Abstract
This article analyzes two types of arguments for mathematical platonism, paying close attention to the deductive argument advanced by Proclus. In the first section of the article, I lay out two arguments for mathematical platonism: a contemporary indispensability argument and Proclus’s more ancient Neoplatonic argument. The former takes an approach based on ‘inference to the best explanation’ and scientific theories, but as a result, faces serious objections. For example, scientific theories change, and because the argument is dependent on the latest scientific theories, it seems that the argument cannot give one epistemic certainty in the conclusion. The latter argument draws on ancient Greek thought—specifically Proclus, and his Commentary on the First Book of Euclid’s Elements. This argument does not rely on scientific knowledge, but metaphysics, and thus seems to establish a conclusion not dependent on changing knowledge. I follow up the exposition of these arguments with two criticisms from the contemporary philosophy of mathematics.
In the second section of the article, I introduce Proclus’s way of thinking about mathematical entities to counter two objections to mathematical platonism: (1) the epistemic access problem, and (2) the causality problem. In contrast to Aristotle, Proclus thinks that the soul contains mathematical forms as latent actualities, or reason principles (λόγοι) in the soul, which account for the possibility of mathematics. Because mathematical entities always are in the soul, and not some ‘separate world’ as modern critics of mathematical platonism think, the epistemic access problem falls away. I then address the causality problem by pointing out that numbers exercise a unique type of causality that physical objects do not. This stems from the use of the Greek word ‘aitia’ (αίτια).
Recommended Citation
Boczar, Bridget
(2025)
"Indispensability Arguments and Proclus’s Deductive Proofs for Mathematical Platonism,"
Acta Cogitata: An Undergraduate Journal in Philosophy: Vol. 12, Article 2.
Available at:
https://commons.emich.edu/ac/vol12/iss1/2
