692 SCIENCE AND HYPOTHESIS 



It is clear that it would be better to replace it by a less objectionable 

 enunciation, one in which, as philosophers would say, final effects do 

 not seem to be substituted for acting causes. 



Thermo-dynamics. The role of the two fundamental principles of 

 thermo-dynamics becomes daily more important in all branches of 

 natural philosophy. Abandoning the ambitious theories of forty years 

 ago, encumbered as they were with molecular hypotheses, we now try 

 to rest on thermo-dynamics alone the entire edifice of mathematical 

 physics. Will the two principles of Mayer and of Clausius assure to it 

 foundations solid enough to last for some time? We all feel it, but 

 whence does our confidence arise? An eminent physicist said to me 

 one day, apropos of the law of errors : every one stoutly believes it, 

 because mathematicians imagine that it is an effect of observation, and 

 observers imagine that it is a mathematical theorem. And this was 

 for a long time the case with the principle of the conservation of 

 energy. It is no longer the same now. There is no one who does not 

 know that it is an experimental fact. But then who gives us the 

 right of attributing to the principle itself more generality and more 

 precision than to the experiments which have served to demonstrate it ? 

 This is asking, if it is legitimate to generalize, as we do every day, 

 empiric data, and I shall not be so foolhardy as to discuss this ques- 

 tion, after so many philosophers have vainly tried to solve it. One 

 thing alone is certain. If this permission were refused to us, science 

 could not exist; or at least would be reduced to a kind of inventory, to 

 the ascertaining of isolated facts. It would no longer be to us of 

 any value, since it could not satisfy our need of order and harmony, 

 and because it would be at the same time incapable of prediction. As 

 the circumstances which have preceded any fact whatever will never 

 again, in all probability, be simultaneously reproduced, we already 

 require a first generalization to predict whether the fact will be 

 renewed as soon as the least of these circumstances is changed. But 

 every proposition may be generalized in an infinite number of ways. 

 Among all possible generalizations we must choose, and we cannot but 

 choose the simplest. We are therefore led to adopt the same course 

 as if a simple law were, other things being equal, more probable than 

 a complex law. A century ago it was frankly confessed and pro- 

 claimed abroad that Nature loves simplicity; but Nature has proved 

 the contrary since then on more than one occasion. We no longer con- 

 fess this tendency, and we only keep of it what is indispensable, so 

 that science may not become impossible. In formulating a general, 

 simple, and formal law, based on a comparatively small number of 

 not altogether consistent experiments, we have only obeyed a neces- 

 sity from which the human mind cannot free itself. But there is 

 something more, and that is why I dwell on this topic. No one doubts 

 that Mayer's principle is not called upon to survive all the particular 



