Téléchargez le livre : Founding Mathematics on Semantic Conventions

Founding Mathematics on Semantic Conventions

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Éditeur :

Springer


Collection :

Synthese Library

Paru le : 2021-11-04

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Description

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.
Pages
256 pages
Collection
Synthese Library
Parution
2021-11-04
Marque
Springer
EAN papier
9783030885335
EAN PDF
9783030885342
Informations sur l'ebook
Nombre pages copiables
2
Nombre pages imprimables
25
Taille du fichier
3656 Ko
Prix
105,49 €
EAN EPUB
9783030885342
Informations sur l'ebook
Nombre pages copiables
2
Nombre pages imprimables
25
Taille du fichier
4465 Ko
Prix
105,49 €

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