Banner Portal
Aristotle’s argument from universal mathematics against the existence of platonic forms
PDF (English)


Platonic forms
Object of scientific knowledge

Como Citar

HASPER, . P. S. Aristotle’s argument from universal mathematics against the existence of platonic forms. Manuscrito: Revista Internacional de Filosofia, Campinas, SP, v. 42, n. 4, p. 544–581, 2019. Disponível em: Acesso em: 29 mar. 2023.


In Metaphysics M.2, 1077a9-14, Aristotle appears to argue against the existence of Platonic Forms on the basis of there being certain universal mathematical proofs which are about things that are ‘beyond’ the ordinary objects of mathematics and that cannot be identified with any of these. It is a very effective argument against Platonism, because it provides a counter-example to the core Platonic idea that there are Forms in order to serve as the object of scientific knowledge: the universal of which theorems of universal mathematics are proven in Greek mathematics is neither Quantity in general nor any of the specific quantities, but Quantity-of-type-x. This universal cannot be a Platonic Form, for it is dependent on the types of quantity over which the variable ranges. Since for both Plato and Aristotle the object of scientific knowledge is that F which explains why G holds, as shown in a ‘direct’ proof about an arbitrary F (they merely disagree about the ontological status of this arbitrary F, whether a Form or a particular used in so far as it is F), Plato cannot maintain that Forms must be there as objects of scientific knowledge - unless the mathematics is changed.

PDF (English)


ACERBI, F. ‘In What Proof would a Geometer use the ΠΟΔΙΑΙΑ?’, Classical Quarterly 58 (2008) 120-126.

ANNAS, J. Aristotle’s Metaphysics Books M and N (Oxford, 1976).

BURNYEAT, M.F. ‘Platonism and Mathematics. A Prelude to Discussion’, in: A. Graeser (ed.), Mathematics and Metaphysics in Aristotle (Bern, 1987) 213-240.

CANTÙ, P. ‘Aristotle’s Prohibition Rule on Kind-Crossing and the Definition of Mathematics as a Science of Quantities’, Synthese 174 (2010), 225-235.

CLEARY, J. Aristotle and Mathematics. Aporetic Method in Cosmology and Metaphysics (Leiden, 1995).

HASPER, P.S. ‘Sources of Delusion in Analytica Posteriora 1.5’, Phronesis 51 (2006), 252-284.

HEATH, T. Mathematics in Aristotle (Oxford, 1949).

LEAR, J. ‘Aristotle’s Philosophy of Mathematics’, Philosophical Review 91 (1982) 161-192.

NEAL, K. From Discrete to Continuous. The Broadening of Number Concepts in Early Modern England (Dordrecht, 2002).

ROSS, W.D. Aristotle’s Metaphysics. A Revised Text with Introduction and Commentary (Oxford, 1924).


Não há dados estatísticos.