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CHAPTER VI. 

 THE SAME SUBJECT CONTINUED. 



1. IN the examination which formed the subject 

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

 those deductive sciences which are commonly repre- 

 sented to be systems of necessary truth, we have 

 been led to the following conclusions. The results 

 of those sciences are indeed necessary, in the sense 

 of necessarily following from certain first prin- 

 ciples, commonly called axioms and definitions ; of 

 being certainly true if those axioms and definitions 

 are so. But their claim to the character of necessity 

 in any sense beyond this, as implying an evidence 

 independent of and superior to observation and expe- 

 rience, must depend upon 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 upon 

 superabundant and obvious evidence. We inquired, 

 whether, since this is the case, it be necessary to 

 suppose any other evidence of those truths than 

 experimental evidence, any other origin for our belief 

 of them than an experimental 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 

 arguments, we have thought ourselves warranted in 

 concluding that axioms are but a class, the highest 

 class, of inductions from experience : the simplest 



