Abraham Fraenkel and Yehoshua Bar-Hillel noted that ‘There is probably no country which has contributed, relative to the size of its population, so much to mathematical logic and the foundations of mathematics’.Reference Fraenkel and Bar-Hillel¹ However, if one were to speculate how the development of mathematical logic would have been predicted around 1920, hardly any mention of Poland would be expected. Twenty years later, Heinrich Scholz called Warszawa one of the capitals of mathematical logic.Reference Scholz² Even if one is sceptical (I am) about such rankings or about the dependence of fruitful logical investigations on the number of inhabitants in particular countries, the development of logic in Poland is a remarkable fact. The papers presented here touch various aspects of the development of logic in Poland mostly in the interwar period; one paper concerns the post-war years. Although the presentation is selective and general, it gives some picture of how Polish logicians worked and what they achieved. This introduction outlines a general background of the development of logic in Poland (see Refs Reference Jordan3–Reference Woleński6 for a more extensive treatment).

Roughly speaking, Polish logic had two parents, namely philosophy and mathematics. In philosophy, almost everything goes to Kazimierz Twardowski (1866–1938), a student of Brentano, professor in Lvov (now Lviv in Ukraine) and the founder of the Lvov-Warsaw School. His metaphilosophical programme, postulating clarity in doing philosophy and insisting that views should be carefully justified, created a natural environment for general logic. He demanded clarity of language and thought and believed in scientific philosophy. Twardowski was also the first person who gave a course in mathematical logic in Poland (1899/1900); it concerned the algebra of logic and was fairly elementary. He trained many philosophers interested in logic, including Jan Łukasiewicz (1878–1956), Kazimierz Ajdukiewicz (1890–1963), Tadeusz Czeżowski (1889–1981), Tadeusz Kotarbiński (1886–1981) and Zygmunt Zawirski (1882–1948); all of them also studied mathematics, mostly under Wacław Sierpiński (1882–1969), who acquainted his students with set theory. Stanisław Leśniewski (1886–1939) joined this circle in 1910.

However, Krakow, not Lvov, became the first serious centre of mathematical logic. Stanisław Zaremba (1863–1942), a distinguished Polish mathematician, had strong interests in logic and the foundations of mathematics. He considered logic as a peripheral branch of mathematics, having only a secondary importance, mainly in teaching mathematicians. He was influenced by the French style of doing mathematics (see Zaremba 1926). Zaremba’s views prevailed among mathematicians in Krakow. On the other hand, the Jagiellonian University in Krakow had a special position in mathematical logic, occupied by Jan Śleszyński (1854–1931). He was the most competent Polish scholar in mathematical logic until the 1920s. Śleszyński’s lectures in Krakow were quite advanced and used the ideas of Frege, Peano and Principia Mathematica. Leon Chwistek (1884–1944), another important figure in Krakow – although he came to logic from philosophy, not from mathematics – very soon began to work in the style of Russell.

Warszawa appeared on the stage in 1915, when the University of Warsaw was reopened (it was closed in 1831). Poland recovered its independence in 1918. This also resulted in a great debate about the tasks and prospects of Polish science and culture, including the development of mathematics. Zygmunt Janiszewski (1888–1920) formulated the programme of the Polish mathematical school (the Janiszewski programme). Roughly speaking, Polish mathematicians, according to Janiszewski, should concentrate on set theory, topology and their applications to other branches of mathematics. This project (see Ref. Reference Kuratowski7 for more details) was accepted by several leading Polish mathematicians, such as Wacław Sierpiński (1882–1969), and Stefan Mazurkiewicz (1888–1945), both working in Warszawa, as well as Stefan Banach (1892–1945) and Hugo Steinhaus (1887–1972) in Lvov. Janiszewski also postulated that Poland should have a special mathematical journal published in international languages. This idea found its realization in Fundamenta Mathematicae (the first volume appeared in 1920). The significance of mathematical logic in the eyes of the founders of the Polish mathematical school found its impressive manifestation in the composition of the Editorial Board of Fundamenta: Mazurkiewicz, Sierpiński, Leśniewski and Łukasiewicz.

