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Studies in Applied Philosophy, Epistemology and Rational Ethics

Philosophy's Loss of Logic to Mathematics

An Inadequately Understood Take-Over

Authors: Park, Woosuk

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  • 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
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About this book

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. 

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)​

Table of contents (12 chapters)

Table of contents (12 chapters)
  • Introduction

    Pages 1-6

    Park, Woosuk

  • Frege’s Distinction Between “Falling Under” and “Subordination”

    Pages 9-30

    Park, Woosuk

  • Scotus, Frege, and Bergmann

    Pages 31-45

    Park, Woosuk

  • On Cocchiarella’s Retroactive Theory of Reference

    Pages 47-56

    Park, Woosuk

  • Zermelo and the Axiomatic Method

    Pages 59-86

    Park, Woosuk

Buy this book

eBook $84.99
price for USA in USD
  • ISBN 978-3-319-95147-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-3-319-95146-1
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
Softcover $74.99
price for USA in USD
  • ISBN 978-3-030-06984-1
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Philosophy's Loss of Logic to Mathematics
Book Subtitle
An Inadequately Understood Take-Over
Authors
Series Title
Studies in Applied Philosophy, Epistemology and Rational Ethics
Series Volume
43
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG, part of Springer Nature
eBook ISBN
978-3-319-95147-8
DOI
10.1007/978-3-319-95147-8
Hardcover ISBN
978-3-319-95146-1
Softcover ISBN
978-3-030-06984-1
Series ISSN
2192-6255
Edition Number
1
Number of Pages
XII, 230
Topics

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