Examples of possible theological influences upon the development of mathematics are indicated. The best known connection can be found in the realm of infinite sets treated by us as known or graspable, which constitutes a divine-like approach. Also the move to treat infinite processes as if they were one finished object that can be identified with its limits is routine in mathematicians, but refers to seemingly super-human power. For centuries this was seen as wrong and even today some philosophers, for (...) example Brian Rotman, talk critically about “theological mathematics”. Theological metaphors, like “God’s view”, are used even by contemporary mathematicians. While rarely appearing in official texts they are rather easily invoked in “the kitchen of mathematics”. There exist theories developing without the assumption of actual infinity the tools of classical mathematics needed for applications. Conclusion: mathematics could have developed in another way. Finally, several specific examples of historical situations are mentioned where, according to some authors, direct theological input into mathematics appeared: the possibility of the ritual genesis of arithmetic and geometry, the importance of the Indian religious background for the emergence of zero, the genesis of the theories of Cantor and Brouwer, the role of Name-worshipping for the research of the Moscow school of topology. Neither these examples nor the previous illustrations of theological metaphors provide a certain proof that religion or theology was directly influencing the development of mathematical ideas. They do suggest, however, common points and connections that merit further exploration. (shrink)

Modern philosophy has benefited immensely from the intelligence and sensitivity, the creative and critical energies, and the lucidity of Polish scholars. Their investigations into the logical and methodological founda­ tions of mathematics, the physical and biological sciences, ethics and esthetics, psychology, linguistics, economics and jurisprudence, and the social sciences - all are marked by profound and imaginative work. To the centers of empiricist philosophy of science in Vienna, Berlin and Cambridge during the first half of this century, one always added (...) the great school of analytic and methodological studies in Warsaw and Lw6w. To the world centers of Marxist theoretical practice in Berlin, Moscow, Paris, Rome and elsewhere, one must add the Poland of the same era, from Ludwig Krzywicki (1859-1941) onward. (From our preface to Wiatr [1979p. Other movements also have been distinctive in Poland. Phenomenology was developed in the impressive school of Roman Ingarden at Cracow, semiotics from the early work of the philosopher and psychologist Kazimierz Twardowski at Lw6w in the 1890's, with masterful develop­ ment by his disciples Kotarbinski and Ajdukiewicz onward, conceptual foundations of physics in the incisive methodological reflections of Marian Smoluchowski, and mathematical logic from Jan I:.ukasiewicz and Stanislaw Lesniewski to Tarski, Mostowski, and many others. (shrink)

Artykuł jest próbą wyodrębnienia i ogólnego opisu aspektów filozoficznych, zawartych w teorii duchowości ekologicznej papieża Franciszka oraz porównania ich z myślą tomistyczną, rozwijaną przez jej polskich przedstawicieli w czasach współczesnych. Aspekty te dostrzeżono na gruncie wielu dyscyplin filozoficznych, ponieważ w tego typu duchowości chodzi o stosunek człowieka do najogólniej pojętej rzeczywistości realnej, czyli do samego siebie, przyrody, kultury i religii. W toku analizy obu stanowisk zauważono liczne analogie, a także pewne rozbieżności w sposobie widzenia przyrody, osoby ludzkiej, kultury oraz religii, (...) które przynajmniej częściowo można tłumaczyć niejednoznacznością niektórych sformułowań papieskich. -------------- Zgłoszono: 19/08/2020. Zrecenzowano: 26/09/2020. Zaakceptowano do publikacji: 18/10/2020. (shrink)

