Chapter II: 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 [Pg xii] 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 [Pg xiii] 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 [Pg xiv] 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 [Pg xv] 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 [Pg xvi] 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 [Pg xvii] 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 [Pg xviii] 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

A SYSTEM OF LOGIC RATIOCINATIVE AND INDUCTIVE, VOLUME II. BEING A CONNECTED VIEW OF THE PRINCIPLES OF EVIDENCE AND THE METHODS OF SCIENTIFIC INVESTIGATION By John Stuart Mill IN TWO VOLUMES SEVENTH EDITION

CONTENTS OF THE SECOND VOLUME

BOOK III. ON INDUCTION.—(Continued.)

Chapter XIV. Of the Limits to the Explanation of Laws of Nature; and of Hypotheses. § 1. Can all the sequences in nature be resolvable into one law? 3 2. Ultimate laws cannot be less numerous than the distinguishable feelings of our nature 4 3. In what sense ultimate facts can be explained 7 4. The proper use of scientific hypotheses 8 5. Their indispensableness 16 6. Legitimate, how distinguished from illegitimate hypotheses 18 7. Some inquiries apparently hypothetical are really inductive 25

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 29 2. —and from the progressiveness of the cause 33 3. Derivative laws generated from a single ultimate law 36

Chapter XVI. Of Empirical Laws. § 1. Definition of an empirical law 38 2. Derivative laws commonly depend on collocations 39 3. The collocations of the permanent causes are not reducible to any law 41 [Pg vi]4. Hence empirical laws cannot be relied on beyond the limits of actual experience 41 5. Generalizations which rest only on the Method of Agreement can only be received as empirical laws 43 6. Signs from which an observed uniformity of sequence may be presumed to be resolvable 44 7. Two kinds of empirical laws 47

Chapter XVII. Of Chance, and its Elimination. § 1. The proof of empirical laws depends on the theory of chance 49 2. Chance defined and characterized 50 3. The elimination of chance 55 4. Discovery of residual phenomena by eliminating chance 57 5. The doctrine of chances 59

Chapter XVIII. Of the Calculation of Chances. § 1. Foundation of the doctrine of chances, as taught by mathematics 61 2. The doctrine tenable 63 3. On what foundation it really rests 64 4. Its ultimate dependence on causation 68 5. Theorem of the doctrine of chances which relates to the cause of a given event 72 6. How applicable to the elimination of chance 74

Chapter XIX. Of the Extension of Derivative Laws to Adjacent Cases. § 1. Derivative laws, when not casual, are almost always contingent on collocations 78 2. On what grounds they can be extended to cases beyond the bounds of actual experience 80 3. Those cases must be adjacent cases 82

Chapter XX. Of Analogy. § 1. Various senses of the word analogy 86 2. Nature of analogical evidence 87 3. On what circumstances its value depends 91 [Pg vii] Chapter XXI. Of the Evidence of the Law of Universal Causation. § 1. The law of causality does not rest on an instinct 95 2. But on an induction by simple enumeration 100 3. In what cases such induction is allowable 102 4. The universal prevalence of the law of causality, on what grounds admissible 105

Chapter XXII. Of Uniformities of Coexistence not dependent on Causation. § 1. Uniformities of coexistence which result from laws of sequence 110 2. The properties of Kinds are uniformities of coexistence 111 3. Some are derivative, others ultimate 113 4. No universal axiom of coexistence 114 5. The evidence of uniformities of coexistence, how measured 117 6. When derivative, their evidence is that of empirical laws 117 7. So also when ultimate 119 8. The evidence stronger in proportion as the law is more general 120 9. Every distinct Kind must be examined 121

Chapter XXIII. Of Approximate Generalizations, and Probable Evidence. § 1. The inferences called probable, rest on approximate generalizations 124 2. Approximate generalizations less useful in science than in life 124 3. In what cases they may be resorted to 126 4. In what manner proved 127 5. With what precautions employed 130 6. The two modes of combining probabilities 131 7. How approximate generalizations may be converted into accurate generalizations equivalent to them 136 [Pg viii] Chapter XXIV. Of the Remaining Laws of Nature. § 1. Propositions which assert mere existence 139 2. Resemblance, considered as a subject of science 141 3. The axioms and theorems of mathematics comprise the principal laws of resemblance 143 4. —and those of order in place, and rest on induction by simple enumeration 145 5. The propositions of arithmetic affirm the modes of formation of some given number 146 6. Those of algebra affirm the equivalence of different modes of formation of numbers generally 151 7. The propositions of geometry are laws of outward nature 154 8. Why geometry is almost entirely deductive 156 9. Function of mathematical truths in the other sciences, and limits of that function 158

Chapter XXV. Of the Grounds of Disbelief. § 1. Improbability and impossibility 161 2. Examination of Hume's doctrine of miracles 162 3. The degrees of improbability correspond to differences in the nature of the generalization with which an assertion conflicts 166 4. A fact is not incredible because the chances are against it 170 5. Are coincidences less credible than other facts? 172 6. An opinion of Laplace examined 175

BOOK IV. OF OPERATIONS SUBSIDIARY TO INDUCTION.

