CONTENTS. 



PAGE 



i 7. Deflnilioiip, though of names only, must be 

 grounded on knowledge of the corre- 

 sponding things IIT 



BOOK II. 



OF REASONING. 



Chaptee I. 0/ h^ference, or Reasoning, in general. 



5 1. Retrospect of the preceding book 121 



2. Inferences improperly so called 122 



3. Inferences proper, distinguished into in- 



ductions and ratiocinations 125 



CuAPTKB II. Of Ratiocination, or Syllogism. 



51. Analysis of the Syllogism 126 



^^2. The dictum de omni not the foundation of 

 reasoning, but a mere identical proposi- 

 tion 132 



3. What is the really fundamental axiom of 



Eatiocination 135 



4. The other form of the axiom 137 



CiiAPTEE III. Of the Functions, and Logical Valtte 

 of the Syllogisin. 



J 1. Is the Syllogism a petitio principii f 139 



2. Insufficiency of the common theory 139 



3. All inference is from particulars to partic- 



ulars 141 



4. General propositions are a record of such 



inferences, and the rules of the syllogism 

 are rules for the interpretation of the 



record 146 



6. The syllogism not the type of reasoning, 

 but a test of it 148 



6. The true type, what — ■ 151 



7. Relation between Induction and Deduc- 



tion 163 



8. Objections answered 164 



9. Of Formal Logic, and its relation to the 



Logic of Truth 156 



Chapter IV. Of Trains of Reasoning, and Deduct- 

 ive Sciences. 



51. Forwhatpurpose trains of reasoning exist. 153 



2. A train of reasoning is a series of induct- 



ive inferences 158 



3. — from particulars to particulars through 



marks of marks 160 



4. Why there are deductive sciences 161 



\ 5. Why other sciences still remain experi- 



> mental 164 



I 6. Experimental sciences may become deduct- 



I y ive by the progress of experiment 165 



^ In what manner this usually takes place.. 166 



CuAPTEK V. Of Demonstration, and Xecessary 

 Truths. 

 5 1. The Theorems of geometry are necessary 

 truths only in the sense of necessarily fol- 

 lowing from hypotheses 168 



2. Those hypotheses are real facts with some 



of their circumstances exaggerated or 

 omitted 170 



3. Some of the first principles of geometry are 



axioms, and these are not hypothetical. . 171 



4. — but are experimental truths 172 



PAGE 



55. Au objection answered 174 



6. Dr. Whewell's opinions on axioms exam- 

 ined 176 



Chapter VI. The same Subject continued. 



5 1. All deductive sciences are inductive 187 



2. The propositions of the science of number 



are not verbal, but generalizations from 

 experience 188 



3. In what sense hypothetical 191 



4. The characteristic property of demonstra- 



tive science is to be hypothetical 192 



5. Definition of demonstrative evidence 193 



Chapter VII. Examination of some Opinions op- 

 posed to the preceding doctrines. y 

 5 1. Doctrine of the Universal Postulate 193 U^ 



2. The test of inconceivability does not rep- 



resent the aggregate of past experience. . 195 



3. — nor is implied in every process of 



thought. 197 



4. Objections answered 201 



5. Sir W. Hamilton's opinion on the Princi- 



ples of Contradiction and Excluded Mid- 

 dle 204 



BOOK III. 

 OF INDUCTION. 



Chapter I. Preliminary Observations on Indtic- 

 tion in general. 



5 1. Importance of an Inductive Logic 207 



2. The logic of science is also that of business 

 and life 208 



Chapter II. Of Indtictions improperly so called. 



{ 1. Inductions distinguished from verbal trans- 

 formations 210 



2. — from inductions, falsely so called, in math- 



ematics 212 



3. — and from descriptions 213 



4. Examination of Dr. Whewell's theory of 



Induction 214 



6. Further illustration of the preceding re- 

 marks 221 



Chapter III. Of the Ground of Induction. 

 51. Axiom of the uniformity of the course of 



nature 223 



2. Not true in every sense. Induction per 



enumerationem simpUcem 226 



3. The question of Inductive Logic stated 227 



Chapter IV. Of Laws of Xature. 



5 1. The general regularity in nature is a tissue 



of partial regularities, called laws 229 



2. Scientific induction must be grounded on 



previous spontaneous inductions 231 



3. Are there any inductions fitted to be a test 



of all others ? 232 



Chapter V. Of the Law of Universal Causation. 

 § 1. The universal law of successive phenomena 



is the Law of Causation 234 



2. — i. e., the law that every consequent has 

 an invariable antecedent 236 



