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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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Modelism and mathematical doxology

Modelism and mathematical doxology

(p.143) 6 Modelism and mathematical doxology
Philosophy and Model Theory

Tim Button

Sean Walsh

Oxford University Press

This chapter outlines a certain attitude to model theory called ‘modelism’. The modelist idea is that structure-talk, as used informally by mathematicians, is to be understood in terms of isomorphism, in the model theorist's sense. For example, modelists will want to explicate talk of ‘the natural numbers' in terms of a particular isomorphism type. As such, modelists face an important doxological question: ‘How can we pick out particular isomorphism types?’ This chapter examines various versions of this question, and in particular what it means to say that it is a doxological question. We also distinguish between objectual and conceptual versions of this question, and show how they relate to Shapiro’s and Hellman’s different versions of structuralism.

Keywords:   Modelism, doxology, objectual vs. conceptual, Hellman

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