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)

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.

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

In this paper I argue that from the point of view of a theist, inclusivism with respect to the issue whether adherents of different religious traditions can have veridical experience of God (or Ultimate Reality) now, is more plausible than the Alstonian exclusivism. I suggest that mystical inclusivism of the kind I imply in this paper may contribute to the development of cross-cultural philosophy of religion, as well as to the theoretical framework for inter-religious dialogue, because (1) it allows for (...) the possibility of veridical experience of God in a variety of religious traditions, but (2) it avoids the radical revisionist postulates of Hickian pluralism and (3) it leaves open the question whether the creed of any specific tradition is a better approximation to the truth about God than the creeds of other traditions. (edited). (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.

Empirical evidence suggests that mindfulness, psychological flexibility, and addiction are interrelated in decision making. In our study, we investigated the relationship of the behavioral profile, composed of mindfulness and psychological flexibility, and smoking status on delay and probability discounting. We demonstrated the interaction of the behavioral profile of mindfulness and psychological flexibility and smoking status on delay discounting. We found that individuals who smoked and displayed higher mindfulness and psychological flexibility devalued rewards at a slower rate, compared to smokers with (...) a lower profile. Importantly, in those with a higher profile, smokers discounted rewards no differently than nonsmokers. Smokers with a lower profile did display, however, increased impulsivity, compared to nonsmokers. These results suggest that behavioral interventions aiming to modify the behavioral profile with regard to mindfulness and psychological flexibility can indeed support the regulation of elevated impulsivity in smokers to equate with that of nonsmokers. In probability discounting, we observed that individuals with a higher profile displayed lower discounting rates, i.e., were less risk-averse, with no other significant main effect or interaction. (shrink)

Traumatic brain injuries to the frontal lobes are associated with many maladaptive forms of behavior. We investigated the association between brain damage and impulsivity, as measured by the rate of delay discounting. The main aim of this study was to test the hypothesis of steeper discounting of different amounts in a group of patients with frontal lobe damage. We used a delay discounting task in the form of a structured interview. A total of 117 participants were divided into five groups: (...) three neurological groups and two groups without brain damage. Our analyses showed that patients with focal damage to the frontal lobes demonstrated steeper delay discounting than other participants. Other clinical groups demonstrated similar discounting rates. The data pattern related to the magnitude effect on the group level suggested that the magnitude effect is absent in the group of patients with damage to the frontal lobes; however, results were less consistent on an individual level. Amount-dependent discounting was observed in only two groups, the healthy control group and the neurological group with other cortical areas damaged. (shrink)

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 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)

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

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)

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)

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)

Paul Edwards' October 1989 essay, ‘Heidegger's Quest for Being’ illustrates the wisdom of the dictum that the only legitimate criticism of a philosopher's position is a constructive criticism. His negative critique amounts to no more than expressions of distaste, dislike, and displeasure, and nothing of philosophical interest follows from his assertions, as the discourse is primarily an argument ad hominem . He grossly misinterprets Heidegger on some elemental and fundamental matters as well. In particular, he sorely misinterprets what he refers (...) to as the ‘Quest for Being’, which only further contributes to the objectionable character of the essay. (shrink)

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.

The first known statements of the deduction theorems for the first-order predicate calculus and the classical sentential logic are due to Herbrand [8] and Tarski [14], respectively. The present paper contains an analysis of closure spaces associated with those sentential logics which admit various deduction theorems. For purely algebraic reasons it is convenient to view deduction theorems in a more general form: given a sentential logic C (identified with a structural consequence operation) in a sentential language I, a quite arbitrary (...) set P of formulas of I built up with at most two distinct sentential variables p and q is called a uniform deduction theorem scheme for C if it satisfies the following condition: for every set X of formulas of I and for any formulas and , C(X{{a}}) iff P(, ) AC(X). [P(, ) denotes the set of formulas which result by the simultaneous substitution of for p and for q in all formulas in P]. The above definition encompasses many particular formulations of theorems considered in the literature to be deduction theorems. Theorem 1.3 gives necessary and sufficient conditions for a logic to have a uniform deduction theorem scheme. Then, given a sentential logic C with a uniform deduction theorem scheme, the lattices of deductive filters on the algebras A similar to the language of C are investigated. It is shown that the join-semilattice of finitely generated (= compact) deductive filters on each algebra A is dually Brouwerian. (shrink)

In the first section logics with an algebraic semantics are investigated. Section 2 is devoted to subdirect products of matrices. There, among others we give the matrix counterpart of a theorem of Jónsson from universal algebra. Some positive results concerning logics with, finite degrees of maximality are presented in Section 3.

The class Matr(C) of all matrices for a prepositional logic (, C) is investigated. The paper contains general results with no special reference to particular logics. The main theorem (Th. (5.1)) which gives the algebraic characterization of the class Matr(C) states the following. Assume C to be the consequence operation on a prepositional language induced by a class K of matrices. Let m be a regular cardinal not less than the cardinality of C. Then Matr (C) is the least class (...) of matrices containing K and closed under m-reduced products, submatrices, matrix homomorphisms, and matrix homomorphic counter-images. (shrink)

The notion of local deduction theorem (which generalizes on the known instances of indeterminate deduction theorems, e.g. for the infinitely-valued ukasiewicz logic C ) is defined. It is then shown that a given finitary non-pathological logic C admits the local deduction theorem iff the class Matr(C) of all matrices validating C has the C-filter extension property (Theorem II.1).

Research on natural and artificial brains is proceeding at a rapid pace. However, the understanding of the essence of consciousness has changed slightly over the millennia, and only the last decade has brought some progress to the area. Scientific ideas emerged that the soul could be a product of the material body and that calculating machines could imitate brain processes. However, the authors of this book reject the previously common dualism—the view that the material and spiritual-psychic processes are separate and (...) require a completely different substance as their foundation. -/- Reductive Model of the Conscious Mind is a forward-thinking book wherein the authors identify processes that are the essence of conscious thinking and place them in the imagined, simplified structure of cells able to memorize and transmit information in the form of impulses, which they call neurons. The purpose of the study is to explain the essence of consciousness to the degree of development of natural sciences, because only the latter can find a way to embed the concept of the conscious mind in material brains. The book is divided into three parts. Part 1 works to convince readers that the emergence of consciousness does not require detailed knowledge of the structure and morphology of the brain, with the exception of some specific properties of the neural network structure that the authors attempt to point out. Part 2 proves that the biological structure of many natural brains fulfills the necessary conditions for consciousness and intelligent thinking. Similarly, Part 3 shows the ways in which artificial creatures imitating natural brains can meet these conditions, which gives great hopes for building artificially intelligent beings endowed with consciousness. Covering topics that include cognitive architecture, the embodied mind, and machine learning, this book is ideal for cognitive scientists, philosophers of mind, neuroscientists, psychologists, researchers, academicians, and advanced-level students. The book can also help to focus the research of linguists, neurologists, and biophysicists on the biophysical basis of postulated information processing into knowledge structures. (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.