Overview
- Explains how mathematics can be based on the human ability to create and use language
- Offers new alternative ways to approach mathematics
- Presents a simple solution to the liar paradox and its derivatives
Part of the book series: Synthese Library (SYLI, volume 446)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This book presents a new nominalistic philosophy of mathematics: semantic conventionalism. Its central thesis is that mathematics should be founded on the human ability to create language – and specifically, the ability to institute conventions for the truth conditions of sentences.
This philosophical stance leads to an alternative way of practicing mathematics: instead of “building” objects out of sets, a mathematician should introduce new syntactical sentence types, together with their truth conditions, as he or she develops a theory.
Semantic conventionalism is justified first through criticism of Cantorian set theory, intuitionism, logicism, and predicativism; then on its own terms; and finally, exemplified by a detailed reconstruction of arithmetic and real analysis.
Also included is a simple solution to the liar paradox and the other paradoxes that have traditionally been recognized as semantic. And since it is argued that mathematics is semantics, thissolution also applies to Russell’s paradox and the other mathematical paradoxes of self-reference.
In addition to philosophers who care about the metaphysics and epistemology of mathematics or the paradoxes of self-reference, this book should appeal to mathematicians interested in alternative approaches.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Founding Mathematics on Semantic Conventions
Authors: Casper Storm Hansen
Series Title: Synthese Library
DOI: https://doi.org/10.1007/978-3-030-88534-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-88533-5Published: 05 November 2021
Softcover ISBN: 978-3-030-88536-6Published: 05 November 2022
eBook ISBN: 978-3-030-88534-2Published: 04 November 2021
Series ISSN: 0166-6991
Series E-ISSN: 2542-8292
Edition Number: 1
Number of Pages: XI, 256
Topics: Philosophy of Mathematics, Mathematical Logic and Foundations, Metaphysics, Philosophy of Language, Analysis