December 2020
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Publications (13)
December 2012
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2 Reads
November 2012
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7 Reads
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9 Citations
January 2000
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2 Reads
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8 Citations
Revista española de la opinión pública
October 1961
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4 Reads
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39 Citations
The Philosophical Quarterly
April 1961
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3 Reads
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2 Citations
Philosophy of Science
In his review of our Gödel's Proof in the April 1960 issue of Philosophy of Science Professor Hilary Putnam severely criticizes the crucial chapter, in which we attempt to make intelligible to the non-specialist the general character of the argument for Gödel's main conclusions. Indeed, he asserts that “the chapter culminates in an extremely serious misstatement,” and that we “fail to give the proof that G [the Gödel sentence upon which the argument hinges] is not provable.” “The book,” he declares, “has thus a serious shortcoming (in a very literal sense of ‘shortcoming’: it comes right up to the heart of Gödel's argument and then stops short with a misstatement')” (p. 205). These assertions impugn the competence of our exposition of Gödel's achievements, and we therefore ask for the privilege of replying to Dr. Putnam's allegations.
January 1961
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6 Reads
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1 Citation
The Journal of Philosophy
June 1956
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13 Reads
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154 Citations
Scientific American
2 Reads
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7 Citations
Journal of Symbolic Logic
51 Reads
Traducción de: Gödel's Proof Pieza fundamental de la historia de la lógica, la obra de Kurt Gödel supuso una gran revolución en esta disciplina. Con tan sólo 25 años de edad, en 1931 dio a conocer el denominado teorema de incompletud de Gödel, según el cual dentro de todo sistema formal que contenga la teoría de los números existen proposiciones que el sistema no logra demostrar ni negar; sostuvo, también, que entre las proposiciones que en un sistema la aritmética no lograba decidir, había también una que, en términos numéricos, expresaba la no-contradictoriedad de toda la teoría formal de los números utilizando un cierto fragmento de la aritmética, la llamada "aritmética finitista".
Citations (4)
... There has been a massive amount of literature on the Anti-Mechanist Arguments due primarily to Lucas and Penrose (see Lucas [34], Penrose [42]) which claim that G1 shows that the human mind cannot be mechanized. The Anti-Mechanist Argument began with Nagel and Newman in [39] and continued with Lucas's publication in [34]. Nagel and Newman's argument was criticized by Putnam in [45], while Lucas's argument was much more widely criticized in the literature. ...
- Citing Article
June 1956
Scientific American
... An example being the Law of Non-Contradiction, the straightforward claim that a proposition and its negation can never obtain at the same time. In 1931, Kurt Gödel published his famous Incompleteness Theorems [15]. These sent shockwaves through the mathematical community. ...
- Citing Article
October 1961
The Philosophical Quarterly
... Note incidentally that entailment relations are connectivefree. The usual reliance on Markov's principle to intuitionistically prove completeness as validity implies provability [22] does not apply (see e.g. [15], [12] for recent studies). ...
- Citing Article
Journal of Symbolic Logic
... El teorema de Gödel vino a darle en el traste al sueño hilbertiano, al demostrar que cualquier sistema axiomático suficientemente rico, como para que contenga la aritmética clásica (es decir, los axiomas de G. Peano (1858-1932)), es inevitablemente incompleto, es decir, que existen proposiciones que siendo verdaderas no son demostrables o deducibles dentro del sistema axiomático en cuestión. Dicho de otra manera, el árbol deductivo asociado al sistema axiomático en examen tiene hoyos inaccesibles por medio de la «escalera deductiva», o lo que es lo mismo, existen proposiciones que son indecidibles dentro del sistema axiomático a la mano, diferenciando de una vez y para siempre las nociones de verdad y demostrabilidad (Nagel y Newman, 2007). ...
- Citing Article
January 2000
Revista española de la opinión pública