Objectivity, Realism, and Proof FilMat Studies in the Philosophy of

This volume covers a wide range of topics in the most recent debates in the philosophy of mathematics, and is dedicated to how semantic, epistemological, ontological and logical issues interact in the attempt to give a satisfactory picture of mathematical

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Francesca Boccuni Andrea Sereni Editors

Objectivity, Realism, and Proof FilMat Studies in the Philosophy of Mathematics

Boston Studies in the Philosophy and History of Science Volume 318

Series editors Alisa Bokulich, Boston University, Boston, MA, USA Robert S. Cohen, Boston University, Boston, MA, USA Jürgen Renn, Max Planck Institute for the History of Science, Berlin, Germany Kostas Gavroglu, University of Athens, Athens, Greece Managing Editor Lindy Divarci, Max Planck Institute for the History of Science Editorial Board Theodore Arabatzis, University of Athens Heather E. Douglas, University of Waterloo Jean Gayon, Université Paris 1 Thomas F. Glick, Boston University Hubert Goenner, University of Goettingen John Heilbron, University of California, Berkeley Diana Kormos-Buchwald, California Institute of Technology Christoph Lehner, Max Planck Institute for the History of Science Peter Mclaughlin, Universität Heidelberg Agustí Nieto-Galan, Universitat Autònoma de Barcelona Nuccio Ordine, Universitá della Calabria Ana Simões, Universidade de Lisboa John J. Stachel, Boston University Sylvan S. Schweber, Harvard University Baichun Zhang, Chinese Academy of Science

The series Boston Studies in the Philosophy and History of Science was conceived in the broadest framework of interdisciplinary and international concerns. Natural scientists, mathematicians, social scientists and philosophers have contributed to the series, as have historians and sociologists of science, linguists, psychologists, physicians, and literary critics. The series has been able to include works by authors from many other countries around the world. The editors believe that the history and philosophy of science should itself be scientific, self-consciously critical, humane as well as rational, sceptical and undogmatic while also receptive to discussion of first principles. One of the aims of Boston Studies, therefore, is to develop collaboration among scientists, historians and philosophers. Boston Studies in the Philosophy and History of Science looks into and reflects on interactions between epistemological and historical dimensions in an effort to understand the scientific enterprise from every viewpoint.

More information about this series at http://www.springer.com/series/5710

Francesca Boccuni Andrea Sereni •

Editors

Objectivity, Realism, and Proof FilMat Studies in the Philosophy of Mathematics

123

Editors Francesca Boccuni Faculty of Philosophy Vita-Salute San Raffaele University Milan Italy

Andrea Sereni NEtS - IUSS Center for Neurocognition Epistemology and theoretical Synthax School of Advanced Studies IUSS Pavia Pavia Italy

ISSN 0068-0346 ISSN 2214-7942 (electronic) Boston Studies in the Philosophy and History of Science ISBN 978-3-319-31642-0 ISBN 978-3-319-31644-4 (eBook) DOI 10.1007/978-3-319-31644-4 Library of Congress Control Number: 2016940354 © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is