Kurt Gödel: revolución en los fundamentos de las mateméticas
DOI:
https://doi.org/10.3989/arbor.2007.i725.113Keywords:
Philosophy of mathematics, mathematical logic, foundations of mathematics, consistency, incompleteness, set theory, metamathematics, Hilbert’s program, platonismAbstract
We offer a survey of Kurt Gödel’s main contributions in the field of Logic and foundations of mathematics, and we analyse their impact, which can well be called revolutionary. The aim is to contribute to an understanding of the aims and methodological orientation of Gödel’s work, and to deal in some detail with their philosophical consequences. Thus, a perspective is offered on how the philosophy of mathematics changed between the dates of birth and death of this great mathematical logician.
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References
Obras completas, Alianza, Madrid, 1989. “La situación presente en los fundamentos de las matemáticas”, en La Gaceta de la Real Sociedad Matemática Española, vol. 9, 3, 2006, 761-771.
Collected Works. Volúmenes I-V. Ed. S. Feferman et al., Oxford University Press, New York, 1986-2003.
Dawson, John W. (1997): Logical Dilemmas: The Life and Work of Kurt Gödel, A. K. Peters, Wellesley (Mass.).
Análisis desde el punto de vista lógico y filosófico
Feferman, Solomon (1998): In the Light of Logic, Oxford University Press, New York, 1998.
Ferreirós, José (1999): “Matemáticas y platonismo(s)”, en La Gaceta de la Real Sociedad Matemática Española, vol. 2, 446-473.
Franzén, Torkel (2005): Gödel’s Theorem. An Incomplete Guide to Its Use and Abuse, A K Peters, Wellesley (Mass.).
Jané, Ignacio (2006): “La obra de Gödel en lógica matemática y teoría de conjuntos”, en La Gaceta de la Real Sociedad Matemática Española, vol. 9, 3, 772-788.
Tait, W. (1981): “Finitism”, Journal of Philosophy, 78; reimpreso en Tait, The Provenance of Pure Reason, Oxford University Press, 2005.
Wang, Hao (1991): Reflexiones sobre Kurt Gödel, Alianza, Madrid.
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