In the paper, pre-Hilbert algebras are defined as a generalization of Hilbert algebras (namely, a Hilbert algebra is just a pre-Hilbert algebra satisfying the property of antisymmetry). Pre-Hilbert algebras have been inspired by Henkin's Positive Implicative Logic. Their properties and characterizations are investigated. Some important results and examples are given. Moreover, positive implicative pre-Hilbert algebras are introduced and studied, their connections with some algebras of logic are presented. The hierarchies existing between the classes of algebras considered here are shown.

The paper will study extensions of t-normal logics S0.5o and S0.5 using some axioms of normal logics. We will prove determination theorems for these extensions by appropriate Kripke-style models. It will allow us to obtain the determinations of the logics K45, KB4 (= KB5), KD45 and S5 without using modal rules.

This paper argues for the idea that the logic of questions should focus its attention on the analysis of arguments in which questions play the role of conclusions. The relevant concepts of validity are discussed and the concept of the logic of questions of a semantically interpreted formalized language is introduced.

A relativized concept of a possiblecorrect answer to a why-question is introduced. Acertain procedure of looking for acceptable answers towhy-questions is analyzed in terms of erotetic logic,i.e., the logic of questions.

Resumen El objetivo del presente artículo es analizar en la historia del español dos tipos de fórmulas de saludo, entendidas como unidades discursivas propias del acto de habla expresivo que sirven para abrir el canal comunicativo de las relaciones sociales. A través de la búsqueda sistemática en textos del CORDE de hasta finales del siglo XIX, intentaremos hallar (i) los factores sociopragmáticos que desempeñan el papel más importante en cada tipo de saludo, (ii) el origen paradigmático de cada fórmula, (iii) (...) su distribución sociocultural y las preferencias discursivas e informativas, y (iv) su nivel de predominio en determinadas épocas. (shrink)

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)

The aim of this article is to present a new Polish translation of Aristotle’s Poetics, namely, those of its central chapters (6–19) that deal with the Stagirite’s explication of the mimesis of tragedy. When interpreting the first five chapters of the treatise, it is important to recognize the mimetic distinctions and forms according to means and objects as well as the question of how poetic creativity takes shape (generally from improvisation through epic to comedy and tragedy). On the basis of (...) these preliminary assumptions, Aristotle proceeds to define tragedy and analyze its components, forms and functions in more detail. Unlike the previous Polish translations of the Poetics, we have attempted here to render Aristotle’s essential technical expressions as faithfully as possible, without distorting them in accord with various concepts of modern aesthetics or literary criticism. We have also sought to preserve the Stagirite’s typical composition and his complex argument. Only in this way can the sense of Aristotle’s leading assumptions and distinctions be properly discerned. For the ease of reading, we also introduce more paragraphs and relevant subject headings into the text. (shrink)

The changes brought about in Poland and elsewhere in Europe by the fall of Communism have given rise to hopes for the establishment of a political system differing from the one which had been the fate of these countries. In place of totalitarianism, a new political system is to be created based on the democratic principles of a state under the rule of law. The transformation from totalitarianism to democracy is a process which has not yet been completed in Poland (...) and still requires many efforts to be made before this goal may be achieved. One may also enumerate various pitfalls jeopardising this process even now. The dangers cannot be avoided if their sources and nature are not identified. Attempts to pervert the law and the political system may only be counteracted by legal means if the system based on the abuse of the law has not yet succeeded in establishing itself. Resistance by means of the law only has any real chance of success provided it is directed against attempts to set up a totalitarian system. Once the powers which are hostile to the state bound by the rule of law take over the institutions of the state, such resistance is doomed to failure. (shrink)

The changes brought about in Poland and elsewhere in Europe by the fall of Communism have given rise to hopes for the establishment of a political system differing from the one which had been the fate of these countries. In place of totalitarianism, a new political system is to be created based on the democratic principles of a state under the rule of law. The transformation from totalitarianism to democracy is a process which has not yet been completed in Poland (...) and still requires many efforts to be made before this goal may be achieved. One may also enumerate various pitfalls jeopardising this process even now. The dangers cannot be avoided if their sources and nature are not identified. Attempts to pervert the law and the political system may only be counteracted by legal means if the system based on the abuse of the law has not yet succeeded in establishing itself. Resistance by means of the law only has any real chance of success provided it is directed against attempts to set up a totalitarian system. Once the powers which are hostile to the state bound by the rule of law take over the institutions of the state, such resistance is doomed to failure. (shrink)

First-order logic is formalized by means of tools taken from the logic of questions. A calculus of questions which is a counterpart of the Pure Calculus of Quantifiers is presented. A direct proof of completeness of the calculus is given.

