The class of equivalential logics comprises all implicative logics in the sense of Rasiowa [9], Suszko's logic SCI and many others. Roughly speaking, a logic is equivalential iff the greatest strict congruences in its matrices are determined by polynomials. The present paper is the first part of the survey in which systematic investigations into this class of logics are undertaken. Using results given in [3] and general theorems from the theory of quasi-varieties of models [5] we give a characterization of (...) all simple C-matrices for any equivalential logic C. In corollaries we give necessary and sufficient conditions for the class of all simple models for a given equivalential logic to be closed under free products. (shrink)

In the late forties, Stanisław Jaśkowski published two papers onthe discursive sentential calculus, D2. He provided a definition of it by an interpretation in the language of S5 of Lewis. The knownaxiomatization of D2 with discursive connectives as primitives was introduced by da Costa, Dubikajtis and Kotas in 1977. It turns out, however,that one of the axioms they used is not a thesis of the real Jaśkowski’s calculus. In fact, they built a new system, D∗2 for short, that differs from (...) D2 inmany respects. The aim of this paper is to introduce a direct Kripke-type semantics for the system, axiomatize it in a new way and prove soundness andcompleteness theorems. Additionally, we present labelled tableaux for D∗2.1. (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)

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.

Analizy przeprowadzone w artykule pozwalają na wyciągnięcie wniosków, ważnych dla filozofa przyrody. Między filozofią a naukami przyrodniczymi istnieje interakcja, którą można określić jako współprzenikanie się obu tych dziedzin wiedzy. To współoddziaływanie filozofii z nauką podobne jest do niedomykającego się koła. Trudno jest owo współprzenikanie jednoznacznie scharakteryzować, ale można wskazać pewne idee towarzyszące mu. Uświadomienie sobie filozoficznego uwikłania teorii naukowej powoduje często rozszerzenie jej rozumienia oraz ujawnia, jak wiele informacji zawartych jest w teorii naukowej na temat głębokiej struktury świata. Sformułowanie „filozofia (...) w nauce” można by uznać za charakterystyczne dla współczesnego ujmowania związku filozofii z naukami przyrodniczymi. Należy pamiętać, że wspólna droga filozofii i nauk przyrodniczych pozwala osiągać interesujące poznawczo wyniki, ważne dla rozumienia świata zewnętrznego. Współprzenikanie się filozofii z nauk jest procesem dynamicznym i twórczym. Tak filozofia, jak i nauka, ulegają ciągłym zmianom, które w istotny sposób wpływają na rozwijanie się procesu współprzenikania. Trudno jest przewidywać, w którą stronę ten proces będzie ewoluował. Ważne jest jednak, jak twierdzi M. Heller, aby w tym twórczym procesie dostrzec, że największym sukcesem nauk empirycznych, trwającym do dziś, jest coraz lepsze ugruntowanie się przekonania, że Wszechświat stopniowo, choć tylko w przybliżeniu, ujawnia nam tajemnice swojej struktury. -------------- Zgłoszono: 12/09/2020. Zrecenzowano: 10/10/2020. Zaakceptowano do publikacji: 29/10/2020. (shrink)

In this paper, we present a calculus of paraconsistent logic. We propose an axiomatisation and a semantics for the calculus, and prove several important meta-theorems. The calculus, denoted as CB1, is an extension of systems PI, C min and B1, and a proper subsystem of Sette’s calculus P1. We also investigate the generalization of CB1 to the hierarchy of related calculi.

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.

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

The paper is a response to recent criticisms of agatheism, a new pluralistic interpretation of religious belief put forward by Janusz Salamon with the aim of accommodating the epistemological challenge of religious diversity. Agatheism is an axiologically grounded religious belief which identifies God, the Absolute or the ultimate reality religiously conceived with the ultimate good as the ultimate end of all human agency and thus an explanation of its irreducibly teleological character and a source of its meaning. Janusz (...) Salamon argues that this grounding of religious belief in the human axiological consciousness makes it immune to falsification by any future science. Replying to the concerns of the critics about about irrationality of doxastic commitment to a particular religious tradition, Janusz Salamon argues that to the extent the fundamental agatheistic religious belief is presupposed in such tradition as its doxastic core, its belief system - if internally coherent and aligned with a worldview that is consistent with undisputed scientific findings - may be considered rational, despite there being a plurality of such belief systems. (shrink)

In 1953, Jerzy Kalinowski published his paper on the logic of normative sentences. The paper is recognized as one of the first publications on the formal system of deontic logic. The aim of this paper is to present a tableau system for Kalinowski’s deontic logic and to discuss some of the topics related to the paradoxes of deontic logic.

