240 THEORIES AND MODELS 



premises may be quite variously involved in the derivations of such 

 relations which, fortunately, far outnumber the "constants" to be 

 evaluated. Consequently the excellent agreement of all the calcu- 

 lated \'alues for a given constant supplies heartening (if inconclu- 

 sive) evidence for the self-consistency of the premises. Moreover, 

 beyond this internal agreement, we can often show that the calcu- 

 lated values agi'ee well with others more directly determined. Thus, 

 from the Millikan oil-drop experiment we obtain for the electronic 

 charge a value wholly independent of the im^olvement of that charge 

 in quantum theories. 



This mode of analysis has an interest beyond its bearing on the 

 question of theoretic self-consistency. Through it we may be brought 

 to recognize which parts of our model are "superfluous." For exam- 

 ple, consider the billiard-ball model on which the kinetic theory of 

 gases was first founded. We find that through the mediation of the 

 theory we can evaluate certain aspects of that model— e.g., from 

 thermal conductivity, viscosity, and diffusion data we derive reason- 

 ably consistent values for the diameter of the gaseous particle; from 

 other measurements we learn something of its 'liardness," or de- 

 formability. But from our theory we can never extract any specific 

 characterization of the "billiard-ballness" of that particle. That is 

 not at all difficult to understand: finding no place in the theoretic 

 premises, this comparison can figure explicitly nowhere in our theory. 

 Indeed, the formal superfluity of the billiard-ball model is made en- 

 tirely patent by our continued use of the kinetic theory, even though 

 today the billiard-ball atom has utterly dissolved, into a localized con- 

 centration of electronic haze. 



Ever seeking maximal parsimony and penury of theoretic postu- 

 lates, we may think it imperative to strip our theories of all such 

 "superfluous" features. Thus Rankine is led sharply to distinguish 

 between two species of scientific theory— the abstractive and the 

 hypothetical— described as follows by Dingle: 



Abstraction is the detection of a common quality in the characteris- 

 tics of a number of diverse observations: it is the method supremely 

 exemplified in the work of Newton and Einstein. ... 



A hypothesis serves the same purpose, but in a diff^erent way. It re- 

 lates apparently diverse experiences, not by directly detecting a com- 

 mon quality in the experiences themselves, but by inventing a fic- 

 titious substance or process or idea, in terms of which the experience 



