Fermat’s Last Theorem Proved in Hilbert Arithmetic. Iii. the Quantum-Information Unification of Fermat’s Last Theorem and Gleason’s Theorem

Пенчев, Васил

doi:10.2139/ssrn.4140028

Cited by 2 publications

(3 citation statements)

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“…as a mathematical statement needing a relevant proof what the nonstandard bijection (discussed in detail in other pares, e.g. Penchev 2022 June 30;2022 May 11;2022 March 11) quantum-mechanical description to the description of the same system in classical mechanics) inherently conditioning incompleteness, the explicit contradiction of their mutual anti-isometry appears immediately.…”

Section: The Gödel Incompleteness Versus the Gentzen Completeness By ...mentioning

confidence: 99%

“…Thus, the former generalizes the latter describing the transition from an infinite set to a finite set rather than a finite set as an ultimate result (being "ready-for-use") meant explicitly by Peano arithmetic by its fundamental concept of "natural number". In other words, that Dedekind-like finiteness means the process of how Peano arithmetic appears from any infinite set, or speaking loosely, from infinity just as Hilbert arithmetic in a wide sense means (for example, in relation to that: Fermat's last theorem to be proved : Penchev 2022 June 30;2022 May 11;2022 March 11).…”

Section: The Dedekind-like Bijection Of Infinite Sets Into Finite Set...mentioning

confidence: 99%

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Gentzen’s ‘Cut Rule’ and Quantum Measurement in Terms of Hilbert Arithmetic. Metaphor and Understanding Modeled Formally

Пенчев

2022

SSRN Journal

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Section: The Gödel Incompleteness Versus the Gentzen Completeness By ...mentioning

confidence: 99%

Section: The Dedekind-like Bijection Of Infinite Sets Into Finite Set...mentioning

confidence: 99%

Gentzen’s ‘Cut Rule’ and Quantum Measurement in Terms of Hilbert Arithmetic. Metaphor and Understanding Modeled Formally

Пенчев

2022

SSRN Journal

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“…as a mathematical statement needing a relevant proof what the nonstandard bijection (discussed in detail in other pares, e.g. Penchev 2022 June 30;2022 May 11;2022 March 11) can deliver by its two dual "directions":…”

Section: The Gödel Incompleteness Versus the Gentzen Completeness By ...mentioning

confidence: 99%

Gentzen’s “Cut Rule” and Quantum Measurement in Terms of Hilbert Arithmetic. Metaphor and Understanding Modeled Formally

Пенчев¹

2022

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Hilbert arithmetic in a wide sense, including Hilbert arithmetic in a narrow sense consisting by two dual and anti-isometric Peano arithmetics, on the one hand, and the qubit Hilbert space (originating for the standard separable complex Hilbert space of quantum mechanics), on the other hand, allows for an arithmetic version of Gentzen’s cut elimination and quantum measurement to be described uniformy as two processes occurring accordingly in those two branches. A philosophical reflection also justifying that unity by quantum neo-Pythagoreanism links it to the opposition of propositional logic, to which Gentzen’s cut rule refers immediately, on the one hand, and the linguistic and mathematical theory of metaphor therefore sharing the same structure borrowed from Hilbert arithmetic in a wide sense. An example by hermeneutical circle modeled as a dual pair of a syllogism (accomplishable also by a Turing machine) and a relevant metaphor (being a formal and logical mistake and thus fundamentally inaccessible to any Turing machine) visualizes human understanding corresponding also to Gentzen’s cut elimination and the Gödel dichotomy about the relation of arithmetic to set theory: either incompleteness or contradiction. The metaphor as the complementing “half” of any understanding of hermeneutical circle is what allows for that Gödel-like incompleteness to be overcome in human thought.

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Fermat’s Last Theorem Proved in Hilbert Arithmetic. Iii. the Quantum-Information Unification of Fermat’s Last Theorem and Gleason’s Theorem

Cited by 2 publications

References 79 publications

Gentzen’s ‘Cut Rule’ and Quantum Measurement in Terms of Hilbert Arithmetic. Metaphor and Understanding Modeled Formally

Gentzen’s ‘Cut Rule’ and Quantum Measurement in Terms of Hilbert Arithmetic. Metaphor and Understanding Modeled Formally

Gentzen’s “Cut Rule” and Quantum Measurement in Terms of Hilbert Arithmetic. Metaphor and Understanding Modeled Formally

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