Explaining Beauty In Mathematics: An Aesthetic Theory Of Mathematics

Synthese Library 370 Ulianov Montano Explaining Beauty in Mathematics: An Aesthetic Theory of Mathematics Explaining Beauty in Mathematics: An Aesthetic Theory of Mathematics SYNTHESE LIBRARY STUDIES IN EPISTEMOLOGY, LOGIC, METHODOLOGY, AND PHILOSOPHY OF SCIENCE Editors-in-Chief: VINCENT F. HENDRICKS, University of Copenhagen, Denmark JOHN SYMONS, University of Texas at El Paso, U.S.A. Honorary Editor: JAAKKO HINTIKKA, Boston University, U.S.A. Editors: DIRK VAN DALEN, University of Utrecht, The Netherlands THEO A.F. KUIPERS, University of Groningen, The Netherlands TEDDY SEIDENFELD, Carnegie Mellon University, U.S.A. PATRICK SUPPES, Stanford University, California, U.S.A. ´ JAN WOLENSKI, Jagiellonian University, Kraków, Poland VOLUME 370 For further volumes: http://www.springer.com/series/6607 Ulianov Montano Explaining Beauty in Mathematics: An Aesthetic Theory of Mathematics 123 Ulianov Montano Mexico City, Mexico ISBN 978-3-319-03451-5 ISBN 978-3-319-03452-2 (eBook) DOI 10.1007/978-3-319-03452-2 Springer Cham Heidelberg New York Dordrecht London Library of Congress Control Number: 2013956239 © 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) Contents Part I Antecedents 1 On Non-literal Approaches .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. 1.1 The Two Cultures, Shaftesbury and Hutchenson .. .. .. .. .. .. .. . .. .. 1.1.1 Unsound Divide ... .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. 1.1.2 Shaftesbury .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. 1.1.3 Hutchenson .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. 1.2 The Epistemic Character of Mathematics .. .. .. .. .. .. .. .. .. .. .. . .. .. 1.2.1 Rota’s Interpretation of Mathematical Beauty . .. .. .. . .. .. 1.2.2 Rota’s Problems ... .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. 1.3 The Rational Character of