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)

1. Metaetyka : nowa rzecz czy nowe słowo? / redaktor tomu Andrzej Szostek -- 2. Etyka niezależna / redaktor tomu Kazimierz Krajewski -- 3. Objawiać osobę / redaktor tomu ks. Alred M. Wierzbicki -- 4. Wolność w prawdzie / redaktor tomu ks. Alred M. Wierzbicki.

Geology is an example of the "historical-natural" sciences, and it combines methodological elements of typical natural sciences, as physics, and the methodological elements of history. As a result, there are some problems with placing it in the classification of sciences. The article consists of two parts. In the first one there is presented in short form process of developing of modern geology. Using as examples the ideas of James Hutton, Georges Cuvier and Charles Lyell the author shows how the opinion (...) about proper method and aims of geology was changing at the turn of 18th and 19th centuries. The final point of the process was the classification of sciences presented by William Whewell, who classified geology as a palaetiological science. The second part of the article is devoted to the place of geology in the contemporary classifications of sciences presented by main Polish methodologists. There are discussed the classifications of Kazimierz Twardowski, Tadeusz Kotarbiński, Władysław Tatarkiewicz, Kazimierz Ajdukiewicz, Władysław Krajewski and Adam Grobler. (shrink)

OPER ACCESS. The correspondence between Meinong and Kazimierz Twardowski highlights the relationship between two philosophers who influenced the history of philosophy and psychology in Austria and Poland. The two correspondents discuss, among other things, their epistemological approach and the university politics of their times. In addition, there is an extensive introduction that places the correspondence in its proper historical and philosophical context.

INTRODUCTION The aim of the present volume is to introduce prominent Polish philosophers of the 20th century as well as their significant accomplishments in ...

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 (For instance, Mycielski’s approach). 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)

The Euclidean ideal of mathematics as well as all the foundational schools in the philosophy of mathematics have been contested by the new approach, called the “maverick” trend in the philosophy of mathematics. Several points made by its main representatives are mentioned – from the revisability of actual proofs to the stress on real mathematical practice as opposed to its idealized reconstruction. Main features of real proofs are then mentioned; for example, whether they are convincing, understandable, and/or explanatory. Therefore, the (...) new approach questions Hilbert’s Thesis, according to which a correct mathematical proof is in principle reducible to a formal proof, based on explicit axioms and logic. (shrink)

This paper considers the method of idealization and factualization as the main method of all advanced empirical science. The procedure is as follows. Some idealizing conditions are assumed: the vanishing of factors $(p_{i}=0)$ which never vanish in the real world. An idealization law is formulated -- a law which is exactly (non-vacuously) fulfilled only in an ideal model, not in any real system. Then the idealizing assumptions are abrogated one by one-it is a process of gradual factualization, of the transition (...) to the factual laws which are fulfilled in real systems. These laws may be directly applied and tested by experience. (shrink)

. ACT, CONTENT, AND OBJECT OF THE PRESENTATION It is one of the best known positions of psychology, hardly contested by anyone, that every mental phenomenon ...

Citizen Science in the Empire. The System Place “Wertlose Einsendungen aus der Bevölkerung” (Worthless Entries from the Population) in the Archives of the Berlin‐Brandenburg Academy of Sciences and Humanities. Between 1871 and 1946, the Berlin‐Brandenburg Academy of Sciences and Humanities maintained a special collection in its archives, which, under the simple name “Entries from the Population”, kept correspondences, projects and proposals, for which a negative expert opinion was issued after thorough examination. The collection offers surprising insights into the pathologies and (...) fantasies of mostly pseudo‐scientific researchers, inventors and discoverers, while at the same time revealing a glimpse of the topics of this epoch that moved the history of science. Using a selection of examples, this essay examines the economic cycles and archive practices of a largely forgotten source of what is now called Citizen Science. (shrink)

Interpretation and politics merge in one the famous story of Joseph's power of dream interpretation in the Hebrew Bible. Rome's College of Augurs reinforces the entwinement of interpretation, power, religion, and folklore that one can also find in the earlier context of the Delphic Oracle. Augury reminds us that understanding happens in the context of an event, a context that presupposes one is missing something, lacking the necessary vision or foresight, and help is called for. Most of the contemporary scholars (...) who write about philosophical hermeneutics, the tradition which includes Martin Heidegger and Hans‐Georg Gadamer, are allergic to politics in the proletarian sense of that word. Party politics and parliamentarian procedures receive almost no attention in the secondary literature on contemporary hermeneutics. Assertion about the political incompetence of philosophy opens the door to an esoteric tradition in philosophy that includes Plato's “secret doctrine”, and stretches back to Pythagoras and Heraclitus. (shrink)

