A System of Logic: Ratiocinative and Inductive, 7th Edition, Vol. Ii

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.

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.

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

Continue reading A System of Logic: Ratiocinative and Inductive, 7th Edition, Vol. Ii free in the Wunder reader →