CONTENTS. Xlll 



CHAPTER V. Of Demonstration, and Necessary Truths. 



PAGE 



1. The theorems of geometry are only necessary truths in 



the *ense of necessarily following from hypotheses . 296 



2. Those hypotheses are real facts with some of their circum- 



stances omitted . I. . "." ' . . . . 301 



3. Some of the first principles of geometry are axioms, and 



these are not hypothetical . ... . 303 



4. but are experimental truths . V . . 305 



6. An objection answered ..... 308 

 6. Mr. Whe well's opinions on axioms examined . .311 



CHAPTER VI. The same Subject continued. 

 1. All deductive sciences are inductive . . . 328 



2. The propositions of the science of number are not verbal, 



but generalizations from experience . . . 330 



3. In what sense hypothetical .... 337 



4. The characteristic property of demonstrative science is to 



be hypothetical .:.... 339 

 6. Definition of demonstrative evidence, and of logical necessity 341 



BOOK III. 

 OF INDUCTION. 



CHAPTER I. Preliminary Observations on Induction in 

 general. 



1. Importance of an Inductive Logic . . . .345 



2. The logic of science is also that of business and life . 347 



CHAPTER II. Of Inductions improperly so called. 



$ 1 . Inductions distinguished from verbal transformations . 352 



2. from inductions, falsely so called, in mathematics . 354 



3. and from descriptions ..... 356 



4. Examination of Mr. WheweU's theory of induction . 359 



CHAPTER III. On the Ground of Induction. 



1. Axiom of the uniformity of the course of nature . . 370 



2. Not true in every sense. Induction per enumerationem 



simplicem . , . . . . 375 



3. The question of Inductive Logic stated , . ^.Y 378 



