This is a Festschrift volume dedicated to Jan Woleński, whose extensive work in the history of Polish logic indeed deserves one. Accordingly, it is mostly devoted to Woleński's main interests: the...

This paper outlines the history of logic in Poland in the years 1918–1939 . The disciplinary and social history of logical investigations in Poland is widely described. The author stresses topics characteristic for Polish logic, namely prepositional calculus, many-valued logic, Lezśniewski's systems, Chwistek's systems and the works in the history of logic.

The Polish logicians' propositional calculi, which consist in a distinct synthesis of the Fregean and Boolean approaches to logic, influenced W. V. Quine's early work in formal logic. This early formal work of Quine's, in turn, can be shown to serve as one of the sources of his holistic conception of natural language.

The volume contains twenty essays devoted to the philosophy of mathematics and the history of logic. They have been divided into four parts: general philosophical problems of mathematics, Hilbert's program vs. the incompleteness phenomenon, philosophy of mathematics in Poland, mathematical logic in Poland. Among considered problems are: epistemology of mathematics, the meaning of the axiomatic method, existence of mathematical objects, distinction between proof and truth, undefinability of truth, Goedel's theorems and computer science, philosophy of mathematics in (...) class='Hi'>Polish mathematical and logical schools, beginnings of mathematical logic in Poland, contribution of Polish logicians to recursion theory. (shrink)

The aim of this book is to present and analyze philosophical conceptions concerning mathematics and logic as formulated by Polish logicians, mathematicians and philosophers in the 1920s and 1930s. It was a remarkable period in the history of Polish science, in particular in the history of Polish logic and mathematics. Therefore, it is justified to ask whether and to what extent the development of logic and mathematics was accompanied by a philosophical reflection. (...) We try to answer those questions by analyzing both works of Polish logicians and mathematicians who have a philosophical temperament as well as their research practice. Works and philosophical views of the following Polish scientists will be analyzed: Wacław Sierpiński, Zygmunt Janiszewski, Stefan Mazurkiewicz, Stefan Banach Hugo Steinhaus, Eustachy Żylińsk and Leon Chwistek, Jan Łukasiewicz, Zygmunt Zawirski, Stanisław Leśniewski, Tadeusz Kotarbiński, Kazimierz Ajdukiewicz, Alfred Tarski, Andrzej Mostowski and Henryk Mehlberg, Jan Sleszyński, Stanisław Zaremba and Witold Wilkosz. To indicate the background of scientists being active in the 1920s and 1930s we consider in Chapter 1 some predecessors, in particular: Jan Śniadecki, Józef Maria Hoene-Wroński, Samuel Dickstein and Edward Stamm. (shrink)

We provide for the first time an exact translation into English of the Polish version of Alfred Tarski's classic 1936 paper, whose title we translate as ?On the Concept of Following Logically?. We also provide in footnotes an exact translation of all respects in which the German version, used as the basis of the previously published and rather inexact English translation, differs from the Polish. Although the two versions are basically identical, to an extent that is even uncanny, (...) we note more than 400 differences. Several dozen of these are substantive differences due to revisions by Tarski to the Polish version which he did not incorporate in the German version. With respect to these revisions the Polish version should be regarded as more authoritative than the German. Hence scholars limited to an English translation should use ours. (shrink)

The paper examines the interplays between logic and politics in the Polish School of Logic starting from 1914. The Polish School of Logic flourished between 1920 and 1939. Philosophically, it was influenced by Kazimierz Twardowski (1866–1938). For Twardowski logic is fundamental for every kind of human activity, professional and private and this means that every argument should be formulated and proceed by correct inferential rules. These rules involve semiotics, formal logic and methodology of (...) science. The paper shows how this position was shared by Twardowski’s students, including Jan Łukasiewicz, Stanisław Leśniewski, Kazimierz Ajdukiewicz and Tadeusz Kotrabiński, as well as by the next generation of logicians and philosophers and especially by Alfred Tarski. These authors considered logic, philosophy and science as completely neutral with respect to politics and ideology but they also considered logical skills as indispensable in political activities. (shrink)

