. Of Plurality of Causes; and of the Intermixture of Effects.
§ 1. One effect may have several causes 482
2. —which is the source of a characteristic imperfection of the Method of Agreement 483
3. Plurality of Causes, how ascertained 487
4. Concurrence of Causes which do not compound their effects 489
5. Difficulties of the investigation, when causes compound their effects 494
6. Three modes of investigating the laws of complex effects 499
7. The method of simple observation inapplicable 500
8. The purely experimental method inapplicable 501
Chapter XI. Of the Deductive Method.
§ 1. First stage; ascertainment of the laws of the separate causes by direct induction 507
2. Second stage; ratiocination from the simple laws of the complex cases 512
3. Third stage; verification by specific experience 514
Chapter XII. Of the Explanation of Laws of Nature.
§ 1. Explanation defined 518
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 coexistence 518
3. Second mode; by the detection of an intermediate link in the sequence 519
4. Laws are always resolved into laws more general than themselves 520
5. Third mode; the subsumption of less general laws under a more general one 524
6. What the explanation of a law of nature amounts to 526
Chapter XIII. Miscellaneous Examples of the Explanation of Laws of Nature.
§ 1. The general theories of the sciences 529
2. Examples from chemical speculations 531
3. Example from Dr. Brown-Séquard's researches on the nervous system 533
4. Examples of following newly-discovered laws into their complex manifestations 534
5. Examples of empirical generalizations, afterwards confirmed and explained deductively 536
6. Example from mental science 538
7. Tendency of all the sciences to become deductive 539