Jaśkowski’s discussive logic D2 was formulated with the help of the modal logic S5 as follows (see [7, 8]): \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A \in {D_{2}}}$$\end{document} iff \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\ulcorner\diamond{{A}^{\bullet}}\urcorner \in {\rm S}5}$$\end{document}, where (–)• is a translation of discussive formulae from Ford into the modal language. We say that a modal logic L defines D2 iff \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm D}_{2} = (...) \{A \in {\rm For^{\rm d}} : \ulcorner\diamond{{A}^{\bullet}}\urcorner \in {\it L}\}}$$\end{document}. In [14] and [10] were respectively presented the weakest normal and the weakest regular logic which (†): have the same theses beginning with ‘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\diamond}$$\end{document}’ as S5. Of course, all logics fulfilling the above condition, define D2. In [10] it was prowed that in the cases of logics closed under congruence the following holds: defining D2 is equivalent to having the property (†). In this paper we show that this equivalence holds also for all modal logics which are closed under replacement of tautological equivalents (rte-logics).We give a general method which, for any class of modal logics determined by a set of joint axioms and rules, generates in the given class the weakest logic having the property (†). Thus, for the class of all modal logics we obtain the weakest modal logic which owns this property. On the other hand, applying the method to various classes of modal logics: rte-logics, congruential, monotonic, regular and normal, we obtain the weakest in a given class logic defining D2. (shrink)

In this paper we present a comparison of certain inconsistencyadaptive logics and Jaśkowski’s logic.

Jaśkowski’s discussive logic D2 was formulated with the help of the modal logic S5 as follows (see [7, 8]): \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A \in {D_{2}}}$$\end{document} iff \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\ulcorner\diamond{{A}^{\bullet}}\urcorner \in {\rm S}5}$$\end{document}, where (–)• is a translation of discussive formulae from Ford into the modal language. We say that a modal logic L defines D2 iff \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm D}_{2} = (...) \{A \in {\rm For^{\rm d}} : \ulcorner\diamond{{A}^{\bullet}}\urcorner \in {\it L}\}}$$\end{document}. In [14] and [10] were respectively presented the weakest normal and the weakest regular logic which (†): have the same theses beginning with ‘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\diamond}$$\end{document}’ as S5. Of course, all logics fulfilling the above condition, define D2. In [10] it was prowed that in the cases of logics closed under congruence the following holds: defining D2 is equivalent to having the property (†). In this paper we show that this equivalence holds also for all modal logics which are closed under replacement of tautological equivalents (rte-logics).We give a general method which, for any class of modal logics determined by a set of joint axioms and rules, generates in the given class the weakest logic having the property (†). Thus, for the class of all modal logics we obtain the weakest modal logic which owns this property. On the other hand, applying the method to various classes of modal logics: rte-logics, congruential, monotonic, regular and normal, we obtain the weakest in a given class logic defining D2. (shrink)

In this paper I would like to argue that Stoic logic is a kind ofrelevant logic rather than the classical logic. To realize this purpose I willtry to keep as close as possible to Stoic calculus as expressed with the helpof their arguments.

In [1] J. Perzanowski formulated, among others, an ontology expressed in the relational language. He presented some interesting connections which hold between these relations. In the present paper we focus on further analysis of these relations.

In the paper we analyse the problem of axiomatizing the minimal variant of discussive logic denoted as $$ {\textsf {D}}_{\textsf {0}}$$ D 0. Our aim is to give its axiomatization that would correspond to a known axiomatization of the original discussive logic $$ {\textsf {D}}_{\textsf {2}}$$ D 2. The considered system is minimal in a class of discussive logics. It is defined similarly, as Jaśkowski’s logic $$ {\textsf {D}}_{\textsf {2}}$$ D 2 but with the help of the deontic normal logic (...) $$\textbf{D}$$ D. Although we focus on the smallest discussive logic and its correspondence to $$ {\textsf {D}}_{\textsf {2}}$$ D 2, we analyse to some extent also its formal aspects, in particular its behaviour with respect to rules that hold for classical logic. In the paper we propose a deductive system for the above recalled discussive logic. While formulating this system, we apply a method of Newton da Costa and Lech Dubikajtis—a modified version of Jerzy Kotas’s method used to axiomatize $$ {\textsf {D}}_{\textsf {2}}$$ D 2. Basically the difference manifests in the result—in the case of da Costa and Dubikajtis, the resulting axiomatization is pure modus ponens-style. In the case of $$ {\textsf {D}}_{\textsf {0}}$$ D 0, we have to use some rules, but they are mostly needed to express some aspects of positive logic. $$ {\textsf {D}}_{\textsf {0}}$$ D 0 understood as a set of theses is contained in $$ {\textsf {D}}_{\textsf {2}}$$ D 2. Additionally, any non-trivial discussive logic expressed by means of Jaśkowski’s model of discussion, applied to any regular modal logic of discussion, contains $$ {\textsf {D}}_{\textsf {0}}$$ D 0. (shrink)

