"The importance of questions is beyond doubt. But the degree of attention paid to them in logic and linguistics is still less than they deserve." What is a question? How to represent questions in formal languages? How to model reasoning in which questions are involved? Can we prove anything by means of pure questioning? How to model goal-directed problem solving? These are the main issues of Andrzej Wi niewski's "Questions, Inferences, and Scenarios." This book offers a state-of-the-art exposition of (...) Inferential Erotetic Logic, that is, an approach to the logic of questions focused on inferences which lead to questions as conclusions. Wi niewski characterizes semantic relations which determine validity of these inferences within the framework of Minimal Erotetic Semantics, applicable to a wide range of formal languages. He elaborates in detail the concept of erotetic search scenario, a tool for modelling problem solving. Moreover, the author presents some applications of Inferential Erotetic Logic in proof theory. Andrzej Wi niewski is one of the most prominent contemporary researchers in the logic of questions. Currently, he is a full professor at the Department of Logic and Cognitive Science, Institute of Psychology, Adam Mickiewicz University in Pozna, Poland. (shrink)

Artykuł jest próbą analizy pojęcia „wstępnego rozumienia”, i stanowi próbę odtworzenia i wyjaśnienia hermeneutyki Arendt, tzn. zrozumienia, o ile to możliwe, problemu wiedzy w sensie w jakim rozumie ją Arendt, na historycznym i filozoficznym gruncie jej myśli. Dokonanie tego zwrotu w hermeneutyce polityki Arendt, a ściślej w jej epistemologicznym aspekcie związanym z pojęciem „wstępnego rozumienia” możliwe stało się na tle odkrycia przez Heideggera „prestruktury rozumienia”.

The formalist point of view maintains that formal derivations underlying proofs, although usually not carried out in practice, contribute to the confidence in mathematical theorems. Opposing this opinion, the main claim of the present paper is that such a gain of confidence obtained from any link between proofs and formal derivations is, even in principle, impossible in the present state of knowledge. Our argument is based on considerations concerning length of formal derivations. Thanks to Jody Azzouni for enlightening discussions concerning (...) the subject of this paper and to anonymous referees whose important remarks permitted us to correct the arguments and improve presentation. The remaining flaws remain, of course, solely the responsibility of the author. This research was partially supported by NSERC discovery grant and by the Research Chair in Distributed Computing at the Université du Québec en Outaouais. CiteULike Connotea Del.icio.us What's this? (shrink)

A new type of formalization of classical first-order logic with equality is introduced on the basis of the sequent calculus. It serves to justify the claim that equality is a logical constant characterised by well-behaved rules satisfying properties usually regarded as essential. The main feature of this approach is the application of sequents built not only from formulae but also from terms. Two variants of sequent calculus are examined, a structural and a logical one. The former is defined in accordance (...) with Dos̆en’s criteria for logical constants. The latter is a standard Gentzen’s sequent calculus and satisfies Hacking’s criteria for logicality, including cut elimination. It is also shown that provided rules are harmonious in the sense advocated by Gratzl and Orlandelli. (shrink)

Three semantic relations are analyzed: the relation of implication of a question by a question and a set of declarative sentences, the relation of implication of a question by a question, and the relation of strong implication of a question by a question and a set of declarative sentences. The connections between these concepts and the concepts of relative soundness, partial answerhood and presupposition are examined. The principal results are theorems about, to speak generally, epistemic reducibility of well-posed questions to (...) sequences of implied yes-no questions. (shrink)

The famous theory of undecidable sentences created by Kurt Godel in 1931 is presented as clearly and as rigorously as possible. Introductory explanations beginning with the necessary facts of arithmetic of integers and progressing to the theory of representability of arithmetical functions and relations in the system (S) prepare the reader for the systematic exposition of the theory of Godel which is taken up in the final chapter and the appendix.

W kontekście wielości pojęć osoby i ich znaczenia dla sposobu organizowania przez człowieka życia jednostkowego i społecznego, sprawą kluczową jest zwrot w kierunku realistycznego pojęcia osoby. W niniejszym studium przeprowadzono krytyczną analizę kilku wybranych relacjonalnych koncepcji osoby z pozycji tomizmu egzystencjalnego. W efekcie przeprowadzonej analizy potwierdzono założoną hipotezę, iż wybrane relacjonalne koncepcje osoby mają charakter aprioryczny, jednakże tylko w odniesieniu do istoty osoby. Studium odpowiada na pytanie, dlaczego analizowane koncepcje nie wyjaśniają samej istoty realnej osoby ludzkiej, a tylko wskazują na (...) jej cechy rozpoznawcze, opisując egzystencję i drogi spełniania się osoby. In search of a realistic concept of person In the context of the multiplicity of concepts of the person and their importance for the way in which man organizes his individual and social life, a turn toward a realistic concept of the person is crucial. In this study, a critical analysis of several selected relational concepts of the person from the position of existential Thomism is carried out. As a result of the analysis, the assumed hypothesis was confirmed that the selected relational conceptions of the person are a priori, however, only with regard to the essence of the person. The study answers the question of why the analysed concepts do not explain the very essence of the real human person, but only point to its identifying features, describing the existence and ways of fulfilment of person. (shrink)

