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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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Mathematical Fictionalism and Constructive Empiricism

Mathematical Fictionalism and Constructive Empiricism

Chapter:
(p.182) 8 Mathematical Fictionalism and Constructive Empiricism
Source:
Mathematics and Reality
Author(s):

Mary Leng (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199280797.003.0008

The fictionalist account of the role of mathematical hypotheses in our scientific theories presented in Chapter 7 suggests that we should not view our scientific theories as true, taken literally, but only as having a true metaphorical content, or as being correct in the picture they paint of their non‐mathematical ‘props’. We can present this claim as the claim that we ought to believe only the nominalistic content of our scientific theories, and not their claims about the mathematical realm. This presentation shows mathematical fictionalism to be analogous in important respects to constructive empiricism, and in this chapter this analogy is probed. It is shown that mathematical fictionalism cannot borrow from constructive empiricism in its account of ‘nominalistic content’, as this account is itself mathematical and therefore unavailable to the fictionalist. Some standard objections to constructive empiricism are considered, and fictionalist responses to these objections are given.

Keywords:   Bas van Fraassen, constructive empiricism, fictionalism, metaphorical content, nominalistic content, acceptance, belief, nominalistic adequacy, empirical adequacy

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