The aim of this essay is to create a coherent theistic model of a solution to the problem of evil. To this end, it is shown that the differences in Kierkegaard’s and Plantinga’s accounts of the problem of evil can be reconciled if looked at from a broader theistic perspective. This requires, on the one hand, that Plantinga’s immanent and logical vision be extended to include Kierkegaard’s spiritual and existential view of evil, and, on the other hand, that a correction (...) be made to Kierkegaard’s view thereof, as a result of the way in which Plantinga presents the relationship between good and moral evil in the world. Consequently, in Plantinga’s Free Will Defense the existence of God is consistent with the existence of evil, not because God has a reason to permit evil in the world, but because evil as a real element of the temporal world does not come from God. In Kierkegaard’s Free Spirit Offense, in turn, the interpretative model applied demonstrates that the existence of moral good must be independent of the existence of spiritual evil, for otherwise the moral evil of immanence would not be able to be forgiven by the spiritual good of transcendence. (shrink)

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)

Artykuł dotyczy zagadnienia wolności indywidualnej i problemu zagrożeń, jakie może pociągać za sobą hołdowanie niektórym jej odmianom. Klasycznie pojmowana wolność, zwana negatywną, utożsamiana z brakiem zewnętrznego przymusu, może stać w opozycji do tak zwanej wolności pozytywnej. To ostatnie pojęcie definiowane jest na ogół poprzez możność, co przywodzi na myśl jego związek z pojęciem władzy. Punktem wyjścia rozważań stała się analiza wybranych aspektów obu wolności. Rozróżnienie tych dwóch fenomenów jest istotne dla zrozumienia niektórych procesów zachodzących we współczesnej wspólnocie politycznej. Konsekwentne odwoływanie (...) się do paradygmatu tzw. wolności pozytywnej może bowiem przynosić trudne do przewidzenia konsekwencje w postaci uzasadnianej ideologicznie ingerencji w wiele sfer ludzkiego działania. Za szczególnie brzemienne w skutki należy uważać konotacje tzw. wolności pozytywnej i równości. W istocie bowiem wolność pozytywna, a szczególnie jej postulat szerzenia równości, staje się pretekstem dla zwiększania zakresu politycznego panowania. Może to wyrażać się w dążności do urzeczywistniania aspiracji jednych grup społecznych kosztem innych. Takie podejście siłą rzeczy stoi w opozycji do poglądów upatrujących fundamentów społecznego porządku w prymacie wolności negatywnej i obowiązywaniu zasad sprawiedliwości. Wspomniana ingerencja instytucji państwa w ludzkie działanie, będąca skutkiem propagowania niektórych aspektów koncepcji „wolności do” może grozić redukcją podmiotowości moralnej osób. (shrink)

Tekst dotyczy krytyki neoliberalizmu. Kierunek ten narodził się w gronie zwolenników tradycji klasycznego liberalizmu wywodzącego się od Johna Locke'a i Adama Smitha. Von Hayek, Mises, Friedman, Eucken i inni wprowadzili tę nazwę niejako w reakcji na zawłaszczenie terminu "liberalizm" przez myśl lewicową. Zastrzeżenia wobec neoliberalizmu dotyczą między innymi niszczenia tkanki społecznej, równości, czy demokracji. Autor rozważa zasadność tych zarzutów w odniesieniu do dwóch różnych rozumień neoliberalizmu: teorii społeczno-ekonomicznej z jednej strony i praktyki politycznej niektórych rządów z drugiej.

The paper refers to selected problems of exploitation in the face of justice. The analysis is based on the definitions of exploitation contained in the Polish Penal and Civil Codes. The main subject of our interest is the identification of the necessary and sufficient conditions for the recognition of exploitation as being unjust. Supplementary question will refer to a specific type of justice which should be considered in this case. In respect to this we should consider retributive, distributive and social (...) justice. Another important factor in this regard is the accepted theory of value. In the considered subject we will focus on the labour theory of value. The principal problem could be reduced to questions whether the exploitation is ipso facto unjust and how these two phenomena are related to each other. (shrink)

The author poses the question concerning the role of the phenomenological approach in human understanding of the world. He points out to ethical motives behind Edmund Husserl’s thought, as well as to his idealistic approach both to the problem of the existence of the world and the issue of time. He also demonstrates Husserl’s gradual coming to a grasp of the difficulty in constructing of a discipline which would be able to deal with condition of man and his world from (...) a detached point of view. According to the author, development of Husserl’s thought, as well as some works of his followers, show that the basic object of phenomenology gradually becomes the problem of understanding human freedom and of the proper way of conduct. This seems to justify Stephan Strasser’s idea of phenomenology as a ‘fundamental moral philosophy’. Key words PHENOMENOLOGY, REALISM, HUSSERL, STRASSER. (shrink)

In his work on the foundations of mathematics, Frege placed the problem in a wider context, namely that of science; the ontological status of thought as the carrier of truthfulness became for him the most important issue. The objectivity of truth and thought seems to require the existence of other people, which consequently requires the existence of the world. Thus, the polemics with epistemological idealism became a key issue for Frege; the topic appears in such works as The Basic Laws (...) of Arithmetic, The Logic, and The Thought. What seems to be most interesting in Frege’s work is his stress on weaknesses of both epistemological realism and immanent idealism. Reflecting upon the examples of the physiological psychology and physiology of the senses he demonstrated the process of entrapment in idealism. It is also interesting that he stressed the realistic character of language as well as the constant possibility of committing a mistake by assuming the existence of reference, and dangers of falling into traps of fiction resulting there from. Key words FREGE, SCIENCE, LANGUAGE. (shrink)