The brief article of 1910 which is translated here is, as the prefatory note explains, significant for understanding both the way in which ?ukasiewicz came to many-valued logic and the influences under which he stood at the time.

This paper reports some attempts undertaken in Poland in the 1930s to modernize Thomism by means of modern logic. In particular, it concerns J.M. Bocheński and J. Salamucha, the leading members of the CracowCircle. They attempted to give precise logical form to the Five Ways of Thomas Aquinas. Other works concerned the concept of transcendentals, the levels of abstraction, and the concept of essence.

In this article the author first described the developments which brought to focus the importance of consistency proofs for mathematics, and which led Hilbert to promote the science of metamathemat-ics. Further comments and remarks concern the (partly analogous) beginnings of the work on the decision problem, Gödel?s theorems and related matters, and general metamathematics. An appendix summarizes a text by the author on completeness and categoricity.

The relevance of metamathematical researches for philosophy of math- ematics is an indubitable matter. In the paper I shall speak about impli- cations of metamathematics for general philosophy, especially for classical epistemological problems. Let us start with a historical observation con- cerning Hilbert's programme, the rst research programme in metamathe- matics as a separate study of formal systems. This programme was strongly in uence by epistemological considerations. In fact, Hilbert wanted to se- cure all classical mathematics against inconsistencies and this (...) aim had be achieved with the help of nitary consistency proof. Hilbert's claim is like the Cartesian project of reduction of all concepts to clarae et distinctae ideae. The epistemological commitment of original Hilbert's programme may be treated as a prelim- inary heuristic motivation for looking for epistemological implications of metamathematical results. It seems reasonable to examine in this respect three so-called limitative theorems: the rst Godel's incompleteness theo- rem , the second Godel's incom- pleteness theorem consistency of S, cannot be proved in S, providing that S is consistent) and Tarski's undenability theorem ; \S" stands for formal system containing elementary number theory. From the above-mentioned theorems we obtain an important, from philosophical point of view, conclusion: semantics of S cannot be expressed in S. Now, I shall present three applications of limitative theorems to the analysis of classical epistemological problems. (shrink)

Adolf Lindenbaum Adolf Lindenbaum was a Polish mathematician and logician who worked in topology, set theory, metalogic, general metamathematics and the foundations of mathematics. He represented an attitude typical of the Polish Mathematical School, consisting of using all admissible methods, independently of whether they were finitary. For example, the axiom of choice was freely applied, … Continue reading Lindenbaum, Adolf →.

The Semantic Theory of Truth The semantic theory of truth was developed by Alfred Tarski in the 1930s. The theory has two separate, although interconnected, aspects. First, it is a formal mathematical theory of truth as a central concept of model theory, one of the most important branches of mathematical logic. Second, it … Continue reading Semantic Theory of Truth →.

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)

Formal semantics is understood either as a formal analysis of semantical features of natural language or as model‐theoretic semantics of formal languages. This paper focuses on the second understanding. The problem is how to identify the formal aspects of formal semantics, if we understand ‘formal’as ‘independent of content’. This is done by showing that the form of semantical interpretation of a language L is given by its syntax and the parallelism of the signature of L and its interpretative structure SI. (...) However, the content of interpretation, that is, the way of correlating of L‐expressions with extralinguistic items depends of informal factors. The discussion shows that semantics is prior to syntax. (shrink)

The book provides a historical and systematic exposition of the semantic theory of truth formulated by Alfred Tarski in the 1930s. This theory became famous very soon and inspired logicians and philosophers. It has two different, but interconnected aspects: formal-logical and philosophical. The book deals with both, but it is intended mostly as a philosophical monograph. It explains Tarski’s motivation and presents discussions about his ideas as well as points out various applications of the semantic theory of truth to philosophical (...) problems. (shrink)

This paper discusses the main logical ideas put forward by Jan Łukasiewicz within their historical context and further development.

This paper presents the life and work of Alfred Tarski, one of the most distinguished and influential logicians in the entire history.

