The main aim of the present paper is to explain a nature of relationships exist between Nelson and Heyting algebras. In the realization, a topological duality theory of Heyting and Nelson algebras based on the topological duality theory of Priestley for bounded distributive lattices are applied. The general method of construction of spaces dual to Nelson algebras from a given dual space to Heyting algebra is described. The algebraic counterpart of this construction being a generalization of the Fidel-Vakarelov construction is (...) also given. These results are applied to compare the equational category N of Nelson algebras and some its subcategories with the equational category H of Heyting algebras. It is proved that the category N is topological over the category H. (shrink)

We examine some extensions of the constructive propositional logic with strong negation in the setting of varieties of $\mathcal{N}$ -lattices. The main aim of the paper is to give a description of all pretabular, primitive and preprimitive varieties of $\mathcal{N}$ -lattices.

The concepta question is reducible to a non-empty set of questions is defined and examined. The basic results are: (1) each question which is sound relative to some of its presuppositions is reducible to some set of binary (i.e. having exactly two direct answers) questions; (b) each question which has a finite number of direct answers is reducible to some finite set of binary questions; (c) if entailment is compact, then each normal question (i.e. sound relative to its presuppositions) is (...) reducible to some finite set of binary questions. (shrink)

The idea of rational understanding lays very close to the heart of Professor Janusz Kuczyński, an advocate of universalism as well as dialogue between diverse philosophical schools and worldviews, and doctoral advisor to the present paper’s author. This idea’s theoretical conceptualisation—a conceptualisation that has proven to be convincing and adequate to the conditions of the modern world—was developed by Professor Jürgen Habermas, whose ideas and theories were also the subject of a doctoral thesis written by this paper’s author in the (...) latter half of the 1970s under Professor Kuczyński’s tutelage. The author shares some grateful memories of his doctoral tutor, and also sets his one-time attempts to apply the theory of communicative action to two experiences of the real socialism era in Poland against his efforts to analyse contemporary Polish realities through the prism of the communicative rationality conception. This comparison shows that the application of a conception of rationality funded by communicative action to the turbulent transformations under real socialism was to a certain extent naïve—though not devoid of critical significance—and also reveals the preconditions for the implementation of the rules of communicative rationality in social and political reality.The paper is in part dedicated to the memory of Professor Kuczyński, therefore it contains a somewhat extensive account of the circumstances which led the author to study the thought of Habermas under Kuczyński’s tutelage, as well as the consequences of this choice, which proved of considerable significance for his further life. However, the main themes are, first, the validity of applying a conception of rationality funded by communicative action to two significant experiences of the real socialism era, and, secondly, the need—revealed by diagnosing contemporary Polish reality with the help of the communicative rationality conception—for certain preconditions enabling the implementation of this type of rationality in social and political reality. One such precondition is the transition of sufficiently broad parts of society from thinking in terms of worldviews to post-metaphysical thinking in terms of the “lifeworld”. (shrink)

It is well known that Husserl clearly recognized the importance of the introduction of idealization in physics and its contribution to the further advancement in natural sciences. The history of the successful applications of idealization in natural sciences encouraged attempts to extend the use of this sophisticated instrument of theoretical investigation and theory construction to other domains of science. Since Husserl designed his phenomenology as the rigorous science of consciousness we have to find out why he did not use the (...) method he understood so well to study experiences, the objects located by him in the domain of consciousness. The paper offers an answer to this question. It explains why Husserl conceived of the method of idealization as a tool of objectivization of previously subjective knowledge. Since idealization is used to objectify knowledge its application to experiences, conscious acts would produce objective knowledge of consciousness. This, however, would contradict phenomenological assertion that subjectivity is an essential component of experience and that the reliable knowledge about conscious acts could not be objectified. It is the core of Husserl's argumentation that there is no place for idealization in the research on consciousness. (shrink)

Provability, Computability and Reflection.

