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Mathematics and Metaphilosophy
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Mathematics and Metaphilosophy

by Justin Clarke-Doane

Book Details

Format Paperback / Softback
Book Series Elements in the Philosophy of Mathematics
ISBN-10 1108995403
ISBN-13 9781108995405
Publisher Cambridge University Press
Imprint Cambridge University Press
Country of Manufacture GB
Country of Publication GB
Publication Date Jun 30th, 2022
Print length 75 Pages
Weight 112 grams
Dimensions 15.10 x 22.80 x 0.70 cms
Product Classification: Philosophy of science
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This Element discusses the problem of mathematical knowledge, and its broader philosophical ramifications. It argues that the challenge to explain the (defeasible) justification of our mathematical beliefs ('the justificatory challenge'), arises insofar as disagreement over axioms bottoms out in disagreement over intuitions.
This Element discusses the problem of mathematical knowledge, and its broader philosophical ramifications. It argues that the challenge to explain 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 challenge to explain their reliability (''the reliability challenge''), arises to the extent that we could have easily had different beliefs. The Element 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 unmysterious. The Element concludes with a complementary ''pluralism'' about modality, logic and normative theory, highlighting its surprising 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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