Ideas for a Deconstruction of Mathematical Platonism through Wittgenstein

Abstract

The aim of this contribution is to extract from Wittgenstein’s remarks on the foundations of mathematics a deconstructive critique of mathematical Platonism. According to the Platonist conception, mathematics is concerned with abstract objects that exist independently of empirical things and of our knowledge, and proofs serve to reveal their essential properties. Wittgenstein challenges this reading: proofs do not uncover ethereal essences, but establish rules and paradigms for the use of concepts within the practices of life. It is thus shown that “mathematical reality” emerges from the interaction between language, demonstrative practice, and paradigmatic modelling, and that Platonism is, ultimately, a conceptual mirage.