176 SCIENCE AND METHOD. 



axis of rotation of solid bodies, which is another 

 imperfect image of the straight Hne ; and lastly, 

 because it is, no doubt, subject to change, so that 

 such and such a line which was straight yesterday 

 will no longer be so to-morrow if some physical cir- 

 cumstance has altered. 



Assume, now, that we succeed in discovering that 

 phosphorus melts not at 44° but at 43'9° centigrade. 

 Shall we conclude that, as phosphorus is by definition 

 that which melts at 44°, this substance that we called 

 phosphorus is not true phosphorus, or, on the contrary, 

 that phosphorus melts at 43 '9°? Here, again, we are 

 free to adopt either definition, and, consequently, either 

 conclusion ; but it would be foolish to adopt the 

 former, because we cannot change the name of a 

 substance every time we add a fresh decimal to its 

 melting-point. 



xni. 



To sum up, Mr. Russell and Mr. Hilbert have both 

 made a great effort, and have both of them written 

 a book full of views that are original, profound, and 

 often very true. These two books furnish us with 

 subject for much thought, and there is much that we 

 can learn from them. Not a few of their results are 

 substantial and destined to survive. 



But to say that they have definitely settled the 

 controversy between Kant and Leibnitz and destroyed 

 the Kantian theory of mathematics is evidently un- 

 true. I do not know whether they actually imagined 

 they had done it, but if they did they were mistaken. 



