Philosophy's Loss of Logic to Mathematics
An Inadequately Understood Take-Over
Authors: Park, Woosuk
Free Preview- 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
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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
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“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)
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Introduction
Pages 1-6
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Frege’s Distinction Between “Falling Under” and “Subordination”
Pages 9-30
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Scotus, Frege, and Bergmann
Pages 31-45
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On Cocchiarella’s Retroactive Theory of Reference
Pages 47-56
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Zermelo and the Axiomatic Method
Pages 59-86
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Table of contents (12 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Philosophy's Loss of Logic to Mathematics
- Book Subtitle
- An Inadequately Understood Take-Over
- Authors
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- Woosuk Park
- 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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