COLLIGATR^ RELATIONS AND SCIENTIFIC LAWS 123 



Rarely would one find in practice any such systematic sequence of 

 explici!: steps. Ordinarily these analyses are conducted unreflectingly, 

 with implicit assumptions. But, however they are made, all these 

 steps must be taken before Boyle's law can be pronounced. We may 

 then wish to reconsider the major discontinuity, in the sequence 

 fact-law-theory, that is commonly alleged to fall between law ("a 

 description") and theory ("an explanation"). Belief in any such dis- 

 continuity founders when, reviewing the progression leading up to 

 Boyle's law, one recognizes the extreme difficulty (if not utter im- 

 possibility) of detecting where observation ends and theoretical 

 manipulation begins— where discovered fact gives way to im^ented 

 abstraction. And we may indeed say of scientific laws generally what 

 Royce has said of scientific theories— that they are 



. . . neither unbiased reports of the actual constitution of an external 

 reality, nor yet arbitrary constructions of fancy. . . . They are con- 

 structions molded, but not predetermined in their details, by ex- 

 perience. We report facts; we let the facts speak; but we, as we in- 

 vestigate, in the popular phrase, "talk back" to the facts. We inteipret 

 as well as report. 



DENOTATIONS: IF INDIRECT, YET SOLIDLY ESTABLISHED 



For its functions as a predictive device, a colligative relation must, 

 we saw earlier, involve only concepts having reasonably clean-cut 

 denotations. Let us now assure ourselves that the situation remains 

 unaltered even when the concepts are notably abstract, and their 

 denotations are established only indirectly, with the aid of an 

 elaborate computation apparently irreducibly "theoretical." Consider, 

 as a representative example, a combined form of Kepler's first and 

 second laws: a planet traverses an elliptic orbit, with the sun at one 

 focus, at such a rate that the radial line sweeps out equal areas in 

 equal times. We readily understand that a "planet" is a presumptive 

 "body" seen as a point of light that moves, more or less irregularly, 

 against the background of the "fixed stars." But now what are we to 

 take as the denotations of "sun-focused elliptic orbits," etc.? A more 

 pedestrian case will point the way. 



Grasping the appropriate conceptual denotations, we all combine 

 certain observable terms in certain ways whenever we measure a 

 "pressure." Just so with "sun-focused elliptic orbits." On the basis of 

 various astronomical obser^^ations, we plot on paper an orbit for the 



