vers in the Ideas,Duvetica Muži Leonida, this difficulty misses them; for they construct spatial magnitudes out of matter and number, lines out of the number planes doubtless out of solids out of or they use other numbers,Boston Celtics Drakter, 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,Canada Goose Hybridge Lite Bunda, as the objects of mathematics contribute nothing. But not even is any theorem true of them, 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,Leicester City Drakt, 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, 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,Canada Goose Livigno Parka, he will be making his elements rather many. And if the principle of each of the two kinds of number is a 1,Moncler Pyrole, unity will be something common to these, and we must inquire how the one is these many things, while at the same time number, according to him,Boca Juniors Drakt, cannot be generated except from one and an indefinite dyad.
All this is absurd, and conflicts both with itself and with the probabilities,Dirk Nowitzki Drakter, 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, whether out of planes or of surface or of seed or of elements which they cannot express,Tmavý Stone, 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,Parajumpers Damskie Denali, it is fair to make some examination of their physical theorics,Golden State Warriors Drakter, but to let them off from the present inquiry; for we are investigating the principles at work in unchangeable things,Ženy Barbour International Bunda, 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
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