222 THEORIES AND MODELS 



ard condition. In "data," but not in data, a significant small-whole- 

 number relation is then easily brought to light. Last, and only mar- 

 ginally distinct, is (4) the abstract analysis yielding "data" unob- 

 served but not in principle unobservable. Thus, for example, from 

 measurements of motion along planes set at various angles to the 

 horizontal, Galileo extrapolates to the limiting case of a plane set at 

 90° to the horizontal. The acceleration calculated for this case he 

 equates with that of the "free fall" he was unable to study directly. 

 We find this "datum" a crude but not unreasonable approximation 

 to the datum our superior experimental tools bring within easy reach. 

 The formal disciplines lend the scientist a sujiport clearly neces- 

 sary and, equally clearly, insufFicient. As earlier implied (p. 178), 

 every scientific application of formal analysis has behind it (and 

 sometimes almost concealed by it) irreducibly physical ideas. No 

 formal argument but a physical hypothesis emboldens Galileo to ex- 

 trapolate through the discontinuity unavoidable in passing from ro- 

 tary motion along a plane to the non-rotary motion of "free fall." The 

 formal analysis conducted by Cannizzaro is inspired and directed 

 by a physical concept of corpuscularity. We cannot arrive at Boyle's 

 law without the physical concepts of pressure and volume, or at 

 Kepler's laws without the concept of heliocentric orbit. Whence 

 derive these physical concepts? From "induction"? 



INDUCTION 



What we may mean by induction is not a little obscure. Is it simply 

 the process by which we pass from particulars to the general? But 

 the conditioned reflex already manifests capacity for such "induc- 

 tion." Trained by repeated electric shocks to turn to left and not to 

 right whenever two tracks are open to him, has the earthworm then 

 "reasoned inductively"? Surely the grandiose concept of "scientific 

 induction" must involve more than straightforward generalization 

 based on the principle of continuity. 



By familiar processes of deduction we reason our way from theo- 

 retical postulates to general colligative relations accommodated in 

 that theory, and, further, to particular predictions drawn (for par- 

 ticular circumstances ) from those relations. I think that induction is 

 for most of us the hypothetical inverse process by which we reason 

 our way from particular observations to general relations, and, fur- 

 ther, to the postulates of the theory accommodating those relations. 



