Неопределенные суждения: трактовки Аристотеля, Боэция и Н. А. Васильева

The paper presents the problem of indeterminate statements in the work of three thinkers: the creator of syllogistic Aristotle (384–322), its translator into Latin and interpreter Severin Boethius (480–525), and the creator of an imaginary (no-aristotle) logic of N. A. Vasiliev (1880–1940). The difference of Aristotle’s and N. A. Vasiliev logic based on different interpretations of indeterminate statements. The paper shows that the accidental opinion of N. A. Vasiliev similar to indeterminate statement of modal syllogistic of Aristotle, namely, the statement of the potentially inherent.В  статье  представлено  решение проблемы  неопределенных  суждений  в трудах  трех  мыслителей:  создателя  силлогистики Аристотеля(384–322), его переводчика на латынь  и  интерпретатора  Северина  Боэция (480 – 525) и создателя воображаемой(неаристотелевой) логики  Н. А. Васильева(1880 – 1940). Различие логик Аристотеля и Н. А. Васильева основано на различных трактовках неопределенных  суждений.  В статье  показано,  что акцидентальное  суждение  Н. А. Васильева аналогично  неопределенному  суждению  модальной силлогистики Аристотеля, а именно суждению о возможно присущем

The logic of forbidden colours

The purpose of this paper is twofold: (1) to clarify Ludwig Wittgenstein’s thesis that colours possess logical structures, focusing on his ‘puzzle proposition’ that “there can be a bluish green but not a reddish green”, (2) to compare modeltheoretical and gametheoretical approaches to the colour exclusion problem. What is gained, then, is a new gametheoretical framework for the logic of ‘forbidden’ (e.g., reddish green and bluish yellow) colours. My larger aim is to discuss phenomenological principles of the demarcation of the bounds of logic as formal ontology of abstract objects

Intensional Semantics for Syllogistics: what Leibniz and Vasiliev Have in Common

This article deals with an alternative interpretation of syllogistics, different from the classical (extensional) one: an intensional one, in which subject and predicate are not associated with a set of individuals (the extension of the concept) but a set of attributes (the content of the concept). The authors of the paper draw attention to the fact that this approach was first proposed by Leibniz in works on logical calculus, which for a long time remained in the shadow of his other philosophical works. Currently, the intensional approach is gaining more and more popularity due to the development of non-classical logics, and the article will present several existing intensional formal syllogistic semantics. The paper will also consider another historical approach to syllogistics, associated with the name of the Russian logician Nikolai Vasiliev, who is not only one of the founders of non-classical (non-Aristotelian logic) but also of a different intensional interpretation of such logic. The authors, along with the already known formalizations of Vasiliev’s ideas, present two new systems. One of them is a reconstruction of one type of imaginary logic with statements of three qualities: affirmative and two types of negative statements (with absolute and ordinary negation). The second system is the one that is adequate to semantics, in which instead of the four classical ones, only three types of statements are presented (two particular statements are replaced by one - accidental), and their significance is determined through the relation of the classical logical entailment. Both of them are interpreted intensionally. The intensional approach in logic and, in particular, in syllogistics allows us to expand the class of accepted principles (which occurs due to the expansion of the class of correct moods of syllogisms)

Black holes in three dimensional higher spin gravity: A review

We review recent progress in the construction of black holes in three dimensional higher spin gravity theories. Starting from spin-3 gravity and working our way toward the theory of an infinite tower of higher spins coupled to matter, we show how to harness higher spin gauge invariance to consistently generalize familiar notions of black holes. We review the construction of black holes with conserved higher spin charges and the computation of their partition functions to leading asymptotic order. In view of the AdS/CFT correspondence as applied to certain vector-like conformal field theories with extended conformal symmetry, we successfully compare to CFT calculations in a generalized Cardy regime. A brief recollection of pertinent aspects of ordinary gravity is also given.Comment: 49 pages, harvmac, invited contribution to J. Phys. A special volume on "Higher Spin Theories and AdS/CFT" edited by M. R. Gaberdiel and M. Vasilie

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

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

Paraconsistent First-Order Logic with infinite hierarchy levels of contradiction

In this paper paraconsistent first-order logic LP^{#} with infinite hierarchy levels of contradiction is proposed. Corresponding paraconsistent set theory KSth^{#} is discussed.Axiomatical system HST^{#}as paraconsistent generalization of Hrbacek set theory HST is considere

Nicolai Vasiliev’s Imaginary Logic and Semantic Foundations for the Logic of Assent

Le philosophe russe Nicolai Vasiliev est connu en tant que précurseur des logiques essentiellement non-classiques, c'est-à-dire de logiques qui diffèrent de la logique classique par l'abandon de principes qui sont corrects en logique classique. La gamme de telles logiques couvre la logique intuitionniste, la logique plurivalente, la logique paraconsistante et les logiques de la pertinence. Dans la première partie de ce texte, j'analyse brièvement les vues de Vasiliev, à savoir sa « logique imaginaire », qu'il présente comme une nouvelle logique non-aristotélicienne. Dans les sections suivantes je discute l'impact des approches de Vasiliev sur la logique du consentement. Ici, les idées essentiellement non-classiques de Vasiliev seront reliées à des logiques non- essentiellement non-classiques, qui ne constituent pas une révision de la logique classique, mais étendent sa puissance expressive.The Russian philosopher Nicolai Vasiliev is known as a forerunner of substantially non-classical logics, i.e., logics that differ from classical logic by dropping principles that are sound in classical logic. The range of such logics covers intuitionistic logic, many-valued logic, paraconsistent logic and relevant logics. In the first part of this paper, I will give a short analysis of Vasiliev's views, namely his Imaginary Logic, which is presented by Vasiliev as a new non-Aristotelian logic. In the following parts I will discuss the impact of Vasiliev's approaches on the logic of assent. Here Vasiliev's essentially non-classical ideas will be connected with non-substantially non-classical logics, which don't constitute a revision of classical logic, but an expansion of the expressive power of classical logic