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Series:   Elements in the Philosophy of Mathematics

Mathematics is (mostly) Analytic

Published online by Cambridge University Press:  09 January 2025

Gregory Lavers
Gregory Lavers
Affiliation:
Concordia University, Montréal

Summary

This Element outlines and defends an account of analyticity according to which mathematics is, for the most part, analytic. The author begins by looking at Quine's arguments against the concepts of analyticity. He shows how Quine's position on analyticity is related to his view on explication and shows how this suggests a way of defining analyticity that would meet Quine's own standards for explication. The author then looks at Boghossian and his distinction between epistemic and metaphysical accounts of analyticity. Here he argues that there is a straightforward way of eliminating the confusion Boghossian sees with what he calls metaphysical accounts. The author demonstrates that the epistemic dimension of his epistemic account is almost entirely superfluous. The author then discusses how analyticity is related to truth, necessity, and questions of ontology. Finally, he discusses the vagueness of analyticity and also the relation of analyticity to the axiomatic method in mathematics.
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Keywords

analyticityQuineCarnapexplicationmathematical truth
Type
Element
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Series: Elements in the Philosophy of Mathematics
Online ISBN: 9781009109925
Publisher: Cambridge University Press
Print publication: 30 January 2025

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Mathematics is (mostly) Analytic
  • Gregory Lavers, Concordia University, Montréal
  • Online ISBN: 9781009109925
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Mathematics is (mostly) Analytic
  • Gregory Lavers, Concordia University, Montréal
  • Online ISBN: 9781009109925
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Mathematics is (mostly) Analytic
  • Gregory Lavers, Concordia University, Montréal
  • Online ISBN: 9781009109925
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