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Paul Hertz y los Orígenes de la Teoría de la Demostración

Authors: Legris, Javier;

Paul Hertz y los Orígenes de la Teoría de la Demostración

Abstract

RESUMEN: El matemático y físico Paul Hertz escribió durante la década de 1920 una serie de trabajos que influyeron en el desarrollo de la teoría de la demostración y, en particular, la obra de Gentzen. Este trabajo se propone examinar en detalle la teoría lógica de Hertz ubicándola en el contexto del programa metamatemático de Hilbert. Se describe su búsqueda de sistemas independientes mínimos y se analizan sus conceptos de Satzsystem y de demostración normal. Entonces, se traza también el camino que va de las proposiciones de Hertz a los secuentes de Gentzen y, finalmente, se toma en consideración la filosofia de la lógica subyacente a las ideas de Hertz, la cual consiste en reducir las constantes lógicas a ciertas reglas de deducción, y se la compara con el enfoque “estructural” debido a Gentzen. Palabras clave: Teoría de la Demostración; Historia de la Lógica Moderna; Filosofía de la Lógica; Programa de Hilbert. PAUL HERTZ AND THE ORIGINS OF PROOF THEORY Abstract: The mathematician and physicist Paul Hertz wrote during the 1920s a series of papers that influenced the development of proof theory and, particularly, Gentzen's work. This paper aims to examine in detail Hertz's logical theory placing ii in the context of Hilbert's metamathematical program. His search for minimal independent systems is described, and his notions of Satzsystems and normal proof are analyzed. Then, the way from Hertz's propositions to Gentzen's sequents is also traced and, finally, the philosophy of logic underlying Hertz's ideas, consisting of a reduction of logical constants to certain deduction rules, is also taken into account and compared with the “structural” approach due to Gentzen. Keywords: Proof Theory; History of Modern Logic; Philosophy of Logic; Hilbert's Program.

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popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
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influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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impulse
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