Opened Access Hilbert, logicism, and mathematical existence

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Autor: Ferreirós Domínguez, José Manuel
Departamento: Universidad de Sevilla. Departamento de Filosofía y Lógica y Filosofía de la Ciencia
Fecha: 2009
Publicado en: Synthese, 170(1), 33-70
Tipo de documento: Artículo
Resumen: David 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 At the same time, careful scrutiny of his published and unpublished work around the turn of the century uncovers deep differences between his ideas about consistency proofs before and after 1904.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 Hil...
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Tamaño: 860.5Kb
Formato: PDF

URI: http://hdl.handle.net/11441/40316

DOI: http://dx.doi.org/10.1007/s11229-008-9347-1

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