126 SCIENCE AND METHOD. 



set the beginner to wrestle with this collection of 

 monstrosities. If you don't do so, the logicians might 

 say, you will only reach exactness by stages, 



6. Possibly this may be true, but we cannot take 

 such poor account of reality, and I do not mean 

 merely the reality of the sensible world, which has 

 its value nevertheless, since it is for battling with 

 it that nine-tenths of our pupils are asking for arms. 

 There is a more subtle reality which constitutes the 

 life of mathematical entities, and is something more 

 than logic. 



Our body is composed of cells, and the cells of 

 atoms, but are these cells and atoms the whole reality 

 of the human body? Is not the manner in which 

 these cells are adjusted, from which results the unity 

 of the individual, also a reality, and of much greater 

 interest ? 



Would a naturalist imagine that he had an adequate 

 knowledge of the elephant if he had never studied the 

 animal except through a microscope ? 



It is the same in mathematics. When the logician 

 has resolved each demonstration into a host of ele- 

 mentary operations, all of them correct, he will not yet 

 be in possession of the whole reality ; that indefinable 

 something that constitutes the unity of the demonstra- 

 tion will still escape him completely. 



What good is it to admire the mason's work in the 

 edifices erected by great architects, if we cannot under- 

 stand the general plan of the master? Now pure logic 

 cannot give us this view of the whole ; it is to intuition 

 we must look for it. 



Take, for instance, the idea of the continuous func- 