The article examines the relationship between Aby Warburg and his library by analysing the media which is involved: first, the arrangement of the books according to the library’s principle of the ‘law of thse good neighbour’, which helps to order the books on the shelves. Second, the handling of the library is even more determined by Aby Warburg’s use of index cards and card indexes. Like his card index which is situated between him and the library, Aby Warburg himself is (...) in between two library paradigms: on the one hand, as a person of the nineteenth century, Warburg belongs to the supporters of the systematic shelving instead of cataloguing the book collection. On the other hand his work is based on swift associations and direct responses to research questions, the associations not only thought up by words, but also visually, manually to be re-arranged on the shelves, which turns out to be a rather clumsy practice. The motor and initiator of these new orders is the card index with its mobile elements, allowing quick connections between the entities and resulting in enormous processes of re-shuffling of whole shelves and systematic arrangements in the book collection. It is especially the combination of these usually incompatible paradigms that makes the Kulturwissenschaftliche Bibliothek Warburg such a unique institution and rich example of knowledge practices in the twentieth century. (shrink)

It is shown that there exists no grammatical translation into classical (propositional) logic of the modal logics, nor of intuitionistic logic and of the relatedness and dependence logics, as defined in Richard L. Epstein's bookThe Semantic foundations of logic. In the book the result is proved for translations without parameters.Classical propositional logicPC can be translated into other logics. Usually the grammatical structure of propositions is preserved, in the sense of the following definition.

This book is devoted to the problems of the growth of science. These prob lems, neglected for a long time by the philosophers of science, have become in the 60's and 70's a subject of vivid discussion. There are philosophers who stress only the dependence of science upon various sociological, psycho logical and other factors and deny any internal laws of the development of knowledge, like approaching the truth. The majority rejects such nihilism and searches for the laws of the (...) growth of science. However, they often overlook the role of the Correspondence Principle which connects the suc cessive scientific theories. On the other hand, some authors, while stressing the role of this principle, overlook logical difficulties connected with it, e. g. the problem of the incompatibility of successive theories, of the falsity of some of their assumptions, etc. I believe the Correspondence Principle to be a basic principle of the pro gress of contemporary physics and, probably, of every advanced science. How ever, this principle must be properly interpreted and the above-mentioned logical difficulties must be solved. Their solution requires, as it seems, revealing the idealizational nature of the basic laws of science, in any case of the quantitative laws of advanced sciences. This point has been recently emphasized by some Polish philosophers, especially in Poznan. (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)

During the first semester of the academic year 1930/31 in the John Casimir University in Lvov Kazimierz Ajdukiewicz delivered a series of lectures on logical semantics. In eight of them, now published for the first time, he presents - in the very clear manner - his fractional method of identifying syntactic categories, and he shows how to use this method to eliminate the antynomies of classes, relations and properties. The Ajdukiewiczian method had been appreciated among logicians and it is (...) considered widely one of the starting points of so-called categorial grammars. (shrink)

This paper introduces the special issue on the Concept of God of the Journal of Applied Logics (College Publications). The issue contains the following articles: Logic and the Concept of God, by Stanisław Krajewski and Ricardo Silvestre; Mathematical Models in Theology. A Buber-inspired Model of God and its Application to “Shema Israel”, by Stanisław Krajewski; Gödel’s God-like Essence, by Talia Leven; A Logical Solution to the Paradox of the Stone, by Héctor Hernández Ortiz and Victor Cantero; No New (...) Solutions to the Logical Problem of the Trinity, by Beau Branson; What Means ‘Tri-’ in ‘Trinity’ ? An Eastern Patristic Approach to the ‘Quasi-Ordinals’, by Basil Lourié; The Éminence Grise of Christology: Porphyry’s Logical Teaching as a Cornerstone of Argumentation in Christological Debates of the Fifth and Sixth Centruies, by Anna Zhyrkova; The Problem of Universals in Late Patristic Theology, by Dirk Krasmüller; Intuitionist Reasoning in the Tri-unitrian Theology of Nicolas of Cues, by Antonino Drago. (shrink)

There are three main kinds of causal connections between two events: the transfer of energy, the transfer of information and the triggering of the transfer of one of them or both. There are also other kinds of causal connections.

In "Handbook of Philosophical Logic" M. Dunn formulated a problem of describing pretabular extensions of relevant logics (cf. M. Dunn [1984], p. 211: M. Dunn, G. Restall [2002], p. 79). The main result of this paper described in the title.

Certainly one of the key German philosophers of the twentieth century, Hans-Georg Gadamer also influenced the study of literature, art, music, sacred and legal texts, and medicine. Indeed, while much attention has been focused on Gadamer's writings about ancient Greek and modern German philosophy, the relevance of his work for other disciplines is only now beginning to be properly considered and understood. In an effort to address this slant, this volume brings together many prominent scholars to assess, re-evaluate, and question (...) Hans-Georg Gadamer's works, as well as his place in intellectual history. The book includes a recent essay by Gadamer on "the task of hermeneutics," as well as essays by distinguished contributors including Jürgen Habermas, Richard Rorty, Gerald Bruns, Georgia Warnke, and many others. The contributors situate Gadamer's views in surprising ways and show that his writings speak to a range of contemporary debates—from constitutional questions to issues of modern art. A controversial final section attempts to uncover and clarify Gadamer's history in relation to National Socialism. More an investigation and questioning than a celebration of this venerable and profoundly influential philosopher, this collection will become a catalyst for any future rethinking of philosophical hermeneutics, as well as a significant starting place for rereading and reviewing Hans-Georg Gadamer. (shrink)