288 THE EVOLUTION OF SCIENTIFIC THEORIES 



past three hundred years is characterized by a chronological and al- 

 most organic sequence in its development which was not found to 

 anything like the same extent in Greek science. It is above all the 

 history of physics from Galileo to our time that makes us realize that 

 science advances toward reality so to say by concentric approxima- 

 tions—each theory contains its forerunner as a "special case." 



How can such correspondence of new and old possibly be attained 

 when the new theory involves fundamentally diflFerent primitive con- 

 cepts? Sometimes very simply indeed. Setting out from the premises 

 of the new theory we may find that, making certain assumptions^ 

 and/or approximations, we obtain certain derivative propositions 

 identifiable with the premises of the older theory. In physical circum- 

 stances that invalidate the assumptions and approximations, the old 

 theory must fail, and is superseded by the new. But, when the physi- 

 cal circumstances are compatible with those assumptions and ap- 

 proximations, the entire pattern of the older theory reappears almost 

 intact, as the limiting form of the new. And that correspondence of- 

 fers something Einstein and Bohr were perhaps the first fully to 

 grasp: a potent new heuristic principle. Hutten comments: 



It is the correspondence principle that shows us how to construct a 

 better and more comprehensive theory, on the basis of a simpler and 

 narrow theory, or of a model. The principle formulates the condition 

 which the new theory must satisfy: there must be an asymptotic 

 agreement between the main formulae of the old and of the new 

 theory. 



In constructing his first theory of the hydrogen atom, Bohr estab- 

 lished the proper mode of quantization by imposing the condition 

 that a relation of classical electrodynamics must appear as the limit- 

 ing case of his own formula. The "scientific revolution" of quantum 

 theory was thus in part achieved by accepting as a principle the 

 evolutionary continuity of scientific theories! 



Perhaps one may regard correspondence as a psychological phe- 

 nomenon. James remarks that "new truth" 



. . . marries old opinion to new fact so as ever to show a minimum of 

 jolt, a maximum of continuity. We hold a theory true just in propor- 

 tion to its success in solving this "problem of maxima and minima." 



But this continuity has also another root, in a logical requirement. 

 In the foregoing chapter we observed that the latest member of a 



