Mathematics in Philosophy: Selected Essays

368 Pages·1983·15.434 MB·English

by  Charles Parsons

Mathematics
in Philosophy
Selected Essays
&l
CHARIEES PARSONS

Mathematics in Philosophy

Mathematics in Philosophy
SELECTED ESSAYS
CHARLES PARSONS
Cornell University Press
ITHACA, NEW YORK
Cornell University Press gratefully acknowledges a grant from the Andrew W.
Mellon Foundation that aided in bringing this book to publication.
Copyright© 1983 by Cornell University Press
All rights reserved. Except for brief quotations in a review, this book, or parts
thereof, must not be reproduced in any form without permission in writing from
the publisher. For information, address Cornell University Press, Sage House,
51 2 East State Street, Ithaca, New York 148 50.
First published 1983 by Cornell University Press.
Published in the United Kingdom by Cornell University Press, Ltd., London.
First printing, Cornell paperbacks, 2005.
Printed in the United States of America
Library of Congress Cataloging in Publication Data
Parsons, Charles, 1933-
Mathematics in philosophy.
Bibliography: p.
Includes index.
1. Mathematics-Philosophy-Addresses, essays,
lectures. I. Title.
QA8.6.P37 1983 510'.1 83-45153
ISBN-13: 978-o-8014-8981-5 (pbk.: alk. paper)
ISBN-10: o-8014-8981-4 (pbk.: alk. paper)
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Paperback printing 10 9 8 7 6 5 4 3 2
To the memory of my father

Contents
Preface 9
Preface to the Cornell Paperbacks Edition
14
Introduction 15
PART ONE. MATHEMATICS, LOGIC, AND ONTOLOGY
1. Ontology and Mathematics 3 7
Appendix 58; Postscript 6o
2. A Plea for Substitutional Quantification 63
3· Informal Axiomatization, Formalization, and the
Concept of Truth 71
PART TWO. INTERPRETATIONS
4· Infinity and Kant's Conception of the "Possibility
of Experience" 95
5· Kant's Philosophy of Arithmetic 1 10
Postscript 142
6. Frege's Theory of Number 150
Postscript 173
7. Quine on the Philosophy of Mathematics 176
PART THREE. SETS, CLASSES, AND TRUTH
8. Sets and Classes 209
9· The Liar Paradox 2 2 1
Postscript 251
10. What Is the Iterative Conception of Set?
7
Contents
1 1. Sets and Modality 298
Appendix 1. Free Modal Logic and Modal Logic with Scope
Operators 33 1; Appendix 2. Relation of Theories of
Potential Sets to Standard Set Theory 336
Bibliography 342
Index 359
8