Although typically realized by free items, degree modification has a number of morphological exponents in Polish, including the neoclassical prefix arcy-, which, while originally attaching to profession-denoting nouns with a view to indicating a higher rank in a hierarchy, has come to perform the function of reinforcement in conjunction with adjectival bases. Since the scarce previous research concerned with the aforementioned prefixal reinforcer builds only on lexicographic material, this paper offers a quantitative, corpus-based account of the productivity of the (...) formative at issue by providing its TTR (type-token ratio) and HTR (hapax-token ratio) measures, calculated by dividing the number of, respectively, types of adjectival bases and hapax adjectives by that of all relevant tokens, in two periods in the history of Polish, namely in the Baroque epoch, when arcy- gained a strong foothold in language practice owing to the then prevalent rhetorical tendency toward a profuse employment of elements of foreign provenance, and in contemporary Polish. The results of the empirical analysis indicate a dramatic decrease in the level of the bound form’s productivity over time, to the point that the probability of an arcy-adjective encountered by a language user being unique fell from nearly 30% in the Baroque period to less than 1% at present time, which can be accounted for in terms of the formative having been superseded by more recent, functionally analogous prefixes, particularly super- and mega-. (shrink)

One can often encounter an opinion that Polish scientific philosophy deserves to be much better known than actually is. This book is thought as a response to such a claim. The papers collected in this volume are divided into two parts: Background and Influence and History and Systematics. However, there is no sharp borderline between themes which are touched in both parts. Generally speaking, all papers of the first part relate the Lvov-Warsaw School to some philosophical movements external (...) to it whereas the papers collected in the second one focus on internal issues connected with the school . Since the Polish school of mathematical logic is much better known than the Polish analytic philosophy we decided to omit here any treatment of the former. Thus, this collection centers on purely philosophical matters. We projected this volume not as an exhaustive panorama of Polish analytic philosophy but rather as a series of essays on particular persons or topic. As a result one can find here papers on Twardowski. Ajdukiewicz, Kotarbinski, Tarski and Lukasiewicz as well as on ethics on science, nominalism, and the methodology of psychology. We hope that this book will contribute to a better knowledge and evaluation of Polish achievements in analytic philosophy. We would like to express our gratitude to Professor Leszek Nowak, the editor-in-chief of Poznan Studies in the Philosophy of the Sciences and the Humanities, who initiated the idea of the collection and helped in its preparation. (shrink)

The book is comprised of three components. The first component analyses the creative contribution to the theory of imperatives and norms provided by 20th-century Polish researchers. The second component summarizes their reflections and considerations. The third component is an anthology of the classic writings of Polish authors of the time; it constitutes an illustration of the first part and indicates that their research covered practically the whole scope of this theory. Author Jacek Jadacki (born 1946) is professor at (...) Warsaw University. His scholarly production includes approximately hundred works spanning almost every domain in philosophy: from logic, through ontology, epistemology, aesthetics and ethics, to the history of these disciplines. Among his more than twenty books are Possible Ontologies (with Zdzislaw Augustynek; 1993), From the Viewpoint of the Lvov-Warsaw School (2003), and Polish Analytical Philosophy (2009). His pupils include such well-known figures of modern Polish thought as Anna Brozek, Mariusz Grygianiec, Joanna Odrowaz-Sypniewska, and Mieszko Talasiewicz. (shrink)

Excerpt from A History of Formal Logic In this edition of the most considerable history Of formal logic yet published, the Opportunity has Of course been taken to make some adjustments seen to be necessary in the original, with the author's full concurrence. Only in 36, however, has the numeration of cited passages been altered owing to the introduction of new matter. Those changes are as follows. About the Publisher Forgotten Books publishes hundreds of thousands of (...) rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

[The paper is in Polish, an English abstract is given only for information.] This article is intended for philosophers and logicians as a short partial introduction to category theory and its peculiar connection with logic. First, we consider CT itself. We give a brief insight into its history, introduce some basic definitions and present examples. In the second part, we focus on categorical topos semantics for propositional logic. We give some properties of logic in toposes, (...) which, in general, is an intuitionistic logic. We next present two families of toposes whose tautologies are identical with those of classical propositional logic. The relatively extensive bibliography is given in order to support further studies. (shrink)

