196 THE LIMITATIONS OF SCIENCE 



we generally do, but sometimes with rather an ill 

 humor." 



" The firm determination to submit to experiment is 

 not enough ; there are still dangerous hypotheses ; first, 

 and above all, those which are tacit and unconscious. 

 Since we make them without knowing it, we are power- 

 less to abandon them. Here again, then, is a service 

 that mathematical physics can render us. By the pre- 

 cision that is characteristic of it, it compels us to 

 formulate all the hypotheses that we should make with- 

 out it, but unconsciously." 



It is just here that I think Poincare begins to leave 

 sure ground, and by a confusion of thought and terms 

 he falls into what seems to me an impossible posi- 

 tion. He first stated that a generalization is an hypoth- 

 esis. It is true that every generalization is speculative 

 to the extent that we cannot verify it by experiment 

 with absolute accuracy or in all possible cases. For in- 

 stance, no one supposes we can ever record all the 

 changes of energy which occur in the universe, yet we 

 state with great confidence that energy is conservative. 

 The justification for our belief is simple. All the 

 cases we have measured confirm the law. And this 

 law is of the kind that can be frequently and readily 

 put to the test of experimental verification; until 

 future experiments shall show it to be in error, we 

 have the right to believe the law correct. But hypoth- 

 esis has a wide range of meanings besides that of 