M. E. Rudin proved, under CH, that for each P-point p there exists a P-point q strictly RK-greater than p. This result was proved under ${\mathfrak {p}= \mathfrak {c}}$ by A. Blass, who also showed that each RK-increasing $ \omega $ -sequence of P-points is upper bounded by a P-point, and that there is an order embedding of the real line into the class of P-points with respect to the RK-ordering. In this paper, the results cited above are proved under (...) the assumption that $\mathfrak { b}=\mathfrak {c}$. A. Blass asked in 1973 which ordinals can be embedded in the set of P-points, and pointed out that such an ordinal cannot be greater than $ \mathfrak {c}^{+}$. In this paper it is proved, under $\mathfrak {b}=\mathfrak {c}$, that for each ordinal $\alpha < \mathfrak {c}^{+}$, there is an order embedding of $ \alpha $ into P-points. It is also proved, under $\mathfrak {b}=\mathfrak {c}$, that there is an embedding of the long line into P-points. (shrink)

The article attempts to characterize three key doctrinal controversies in the Carolingian Renaissance, namely: the disputes over the Eucharist, the so-called trina deitas, and predestination. The core of the article is an exposition of the controversy concerning predestination, whose main protagonist is Gottschalk of Orbais. The article discusses four crucial issues related to the problem: (i) the concept of God, (ii) the understanding of grace, nature and free will, (iii) the relation of foreknowledge to predestination, and (iv) the doctrine of (...) redemption, i.e., specifically the relationship betweenjustice and mercy. The article is largely an attempt at an interpretation of the texts of the epoch, mainly those of Gottschalk of Orbais and his adversary, Hincmar of Reims. The conclusions point to difficulties in the issues discussed and outline what attempts at solving this problem have taken place in the coming centuries. (shrink)

We examine some extensions of the constructive propositional logic with strong negation in the setting of varieties of $\mathcal{N}$ -lattices. The main aim of the paper is to give a description of all pretabular, primitive and preprimitive varieties of $\mathcal{N}$ -lattices.

Basic theses of the article are the following: 1) Politics is inexplicable without relating it to the category of commonweal. 2) Acceptation of this category has some philosophical and ethical implications: it involves universalism, rationalism, personalistic character of participation. Finally, politics is defined as,,a wise endeavour after commonweal”.

We provide an application of a sequent calculus framework to the formalization of definite descriptions. It is a continuation of research undertaken in [20, 22]. In the present paper a so-called free description theory is examined in the context of different kinds of free logic, including systems applied in computer science and constructive mathematics for dealing with partial functions. It is shown that the same theory in different logics may be formalised by means of different rules and gives results of (...) varying strength. For all presented calculi a constructive cut elimination is provided. (shrink)

Artykuł porusza problem rozumienia w filozofii psychiatrii. Autor koncentruje się na klasycznym już podziale w naukach humanistycznych – na rozumienie/wyjaśnianie oraz nomotetyczne/idiograficzne - i próbuje nakreślić jego konsekwencje dla psychiatrii i problematyki zaburzeń psychicznych. Przegląd wybranych zagadnie metodologicznych filozofii psychiatrii ujawnia antropologiczne aspekty nowożytnej psychiatrii oraz ograniczenia modelu biomedycznego. Ostatnia część artykułu omawia wybrany przypadek kliniczny, aby wskazać na praktyczne konsekwencje indywidualnego i idiograficznego podejścia do psychiatrii.

In pre-revolutionary Russia, law was criticized from many points of view: in the name of Christ or the name of Marx, in defense of anarchism or of an idealized autocracy, on behalf of the "Russian soul" or of universal progress towards socialism. Examining the rich tradition of hostility to law, Walicki presents those Russian thinkers who boldly challenged this legacy of anti-legal prejudice by developing liberal philosophies of law, vindicating the value of human rights and rule of law. He discusses (...) six leading theorists--Boris Chicherin, Vladimir Soloviev, Leon Petrazycki, Pavel Novgorodtsev, Bogdan Kistiakovsky, and Sergius Hessen--all of whom viewed law in the context of wider philosophical and social problems. (shrink)

This paper is closely related to investigations of abstract properties of basic logical notions expressible in terms of closure spaces as they were begun by A. Tarski (see [6]). We shall prove many properties of -conjunctive closure spaces (X is -conjunctive provided that for every two elements of X their conjunction in X exists). For example we prove the following theorems:1. For every closed and proper subset of an -conjunctive closure space its interior is empty (i.e. it is a boundary (...) set). 2. If X is an -conjunctive closure space which satisfies the -compactness theorem and [X] is a meet-distributive semilattice (see [3]), then the lattice of all closed subsets in X is a Heyting lattice. 3. A closure space is linear iff it is an -conjunctive and topological space. 4. Every continuous function preserves all conjunctions. (shrink)