In Béziau a logic \ was defined with the help of the modal logic \. In it, the negation operator is understood as meaning ‘it is not necessary that’. The strong soundness–completeness result for \ with respect to a version of Kripke semantics was also given there. Following the formulation of \ we can talk about \-like logics or Beziau-style logics if we consider other modal logics instead of \—such a possibility has been mentioned in [1]. The correspondence result between (...) modal logics and respective Beziau-style logics has been generalised for the case of normal logics naturally leading to soundness–completeness results [see Marcos :279–300, 2005) and Mruczek-Nasieniewska and Nasieniewski :229–248, 2005)]. In Mruczek-Nasieniewska and Nasieniewski :185–196, 2008), :189–203, 2009) some partial results for non-normal cases are given. In the present paper we try to give similar but more general correspondence results for the non-normal-worlds case. To achieve this aim we have to enrich original Beziau’s language with an additional negation operator understood as ‘it is necessary that not’. (shrink)

In the context of modal logics one standardly considers two modal operators: possibility ) and necessity ) [see for example Chellas ]. If the classical negation is present these operators can be treated as inter-definable. However, negative modalities ) and ) are also considered in the literature [see for example Béziau ; Došen :3–14, 1984); Gödel, in: Feferman, Collected works, vol 1, Publications 1929–1936, Oxford University Press, New York, 1986, p. 300; Lewis and Langford ]. Both of them can be (...) treated as negations. In Béziau a logic \ has been defined on the basis of the modal logic \. \ is proposed as a solution of so-called Jaśkowski’s problem [see also Jaśkowski ]. The only negation considered in the language of \ is ‘it is not necessary’. It appears that logic \ and \ inter-definable. This initial correspondence result between \ and \ has been generalised for the case of normal logics, in particular soundness-completeness results were obtained [see Marcos :279–300, 2005); Mruczek-Nasieniewska and Nasieniewski :229–248, 2005)]. In Mruczek-Nasieniewska and Nasieniewski it has been proved that there is a correspondence between \-like logics and regular extensions of the smallest deontic logic. To obtain this result both negative modalities were used. This result has been strengthened in Mruczek-Nasieniewska and Nasieniewski :261–280, 2017) since on the basis of classical positive logic it is enough to solely use \ to equivalently express both positive modalities and negation. Here we strengthen results given in Mruczek-Nasieniewska and Nasieniewski by showing correspondence for the smallest regular logic. In particular we give a syntactic formulation of a logic that corresponds to the smallest regular logic. As a result we characterise all logics that arise from regular logics. From this follows via respective translations a characterisation of a class of logics corresponding to some quasi-regular logics where \ is the smallest element. Moreover, if a given quasi-regular logic is characterised by some class of models, the same class can be used to semantically characterise the logic obtained by our translation. (shrink)

In [1] J.-Y. Bèziau formulated a logic called Z. Bèziau’s idea was generalized independently in [6] and [7]. A family of logics to which Z belongs is denoted in [7] by K. In particular; it has been shown in [6] and [7] that there is a correspondence between normal modal logics and logics from the class K. Similar; but only partial results has been obtained also for regular logics. In a logic N has been investigated in the language with negation; (...) implication; conjunction and disjunction by axioms of positive intuitionistic logic; the right-to-left part of the second de Morgan law; and the rules of modus ponens and contraposition. From the semantical point of view the negation used by Došen is the modal operator of impossibility. It is known this operator is a characteristic of the modal interpretation of intuitionistic negation. In the present paper we consider an extension of N denoted by N+. We will prove that every extension of N+ that is closed under the same rules as N+; corresponds to a regular logic being an extension of the regular deontic logic D21. The proved correspondence allows to obtain from soundnesscompleteness result for any given regular logic containing D2, similar adequacy theorem for the respective extension of the logic N+. (shrink)

