From Logic to Practice

Italian Studies in the Philosophy of Mathematics

  • Gabriele Lolli
  • Marco Panza
  • Giorgio Venturi

Part of the Boston Studies in the Philosophy and History of Science book series (BSPS, volume 308)

Table of contents

  1. Front Matter
    Pages i-xix
  2. The Historical Dimension of Mathematics

  3. Looking at Mathematics Through Logic

  4. Philosophy and Mathematics

    1. Front Matter
      Pages 201-201
    2. Michele Ginammi
      Pages 203-222
    3. Marco Panza, Andrea Sereni
      Pages 241-276
    4. Luca San Mauro, Giorgio Venturi
      Pages 277-313
    5. Silvia De Toffoli, Valeria Giardino
      Pages 315-336

About this book

Introduction

This book brings together young researchers from a variety of fields within mathematics, philosophy and logic. It discusses questions that arise in their work, as well as themes and reactions that appear to be similar in different contexts. The book shows that a fairly intensive activity in the philosophy of mathematics is underway, due on the one hand to the disillusionment with respect to traditional answers, on the other to exciting new features of present day mathematics. The book explains how the problem of applicability once again plays a central role in the development of mathematics. It examines how new languages different from the logical ones (mostly figural), are recognized as valid and experimented with and how unifying concepts (structure, category, set) are in competition for those who look at this form of unification. It further shows that traditional philosophies, such as constructivism, while still lively, are no longer only philosophies, but guidelines for research. Finally, the book demonstrates that the search for and validation of new axioms is analyzed with a blend of mathematical historical, philosophical, psychological considerations.​

Keywords

Axioms of Set Theory Church’s Thesis and Naturalness of Axioms Constructibility, Naturalism, Axiomatics Constructive Approach to the Infinitesimal Analysis Dynamics of Diagrams in Knot Theory Fundamental Theorem of Algebra Gottlob Frege’s Grundgesetze Husserl Raumbuch Intuitionism and Cognitive Sciences Languages and the Extension of Knowledge Mathematics is a Science of Structures Parametric Polymorphism Philosophy of Mathematics Structuralism, Categorical and Set Theoretical Foundations

Editors and affiliations

  • Gabriele Lolli
    • 1
  • Marco Panza
    • 2
  • Giorgio Venturi
    • 3
  1. 1.Scuola Normale SuperiorePisaItaly
  2. 2.Panthéon-SorbonneIHPST, CNRS, University of Paris 1ParisFrance
  3. 3.FAPESP&Centre for Logic,Epistemology&the History of ScienceState University of CampinasSão PauloBrazil

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-10434-8
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Humanities, Social Sciences and Law
  • Print ISBN 978-3-319-10433-1
  • Online ISBN 978-3-319-10434-8
  • Series Print ISSN 0068-0346
  • Series Online ISSN 2214-7942
  • About this book