TEE VALUE OF SCIENCE 447 



shades, in number infinite, that my impressions might cover. When I 

 say : It grows dark, that well expresses the impressions I feel in being 

 present at an eclipse; but even in obscurity a multitude of shades 

 could be imagined, and if, instead of that actually realized, had hap- 

 pened a slightly different shade, yet I should still have enunciated this 

 other fact by saying: It grows dark. 



Second remark : even at the second stage, the enunciation of a fact 

 can only be true or false. This is not so of any proposition; if this 

 proposition is the enunciation of a convention, it can not be said that 

 this enunciation is true, in the proper sense of the word, since it could 

 not be true apart from me and is true only because I wish it to be. 



When, for instance, I say the unit for length is the meter, this is 

 a decree that I promulgate, it is not something ascertained which 

 forces itself upon me. It is the same, as I think I have elsewhere 

 shown, when it is a question for example of Euclid's postulate. 



When I am asked: Is it growing dark? I always know whether I 

 ought to reply yes or no. Although an infinity of possible facts may be 

 susceptible of this same enunciation: it grows dark, I shall always 

 know whether the fact realized belongs or does not belong among those 

 which answer to this enunciation. Facts are classed in categories, and 

 if I am asked whether the fact that I ascertain belongs or does not 

 belong in such a category, I shall not hesitate. 



Doubtless this classification is sufficiently arbitrary to leave a large 

 part to man's freedom or caprice. In a word, this classification is a 

 convention. This convention being given, if I am asked: Is such a 

 fact true ? I shall always know what to answer, and my reply will be 

 imposed upon me by the witness of my senses. 



If, therefore, during an eclipse, it is asked: Is it growing dark? 

 All the world will answer yes. Doubtless those speaking a language 

 where bright was called dark, and dark bright, would answer no. But 

 of what importance is that ? 



In the same way, in mathematics, when I have laid down the 

 definitions, and the postulates which are conventions, a theorem hence- 

 forth can only be true or false. But to answer the question: Is this 

 theorem true? It is no longer to the witness of my senses that I 

 shall have recourse, but to reasoning. 



A statement of fact is always verifiable, and for the verification we 

 have recourse either to the witness of our senses, or to the memory 

 of this witness. This is properly what characterizes a fact. If you 

 put the question to me : Is such a fact true ? I shall begin by asking 

 you, if there is occasion, to state precisely the conventions, by asking 

 you, in other words, what language you have spoken; then once 

 settled on this point, I shall interrogate my senses and shall answer 

 yes or no. But it will be my senses that will have made answer, it 



