Introductory 



I. On Rating a Theory 



EVERY new speculation of science, every hy- 

 pothesis or theory, that merits and receives 

 a hearing is subjected to critical examination, and 

 then rated according to well-defined and estab- 

 lished criteria. 



That hypothesis is an indispensable mental tool, 

 "a legitimate instrument of logic," is not questioned. 

 Mathematical reasoning is legitimate wherever there 

 are "any premises sufficiently precise to make it 

 possible to draw necessary conclusions from them." 



T. U. Thiele, of the Copenhagen Observatory, in 

 his Theory of Observations, states a fact which is 

 generally recognized and frequently repeated when 

 he says: "It will be found that every applied 

 science, which is well developed, may be divided 

 into two parts, a theoretical (speculative or mathe- 

 matical) part and an empirical (observational) one. 

 Both are absolutely necessary, and the growth of a 



Note. — In this chapter copious direct quoting seems the best way to em- 

 phasize the fact that the rules for rating a theory are thoroughly established, 

 and nothing remains but to recognize and accept them. 



23 



