56 SCIENCE (and common sense) 



sophistication— important though all of these may be. The crucial 

 diflFerence is, I think, simply this: beyond investing us with predic- 

 tive powers, the scientific relation lends itself to that fourth stage of 

 organization sought by science but inaccessible, and quite unknown, 

 to common sense. 



^^'ith Poincare, let us imagine our science systematically built up 

 from relations, as a house is with stones. Common sense provides us 

 with a heap of stones; natural history with heaps of stones carefully 

 assorted according to size, shape, texture, etc. But only in the edifice 

 of science do we have a coherent structure in which the individual 

 stones are bound together in an orderly fashion by the mortar of logic 

 and mathematics. We hope to learn to know the stone by recogniz- 

 ing its position in the house, to master the individual relation by 

 seeing it in the larger context of a postulational system in which it 

 appears as logically derivative. So hoping, we demand that scientific 

 laws lend themselves to such seeing, demand that they constitute 

 subjects suited to the thoughts of men seeking a thorough- going ra- 

 tionalization of experience. The superficially absurd abstractions like 

 the ideal lever here come fully into their own. 



We think of science as based on our experience of the world, and 

 so it is. Yet sometimes we seem to ignore that experience, even to 

 deny it. Rather than pondering our real experience of real lever sys- 

 tems we set ourselves to contemplate fictions— an ideal lever and the 

 ideal law thereof. In so doing we make an immense gain. The raw 

 phenomena are complicated and variable; the ideal law, which only 

 sketches them, offers an ideally simple statement about "ideal" phe- 

 nomena. Considering the colligative relation, we can forget for the 

 time being all the "imperfections" reflected in our actual experience 

 —confused by the only partially determinate effects of a multitude 

 of "secondary factors"— and take as subject a "pure" relation. We be- 

 gin the difficult task of theoretic construction with ideally simple 

 entities and relations— with readily manipulable fictions represented 

 in terse, abstract, often symbolic form. Such entities are the partless 

 points and widthless lines of geometry, the mass-points (and ideal 

 lever) of mechanics, the ideal gas of pneumatics, the ideal solutions 

 of chemistry— all of them represented by ideal laws. Setting out from 

 these, we may be able to arrive at a conception of some very general 

 postulates from which "follow" a multitude of colligative relations. 



