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Mathematics and Methaphilosophy

Justin Clarke-Doane

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Description: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 revisionary implications. Metaphysically, pluralism engenders a kind of perspectivalism and indeterminacy. Methodologically, it vindicates Carnap’s pragmatism, transposed to the key of realism.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Mathematics and Methaphilosophy. To get started finding Mathematics and Methaphilosophy, you are right to find our website which has a comprehensive collection of manuals listed.
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Pages: 75

Format: PDF, EPUB & Kindle Edition

Publisher: Cambridge University Press

Release: 2022

ISBN: 1108995403

Description: 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 revisionary implications. Metaphysically, pluralism engenders a kind of perspectivalism and indeterminacy. Methodologically, it vindicates Carnap’s pragmatism, transposed to the key of realism.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Mathematics and Methaphilosophy. To get started finding Mathematics and Methaphilosophy, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

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Mathematics and Methaphilosophy

Mathematics and Methaphilosophy

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