230 THEORIES AND MODELS 



Models 



Qualitath'e diflFerences in the models on which they are founded will 

 make scientific theories notably different in appearance. Beginning 

 with those theories that do indeed seem "purely mathematical," let 

 us consider the adequacy of Bridgman's very persuasive analysis of 

 their status. 



Formerly mathematical theories usually had in the background a phys- 

 ical model of some sort, as, for example, the kinetic theory of gases 

 had in the background a model consisting of idealized molecules, 

 . . . The molecules were so simplified that they were amenable to 

 mathematical treatment. We had then a sort of double theory— a 

 mathematical theory of the idealized model, and then a physical 

 theory consisting of the statement that there was a correspondence 

 between the idealized model and the actual physical system suffi- 

 ciently close so that certain properties of the physical system were 

 reproduced by the model. The point in making such an idealized phys- 

 ical model was that it had a mathematical theory simple enough to 

 be handled. 



It presently appeared to reflection, howev'er, that there was an 

 unnecessary step here— since all that could be done in any event was 

 to set up certain correspondences between the results of the mathe- 

 matical manipulations and the physical system, why have the in- 

 termediate step of the idealized physical model, since a con-espond- 

 ence to a correspondence is also a correspondence? This of course is 

 exactly what has been done in recent wave mechanical theories, par- 

 ticularly that of Dirac, and we know that such a procedure has been 

 brilliantly successful. I think that the reason that this change of 

 attitude was so long deferred was that it was not realized that there 

 was an intermediate step— . . . the model was actually identified 

 with the physical system. 



What we now have is in effect mathematical models rather than 

 physical models . . . 



Can a mathematical model thus replace the physical model? A 

 strictly formal system, we saw earlier, is characterized primarily by 

 its vacancy. Were scientific theories purely mathematical, how could 

 they at all refer to experience? 



Bridgman considers the physical model an "unnecessary step" be- 

 cause "a correspondence to a correspondence is also a correspond- 



