David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
International Journal of Philosophical Studies 8 (1):23 – 45 (2000)
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.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
Penelope Maddy (1990). Realism in Mathematics. Oxford University Prress.
Paul Benacerraf (1965). What Numbers Could Not Be. Philosophical Review 74 (1):47-73.
Hilary Putnam (1967). Mathematics Without Foundations. Journal of Philosophy 64 (1):5-22.
John J. Cleary (1995). Aristotle and Mathematics: Aporetic Method in Cosmology and Metaphysics. E.J. Brill.
W. D. Ross (1951/1976). Plato's Theory of Ideas. Greenwood Press.
Citations of this work BETA
No citations found.
Similar books and articles
David Robjant (2012). The Earthy Realism of Plato's Metaphysics, Or: What Shall We Do with Iris Murdoch? Philosophical Investigations 35 (1):43-67.
Jeremy Gwiazda (2012). On Infinite Number and Distance. Constructivist Foundations 7 (2):126-130.
Syrianus (2006). On Aristotle's "Metaphysics 13-14". Cornell University Press.
A. E. Taylor (1976/1968). Philosophical Studies. Arno Press.
Zvonimir Šikić (1996). What Are Numbers? International Studies in the Philosophy of Science 10 (2):159-171.
Zvonimir Šikić (1996). What Are Numbers? International Studies in the Philosophy of Science 10 (2):159 – 171.
Svetla Slaveva-Griffin (2009). Plotinus on Number. Oxford University Press.
Added to index2009-01-28
Total downloads30 ( #128,606 of 1,793,258 )
Recent downloads (6 months)1 ( #463,804 of 1,793,258 )
How can I increase my downloads?