Several Gentzen-style syntactic type calculi with product are considered. They form a hierarchy in such a way that one calculus results from another by imposing a new condition upon the sequent-forming operation. It turns out that, at some steps of this process, two different functors collapse to a single one. For the remaining stages of the hierarchy, analogues of Wajsbergs's theorem on non-mutual-definability are proved.

In [4], I proved that the product-free fragment L of Lambek's syntactic calculus (cf. Lambek [2]) is not finitely axiomatizable if the only rule of inference admitted is Lambek's cut-rule. The proof (which is rather complicated and roundabout) was subsequently adapted by Kandulski [1] to the non-associative variant NL of L (cf. Lambek [3]). It turns out, however, that there exists an extremely simple method of non-finite-axiomatizability proofs which works uniformly for different subsystems of L (in particular, for NL). We (...) present it below to the use of those who refer to the results of [1] and [4]. (shrink)

In Zielonka (1981a, 1989), I found an axiomatics for the product-free calculus L of Lambek whose only rule is the cut rule. Following Buszkowski (1987), we shall call such an axiomatics linear. It was proved that there is no finite axiomatics of that kind. In Lambek's original version of the calculus (cf. Lambek, 1958), sequent antecedents are non empty. By dropping this restriction, we obtain the variant L0 of L. This modification, introduced in the early 1980s (see, e.g., Buszkowski, (...) 1985; Zielonka, 1981b), did not gain much popularity initially; a more common use of L0 has only occurred within the last few years (cf. Roorda, 1991: 29). In Zielonka (1988), I established analogous results for the restriction of L0 to sequents without left (or, equivalently, right) division. Here, I present a similar (cut-rule) axiomatics for the whole of L0.This paper is an extended, corrected, and completed version of Zielonka (1997). Unlike in Zielonka (1997), the notion of rank of an axiom is introduced which, although inessential for the results given below, may be useful for the expected non-finite-axiomatizability proof.The paper follows the same way of subject exposition as Zielonka (2000) but it is technically much less complicated. I restrict myself to giving bare results; all the ideological background is exactly the same as in case of the non-associative calculusNL0 and those who are interested in it are requested to consult the introductory section of Zielonka (2000). (shrink)

In [2], Bar-Hillel, Gaifman, and Shamir prove that the simple phrase structure grammars (SPGs) defined by Chomsky are equivalent in a certain sense to Bar-Hillel's bidirectional categorial grammars (BCGs). On the other hand, Cohen [3] proves the equivalence of the latter ones to what the calls free categorial grammars (FCGs). They are closely related to Lambek's syntactic calculus which, in turn, is based on the idea due to Ajdukiewicz [1]. For the reasons which will be discussed in the last section, (...) Cohen's proof seems to be at least incomplete. This paper yields a direct proof of the equivalence ofFCGs andSPGs. (shrink)

In Zielonka (1981a, 1989), I found an axiomatics for the product-free calculus L of Lambek whose only rule is the cut rule. Following Buszkowski (1987), we shall call such an axiomatics linear. It was proved that there is no finite axiomatics of that kind. In Lambek's original version of the calculus (cf. Lambek, 1958), sequent antecedents are non empty. By dropping this restriction, we obtain the variant L 0 of L. This modification, introduced in the early 1980s (see, e.g., (...) Buszkowski, 1985; Zielonka, 1981b), did not gain much popularity initially; a more common use of L 0 has only occurred within the last few years (cf. Roorda, 1991: 29). In Zielonka (1988), I established analogous results for the restriction of L 0 to sequents without left (or, equivalently, right) division. Here, I present a similar (cut-rule) axiomatics for the whole of L 0. This paper is an extended, corrected, and completed version of Zielonka (1997). Unlike in Zielonka (1997), the notion of rank of an axiom is introduced which, although inessential for the results given below, may be useful for the expected non-finite-axiomatizability proof. (shrink)

An axiomatics of the product-free syntactic calculus L ofLambek has been presented whose only rule is the cut rule. It was alsoproved that there is no finite axiomatics of that kind. The proofs weresubsequently simplified. Analogous results for the nonassociativevariant NL of L were obtained by Kandulski. InLambek's original version of the calculus, sequent antecedents arerequired to be nonempty. By removing this restriction, we obtain theextensions L 0 and NL 0 ofL and NL, respectively. Later, the finiteaxiomatization problem for L (...) 0 andNL 0 was partially solved, viz., for formulas withoutleft (or, equivalently, right) division and an (infinite) cut-ruleaxiomatics for the whole of L 0 has been given. Thepresent paper yields an analogous axiomatics forNL 0. Like in the author's previous work, the notionof rank of an axiom is introduced which, although inessentialfor the results given below, may be useful for the expectednonfinite-axiomatizability proof. (shrink)

