Kant’s Refutation of Hume’s Position on Causality

Henschen, Tobias

doi:10.1515/9783110467888-129

Cited by 4 publications

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“…Biondi, Groarke, eds. 2014;Qu 2014;Steel 2010;Tucker 2009;Hetherington 2008;Weintraub 2008;1995;Loeb 2006;Okasha 2005;Boulter 2002;Lipton 2002;Helm 1993;Jakobson 1987;Parush 1977) or causality as "Hume's theory" of it (e.g : Henschen 2018;McBreen 2007;Watkins 2005;Jakobson 1986;Röd 1983;Ducasse 1966…”

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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

Пенчев

2022

SSRN Journal

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confidence: 99%

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

Пенчев

2022

SSRN Journal

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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

Пенчев¹

2022

Preprint

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The previous two parts of the paper (correspondingly, https://philpapers.org/rec/PENFLT-2 and https://philpapers.org/rec/PENFLT-3) demonstrate that the interpretation of Fermat’s last theorem (FLT) in Hilbert arithmetic meant both in a narrow sense and in a wide sense can suggest a proof by induction in Part I and by means of the Kochen - Specker theorem in Part II. The same interpretation can serve also for a proof FLT based on Gleason’s theorem and partly similar to that in Part II. The concept of (probabilistic) measure of a subspace of Hilbert space and especially its uniqueness can be unambiguously linked to that of partial algebra or incommensurability, or interpreted as a relation of the two dual branches of Hilbert arithmetic in a wide sense. The investigation of the last relation allows for FLT and Gleason’s theorem to be equated in a sense, as two dual counterparts, and the former to be inferred from the latter, as well as vice versa under an additional condition relevant to the Gödel incompleteness of arithmetic to set theory. The qubit Hilbert space itself in turn can be interpreted by the unity of FLT and Gleason’s theorem. The proof of such a fundamental result in number theory as FLT by means of Hilbert arithmetic in a wide sense can be generalized to an idea about “quantum number theory”. It is able to research mathematically the origin of Peano arithmetic from Hilbert arithmetic by mediation of the “nonstandard bijection” and its two dual branches inherently linking it to information theory. Then, infinitesimal analysis and its revolutionary application to physics can be also re-realized in that wider context, for example, as an exploration of the way for physical quantity of time (respectively, for time derivative in any temporal process considered in physics) to appear at all. Finally, the result admits a philosophical reflection of how any hierarchy arises or changes itself only thanks to its dual and idempotent counterpart.

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Kant-Bibliographie 2018

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2020

Kant-Studien

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Kant’s Refutation of Hume’s Position on Causality

Cited by 4 publications

References 0 publications

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

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

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

Kant-Bibliographie 2018

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