524 POPULAR SCIENCE MONTHLY 



THE VALUE OF SCIENCE 



By m. h. poincare 



MEMBER OF THE INSTITUTE OF FRANCE 



4. 'Nominalism' and 'the Universal Invariant' 



IF from facts we pass to laws, it is clear that the part of the free ac- 

 tivity of the scientist will become much greater. But did not M. 

 LeKoy make it still too great ? This is what we are about to examine. 



Kecall first the examples he has given. When I say: Phosphorus 

 melts at 44°, I think I am enunciating a law; in reality it is just the 

 definition of phosphorus; if one should discover a body which, pos- 

 sessing otherwise all the properties of phosphorus, did not melt at 44°, 

 we should give it another name, that is all, and the law would remain 

 true. 



Just so when I say: Heavy bodies falling freely pass over spaces 

 proportional to the squares of the times, I only give the definition of 

 free fall. Whenever the condition shall not be fulfilled, I shall say 

 that the fall is not free, so that the law will never be wrong. 



It is clear that if laws were reduced to that, they could not serve 

 in prediction; then they would be good for nothing, either as means 

 of knowledge, or as principle of action. 



When I say: Phosphorus melts at 44°, I mean by that: All bodies 

 possessing such or such a property (to wit, all the properties of phos- 

 phorus, save fusing-point) fuse at 44°. So understood, my proposi- 

 tion is indeed a law, and this law may be useful to me, because if I 

 meet a body possessing these properties I shall be able to predict that 

 it will fuse at 44°. 



Doubtless the law may be found to be false. Then we shall read 

 in the treatises on chemistry : " There are two bodies which chemists 

 long confounded under the name of phosphorus ; these two bodies differ 

 only by their points of fusion." That would evidently not be the 

 first time for chemists to attain to the separation of two bodies they 

 were at first not able to distinguish; such, for example, are neodymium 

 and praseodymium, long confounded under the name of didymium. 



I do not think the chemists much fear that a like mischance will 

 ever happen to phosphorus. And if, to suppose the impossible, it 

 should happen, the two bodies would probably not have identically the 

 same density, identically the same specific heat, etc., so that, after 

 having determined with care the density, for instance, one could still 

 foresee the fusion point. 



