in GEOMETRY AND INDUCTION 227 



to-morrow, no matter when to-morrow may be. What 

 is there at the base of this belief ? Notice that the belief 

 is more or less assured, according as the case may be, but 

 that it is forced upon the mind as an absolute necessity 

 when the microcosm considered contains only magni 

 tudes. If two numbers be given, I am not free to 

 choose their difference. If two sides of a triangle and 

 the contained angle are given, the third side arises of 

 itself and the triangle completes itself automatically. 

 I can, it matters not where and it matters not when, 

 trace the same two sides containing the same angle : it 

 is evident that the new triangles so formed can be 

 superposed on the first, and that consequently the same 

 third side will come to complete the system. Now, if 

 my certitude is perfect in the case in which I reason on 

 pure space determinations, must I not suppose that, in 

 the other cases, the certitude is greater the nearer it 

 approaches this extreme case ? Indeed, may it not be 

 the limiting case which is seen through all the others 

 and which colours them, accordingly as they are more or 

 less transparent, with a more or less pronounced tinge 

 of geometrical necessity ? 1 In fact, when I say that 

 the water on the fire will boil to-day as it did yesterday, 

 and that this is an absolute necessity, I feel vaguely 

 that my imagination is placing the stove of yesterday 

 on that of to-day, kettle on kettle, water on water, 

 duration on duration, and it seems then that the rest 

 must coincide also, for the same reason that, when two 

 triangles are superposed and two of their sides coincide, 

 their third sides coincide also. But my imagination 

 acts thus only because it shuts its eyes to two essential 

 points. For the system of to-day actually to be 



1 We have dwelt on this point in a former work. See the Essai sur / 

 donnfes imm/diates de la conscience, Paris, 1889, pp. 155-160. 