Chapter I. Of Observation and Description. § 1. Observation, how far a subject of logic 183 2. A great part of what seems observation is really inference 184 3. The description of an observation affirms more than is contained in the observation 187 4. —namely an agreement among phenomena; and the comparison of phenomena to ascertain such agreements is a preliminary to induction 190 [Pg ix] Chapter II. Of Abstraction, or the Formation of Conceptions. § 1. The comparison which is a preliminary to induction implies general conceptions 193 2. —but these need not be pre-existent 194 3. A general conception, originally the result of a comparison, becomes itself the type of comparison 198 4. What is meant by appropriate conceptions 200 5. —and by clear conceptions 203 6. Further illustration of the subject 205

Chapter III. Of Naming, as subsidiary to Induction. § 1. The fundamental property of names as an instrument of thought 209 2. Names are not indispensable to induction 210 3. In what manner subservient to it 211 4. General names not a mere contrivance to economize the use of language 213

Chapter 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 every general name 215 2. Names in common use have often a loose connotation 215 3. —which the logician should fix, with as little alteration as possible 218 4. Why definition is often a question not of words but of things 220 5. How the logician should deal with the transitive applications of words 224 6. Evil consequences of casting off any portion of the customary connotation of words 229 [Pg x] Chapter V. On the Natural History of the Variations in the Meaning of Terms. § 1. How circumstances originally accidental become incorporated into the meaning of words 236 2. —and sometimes become the whole meaning 238 3. Tendency of words to become generalized 240 4. —and to become specialized 243

Chapter VI. The Principles of a Philosophical Language further considered. § 1. Second requisite of philosophical language, a name for every important meaning 248 2. —viz. first, an accurate descriptive terminology 248 3. —secondly, a name for each of the more important results of scientific abstraction 252 4. —thirdly, a nomenclature, or system of the names of Kinds 255 5. Peculiar nature of the connotation of names which belong to a nomenclature 257 6. In what cases language may, and may not, be used mechanically 259

Chapter VII. Of Classification, as subsidiary to Induction. § 1. Classification as here treated of, wherein different from the classification implied in naming 266 2. Theory of natural groups 267 3. Are natural groups given by type, or by definition? 271 4. Kinds are natural groups 274 5. How the names of Kinds should be constructed 280

Chapter VIII. Of Classification by Series. § 1. Natural groups should be arranged in a natural series 284 2. The arrangement should follow the degrees of the main phenomenon 285 3. —which implies the assumption of a type-species 287 [Pg xi]4. How the divisions of the series should be determined 288 5. Zoology affords the completest type of scientific classification 289

BOOK V. ON FALLACIES.

Chapter I. Of Fallacies in General. § 1. Theory of fallacies a necessary part of logic 295 2. Casual mistakes are not fallacies 297 3. The moral sources of erroneous opinion, how related to the intellectual 297

Chapter II. Classification of Fallacies. § 1. On what criteria a classification of fallacies should be grounded 301 2. The five classes of fallacies 302 3. The reference of a fallacy to one or another class is sometimes arbitrary 305

Chapter III. Fallacies of Simple Inspection, or à priori Fallacies. § 1. Character of this class of Fallacies 309 2. Natural prejudice of mistaking subjective laws for objective, exemplified in popular superstitions 310 3. Natural prejudices, that things which we think of together must exist together, and that what is inconceivable must be false 314 4. Natural prejudice, of ascribing objective existence to abstractions 321 5. Fallacy of the Sufficient Reason 322 6. Natural prejudice, that the differences in nature correspond to the distinctions in language 325 7. Prejudice, that a phenomenon cannot have more than one cause 329 8. Prejudice, that the conditions of a phenomenon must resemble the phenomenon 332 [Pg xii] Chapter IV. Fallacies of Observation. § 1. Non-observation, and Mal-observation 341 2. Non-observation of instances, and non-observation of circumstances 341 3. Examples of the former 342 4. —and of the latter 347 5. Mal-observation characterized and exemplified 352

Chapter V. Fallacies of Generalization. § 1. Character of the class 356 2. Certain kinds of generalization must always be groundless 356 3. Attempts to resolve phenomena radically different into the same 357 4. Fallacy of mistaking empirical for causal laws 359 5. Post hoc, ergo propter hoc; and the deductive fallacy corresponding to it 364 6. Fallacy of False Analogies 366 7. Function of metaphors in reasoning 373 8. How fallacies of generalization grow out of bad classification 375

