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

W niniejszym tekście przedstawiam sylwetkę filozoficzną Stanisława Judyckiego. Odwołując się do koncepcji filozofii zarysowanej w tekście prof. Judyckiego zatytułowanym „Dlaczego filozofia jest trudna?” staram się pokazać w jaki sposób autor tejże koncepcji pozostał jej wierny w swojej oryginalnej twórczości filozoficznej. Staram się zatem wydobyć i omówić najważniejsze cechy sposobu uprawiania filozofii przez Stanisława Judyckiego jak i charakterystyczne cechy filozofii, która jest jego efektem. Omawiam również w skrótowej formie niektóre z najważniejszych wątków i problemów podejmowanych przez Stanisława Judyckiego oraz charakterystyczne cechy (...) jego pisarstwa filozoficznego. (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 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.

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)

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 main result of the present paper — Theorem 3 — establishes the equivalence of the interpolation and amalgamation properties for a large family of logics and their associated classes of matrices.

The Center of Interdisciplinary Studies in Cracow has a very rich tradition that has been studied by many and recently by Kamil Trombik. The very difficult period for the Church and for philosophy during the materialistic Marxist ideology was an opportunity for card. K. Wojtyła to outline a new mode of dialog between science and religion. The future Center, organized by Michał Heller and Józef Życiński not only captured this idea but transformed it into an academic institution centered on the (...) idea of philosophy in science, which was also developed at the Vatican Observatory by W.G. Stoeger et al. Trombik’s book is an excellent study of the historical context and initial years of activity of the Center and its development. (shrink)

The philosophical challenge that religious diversity poses for religious belief has become in recent years the focal point of a very engaging theological and philosophical debate. The debate began in the Christian context and it would be fair to say that its main issue remains the relationship of Christianity to other major religions. Traditionally Christian thinkers faced with the fact of religious plurality have assumed that Christianity is the only way to salvation, and the truth-claims of other religions can be (...) refuted by way of argument. This position is described today as 'exclusivist'. John Hick's name has become synonymous with a radically different approach to the whole issue. Hick argues that all religious traditions make contact with the same Ultimate Reality, each encountering it through a variety of culturally shaped forms of thought and experience, but all offering equally effective paths to 'salvation/liberation'. Hick's pluralistic hypothesis, although very popular in some quarters, appears to many Christian and non-Christian thinkers as highly controversial. (shrink)

Although it became customary to warn against confusing postmodernism with deconstructionism, it seems plausible to suggest that their central agendas are not dissimilar. Moreover, from the philosophical point of view, it is the idea of the 'deconstruction of meaning' that can be said to constitute the foundation of postmodernism understood here as an intellectual movement. It is true that grounded in the poststructuralist language analysis, deconstructionism seeks primarily to challenge the attempts inherent in the Western philosophical tradition to establish ultimate (...) meaning in a text. However, as one might have anticipated, the deconstruction of meaning of texts provided a basis for a large scale project leading to deconstruction of all 'truths', as conceived in the mainstream philosophical tradition. And it did it by questioning the coherence of the very concept of 'truth'. Eclectic as postmodernism is, it can be recognized by the fundamental assumption that there is no common denominator that guarantees the one-ness of the world, or the possibility of objective or neutral thought. This assumption would suffice to make one expect that postmodernism will challenge the very foundations of any metaphysical or religious system of beliefs. And so it does. In this paper I would like to ellucidate just one way this challange may be construed, poiting to the example of Don Cupitt, the leading exponent of the 'antirealist' critique of the discourse of theism. (shrink)

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 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.

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)

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.

ABSTRACTAlthough the British Idealists did not provide a systematic account of language as a distinct philosophical phenomenon, language is nonetheless a fundamental element of Idealist social and political philosophy. This is seen mostly in the Idealist treatment of the concept of general will, which resulted in a Hegelian theory of community, constituted by shared understandings and a shared account of the common good and common interest. This article contains analysis of the relations between language and socio-political institutions in British Idealist (...) writings. The narrative focuses on Thomas Hill Green and Bernard Bosanquet – two major political thinkers representing the said philosophical tradition. The argument proceeds as follows: firstly, possible linguistic interpretations of the Idealist philosophical tradition are introduced. Then the author turns to Green’s conception of general will as the foundation of socio-political order and political sovereignty. In the third section, he... (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).

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.

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.

Rozdział szósty podsumowuje całą pracę. Staram się w nim sprecyzować znaczenie terminu "kryterium logiczności" i pokazać jaką budowę powinny mieć takie kryteria. Analizując trzy spośród sformułowanych w poprzednich rozdziałach kryteriów logiczności, podejmuję dyskusję na temat zakresu ich stosowania. Na zakończenie szkicuję sposób konstruowania złożonych kryteriów logiczności i pokazuję, że zaproponowane przeze mnie kryterium jest spełnione przez logikę klasyczną i przez intuicjonistyczny rachunek predykatów. [ZE WSTĘPU AUTORA].

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)

In this, the latest volume of the Rocznik Filozoficzny Ignatianum, the first few texts are dedicated to the cultural significance of architecture. For time immemorial architecture has been a means of expressing ideas, harmony and proportion. In the ancient and medieval times the task of architecture was to reflect the principles of balance and symmetry found in the surrounding world. During the Renaissance architecture ceased being classified as a merely technical endeavor and began to be viewed also in a humanistic (...) context. It was recognized that architecture is not merely proper building construction, but through the use of symbols and aesthetics it exerts a strong influence on culture and society. Both monumental structures (temples, university buildings, seats of power), as well as ordinary residences were designed to reflect the social needs of the time. Simplicity and symmetry vied with extravagance, dynamism and theatricality of form. The search for the root causes of these phenomena is the main thrust of the ideas presented in the texts below. (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.

The present paper is thought as a formal study of distributive closure systems which arise in the domain of sentential logics. Special stress is laid on the notion of a C-filter, playing the role analogous to that of a congruence in universal algebra. A sentential logic C is called filter distributive if the lattice of C-filters in every algebra similar to the language of C is distributive. Theorem IV.2 in Section IV gives a method of axiomatization of those filter distributive (...) logics for which the class Matr (C) prime of C-prime matrices (models) is axiomatizable. In Section V, the attention is focused on axiomatic strengthenings of filter distributive logics. The theorems placed there may be regarded, to some extent, as the matrix counterparts of Baker's well-known theorem from universal algebra [9, § 62, Theorem 2]. (shrink)

We propose a new schema for the deduction theorem and prove that the deductive system S of a prepositional logic L fulfills the proposed schema if and only if there exists a finite set A(p, q) of propositional formulae involving only prepositional letters p and q such that A(p, p) L and p, A(p, q) s q.