Abstract
The status of mathematical facts has long been taken to be unclear in Wittgenstein's philosophy of mathematics, and often, it seems that he wants to eliminate mathematical facts in favour of facts about our beliefs or behaviour. In this paper, I argue that by reading Wittgenstein as a radical conventionalist, we can give a reading of the relevant passages according to which Wittgenstein doesn't deny that there are mathematical facts, but rather denies that one needs a metaphysical account of what mathematical facts are and how they relate to the world that goes beyond the minimal claims of radical conventionalism—that empirical facts about how we would find natural to project our training into new cases and the constitution of concepts by our agreement are enough. At the end of the paper, I discuss the implications of this reading on how to understand a rule's determination of its own application.
Original language | English |
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Pages (from-to) | 501-522 |
Number of pages | 22 |
Journal | Philosophical Investigations |
Volume | 47 |
Issue number | 4 |
DOIs | |
Publication status | Published - Oct 2024 |
Bibliographical note
Publisher Copyright:© 2024 The Author(s). Philosophical Investigations published by John Wiley & Sons Ltd.