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Philosophy and Model Theory$
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Tim Button and Sean Walsh

Print publication date: 2018

Print ISBN-13: 9780198790396

Published to Oxford Scholarship Online: May 2018

DOI: 10.1093/oso/9780198790396.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 28 October 2021

Permutations and referential indeterminacy

Permutations and referential indeterminacy

(p.35) 2 Permutations and referential indeterminacy
Philosophy and Model Theory

Tim Button

Sean Walsh

Oxford University Press

This chapter begins with a definition of isomorphism, and then introduces the Push-Through Construction, which allows us to generate many distinct isomorphic copies of a model. Benacerraf and Putnam have used this construction to raise certain problems for realism and the determinacy of reference. These problems seem most threatening in the case of mathematics, where nothing like causation could help pin down reference. In this connection, we introduce Putnam’s famous just-more-theory manoeuvre for the first time, and a position which is vulnerable to it, namely moderate objects-platonism. We then evaluate various attempts to salvage determinacy of reference, including Shapiro’s ante rem structuralism, before outlining a supervaluationist semantics which allows for referential indeterminacy. The appendices to this chapter contain a proof that isomorphism implies elementary equivalence, and a discussion of recent work on eligibility.

Keywords:   The Push-Through Construction, The Permutation Argument, The Just-More-Theory Manoeuvre, Shapiro’s ante rem structuralism, Supervaluationism

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