THEORIES AND MODELS 235 



another. "Mass" is perhaps measured, relative to a standard, with an 

 equal-arm balance; and "force" is measured with this same instru- 

 ment or with elastic systems that obey Hooke's law. Here then New- 

 ton's system gains its experiential relevance, as does Euclid's, in the 

 simplest way imaginable: through the attachment of denotations to 

 its primitive concepts, and thence automatically to all derivative 

 terms and relations. 



For his primitive concepts Euclid furnished definitions wholly in- 

 sufficient to establish the working denotations. Newton did exactly 

 the same. The inadequacy of his definitions of absolute time and space 

 was recognized long before relativity theory came to underline that 

 inadequacy. Mass he defines as the product of density and volume— 

 which is an obvious and immediate circularity since we need the 

 concept of mass to define density. We have then no denotation for 

 mass and— since Newton's definition of force involves the concept of 

 mass— that definition equally fails to establish a semantic rule. How 

 then are the denotations of these concepts established? 



Euclid's explicit definitions do not themselves supply denotations, 

 but they are sufficiently suggesti\'e to lead us toward models from 

 which we draw the requisite denotations. Newton's definitions func- 

 tion in exactly the same way. \A^e may, for example, conceive space 

 and time in the sensorium of divinity as somewhat analogous to our 

 own awareness of visual space and subjective time. Force we may 

 concei\ e as somehow related to the muscular. eflFort we experience 

 from both the producing and the receiving ends. And mass we may 

 conceive, as did Lavoisier, Laplace, and Newton himself, as some- 

 thing to do with the "quantity of matter." Grasping these ideas, we 

 are led to the working denotations indicated above. We read New- 

 ton's definitions intuitively, as we do Euclid's, and extract something 

 they do not themselves contain. 



Why didn't Newton state the working denotations explicidy, as 

 semantic rules? Simply because, as has been emphasized repeatedly, 

 amj rigid specifications of the denotations of concepts must invariably 

 restrict their applicability. This point emerges in high relief from a 

 very painstaking analysis that brings Braithwaite to the following 

 conclusion: 



It is only in theories which are not intended to have any function 

 except that of systematizing empirical generalizations already known 

 that the theoretical terms can harmlessly be explicitly defined. A the- 



