The aim of this book is to present the fundamental theoretical results concerning inference rules in deductive formal systems. Primary attention is focused on: admissible or permissible inference rules the derivability of the admissible inference rules the structural completeness of logics the bases for admissible and valid inference rules. There is particular emphasis on propositional non-standard logics (primary, superintuitionistic and modal logics) but general logical consequence relations and classical first-order theories are also considered. The book is basically self-contained and special (...) attention has been made to present the material in a convenient manner for the reader. Proofs of results, many of which are not readily available elsewhere, are also included. The book is written at a level appropriate for first-year graduate students in mathematics or computer science. Although some knowledge of elementary logic and universal algebra are necessary, the first chapter includes all the results from universal algebra and logic that the reader needs. For graduate students in mathematics and computer science the book is an excellent textbook. (shrink)

In this paper we prove the following theorem: Any one-dimensional definably connected group G over an o-minimal structure is, as an abstract group, isomorphic to either pPp∞δ or δ.

We find an explicit basis for all admissible rules of the modal logic S4. Our basis consists of an infinite sequence of rules which have compact and simple, readable form and depend on increasing set of variables. This gives a basis for all quasi-identities valid in the free modal algebra ℱS4 of countable rank.

Our investigation is concerned with the finite model property with respect to admissible rules. We establish general sufficient conditions for absence of fmp w. r. t. admissibility which are applicable to modal logics containing K4: Theorem 3.1 says that no logic λ containing K4 with the co-cover property and of width > 2 has fmp w. r. t. admissibility. Surprisingly many, if not to say all, important modal logics of width > 2 are within the scope of this theorem–K4 itself, (...) S4, GL, K4.1, K4.2, S4.1, S4.2, GL.2, etc. Thus the situation is completely opposite to the case of the ordinary fmp–the absolute majority of important logics have fmp, but not with respect to admissibility. As regards logics of width ≤ 2, there exists a zone for fmp w. r. t. admissibility. It is shown that all modal logics A of width ≤ 2 extending S4 which are not sub-logics of three special tabular logics have fmp w.r.t. admissibility. (shrink)

This report of the roundtable that took place on 25 November 2021 at The Peoples’ Friendship University of Russia attempts to explain the obvious growth of interest in Neo-Kantian philosophy in general and the philosophy of the head of the Marburg School of Neo-Kantianism, Hermann Cohen, in particular. In their contributions, the participants in the discussion demonstrated that the current interest in Neo-Kantianism does not solely or even largely have to do with the history of philosophy but rather with the (...) relevance of many of the ideas of Marburg Neo-Kantianism for the modern theory of cognition, the philosophy of culture, ethics and the philosophy of religion. The course of the discussion highlighted the relevance of Cohen’s theory of cognition based on logic and rationality. The main outcome of the discussion was the conviction that the potential of many of Cohen’s ideas has yet to be fully tapped and there are grounds for considering them to be heralds of a new philosophy which, in many of its features, is only maturing. (shrink)

This paper offers a brief analysis of the unification problem in modal transitive logics related to the logic S4 : S4 itself, K4, Grz and Gödel-Löb provability logic GL . As a result, new, but not the first, algorithms for the construction of ‘best’ unifiers in these logics are being proposed. The proposed algorithms are based on our earlier approach to solve in an algorithmic way the admissibility problem of inference rules for S4 and Grz . The first algorithms for (...) the construction of ‘best’ unifiers in the above mentioned logics have been given by S. Ghilardi in [ 16 ]. Both the algorithms in [ 16 ] and ours are not much computationally efficient. They have, however, an obvious significant theoretical value a portion of which seems to be the fact that they stem from two different methodological approaches. (shrink)

Trata-se de discutir a centralidade do trabalho como categoria de reconhecimento através da problematização de sua natureza disciplinar. Isto nos levará a um duplo movimento: primeiro, a categoria de trabalho em Marx será relida à luz não apenas da temática da espoliação econômica da mais-valia, mas também da espoliação psíquica das relações de estranhamento entre sujeito e objeto; segundo, as modificações recentes no mundo do trabalho e as modalidades de sofrimento psíquico a elas associadas serão interpretadas a partir do impacto (...) social de tal forma de espoliação. (shrink)

What do we learn when we find out that an argument is logically incorrect? If logically incorrect means the same as not logically correct, which in turn means not having a valid logical form, it seems that we do not learn anything too useful—an argument which is logically incorrect can still be conclusive. Thus, it seems that it makes sense to fix a stronger interpretation of the term under which a logically incorrect argument is guaranteed to be wrong. In this (...) paper, we show that pinpointing this stronger sense is much trickier than one would expect; but eventually we reach an explication of the notion of logical incorrectness which we find non-trivial and viable. (shrink)