W artykule poruszono problem perspektyw rozwoju, a tym samym przyszłości filozofii tomistycznej na podstawie sytuacji w Polsce. Otóż taką szansę widzi się dla tej filozofii w badaniach bardziej partykularnych, znajdujących się poza głównym obiektem zainteresowań metafizyki ogólnej. Każdorazowo przybierają one postać metafizyk szczegółowych i stosowanych. Pierwsza z nazw nawiązuje do zawężonego pola badań, druga natomiast jest uzasadniona korzystaniem z dorobku innych nauk filozoficznych, bardziej podstawowych, włącznie z metafizyką ogólną. Metafizyki tego rodzaju stanowią szeroko pojęte studium tego, co jest najbardziej fundamentalne (...) nie dla bytu jako takiego, ale dla wszelkich podstawowych typów przedmiotów w sferze natury i kultury. Nie stanowią one jednak alternatywy dla metafizyki ogólnej, która bada rzeczywistość w wymiarze transcendentalnym, ponieważ korzystając z jej dorobku, zachowują z nią łączność oraz stanowią jej konieczne dopełnienie. Jako zaś typowe dyscypliny filozoficzne, dające możliwość rozwijania owych metafizyk, podano w artykule filozofię przyrody, antropologię filozoficzną oraz dwie formy filozofii ludzkiego działania, czyli religię i moralność. W ich przypadku wskazywano zarówno na tematy już podjęte przez wielu przedstawicieli myśli tomistycznej w Polsce oraz na te, jakie są możliwe do podjęcia. Realizacja tych form metafizyki odpowiada nie tylko strukturze rzeczywistości pluralistycznej i jednocześnie powiązanej ze sobą szeregiem zależności, ale też problemom aktualnym, nowym, wymagającym ujęcia gruntownego i całościowego, jakie stwarza dopiero perspektywa metafizyczna, rozpatrywana z pozycji filozofii tomistycznej. (shrink)

The volume is a collection of essays about prominent Polish 20th century philosophers of science and scientists who were concerned with problems in the philosophy of science. The contribution made by Polish logicians, especially those from the Lvov-Warsaw School, like Lukasiewicz, Kotarbiński, Czeżowski or Ajdukiewicz, is already well known. One of the aims of the volume is to offer a broader perspective. The papers collected here are devoted to the work of such philosophers as Zawirski, Metallmann, Dąmbska, Mehlberg, Szaniawski and (...) Giedymin as well as to the work of such scientists as Smoluchowski, Fleck, Infeld and Chyliński. The introduction to the volume, written by the editor and Jacek Jadacki, presents an overview of the history of the Polish philosophy of science from the foundation of the Cracow Academy (in 1364) to the present. (shrink)

In the paper some varieties E s n of BCK-algebras with condition defined by W. H. Cornish [1] are considered. A characterization of simple algebras in E s 2 is given and some properties of simple algebras in E s 3 are indicated.

Autor porusza zagadnienie struktury Peryta, która posiada tę właściwość, iż środkiem świata jest miejsce założone przez obserwatora. W ten sposób zmienia się charakter zjawisk geometrycznych, w tym perspektywy.

The contemporary development of socialist economy is featured not only by high dynamics, but also by essential structural and qualitative changes. The economic policy and the socialist planning in particular tendtowards optimalization of economic growth, then to engage for its proper directions, structure and rythmicality. The every year growing national product ought to be, as it is possible, most suitable and useful for implementation of threefold objective: 1° the better satisfaction with the necessities of population, 2° the quicker modernization of (...) the national economy, and 3° the effective development of the foreign trade as well as the international cooperation.The superiority of a set of social criteria is becoming the general assumption of economic policy. A vision of the future human being and the mature society is determining prospective objectives and aims of the development as well is indicating ways and means for their realization by economic policy.The economic growth is not objective by itself, but has to serve for a comprehensive social advancement. At the same time the factors of social advancement advantageously impact the labour productivity and otherwisethey perform a role of additional stimulatives of the economic growth.The objectives of social advancement should be realized gradually basing on staging patterns of systematic raise of the living standards of the population. A hierarchy and a sequence of satisfaction with the both individual and collective necessities demand a skillful application of the criteria of the economic and social choice. We are using here the principle of social and economic rationality.Hence the factors of social advancement, involving the scientific and technical progress, belang to the fundumatel elements of the present economic and social policy. At the same time objectives and means of modern economic and social advancement are here strictly interlaced. (shrink)

