THE EVOLUTION OF SCIENTIFIC THEORIES 255 



tions, dj.^ Undertaking a series of trials with different conditions 

 represented as x = 1, x = 2, x = 3, . . . y = I, y = 2, . . . and so 

 on, I then predict that I will obtain certain sets of results if each of 

 the relations is sound. 



If A(x,fl,,), thenfli, fl2, fl3, . . . 

 liB{y,by), thenbi,b2, . . . 

 If C {z,Cz), then ci, ... 



Hence I predict that in certain circumstances some particular ob- 

 servable results will be obtained // the theory is sound. 



If (MF), then ai,fl2, as, . . . 

 bi, bz, . . . 



Cl, ... 



This is an amply general schema and, as we will see, also a some- 

 what oversimplified one. 



Let us suppose that I confirm a great multitude of predictions 

 fli . . . The theory (MF) is then confirmed, but it is not verified. 

 Each additional prediction borne out adds some measure of evidence 

 for the theory, and the sheer number of successful confirmations may 

 seem to place it beyond any reasonable doubt. But all these meas- 

 ures together fall far short of proof in any logical sense. Indeed, they 

 can show neither the necessity of the theory {i.e., the impossibility 

 of an alternate theory, perhaps not as yet conceived) nor even its 

 universal sufficiency ( i.e., the impossibility of contradictory data, not 

 as yet discovered). Thus, toward the end of the 19th century the 

 system of Newtonian mechanics had been exhaustively confirmed by 

 observations of the most diverse sorts. But only a few years later this 

 classical mechanics was held insufficient, and all the observations by 

 which it had earlier seemed "verified" were shown predictable also 

 from Einstein's new relativistic mechanics. 



We can no more think of verifying a theory of physics than a doc- 

 trine of metaphysics. But, because the experiential relevance of a 

 scientific theory is always guarded, we can take advantage of a strik- 



* The variables comprised under a and x are in large degree interchangeable, but 

 this does not affect our present concern. 



