6 DOGMATISM AND EVOLUTION 



perfectly obvious fashion. At its basis were conceived to be a" 

 certain number of indemonstrable but self-evident propositions, 

 involving a certain number of indefinable but self-explanatory 

 terms. Resting upon this basis were series of propositions of 

 ever narrowing generality and increasing complexity. The truth 

 of the later propositions was supposed to result from, and to be 

 guaranteed by, that of the earlier propositions, without giving 

 to these any reciprocal support. It seems to have been popularly 

 supposed that the order in which the propositions followed upon 

 one another was quite fixed, or admitted, at any rate, of no radical 

 alteration; and, although, of course, mathematicians were well 

 aware that this was not the case, they were nevertheless inclined 

 to think that one order alone could represent with perfect clear- 

 ness the exact interrelations of the concepts involved, and that 

 all others were therefore open to ultimate logical criticism. The 

 discovery of this ideal order was therefore regarded as a very 

 great desideratum. 



The influence of mathematical conceptions upon philosophy 

 was due in part to the fact that two of the great rationalists, 

 Descartes and Leibniz, were among the founders of modern math- 

 ematical science, and that many lesser members of the school 

 were competent mathematicians. With Descartes, indeed, whose 

 system was the point of departure for the whole movement, the 

 philosophy was the result of a deliberate attempt at an extension 

 of the mathematics. Inspired by his success in developing the 

 great discovery of his early manhood the application of alge- 

 braic analysis to the solution of geometrical problems he 

 thought to apply a similar analysis to the fundamental problems 

 of all departments of science. Had Descartes lived a little earlier, 

 Bacon would surely have cited his system as the superlative 

 instance in all history, of the Idol of the Cave. After telling us 

 how Aristotle, when he had discovered and classified the various 

 forms of demonstration, was thenceforth driven to interpret all 

 the phenomena of nature and society in terms of this new logic; 

 and after taking his fling at his countryman Gilbert, who had 



