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A
SYSTEM OF LOGIC
RATIOCINATIVE AND INDUCTIVE
VOL. II.
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
IN TWO VOLUMES
VOL. II.
SEVENTH EDITION
LONDON:
LONGMANS, GREEN, READER, AND DYER
MDCCCLXVIII
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
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
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
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
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
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
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
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
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
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
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
BOOK III.
_CONTINUED._
OF INDUCTION.
"In such cases the inductive and deductive methods of inquiry may be
said to go hand in hand, the one verifying the conclusions deduced by
the other; and the combination of experiment and theory, which may thus
be brought to bear in such cases, forms an engine of discovery
infinitely more powerful than either taken separately. This state of any
department of science is perhaps of all others the most interesting, and
that which promises the most to research."--SIR J. HERSCHEL, _Discourse
on the Study of Natural Philosophy_.