We introduce a general technique for finding sets of axioms for a given class of semigroups. To illustrate the technique, we provide new sets of defining axioms for groups of exponent n, bands, and semilattices.

Agresja putinowskiej Rosji na Ukrainę postawiła wobec dramatycznego wyzwania nobliwą doktrynę non‑violence. Zgodnie ze sformułowanym w latach 80. XX wieku wywodem antysowieckiego dysydenta rosyjskiego Władimira Bukowskiego to nie wojna jest przeciwieństwem pokoju, lecz przemoc, a do jej powstrzymania niekiedy konieczny jest zbrojny opór, czyli prowadzenie wojny. Według Clausewitza do wywołania stanu wojny nie wystarczy militarna agresja, lecz konieczne jest przeciwstawienie się jej, czyli aktywna obrona ze strony napadniętego, chcąc zatem uniknąć wojny, nie należy stawiać oporu agresorowi. Agresja na Ukrainę (...) złamała dwie zasady prowadzenia wojen: ius ad bellum i ius in bello. Według typologii Michaela Walzera jest to zatem niesprawiedliwa wojna prowadzona niesprawiedliwymi metodami, więc przeciwstawianie się jej, także militarne, jest prowadzeniem wojny sprawiedliwej. Zgodnie z analizą Slavoja Žižka tworzy to klarowną z etycznego punktu widzenia sytuację, zło jest łatwo identyfikowalne, a przeciwstawienie się mu stanowi etyczny obowiązek. Według filozofa Étienne’a Balibara w tej sytuacji pacyfizm nie jest żadną opcją. Helplessness as Acquiescence to Evil The aggression of Putin’s Russia towards Ukraine has posed a dramatic challenge to the noble doctrine of non-violence. In line with an argument made in the 1980s by anti-Soviet Russian dissident Vladimir Bukovsky, war is not the opposite of peace; instead, violence is. Armed resistance, or warfare, is sometimes necessary to stop violence. According to Clausewitz, military aggression is insufficient to evoke a state of war; in its place, it is necessary to oppose aggression, i.e., actively mount a defense by the attacked party, thereby avoiding war requires not resisting the aggressor. However, the aggression against Ukraine broke two tenets of warfare: ius ad bellum and ius in bello. According to Michael Walzer’s typology, it is an unjust war waged by unjust methods, so resisting it, including militarily, amounts to waging a just war. According to Slavoj Žižek’s analysis, this establishes an ethically clear situation: evil is easily identifiable, and opposing it is an ethical duty. According to the philosopher Étienne Balibar, pacifism is not an option in such a situation. (shrink)

We propose in this paper a new family of belief merging operators, that is based on a game between sources : until a coherent set of sources is reached, at each round a contest is organized to find out the weakest sources, then those sources has to concede. This idea leads to numerous new interesting operators and opens new perspectives for belief merging. Some existing operators are also recovered as particular cases. Those operators can be seen as a special case (...) of Booth's Belief Negotiation Models [BOO 02], but the achieved restriction forms a consistent family of merging operators that worths to be studied on its own. (shrink)

ABSTRACT We consider in this work the problem of iterated belief revision. We propose a family of belief revision operators called revision with memory operators and we give a logical (both syntactical and semantical) characterization of these operators. They obey what we call the principle of strong primacy of update: when one revises his beliefs by a new evidence, then all possible worlds that satisfy this new evidence become more reliable than those that do not. We show that those operators (...) have a satisfying behaviour concerning the iteration of the revision process. Then we provide four particular operators of this family. (shrink)

We examine the notion of primitive satisfaction in logical matrices. Theorem II. 1, being the matrix counterpart of Baker's well-known result for congruently distributive varieties of algebras (cf [1], Thm. 1.5), links the notions of primitive and standard satisfaction. As a corollary we give the matrix version of Jónsson's Lemma, proved earlier in [4]. Then we investigate propositional logics with disjunction. The main result, Theorem III. 2, states a necessary and sufficient condition for such logics to be finitely based.