This article attempts to answer the question: what has the current migration crisis revealed in relations between Christianity and Islam, two religions with common Abrahamic roots? What conclusions can be drawn about the state of these relations, particularly with regard to ordinary members of the two religions? How should we assess the reaction of Christians in Europe to the inflow of refugees from Muslim countries in the light of the Gospel, the Second Vatican Council and the teaching of Pope Francis?The (...) article consists of four parts. Part I briefly presents Christian-Muslim relationships over the centuries. Part II focuses on the sense of danger occurring in European societies in connection with the influx of Muslims during the migration crisis. Part III presents the teachings of the Second Vatican Council about Islam and Part IV describes Pope Francis’s attitude towards refugees from Muslim countries. (shrink)

This volume explores the range of Alfred North Whitehead's philosophy and his relevance to contemporary philosophical traditions.

Peter Millican and Branden Thornhill-Miller have recently argued that contradictions between different religious belief systems, in conjunction with the host of defeaters based on empirical research concerning alleged sources of evidence for ‘perceived supernatural agency’, render all ‘first-order’, that is actual, religious traditions positively irrational, and a source of discord on a global scale. However, since the authors recognise that the ‘secularisation thesis’ appears to be incorrect, and that empirical research provides evidence that religious belief also has beneficial individual and (...) social effects, they put forward a hypothesis of a ‘second-order religious belief ’, with Universalist overtones and thus free of intergroup conflict, and free of irrationality, since supported (solely) by the Fine-Tuning Argument. While granting most of their arguments based on empirical research and embracing the new paradigm of the atheism/religion debate implicit in their paper, I contend that Millican’s and Thornhill-Miller’s proposal is unlikely to appeal to religious believers, because it misconstrues the nature and grounds of religious belief. I suggest that their hypothesis may be refined by taking into account a view of axiologically grounded religious belief that I refer to as ‘agatheism’, since it identifies God or the Ultimate Reality with the ultimate good (to agathon). (shrink)

This study investigates performance of portfolios composed of British socially responsible investments (SRI) stocks. Using the ‘Global-100 Most Sustainable Corporations in the World’ list (known also as ‘Global-100’) to select the SRI companies, we found that, in the period 2000–2010, the returns of the SRI portfolios were on average higher compared with the corresponding returns of the market indexes. The annual average difference in returns of the SRI portfolios (with dividends) was 5.26 % and 5.69 % relative to the FTSE100 (...) and FTSE4GOOD indexes (the total return versions), respectively, but the differences in returns in the whole period, in individual years and in other sub-periods were in most cases not statistically significant. Positive performance of SRI stocks in the whole sample is, however, evidenced by risk-adjusted measures such as the modified Sharpe ratio (MSR) and certainty equivalent (CEQ) returns, as well as by incorporating various levels of transaction costs. Furthermore, a simple trading strategy relying on selection of SRI stocks from the Global-100 list would beat the market indexes in the whole period 2000–2010, even after inclusion of various levels of transaction costs. We also estimated the Fama–French and Carhart multi-factor models and found that the returns of the SRI portfolios cannot be consistently explained by conventional factors other than the market factor. (shrink)

The class of equivalential logics comprises all implicative logics in the sense of Rasiowa [9], Suszko's logicSCI and many Others. Roughly speaking, a logic is equivalential iff the greatest strict congruences in its matrices (models) are determined by polynomials. The present paper is the first part of the survey in which systematic investigations into this class of logics are undertaken. Using results given in [3] and general theorems from the theory of quasi-varieties of models [5] we give a characterization of (...) all simpleC-matrices for any equivalential logicC (Theorem I.14). In corollaries we give necessary and sufficient conditions for the class of all simple models for a given equivalential logic to be closed under free products (Theorem I.18). (shrink)