Chap. II. ANTIENT METAPHYSICS. 325 



taught that kind of arithmetic we call fradlons, but which was un- 

 known to the antients, and is truly the arithmetic of ratios. 



It will be faid, that the idea of number^ thus abftra6ted from all fen- 

 fiblc things, or, even a general triangle, cannot be apprehended by the 

 fenfe, or pidlured in the imagination. And this, no doubt, is true ; 

 and if, like the brutes, we had no other faculties except fenfe and ima- 

 gination, like them, too, we fhould have no ideas : But we have ano- 

 ther faculty, and that a much fuperior one, I mean intellect : And 

 the fundamental error of thofe philofophers, and which leads, as I 

 have fhown elfewhere *, to the moft dangerous confequences, is their 

 confounding intclledl with fenfe or imagination. The confequence of 

 whlcbis, no doubt, what the author of the Eflays maintains, that ideas 

 and fenfations differ only in the degree of impreffion they make upon 

 the mind, not in kind. 



That, without ideas, there can be no fcience, will be evident from 

 the follov^'Ing confideratlon, that all material things are perpetually in 

 motion of one kind or another, and therefore conflantly changing. 

 This v»'as known to the philofophers of Greece, as early as the days of 

 Heraclitus, who faid that every thing was in a perpetual flux, and con- 

 tinually paffing, like a river : So that, by our fenfes, wc never can 

 apprehend the fame thing twice, any more than we can i)athe twice 

 in the fame river '|\ And this philofophy of his was adopted, as Ari- 

 ftotle tells us J, by Plato, who every where fpeaks of material things 



as 



* Page 142 — 200. 



fCratylus, a follower of Heraclitus, found fault with his maftcr, becaufe he faid that 

 one could not bathe twice in the fame river •, for, fays he, he cannot bathe once in 

 the fame river. And he carried the matter fo far, at laft, as to aflirm nothing, bat 

 only to point -with his finger, things being conftantly in motion, and nothing ftand- 

 ing flill, fo long as that any thing can be aflirmed of them. Arijiot. lib. 4. Metaph. 

 cap. 5. p. 378. edit. Da Fa/. And, no doubt, this is the necellary confequence of 

 the do£trine of Heraclitus, and every fyftem of materialifm. 



J Metaph. lib. i. cap. 6. See what I have further faid upon this fubjedl, Orig. and 

 Prog, of La))g. vol; I. book i. cap. 9. p. 114. 2d edition. 