Belief merging aims at combining several pieces of information coming from different sources. In this paper we review the works on belief merging of propositional bases. We discuss the relationship between merging, revision, update and confluence, and some links between belief merging and social choice theory. Finally we mention the main generalizations of these works in other logical frameworks.

This book is both suitable for logically and algebraically minded graduate and advanced graduate students of mathematics, computer science and philosophy, and ...

The objective of the presented research was to test whether working memory, measured using the Spin the Pots task, is an important factor in passive vocabulary development in 2- and 3-year-old children. Two longitudinal studies were conducted. In the first, 135 children participated in the first study. At 18 months their responding to joint attention was measured, and then at 24 months their working memory and passive vocabulary was tested. It was demonstrated that responding to joint attention predicts the level (...) of development of working memory, which in turn influences the extent of the passive vocabulary. In the second study, 113 children participated - at 30 months their working memory was measured, and at 24 months and then 36 months their passive vocabulary was tested. It was observed that at the age of 3 working memory is still a significant predictor of passive vocabulary. The usefulness of the Spin the Pots task for measuring the working memory of young children was shown and discussed in conclusions. (shrink)

As a specific type of operational behaviour intended to furnish solutions of social problems social engineering functions in virtue of certain moral norms and evaluations. The directives and methods of social engineering are conceived and applied in accordance with a moral point of view held by the social engineer. This moral point of view, with its characteristic values, goals, norms and evaluations, influences the selection of the ways and means that he makes to realize his project. The social engineer is (...) both a specialist who designs and applies certain norms, and a moralist who identifies, explains and justifies the motives and objectives underlying them. The directives of the adherent to a moral system and those of the engineer with a certain professional specialization constitute independent variables in his mind. (shrink)

Książka ta jest obszerną pracą o ścisłe historyczno-naukowym charakterze, przedstawiającą życie Stanisława Wydry, jezuity, profesora matematyki na Uniwersytecie w Pradze. Składa się ona z Wprowadzenia i rozdziałów poświęconych: oświeceniu i odrodzeniu narodowemu w Czechach; sytuacji uniwersytetu w Pradze, a w szczególności - Wydziału Filozoficznego; następnie – podręcznikom do matematyki na osiemnastowiecznym uniwersytecie w Pradze; życiu Stanisława Wydry oraz jego pracom naukowym - w tym kilku w szczególności, i wreszcie - jego oddziaływaniu na matematykę i kulturę Czech. Po Dodatku umieszczono wykaz (...) literatury oraz szereg skorowidzów. (shrink)

Any finite support iteration of posets with precalibre ℵ 1 which has the length of cofinality greater than ω 1 yields a model for the dual Borel conjecture in which the real line is covered by ℵ 1 strong measure zero sets.

Discursive (or discussive) logic, D₂, introduced by Jaśkowski, is widely recognized as a first formal approach to paraconsistency. Jaśkowski applied a quite extraordinary technique at that time to describe his logic. He neither gave a set of the axiom schemata nor presented a direct semantics for D₂ but used a translation function to express his philosophical and logical intuitions. Discursive logic was defined by an interpretation in the language of S₅ of Lewis. The aim of this paper is to present (...) a modified system of the discursive logic that allows some of the weaker versions of Duns Scotus's thesis to be valid. The initial idea is to consider a different characteristic of the connective of negation. We introduce both a direct semantics and an axiomatization of the new system, prove the key metatheorems, and describe labeled tableaux for the system. (shrink)

In 1948, Stanis aw Ja kowski defined a logical system D2 of a discursive 1 sentential calculus. The aim of this paper is to introduce the reader to the basic ideas of the discursive logic and to show, in a historical perspective, its development originating from the two germ papers [19] and [20]. We intend to present some problems connected with it and outline the solutions they have received up to the present day.

