CONTENTS. 



The two modes of combining proba- 

 bilities 356 



How approximate generalizations 

 may be converted into accurate 

 generalizations equivalent to them 358 



CHAPTER XXIV. 



Of the Remaining Laws of Nature. 

 Propositions which assert mere ex- 



sub- 



360 



istence .... 



Resemblance, considered as 

 ject of science .... 361 



The axioms and theorems of mathe- 

 matics comprise the principal laws 

 of resemblance .... 363 



— and those of order in place, and 

 rest upon induction by simple 

 enumeration 364 



The propositions of arithmetic affirm 

 the modes of formation of some 

 given number . . . . ib. 



Those of algebra affirm the equiva- 

 lence of different modes of forma- 

 tion of numbers generally . . 367 



The propositions of geometry are 

 laws of outward nature . .369 



Why geometry is almost entirely 

 deductive 371 



Function of mathematical truths in 

 the other sciences, and limits of 

 that function 372 



CHAPTER XXV. 



Of the Grounds of Disbelief . 



Improbability and impossibility . 374 



Examination of Hume's doctrine of 

 miracles ib. 



The degrees of improbability cor- 

 respond to differences in the na- 

 ture of the generalization with 

 which an assertion contlicts . . 377 



A fact is not incredible because the 

 chances are against it . . . 379 



An opinion of Laplace examined . 380 



BOOK IV. 



CHAPTER I. 



Of Observation and Description. 

 ^ 1. Observation, how far a subject of 



logic .383 



2. A great part of what seems observa- 



tion is really inference . . . 384 



3. The description of an observation 



affirms more than is contained in 

 the observation . . . .386 



4. — natnely,an agreement among phe- 



nomena ; and the comparison of 

 phenomena to ascertain such 

 agreements is a preliminary to in- 

 duction 387 



CHAPTER n. 



Of Abstraction, or the Formation of Conceptions. 



(j 1. The comparison which is a pre- 

 liminary to induction implies 

 general conceptions . . . 389 

 2. — but these need not be preexistent 390 



Page 



§ 3 A general conception. Originally the 

 result of a comparison, becomes 

 itself the type of comparison . 392 



4. What is meant by appropriate con- 



ceptions 394 



5. — and by clear conceptions . . 395 



6. Cases in which the conception must 



preexist 396 



CHAPTER III. 



Of Naming, as subsidiary to Induction. 



^ 1. The fundamental property of names 



as an instrument of thought . . 397 



2. Names are not indispensable to in- 



duction 398 



3. In what manner subservient to it . 399 



4. General names not a mere contriv- 



ance to economize the use of lan- 

 guage 400 



CHAPTER IV. 



Of the Requisites of a Philosophical Language ; 

 and the Principles of Definition. 



^ 1. First requisite of philosophical lan- 

 guage, a steady and determinate 

 meaning for every general name . 400 



2. Names in common use have often a 



loose connotation .... 401 



3. — which the logician should fix, with 



as little alteration as possible . 402 



4. Why definition is often a question 



not of words but of things . . 404 



5. How the logician should deal with 



the transitive applications of words 406 

 0. Evil consequences of casting off any 

 portion of the customary connota- 

 tion of words 409 



CHAPTER V. 



Of the Natural History of the Variations in the 

 Meaning of Terms. 



() 1. How circumstances originally acci- 

 dental become incorporated into 

 the meaning of words . . . 414 



2. — and sometimes become the whole 



meaning 415 



3. Tendency of words to become gen- 



eralized 410 



4. — and to become specialized . . 418 



CHAPTER VI. 



The Principles of a Philosophical Language 

 further considered. 



ij 1. Second requisite of philosophical 

 language, a name for every im- 

 portant meaning .... 421 



2. — viz., first, an accurate descriptive 



terminology ib. 



3. — secondly, a name for each of the 



more important results of scientific 

 abstraction 424 



4. — thirdly, a nomenclature, or system 



of the names of kinds . . . 426 



5. Peculiar nature of the connotation 



of names which belong to a no- 

 menclature 427 



6. In what cases language may, and 



may not, be used mechanically . 423 



