00779nam0-22002771i-450-99000750352040332120060613165139.00-631-18424-4000750352FED01000750352(Aleph)000750352FED0100075035220030814d2001----km-y0itay50------baitaTransnational urbanismlocating globalizationMichael Peter Smith.Malden (Mass.)Blackwell2001.IX, 221 p.24 cmCITTASmith,Michael Peter129756ITUNINARICAUNIMARCBK990007503520403321A-G 0603B.F.L.F.35598ILFGEILFGETransnational urbanism676581UNINA03951nam 22006975 450 991050846950332120251113193649.03-030-88534-810.1007/978-3-030-88534-2(CKB)4940000000615689(MiAaPQ)EBC6799131(Au-PeEL)EBL6799131(OCoLC)1284875998(PPN)258839023(DE-He213)978-3-030-88534-2(EXLCZ)99494000000061568920211104d2021 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierFounding Mathematics on Semantic Conventions /by Casper Storm Hansen1st ed. 2021.Cham :Springer International Publishing :Imprint: Springer,2021.1 online resource (259 pages)Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science,2542-8292 ;4463-030-88533-X Includes bibliographical references and index.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.Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science,2542-8292 ;446MathematicsPhilosophyMathematical logicMetaphysicsLanguage and languagesPhilosophyMathematical analysisPhilosophy of MathematicsMathematical Logic and FoundationsMetaphysicsPhilosophy of LanguageAnalysisMathematicsPhilosophy.Mathematical logic.Metaphysics.Language and languagesPhilosophy.Mathematical analysis.Philosophy of Mathematics.Mathematical Logic and Foundations.Metaphysics.Philosophy of Language.Analysis.510.1Hansen Casper Storm1052511MiAaPQMiAaPQMiAaPQBOOK9910508469503321Founding Mathematics on Semantic Conventions2483844UNINA