ABSTRACTAlthough the British Idealists did not provide a systematic account of language as a distinct philosophical phenomenon, language is nonetheless a fundamental element of Idealist social and political philosophy. This is seen mostly in the Idealist treatment of the concept of general will, which resulted in a Hegelian theory of community, constituted by shared understandings and a shared account of the common good and common interest. This article contains analysis of the relations between language and socio-political institutions in British Idealist (...) writings. The narrative focuses on Thomas Hill Green and Bernard Bosanquet – two major political thinkers representing the said philosophical tradition. The argument proceeds as follows: firstly, possible linguistic interpretations of the Idealist philosophical tradition are introduced. Then the author turns to Green’s conception of general will as the foundation of socio-political order and political sovereignty. In the third section, he... (shrink)

The article begins from a consideration of the relationships between ethics and method, dignity and trustworthiness of the scholar in his normal activity. Then the views of Stanisław Ossowski are presented concerning the conditions of the permanence and development of the normal academic life, and his commandments for the academic professions are quoted safeguarding the normal academic life. A discussion of the question of freedom and responsibility in academic research is combined with Ossowski’s conception of philosophy of science. Ossowski had (...) a conception of the historical mission and function of science. With it was connected a notion of indispensable freedom of the scientists which they must possess to be able to perform their professional tasks normally. Ossowski also had a conception of the duties and professional responsibility of the scientists. The article ends with a review of threats to the normal functioning of science and of the countermeasures that should be used, according to Ossowski, in order to ensure growth of science and unencumbered performance of scholarly tasks. (shrink)

One can speak about mathematics too simplistically. On the one hand, school programs are such examples. On the other hand, the function of mathematics in elementary physics very much indicates the profound philosophical significance of mathematics: the author claims that mathematical language is a kind of command language, i.e. it is not just a description, but a control which has a specific power to manage the reality. This language has its proper hierarchy and structures which humans only are just starting (...) to understand and to use in basic ways, not without errors. Therefore some ethics regarding human mathematical thinking are needed: the affirmation of life. (shrink)

Fr. Roberto Busa was an Italian Jesuit. In this article his biography will briefly be presented, and some issues raised by his philosophy analyzed. Busa was known as a pioneer of computerized research in the humanities. With the support of IBM he constructed the Index Thomisticus, containing all the works of St. Thomas Aquinas. He believed that expressions of the human can be mathematically modeled. He was the originator of a specific conception of hypertext, in which logically structured programs are (...) able to challenge the general linguistic mode of thinking, in order to make better communication and understanding possible. However, Busa was also con- scious of the general ethical problems involved (Babel), and he hoped that the basic logic of objects could progress towards the truth of being. (shrink)

The aim of the paper is to present how the late medieval plague pandemic affected the societies of Western and Eastern Europe. The author used chronicles and works of literature of that time, on top of the abundant literature on the subject. Based on this bibliography, he carried out a critical analysis of the content, revealing the similarities and differences in the course of the Black Death epidemic across parts of Europe. The plague was taking its toll on all age (...) groups and at all levels of society. The main reason for this was that physicians, not knowing what was causing the disease, could not help the infected for a long time. The epidemic exposed the poor level of the contemporary medics’ knowledge and their unpreparedness for saving human lives. It also showed that university studies neither equipped them with sufficient knowledge nor gave them the practical skills needed to fight the dangerous disease. The Black Death particularly disorganized the economic and social life of Western and Southern European countries. Although the plague first struck Central Europe with less intensity than it did the West, it did take its toll on it. Its subsequent waves had an especially dramatic impact on the large trading towns such as Wroclaw and Krakow. A pervasive fear of the plague also contributed to the resentment towards those seen as aliens, especially Jews. They were the ones accused of poisoning wells and supplies, and spreading the disease. In Wroclaw, the capital city of Silesia, which was then part of the Kingdom of Bohemia, the attack on Jews was initiated by John of Capistrano – the papal inquisitor. It led to a much publicized trial that resulted in the death sentences death sentences given to several dozen people. Seeking to understand the reason behind Capistrano’s actions, the author analyzed his treatise on the duties of physicians and clergy toward plague patients. It results from that work that the course of the epidemic in Central Europe, despite its local variations, was not significantly different from that observed in Western countries. (shrink)