In a previous paper, an elementary and thoroughly arithmetical proof of Fermat’s last theorem by induction has been demonstrated if the case for “n = 3” is granted as proved only arithmetically (which is a fact a long time ago), furthermore in a way accessible to Fermat himself though without being absolutely and precisely correct. The present paper elucidates the contemporary mathematical background, from which an inductive proof of FLT can be inferred since its proof for the case for “n (...) = 3” has been known for a long time. It needs “Hilbert mathematics”, which is inherently complete unlike the usual “Gödel mathematics”, and based on “Hilbert arithmetic” to generalize Peano arithmetic in a way to unify it with the qubit Hilbert space of quantum information. An “epoché to infinity” (similar to Husserl’s “epoché to reality”) is necessary to map Hilbert arithmetic into Peano arithmetic in order to be relevant to Fermat’s age. Furthermore, the two linked semigroups originating from addition and multiplication and from the Peano axioms in the final analysis can be postulated algebraically as independent of each other in a “Hamilton” modification of arithmetic supposedly equivalent to Peano arithmetic. The inductive proof of FLT can be deduced absolutely precisely in that Hamilton arithmetic and the pransfered as a corollary in the standard Peano arithmetic furthermore in a way accessible in Fermat’s epoch and thus, to himself in principle. A future, second part of the paper is outlined, getting directed to an eventual proof of the case “n=3” based on the qubit Hilbert space and the Kochen-Specker theorem inferable from it. (shrink)

"Да резюмираме: отказът от всяка форма на либерализъм и разделяне на властите, госnодството на една nартия и монополната власт, отказът от всякакъв идеологически · неутралитет и култивиране на единодушие, nреобладаване на бюрокрацията, олицетворяваща nроизвола и тайната, nрезрението към nравото и nак nоявата на политически nрестъnления и наказания за умисъл или "азиатското nрезрение към човешкия живот" - всичко това nоказва, че комунистическият режим е бил не само е наследник на Маркс, но в не по-малка стеnен - наследник на царското самодържавие. Това (...) чудовищно сдвояване на царското самодържавие с ленинския марксизъм е nричината за бъдещия сталинизъм" (Кокен 1996: 350). (shrink)

The paper is a continuation of another paper published as Part I. Now, the case of “n=3” is inferred as a corollary from the Kochen and Specker theorem (1967): the eventual solutions of Fermat’s equation for “n=3” would correspond to an admissible disjunctive division of qubit into two absolutely independent parts therefore versus the contextuality of any qubit, implied by the Kochen – Specker theorem. Incommensurability (implied by the absence of hidden variables) is considered as dual to quantum contextuality. The (...) relevant mathematical structure is Hilbert arithmetic in a wide sense, in the framework of which Hilbert arithmetic in a narrow sense and the qubit Hilbert space are dual to each other. A few cases involving set theory are possible: (1) only within the case “n=3” and implicitly, within any next level of “n” in Fermat’s equation; (2) the identification of the case “n=3” and the general case utilizing the axiom of choice rather than the axiom of induction. If the former is the case, the application of set theory and arithmetic can remain disjunctively divided: set theory, “locally”, within any level; and arithmetic, “globally”, to all levels. If the latter is the case, the proof is thoroughly within set theory. Thus, the relevance of Yablo’s paradox to the statement of Fermat’s last theorem is avoided in both cases. The idea of “arithmetic mechanics” is sketched: it might deduce the basic physical dimensions of mechanics (mass, time, distance) from the axioms of arithmetic after a relevant generalization, Furthermore, a future Part III of the paper is suggested: FLT by mediation of Hilbert arithmetic in a wide sense can be considered as another expression of Gleason’s theorem in quantum mechanics: the exclusions about (n = 1, 2) in both theorems as well as the validity for all the rest values of “n” can be unified after the theory of quantum information. The availability (respectively, non-availability) of solutions of Fermat’s equation can be proved as equivalent to the non-availability (respectively, availability) of a single probabilistic measure as to Gleason’s theorem. (shrink)

A proof of Fermat’s last theorem is demonstrated. It is very brief, simple, elementary, and absolutely arithmetical. The necessary premises for the proof are only: the three definitive properties of the relation of equality (identity, symmetry, and transitivity), modus tollens, axiom of induction, the proof of Fermat’s last theorem in the case of n = 3 as well as the premises necessary for the formulation of the theorem itself. It involves a modification of Fermat’s approach of infinite descent. The infinite (...) descent is linked to induction starting from n = 3 by modus tollens. An inductive series of modus tollens is constructed. The proof of the series by induction is equivalent to Fermat’s last theorem. As far as Fermat had been proved the theorem for n = 4, one can suggest that the proof for n ≥ 4 was accessible to him. An idea for an elementary arithmetical proof of Fermat’s last theorem (FLT) by induction is suggested. It would be accessible to Fermat unlike Wiles’s proof (1995). (shrink)

Тhе question which animates Heidegger's paper (''Die onto-theo-logische Verfassung der Metaphysik:) is: "How are God coming in phi1osophy?"; and it is only а sharpening of "th.e question of the onto-theologic character of philosophy". Hegel and Heidegger are bothunited and opposed as identity and difference. Both being and existing descend from difference. Equilibrium (Aпstrag) arranges the unit of being and existing.

