

On the Fundamental Principles of Mathematics. 179 



[It might be true, in so far as we can discern, that heavy bodies 



should have been so constituted as in every case, to fall to the 



earth in an arc of a circle, or any other given curve. It is a fact 



that heavy bodies, falling freely, always fall to the earth in straight 

 lines. 



Glass might, perhaps, be so constituted under a new arrange- 

 ment of things, that every known liquid would dissolve it ; and 

 this, without ceasing to be essentially what it now is. As things 

 are now constituted, scarcely one or two of the known liquids 

 will touch it. 



In Metaphysics, moreover, one of the primary inquiries is 

 not, whether it be s opposable that man should be endowed with 

 such faculties as reason, memory, &c; but whether he in fact 

 possesses them.] 



Not to multiply examples, but recapitulating the characteristics 

 already mentioned, we observe, that 



That is true in Mathematics, which, under the existing system 

 of things, is supposable — That is true in Physics and (with some 

 restrictions) in Metaphysics, which has been permitted to exist. 



That is true, in matters of Taste, which is consistent with the 

 laws of beauty founded upon the relations of things actual — and 

 that is true in Morals (in the highest and best sense, in which 

 *t is good); — that is true, in this sense, which is consistent with 

 what is to be found in the great source of all good. Or in 

 general — due regard being had to its object — it may be asserted, 

 that it is the perfect consistency with that which may be, or that 

 which is, or that which ought to be, that constitutes the great 

 characteristic feature of truth. 



of Mathematical Research 



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This is most manifestly true with regard to number, length, 

 surface, capacity or volume, &c. For there are no such things 

 as 2. 3 ? 7^ £ c ^ separately considered; nor can length, breadth, 

 thickness, &c, exist apart from the things to which they belong, 

 but only that room for them, which is to be found in space. 



Thus also, mechanical force, motion or (in its qualified form) 

 velocity, rest, time, &C, in so far as we have to do with them. 



f & 



ev en the earth's orbit no where exists definitely in space ; though, 

 heing a di s t ur bed ellipse, of known dimensions, &c, it may 

 he accurately prescribed. 



(3.) Upon the fundamental fact, thus exhibited, depends the 

 ^curacy of mathematical reasoning. For, the relations of things 

 w ith which it has to do, admit of being accurately ascertained 

 and defined ; which can by no means be always asserted of the 



