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Mathematics and Reality$
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Mary Leng

Print publication date: 2010

Print ISBN-13: 9780199280797

Published to Oxford Scholarship Online: May 2010

DOI: 10.1093/acprof:oso/9780199280797.001.0001

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Mathematics and Make‐Believe

Mathematics and Make‐Believe

Chapter:
(p.155) 7 Mathematics and Make‐Believe
Source:
Mathematics and Reality
Author(s):

Mary Leng (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199280797.003.0007

This chapter presents in detail Kendall L. Walton's account of metaphor as prop‐oriented make‐believe, and discusses how this account can be used to provide an anti‐realist account of the ideal models used in empirical science. It goes on to consider how, specifically, the mathematical assumptions of our scientific theories could be considered to be fictional in the context of a make‐believe, and how such hypotheses can be used to represent, indirectly, how things are taken to be with non‐mathematical ‘props’. It is suggested that, if we take the assumptions of set theory with non‐mathematical urelements as generative assumptions of a fiction, utterances that are fictional against the backdrop of these generative assumptions will have some objective metaphorical content, as claims about the non‐mathematical realm. It is argued that we should view scientific inquiry in the context of mathematically stated scientific theories as inquiry into what is fictional in this game.

Keywords:   Kendall L. Walton, fiction, metaphor, prop‐oriented, make‐believe, set theory with urelements, props, fictional

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