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Plato’s Dialectic of Numbers

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jordaens-prometheus

???? ??? ??? ????????? ?????, ?? ?? ???????????? ????, ????? ?? ???? ?????? ??? ????? ????????? ??? ???????? ???? ????: ??? ?? ??? ???????, ?????????? ???? ??? ???????? ???? ?????????, ?????? ????? ?????????, ?? ?? ???? ??? ??? ?????? ????? ??? ??? ????????? ?????, ????? ?? ??? ???????? ?? ?????? ???????? ???????. ???? ??? ???? ?????? ???? ??????????????? ??? ???? ????? ???? ?????? ???????? ???????? ??????–???????? ??? ???????– ??? ??? ???????????, ???? ???? ???, ?? ??? ????, ???????, ?? ?? ??, ????? ? ???? ????? ???????, ??? ??? ?? ??????? ??????? ????? ???????, ???????? ?? ?? ???’ ????? ?? ?? ??? ?? ??? ????? ??? ?????? ???? ????? ??? ???, ???? ??? ?????: ??? ?? ??? ??????? ????? ???? ?? ?????? ?? ?????????? ???? ?? ??? ??? ??????? ????? ????? ?????? ??? ?????? ??? ??????? ?? ??? ??? ????, ???? ?’ ??? ?? ?? ??????? ??? ?????? ??? ?? ??????? ??????? ??????? ???. ?? ??? ??? ????, ???? ?????, ????? ???? ????????? ??????? ??? ????????? ??? ????????? ????????: ?? ?? ??? ??? ???????? ????? ?? ???, ???? ?? ??????, ??? ????? ?????? ??? ?????????? ??????? ??? ???????, ???? ?? ?? ?? ?????? ?????, ?? ?? ???? ?????? ????????–??? ????????????? ?? ?? ??????????? ????? ??? ?? ????????? ???? ????????? ???? ???????? ???? ??????.

A gift of gods to men, as I believe, was tossed down from some divine source through the agency of a Prometheus together with a gleaming fire; and the ancients, who were better than we and lived nearer the gods, handed down the tradition that all the things which are ever said to exist are sprung from one and many and have inherent in them the finite and the infinite. This being the way in which these things are arranged, we must always assume that there is in every case one idea of everything and must look for it–for we shall find that it is there–and if we get a grasp of this, we must look next for two, if there be two, and if not, for three or some other number; and again we must treat each of those units in the same way, until we can see not only that the original unit is one and many and infinite, but just how many it is. And we must not apply the idea of infinite to plurality until we have a view of its whole number between infinity and one; then, and not before, we may let each unit of everything pass on unhindered into infinity. The gods, then, as I said, handed down to us this mode of investigating, learning, and teaching one another; but the wise men of the present day make the one and the many too quickly or too slowly, in haphazard fashion, and they put infinity immediately after unity; they disregard all that lies between them, and this it is which distinguishes between the dialectic and the disputatious methods of discussion.

Plato (??????), Philebus (???????) 16c-17a (ca. 350 BCE)(J. Burnet transl. 1903)

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