Accommodationism in Mathematics : Reference, Knowledge, and Realism

Accommodationism in Mathematics: Reference, Knowledge, and Realism (Routledge Studies in the Philosophy of Mathematics and Physics)

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Accommodationism in Mathematics : Reference, Knowledge, and Realism

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Accommodationism in Mathematics: Reference, Knowledge, and Realism (Routledge Studies in the Philosophy of Mathematics and Physics)

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Mathematics presents a fundamental puzzle: we possess extraordinary confidence in mathematical knowledge while struggling to explain how such knowledge is possible, especially in light of traditional realist conceptions of mathematics.This book solves this puzzle via resolving the tension between mathematical knowledge and mathematical realism by developing an innovative accommodationist theory of reference in mathematics. The book provides an account of mathematical reference utilizing detailed case studies of mathematical induction, aspects of computability theory, and compactness phenomena in mathematics and logic.It answers two of the most significant and persistent open questions in the philosophy of mathematics: the Benacerraf-Field Challenge, which defies us to explain the reliability of mathematicians' mathematical beliefs, and the question of mathematical realism.By adapting Richard Boyd's influential theory of scientific reference to mathematics, the book shows how mathematic
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