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  2. Emner i filosofi
  3. Filosofi: metafysik og ontologi

Founding Mathematics on Semantic Conventions

Af: Casper Storm Hansen Engelsk Hardback

Founding Mathematics on Semantic Conventions

Af: Casper Storm Hansen Engelsk Hardback
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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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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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Produktdetaljer
Sprog: Engelsk
Sider: 256
ISBN-13: 9783030885335
Indbinding: Hardback
Udgave:
ISBN-10: 303088533X
Kategori: Filosofi: metafysik og ontologi
Udg. Dato: 5 nov 2021
Længde: 0mm
Bredde: 155mm
Højde: 235mm
Forlag: Springer Nature Switzerland AG
Oplagsdato: 5 nov 2021
Forfatter(e): Casper Storm Hansen
Forfatter(e) Casper Storm Hansen

Kategori Filosofi: metafysik og ontologi

ISBN-13 9783030885335

Sprog Engelsk

Indbinding Hardback

Sider 256

Udgave

Længde 0mm

Bredde 155mm

Højde 235mm

Udg. Dato 5 nov 2021

Oplagsdato 5 nov 2021

Forlag Springer Nature Switzerland AG

Kategori sammenhænge