CHAPTER VI. 



THE SAME SUBJECT CONTINUED. 



1. IN the examination which formed the suhject of 

 the last chapter, into the nature of the evidence of those 

 deductive sciences which are commonly represented to be 

 systems of necessary truth, we have been led to the following 

 conclusions. The results of those sciences are indeed neces- 

 sary, in the sense of necessarily following from certain first 

 principles, commonly called axioms and definitions; that is, 

 of being certainly true if those axioms and definitions are so ; 

 for the word necessity, even in this acceptation of it, means 

 no more than certainty. But their claim to the character of 

 necessity in any sense beyond this, as implying an evidence 

 independent of and superior to observation and experience, 

 must depend on the previous establishment of such a claim in 

 favour of the definitions and axioms themselves. With regard 

 to axioms, we found that, considered as experimental truths, 

 they rest on superabundant and obvious evidence. We in- 

 quired, whether, since this is the case, it be imperative to 

 suppose any other evidence of those truths than experimental 

 evidence, any other origin for our belief of them than an expe- 

 rimental origin. We decided, that the burden of proof lies 

 with those who maintain the affirmative, and we examined, at 

 considerable length, such arguments as they have produced. 

 The examination having led to the rejection of those argu- 

 ments, we have thought ourselves warranted in concluding 

 that axioms are but a class, the most universal class, of in- 

 ductions from experience ; the simplest and easiest cases of 

 generalization from the facts furnished to us by our senses or 

 by our internal consciousness. 



While the axioms of demonstrative sciences thus ap- 



