Landsman, Klaas (2023) Is mathematics like a game? [Preprint]

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Abstract

We re-examine the old question to what extent mathematics may be compared with a game. Mainly inspired by Hilbert and Wittgenstein, our answer is that mathematics is something like a “rhododendron of language games”, where the rules are inferential. The pure side of mathematics is essentially formalist, where we propose that truth is not carried by theorems corresponding to whatever independent reality and arrived at through proof, but is defined by
correctness of rule-following (and as such is objective given these rules). Gödel’s theorems, which are often seen as a threat to formalist philosophies of mathematics, actually strengthen our concept of truth. The applied side of mathematics arises from two practices: first, the dual nature of axiomatization as taking from heuristic practices like physics and informal mathematics whilst giving proofs and logical analysis; and second, the ability of using the inferential role of theorems to make “surrogative” inferences about natural phenomena. Our framework is pluralist, combining various (non-referential) philosophies of mathematics.

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Item Type:	Preprint
Creators:	Creators Email ORCID Landsman, Klaas landsman@math.ru.nl 0000-0003-2651-2613
Additional Information:	New version is preprint version of paper to be published in the Journal for General Philosophy of Science except that in this preprint all quotations are given in English.
Keywords:	Hilbert, Wittgenstein, philosophy of mathematics
Subjects:	Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > History of Philosophy Specific Sciences > Mathematics
Depositing User:	Nicolaas P. Landsman
Date Deposited:	13 Aug 2025 20:32
Last Modified:	13 Aug 2025 20:32
Item ID:	26153
Subjects:	Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > History of Philosophy Specific Sciences > Mathematics
Date:	21 November 2023
URI:	https://philsci-archive.pitt.edu/id/eprint/26153

Available Versions of this Item

• Is mathematics a game? (deposited 21 Nov 2023 16:53)
  • Is mathematics like a game? (deposited 13 Aug 2025 20:32) [Currently Displayed]
  • Is mathematics a game? (deposited 15 Nov 2024 17:13)

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