The dawn of paraconsistency: Russia's logical thought in the turn of XX century

Bazhanov, Valentin A.

doi:10.1590/s0100-60452011000100004

Cited by 5 publications

(4 citation statements)

References 3 publications

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“…A predecessor of paraconsistent and multi-valued logics was Vasiliev. See da Costa et al [71] and Bazhanov [20].…”

Section: Results In Ecqmentioning

confidence: 99%

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Analytic Continuation of $ζ(s)$ Violates the Law of Non-Contradiction (LNC)

Sharon

2018

Preprint

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The Dirichlet series of ζ(s) was long ago proven to be divergent throughout half-plane Re(s) ≤ 1. If also Riemann's proposition is true, that there exists an "expression" of ζ(s) that is convergent at all s (except at s = 1), then ζ(s) is both divergent and convergent throughout half-plane Re(s) ≤ 1 (except at s = 1).This result violates all three of Aristotle's "Laws of Thought": the Law of Identity (LOI), the Law of the Excluded Middle (LEM), and the Law of Non-Contradition (LNC). In classical and intuitionistic logics, the violation of LNC also triggers the "Principle of Explosion" / Ex Contradictione Quodlibet (ECQ).In addition, the Hankel contour used in Riemann's analytic continuation of ζ(s) violates Cauchy's integral theorem, providing another proof of the invalidity of Riemann's ζ(s). Riemann's ζ(s) is one of the L-functions, which are all invalid due to analytic continuation. This result renders unsound all theorems (e.g. Modularity, Fermat's last) and conjectures (e.g. BSD, Tate, Hodge, Yang-Mills) that assume that an L-function (e.g. Riemann's ζ(s)) is valid.We also show that the Riemann Hypothesis (RH) is not "non-trivially true" in classical logic, intuitionistic logic, or three-valued logics (3VLs) that assign a third truth-value to paradoxes (Bochvar's 3VL, Priest's LP ).

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“…A predecessor of paraconsistent and multi-valued logics was Vasiliev. See da Costa et al [71] and Bazhanov [20].…”

Section: Results In Ecqmentioning

confidence: 99%

“…Kleene's 3VL (c. 1952), 19 is over 65 years old. Priest's "Logic of Paradox" (LP ) (c. 1979) 20 is by far the youngest logic of this group, at "only" 40 years old.…”

Section: Attacking the Most Specific Problem With The Oldest Ideasmentioning

confidence: 99%

Analytic Continuation of $ζ(s)$ Violates the Law of Non-Contradiction (LNC)

Sharon

2018

Preprint

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“…Quite surprisingly, Florensky saw in this logical puzzle a profound expression of a crucial problem of the logic of religion. 5 He urged that it is not "extraordinary and artificially concocted difficulty, which has no significance for life", but rather "evoked by a real need" [18, p. 355], which concerns the relationship between rationality and faith. That is why, according to Florensky, "for a greater understanding of the step we take when we believe in the Truth", it is useful to "solve the aforementioned logical problem in its general form" [18, p. 335].…”

Section: The Analysis Of Lewis Carroll's Puzzlementioning

confidence: 99%

“…As I indicated, that was not a unique idea among logicians of his time. Florensky shared some intuitions with Lukasiewicz or Vasiliev, which are now recognized as forerunners of the idea of paraconsistency [2,3,5,26]. Paraconsistent logic seems therefore to be the most natural context for the interpretation of Florensky's views.…”

Section: Paraconsistent Logicsmentioning

confidence: 99%

Pavel Florensky’s Theory of Religious Antinomies

Rojek

2019

Log. Univers.

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Pavel Florensky (1882-1937), a Russian theologian, philosopher, and mathematician, argued that the religious discourse is essentially contradictory and put forward the idea of the logical theory of antinomies. Recently his views raised interesting discussions among logicians who consider him a forerunner of many non-classical logics. In this paper I discuss four interpretations of Florensky's views: paraconsistent, L-contradictory, non-monotonic and rhetorical. In conclusion I argue for the integral interpretation which unites these four approaches.

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The Historical and Cultural Context

Raspa

2017

Synthese Library

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The dawn of paraconsistency: Russia's logical thought in the turn of XX century

Cited by 5 publications

References 3 publications

Analytic Continuation of $ζ(s)$ Violates the Law of Non-Contradiction (LNC)

Analytic Continuation of $ζ(s)$ Violates the Law of Non-Contradiction (LNC)

Pavel Florensky’s Theory of Religious Antinomies

The Historical and Cultural Context

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