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)

The book is devoted to the thought of one of the 20th century's most interesting philosophers of religion. Heschel, a traditional Polish Jew who became a modern thinker, was also an impressive prophet of interreligious dialogue.

Context is essential in virtually all human activities. Yet some logical notions seem to be context-free. For example, the nature of the universal quantifier, the very meaning of “all”, seems to be independent of the context. At the same time, there are many quantifier expressions, and some are context-independent, while others are not. Similarly, purely logical consequence seems to be context-independent. Yet often we encounter strong inferences, good enough for practical purposes, but not valid. The two types of examples suggest (...) a general problem: how to characterise the context-free logical concepts in their natural environment, that is, in the field of their context-dependent associates. A general Thesis on Quantifiers is formulated: among all quantifiers, the context-free ones are just those definable by the universal quantifier. The issue of inferences is treated following the approach introduced by Richard L. Epstein: valid ones are an extreme case, the result of the disappearance of context-dependence. This idea can be applied to an analysis of a form of abduction, called “reductive inference” in Polish literature on logic. A tentative Thesis on Inferences identifies the validity of a strong inference that is context-independent. (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.

Scholarly dissertations dealing with the Jesuit educational system in Poland would more frequently emphasize the aspects of its decline rather than those of its prosperity. More recent research, however, based on numerous sources, enables one to see this system in a new, more objective light as well as giving an unbiased picture of the situation. Written by Roman Darowski SJ, eminent specialist in scholastic philosophy, it is the first work to be devoted to the philosophy of Polish Jesuits, which was (...) inseparable from their scholarly and didactic activities. It spans the last three decades of the sixteenth century and a few years of the seventeenth century, i.e. the beginning of the activity of the Societas Jesu in this country. (shrink)

Scholarly dissertations dealing with the Jesuit educational system in Poland would more frequently emphasize the aspects of its decline rather than those of its prosperity. More recent research, however, based on numerous sources, enables one to see this system in a new, more objective light as well as giving an unbiased picture of the situation. Written by Roman Darowski SJ, eminent specialist in scholastic philosophy, it is the first work to be devoted to the philosophy of Polish Jesuits, which was (...) inseparable from their scholarly and didactic activities. It spans the last three decades of the sixteenth century and a few years of the seventeenth century, i.e. the beginning of the activity of the Societas Jesu in this country. (shrink)

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)

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)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Critical Conditions: Postmodernity and the Question of FoundationsBruce KrajewskiCritical Conditions: Postmodernity and the Question of Foundations, by Horace L. Fairlamb; xii & 271 pp. New York: Cambridge University Press, 1994, $59.95 cloth, $17.95 paper.Some theories might be in critical condition, but others are terminal, run aground by their own illogic, according to Horace Fairlamb. Despite some theories’ terminal state, Fairlamb still senses dangers, for as he says in (...) his introduction: “If critical authority cannot turn to metaphysical permanence, transcendental subjectivity, scientific objectivity, formal systematicity, methodological closure, or any other transcending constraints for its authority, are we not left with nothing firmer than Nietzschean perspectivism and an anarchy of wills to power? Might not the respectable looking Trojan Horse of philosophical hermeneutics be filled with sophists, gamesters, and fascists?” Well, yes and no and maybe.Fairlamb explores the issue of foundationalism, later called foundationism, in eight chapters, an introduction, and a conclusion. Most of the eight chapters are labeled as devoted to single contemporary thinkers and theorists, all male: Stanley Fish, Jacques Derrida, Hans-Georg Gadamer, Michel Foucault, Jürgen Habermas. Fairlamb has problems with all these people, and he is very good at laying out objections, based in logic, that arise from the main positions of each. He wants to provide “an analysis of how certain strategies fail to address foundational problems” (p. xi).This analysis consists mainly of turning positions back on themselves, so that when Fish or Habermas or any one of the people addressed in the book makes a claim that indicates an anti-foundational position, Fairlamb jumps in to ask: where is the foundation for the anti-foundational positions? This tactic fills the book, and becomes the driving force of a number of questions and assertions that follow a similar pattern. For instance: “Fish’s radical hermeneutics condemns universalism, but constantly practices it” (p. 40), or “Gadamer’s vision of philosophical hermeneutics must have non-historical authority lest it reduce to his historically bound prejudices” (p. 127). At the end, Fairlamb feels he has demonstrated the logical paradoxes and argumentative blind spots of the various theorists and thinkers mentioned above, and he proposes instead what he calls “a heterological foundationism [that] is able to account for both what changes and what stays the same, and thereby account for the failure of both reductive foundationism and relativism” (p. 263).While I can applaud Fairlamb the logician, I cannot recommend the book. The deck is stacked from the beginning, as he admits early on: “I do not claim to represent the entire range of these authors’ works and thought, nor all their subsequent revisions and recantations” (p. xi). The game here is not to think about the thinkers at all, which is perhaps why Fairlamb rehearses some knee-jerk positions, such as an attack (p. 25) on Derrida’s too-famous statement “there is nothing outside the text.” While he cites (p. 266) Rodolphe Gasché’s [End Page 271] The Tain of the Mirror, Fairlamb apparently refuses Gasché’s reading of the sentence that “does not permit the conclusion that there is nothing else but texts, or for that matter, that all is language” (Tain, p. 281).By dealing only with the logic of some works, Fairlamb unburdens himself of the need, for instance, to attend to Gadamer’s Gesammelte Werke, or to any of the thinkers’ writings in their original languages, a task even some postmodernists agree is foundational for basic scholarship. One can only guess that the universal language of logic has no patience with foreign languages, except to lay bare the inconsistencies and paradoxes of selected bits of syntax.Bruce KrajewskiLaurentian UniversityCopyright © 1996 The Johns Hopkins University Press... (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)

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.