В книге представлены статьи современных российских философов, писателей, литературоведов о творчестве и миросозерцании русского философа и писателя Василия Васильевича Розанова (1856-1919). Труды розановедов собраны за последние 25 лет.

Цель данного издания - познакомить широкий круг читателей с основными вехами жизни ученого, организатора, ее научными трудами, литературой о ней.

Here we suggest a formal using of N.A. Vasil’ev’s logical ideas in categorical logic: the idea of “accidental” assertion is formalized with topoi and the idea of the notion of nonclassical negation, that is not based on incompatibility, is formalized in special cases of monoidal categories. For these cases, the variant of the law of “excluded n-th” suggested by Vasil’ev instead of the tertium non datur is obtained in some special cases of these categories. The paraconsistent law suggested (...) by Vasil’ev is also demonstrated with linear and tensor logics but in a form weaker than he supposed. As we have, in fact, many truth-values in linear logic and topos logic, the admissibility of the traditional notion of inference in the categorical interpretation of linear and intuitionistic proof theory is discussed. (shrink)

The solution of the problem of the future random events truth is considered in Vasil’ev’s logic. N. A. Vasil’ev graded the logic according to two levels—the level of facts, i.e. time fixed events, and the level of notions or rules, governing these facts. The mathematical construction previously suggested for imaginary Vasil’ev’s logic, extends to the early variant of his logic—a logic of notions. In the paper, we investigate the meaning of problematic and uncertain assertions introduced by (...) class='Hi'>Vasil’ev. As a result, we developed a model of Vasil’ev’s logic of facts that resolves also the truth problem of future random events. The imaginary logic has also been extended to the level of notions, and the law of the excluded eighth is gotten in it. The correspondence between Vasil’ev’s terms “some” and “all” and modern quantifiers is discussed. (shrink)

BOOK REVIEWS: Valentin A. Bazhanov, “N.A. Vasil’ev and his Imaginary Logic”, Kanon+, Reabilitatsiia, Moscow, 2009, 240 pp., ISBN 9785883731968.

[1]Aldanov, M. A. [i dr.] Religīoznyi︠a︡ i obshchestvennyi︠a︡ iskanīi︠a︡.--[2]Melgunov, S. P. N. V. Chaĭkovskīĭ v gody grazhdanskoĭ voĭny.

Volume 40, Issue 3, August 2019, Page 298-303.

The paper investigates the system of 'Imaginary Logic' created by the Russian logician N.A. Vasil'ev (1880-1940), considered by some to be a forerunner of paraconsistent or intuitionistic logics. It is shown how he constructs a logic without the law of contradiction redefining the concept of negation. Vasil'ev singles out two levels of logic, an external one which is absolute and one depending on commitments in relation to cognizable objects which is not absolute. His reconstruction of the syllogism shows (...) the viability of his system and indicates how, indeed, he may be called an initiator of nonclassical logics. (shrink)

As it happened, I became acquainted with E.V. Il'enkov quite late, in the mid- or even the late 1960s. It was only a bit more than ten years before his death that I began to feel at home in his house, was able to visit without calling ahead, and was able to call him by his first name and the familiar "you"—that is, like many, many of not only his true friends but also like-minded thinkers, who became his close acquaintances, (...) most of whom justly considered themselves his pupils … The door would open wide, and Olia, Professor K.I. Salimova, Eval'd's wife and most devoted friend, not at all surprised by the unexpected guest and seemingly even quite happy at his arrival , would try first to draw him into the kitchen and feed him … which she more often than not succeeded in doing. I am not talking about myself: there were always many guests, and this is precisely how they arrived at the Il'enkovs' apartment. Recently, a critic in Literaturnaia gazeta recalled those whom he met in Eval'd's apartment in the 1960s: "This was a tight circle of like-minded thinkers," wrote the critic. "But some of them are no longer with us, while most are far away, beyond our borders." Obviously, he had not been in the house often or had forgotten things over the distance of years. There was no "circle," nor could there have been one—not with this host, not with his lifestyle and way of relating to people. I met a good hundred fine and various people in Eval'd's home: I.N. Korzhavin, V. Davydov, A. Meshcheriakov, S. Vinogradova, N. Dubinin, V. Zinchenko, A. Zinov'ev, Iu. Kamiakin, and … indeed, five pages would not be enough to list the quite famous and the not-quite-so-famous, simply ordinary people with no claim to fame. Nazym Khikmet, A.N. Leont'ev, and B.M. Kedrov were friends of the house … Ever new faces, figures, and words come to mind. I cannot forgive myself: once Eval'd Vasil'evich wanted to take me along to Iurii Liubimov's to read his play Neither God nor Tsar nor Hero … [Ni bog, ni tsar' i ni geroi], but I had some other business, something so important that I do not even remember now what it was, and it is probably not worth remembering. But most likely I was too timid to appear uninvited at the house of a person burning with creativity. The same thing happened with Galich … Eval'd liked especially his song about Zoshchenko. He did not sing it; he narrated it, but in such a way that tears always came to one's eyes. (shrink)

Analytical study of the social theories of Muslim philosophers belonged to 9th to 18th centuries.

Tomo I. Una antología comentada de su obra -- Tomo II. Una antología comentada.