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© 2018

Philosophy's Loss of Logic to Mathematics

An Inadequately Understood Take-Over

  • Discusses logical, methodological, epistemological, and ontological issues relevant to understanding the development of modern logic

  • Explores the main reasons motivating the giants who established modern logic and philosophy of mathematics

  • Analyzes key philosophical problems of logic and mathematics in their historical context

  • Offers a fresh perspective on Aristotelian philosophy of logic and mathematics

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

  1. 1.Humanities and Social SciencesKAISTDaejeonKorea (Republic of)

Bibliographic information

Reviews

“The book provides a very interesting and accessible treatment of some of the relevant work of the mathematicians and logicians already mentioned, as well as a philosopher’s analysis of classical problems abutting to logic, e.g. certain ontological themes addressed by Duns Scotus.” (Michael Berg, MAA Reviews, January, 2019)​