220 THEORIES AND MODELS 



are reciprocally proportional to the distance between their centers, 

 will make up an elastic fluid the density of which is proportional to 

 the pressure. 



Newton's insight was far too penetrating to leave him deceived about 

 the significance of any such demonstration. He explicitly called at- 

 tention to its status in the following qualifying statement: 



But whether elastic fluids do really consist of particles so repelling 

 each other is a physical question. We have here demonstrated mathe- 

 matically the property of fluids consisting of particles of this kind, 

 that hence [natural] philosophers may take occasion to discuss that 

 question. 



I have italicized the two words making the key distinction, so ob- 

 vious one might think it hardly worth mentioning. But the force of 

 the qualification was entirely lost on many of Newton's successors. 

 Given that gases do conform to Boyle's law, they promptly concluded 

 that Newton had proved the corpuscular nature of gases. This was 

 certainly the opinion of John Dalton, to whose intelligence we owe 

 the creation of what has become the modern atomic theory. 



The line I draw between science and pure mathematics has of 

 course been crossed repeatedly, and in both directions, by such as 

 Archimedes, Newton, Laplace, Gauss, Bessel, Eddington, etc. Or- 

 dinarily, however, the modern scientist need not and does not cross 

 it. In the immense stockpile of fully developed formalisms he usually 

 can find at least one competent to correlate his subject matter. The 

 antecedent explorations of logicians and mathematicians then at 

 once make him master of all the formally "necessary" consequences 

 arising from adoption of any given set of abstract premises. An 

 Einstein, Born, or Heisenberg thus acquires completely worked-out 

 systems of non-Euclidean geometry, matrix algebra, tensor calculus, 

 etc. The extent to which such formalisms have successfully been 

 emptied, or divested, of experiential associations becomes now the 

 measure of the generalized applicability for which they are prized 

 by scientists. Because the formalisms are vacant, we can give them 

 whatever content we please and examine the consequences. We as- 

 sociate concepts having experiential denotations with the abstract 

 terms appearing in formal relations, and in systems of formal rela- 

 tions—and so acquire the potential scientific laws and theories from 