This Handbook documents the main trends in current research between logic and language, including its broader influence in computer science, linguistic theory and cognitive science. The history of the combined study of Logic and Linguistics goes back a long way, at least to the work of the scholastic philosophers in the Middle Ages. At the beginning of this century, the subject was revitalized through the pioneering efforts of Gottlob Frege, Bertrand Russell, and Polish philosophical logicians such (...) as Kazimierz Ajdukiewicz. Around 1970, the landmark achievements of Richard Montague established a junction between state-of-the-art mathematical logic and generative linguistic theory. Over the subsequent decades, this enterprise of Montague Grammar has flourished and diversified into a number of research programs with empirical and theoretical substance. This appears to be the first Handbook to bring logic-language interface to the fore. Both aspects of the interaction between logic and language are demonstrated in the book i.e. firstly, how logical systems are designed and modified in response to linguistic needs and secondly, how mathematical theory arises in this process and how it affects subsequent linguistic theory. The Handbook presents concise, impartial accounts of the topics covered. Where possible, an author and a commentator have cooperated to ensure the proper breadth and technical content of the papers. The Handbook is self-contained, and individual articles are of the highest quality. (shrink)

“Trends in Logic XVI: Consistency, Contradiction, Paraconsistency, and Reasoning - 40 years of CLE” is being organized by the Centre for Logic, Epistemology and the History of Science at the State University of Campinas (CLEUnicamp) from September 12th to 15th, 2016, with the auspices of the Brazilian Logic Society, Studia Logica and the Polish Academy of Sciences. The conference is intended to celebrate the 40th anniversary of CLE, and is centered around the areas of (...) class='Hi'>logic, epistemology, philosophy and history of science, while bringing together scholars in the fields of philosophy, logic, mathematics, computer science and other disciplines who have contributed significantly to what Studia Logica is today and to what CLE has achieved in its four decades of existence. It intends to celebrate CLE’s strong influence in Brazil and Latin America and the tradition of investigating formal methods inspired by, and devoted to, philosophical views, as well as philosophical problems approached by means of formal methods. The title of the event commemorates one of the three main areas of CLE, what has been called the “Brazilian school of paraconsistency”, combining such a pluralist view about logic and reasoning. (shrink)

Summary of the talk given to the 22nd Conference on the History of Logic, Cracow (Poland), July 5–9, 1976.

I. THE ORIGINS OF THE COMPLEMENTARITY CONCEPT IN SECULAR AND RELIGIOUS UNIVERSALISMa) Keywords, categoriesb) G. McLean: the emergence of philosophical and social complementarity from the Polish dialogue and Solidarityc) Secularity open to all human dimensions including the sacral (the structure of religious values approved not ontologically but on the ethical and cultural plane)d) The Catholicism of John Paul from Cracow and Rome as realistic global and dialogue-based universalisme) Laborem Exercens—source of modern universalismf) “John Paul II’s ‘Labour Manifesto’ and universal (...) society visiong) Sacrality as the highest form of recognitionII. DŁUGIE NARODZINY I KSZTAŁTOWANIE SIĘ SEKULARYZMU [LAICYZMU?] HUMANISTYCZNEGO I PRZEŁOM – KU UNIWERSALIZMOWI, KOMPLEMENTARNYM AKCEPTOWANIEM SEKULARNOŚCI I SAKRALNOŚCIa) Narodziny dialogu z ducha Polskiego Października: od tylko ekskluzji do „dialogu przeciwieństw” b) Laicyzm, a nie ateizm, czyli uznanie pluralizmu za cenę obojętności: ideologia „naszej małej stabilizacji”c) Kontrpartner światopoglądowy jako sojusznik w praktyce społecznejd) Współpraca międzynarodowa jako inspiracja najszersza i ‘parasol ochronny’e) Patriotyzm jako ‘religia obywatelska’ oraz jako mediatyzacja materializmu i chrześcijaństwaIII. KU NOWEMU ETAPOWI UNIWERSALIZMU, RODZĄCEGO SIĘ Z KOMPLEMENTARNOŚCI I SYNERGIIa) Nazwy, problemyb) Synopsis i aktualizacjac) Kolejny etap eksperymentalnej realizacji projektu UW D&UThe present issue of Dialogue and Universalism is exceptional in that it marks out a new phase—not only for our periodical, but also the historical path it attempts to illuminate—and at times even co-create.In fact, similarly as Plato’s great concept, this can be well expressed by one idea, an idea that in its unique, mutually penetrating relation to existence is at once a summary and an illumination. An idea which, like the Sun, brings out diffused things and facts from the darkness of fragmentary, in a sense undeveloped and almost empty existence and the absurdity of mutually-destructive objects, events and people.Yes—this idea is a path leading away from absurdity and the logical, or, rather, ontological partiality and particularism (hence, in a sense, social meaninglessness) of mutually-destructive and mutually-degrading “incomplete existences”.It is, of course, no new idea—it is present in the history of philosophy, anthropology and biology, and in quantum mechanics: complementarity. However, thanks to the penetrating visions of George McLean, this idea now appears in a new role—putting it most simply (if somewhat impoverishingly): as an instrument enabling comprehension of society, including human relations, over history. This, however, will only be possible if we rise above fact—and even regularity—towards the essence of life and history in their most all-embracing sense. In other words, towards the essence of existence, history and the world. And the key to this will be our understanding and application of complementarity.Complementarity in the here-proposed understanding emerges from the historical process and historical theory as a unique form of maturity, a synthesis bearing the most precious intellectual and moral values for all sides involved in co-creating it. (shrink)

