Abstract
I argue here that a properly Platonic theory of the nature of number is still viable today. By properly Platonic, I mean one consistent with Plato's own theory, with appropriate extensions to take into account subsequent developments in mathematics. At Parmenides 143a-4a the existence of numbers is proven from our capacity to count, whereby I establish as Plato's the theory that numbers are originally ordinal, a sequence of forms differentiated by position. I defend and interpret Aristotle's report of a Platonic distinction between form and mathematical numbers, arguing that mathematical numbers alone are cardinals, by reference to certain non-technical features of a set-theoretical approach and other considerations in philosophy of mathematics. Finally I respond to the objections that such a conception of number was unavailable in antiquity and that this theory is contradicted by Aristotle's report in Metaph . XIII that Platonic numbers are collections of units. I argue that Aristotle reveals his own misinterpretation of the terms in which Plato's theory was expressed.
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DOI 10.1080/096725500341701
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References found in this work BETA

Realism in Mathematics.Penelope MADDY - 1990 - Oxford University Prress.
What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Realism in Mathematics.Shaughan Lavine - 1992 - Journal of Philosophy 89 (6):321-326.
Mathematics Without Foundations.Hilary Putnam - 1967 - Journal of Philosophy 64 (1):5-22.
Philosophy of Mathematics.Paul Benacerraf - 1964 - Englewood Cliffs, N.J., Prentice-Hall.

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Citations of this work BETA

Desire and Reason in Plato's Republic.Hendrik Lorenz - 2004 - Oxford Studies in Ancient Philosophy 27:83-116.

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