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.

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

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.

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)

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)

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)

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)

The paper is conceived as a first study on the Suszko operator. The purpose of this paper is to indicate the existence of close relations holding between the properties of the Suszko operator and the structural properties of the model class for various sentential logics. The emphasis is put on generality both of the results and methods of tackling the problems that arise in the theory of this operator. The attempt is made here to develop the theory for non-protoalgebraic logics.

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 reviews the book Jak to jest być świadomym? Analityczne teorie umysłu a problem świadomości [What Is It Like to be Conscious? Analytical Theories of Mind and the Problem of Consciousness], by Józef Bremer.

In the domain of astronomy the object oriented paradigm of informatics needs to construct an ontology to be able to reason about concepts and to construct queries in a computerized knowledge system. The article presents approaches to ontology in philosophy, the natural sciences and informatics and shows their limits and reciprocity.

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)

This text offers the report on the activities of The Centre for Interdisciplinary Studies in Cracow—a research and educational institution at the Department of Philosophy of the Pontifical Academy of Philosophy in the Cracow. The main areas of its research are the philosophy of science, the history of science, and problems connected with the interrelations between philosophy, theology and the sciences.

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)

We are facing a crisis of trust in expertise today. Fewer and fewer people trust experts, and more and more politicians openly ignore expert consensus. 'Democracy in the Post-Truth Era' asks what might happen to democracy if we reject the fundamental liberal assumption that people are capable of making informed choices. The book explores the potential impact on society if people, including politicians, never appreciate the relevance of expert opinions. What if people cannot choose between supporters and opponents of key (...) issues such as the causes of climate change, effectiveness of vaccines and ways of combating economic and social crises? Applying social epistemology to these questions, the book considers whether democracy can be defended in the post-truth era. (shrink)

In the paper we study the class of weakly algebraizable logics, characterized by the monotonicity and injectivity of the Leibniz operator on the theories of the logic. This class forms a new level in the non-linear hierarchy of protoalgebraic logics.

An explanation is given of why, after adding to a model M of ZFC first a Solovay real r and next a Cohen real c, in M[ r][ c] a Cohen real over M[ c] is produced. It is also shown that a Solovay algebra iterated with a Cohen algebra can be embedded into a Cohen algebra iterated with a Solovay algebra.

The main result of the present paper — Theorem 3 — establishes the equivalence of the interpolation and amalgamation properties for a large family of logics and their associated classes of matrices.