"General Survey. The succession of thinkers and schools. The history of ancient philosophy covers about eleven centuries, from Thales who lived during the sixth century B.C. to Boethius and Simplicius who flourished at the beginning of the sixth A.D. From the point of view of the history of formal logic this long epoch may be divided into three periods. (1) The pre-Aristotelian period, from the beginnings to the time at which Aristotle..

Introduction -- Philosophy in the Middle Ages -- Polish philosophy in the Renaissance and Baroque -- Polish philosophy in the Enlightenment -- Polish philosophy of the Romantic era -- The philosophy of Polish positivism -- Polish philosophy in the age of modernism --Polish philosophy in the interwar period -- Polish philosophy after World War II -- A selection of post-war general literature on the subject -- Conclusion.

Tadeusz Kotarbinski is one of towering figures in contemporary Polish philosophy. He was a great thinker, a great teacher, a great organizer of philosophical and scientific life, and, last but not least, a great moral authority. He died at the age of 96 on October 3, 1981. Kotarbinski was active in almost all branches of philosophy. He made many significant contributions to logic, semantics, ontology, epistemology, history of philosophy, and ethics. He created a new field, namely praxiology. (...) Thus, using an ancient distinction, he contributed to theoretical as well as practical philoso~hy. Kotarbinski regarded praxiology as his major philosophical "child". Doubtless, praxiology belongs to practical philosophy. This collection, howewer, is mainly devoted to Kotarbinski' s theoretical philosophy. Reism - Kotarbinski' s fundamental idea of ontology and semantics - is the central topic of most papers included here; even Pszczolowski' s essay on praxiology considers its ontological basis.,Only two papers, namely that of Zarnecka-Bialy and that of Wolenski, are not linked with reism. However, both fall under the general label "Kotarbinski: logic, semantics and ontology". The collection partly consists of earlier published papers. (shrink)

This paper is an historical study of Tarski's methodology of deductive sciences (in which a logic S is identified with an operator Cn S, called the consequence operator, on a given set of expressions), from its appearance in 1930 to the end of the 1970s, focusing on the work done in the field by Roberto Magari, Piero Mangani and by some of their pupils between 1965 and 1974, and comparing it with the results achieved by Tarski and the (...) class='Hi'>Polish school (Łoś, Suszko, Słupecki, Pogorzelski, Wójcicki). In the last section of the paper we will then compare these works with some recent developments in algebraic logic: this will lead to a better understanding of the results of the methodology of deductive science, but at the same time will show some intrinsic limits to such an approach to logic. Even if Magari's work on diagonizable algebras and universal algebra and Mangani's axiomatization of MV-algebras and results in model theory are rather famous, the articles on closure operators, published in the 1960s, are almost totally unknown outside Italy (mainly because of a linguistic limitation, the papers we analyse having been written and published in Italian). This paper aims to fill the gap in the literature and to enable the international community to get acquainted with this part of Italian logic. The same applies to some works published in Barcelona (in Catalan) at the end of the 1970s, analysed in the last section. (shrink)

Among the extraordinary Polish philosophers of the past one hundred years, Zygmunt Zawirski deserves to be given particular attention for his fusion of analytic and historical scholarship. Strikingly versatile, and con tributing original work in all his fields of competence, Zawirski thought through issues in the philosophical aspects of relativity theory, on the claims of intuitionalistic foundations of mathematics, on the nature and usefulness of many-value Logics, and on the calculus of probability, on the axiomatic method in science and (...) in the philosophy of science, on the genesis and development of scientific and philosophical concepts, and in his crowning achievement, the conceptual history of notions of time. His work has been too little known in English despite the respect which has been so clearly shown by his Polish COlleagues and students. In this generous selection from his papers and from his great critical study L' Evolution de la Notion du Temps, Dr. Irena Szumilewicz-Lachman has provided a clear account of Zawirski's achievement; and she has written a fine comprehensive introductory essay which provides both the personal and historical context of his work and a systematic survey of his principal publications. (shrink)

