Founding mathematics on semantic conventions / Casper Storm Hansen.
Hansen, Casper Storm.
2021
QA8.4
Available Online

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Title Founding mathematics on semantic conventions / Casper Storm Hansen.
Author Hansen, Casper Storm.
ISBN 9783030885342 (electronic bk.)
3030885348 (electronic bk.)
303088533X
9783030885335
DOI https://doi.org/10.1007/978-3-030-88534-2
Publication Details Cham, Switzerland : Springer, 2021.
Language English
Description 1 online resource
Item Number 10.1007/978-3-030-88534-2 doi
Call Number QA8.4
Dewey Decimal Classification 510.1
Summary 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, this solution 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Digital File Characteristics text file
PDF
Source of Description Online resource; title from PDF title page (SpringerLink, viewed November 9, 2021).
Series Synthese library ; v. 446. 2542-8292
Available in Other Form Founding mathematics on semantic conventions.
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1. Introduction
2. Classical Mathematics and Plenitudinous Combinatorialism
3 Intuitionism and Choice Sequences
4. From Logicism to Predicativism
5. Conventional Truth
6. Semantic Conventionalism for Mathematics
7. A Convention for a Type-free Language
8. Basic Mathematics
9. Real Analysis
10. Possibility
References
Index of symbols
General index.

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