This essay explores social forces which contributed to regaining independence by the Polish people and sovereignty by the Polish state after 45 years of Soviet domination There were four major factors or forces of historical change: workers' resistance (big-industry working class); intellectual opposition (dissidents); grass-roots movement (families, households and their microeconmuc activity); and the Catholic Church (in the late phase of the Polish People's Republic). The preliminary thesis is that Poland succeeded in transcending communism and Soviet domination as quickly as (...) it did thanks to its civil society traditions. In particular, universities and their intellectual influence on the young generations of Poles helped nurture the political opposition Equally, the grass-roots movement of Polish family households undermined the unrealistic, strange system of national (planned) economy, which otherwise could have lasted much longer in Poland, as it did in all of Eastem Europe. The conclusion follows that the historically formed cultural capital of the Polish people was the decisive factor in the nation's liberation from totalitarian rule. (shrink)

Modern Polish philosophy has an impressive record as a powerful, innovating tradition, in many respects parallel to but independent of the development of analytical philosophy in Britain and America. Owing to an absence of adequate translations however, the work of its leading exponents has generally only been encountered second-hand. To remedy this, Quinton and Skolimowski have translated an introduction to philosophy written by Kazimierz Ajdukiewicz, probably the outstanding representative of the generation. Problems and Theories of Philosophy surveys concisely and, (...) so far as possible, systematically the main problems in epistemology and metaphysics and the most historically important of the solutions proposed to them. The book still reads freshly and displays many of the characteristic intellectual virtues of Polish philosophy: clarity and straightforwardness of presentation combined with a bracing rigour and precision. It is in no sense parochial to its Polish origins and can stand beside the classic English introductions to the subject as stimulating and lucid analysis of perennial philosophical problems and strategies. (shrink)

When asked in 1962 on what he was working Kazimierz Ajdukiewicz replied: Several years ago Polish Scientific Publishers suggested that I pre pare a new edition of The Logical Foundations of Teaching, which I wrote 1 before 1939 as a contribution to The Encyclopaedia of Education. It was a small booklet covering elementary information about logical semantics and scientific methodology, information which in my opinion was necessary as a foundation of teaching and as an element of the education of (...) any teacher. When I recently set to preparing the new edition, I rewrote practically everything, and a booklet of some 100 pages swelled into a bulky volume almost five times bigger. The issues have remained practically the same, but they are now analysed much more thoroughly and the threshold of difficulty is much higher now. The main stress has been laid on the methods used in the empirical sciences, and within that field, on the theory of measurement and the methods of statistical inference. I am now working on the last chapter of the book, concerned with explanation procedures and theory construction in the empirical sciences. When that book, which I intend to entitle Pragmatic Logic, is com pleted I intend to prepare for the press Vol. 2 of my minor writings, 2 Language and Cognition, which will cover some of my post-war pa pers. (shrink)

The story of Abraham and Isaac belongs to the plots frequently recurring in the school drama of sixteenth century Europe. Two related texts are related in the article: Theodore de Bčze’s drama with the title Abraham sacrificanl (staged in Lausanne in 1550) and an anonymous Polish text dating from the end of the sixteenth century Ofiarowanie Izaaka [The Sacrifice of Isaac]. Both the dramas begin with the Prologue, heralding the main events of the story. The works share a three-part, biblical (...) structure (Ofiarowanie Izaaka is composed of three acts), the motif of a father’s love for his son, Abraham’s and Sarah’s care for their son, Abraham’s perplexity and finally the ending, where an angel, a pre-figuration of Christ, appears. The main differences lie in the way in which the protagonists have been grouped - the amusing characters of, among others, Achne, the servant, enrich the play with comical, realistic elements. The similarities between the two texts result not only from their chronology, the common repertoire of school theatres, and the cosmopolitan character of school education. The congruence (despite some apparent differences between the staging possibilities of Lausanne and Cracow) confirms a close relationship between Polish Renaissance drama and the culture of Western Europe and emphasizes its creative character in the presentation of Biblical plots, extending beyond the Bible. (shrink)