Kurt Gödel's Anticipation of the Turing Machine: A Vitalistic Approach

Lethen, Tim

doi:10.1080/01445340.2020.1768461

Cited by 6 publications

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Section: Tim Lethenmentioning

confidence: 96%

“…43 Kurt Gödel Papers, Box 6b, Folder 78, item accession 030106 and 030107. These books, henceforth simply abbreviated QM1 and QM2, have briefly been described in Lethen (2020a) and will be published in Lethen & Passon (2021).…”

Section: Tim Lethenmentioning

confidence: 99%

“…D.h., welches ist die Struktur derjenigen 46 Folge von Theorien, welche die klassische Theorie einer 43 Kurt G ödel Papers, Box 6b, Folder 78, item accession 030106 and 030107. These books, henceforth simply abbreviated QM1 and QM2, have briefly been described in [19] and will be published in [22]. 44 Kurt G ödel Papers, Box 6a, Folder 59, item accession 030082.…”

Section: Russell's Antinomymentioning

confidence: 99%

“…And in his notebooks on quantum mechanics written in 1935, G ödel himself uses Richard's paradox to show that the notion of "lawlike sequence" cannot be defined as "produced by a machine," thus anticipating Turing's famous results. This proof has been reconstructed in [19]. G ödel's general interest in the antinomies is most clearly expressed in notes preparing a course on elementary logic at the University of Notre Dame in the spring of 1939.…”

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Kurt Gödel on Logical, Theological, and Physical Antinomies

Lethen¹

2021

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This paper presents hitherto unpublished writings of Kurt Gödel concerning logical, epistemological, theological, and physical antinomies, which he generally considered as "the most interesting facts in modern logic," and which he used as a basis for his famous metamathematical results. After investigating different perspectives on the notion of the logical structure of the antinomies and presenting two "antinomies of the intensional," a new kind of paradox closely related to Gödel's ontological proof for the existence of God is introduced and completed by a compilation of further theological antinomies. Finally, after a presentation of unpublished general philosophical remarks concerning the antinomies, Gödel's type-theoretic variant of Leibniz' Monadology, discovered in his notes on the foundations of quantum mechanics, is examined. Most of the material presented here has been transcribed from the Gabelsberger shorthand system for the first time. §1. Introduction. As Kurt Gödel repeatedly stressed, his famous first incompleteness theorem is firmly based on the Liar paradox, which, in its simplest form, consists of the statement "This sentence is false," in which he replaced "false" (for a specific formal theory T ) by "unprovable in T ." Many of Gödel's writings, though, reveal the conviction that the proof of the incompleteness theorem may as well be based on other antinomies, notably Richard's antinomy. In his goundbreaking 1931 publication "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I," Gödel writes: "The analogy between this result and Richard's antinomy leaps to the eye; there is also a close relationsship with the 'liar' antinomy," and in a footnote he continues: "Every epistemological antinomy can likewise be used for a similar undecidability proof." (Gödel, 1931, p. 175) Also, in one of his notebooks 1 preparing his publication, Gödel writes:Man erkennt den nahen Zusammenhang dieses Beweises mit der Ant. Rich., und es lässt sich erwarten, dass auch die anderen 2 epist. Ant. ebenfalls sich zu analogen Beweisen umgestalten lassen, was auch tatsächlich zutrifft.One recognises the close connection of this proof with the Richard antinomy, and it can be expected that also the other 3 epistemological antinomies can be reshaped into analogous proofs, something that actually happens.Gödel considered as one of the main ingredients of these "analogous proofs" the formal reproduction of the epistemological or semantical antinomies, focusing on their inner logical "shape" (Gestalt). In a typewritten manuscript of a lecture 4 given in Bad Elster in

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Section: Tim Lethenmentioning

confidence: 96%

Section: Tim Lethenmentioning

confidence: 99%

Section: Russell's Antinomymentioning

confidence: 99%

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