CONTENTS. XV 



CHAPTER V. Of Demonstration, and Necessary Truths. 



T ftf ~*+&amp;gt;** PA &E 



1. The Theorems of geometry are necessary truths only in 



the sense of necessarily following from hypotheses . 251 



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



stances exaggerated or omitted .... 255 



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



these are not hypothetical .... 256 



4. but are experimental truths .... 258 



5. An objection answered ..... 261 



6. Dr. WhewelTs opinions on axioms examined . . 264 



CHAPTER VI. The same Subject continued. 



1. All deductive sciences are inductive . . . 281 



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



but generalizations from experience . . . 284 



3. In what sense hypothetical ..... 289 



4. The characteristic property of demonstrative science is to 



be hypothetical ...... 290 



5. Definition of demonstrative evidence . . . 292 



CHAPTER VII. ^Examination of some Opinions opposed to 

 the preceding doctrines. 



1. Doctrine of the Universal Postulate . . . 294 



2. The test of inconceivability does not represent the aggre 



gate of past experience ..... 296 



3. nor is implied in every process of thought . . 299 



4. Sir W. Hamilton s opinion on the Principles of Contra 



diction and Excluded Middle .... 306 \ 



BOOK III. 



OF INDUCTION. 



CHAPTER I. Preliminary Observations on Induction in general. 



1. Importance of an Inductive Logic .... 313 

 2. The logic of science is also that of business and life . 314 



CHAPTER II. Of Inductions improperly so called. 



1. Inductions distinguished from verbal transformations . 319 



2. from inductions, falsely so called, in mathematics . 321 



3. and from descriptions ..... 323 



4. Examination of Dr. Whewell s theory of Induction . 326 



5. Further illustration of the preceding remarks . . 336 