"The role of logic in the Middle Ages. Regarding the role of logic within the framework of arts and sciences during the Middle Ages, we have to distinguish two related aspects, one institutional and the other scientific. As to the first aspect, we have to remember that the medieval educational system was based on the seven liberal arts, which were divided into the trivium, i.e., three arts of language, and the quadrivium, i.e., four mathematical arts. The so-called trivial (...) arts were grammar, rhetoric, and logic, and during a period of several centuries virtually every educated person, at least every university graduate, received a training in these matters, especially in logic. Students in the medieval faculty of arts probably spent more time studying logic than any other discipline. This first -- institutional -- aspect concerning the role of logic is explained by the second -- scientific -- aspect. The trivial disciplines provided techniques of analysis and a technical vocabulary that permeate philosophical, scientific and theological writings. Logic, as mentioned before, was referred to and was generally regarded as the art of arts and the science of sciences. The increasing cultural dominance of the universities with their obligatory disputationes and their hierarchy of examinations on the one hand and the outstanding status of logic on the other were corresponding features of the educational world of the 13th century. The core of the logic curriculum from the 12th century onwards was provided by the logical works of Aristotle. These represented the material for the study of types of predication, the analysis of simple propositions or statements (2) and their relations of inference and equivalence, the analysis of modal propositions, of the structure and the types of the syllogism, dialectical topics, fallacies and scientific reasoning as based on the demonstrative syllogism. Medieval logicians, however, realized that there were other, non-Aristotelian, approaches to logical subjects, questions and methods that could be investigated.. (shrink)

Drawing on recently published correspondence as well as on a survey of Polish and international philosophical activity published in 1937 and details concerning the publisher and bookseller Aleksander Mazzucato, I provide evidence that, contrary to some recent assertions (but in line with older bibliographical entries), Tarski's ‘Der Wahrheitsbegriff in den formalisierten Sprachen’ was not published in journal form until 1936, although preprints, lacking two corrections and a small addendum, were likely available in the late months of 1935.

A Bilingual International Conference on the History and Actuality of the Polish Contribution, from the Lvov-Warsaw school to phenomenology, to Twentieth Century Philosophy. Colloque international bilingue portant sur l'histoire et l'actualité de la contribution polonaise, de l'école de Lvov-Varsovie à la phénoménologie, à la philosophie du vingtième siècle.

The “official” history of connexive logic was written in 2012 by Storrs McCall who argued that connexive logic was founded by ancient logicians like Aristotle, Chrysippus, and Boethius; that it was further developed by medieval logicians like Abelard, Kilwardby, and Paul of Venice; and that it was rediscovered in the 19th and twentieth century by Lewis Carroll, Hugh MacColl, Frank P. Ramsey, and Everett J. Nelson. From 1960 onwards, connexive logic was finally transformed into non-classical calculi (...) which partly concur with systems of relevance logic and paraconsistent logic. In this paper it will be argued that McCall’s historical analysis is fundamentally mistaken since it doesn’t take into account two versions of connexivism. While “humble” connexivism maintains that connexive properties only apply to “normal” antecedents, “hardcore” connexivism insists that they also hold for “abnormal” propositions. It is shown that the overwhelming majority of the forerunners of connexive logic were only “humble” connexivists. Their ideas concerning connexive implication don’t give rise, however, to anything like a non-classical logic. (shrink)

The article presents interpersonal relations and mutual influences between German logician Heinrich Scholz and Polish scholars, first of all Jan Łukasiewicz. The background for presenting these relationships consists of reflections on the development of logic in Poland and various conceptions of how to apply logic to philosophical issues. Firstly, Jan Łukasiewicz’s program of logicisation of philosophy and his search for allies is presented. Secondly, the forms of cooperation between Łukasiewicz and Scholz, as well as contacts between the (...) latter and other Polish scholars are sketched. Finally, forms of Scholz’s help to Polish friends during the tumultuous period of World War II are examined. The article provides also some reflections on the approach to logic in various European centers of analytic philosophy and historical comments on the continuity of philosophical and logical schools. (shrink)

ABSTRACT: A comprehensive introduction to ancient (western) logic from earliest times to the 6th century CE, with a focus on issues that may be of interest to contemporary logicians and covering important topics in Post-Aristotelian logic that are frequently neglected (such as Peripatetic hypothetical syllogistic, the Stoic axiomatic system of propositional logic and various later ancient developments).

