MATHEMATICS VERSUS PSYCHOLOGY 5 



show itself more clearly than in the control which it exerted over 

 the development of rationalism in the seventeenth century. 

 A good part of Hobbes's Compulation, or Logic is scarcely more 

 than a simplified restatement of the leading principles of Aris- 

 totle's methodology, in terms of the already traditional English 

 nominalism, and not improbably profited by some study of the 

 Greek original. In the case of the continental rationalists, the 

 dependence is generally more indirect through the continued 

 prevalence of conceptions inherited from scholasticism but not 

 less evident. The opening paragraphs of Descartes's Discourse 

 on Method afford a singular illustration of this. He is inclined 

 to think that the intellectual differences between men cannot 

 have to do with their reason, because that faculty is the distin- 

 guishing characteristic of the human species, which completes 

 its definition, and consequently must be present equally in all 

 members of the species. From this one fossil vestige, well-nigh 

 the whole skeleton of the classical logic might be safely recon- 

 structed. 



The other influence to which we referred was that of the 

 mathematical sciences, and especially of the geometry of Euclid. 

 It is difficult for us today to realize what the possession of this 

 work meant to the thinkers of the later renaissance. To these 

 pioneers of modern science it was the very image of all that they 

 hoped to do, and, more than that, an unquestionable guarantee 

 of the competence of the human mind to solve the riddles of the 

 universe. While physics and physiology were still the sport of/ 

 vain and conflicting theories, here, at least, was a science. With 

 all of the unfounded pretensions and lamentable failures of the 

 Greeks, so much they had accomplished. This was their great 

 bequest to the modern world. Accordingly we can understand 

 that in the seventeenth century the hope of a science meant the 

 hope of a new geometry. Whatever modern methods, experi- 

 mental or analytical, might be employed in its construction, the 

 finished product was to be of the one uniform type. 



How was this type understood? In the most natural and 