This is an extended version of the lectures given during the 12-thConference on Applications of Logic in Philosophy and in the Foundationsof Mathematics in Szklarska Poręba. It contains a surveyof modal hybrid logic, one of the branches of contemporary modal logic. Inthe first part a variety of hybrid languages and logics is presented with adiscussion of expressivity matters. The second part is devoted to thoroughexposition of proof methods for hybrid logics. The main point is to showthat application of hybrid logics (...) may remarkably improve the situation inmodal proof theory. (shrink)

In the paper a decision procedure for S5 is presented which uses a cut-free sequent calculus with additional rules allowing a reduction to normal modal forms. It utilizes the fact that in S5 every formula is equivalent to some 1-degree formula, i.e. a modally-flat formula with modal functors having only boolean formulas in its scope. In contrast to many sequent calculi for S5 the presented system does not introduce any extra devices. Thus it is a standard version of SC but (...) with some additional simple rewrite rules. The procedure combines the proces of saturation of sequents with reduction of their elements to some normal modal form. (shrink)

The paper presents a comparison of two generalised sequent calculi for temporal logics. In both cases the main technical solution is the multiplication of the sorts of sequents and, additionally, the application of some kind of labelling to formulae. The first approach was proposed by Kaziemierz Trzęsicki at the 1980s. The second, called Multiple Sequent Calculus (MSC), was proposed in the beginning of the present century. Both approaches are examples of the family of multisequent calculi.

The paper is devoted to the concise description of some Natural Deduction System (ND for short) for Linear Temporal Logic. The system's distinctive feature is that it is labelled and analytical. Labels convey necessary semantic information connected with the rules for temporal functors while the analytical character of the rules lets the system work as a decision procedure. It makes it more similar to Labelled Tableau Systems than to standard Natural Deduction. In fact, our solution of linearity representation is rather (...) independent of the underlying proof method, provided that some form of (analytic) cut is admissible. We will also discuss some generalisations of the system and compare it with other formalizations of linearity. (shrink)

There are many religions in the human world, and people manifest their religiousness in many different ways. The main problem this paper addresses concerns the possibility of sorting out this complex world of human religiousness by showing that it can be phenomenologically reduced to a few very basic existential attitudes. These attitudes express the main types of ways in which a human being relates to his or herself and the world, independently of the worldview or religion professed by the individual. (...) I use Kierkegaard’s theories of the stages of existence and subjective truth as a model. The theory of the stages of existence provides five basic existential attitudes on the basis of which religious attitudes can develop: spiritlessness, the aesthetic, the ethical, religiousness A, and religiousness B. The theory of subjective truth shows how the concept of truth functions in an ethical and existential sense as the personal truth of an individual engaged in building their religious identity. In turn, I discuss the problem of the relation of Kierkegaard’s philosophy to phenomenology, briefly introduce his concept of subjective truth and the stages of existence, and show how existential attitudes can be transformed into religious ones. I also consider the problem of the demonic as the inverted order of this anthropological and existential model. Finally, I argue that the model developed herein may be useful for further research into the phenomenology of religious attitudes. (shrink)

This paper is an attempt to clash the problem of forgiveness as formulated in contemporary secular and Christian ethics with Kierkegaard’s considerations concerning this issue. Kierkegaard’s thought is increasingly used in the modern debate on forgiveness. It is therefore worth investigating whether Kierkegaard’s considerations are really able to overcome in any way contemporary disputes concerning this problem or enrich our thinking in this area. The main thesis of this paper states that there is a fundamental, ontological difference between Kierkegaard’s understanding (...) of forgiveness and that of modern thinkers. While the Danish philosopher refers to the transcendent reality of spirit, where the act of forgiveness is always performed by God, in contemporary ethical and Christian thought, forgiveness is first and foremost formulated from an immanent point of view that appeals to the world of human values. This difference is demonstrated by analyzing the four main themes corresponding to the most important issues taken up in the contemporary debate on forgiveness. These are: the victim-offender relation, the conditionality and unconditionality of forgiveness, the issue of condonation, and the problem of the unforgivable. As a result of the analyses presented herein, the impossibility of directly applying Kierkegaard’s transcendent theses to ethical thought of the immanent variety will be shown. (shrink)

Name der Zeitschrift: Kierkegaard Studies Yearbook Jahrgang: 23 Heft: 1 Seiten: 179-203.

The status of the equality predicate as a logical constant is problematic. In the paper we look at the problem from the proof-theoretic standpoint and survey several ways of treating equality in formal systems of different sorts. In particular, we focus on the framework of sequent calculus and examine equality in the light of criteria of logicality proposed by Hacking and Došen. Both attempts were formulated in terms of sequent calculus rules, although in the case of Došen it has a (...) nonstandard character. It will be shown that equality can be characterised in a way which satisfies Došen’s criteria of logicality. In the case of Hacking’s approach the fully satisfying result can be obtained only for languages with a nonempty, finite set of predicate constants other than equality. Otherwise, cut elimination theorem fails to hold. (shrink)