Mathematics and Metaphilosophy

Cambridge: Cambridge University Press (2022)
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Abstract

This book discusses the problem of mathematical knowledge, and its broader philosophical ramifications. It argues that the problem of explaining the (defeasible) justification of our mathematical beliefs (‘the justificatory challenge’), arises insofar as disagreement over axioms bottoms out in disagreement over intuitions. And it argues that the problem of explaining their reliability (‘the reliability challenge’), arises to the extent that we could have easily had different beliefs. The book shows that mathematical facts are not, in general, empirically accessible, contra Quine, and that they cannot be dispensed with, contra Field. However, it argues that they might be so plentiful that our knowledge of them is intelligible. The book concludes with a complementary ‘pluralism’ about modality, logic and normative theory, highlighting its revisionary implications. Metaphysically, pluralism engenders a kind of perspectivalism and indeterminacy. Methodologically, it vindicates Carnap’s pragmatism, transposed to the key of realism.

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Justin Clarke-Doane
Columbia University

Citations of this work

Replies to Rosen, Leiter, and Dutilh Novaes.Justin Clarke-Doane - 2023 - Philosophy and Phenomenological Research 107 (3):817-837.
What is Logical Monism?Justin Clarke-Doane - forthcoming - In Christopher Peacocke & Paul Boghossian (eds.), Normative Realism.

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References found in this work

Writing the Book of the World.Theodore Sider - 2011 - Oxford, England: Oxford University Press.
On the Plurality of Worlds.David K. Lewis - 1986 - Malden, Mass.: Wiley-Blackwell.
The Meta-Problem of Consciousness.David Chalmers - 2018 - Journal of Consciousness Studies 25 (9-10):6-61.

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