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A Subject With No ObjectStrategies for Nominalistic Interpretation of Mathematics$
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John P. Burgess and Gideon Rosen

Print publication date: 1999

Print ISBN-13: 9780198250128

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198250126.001.0001

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Introduction

Introduction

Chapter:
(p.3) A Introduction
Source:
A Subject With No Object
Author(s):

John P. Burgess (Contributor Webpage)

Gideon Rosen (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0198250126.003.0001

Begins by distinguishing different varieties of nominalism. All adherents of nominalism agree in rejecting mathematical and other abstract entities, and many have attempted to develop nominalist interpretations of scientific theories that appear to involve mathematical objects, with some (hermeneutic nominalists) claiming that these interpretations reveal what the theories really meant all along, and others (revolutionary nominalists) admitting that what they are developing are new, replacement theories. Before beginning our examination of these interpretative projects, we stop to examine critically their presuppositions, beginning with the distinction between abstract objects and concrete objects. We devote special attention to epistemological arguments and semantical arguments for nominalism, based on causal theories of knowledge and causal theories of reference. We also consider why more nominalists have not been content simply to adopt instrumentalism, which declares science to be a useful fiction, and offers no reinterpretation to turn theory into fact.

Keywords:   abstract objects, causal theory of knowledge, causal theory of reference, concrete objects, hermeneutic nominalism, instrumentalism, nominalism, revolutionary nominalism

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