The paper continues a series of results on cut-rule axiomatizability of the Lambek calculus. It provides a complete solution of a problem which was solved partially in one of the author''s earlier papers. It is proved that the product-free Lambek Calculus with the empty string (L 0) is not finitely axiomatizable if the only rule of inference admitted is Lambek''s cut rule. The proof makes use of the (infinitely) cut-rule axiomatized calculus C designed by the author exactly for this purpose.

Joel M. Cohen , pp. 475- 484) claims that Lambek’s categorial grammars are equivalent in a certain natural sense to those of Bar-Hillel, Gaifman, and Shamir. Unfortunately, it turns out that Cohen’s proof is based on a false lemma. Thus the equivalence of both kinds of grammars is still an open problem although there is much evidence in its favor. This paper yields a counterexample to Cohen’s lemma.

Axiomatics which do not employ rules of inference other than the cut rule are given for commutative product-free Lambek calculus in two variants: with and without the empty string. Unlike the former variant, the latter one turns out not to be finitely axiomatizable in that way.

In [2], Bar-Hillel, Gaifman, and Shamir prove that the simple phrase structure grammars dened by Chomsky are equivalent in a cer- tain sense to Bar-Hillel's bidirectional categorial grammars . On the other hand, Cohen [3] proves the equivalence of the latter ones to what he calls free categorial grammars . They are closely related to Lambek's syntactic calculus which is, in turn, based on the idea due to Ajdukiewicz [1]. For some reasons, Cohen's proof seems to be at least in- (...) complete. Here, I give a short outline of the direct proof of the equivalence between SF G's and F CG's. (shrink)

The calculus DNL results from the non-associative Lambek calculus NL by splitting the product functor into the right (⊲) and left (⊳) product interacting respectively with the right (/) and left () residuation. Unlike NL, sequent antecedents in the Gentzen-style axiomatics of DNL are not phrase structures (i.e., bracketed strings) but functor-argument structures. DNL − is a weaker variant of DNL restricted to fa-structures of order ≤ 1. When axiomatized by means of introduction/elimination rules for / and , it shows (...) a perfect analogy to NL which DNL lacks. (shrink)

Contents: Preface. SCIENTIFIC WORKS OF MARIA STEFFEN-BATÓG AND TADEUSZ BATÓG. List of Publications of Maria Steffen-Batóg. List of Publications of Tadeusz Batóg. Jerzy POGONOWSKI: On the Scientific Works of Maria Steffen-Batóg. Jerzy POGONOWSKI: On the Scientific Works of Tadeusz Batóg. W??l??odzimierz LAPIS: How Should Sounds Be Phonemicized? Pawe??l?? NOWAKOWSKI: On Applications of Algorithms for Phonetic Transcription in Linguistic Research. Jerzy POGONOWSKI: Tadeusz Batóg's Phonological Systems. MATHEMATICAL LOGIC. Wojciech BUSZKOWSKI: Incomplete Information Systems and Kleene 3-valued Logic. Maciej KANDULSKI: Categorial Grammars (...) with Structural Rules. Miros??l??awa KO??L??OWSKA-GAWIEJNOWICZ: Labelled Deductive Systems for the Lambek Calculus. Roman MURAWSKI: Satisfaction Classes - a Survey. Kazimierz _WIRYDOWICZ: A New Approach to Dyadic Deontic Logic and the Normative Consequence Relation. Wojciech ZIELONKA: More about the Axiomatics of the Lambek Calculus. THEORETICAL LINGUISTICS. Jacek Juliusz JADACKI: Troubles with Categorial Interpretation of Natural Language. Maciej KARPI??N??SKI: Conversational Devices in Human-Computer Communication Using WIMP UI. Witold MACIEJEWSKI: Qualitative Orientation and Grammatical Categories. Zygmunt VETULANI: A System of Computer Understanding of Texts. Andrzej WÓJCIK: The Formal Development of van Sandt's Presupposition Theory. W??l??adys??l??aw ZABROCKI: Psychologism in Noam Chomsky's Theory . Ryszard ZUBER: Defining Presupposition without Negation. PHILOSOPHY OF LANGUAGE AND METHODOLOGY OF SCIENCES. Jerzy KMITA: Philosophical Antifundamentalism. Anna LUCHOWSKA: Peirce and Quine: Two Views on Meaning. Stefan WIERTLEWSKI: Method According to Feyerabend. Jan WOLE??N??SKI: Wittgenstein and Ordinary Language. Krystyna ZAMIARA: Context of Discovery - Context of Justification and the Problem of Psychologism. (shrink)

