Chap. VIIL ANTIENT METAPHYSICS. 451 



ged to be converfant with the pure ideal form, altogether unafTilled 

 by the fenfes. 



And yet, however remote numbers may be from fenfe and fenfible 

 objeds, it is certain that the knowledge of them was the firft thing 

 like fcience among men. The reafon of which is, that men could 

 not live together in fociety, nor carry on any common bufmefs, either 

 for their fuftentatlon, or for their defence, without the ufe of num- 

 bers *. Now, necejfity^ according to the common faying, is the mother 

 of invention ; and therefore it is not to be wondered, that fo urgent a 

 neceiTuy produced fo early even thefe mod abftra6t ideas of numbers, 

 in which they were fo far affiled by the fenfes, that whereas other 

 ideas are abitradted only from particular fenfes, fuch as our ideas of 

 vifible objeds trom the fight, of audible objeds from the hearing, the 

 idea of nu nber is furnilhed by every fenfe ; for we diftinguiih one^ 

 tivo; three, not only in what we fee or hear, but in what we touch, 

 taile, and fmell. And further, we have the idea of it from the con- 

 fcioulnefs of what pafTes in our own minds ; for we know that we 

 have different thoughts, in order one after another, and which, there- 

 fore, we can count. 



Thus, I have endeavoured to fhow in what fenfe geom.etry is a 

 hypothetical fcience ; and that even arithmetic, though a more ab- 

 ftrad fcience than geometry, is hypothetical, in fo far as it fuppofes 

 the exiftence of things to be numbered. 



L 1 1 2 In 



• It is well obferved by Plato, de Republica, lib. 7. p. 697. edit. Ficiniy that it was a 

 moft abfurd fiaion of the tragic poets in Athens, that Palamedes, at the fiege cf IVoy, 

 invented numbers, and taught the Greeks to count their army and their fleet • as if it 

 had been poflible that the Greeks were fo far advanced in the arts of life, as to have 

 government, religion, and navigation, and to carry on fo great a war on the other fide 

 of the fta, without the ufe of numbers. « What a ridiculous general,' fays Plato, 

 « would Agamemnon have been, if he had not known how many legs or arms he 

 • had !' 



