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Founding mathematics on semantic con...

Hansen, Casper Storm.

Founding mathematics on semantic conventions

Record Type:	Electronic resources : Monograph/item
Title/Author:	Founding mathematics on semantic conventionsby Casper Storm Hansen.
Author:	Hansen, Casper Storm.
Published:	Cham :Springer International Publishing :2021.
Description:	xi, 256 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	MathematicsPhilosophy.
Online resource:	https://doi.org/10.1007/978-3-030-88534-2
ISBN:	9783030885342$q(electronic bk.)

Founding mathematics on semantic conventions
Hansen, Casper Storm.

Founding mathematics on semantic conventions[electronic resource] /by Casper Storm Hansen. - Cham :Springer International Publishing :2021. - xi, 256 p. :ill., digital ;24 cm. - Synthese library, studies in epistemology, logic, methodology, and philosophy of science,v. 4462542-8292 ;. - Synthese library, studies in epistemology, logic, methodology, and philosophy of science ;v.375..

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.

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.

ISBN: 9783030885342$q(electronic bk.)

Standard No.: 10.1007/978-3-030-88534-2doiSubjects--Topical Terms:

187658
Mathematics
--Philosophy.

LC Class. No.: QA8.4 / .H35 2021

Dewey Class. No.: 510.1

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505 0 $a 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.
520 $a 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.
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