Australasian Philosophical Review 1 (2):133-142 (2017)

Mary Leng
University of York
ABSTRACT‘expressionist’ accounts of applied mathematics seek to avoid the apparent Platonistic commitments of our scientific theories by holding that we ought only to believe their mathematics-free nominalistic content. The notion of ‘nominalistic content’ is, however, notoriously slippery. Yablo's account of non-catastrophic presupposition failure offers a way of pinning down this notion. However, I argue, its reliance on possible worlds machinery begs key questions against Platonism. I propose instead that abstract expressionists follow Geoffrey Hellman's lead in taking the assertoric content of empirical science to be irreducibly modal, using the ‘non-interference’ of mathematical objects as justification for detaching nominalistic consequences.
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DOI 10.1080/24740500.2017.1346417
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References found in this work BETA

Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
Mathematics and Reality.Mary Leng (ed.) - 2010 - Oxford, England: Oxford University Press.
Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 1997 - Oxford, England: Oxford University Press USA.
Mathematics and Reality.Mary Leng - 2011 - Bulletin of Symbolic Logic 17 (2):267-268.

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Citations of this work BETA

The Limits of Subtraction.Mark Colyvan - 2017 - Australasian Philosophical Review 1 (2):168-172.
If-Thenism—A Nominalistic Account of Talk About Abstracta?Katharina Felka - 2017 - Australasian Philosophical Review 1 (2):179-183.
The Problem of (Fully) Empty Predicates.Bradley Armour-Garb & Frederick Kroon - 2017 - Australasian Philosophical Review 1 (2):163-167.

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