Mathematics and Its Applications A Transcendental-Idealist Perspecti
This monograph offers a fresh perspective on the applicability of mathematics in science. It explores what mathematics must be so that its applications to the empirical world do not constitute a mystery. In the process, readers are presented with a new ve
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Jairo José da Silva
Mathematics and Its Applications A Transcendental-Idealist Perspective
Synthese Library Studies in Epistemology, Logic, Methodology, and Philosophy of Science Volume 385
Editor-in-Chief Otávio Bueno, University of Miami, Department of Philosophy, USA Editors Berit Brogaard, University of Miami, USA Anjan Chakravartty, University of Notre Dame, USA Steven French, University of Leeds, UK Catarina Dutilh Novaes, University of Groningen, The Netherlands
More information about this series at http://www.springer.com/series/6607
Jairo José da Silva
Mathematics and Its Applications A Transcendental-Idealist Perspective
Jairo José da Silva Researcher - CNPq, Ministry of Science, Technology, Innovation and Communication - Brazil Brasilia, DF, Brazil
Synthese Library ISBN 978-3-319-63072-4 ISBN 978-3-319-63073-1 (eBook) DOI 10.1007/978-3-319-63073-1 Library of Congress Control Number: 2017945752 © Springer International Publishing AG 2017 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. 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
To the memory of my sweet Shoshana April 1, 2006–August 7, 2016 A little fat star that shone across my sky
Contents
1 Introduction.............................................................................................. 1 2 Phenomenology........................................................................................ 11 3 Logic.......................................................................................................... 67 4 Numbers.................................................................................................... 93 5 Sets.................................................................
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