THEORIES AND MODELS 231 



ence." In the formal realm we find multiple abstract theorems in 

 logical correspondence with abstract premises. In the physical realm 

 we find multiple colligative relations which, by virtue of the deno- 

 tations attaching to their concepts, stand in correspondence with ele- 

 ments of experience. But where is the correspondence between these 

 correspondences? How can we pass from formal theorem to physi- 

 cally relevant colligative relation? Clearly we must identify some of 

 the abstract symbols with indicative concepts. Even a quite vague 

 implicit model may still furnish clues sufficient for this identification, 

 and it is thus that the model becomes the link between theory and 

 experiment. But with no physical model there is no link, and we 

 can then find in a purely mathematical construction no scientific 

 theory. Thus, Hutten emphasizes, quite aside from their well-known 

 psychological values (and dangers), models have also an indispen- 

 sable logical function: from them alone we draw the semantic rules 

 that first give some physical interpretations to what are otherwise 

 only formalisms. 



... it is often said that the model may be abandoned after it has 

 served its [heuristic] puipose. This would be so if our theories were 

 given as formalized systems and if we could state explicitly all the 

 rules necessary for determining the meaning of any sentence within 

 the theory. In fact, this cannot be done for any present-day theory, 

 and so we need the model also for climbing down the [deductive] 

 ladder to reach the experiment. We may know all the mathematics 

 needed for quantum mechanics, but its interpretation cannot be said 

 to be complete, in the strictly logical sense of this term; and how 

 about meson theory? 



Dirac's quantum mechanics, cited by Bridgman, is the generally 

 cited paradigm of the formalism that functions as a scientific theory. 

 But, in introducing his theory, Dirac himself emphasizes not the 

 formal but the physical ideas. 



. . . the mathematics is only a tool and one should learn to hold the 

 physical ideas in one's mind without reference to the mathematical 

 form. 



The better to grasp such physical ideas, we always seek models or 

 analogies. And to be sure, Hesse finds something of the sort even in 

 Dirac's highly formal theory. 