Logical theory codifies rules of correct inferences. On the other hand, logical reasoning is typically considered as one of the most fundamental cognitive activities. Thus, cognitive science is a natural meeting-point for investigations about the place of logic in human cognition. Investigations in this perspective strongly depend on a possible understanding of logic. This paper focuses on logic in the strict sense; that is, the theory of deductive inferences. Two problems are taken into account, namely: do humans apply logical rules (...) in ordinary reasoning?; the genesis of logic. The second issue is analyzed from the naturalistic point of view. (shrink)

This volume is a result of the international symposium “The Tradition of the Lvov-Warsaw School in European Culture,” which took place in Warsaw, Poland, September 2015. It collects almost all the papers presented at the symposium as well as some additional ones. The contributors include scholars from Austria, the Netherlands, Ireland, and Poland. The papers are devoted to the history and reception of the Lvov-Warsaw School, a Polish branch of analytic philosophy. They present the School’s achievements as well as its (...) connections to other analytic groups. The contributors also show how the tradition of the School is developed contemporarily. The title will appeal to historians of analytic philosophy as well as historians of philosophy in Central Europe. (shrink)

It is a Preface to Volume 8:2 (2019) consisting of articles presented at the International Interdisciplinary Conference anniversary of the birth of Jan Łukasiewicz, Rzeszów, Poland.

This paper investigates the concept of aletheia in ancient philosophy from the pre-Socratics until Aristotle. The meaning of aletheia in archaic Greek is taken as the starting point. It is followed by remarks about the concept of truth in the Seven Sages. The author discusses this concept as it appears in views and works of philosophers and historians. A special section is devoted to the epistemological and ontological understanding of truth. On this occasion, influential views of Heidegger are examined. The (...) paper is concluded by a review of various meanings of truth in Aristotle. (shrink)

Józef M. Bocheński began his philosophical career as an eclectic philosopher, then switched to Thomism and finally became a representative of the analytic school. As a Thomist he wanted to reform this orientation by the resources of modern formal logic. This tendency culminated in the establishment of the Cracow Circle (established in 1936) whose members were Bocheński, Jan F. Drewnowski, Jan Salamucha, and Bolesław Sobociński. However, the program of the Cracow Circle was rejected by most Thomists who considered traditional logic (...) as an entirely sufficient device of philosophy. Bocheński was very disappointed by this attitude of his Thomist fellows. His evolution toward analytic philosophy, free of any ideological pressure, can be regarded as his reaction to the conservatism of Thomism. (shrink)

This paper reports some attempts undertaken in Poland in the 1930s to modernize Thomism by means of modern logic. In particular, it concerns J.M. Bocheski and J. Salamucha, the leading members of the CracowCircle. They attempted to give precise logical form to the Five Ways of Thomas Aquinas. Other works concerned the concept of transcendentals, the levels of abstraction, and the concept of essence.

This paper provides an interpretation of Father Bocheński’s saying “Beyond logic there is only nonsense.” He considered the battle against superstitions of various kinds as one of the most important intellectual and social duties. The phrase in itself suggests that logic is a weapon in the mentioned battle. Logic is understood broadly, that is, as semantics, formal logic and the methodology of science, and was considered by Bocheński as the main instrument of rational philosophy. Hence, the formula under discussion has (...) an explicit metaphilosophical significance, although Bochenski’s understanding of the concept of differs from that of the Vienna Circle. (shrink)

Hence, the title The Heritage of Kazimierz Ajdukiewicz seems to reflect the general idea of this collection. Most papers collected here were specially ...

. This papers examines formal properties of logical squares and their generalizations in the form of hexagons and octagons. Then, several applications of these constructions in philosophical analysis are elaborated. They concern contingency (accidentality), possibility, permission, axiological concepts (bonum and malum), the generalized Hume thesis (deontic and epistemic modalities), determinism, truth and consistency (in various senses. It is shown that relations between notions used in various branches of philosophy fall into the same formal scheme.

Popper's definition of verisimilitude was criticized for its paradoxical consequences in the case of false theories. The aim of this paper is to show that paradoxes disappear if the falsity content of a theory is defined with help of dCn or Cn –1.

