vers in the Ideas, this difficulty misses them; for they construct spatial magnitudes out of matter and number,Dame Moncler Melina, lines out of the number planes doubtless out of solids out of or they use other numbers,Wasp, which makes no difference. But will these magnitudes be Ideas, or what is their manner of existence, and what do they contribute to things? These contribute nothing,Maillot Hummels Pas Cher, as the objects of mathematics contribute nothing. But not even is any theorem true of them,Ralph Lauren Långärmad Polos, unless we want to change the objects of mathematics and invent doctrines of our own. But it is not hard to assume any random hypotheses and spin out a long string of conclusions. These thinkers, then, are wrong in this way,Dame Moncler Safran Norge Salg, in wanting to unite the objects of mathematics with the Ideas. And those who first posited two kinds of number, that of the Forms and that which is mathematical,Menn Moncler Edward Norge Salg, neither have said nor can say how mathematical number is to exist and of what it is to consist. For they place it between ideal and sensible number. If (i) it consists of the great and small, it will be the same as the other-ideal-number (he makes spatial magnitudes out of some other small and great). And if (ii) he names some other element,Maillot Neymar JR Pas Cher, he will be making his elements rather many. And if the principle of each of the two kinds of number is a 1,PJS Dameklær Adirondack Strøk, unity will be something common to these,Moncler Polo Skjorte, and we must inquire how the one is these many things, while at the same time number, according to him, cannot be generated except from one and an indefinite dyad.
All this is absurd, and conflicts both with itself and with the probabilities,Maillot Dempsey Pas Cher, and we seem to see in it Simonides ‘long rigmarole’ for the long rigmarole comes into play, like those of slaves,CG Dame Whistler Parka Norge Salg, when men have nothing sound to say. And the very elements-the great and the small-seem to cry out against the violence that is done to them; for they cannot in any way generate numbers other than those got from 1 by doubling.
It is strange also to attribute generation to things that are eternal, or rather this is one of the things that are impossible. There need be no doubt whether the Pythagoreans attribute generation to them or not; for they say plainly that when the one had been constructed, whether out of planes or of surface or of seed or of elements which they cannot express, immediately the nearest part of the unlimited began to be constrained and limited by the limit. But since they are constructing a world and wish to speak the language of natural science,Dame Moncler Safran, it is fair to make some examination of their physical theorics, but to let them off from the present inquiry; for we are investigating the principles at work in unchangeable things, so that it is numbers of this kind whose genesis we must study.
Book XIV Chapter 4
These thinkers say there is no generation of the odd number, which evidently implies that there is generation of the even; and some present the even as produced first from unequals-the great and the small-when these are equalized. The inequality, then, must belong to them before they are equalized. If they had always been e
相关的主题文章：
http://www.gymfan.com/board/step.cgi
http://www13.plala.or.jp/white_roots/gwbbs/gwbbs.cgi
http://www.matsue-yado.com/otoku/clip.cgi |
