lunes, 17 de marzo de 2014

Plato´s philosophy of mathematics de Paul Pritchard

Págs 59-60: Sobre distintintas concepciones de número en la antigüedad

   Ecquis enim cum audit numerum 6, non statim cogitat sex unitates? Quid ergo necesse  est sex unitates dicere, cum sufficiat dicere, sex?
   Does anyone, on hearing number six, not thing inmediatly of six units? So why is it necessary to say six units, when it is enaough to say "six"?

    For Diophantus, "six units" is an arithmos; "six" does not denote anything in being at all.

   From the point of view of Plato´s theory of Ideas both the common Greek and Pythagorean conception of number appear very imperfect. Since numbers are predicated of many particular collections of objects, the number themselves must- according to the theory of Ideas- be certain ideal entities above those collections. But the pythagorean view reduces numbers to material instances of them: it identifies the number 1 with one point, the number 2 with two points, and so on. Although Plato was probably strongly influenced by the Pythagorean doctrine, obviously he could not accept it as it stands. The common Greek definition of number as "plurality of units" tells us merely of what numbers are predicated, not what numbers are in themselves. Plato cannot have been satisfied with it.

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