Chapter

Mathematical Objectivity and Mathematical Objects

Hartry Field

in Truth and the Absence of Fact

Published in print March 2001 | ISBN: 9780199242894
Published online November 2003 | e-ISBN: 9780191597381 | DOI: http://dx.doi.org/10.1093/0199242895.003.0011
 Mathematical Objectivity and Mathematical Objects

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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

Chapter.  8616 words. 

Subjects: Philosophy

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