This book challenges the widespread view of Kierkegaard’s idiosyncratic and predominantly religious position on mimesis. -/- Taking mimesis as a crucial conceptual point of reference in reading Kierkegaard, this book offers a nuanced understanding of the relation between aesthetics and religion in his thought. Kaftanski shows how Kierkegaard's dialectical-existential reading of mimesis interlaces aesthetic and religious themes, including the familiar core concepts of imitation, repetition, and admiration as well as the newly arisen notions of affectivity, contagion, and crowd behavior. Kierkegaard’s (...) enduring relevance to the malaises of our own day is firmly established by his classic concern for the meaning of human life informed by reflective meditation on the mimeticorigins of the contemporary age.​ -/- Kierkegaard, Mimesis, and Modernity will be of interest to scholars and advanced students working on Kierkegaard, Continental philosophy, the history of aesthetics, and critical and religious studies. (shrink)

Celem artykułu jest przedstawienie twórczości Pawła Jaszczuka, który dzięki swoim dokonaniom stał się reprezentatywny, zarówno dla literatury kryminalnej, jak i dla środowiska Warmii i Mazur. Od wielu lat pisze powieści kryminalne, przyczyniając się do rozwoju odmian gatunku, a jednocześnie korzystając z tej formy, porusza ważne współcześnie tematy. W jego utworach widać także przebieg pewnego procesu: rozpoczynając od narracji historycznej, w której ważne miejsce pełniła przeszłość, coraz częściej zabiera głos w sprawie teraźniejszości i jej wyznaczników: dominacji polityki w życiu, rozprzestrzeniania się (...) kultury masowej, rozpadu rodziny czy wszechobecnego ageizmu. Przedstawienie jego powieści kryminalnych ma wykazać, że w jego metodzie twórczej z jednej strony widoczna jest tendencja do eksponowania tematów związanych z przeszłością, a z drugiej strony mechanizm łączenia narracji historycznej z wątkami popkulturowymi. (shrink)

Polskie przepisy prawne formułujące warunki dopuszczalności eksperymentu medycznego, a więc ipso facto wyznaczające jego granice, można różnorako interpretować, zwłaszcza w tym zakresie, w jakim określają wymagany dla przeprowadzenia eksperymentu bilans związanych z nim możliwych korzyści i szkód. W artykułach prawniczych komentujących te przepisy w zasadzie jednak brak prób systematycznego i (na tyle, na ile pozwala na to sam przedmiot analizy) ścisłego wyróżnienia tych interpretacji w języku tzw. teorii racjonalnego wyboru (rational choice theory), teorii szczególnie przydatnej w tym kontekście z uwagi (...) na jej rozbudowany aparat pojęciowy pozwalający badać różnorakie konfiguracje relacji między costs i benefits. Artykuł próbuje wypełnić tę lukę: wyróżnione w nim zostały różne interpretacje przepisów prawnych określających warunki dopuszczalności eksperymentu medycznego; interpretacje te zostały również poddane ocenie. (shrink)

The monograph of Jacek Zieliński, The Concept of Creatio ex Nihilo in the Thought of the Greek Apologists of the 2nd century, published by Wroclaw’s Atut in 2013, discusses an important problem of the theory of creation from nothing. It also asks an important question, how far the elements of the concept, articulated in its final form only by Augustine of Hippo can be found in the writings of the Christian apologists of the 2nd century. It is an important question, (...) especially that the Bible in its canonical form, the early extra-biblical Jewish literature or – even more – Greek tradition does not unambiguously advocate the concept creatio ex nihilo. Hence the question how, when and why the concept was articulated, since it played such an important role in the Christian thought of later centuries. In addition, the book of Jacek Zielinski is important in Polish market, because there are only a few serious publications dealing with the issue. The article gives a description and short analysis of the book, pinpointing its strong sights and showing areas, which could be strengthened in this and — hopefully — following publications on creatio ex nihilo by Jacek Zieliński. (shrink)

