CONTENTS. 



ht 



Chapter IV. 



0/ Trains of Reasoning, and Deduc- 

 tive Sciences. 



SEC PAGE 



1. For what purpose trains of reason- 



ing exist 



2. A train of reasoning is a series of 



inductive Inferences 



3. — from particulars to particulars 



through marks of marks . . 



4. Why there are deductive sciences 



5. Why otlier sciences still remain 



expeiimental 



6. Experimental sciences may become 



deductive by the progress of 

 experiment 



7. In what manner this usually takes 



place 



137 



138 



139 

 141 



143 



M5 



145 



Chapter V. 



Of Demonstration, and Ifecessar^ 

 Truths. 



The Theorems of Geometry are 

 necessary truths i-uly in the 

 sense of necessarily following 

 from hypotheses 



Those liypotheses are real facts 

 with some of their circumstances 

 exaggerated or omitted . . 



Some of the first principles of 

 Geometry are axioms, and these 

 are not hypothetical 



— but are experimental truths . . 



An objection answered 



SEC. PAGE 



6. Dr. Whewell's opinions on axioms 



examined . . 156 



Chapter VI. 

 The same Subject continued. 



1. All deductive sciences are induc- 



tive 164 



2. The propositions of the Science of 



Number are not verbal, but gene- 

 ralisations from experience . . 166 



3. In what sense hypothetical . . 169 



4. The characteristic property of de- 



monstrative science is to be 

 hypothetical .. .. .. 170 



5. Definition of demonstrative evi- 



dence 171 



Chapter VII. 



Examination of some Opinions op- 

 posed to the preceding doctrines. 



172 



173 



Doctrine of the Universal Pos- 

 tulate . . 



The test of inconceivability does 

 not represent the aggregate of 

 past experience 



— nor is implied in every process 

 of thought 175 



Objections answered .. .. 179 



Sir W. Hamilton's opinion on the 

 Principles of Contradiction and 

 Excluded Middle 182 



BOOK III. 

 OF INDUCTION. 



Chapter I. 



Preliminary Ohstrvations on Induc- 

 tion in General. 



1. Importance of an Inductive Logic 185 



2. The Logic of Science is also that of 



business and life 185 



Chapter II. 

 Of Inductions im,properly so called. 



1. Inductions distinguished from ver- 



bal transformations . . . . 18 



2. — from inductions, falsely so 



called, in mathem-atics . . . . 19 



3. — and from descriptions . . . . 19 



4. Examination of Dr. Whewell's 



theory of Induction 



5. Further illustration of the preced 



ing remarks 198 



192 



Chapter III. 

 Od the G-round of Induction. 



Axiom of the uniformity of the 

 course of Nature . . . . . . 200 



Not true in every sense. Induc- 

 tion per enumerationem simplicem 203 



The question of Inductive Logic 

 stated 20s 



Chapter IV. 

 Of Laivs of Nature. 



The general regularity in nature 

 is a tissue of partial regularities, 

 called laws ao6 



Scientific induction must be 

 grounded on previous spon- 

 tanei 'US inductions .. .. 208 



Ate there any inductions fitted to 

 be a test of all others ? . . . . 20Q 



