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CHAPTER XII. 



THE RATIONALE OF PHILOSOPHICAL THOUGHT. 

 I. 



1. To the popular mind the science of Mathematics on the 

 maticsand one side and that of Metaphysics on the other stand in 



Meta- 

 physics, marked contrast. The former represents, as it were, the 



most certain, the latter the most uncertain, form of 

 Knowledge which the human mind is possessed of. It 

 is, however, worth noting that nevertheless these two 

 forms of Knowledge have, according to the popular 

 opinion, one quality in common, neither of them seems 

 capable of any real progress. The absolute fixity of the 

 fundamental principles of the one makes a real advance 

 seemingly as impossible as the absolute uncertainty of 

 the principles of the other. 



In the concluding chapter of the first section of this 

 History I tried to show how, so far as Mathematics are 

 concerned, the popular view is erroneous ; no science 



2 . has advanced and changed during the nineteenth century 

 progressive, more than that of mathematics. In the present chapter, 



which will conclude the second section of this History, I 

 shall endeavour similarly to refute the second opinion, 



