Abstract
On what can be considered the received view of mathematical content, mathematical theorems are thought of as having a content that is completely independent of the context in which such theorems are formulated: if a mathematical statement is true, it is necessarily true (true in any context). In this paper, I argue that this is not the case: theorems in mathematics are highly sensitive to the mathematical context in which they are expressed: they depend on the assumptions that are built into them, on the underlying logic, and, when applied to the world, on the way in which the concepts involved in the formulation of such theorems are interpreted. This suggests that, contrary to the received view, mathematical theorems are significantly context-dependent. A naturalist approach to such content, sensitive to mathematical practice, is then advanced.
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Acknowledgements
My thanks go to Eli Chudnoff, Mark Colyvan, Steven French, Chris Pincock, and Steve Yablo for helpful discussions on the issues examined in this paper. Thanks are also due to Shyam Wuppuluri for all the support during the writing of this work.
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Bueno, O. (2022). Content, Context, and Naturalism in Mathematics. In: Wuppuluri, S., Stewart, I. (eds) From Electrons to Elephants and Elections. The Frontiers Collection. Springer, Cham. https://doi.org/10.1007/978-3-030-92192-7_17
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