THE PRINCIPLES OF SCIENCE 173 



sumes both existent and discoverable— in quest of explanation of 

 those laws. This quest seeks consummation in the construction of 

 postulational system(s) in which the laws are demonstrated to be 

 necessary consequences of theoretical premises we accept. But now- 

 having learned to reject, as delusive, the hope that theoretical prem- 

 ises are, or can be made, self-evident— we cannot but recognize that 

 always our explanations are incomplete. Hall attributes to Galilea 

 and Newton the opinion that: 



The explanation of phenomena at one level is the description of phe- 

 nomena at a more fundamental level, . . . 



Complete understanding then fails by the margin of those theoretical 

 premises which are stipulated, perhaps "described," but certainly 

 not themselves explained or explicable for so long as they remain our 

 ultimate premises. 



Parsimony. Resolved to maximize our understanding, we find our- 

 selves committed to a highly characteristic eflFort to minimize the 

 number of theoretical premises required for explanation. Einstein 

 speaks of: 



. . . the grand aim of all science, which is to cover the greatest pos- 

 sible number of empirical facts by logical deductions from the small- 

 est possible number of hypotheses or axioms. 



Some centuries earlier Newton had expressed the same "grand aim" 

 in the first of his Rules of Reasoning: 



We are to admit no more causes of natural things than such as are 

 both true and sufficient to explain their appearances. 



This is in turn the millennially remote echo of the "master of those 

 who know," writing when the principle of intelligibility was in its 

 infancy. 



That is done in vain by many means -which may equally well be done 

 with fewer. 



Major differences of attitude and meaning presumably underlie 

 these statements. Quite clearly, however, acceptance of the principle 

 of intelligibility has always provoked, must always provoke, a con- 

 tinuing endeavor to devise theories of ever-increasing comprehen- 

 siveness founded on ever-narrower postulational foundations. Of 

 many specific manifestations of this endeavor, a particularly signifi- 



