322 



PHILOSOPHICAL THOUGHT. 



24. 

 Mathe- 

 matical 

 methods. 



and an extended reality, and he thereby fixed the im- 

 mediate problem for the speculations of his followers. 



For our present purpose it is unnecessary to dwell 

 upon the questionable logic in Descartes' reasoning; it is 

 sufficient to point out that nearly all the different aspects 

 which the problem of knowledge presents, and which 

 have occupied thinkers up to the present day, are either 

 implied or distinctly brought out in Descartes' speculation. 

 Such are, e.g., the question of innate ideas, of the deduc- 

 tive as compared with the inductive processes of thought, 

 the identification of certainty with mathematical precision 

 or clearness, and many others. The way out of the un- 

 certainty of knowledge, which for Continental thinkers 

 was at that time by far the most important problem, 

 seemed indeed to be solved in a promising manner by 

 the appeal to the mathematical method. This was 

 exactly that aspect of thought for which the philosophy 

 of Bacon had no appreciation. The latter seemed to be 

 unaware of the important part which the application of 

 mathematics was to play in the extension of natural know- 

 ledge as well as in giving it precision and value.-^ The 

 exact methods practised by Galileo were extended and 



^ It is, however, well to remem- 

 ber that Bacon (1561-1626) preceded 

 Descartes (1596-1650) in time; 

 that his most important works 

 dealing with the "advancement of 

 learning " were written in the first 

 years of the seventeenth century ; 

 that at that time neither ' Kepler's 

 Laws' (1609-1618) nor Galileo's 

 •Laws of Falling Bodies' (1612) 

 were yet known or published ; that 

 the principal discoveries which were 

 accessible to Bacon, such as those 

 of Gilbert ('de Magnete,' 1600) and 

 Harvey (' Circulation of the Blood,' 



1619), had nothing to do with 

 mathematics. The Works of Hariot 

 and the ' Logarithmic Tables ' 

 (1594-1614) of Napier, on the other 

 side, were probably too exclusively 

 mathematical to come within the 

 sphere of Bacon's interest in the 

 extension of natural knowledge. 

 Descartes' ' Discourse on Method ' 

 appeared in 1637. He had thus 

 before him much of the best that, 

 during that age, had been achieved 

 in asti'onomy and physics through 

 the application of measurement and 

 calculation. 



