By Evert W. Beth

Traducción del capítulo 17 del libro de Evert W. Beth the principles of arithmetic

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Additional info for Las paradojas de la lógica

Sample text

16, 1905, p. 541. Reimpreso en Acta Mathematica, vol. 30, 1906, pp. 295-296) PARADOJA DE RUSSELL l. FORMULACIÓN INICIAL (1902): Carta de Russell a Frege (16 de Junio de 1902): . . "Existe justamente un punto en el que he encontrado una dificultad. Usted establece (p. nto indeterminado. Eso mismo pensaba yo antes, pero ahora este punto de vista me parece dudoso por la siguiente contradicción. Sea w el predicado: ser un predicado que no puede ser predicado de sí mismo. ¿Puede w ser predicado de sí mismo?

Por lo tanto, debemos concluir que w no es un predicado. Del mismo modo, no existe la clase (como una totalidad) de aquellas clases que, tomadas cada una como una totalidad, no pertenecen a sí mismas. De donde concluyo que, bajo ciertas circunstancias, un conjunto definible no forma una totalidad ... :::>: W E W. =. , E W. " 70 (Cfr. , "From Frege to GOdel", A Source Book in Mathematical Logic, 1879-1931, Cambridge, Mass. 1967, pp. ) .. Carta de Frege a Russell (22 de Junio de 1902): . . "Su descubrimiento de la contradicción me produjo la mayor sorpresa, incluso, yo diría, la mayor consternación, porque ha hecho tambalear los cimientos sobre los que yo intentaba construir la aritmética.

R: "l " BIBLIOGRAFfA Sobre las paradojas lógicas y de la teoría de conjuntos ·' "'~ "" ,• , '. ;. - .. , "Widerspruchsfreier Aufbau der Logik: l. Typenfreies System ohne Tertium non datur," The Journal o/ Symbolic Logic, vol. 15, 1950. " Jahresbericht der Deutschen Mathematiker~ Vereinigung, vol. 40, 1931, pp. 37-48. - - - , "The Paradoxes of Logic," en Mind, vol. 46, 1937, pp. 218-221. , en "Actes du 11 Congres International de l'Union Internationale de Philosophie · des Sciences", vol. JI, Paris, 1955, pp.

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