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Philosophy's Loss of Logic to Mathematics

An Inadequately Understood Take-Over

  • Woosuk Park
Book

Part of the Studies in Applied Philosophy, Epistemology and Rational Ethics book series (SAPERE, volume 43)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Woosuk Park
    Pages 1-6
  3. Part I The Fregean Legacy

  4. Part II The Hilbert School

  5. Part III Goedel and Tarski

    1. Front Matter
      Pages 121-121
  6. Part IV Back to Aristotle

    1. Front Matter
      Pages 155-155
    2. Woosuk Park
      Pages 189-206
    3. Woosuk Park
      Pages 207-221
  7. Back Matter
    Pages 223-230

About this book

Introduction

This book offers a historical explanation of important philosophical problems in logic and mathematics, which have been neglected by the official history of modern logic.  It offers extensive information on Gottlob Frege’s logic, discussing which aspects of his logic can be considered truly innovative in its revolution against the Aristotelian logic. It presents the work of Hilbert and his associates and followers with the aim of understanding the revolutionary change in the axiomatic method. Moreover, it offers useful tools to understand Tarski’s and Gödel’s work, explaining why the problems they discussed are still unsolved. Finally, the book reports on some of the most influential positions in contemporary philosophy of mathematics, i.e., Maddy’s mathematical naturalism and Shapiro’s mathematical structuralism. Last but not least, the book introduces Biancani’s Aristotelian philosophy of mathematics as this is considered important to understand current philosophical issue in the applications of mathematics. One of the main purposes of the book is to stimulate readers to reconsider the Aristotelian position, which disappeared almost completely from the scene in logic and mathematics in the early twentieth century. 

Keywords

Axiomatic Method Implicit Definition Maddy’s Mathematical Naturalism Shapiro’s Mathematical Structuralism Gottlob Frege Aristotelian Logic Haecceity Implicit Definition Axiomatizing Set Theory Logic and Ontology

Authors and affiliations

  • Woosuk Park
    • 1
  1. 1.Humanities and Social SciencesKAISTDaejeonKorea (Republic of)

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-95147-8
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Religion and Philosophy
  • Print ISBN 978-3-319-95146-1
  • Online ISBN 978-3-319-95147-8
  • Series Print ISSN 2192-6255
  • Series Online ISSN 2192-6263
  • Buy this book on publisher's site