UDC: 101.1
https://doi.org/10.25198/2077-7175-2026-3-114
EDN: CKHRBA


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WHY ARE PLATONISM AND NATURALISM INCOMPATIBLE?

D. V. Ankin
Ural Federal University named after the first President of Russia B. N. Yeltsin, Yekaterinburg, Russia
e-mail: dmitryankin@gmail.com

Abstract. This article is inspired by the current debates about Platonism in the philosophy of mathematics and aims to clarify the terminology used in this field, primarily from the perspective of its ontological foundations. The difficulty lies in the fact that mathematics deals with special objects, if objects are recognized, and/or with special structures, if certain structures are recognized instead of objects.

The purpose of this study is to demonstrate the incompatibility of Platonism and naturalism. The term «realism» is polysemantic. It encompasses not only Platonism (which is quite traditional), but also certain variants of naturalism, as we attempt to demonstrate in this article. Platonism is incompatible with nominalism, according to existing historical-philosophical classifications, but realism, in some versions, can likely be compatible with naturalism.

The main «points of support» for our research will be the positions of Willard Quine and Hilary Putnam in the philosophy of mathematics, which, as we have attempted to demonstrate, consist of an attempt to combine certain forms of realism with: 1) naturalistic nominalism (W. Quine); 2) conceptualism (H. Putnam).

Our solution to the classification problems is demonstrated using the example of W. Quine’s philosophy of mathematics, which has a direct connection both with the ideas of nominalistic metaphysics and with the ideas of a naturalistic-realistic interpretation of mathematical objects. By unraveling this knot, we will be able to clarify a number of metaphysical and ontological problems. A novel feature is our proof that W. Quine cannot be called a Platonist.

Translating into Quine’s terminology, we can say that the operation of hypostatizing abstract objects, necessary for any Platonism, occurs at the level of the theory’s ideology, that is, exclusively at the level of language. The operation of endowing them with existence, however, is carried out not in language itself, but in a manner internal to theory – based on the quantification of free variables. This defines the boundaries between metaphysics and ontology sought in this article. In the example of W. Quine, we obtain an anti-Platonist metaphysics accompanied by a moderately realist ontology that allows for a plurality of naturalistic models.

Key words: platonism, realism, nominalism, ontological commitments, Putnam, Quine, metaphysics, ontology, philosophy of mathematics.

Cite as: Ankin, D. V. (2026) [Why are Platonism and Naturalism incompatible?]. Intellekt. Innovacii. Investicii [Intellect. Innovations. Investments]. Vol. 3, pp. 114–122. – https://doi.org/10.25198/2077-7175-2026-3-114.


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