88 THE FOUNDATIONS OF SCIENCE 



of logic and pure mathematics, and leave to experi- 

 ence and experiment the task of examining how far 

 they are true in substance and in fact in the concrete 

 cases of the external world of phenomena. Neverthe- 

 less, the evidence for the external particular truth of 

 such principles is greater in degree, perhaps different 

 in kind, to the evidence for the truth of any one 

 physical law, such as the proportionality between elec- 

 tromotive force and electric current, or any physical 

 theory such as Newton's theory of gravity. The 

 evidence for such laws and theories is special in kind, 

 though it may be of very great extent. But the 

 evidence that logical principles are of true applica- 

 tion in nature is not special but general. All our 

 experience of whatever kind is consistent with it, 

 and hopeless intellectual confusion would follow any 

 breach in its observance : no science, no ordered 

 knowledge would be possible. 



Formal logic has made great progress since it 

 began to use symbols, already familiar in mathe- 

 matics. Symbols not only serve as a shorthand 

 method of writing down relations which it would 

 be tedious and cumbersome to express in words, 

 but also they represent an analysis of ideas and an 

 almost pictorial representation of them. 



Thus it is one of the fundamental laws of algebra 

 that a first number (x) multiplied by a second number 

 (y) gives a product which is equal to the product 

 obtained by multiplying the second number by the 