In Jaśkowski’s model of discussion, discussive connectives represent certain interactions that can hold between debaters. However, it is not possible within the model for participants to use explicit modal operators. In the paper we present a modal extension of the discussive logic $\textbf{D}_{\textbf{2}}$ that formally corresponds to an extended version of Jaśkowski’s model of discussion that permits such a use. This logic is denoted by $\textbf{m}\textbf{D}_{\textbf{2}}$. We present philosophical motivations for the formulation of this logic. We also give syntactic characterizations (...) of the logic and propose a comparison with certain other modal systems. In particular, we prove that $\textbf{m}\textbf{D}_{\textbf{2}}$ is neither normal nor regular. On the basis of the axiomatization of $\textbf{D}_{\textbf{2}}$, we give an axiomatization of $\textbf{m}\textbf{D}_{\textbf{2}}$. We also give another axiomatization which is not based on the axiomatization of $\textbf{D}_{\textbf{2}}$. Furthermore, we give a natural Kripke-style semantics for $\textbf{m}\textbf{D}_{\textbf{2}}$ and prove the respective adequacy theorems. (shrink)

In the paper, we tackle the matter of non-classical logics, in particular, paraconsistent ones, for which not every formula follows in general from inconsistent premisses. Our benchmark is Jaśkowski’s logic, modeled with the help of discussion. The second key origin of this paper is the matter of being tabular, i.e. being adequately expressible by finitely many finite matrices. We analyse Jaśkowski’s non-tabular discussive (discursive) logic $ \textbf {D}_{2}$, one of the first paraconsistent logics, from the perspective of a trivalent tabular (...) logic. We are motivated to step down from the ongoing modal $ \textbf {S5}$-perspective of developing $ \textbf {D}_{2}$ both by certain mysteries that have been surrounding it and by gaps in Jaśkowski’s arguments contra the multivalent tabular perspective. Although Jaśkowski’s idea to use $ \textbf {S5}$ in order to define $ \textbf {D}_{2}$ is very attractive since it allows one to benefit from the tools and results of modal logic, it also gives a ‘non-direct’ formulation and, as it appeared later, is superfluous with respect to what is meant to be achieved since one can define the very same logic but using modal logics weaker than S5. It is also known, due to Kotas, that discussive logic is not finite-valued. So, in light of Kotas’s result that $ \textbf {D}_{2}$ is non-tabular, we propose to associate it with a few dozen discussive formulae that Jaśkowski unequivocally and illustratively suggests to be its theorems or non-theorems rather than with axioms of its modern axiomatizations (one of which Kotas employs) in order to be capable of performing a computer-aided brute-force search for suitable trivalent matrices in the cases of one and two designated values. As a result, we find trivalent matrices with two designated values that might be dubbed ‘discussive’ because they meet Jaśkowski’s suggestion to validate and invalidate the litmus theorems and non-theorems, respectively, despite the fact that none of them validates all the negation axioms in the modern axiomatizations of $ \textbf {D}_{2}$. The matrices found are then analysed along with highlighting the ones that were previously mentioned in the literature. We conclude the paper with a comparative analysis of Omori’s results and a test of Karpenko’s hypothesis. (shrink)

The monograph is aimed at an analysis of the reasons for theory change in science. The writer develops a model of theory change according to which the origins of scientific revolutions lie not in a clash of fundamental theories with facts, but of ‘old’ fundamental theories with each other.

Kuala Lumpur is a diverse city representing many different religions and nationalities. Recent government policy has actively promoted unity and cohesion throughout the city; and the country of Malaysia, with the implementation of a programme called 1Malaysia. In this book, the authors investigate the aims of this programme – predominantly to unify the Malaysian society – and how these objectives resonate in the daily spatial practices of the city’s residents. -/- This book argues that elements of urban infrastructure could work (...) as an essential mediator ‘beyond community’, allowing inclusive social structures to be built, despite cultural and religious tensions existing within the city. It builds on the premise of an empirical study which explores the ways in which different communities use the same spaces, supported through the implementation of a theoretical framework which looks at both Western and Islamic conceptualisations of the notion of community. Through the analysis of Kuala Lumpur, this book contributes towards the creation of more inclusive places in multi-ethnic, multi-cultural and multi-religious communities across the world. (shrink)

