METHODS OF SCIENCE; NUMBERS 21 



that none of our foundations are perfectly 

 strong, we attempt to make them all of sufficient 

 strength and do not expend all of our effort on 

 one corner stone. As we proceed to the upper 

 stories of our scientific structure we may use 

 lighter and lighter materials, but in each story 

 we strive for uniform strength. We recognize 

 the existence of different levels of logic, al- 

 though in any one science we may build upon 

 several of these levels, as will be illustrated in 

 the next lecture. 



However, this simile of a building with its 

 several stories gives too much the idea of a man- 

 made, lifeless thing. Let us think rather of the 

 tree of knowledge which, while its branches are 

 continually growing upward through the fog 

 of the unexplored, is sending its roots deeper 

 through the strata and substrata of our in- 

 stincts and heritage, of our common thought 

 and common speech. 



The problem of language is so vast that I 

 hardly dare to peek into it. But when the illus- 

 trious Willard Gibbs remarked, "Mathematics 

 is a language," I cannot feel that he meant that 

 mathematics is merely a dry assemblage of sym- 

 bols (for to him mathematics was no formal 

 thing), but rather that in some aspects Ian- 