The origin of paraconsistent logic is closely related with the argument, ‘from the assertion of two mutually contradictory statements any other statement can be deduced’; this can be referred to as ex contradictione sequitur quodlibet (ECSQ). Despite its medieval origin, only by the 1930s did it become the main reason for the unfeasibility of having contradictions in a deductive system. The purpose of this article is to study what happened earlier: from Principia Mathematica to that time, when it became (...) well established. The two main historical claims that I am going to advance are the following: (1) the first explicit use of ECSQ as the main argument for supporting the necessity of excluding any contradiction from deductive systems is to be found in the first edition of the book Grundzüge der Theoretischen Logik (Hilbert, D. and Ackermann, W. 1928. Grundzüge der Theoretischen Logik. Berlin: Julius Springer Verlag); (2) Łukasiewicz's position regarding the logical constraints against contradictions varies considerably from his studies on the principle of (non-) contradiction in Aristotle, published in 1910 and what is stated in his `authorized lectured notes' on mathematical logic that appeared in 1929. The two texts are: 1) a paper in German (Łukasiewicz, J. 1910. `Über den Satz des Widerspruchs bei Aristotles'. Bulletin International de l'Académie des sciences de Cracovie, Classe d'Histoire et de Philosophie, pp. 15–38) [English translation: Łukasiewicz, J. 1971. ‘On the principle of contradiction in Aristotle’, Review of Metaphysics, XXIV, 485–509]; and 2) a book in Polish. Łukasiewicz, J. 1910. O zasadzie sprzecznosci u Aristotelesa Studium krytyczne, Warsaw: Panstwowe Wydawnictwo Naukowe [German translation: Łukasiewicz, J. 1993. Über den Satz des Widerspruchs bei Aristotles. Hildesheim: Georg Olms Verlag]. The lecture notes were then published as a book (Łukasiewicz, J. 1958. Elementy Logiki Matematycznej. Warszawa: Panstwowe Wydawnictwo Naukowe [PWN] and then translated into English (Łukasiewicz, J. 1963. Elements of Mathematical Logic. Oxford, New York: Pergamon Press/the Macmillan Company). The second half of this article will concentrate on Łukasiewicz's position on ECSQ. This will lead me to propose that to regard him as a forerunner of paraconsistent logic by virtue of those early writings is accurate only if his book published in Polish is considered but not if the analysis is restricted to the paper originally published in German (as has been the case for the principal reconstructions of the history of paraconsistent logic). Furthermore, I will stress that in the 1929 book he presented one formalization of ECSQ as an axiom for sentential calculus and, also, he used ECSQ to defend the necessity of consistency, apparently independently of Hilbert and Ackermann's book. At the end, I will suggest that the aim of twentieth century usage of ECSQ was to change from the centuries-long philosophical discussion about contradictions to a more ‘technical’ one. But with paraconsistent logic viewed as a technical solution to this restriction, then, the philosophical problem revives but having now at one's disposal an improved understanding of it. Finally, Łukasiewicz's two different positions about ECSQ open an interesting question about the history of paraconsistent logic: do we have to attempt a consistent reconstruction of it, or are we prepared to admit inconsistencies within it? (shrink)

The volume consists of thirteen papers devoted to various problems of the philosophy of logic and mathematics. They can be divided into two groups. The first group contains papers devoted to some general problems of the philosophy of mathematics whereas the second group - papers devoted to the history of logic in Poland and to the work of Polish logicians and math-ematicians in the philosophy of mathematics and logic. Among considered problems are: meaning of reverse (...) mathematics, proof in mathematics, the status of Church's Thesis, phenomenology in the philosophy of mathematics, mathematics vs. theology, the problem of truth, philosophy of logic and mathematics in the interwar Poland. (shrink)

This paper describes the work of the Polish logician Jan Kalicki (1922?1953). After a biographical introduction, his work on logical matrices and equational logic is appraised. A bibliography of his papers and reviews is also included.