This article engages the considerations of imagination in Kierkegaard and Ricoeur to argue for a moral dimension of the imagination and its objects. Imaginary objects are taken to be mental representations in images and narratives of people or courses of action that are not real in the sense that they are not actual, or have not yet happened. Three claims are made in the article. First, by drawing on the category of possibility, a conceptual distinction is established between imagination and (...) fantasy, (1) I claim that imagination has a moral dimension because it is engaged in considering real-life possibilities. Second, (2) drawing on Kierkegaard and Ricoeur, it is argued that mental representations of selfhood in imagination have a moral dimension because they essentially allow people to understand the development of agency in human selfhood by means of representations of would-be selves and narrative figurations of the self. Third, (3) mental representations of human selves have a moral dimension because they form important points of reference for moral orientations in the field of human praxis (moral pointers). (shrink)

We explore how conspiracy beliefs change the effectiveness of gain- vs. loss-framed messages in promoting health-protective behavior. We focused on various recommended COVID-19 protective measures, not only vaccinations but also other preventive (like wearing masks) and detection behaviors (like testing). Our results indicate that conspiracy beliefs moderate the effectiveness of gain vs. loss framing. When participants endorse conspiracy worldviews above the average level, the gain frame may be more effective than the loss frame. In other words, in the loss frame (...) condition, conspiracy beliefs negatively and significantly predicted attitudes toward the behavior recommended. However, in the case of the gain frame, the relationship between conspiracist views and attitudes toward promoted behavior was weaker or even nonsignificant. We also found, although only in the case of one behavior, that when participants' eagerness to look for conspiracies almost does not exist, the loss frame may be a better option than the gain frame. Finally, neither of these effects was mediated by emotional reactance or anxiety. (shrink)

The presented study includes an analysis of the category of ‘good’ on the basis of philosophy and economics. Particular attention was paid here to the factors determining the monetary value (price) of an economic good. While achieving the assumed objective of the research, answers to the following questions were sought: What is the difference, therefore, in the interpretation of good as an axiomatic category and good which the economy deals with? What is the basis for the valuation of goods which (...) are the subject of economic analysis? While seeking answers to these questions, an attempt was made to justify the thesis according to which contemporary understanding of the way of valuating goods by the market is limited to accepting the price understood as a variable representing a kind of relationship set in a given time period. (shrink)

Qu'est-ce que l'homme? En se basant sur l'anthropologie à la fois d'Aristote et de Saint Thomas d'Aquin, Maritain propose une conception de l'homme dans laquelle la morale est étroitement liée aux composantes ontologiques dans l'être humain. Le personnalisme de Maritain met l'accent sur le caractère communautaire de l'humanisme. L'homme s'accomplit au moment où il se donne à soi-même et aux autres. Ces deux dimensions du don sont constitutives pour que l'homme s'épanouisse intégralement et pleinement : le don à l'égard de (...) soi-même (la surexistence en connaissance et en amour) et le don à l'égard des autres (le service du bien commun). (shrink)

The article is dedicated to the problems of European political identity and European identity as a whole conception and as a foundation for European integration. Before 24 February 2022, European political identity had been in crisis. The contradictions between the EU member states seemed to be hardly resolvable. The Russian aggression against Ukraine gave a strong impetus to the formation of European identity. However, it is still a negative incentive for unity and solidarity rather than cohesion around positive values, as (...) well as from the outset the European integration was caused by devastating World War II as a negative experience, which should never be repeated. The text makes use of methods peculiar to the philosophical sciences, i.e. critical textual analysis, historical-analytical and comparative methods. (shrink)

The thesis that legal norms are rooted in theology is not new. It is worth considering, however, to what extent not only singular norms, but also models of normativity are the structural representation of theological concepts. In this article, I consider transubstantiation as one of such ideas. I analyse its place in two political theologies published at the same time (in 1922): Carl Schmitt’s Political Theology and James Joyce’s Ulysses. I argue that both thinkers used the idea of transubstantiation as (...) a normative mechanism to deal with anomie that encompassed European societies after the First World War. (shrink)

In this work, an intuitionistic propositional logic with a Galois connection is introduced. In addition to the intuitionistic logic axioms and inference rule of modus ponens, the logic contains only two rules of inference mimicking the performance of Galois connections. Both Kripke-style and algebraic semantics are presented for IntGC, and IntGC is proved to be complete with respect to both of these semantics. We show that IntGC has the finite model property and is decidable, but Glivenko's Theorem does not hold. (...) Duality between algebraic and Kripke semantics is presented, and a representation theorem for Heyting algebras with Galois connections is proved. In addition, an application to rough L-valued sets is presented. (shrink)