Chapter VI. Fallacies of Ratiocination. § 1. Introductory Remarks 377 2. Fallacies in the conversion and æquipollency of propositions 377 3. Fallacies in the syllogistic process 379 4. Fallacy of changing the premises 379

Chapter VII. Fallacies of Confusion. § 1. Fallacy of Ambiguous Terms 384 2. Fallacy of Petitio Principii 396 3. Fallacy of Ignoratio Elenchi 405 [Pg xiii] BOOK VI. ON THE LOGIC OF THE MORAL SCIENCES.

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 extended and generalized 413 2. How far this can be attempted in the present work 415

Chapter II. Of Liberty and Necessity. § 1. Are human actions subject to the law of causality? 417 2. The doctrine commonly called Philosophical Necessity, in what sense true 418 3. Inappropriateness and pernicious effect of the term Necessity 420 4. A motive not always the anticipation of a pleasure or a pain 424

Chapter III. That there is, or may be, a Science of Human Nature. § 1. There may be sciences which are not exact sciences 426 2. To what scientific type the Science of Human Nature corresponds 429

Chapter IV. Of the Laws of Mind. § 1. What is meant by Laws of Mind 432 2. Is there a science of Psychology? 433 3. The principal investigations of Psychology characterized 435 4. Relation of mental facts to physical conditions 440

Chapter V. Of Ethology, or the Science of the Formation of Character. § 1. The Empirical Laws of Human Nature 445 2. —are merely approximate generalizations. The universal laws are those of the formation of character 447 [Pg xiv]3. The laws of the formation of character cannot be ascertained by observation and experiment 449 4. —but must be studied deductively 454 5. The Principles of Ethology are the axiomata media of mental science 455 6. Ethology characterized 459

Chapter VI. General Considerations on the Social Science. § 1. Are Social Phenomena a subject of Science? 461 2. Of what nature the Social Science must be 463

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 466 2. In the Social Science experiments are impossible 468 3. —the Method of Difference inapplicable 469 4. —and the Methods of Agreement, and of Concomitant Variations, inconclusive 471 5. The Method of Residues also inconclusive, and presupposes Deduction 472

Chapter VIII. Of the Geometrical, or Abstract Method. § 1. Characters of this mode of thinking 476 2. Examples of the Geometrical Method 478 3. The interest-philosophy of the Bentham school 479

Chapter IX. Of the Physical, or Concrete Deductive Method. § 1. The Direct and Inverse Deductive Methods 486 2. Difficulties of the Direct Deductive Method in the Social Science 489 3. To what extent the different branches of sociological speculation can be studied apart. Political Economy characterized 492 4. Political Ethology, or the science of national character 497 5. The Empirical Laws of the Social Science 500 6. The Verification of the Social Science 502 [Pg xv] Chapter X. Of the Inverse Deductive, or Historical Method. § 1. Distinction between the general Science of Society, and special sociological inquiries 506 2. What is meant by a State of Society? 506 3. The Progressiveness of Man and Society 508 4. The laws of the succession of states of society can only be ascertained by the Inverse Deductive Method 511 5. Social Statics, or the science of the Coexistences of Social Phenomena 513 6. Social Dynamics, or the science of the Successions of Social Phenomena 521 7. Outlines of the Historical Method 522 8. Future prospects of Sociological Inquiry 525

Chapter XI. Additional Elucidations of the Science of History. § 1. The subjection of historical facts to uniform laws is verified by statistics 529 2. —does not imply the insignificance of moral causes 532 3. —nor the inefficacy of the characters of individuals and of the acts of governments 535 4. The historical importance of eminent men and of the policy of governments illustrated 540

Chapter XII. Of the Logic of Practice, or Art; including Morality and Policy. § 1. Morality not a science, but an Art 544 2. Relation between rules of art and the theorems of the corresponding science 544 3. What is the proper function of rules of art? 546 4. Art cannot be Deductive 548 5. Every Art consists of truths of Science, arranged in the order suitable for some practical use 549 6. Teleology, or the Doctrine of Ends 550 7. Necessity of an ultimate standard, or first principle of Teleology 552 8. Conclusion 554

A SYSTEM OF LOGIC, RATIOCINATIVE AND INDUCTIVE BEING A CONNECTED VIEW OF THE PRINCIPLES OF EVIDENCE, AND THE METHODS OF SCIENTIFIC INVESTIGATION. By John Stuart Mill CONTENTS Preface To The First Edition. Preface To The Third And Fourth Editions. Introduction.