In reply to the polemics and comments on my bookLogic and ArgumentationThis article contains the reply to the polemics and comments on my book Logic and argumentation. Since the most controversial issue among the commentators was my “radical attack on formal logic”, the first part of the text generally addresses this criticism. Firstly, I thoroughly explain what my doubts regarding the formal logic are. I am not questioning the great, even spectacular, successes of formal logic in the field of mathematical (...) logic, nor its extraordinary contribution to the foundation of computer technology. I only find that for the traditional goal of logic — that of studying the principles of reasoning, inference and definition — formal methods have failed in confrontation with practice. I am developing this thesis in detail and I am trying to justify it, first of all by referring to the practice of reasoning in the field of mathematics. In the second part, I respond to specific criticisms and comments from individual authors. Many of the comments are correct, some are based on misunderstandings, while some, in my opinion, are wrong. (shrink)

The time of mechanics is the eternal and unchangeable time of Parmenides, it is Plato’s idea of time, whereas the time of thermodynamics is Heraclitus’ flowing time, Thomas Aquinas’ time measured by various phenomena. I once wrote [2] that people who are not used to a physicist’s way of thinking are (at best) confused by the idea of a symmetrical time of mechanics. Physicists on the other hand often believe that the time of thermodynamics (irreversibility) does not really exist, and (...) is merely an illusion. It seems therefore that both of these aspects of time, the time of mechanics and the time of thermodynamics, should be treated as complementary, in anticipation of a future “theory of everything” which will somehow reconcile them. (shrink)

L’objet de cet article est constitué par les motifs cartésiens dans la pensée de Leszek Kołakowski, l’un des philosophes polonais les plus connus et influents de la seconde moitié du xx e siècle. On essaiera ici de montrer que ce qui a organisé la pensée de Kołakowski, et ce non seulement dans sa dimension philosophique, mais tout autant politique, était une réflexion critique sur la légitimité et les limites de la quête cartésienne du savoir fondé sur l’évidence et, à la (...) fois, objectif et vrai. Pour l’auteur de cet article Kołakowski – et avec lui, toute une formation intellectuelle, dont il faisait partie, connue sous le nom d’École d’histoire des idées de Varsovie – interprétait le cartésianisme comme un essai de mise en place du radicalisme intégral, tant philosophique que politique. Dans cet article, on défendra également la thèse suivante : pour Kołakowski et pour bon nombre de ses collègues – anciens marxistes –, le cartésianisme était une philosophie radicale non seulement de la vérité, mais aussi de la liberté. La question que Kołakowski adressait aussi bien à Husserl qu’à Descartes, notamment celle de savoir s’il est possible de découvrir les fondements du savoir, inébranlables et absolument incontestables, sera présentée comme un élément de sa stratégie pour surmonter le marxisme envisagé comme une idéologie qui réduit la liberté humaine à un simple épiphénomène. (shrink)

The aim of the paper is to reconstruct the theoretical background and practical meaning of the so called war writings which emerged within the phenomenological movement during the First World War. The author exemplifies it by researching the works of two German representatives of this movement, Max Scheler and Kurt Stavenhagen. He focuses on their application of the phenomenological method to the analysis of Russian national identity, and historical as well as cultural foundations of Russian state. The paper’s main thesis (...) is that the politicization and militarization of phenomenology consisted in both “personalization” and “sociologization” of the phenomenological approach to the problem of the state. While interpreting Scheler’s personalism as an exemplification of the approach to the state as a problem of social ontology, the author reconstructs the theoretical conditions of analyzing the Russian imperial state in terms of the “world.” The focus of the paper is particularly on the phenomenology of, as Scheler put it, Russian collective personality and Russian national consciousness or “soul” as well as on the question of legitimacy of Ukrainian resistance against Russian imperialism. (shrink)

This summary was delivered at the closing session of the “Korczak: A New Anthropology of Education” conference on September 21, 2002 in the Polish Culture Institute of Warsaw University’s Polish Studies Faculty. Author points that the primary goal of the conference was to set Korczak’s work against modern-day thought trends and cultural dilemmas. Summing up the result of the conference author notices that the deepest roots of the Korczak’s work lies in the Judaic and Christian traditions but it also draws (...) on European enlightenment, Polish romanticism, and positivism. (shrink)