Since the publication of ChatGPT and Dall-E, there has been heavy discussions on the possible dangers of generative artificial intelligence (AI) for society. These discussions question the extent to which the development of AI can be regulated by politics, law, and civic actors. An important arena for discourse on AI is the news media. The news media discursively construct AI as a technology that is more or less possible to regulate. There are various reasons for an assumed regulatability. Some voices (...) highlight the predominant capitalism of modern society as an ideology that enforces an uncontrolled development of AI. Others call on the rationality of civic society, which will push AI toward a development that serves humankind. Summarized, the discourse on AI floats between positions of technological and social determinism. The article conducts a discourse analysis on 113 articles from the German newspapers Süddeutsche Zeitung and Frankfurter Allgemeine Zeitung. The analysis shows how these center-left and center-right media frame the AI development in terms of social and technological determinism. As these newspapers reach out to a large audience, the article shows the kinds of perspectives on AI that confront civic society in Germany every day. News media can motivate or impede social action, as they frame the potential necessity of society and its members to intervene against certain developments. The article shows how the newspapers promote an understanding of AI, by which citizens will feel motivated to insist on a regulation of AI by politics and law. (shrink)

Predictive Processing theory, hotly debated in neuroscience, psychology and philosophy, promises to explain a number of perceptual and cognitive phenomena in a simple and elegant manner. In some of its versions, the theory is ambitiously advertised as a new theory of conscious perception. The task of this paper is to assess whether this claim is realistic. We will be arguing that the Predictive Processing theory cannot explain the transition from unconscious to conscious perception in its proprietary terms. The explanations offer (...) by PP theorists mostly concern the preconditions of conscious perception, leaving the genuine material substrate of consciousness untouched. (shrink)

This book develops a new approach to naturalizing phenomenology. The author proposes to integrate phenomenology with the mechanistic framework that offers new methodological perspectives for studying complex mental phenomena such as consciousness. While mechanistic explanatory models are widely applied in cognitive science, their approach to describing subjective phenomena is limited. The author argues that phenomenology can fill this gap. He proposes two novel ways of integrating phenomenology and mechanism. First, he presents a new reading of phenomenological analyses as functional analyses. (...) Such functional phenomenology delivers a functional sketch of a target system and provides constraints on the space of possible mechanisms. Second, he develops the neurophenomenological approach in the direction of dynamic modeling of experience. He shows that neurophenomenology can deliver dynamical constraints on mechanistic models and thus inform the search for an underlying mechanism. (shrink)

In the former socialist countries the relation of philosophy to social reality, as shaped by the political interests of the State, must be considered for each particular case with a view to the historical dynamics of its own development. The Polish case is not typical in this regard -- it was determined by the failure of forced sovietization at the institutional, cultural level and the maintenance of Poland's traditional contacts with Western European culture. In this regard Polish universities played an (...) important role since they preserved 'normal' structures of academic activity. Philosophy in Poland has been marked by three currents which managed to rebuff the advances of Marxism. Best known among them is the Lwów-Warsaw school of logic and analytic philosophy. Its contribution is especially important in the methodology of philosophical inquiry and the style of responsible philosophical discourse. Though not a bed of political opposition the school's members mounted a 'spiritual opposition' to Marxism, especially during the Solidarity period. Catholic philosophy, as represented by the Catholic University of Lublin, has been and remains a completely independent force in Eastern and Central Europe. Doctrinally, Catholic philosophy in Poland has been divided between a more traditional, dated Thomism and the more progressive circles in Cracow where Western European philosophy, especially phenomenology, existentialism, and hermeneutics, has been influential. The third major current, centered in Cracow, is the phenomenology of Roman Ingarden, whose influence is manifest in a style of philosophizing that has attracted professional philosophers as well as committed intellectuals from different disciplines. Against this diversified background Marxism had to prove its mettle, a requirement that explains the unique internal differentiation and pluralism within Polish Marxist philosophy. The decisive factors in its development were its rejection of Soviet Marxism-Leninism and the opening to Western Marxism. The often remarked 'revisionist' character of Polish Marxism consists in the recognition by its most talented representatives of the fundamental incompatibility between Marxism as the ideological legitimation of the Communist state and as a philosophy subject to rational criteria. In effect, Polish Marxists thought the theory through to its end, and in this sense brought to light its inherently unstable nature: to be a philosophy it would have to cease to be Marxist, to be Marxist means having to pander to ideology. The confrontation of the diverse currents in Polish philosophy contributed to an unfortunate result: for political reasons non-Marxists steered clear of social philosophical questions, while official Marxism, which suppressed the 'revisionist' trend, obfuscated the relation between philosophy and social reality. Today philosophy in Poland has the urgent task to contribute to the reconstruction of a social rationality combining a critical consciousness with moral elements of commitment and responsibility. (shrink)

