242 THEORIES AND MODELS 



For Diihem the explanations are parasitic upon the "purely repre- 

 sentati\'e" function of theories he considered as primarily correlative 

 devices. But is not the "superfluous explanation" in itself a wonder- 

 fully effective correlative device? Given our previous knowledge of 

 classical dynamics, the very words "billiard-ball atom" conjure up 

 the major part of the kinetic theory. We imply the axioms and formal- 

 ism of Newtonian mechanics, earlier found applicable to the colli- 

 sions of ("ideal") billiard balls. From these we arrive at deduced 

 theorems rendered colligative relations when, on the strength of the 

 model, we identify certain terms with indicative concepts like "pres- 

 sure." We thus acquire the semantic rules we need and, though 

 today the model is quite passe, the memory of that Cheshire cat is 

 still active in eliciting our recognition of what passes as its grin. Be- 

 yond all this, the model supplies the notion of appreciation that helps 

 lis use the formalism, and suggests also a multitude of auxiliary 

 assumptions often helpful and sometimes indispensable. In certain 

 cases (though surely not in all) some such assumptions may later 

 prove fallacious. Suppose we try to avoid this danger, by seeking a 

 completely explicit statement of premises, syntactic rules, and se- 

 mantic rules. However "purer" formally, our statement of the theory 

 is now vastly more complex. 



Gi\'en the model, we readily gain command of the theory to which 

 it gives such compact expression. This situation is, of course, a quite 

 general one. Thus, given our previous knowledge of hydrostatics, the 

 phrase "sea of the air" by itself constitutes an essentially complete 

 aerostatic theory almost infinitely more difficult to express in any 

 substantially formal way. Rather than accept such complications, we 

 ordinarily welcome the support of the "superfluous" model. If it 

 leads us automatically to fill out premises and syntactic rules with 

 implicit assumptions, so much the better. If deductive ladders in- 

 volve rungs unseen by the eye but unerringly found by the foot, we 

 may use those ladders to good advantage even though, one day, the 

 hitherto unseen rungs crumble under the gaze of eyes newly critical. 

 This will seem a catastrophe only to those who confound scientific 

 theories with ageless truths— but there are some such people. 



The positivists "theory without superfluity'' In accordance with 

 the earlier diagnoses of Comte and Mach, Duhem found science 

 weakened by its chronic infection with metaphysics. All thought to 

 create a science resistant to that infection. Such a science will eventu- 



