2J6 MYTH AND SCIENCE. 



universal process of cosmic life are concerned. The 

 reason of the number must depend upon the substance, 

 by the configurations of which it is defined, divided, 

 added, and multiplied, and to this geometry is added, 

 which measures all things in relation to themselves 

 and others. This eternal cause makes it intelligible 

 that if immaterial principles precede and govern the 

 whole material world, it is also by means of these that 

 the classification of science is in intrinsic agreement 

 with that of nature. Numbers have their value in 

 music, in gymnastics, in medicine, in morals, in 

 politics, in all branches of science. The Pythagorean 

 arithmetic is the bond and universal logic of the 

 knowable. But at the same time Pythagoras and his 

 school peopled the world with demons and genii, which 

 were the causes of disease ; they did not abandon the 

 old mythical ideas of the incarnation of spirits and the 

 transmigration of souls theories and beliefs which 

 recur in nearly all primitive and savage peoples. 



In this vast Pythagorean scheme, which contrasts 

 with that of the Ionic school of physics, thought is 

 more explicitly freed from the ruder mythical ideas, 

 and rises to a more intelligent and rational conception 

 of the world, but the ancient popular traditions still 

 persist, and there is an evident cntlfication of number. 

 The primitive monad, numbers, their genesis and 

 relations, are not regarded as abstract conceptions, 

 necessary for understanding the order of nature, and 

 a merely logical function of the mind ; they are the 



