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On Certainty, Change, and "Mathematical Hinges"

Martin, James V. (2022) On Certainty, Change, and "Mathematical Hinges". [Preprint]

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Abstract

Annalisa Coliva (Int J Study Skept 10(3–4):346–366, 2020) asks, "Are there mathematical hinges?" I argue here, against Coliva's own conclusion, that there are. I further claim that this affirmative answer allows a case to be made for taking the concept of a hinge to be a useful and general-purpose tool for studying mathematical practice in its real complexity. Seeing how Wittgenstein can, and why he would, countenance mathematical hinges additionally gives us a deeper understanding of some of his latest thoughts on mathematics. For example, a view of how mathematical hinges relate to Wittgenstein's well-known river-bed analogy enables us to see how his way of thinking about mathematics can account nicely for a "dynamics of change" within mathematical research---something his philosophy of mathematics has been accused of missing (e.g., by Robert Ackermann (Wittgenstein's City, 1988) and Mark Wilson (Wandering Significance: An Essay on Conceptual Behavior, 2006). Finally, the perspective on mathematical hinges ultimately arrived at will be seen to provide us with illuminating examples of how our conceptual choices and theories can be ungrounded but nevertheless the right ones (in a sense to be explained).


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Martin, James V.james.v.martin@wmich.edu0000-0003-4924-4578
Keywords: Wittgenstein; On Certainty; mathematical innovation; hinge epistemology; philosophy of mathematics
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Practice
Specific Sciences > Mathematics
Depositing User: James Martin
Date Deposited: 13 Dec 2022 15:33
Last Modified: 13 Dec 2022 15:33
Item ID: 21546
Official URL: https://link.springer.com/article/10.1007/s11229-0...
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Practice
Specific Sciences > Mathematics
Date: 2022
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/21546

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