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＜電子ブック＞
Founding Mathematics on Semantic Conventions / by Casper Storm Hansen
(Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science. ISSN:25428292 ; 446)

版	1st ed. 2021.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2021
大きさ	XI, 256 p : online resource
著者標目	*Hansen, Casper Storm author SpringerLink (Online service)
件　名	LCSH:Mathematics—Philosophy LCSH:Mathematical logic LCSH:Metaphysics LCSH:Language and languages—Philosophy LCSH:Mathematical analysis FREE:Philosophy of Mathematics FREE:Mathematical Logic and Foundations FREE:Metaphysics FREE:Philosophy of Language FREE:Analysis
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-030-88534-2

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