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dc.creatorFerreirós Domínguez, José Manueles
dc.date.accessioned2016-04-22T11:21:28Z
dc.date.available2016-04-22T11:21:28Z
dc.date.issued2009
dc.identifier.issn0039-7857 (print)es
dc.identifier.issn1573-0964 (online)es
dc.identifier.urihttp://hdl.handle.net/11441/40316
dc.description.abstractDavid Hilbert’s early foundational views, especially those corresponding to the 1890s, are analysed here. I consider strong evidence for the fact that Hilbert was a logicist at that time, following upon Dedekind’s footsteps in his understanding of pure mathematics. This insight makes it possible to throw new light on the evolution of Hilbert’s foundational ideas, including his early contributions to the foundations of geometry and the real number system. The context of Dedekind-style logicism makes it possible to offer a new analysis of the emergence of Hilbert’s famous ideas on mathematical existence, now seen as a revision of basic principles of the “naive logic” of sets. At the same time, careful scrutiny of his published and unpublished work around the turn of the century uncovers deep differences between his ideas about consistency proofs before and after 1904. Along the way, we cover topics such as the role of sets and of the dichotomic conception of set theory in Hilbert’s early axiomatics, and offer detailed analyses of Hilbert’s paradox and of his completeness axiom (Vollständigkeitsaxiom).es
dc.formatapplication/pdfes
dc.language.isoenges
dc.publisherSpringeres
dc.relation.ispartofSynthese, 170(1), 33-70es
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectDavid Hilbertes
dc.subjectFoundations of mathematicses
dc.subjectMathematical existencees
dc.subjectLogicismes
dc.subjectRichard Dedekindes
dc.subjectSet theoryes
dc.subjectAxiomaticses
dc.subjectMathematical logices
dc.subjectReal number systemes
dc.subjectParadoxeses
dc.subjectGeorg Cantores
dc.subjectConsistency proofses
dc.subjectModelses
dc.titleHilbert, logicism, and mathematical existencees
dc.typeinfo:eu-repo/semantics/articlees
dc.type.versioninfo:eu-repo/semantics/acceptedVersiones
dc.rights.accessrightsinfo:eu-repo/semantics/openAccesses
dc.contributor.affiliationUniversidad de Sevilla. Departamento de Filosofía y Lógica y Filosofía de la Cienciaes
dc.relation.publisherversionhttp://link.springer.com/article/10.1007%2Fs11229-008-9347-1es
dc.identifier.doihttp://dx.doi.org/10.1007/s11229-008-9347-1es
idus.format.extent37 p.es
dc.identifier.idushttps://idus.us.es/xmlui/handle/11441/40316

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