The free association method is often employed in marketing research to investigate perceptions of a particular product or brand in different socio-cultural groups of customers. In our research, international and domestic students produced free associations in response to photographs of outdoor billboards from two different locations in one city (city centre and outskirts). The results indicate that free associations can depict qualitative aspects of outdoor billboards like poor quality (relating to the categories of amateurish and fake), problematic content (relating to (...) female stereotypes, gender stereotypes and cultural differences), and that they have the potential to capture the general atmosphere of the neighbourhood (categories of decay, depression, danger and past). (shrink)

Referring to basic Weberian notions of rationalization and secularization, I try to find a more accurate sense of the term “secularization”, intending to describe adequately the position of religion in modernity. The result of this query is—or at least should be—a new, original conceptualization of religion as one of finite provinces of meaning within one paramount reality of the life-world, as defined by Alfred Schutz. I proceed by exposing a well known, major oversimplification of the Weberian concept of secularization, very (...) well outlined in Peter Berger’s The sacred canopy, in order to point to the genuine, much more differentiated position of Max Weber in this matter (especially from the period of Foundations of social economic and Economy and society), and, consequently, to return to the roots of Berger’s thought: phenomenological sociology of Alfred Schutz, an attempt to assure the philosophical foundations of Weber’s sociological theory. At a closer glimpse, transformation of religion in the modern process of rationalization does not consist—according to Weber—in eliminating religion and thus depriving society of the religious source of meaning, but in parallel emancipation of many different domains of rationality, including religion itself. Using Schutz’s analysis of the social world as a complex structure of many different final provinces of meaning, I describe religion as such a province and show what does the process of rationalization of this province consist and what it should consist in: a complex, ongoing exchange of cognitive relevances and contents, combined with growing autonomy of many different sub-worlds. Schutz’s theory of symbol, rooted in Edmund Husserl’s description of constitution of complex objects in mono- and polythetic acts of consciousness, moves the analysis to the epistemological level, pointing to a chance of intensifying our cognitive relation to reality through increasing interpenetration of various sub-universes of meaning. (shrink)

Purpose of the article is to present in two parts the selected aspects of application of monetary policy in the euro area pre and post 2008 as well as insitutional adaptations brought by the EU legislator. Methodology/methods In order to better explain these points, the article relies partially on a comparison with the framework and application of the monetary policy by the Federal Reserve as well as on a historic method when outlining the influence of definition of financial stability from (...) the ECB/eurosystem towards other prominent central banks. Scientific aim The article presents selected aspects of the monetary policy in the part of the EU where single currency was introduced in order to outline state of the art governance structure as well as a certain institutional creativity in application of powers conferred upon the central banks by the Treaty on the Functioning of the European Union and Protocol on the Statute of the European System of Central Banks and of the European Central Bank. The goal is to prove the hypothesis of robustness of the framework and present the limits that can only be pushed further by the legislative power. The conclusions confirm on the one hand that the framework of monetary policy based on strong institutional safeguards such as legislative power and independence is very resilient and can prove efficient and creative enough to stabilise an innovative monetary system, however, on the other hand, validate the hypothesis that certain adaptations can only be performed on the basis of a legislative adaptations. (shrink)

Purpose of the article is to present in two parts the selected aspects of application of monetary policy in the euro area pre and post 2008 as well as insitutional adaptations brought by the EU legislator. Methodology/methods In order to better explain these points, the article relies partially on a comparison with the framework and application of the monetary policy by the Federal Reserve as well as on a historic method when outlining the influence of definition of financial stability from (...) the ECB/eurosystem towards other prominent central banks. Scientific aim The article presents selected aspects of the monetary policy in the part of the EU where single currency was introduced in order to outline state of the art governance structure as well as a certain institutional creativity in application of powers conferred upon the central banks by the Treaty on the Functioning of the European Union and Protocol on the Statute of the European System of Central Banks and of the European Central Bank. The goal is to prove the hypothesis of robustness of the framework and present the limits that can only be pushed further by the legislative power. The conclusions confirm on the one hand that the framework of monetary policy based on strong institutional safeguards such as legislative power and independence is very resilient and can prove efficient and creative enough to stabilise an innovative monetary system, however, on the other hand, validate the hypothesis that certain adaptations can only be performed on the basis of a legislative adaptations. (shrink)