The Logics of Hegel and Russell

Ushenko, A. P.

doi:10.2307/2103250

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“…The same metaphor in relation to infinity and in the context of Hegel's dialectics or dialectical logic can be revealed in Usó-Doménech,. Selva, Antonio, M. B. Requena, Segura-Abad (2017); Usó-Doménech, Selva, Requena (2016), or even inUshenko (1949); andPosy (2008) links infinity to Kant's intuition. The logic of infinity is the subject ofSheppard (2011).…”

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Gödel Mathematics Versus Hilbert Mathematics. II Logicism and Hilbert Mathematics, the Identification of Logic and Set Theory, and Gödel’s 'Completeness Paper' (1930)

Penchev

2022

SSRN Journal

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confidence: 99%

Gödel Mathematics Versus Hilbert Mathematics. II Logicism and Hilbert Mathematics, the Identification of Logic and Set Theory, and Gödel’s 'Completeness Paper' (1930)

Penchev

2022

SSRN Journal

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Gödel mathematics versus Hilbert mathematics. II Logicism and Hilbert mathematics, the identification of logic and set theory, and Gödel’s “completeness paper” (1930)

Пенчев

2023

Preprint

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The previous Part I of the paper (https://doi.org/10.33774/coe-2022-wlr02) discusses the option of the Gödel incompleteness statement (1931: whether “Satz VI” or “Satz X”) to be an axiom due to the pair of the axiom of induction in arithmetic and the axiom of infinity in set theory after interpreting them as logical negations to each other. The present Part II considers the previous Gödel’s paper (1930) (and more precisely, the negation of “Satz VII”, or “the completeness theorem”) as a necessary condition for granting the Gödel incompleteness statement to be a theorem just as the statement itself, to be an axiom. Then, the “completeness paper” can be interpreted as relevant to Hilbert mathematics, according to which mathematics and reality as well as arithmetic and set theory are rather entangled or complementary rather than mathematics to obey reality able only to create models of the latter.

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The Logics of Hegel and Russell

Cited by 2 publications

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Gödel Mathematics Versus Hilbert Mathematics. II Logicism and Hilbert Mathematics, the Identification of Logic and Set Theory, and Gödel’s 'Completeness Paper' (1930)

Gödel Mathematics Versus Hilbert Mathematics. II Logicism and Hilbert Mathematics, the Identification of Logic and Set Theory, and Gödel’s 'Completeness Paper' (1930)

Gödel mathematics versus Hilbert mathematics. II Logicism and Hilbert mathematics, the identification of logic and set theory, and Gödel’s “completeness paper” (1930)

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