Reasoning Under a Presupposition and the Export Problem: The Case of Applied Mathematics

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

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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Mary Leng
University of York

Citations of this work

Applied Mathematics without Numbers.Jack Himelright - 2023 - Philosophia Mathematica 31 (2):147-175.
The Problem of (Fully) Empty Predicates.Bradley Armour-Garb & Frederick Kroon - 2017 - Australasian Philosophical Review 1 (2):163-167.
If-Thenism—A Nominalistic Account of Talk About Abstracta?Katharina Felka - 2017 - Australasian Philosophical Review 1 (2):179-183.
A Critique of Yablo’s If-thenism.Bradley Armour-Garb & Frederick Kroon - 2023 - Philosophia Mathematica 31 (3):360-371.

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References found in this work

Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 1997 - Oxford, England: Oxford University Press USA.
Realism, Mathematics, and Modality.Hartry Field - 1988 - Philosophical Topics 16 (1):57-107.
Mathematics and Reality.Mary Leng - 2010 - Oxford: Oxford University Press.

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