The article draws a conceptual distinction the (French) structuralism of the 50’s–60’s and the post-structuralism of the 70’s, which are discussed as overlapping in their intellectual paths; their mutual dynamics is defined as a reaction of the intelligence to the pressure of depersonalized unified schemes within the logic of structuralism against free improvisation and loose interpretation instead of total explanations in the post-structuralism interpretation. The article establishes a conceptual identity of the paradoxical nature between post-structuralism (and deconstructionism, which is homogeneous (...) and identical thereto in a number of aspects), on the one hand, and constructionism with its specific process of language dismantling – social/ideological languages, social group dialects, on the other hand, which naturally leads the authors to the analysis of the paradoxicality principles, defined by post-structuralism (five principles of paradoxicality of Gilles Deleuze – paradox of regress, paradox of sterile reiteration, paradox of neutrality, paradox of absurd, paradox of Levi-Strauss); poststructuralists’ paralogisms are examined through paradoxical denotation; the late Roland Barthes’ phenomenon of paradoxicality, becoming a plot-forming principle of narration, is analyzed. Poststructuralism is conceptualized in the article as the first decisive step of post-modernism; the affinity of post-structuralist and postmodernist commitment to parody, game and irony is stated; the theory of language games in post-modern interpretation is explored; one of those games – a game of carnival – is explored within the diachronic retrospective; the affinity of parody and carnival tradition of post-structuralism and post-modernism to the romantic irony of the XIXth century and its inconsistency with the popular culture of laugh is established. The genesis of poststructuralism and post-modernism is connected with the ideological restart of the Western society before the “very end” of the Resistance ideas and the disappointment of the left European intellectuals in the “great legends” and illusions of Marxism. The blurred concepts of relativism are connected with the mutual disproportion of different layers of historical experience. (shrink)

Trata-se de analisar os usos da racionalidade mimética em Jacques Lacan e Theodor Adorno, isto a fim de mostrar como, nos dois casos, encontramos uma estratégia de reflexão sobre a mimesis que a eleva à condição de elemento fundamental para uma teoria do reconhecimento que não se esgote na temática da intersubjetividade. Neste sentido, este estudo insere-se em uma pesquisa mais ampla a respeito dos modos de aproximação entre psicanálise lacaniana e Escola de Frankfurt no que diz respeito ao problema (...) dos destinos da categoria de sujeito e dos processos de reconhecimento. (shrink)

Im Unterschied zum christlichen Begriff der Gerechtigkeit als einer sittlichen Tugend, wie es Thomas von Aquin zusammenfasste, als einer Einstellung, kraft deren ein Mensch festen und steten Willens jedem sein Recht zukommen lässt, erkennt Nietzsche die Herkunft der Gerechtigkeit im Ausgleich oder Kompromiss zwischen ungefähr gleich Mächtigen sowie im Zwang der weniger Mächtigen zu einem Ausgleich. Zur Untermauerung dieser Einstellung, die sich auf der Behauptung gründet, dass das Leben seinem innersten Wesen nach eine Aneignung sei bzw. dass der Wille zur (...) Macht den Lebenswillen schlechthin ausmache, griff Nietzsche auf den von Thukydides geschilderten Dialog der Athener und Melier zurück. Der Autor kommt jedoch zu dem Schluss, dass Nietzsche nicht nur ein Denker der Macht war, sondern nach einem neuen Verständnis der Gerechtigkeit trachtete, das aus der Gesamtheit seines Denkens zu deuten sei. (shrink)

Alan Baker argues that mathematical objects play an indispensable explanatory role in science. There are several examples cited in the literature as solid candidates for such a role. We discuss two such examples and show that they are very different in their strength and (im)perfection, although both are recognized by the scientific community as examples of the best scientific explanations of particular phenomena. More specifically, it will be shown that the explanation of the cicada case has serious shortcomings compared with (...) the explanation of the case of Königsberg’s bridges. We will argue that the latter is a perfectly reliable scientific explanation that employs mathematical reasoning whereas the former is not. (shrink)

This commentary discusses dozens of ecologically powerful social-psychological experiments from the1960s and 1970s, which are highly relevant especially for predicting the consequences of revenge. McCullough et al. omitted this work catharsisni's anger-aggression bidirectional-causation (AABC) model and can be usefully incorporated in an adaptationist view of revenge.

There are many methodological considerations that adversely affect external validity as much as, or even more than, unrepresentative sampling does. Among suspect applications, especially worrisome is the incorporation of WEIRD-based findings regarding moral reasoning and retribution into normative expectations, such as might be held by international criminal tribunals in war-torn areas.