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001440825 001__ 1440825
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001440825 019__ $$a1294364668
001440825 020__ $$a9783030885342$$q(electronic bk.)
001440825 020__ $$a3030885348$$q(electronic bk.)
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001440825 0247_ $$a10.1007/978-3-030-88534-2$$2doi
001440825 035__ $$aSP(OCoLC)1284875998
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001440825 049__ $$aISEA
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001440825 08204 $$a510.1$$223
001440825 1001_ $$aHansen, Casper Storm.
001440825 24510 $$aFounding mathematics on semantic conventions /$$cCasper Storm Hansen.
001440825 260__ $$aCham, Switzerland :$$bSpringer,$$c2021.
001440825 300__ $$a1 online resource
001440825 336__ $$atext$$btxt$$2rdacontent
001440825 337__ $$acomputer$$bc$$2rdamedia
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001440825 347__ $$atext file
001440825 347__ $$bPDF
001440825 4901_ $$aSynthese Library,$$x2542-8292 ;$$vv. 446
001440825 504__ $$aIncludes bibliographical references and index.
001440825 5050_ $$a1. Introduction -- 2. Classical Mathematics and Plenitudinous Combinatorialism -- 3 Intuitionism and Choice Sequences -- 4. From Logicism to Predicativism -- 5. Conventional Truth -- 6. Semantic Conventionalism for Mathematics -- 7. A Convention for a Type-free Language -- 8. Basic Mathematics -- 9. Real Analysis -- 10. Possibility -- References -- Index of symbols -- General index.
001440825 506__ $$aAccess limited to authorized users.
001440825 520__ $$aThis book presents a new nominalistic philosophy of mathematics: semantic conventionalism. Its central thesis is that mathematics should be founded on the human ability to create language and specifically, the ability to institute conventions for the truth conditions of sentences. This philosophical stance leads to an alternative way of practicing mathematics: instead of building objects out of sets, a mathematician should introduce new syntactical sentence types, together with their truth conditions, as he or she develops a theory. Semantic conventionalism is justified first through criticism of Cantorian set theory, intuitionism, logicism, and predicativism; then on its own terms; and finally, exemplified by a detailed reconstruction of arithmetic and real analysis. Also included is a simple solution to the liar paradox and the other paradoxes that have traditionally been recognized as semantic. And since it is argued that mathematics is semantics, this solution also applies to Russell's paradox and the other mathematical paradoxes of self-reference. In addition to philosophers who care about the metaphysics and epistemology of mathematics or the paradoxes of self-reference, this book should appeal to mathematicians interested in alternative approaches.
001440825 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed November 9, 2021).
001440825 650_0 $$aMathematics$$xPhilosophy.
001440825 650_0 $$aLogic, Symbolic and mathematical.
001440825 650_6 $$aMathématiques$$xPhilosophie.
001440825 650_6 $$aLogique symbolique et mathématique.
001440825 655_0 $$aElectronic books.
001440825 77608 $$iPrint version:$$aHansen, Casper Storm.$$tFounding mathematics on semantic conventions.$$dCham, Switzerland : Springer, 2021$$z303088533X$$z9783030885335$$w(OCoLC)1266896257
001440825 830_0 $$aSynthese library ;$$vv. 446.$$x2542-8292
001440825 852__ $$bebk
001440825 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-88534-2$$zOnline Access$$91397441.1
001440825 909CO $$ooai:library.usi.edu:1440825$$pGLOBAL_SET
001440825 980__ $$aBIB
001440825 980__ $$aEBOOK
001440825 982__ $$aEbook
001440825 983__ $$aOnline
001440825 994__ $$a92$$bISE