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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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(p.1) 1 Introduction
Mathematics and Reality

Mary Leng (Contributor Webpage)

Oxford University Press

This chapter introduces the indispensability argument for the existence of mathematical objects, presenting it as relying on three premises: (P1) Naturalism, (P2) Confirmational Holism, and (P3) Indispensability. It lays out the argumentative strategy of the book, noting that, while the assumptions of naturalism and the indispensability of mathematics are accepted, confirmational holism will be called into question. It finishes with notes on two assumptions that form part of the backdrop for the argument of the book. Firstly, that the ‘there is’ of existential quantification is to be read as ontologically committing, so that a commitment to the literal truth of the sentence ‘There are Fs’ amounts to a commitment to the existence of Fs. And secondly, that no anti‐platonist account of the nature of mathematical objects is available.

Keywords:   naturalism, confirmational holism, indispensability, existential quantification, ontological commitment, platonism, anti‐platonism, mathematical objects

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