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035   $a(DE-He213)978-3-030-88534-2
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100   $a20211104d2021      u|         0
101 0 $aeng
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181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aFounding Mathematics on Semantic Conventions /$fby Casper Storm Hansen
205   $a1st ed. 2021.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021.
215   $a1 online resource (259 pages)
225 1 $aSynthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science,$x2542-8292 ;$v446
311 08$a3-030-88533-X 
320   $aIncludes bibliographical references and index.
327   $a1. 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.
330   $aThis book presents a new nominalistic philosophy of mathematics: semantic conventionalism. Its central thesis is that mathematics should be founded on the human ability to create language ? and specifically, the ability to institute conventions for the truth conditions of sentences. This philosophical stance leads to an alternative way of practicing mathematics: instead of ?building? objects out of sets, a mathematician should introduce new syntactical sentence types, together with their truth conditions, as he or she develops a theory. Semantic conventionalism is justified first through criticism of Cantorian set theory, intuitionism, logicism, and predicativism; then on its own terms; and finally, exemplified by a detailed reconstruction of arithmetic and real analysis. Also included is a simple solution to the liar paradox and the other paradoxes that have traditionally been recognized as semantic. And since it is argued that mathematics is semantics, this solution also applies to Russell?s paradox and the other mathematical paradoxes of self-reference. In addition to philosophers who care about the metaphysics and epistemology of mathematics or the paradoxes of self-reference, this book should appeal to mathematicians interested in alternative approaches.
410  0$aSynthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science,$x2542-8292 ;$v446
606   $aMathematics$xPhilosophy
606   $aMathematical logic
606   $aMetaphysics
606   $aLanguage and languages$xPhilosophy
606   $aMathematical analysis
606   $aPhilosophy of Mathematics
606   $aMathematical Logic and Foundations
606   $aMetaphysics
606   $aPhilosophy of Language
606   $aAnalysis
615  0$aMathematics$xPhilosophy.
615  0$aMathematical logic.
615  0$aMetaphysics.
615  0$aLanguage and languages$xPhilosophy.
615  0$aMathematical analysis.
615 14$aPhilosophy of Mathematics.
615 24$aMathematical Logic and Foundations.
615 24$aMetaphysics.
615 24$aPhilosophy of Language.
615 24$aAnalysis.
676   $a510.1
700   $aHansen$b Casper Storm$01052511
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910508469503321
996   $aFounding Mathematics on Semantic Conventions$92483844
997   $aUNINA