Communications in Humanities Research ISSN: 2753-7072
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Research Article

Platonism and Its Critics: Exploring Realism and Alternatives in Mathematical Philosophy

Haoxi YuUniversity of Southern California*

* Corresponding author: [email protected]

Abstract

This paper aims to examine the central role of Platonism in the philosophy of mathematics and evaluates a range of critiques that challenge its ontological and epistemological assumptions. Beginning with Plato’s theory of Forms and the indispensability argument, the discussion traces the development of realism through Gödel, Benacerraf, and Field, before turning to alternatives such as intuitionism, formalism, social constructivism, and structuralism. Particular attention is paid to how Benacerraf’s identification and epistemological problems motivated later approaches, and how Field’s fictionalism reshaped the indispensability debate. Recent perspectives, including practice-based accounts, explanatory indispensability, and conceptual structuralism, are incorporated to highlight how contemporary debates extend beyond classical disputes. By integrating both historical and modern treatments, the paper argues that while Platonism continues to provide an appealing account of mathematical objectivity, its explanatory and epistemological difficulties encourage a pluralist outlook, in which structural, social, and cognitive perspectives together illuminate the evolving nature of mathematics.

Keywords: Platonism; indispensability argument; structuralism; intuitionism; philosophy of mathematics.
Published: October 2, 2025
DOI: 10.54254/2753-7064/2025.HT27914
Volume: CHR Vol.85
pp. 152-158
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