Table Of ContentABSTRACT ENTITIES
Think of a number, any number, or properties like fragility and humanity. These and
other abstract entities are radically different from concrete entities like electrons
and elbows. While concrete entities are located in space and time, have causes and
effects, and are known through empirical means, abstract entities like meanings
and possibilities are remarkably different. They seem to be immutable and imper-
ceptible and to exist “outside” of space and time.
This book provides a comprehensive critical assessment of the problems raised
by abstract entities and the debates about existence, truth, and knowledge that sur-
round them. It sets out the key issues that inform the metaphysical disagreement
between platonists who accept abstract entities and nominalists who deny abstract
entities exist. Beginning with the essentials of the platonist–nominalist debate, it
explores the key arguments and issues informing the contemporary debate over
abstract reality:
• arguments for platonism and their connections to semantics, science, and meta-
physical explanation
• the abstract–concrete distinction and views about the nature of abstract reality
• epistemological puzzles surrounding our knowledge of mathematical entities and
other abstract entities
• arguments for nominalism premised upon concerns about paradox, parsimony,
infinite regresses, underdetermination, and causal isolation
• nominalist options that seek to dispense with abstract entities.
Including chapter summaries, annotated further reading, and a glossary, Abstract
Entities is essential reading for anyone seeking a clear and authoritative introduction
to the problems raised by abstract entities.
Sam Cowling is Assistant Professor, Denison University, USA.
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ABSTRACT ENTITIES
Sam Cowling
First published 2017
by Routledge
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Routledge is an imprint of the Taylor & Francis Group, an informa business
© 2017 Sam Cowling
The right of Sam Cowling to be identified as the author of this work has been
asserted by him in accordance with sections 77 and 78 of the Copyright, Designs
and Patents Act 1988.
All rights reserved. No part of this book may be reprinted or reproduced or
utilised in any form or by any electronic, mechanical, or other means, now
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information storage or retrieval system, without permission in writing from the
publishers.
Trademark notice: Product or corporate names may be trademarks or registered
trademarks, and are used only for identification and explanation without intent
to infringe.
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
Library of Congress Cataloging in Publication Data
Names: Cowling, Sam, author.
Title: Abstract entities / by Sam Cowling.
Description: 1 [edition]. | New York : Routledge, 2017. | Series: New problems
of philosophy | Includes bibliographical references and index.
Identifiers: LCCN 2016038051| ISBN 9781138827585 (hardback : alk. paper) |
ISBN 9781138827592 (pbk. : alk. paper) | ISBN 9781315266619 (e-book)
Subjects: LCSH: Entity (Philosophy) | Abstraction.
Classification: LCC BD336 .C69 2017 | DDC 111—dc23
LC record available at https://lccn.loc.gov/2016038051
ISBN: 978-1-138-82758-5 (hbk)
ISBN: 978-1-138-82759-2 (pbk)
ISBN: 978-1-315-26661-9 (ebk)
Typeset in Joanna and Scala Sans
by Swales & Willis Ltd, Exeter, Devon, UK
For My Folks
CONTENTS
Acknowledgements ix
Introduction 1
1 The case for platonism 23
1.1 Platonism 23
1.2 Semantic arguments 26
1.3 Alethic arguments 38
1.4 Indispensability arguments 47
1.5 Metaphysical explanation 57
2 The abstract–concrete distinction 69
2.1 The standard view 70
2.2 Analyzing abstractness 74
2.3 Primitivism 92
2.4 Eliminativism 97
3 Paradox, parsimony, and infinite regresses 106
3.1 Paradox 107
3.2 Parsimony 114
3.3 Infinite regresses 120
4 Causal concerns 130
4.1 Epistemic access 130
4.2 Ensuring epistemic access 138
4.3 Semantic access 147
4.4 Cognitive access 150
4.5 Eleaticism 155
viii CONTENTS
5 Non-uniqueness 162
5.1 The non-uniqueness problem 162
5.2 Living with non-uniqueness 169
5.3 Metaphysical underdetermination 177
5.4 Overcoming underdetermination 179
6 Modal objections 189
6.1 Necessary existents 190
6.2 Necessary connections 196
6.3 Contingent platonism 201
6.4 Abstracta and actuality 206
7 Nominalist options 214
7.1 Nominalisms 214
7.2 Meaning 216
7.3 Truth 220
7.4 Commitment 228
7.5 Harvard nominalism revisited 234
Conclusion 247
Glossary 252
References 256
Index 273
ACKNOWLEDGEMENTS
Thanks to the many folks who provided helpful comments on various
parts of this book. Among others, my thanks to Marc Alspector-Kelly,
Chloe Armstrong, Wesley Cray, Gus Evans, Arthur Falk, Ed Ferrier, Barak
Krakauer, Anthony Kulic, Kelly McCormick, Michaela McSweeney, Kevin
Morris, Joshua Spencer, Chris Tillman, Jenn Wang, and audiences at the
University of Massachusetts-Amherst, the 2015 Central division of the
American Philosophical Association, the 2015 Canadian Philosophical
Association, and the 2016 Junior Metaphysics Workshop. I am espe-
cially grateful to James Davies, Cameron Gibbs, Dan Giberman, Bradley
Rettler, and Kelly Trogdon for providing extensive comments on the
manuscript. Additional thanks are owed to my excellent colleagues at
Denison University for their kind support. Thanks also to my editors at
Routledge, Tony Bruce and Adam Johnson, and to four anonymous referees
for their helpful comments.
This book project began during a seminar on abstract entities at
Western Michigan University in 2013 and was helped along by a class
on the same topic at Denison in 2015. My thanks to all the students
involved in those courses. My good fortune in teaching those classes (or
anywhere at all, for that matter) owes to the many professors who have
taught me over the years. I am especially grateful to Phil Bricker and Ben
Caplan in this regard. Given their remarkable philosophical acumen, the
