Chapter I: Front Matter

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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