Johannes Steuchius’ disputatio uses Arabic logic to present an historical account of the development of philosophical thought in Arabia before and after the emergence of Islam. Steuchius first proposes that philosophy drew its origins from the East. His evidence for this claim is that many of the Greek philosophers, considered the forefathers of European philosophy, began cultivating their philosophical thinking as a result of exposure to ancient Eastern philosophy. After the introduction of Greek philosophy, it is agreed that dialectic (...) was among the first of the arts the Arabs practiced. (shrink)

This book treats ancient logic: the logic that originated in Greece by Aristotle and the Stoics, mainly in the hundred year period beginning about 350 BCE. Ancient logic was never completely ignored by modern logic from its Boolean origin in the middle 1800s: it was prominent in Boole’s writings and it was mentioned by Frege and by Hilbert. Nevertheless, the first century of mathematical logic did not take it seriously enough to study the ancient (...) class='Hi'>logic texts. A renaissance in ancient logic studies occurred in the early 1950s with the publication of the landmark Aristotle’s Syllogistic by Jan Łukasiewicz, Oxford UP 1951, 2nd ed. 1957. Despite its title, it treats the logic of the Stoics as well as that of Aristotle. Łukasiewicz was a distinguished mathematical logician. He had created many-valued logic and the parenthesis-free prefix notation known as Polish notation. He co-authored with Alfred Tarski’s an important paper on metatheory of propositional logic and he was one of Tarski’s the three main teachers at the University of Warsaw. Łukasiewicz’s stature was just short of that of the giants: Aristotle, Boole, Frege, Tarski and Gödel. No mathematical logician of his caliber had ever before quoted the actual teachings of ancient logicians. -/- Not only did Łukasiewicz inject fresh hypotheses, new concepts, and imaginative modern perspectives into the field, his enormous prestige and that of the Warsaw School of Logic reflected on the whole field of ancient logic studies. Suddenly, this previously somewhat dormant and obscure field became active and gained in respectability and importance in the eyes of logicians, mathematicians, linguists, analytic philosophers, and historians. Next to Aristotle himself and perhaps the Stoic logician Chrysippus, Łukasiewicz is the most prominent figure in ancient logic studies. A huge literature traces its origins to Łukasiewicz. -/- This Ancient Logic and Its Modern Interpretations, is based on the 1973 Buffalo Symposium on Modernist Interpretations of Ancient Logic, the first conference devoted entirely to critical assessment of the state of ancient logic studies. (shrink)

Johannes Steuchius was a prominent Swedish Lutheran theologian and academic, a descendant of celebrated Lutheran bishops and academics. Born in 1676 in Härnösand in northern Sweden, Steuchius moved with his family to Lund in 1694 when his father, Matthias Steuchius, the renowned academic and theologian, was appointed Bishop of Lund. After completing his studies in logic and metaphysics at Uppsala University, Steuchius was given the opportunity to attend some of Europe’s foremost Protestant academic institutions, a luxury afforded to few. (...) Steuchius’ disputatio uses Arabic logic to present an historical account of the development of philosophical thought in Arabia before and after the emergence of Islam. He first proposes that philosophy drew its origins from the East. His evidence for this claim is that many of the Greek philosophers, considered the forefathers of European philosophy, began cultivating their philosophical thinking as a result of exposure to ancient Eastern philosophy. After the introduction of Greek philosophy, it is agreed that dialectic was among the first of the arts the Arabs practiced. (shrink)

The discovery of the importance of mereology follows and does not precede the formalisation of the theory. In particular, it was only after the construction of an axiomatic theory of the part-whole relation by the Polish logician Stanisław Leśniewski that any attempt was made to reinterpret some periods in the history of philosophy in the light of the theory of parts and wholes. Secondly, the push for formalisation - and the individuation of mereology as a specific theoretical field (...) - arise from several particular theories, first from biology and then from psychology. Mereological considerations were explicitly developed within the school of Brentano, by Brentano himself- starting from the problem of the unity of consciousness - and by his students, particularly Stumpl, Twardowski and the Gestaltists. The most complete result of this tradition is undoubtedly the third of Husserl's Logical Investigations, called "the single most important contribution to realist (Aristotelian) ontology in the modern period". (shrink)

This article reviews the book Selected Issues in the History of Polish Philosophy, by Tomasz Mróz.