A Mathematical Prelude to the Philosophy of Mathematics
This book is based on two premises: one cannot understand philosophy of mathematics without understanding mathematics and one cannot understand mathematics without doing mathematics. It draws readers into philosophy of mathematics by having them do m
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A Mathematical Prelude to the Philosophy of Mathematics
A Mathematical Prelude to the Philosophy of Mathematics
Stephen Pollard
A Mathematical Prelude to the Philosophy of Mathematics
123
Stephen Pollard Department of Philosophy and Religion Truman State University Kirksville, MO USA
ISBN 978-3-319-05815-3 ISBN978-3-319-05816-0 DOI 10.1007/978-3-319-05816-0 Springer Cham Heidelberg New York Dordrecht London
(eBook)
Library of Congress Control Number: 2014936236 Springer International Publishing Switzerland 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
In memory of Dean Randall Pollard
Preface
I have a principled argument for why this book should exist. I have no such argument for why it contains just what it contains. The principles are these: • You cannot understand philosophy of mathematics without understanding mathematics. • You cannot understand mathematics without doing mathematics. The main point of this book, with its 298 exercises, is to give students opportunities to recreate some mathematics that will illuminate important readings in philosophy of mathematics. As for the particular mathematical materials I have chosen: they are the unforced fruits of lengthy experience. I have taught undergraduates for three decades. In the 14 tim
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