SCIENCE (and common SENSE ) 49 



Galileo worked do not merely relate objects but, in a sense, create 

 order. Consider that, in his experiments, Galileo could not observe 

 "velocity"; he could observe only that a moving body occupies vari- 

 ous spatial positions at various times. The concept of velocity sug- 

 gests a particular co-ordination of these observations. We divide "dis- 

 tances tra\'eled" by "elapsed times." The quotients so extracted from 

 the actual observations are what we call "velocities." The virtue of 

 such indirection becomes manifest if, for example, we encounter a 

 case of uniform motion: underlying all the changes of position with 

 time we find an unchanging "velocity," in the apparent chaos of kine- 

 matic experience we find an element of identity. 



Suppose we find no such case of uniform motion. We may then 

 seek through still more abstract concepts for the elusive element of 

 identity we hope and expect to find underlying all change. We can 

 turn to the subtle concept of "acceleration." Accelerations we may 

 extract from the elapsed times and the previously calculated veloci- 

 ties. And in cases of free fall Galileo's intuition finds its triumph. 

 Underlying the changing times and positions of falling bodies gen- 

 erally, there is an unchanging acceleration. Thus we have found not 

 merely order but a genuine element of identity where common sense 

 finds none. Common sense fails here because— no prolific constructor 

 of new concepts— it is most unlikely to create quality-concepts re- 

 ferring to no particular observables but to special, superficially mys- 

 terious combinations thereof. Scientific quality-concepts involving 

 such combinations are of course in no way peculiar to kinematics. 

 Thus the concept density teaches us to see— underlying all our experi- 

 ences of weight and volume with a given substance— a "something 

 constant": the quotients of weights divided by volumes. Such dis- 

 coveries, investing us with new predictive powers, we express in 

 colligative relations. 



COLLIGATIVE RELATIONS ("LAWS") 



The relations we can find and express depend on the indicative con- 

 cepts we devise and deploy. Science here enjoys a superiority quali- 

 tative as well as quantitative. The abundant stock of scientific con- 

 cepts makes possible specialization of function; precision of denota- 

 tion need not be so deeply compromised by the search for general 

 applicability. In science we thus arrive at colligative relations ap- 

 parently so far superior to those of common sense we regard them as 