This paper examines two arguments againstpsychologism advanced by Frege andHusserl. The first argument says that thelaws of logic cannot be justified by thelaws of psychology, because the formerand a priori and certain, but the latterare probable only. The second argumentpoints out that the status of logicallaws as universal principles of thinking isnot intelligible on the psychologisticinterpretation of logic. The author tries toshow how to examine both arguments bymetalogical devices.

Jan Łukasiewicz a élaboré un programme de recherche portant sur l’histoire de la logique. À son avis, la logique mathématique contemporaine (modern) est en continuité directe avec la logique formelle du passé. En conséquence, une interprétation correcte et fidèle des idées anciennes exige une application des outils logiques contemporains. Autrement dit, de bonnes études historiques sur la logique doivent consister à examiner la logique d’autrefois à travers les lunettes logiques contemporaine...

For decades Ryszard Wójcicki has been a highly influential scholar in the community of logicians and philosophers. Our aim is to outline and comment on some essential issues on logic, methodology of science and semantics as seen from the perspective of distinguished contributions of Wójcicki to these areas of philosophical investigations.

The larger part of Yearbook 6 of the Institute Vienna Circle constitutes the proceedings of a symposium on Alfred Tarski and his influence on and interchanges with the Vienna Circle, especially those on and with Rudolf Carnap and Kurt Gödel. It is the first time that this topic has been treated on such a scale and in such depth. Attention is mainly paid to the origins, development and subsequent role of Tarski's definition of truth. Some contributions are primarily historical, others (...) analyze logical aspects of the concept of truth. Contributors include Anita and Saul Feferman, Jan Wolenski, Jan Tarski and Hans Sluga. Several Polish logicians contributed: Gzegorczyk, Wójcicki, Murawski and Rojszczak. The volume presents entirely new biographical material on Tarski, both from his Polish period and on his influential career in the United States: at Harvard, in Princeton, at Hunter, and at the University of California at Berkeley. The high point of the analysis involves Tarski's influence on Carnap's evolution from a narrow syntactical view of language, to the ontologically more sophisticated but more controversial semantical view. Another highlight involves the interchange between Tarski and Gödel on the connection between truth and proof and on the nature of metalanguages. The concluding part of Yearbook 6 includes documentation, book reviews and a summary of current activities of the Institute Vienna Circle. Jan Tarski introduces letters written by his father to Gödel; Paolo Parrini reports on the Vienna Circle's influence in Italy; several reviews cover recent books on logical empiricism, on Gödel, on cosmology, on holistic approaches in Germany, and on Mauthner. (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)

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 examines relations between reism, the metaphysical theory invented by Tadeusz Kotarbi?ski, and Le?niewski's calculus of names. It is shown that Kotarbi?ski's interpretation of common nouns as genuine names, i.e. names of things is essentially based on Le?niewski's logical ideas. It is pointed out that Le?niewskian semantics offers better prospects for nominalism than does semantics of the standard firstorder predicate calculus.

Kazimierz Twardowski is most commonly known as the teacher of great philosophers and the founder of the Lvov-Warsaw School. As a philosopher however, he is primarily remembered for his famous comparison of the contents and objects of various kinds of representations, a comparison that remains enshrined in European thought.In fact, he attained important results in many other branches of philosophy as well. For instance, in ontology, he laid the foundations for the modern theory of formal structure of objects, and he (...) introduced the theoretically fruitful pair of terms, action-product. In epistemology, he developed a profound analysis of the notion and criteria of truth; and he provided a forceful account of the errors underlying relativist theories of truth. In methodology, he drew an explicit distinction between the processes of discovering, systematising, and grounding in science, and he offered accurate descriptions of the nature of psychology and other humanities. In logic, he offered decisive arguments on behalf of the idiogenetic conception of judgement, and he improved the traditional typology of adjectives.These achievements are of significance that is not only historical. Kazimierz Twardowski's work, formulated in plain, precise language, are instructive and inspiring for contemporary students of philosophy. (shrink)