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Truth and the Absence of Fact$
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Hartry Field

Print publication date: 2001

Print ISBN-13: 9780199242894

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0199242895.001.0001

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Mathematical Objectivity and Mathematical Objects

Mathematical Objectivity and Mathematical Objects

Chapter:
(p.315) 11 Mathematical Objectivity and Mathematical Objects
Source:
Truth and the Absence of Fact
Author(s):

Hartry Field (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0199242895.003.0011

Focuses on an issue about the objectivity of mathematics—the extent to which undecidable sentences have determinate truth‐value—and argues that this issue is more important than the issue of the existence of mathematical objects. It argues that certain familiar problems for those who postulate mathematical objects, such as Benacerraf's access argument, are serious for those with highly ‘objectivist’ pictures of mathematics, but dissolve for those who allow for sufficient indeterminacy about undecidable sentences. The nominalist view that does without mathematical entities is simply one among several ways of accomplishing the important task of doing without excess objectivity. There is also a discussion arguing for one kind of structuralism but against another.

Keywords:   Paul Benacerraf, continuum hypothesis, finiteness, indeterminacy, mathematical objects, mathematics, nominalism, objectivity, Platonism, structuralism, undecidability

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