370 THE REAL WORLD 



Still denying the significance of a theory's display of heuristic 

 power, one perhaps argues that the appearance of such power re- 

 flects no more than the theory's nice concordance with human ra- 

 tionality. Unquestionably significant, this is again a point unques- 

 tionably insufficient. As metaphor consider that however nicely the 

 handle of a panel saw may be adapted to my grip, I find it ineffec- 

 tive as a tool for cutting concrete. At its handle end an effectual tool 

 must make some match with its user but, in addition, at its business 

 end it must make some match with that on which it is used. From a 

 theory I easily conceive I may readily draw predictions of new phe- 

 nomena; but the theory is quite incapable of ensuring the success of 

 my search for them. When, on Newton's theory, I predict a polar 

 flattening of the earth, my expectation does not produce the results 

 that confirm that flattening; when Stern predicts a certain kind of 

 smear of silver on glass, his expectation does not produce the smear. 

 Such heuristic displays are irreducible to manifestations of "sub- 

 jective" felicity. That a scientific theory sets me to look for many par- 

 ticular things I find seems rather to point to some degree of objec- 

 tivity in the theory's picture of the world. We can then justifiably 

 generalize the thrust of Cohen's commentary on a particular ex- 

 ample: the highly mathematical theory of elastic vibrations. 



"What," Mach naively asks, "have vibrating strings to do with circu- 

 lar functions?" "But," we may ask in turn, "how could these functions 

 guide us to the discovery of so many physical properties of vibrating 

 strings and other phenomena, if they had nothing to do with the 

 physical facts?" Mach and others are misled by the fact that mathe- 

 matical functions are not copies of sensational elements. This, how- 

 ever, need not prevent these functions from significantly representing 

 groups of relations which do characterize physical processes. 



Still the significance of the alleged heuristic power of scientific 

 theories can be resisted. May it not be argued that all appearance of 

 heuristic power is nothing but an artifact of human memory: we for- 

 get all the cases in which predictions of new phenomena failed, with 

 consequent amendment of the theory, and remember as "brilliant 

 heuristic successes" only the remaining cases in which the predictions 

 were borne out? No: that position is, I think, one patently untenable. 

 From the time of Newton to the time of Einstein a veritable galaxy of 

 brilliant discoveries develops from exploitation of the heuristic power 



