MATHEMATICS VERSUS PSYCHOLOGY 7 



pondered for years over a magnet, until he saw magnetism every- 

 where and in everything; he would have capped the climax with 

 the inventor of analytical geometry and author of the Discourse 

 on Method. 



But rationalists who were by no means distinguished as mathe- 

 maticians were scarcely, if at all, less under the influence of 

 mathematical conceptions. The most obvious example is Spi- 

 noza, composing his Ethics in "geometrical order," and illustrating 

 the invariability of natural causation by the necessity with which 

 the idea of a triangle implies that the sum of its angles is two 

 right angles. Hobbes, too, who was so far from competence in 

 geometry that he is remembered in its history only as the most fat- 

 uous of circle-squarers, must nevertheless be said to have owed the 

 first flush of his enthusiasm for science, as well as his first clear 

 conceptions of scientific method, to a copy of Euclid's Elements. 

 On the other hand, Leibniz, the greatest mathematician of the 

 whole group, was not least a slave to mathematical notions, 

 though in various directions he strained these notions to their 

 breaking-point. His writings are, indeed, remarkable for their 

 constant use of principles which in their manifest implications 

 far transcend the rationalistic standpoint. More than any other 

 modern philosopher except perhaps Bacon he was a man of 

 the world with the most far-reaching social and political interests. 

 Yet his logical theory remained mathematical to the core, though 

 the uses to which he endeavored to put it were strikingly, nay 

 absurdly, concrete. Thus, for example, he was not above en- 

 forcing a practical social optimism by a reference to the law of the 

 parallelogram of forces. That this is the best of possible worlds 

 might be seen in the fact, that every change that takes place in 

 the world comes about with the least possible expenditure of 

 energy; so that, considering the state of affairs at each moment 

 of the world's history, as much as possible is always happening! 



We have mentioned several dogmas upon which all the great 

 rationalists are found to be united. The essential point is prob- 



