3ui 



CONTENTS. 



Chapter XXI. 



Of the Evidence of the Law of Universal 

 Causation. 



SKC. PAGE 



1. The law of causality does not rest 



on an instinct 368 



2. But on an induction by simple 



enumeration 371 



3. In what cases such induction is 



allowable 373 



4. The universal prevalence of the law 



of causality, on what grounds ad- 

 missible 374 



Chapter XXII. 



Of Uniformities of Co-existence not de- 

 pendent on Causation. 



377 



379 



380 

 381 



382 



382 

 383 



384 



1. Uniformities of co-existence which 



result from laws of sequence 



2. The pro()erties of Kinds are uni 



formities of co-existence . . 



3. Some are derivative, others ulti 



mate 



4. No universal axiom of co-existence 



5. The evidence of uniformities of co- 



existence, how measured . . 



6. When derivative, their evidence is 



that of empirical laws 



7. So also when ultimate 



8. Ttie evidence stronger in propor- 



tion as tiie law is more general . . 



9. Every distinct Kind must be exa- 



mined 385 



Chapter XXIII. 



Of Approximate Genei'alisations, and 

 Probable Evidence. 



1. The inferences called probable rest 



on approximate generalisations. . 386 



2. Approximate generalisations less 



usef id in science than in life . . 387 



3. In what cases they may be resoi-ted 



to 388 



4. In what manner proved . . . . 389 



5. With what precautions employed 390 



SEC. pagb 



6. The two modes of combining pro- 



babilities 391 



7. How approximate generalisations 



may be converted into accurate 

 generalisations equivalent to them 394 



Chapter XXIV. 

 Of the Remaining Laws of Nature. 



1. Propositions which assert mere ex- 



istence 2,gs 



2. Resemblance considered as a sub- 



ject of science 



3. The axioms and theorems of mathe- 



matics comprise the principal laws 

 of resemblance 



4. — and those of order in place, and 



rest on induction by simple enu- 

 meration 



5. The propositions of arithmetic 



aflSrm the modes of formation of 

 some given number 



6. Those of algebra affirm the equiva- 



lence of different modes of forma- 

 tion of numbei's generally 



7. The propositions of Geometry are 



laws of outward nature . . 



8. Why Geometry is almost entirely 



deductive 



9. Function of mathematical truths 



in the other sciences, and limits 

 of that function 



Chapter XXV. 

 Of the Grounds of Disbelief. 



1. Improbability and impossibility . . 



2. Examination of Hume's doctrine of 



miracles 



3. The degrees of improbability corre- 



spond to differences in the nature 

 of the generalisation with which 

 an assertion conflicts 



4. A fact is not incredible because the 



chances are against it 



5. Are coincidences less credible than 



other facts? 



6. An opinion of Laplace examined . . 



396 



397 



398 



405 



406 



407 

 408 



413 

 415 



BOOK IV. 



OF OPERATIONS SUBSIDIARY TO INDUCTION. 



Chapter I. 

 Of Observation and Description. 



I. Observation, how far a subject of 



Logic .. .. .. .. .. 419 



a. A great part of what seems obser- 

 vation iti really inference . . . . 420 



The description of an observation 

 affirms more than is contained in 

 the observation 422 



— namely, an agreement among 

 phenomena ; and the comparison 

 of phenomena to ascertain such 

 agreements is a preliminary to 

 induction 423 



