THEORIES AND MODELS 241 



can be expressed. A hypothesis, in brief, correlates obsei-vations by 

 adding something to them, while abstraction achieves the same end 

 by subtracting something. 



Surely the distinction is here drawn oversharply. Dingle himself 

 recognizes elsewhere that Newton's conception of universal gravita- 

 tion is a genuine invention, a "something added," and no simple ab- 

 straction. Nevertheless, there does appear to be a real difference 

 between a hypothetical theory, like that involving the billiard-ball 

 atom, and an abstractive theory, like thermodynairdcs. The element of 

 addition, and "superfluity," looms much larger in the former— as it 

 does in corpuscular theories generally. What can we lose if we reject 

 such "superfluity"? 



Campbell correctly observes that: 



The explanation offered by a theory ... is always based on an 

 analogy, and the system with which an analogy is traced is always 

 one of which the laws are known; . . . Thus our theory of gases 

 explains the laws of gases on the analogy of a system subject to 

 dynamical laws. 



This system hypothetically consists of particles perfectly elastic in 

 their collisions, and such particles and collisions are of course unlike 

 any known to us. The explanation the theory provides thus becomes 

 a function of the extent to which it indicates some reasonable approx- 

 imation to such particles and collisions. The billiard-ball analogy 

 offers the best possible approximation and, rejecting this "superflu- 

 ity," we at once lose most of the sense of explanation we find in the 

 kinetic theory. But is this a loss of any real importance? Does the 

 scientific function of a theory have anything whatever to do with the 

 purely subjective feeling of explanation it arouses in us? Duhem 

 answers in the negative, stressing also that the explanations are often 

 the least durable features of theories. 



When the progress of experimental physics goes counter to a theory 

 and compels it to be modified or transfonned, the purely representa- 

 tive part enters nearly whole in the new theory, bringing to it the in- 

 heritance of all the valuable possessions of the old theory, whereas the 

 explanatory part falls out in order to give way to another explana- 

 tion, , . . 



This continuity of tradition is not visible to the superficial obsei-ver 

 due to the constant breaking-out of explanations which arise only to 

 be quelled. 