The Limits of Cognition and the Shape of Being Based on the Thought of Karl Jaspers The article points out the elements of Karl Jaspers’ epistemological conception that cross out the possibility of a comprehensive account of being. The key issue here is the limits of cognition, which take the form of object cognition. The theme of limits points to the inadequacies of human thinking in the context of quantifiable and absolutist representations of reality. The impossibility of adequately grasping the (...) totality of reality will be illustrated here by means of the criticism Jaspers levelled at absolutising metaphysics. In connection with the description of the structure of cognition proposed by Jaspers, the article points out the conceptual proximity of the issue of worldview and metaphysics in the light of the thought of the cited author. (shrink)

Recenzja: Mark van Roojen, Metaethics: A Contemporary Introduction, New York and London, Routledge, 2015.

Tekst stanowi próbę pomyślenia instytucji stanu wyjątkowego w ramach logiki monistycznej, która by nie naruszała podstaw demokracji liberalnej: jako instrumentu prawnego do zwalczenia zagrożenia, przed którym stoi państwo, przy użyciu narzędzi z porządku norm sprzed wystąpienia sytuacji ekstraordynaryjnej. Autor analizuje trzy możliwości takiej logiki, wywodząc ją z koncepcji m. in. libertarianizmu Roberta Nozicka, instytucjonalizmu Nomi Claire Lazar czy liberalnego realizmu Jeremy’ego Waldrona i aplikując do zapisów Konstytucji RP z 1997 r.

Le Maitre de Claville należy do tradycji moralistycznej klasycyzmu francuskiego i stara się podołać niebagatelnemu zadaniu stworzenia portretu człowieka godnego, honnete homme’a. Usiłując zdefiniować pojęcie cnoty, odwołuje się do własnego smaku estetycznego, subiektywnych emocji radości, zachwytu i rozkoszy wynikających z obcowania z pięknem. Z dużą dowolnością wybiera to, co sam uważa za najdoskonalsze z antyku, Biblii i w najnowszych prądach myślowych swego czasu: m.in. racjonalizmu. Połączenie tych trzech elementow nie jest łatwe. W jego rozważaniach ujawnia się wysiłek moralisty starającego się (...) nadać swej koncepcji kształt logicznie uporządkowanej doktryny, z elementow swobodnie wybranych, nie zawsze ze sobą zgodnych. (shrink)

We propose a non-standard interpretation of Alternating-time Temporal Logic with imperfect information, for which no commonly accepted semantics has been proposed yet. Rather than changing the semantic structures, we generalize the usual interpretation of formulae in single states to sets of states. We also propose a new epistemic operator for ?practical? or ?constructive? knowledge, and we show that the new logic (which we call Constructive Strategic Logic) is strictly more expressive than most existing solutions, while it retains the same model (...) checking complexity. Finally, we study properties of constructive knowledge and other operators in this non-standard semantics. (shrink)

The presentation of the formal conception of noemata is the main aim of the article. In the first section, three informal approaches to noemata are discussed. The goal of this chapter is specifying main controversies and their sources concerned with different ways of the understanding of noemata. In the second section, basic assumptions determining the proposed way of understanding noemata are presented. The third section is devoted to the formal set-theoretic construction needed for the formal comprehension of noemata. In the (...) fourth section, definitions of noemata and their various kinds, as well as definitions of other phenomenological notions are formulated. In the last section, possibilities of further developing the proposed formal conception are indicated. (shrink)

During the last half of the twentieth century, legal philosophy (or legal theory or jurisprudence) has grown significantly. It is no longer the domain of a few isolated scholars in law and philosophy. Hundreds of scholars from diverse fields attend international meetings on the subject. In some universities, large lecture courses of five hundred students or more study it. The primary aim of the Law and Philosophy Library is to present some of the best original work on legal philosophy from (...) both the Anglo-American and European traditions. Not only does it help make some of the best work avail able to an international audience, but it also encourages increased awareness of, and interaction between, the two major traditions. The primary focus is on full-length scholarly monographs, although some edited volumes of original papers are also included. The Library editors are assisted by an Editorial Advisory Board of internationally renowed scholars. Legal philosophy should not be considered a narrowly circumscribed field. (shrink)