54 SCIENCE (and common sense) 



results are not perfectly represented by the ideally simple law, we 

 concei\^e an ideal lever to which, we say, the law would perfectly 

 apply. The practical situation remains wholly unaltered: the intel- 

 lectual thrust is wholly diflFerent. The man of common sense matches 

 law and observation by holding that the ideal law of the lever is only 

 approximate— only a rough but useful description of actual observa- 

 tions. The scientist matches law and obsers^ation by holding that the 

 law of the ideal lever is r/gorow5— adding only that actual observa- 

 tions with real levers are only more or less imperfect approximations 

 to what we would observe were there in the real world ideal levers 

 with which to work. This was essentially the procedure adopted by 

 Archimedes. It represents an immense abstraction. 



Denotation. For all its abstractness, the law of the lever remains a 

 colligative relation: its statement involves only concepts with reason- 

 ably clear denotations. In "weight" we may seem to deal with an 

 adjectival quality-concept, "weighty," dangerously and absurdly mas- 

 queraded as a noun— a "real quality." And "distance" seems an ab- 

 straction equally extreme. But unlike the philosophic "qualities," our 

 concepts do have denotations. "Weight" is something crudely indi- 

 cated by muscular effort and, more precisely, by measurement with 

 an equal-arm balance; "distance" is something given crudely by 

 visual inspection and, more precisely, by measurement with a meter 

 stick. 



The instruments somewhat sharpen and clarify the conceptLial de- 

 notations, but there remain major problems they do not even begin 

 to solve. This is nowhere clearer than in the matter of our concept of 

 "lever." The ideal lever, to which alone the ideal law applies rigor- 

 ously, exists only in our minds. We might embark on elaborate speci- 

 fications of certain particular "levers" we have found to be adequate 

 approximations to the ideal. Yet we do not; only by foregoing such 

 specifications do we first gain power to make predictions about sys- 

 tems substantially different from those with which we have already 

 worked. Having in mind the ideal lever— knowing what we're looking 

 for— we can discern lever action in systems in which the presence of 

 any Xevex is far from evident. We come thereby to make excellent 

 predictions about the performance of such devices as wheel (or 

 crank) and axle, compound pulleys, and the like. As always, such 

 generality is purchased only at cost to reliability. Experience alone 



