# Aristotle’s argument from universal mathematics against the existence of platonic forms

*Manuscrito*42 (4):544-581 (2019)

**Abstract**

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.

**Keywords**

**Categories**

**PhilPapers/Archive ID**

HASAAF-2

**Revision history**

Archival date: 2019-11-26

View upload history

View upload history

References found in this work BETA

Aristotle’s Prohibition Rule on Kind-Crossing and the Definition of Mathematics as a Science of Quantities.Paola Cantù - 2010 -

*Synthese*174 (2):225-235.Aristotle's Philosophy of Mathematics.Lear, Jonathan

Sources of Delusion in Analytica Posteriora 1.5.Hasper, Pieter Sjoerd

Sources of Delusion in Analytica Posteriora 1.5.Hasper, Pieter Sjoerd

In What Proof Would a Geometer Use the [Pi][Omicron][Delta][Iota][Alpha] [Iota][Alpha]?Acerbi, Fabio

View all 6 references / Add more references

Citations of this work BETA

No citations found.

**Added to PP index**

2019-11-21

**Total views**

21 ( #42,770 of 44,300 )

**Recent downloads (6 months)**

21 ( #29,516 of 44,300 )

How can I increase my downloads?

**Downloads since first upload**

*This graph includes both downloads from PhilArchive and clicks to external links.*