vers in the Ideas, this difficulty misses them; for they construct spatial magnitudes out of matter and number,Ukraina Landslagsdrakt, lines out of the number planes doubtless out of solids out of or they use other numbers,CG Menn Manitoba Jakke, which makes no difference. But will these magnitudes be Ideas,Karim Benzema Drakt, or what is their manner of existence,Duvetica Bunda, and what do they contribute to things? These contribute nothing, as the objects of mathematics contribute nothing. But not even is any theorem true of them,UGG Classic Short Czyścibut 5825, 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,Dame Moncler Gueran, are wrong in this way, 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,Air Jordan Retro 7 Damskie, 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,Belstaff Muži Bunda, he will be making his elements rather many. And if the principle of each of the two kinds of number is a 1,Air Jordan Retro 11 Męskie, unity will be something common to these, and we must inquire how the one is these many things,Wayne Rooney Drakt, 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, and we seem to see in it Simonides ‘long rigmarole’ for the long rigmarole comes into play, like those of slaves, 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,Duvetica Muži Eracle, 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, 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,Sunburst Tall Czyścibut 5359, must belong to them before they are equalized. If they had always been e
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