Janiszewski’s programme attributed a great role to mathematical logic and the foundations of mathematics considered as autonomous branches of mathematics, having their own problems and not dependent on their applications in mathematics or on other practical functions. The placement of logic and the foundations at the heart of mathematics required definite steps in the sphere of organization. The University of Warsaw had a Faculty of Mathematical and Natural Sciences. The Department of the Philosophy of Mathematics was very soon organized and Leśniewski became its head. Łukasiewicz left the University in 1918 in order to act as the Minister of Religious Confessions and Education in the government under Ignacy Paderewski. He returned to the academic staff in 1919 and the University established for him a special position in philosophy at the Faculty of Mathematics and Natural Sciences. Both professors began intensive teaching of mathematical logic, mostly among mathematicians but also among philosophers. Alfred Tarski (1901–1983) opened the list of young mathematicians and philosophers attracted by logic in Warszawa. The logical community in this city included (in alphabetical order and covering the whole interwar period: Stanisław Jaśkowski (1906–1965), Adolf Lindenbaum (1904–1941?), Andrzej Mostowski (1913–1975), Moses Presburger (1904–1943?), Jerzy Słupecki (1904–1984), Bolesław Sobociński (1904–1980); a philosopher by training, and Mordechaj Wajsberg (1902–1942?). The names of three other of logicians who graduated shortly before 1939 or studied during the Second War World and began their academic work after 1945 should be added to this list, namely Jan Kalicki (1922–1953; a mathematician), Czesław Lejewski (1913–2001; a classicist and philosopher) and Henryk Hiż (1917–; a philosopher). The development of logic in Warszawa had two subperiods in 1918–1939, namely 1918–1929 and 1929–1939. The first decade consisted in intensive teaching and scientific work at the seminars of Leśniewski and Łukasiewicz, but the second period brought important publications and international recognition. The fruitful co-operation of mathematicians and philosophers in Warszawa had the utmost significance for the shape of logic in this centre. The founders of the Polish mathematical school made a brave experiment consisting of inviting two philosophers with a modest mathematical background as professors at the Faculty of Mathematics and Natural Sciences; this did not happen in any other country.

The situation in Lvov was different. Mathematicians tolerated mathematical logic in a friendly way but did not consider it to be something central to mathematics. At first, Ajdukiewicz conducted courses in mathematical logic. In 1928, the Jan Kazimierz University in Lvov decided to establish the Department of Mathematical Logic. Two candidates went into competition, namely Chwistek and Tarski, and the former was chosen after a long and even dramatic competition; Russell’s opinion, more favourable for Chwistek than for Tarski, was of decisive importance. Chwistek brought some people from Krakow; in particular, Władysław Hetper (190?–1941?) should be mentioned. The group of Lvov logicians also included: Józef Pepis (190?–1942?) and Eustachy Żyliński (1880–1954). The position of logic in Krakow gradually weakened. After Śleszyński’s retirement (1924), the professorship in logic was cancelled. These difficulties were related to the attitude of Zaremba who did not accept the Janiszewski programme and considered logic as located at the peripheries of mathematics.

The Adam Mickiewicz University in Poznan established a position in logic in 1919. It was given to Zawirski in 1924; he moved to the Jagiellonian University in 1937 but as a professor of philosophy, not logic. Logic at the University of Wilno (now Vilnius in Lithuania) was popularized by Czeżowski, a professor of philosophy (mathematicians in Wilno were not particularly interested in logic). Although logic had no significance in the Catholic University in Lublin, two Thomists, namely Father Józef M. Bocheński (1902–1995) and Father Jan Salamucha (1904–1944) were logicians. The former lived in Italy and Switzerland, while Salamucha taught in Kraków at the Theological Faculty. This brief survey is sufficient to show how important the support for logic was from the side of mathematicians, great in Warszawa, moderate but sympathetic in Lvov, and rather negative or even hostile in Cracow; other universities were established (Poznan, Lublin) or reopened after 1918 but did not create their own traditions in logic, being too young. In fact, the Polish mathematical community was deeply divided. The Polish mathematical school based mathematics on set theory and logic, but Zaremba strongly opposed this programme. This opposition was also caused by conflicts that originated in Łukasiewicz’s criticism of Zaremba, mentioned by KuratowskiReference Kuratowski⁷ and supported by some Warsaw mathematicians. Nevertheless, Poland had (taking into account all activity in various years) five professorships in mathematical logic. By comparison, outside of Poland there was only one, in Münster in Germany. Łukasiewicz proposed that a special logical journal should be established in Poland. Financial difficulties delayed the journal, but the two first volumes of Collectanea Logica went to the printing house just before the start of the Second World War. Fire destroyed them in September 1939; only preprints survived. Finally, let me mention that the Polish Logical Society was established in 1936.

Łukasiewicz considered logic as ‘morality of thought and speech’. In general, Polish logicians maintained that although logic gives no recipe for various tender spots of the world, it may contribute to the world’s improvement by helping people understand each other. Thus, according to this view, doing logic and teaching resulted in an important social service. Perhaps this explains to some extent the passion that was a characteristic feature of the logical research done in Poland. This passionate attitude to logic eliminated, to some extent, various political and social differences and tensions among logicians in Warszawa. In fact, the Warsaw school of logic, although unified by the common scientific enterprise, was quite differentiated from the sociological point of view. Some of its members, Lindenbaum for instance, came from rich families, other, such as Tarski or Presburger, had serious financial difficulties. Lindenbaum shared communist views, but Łukasiewicz supported conservatism. The latter, twice elected as Rector Magnificus, belonged to the academic VIPs, but Wajsberg worked as a modest teacher in a Jewish secondary school. Tarski, Lindenbaum, Presburger and Wajsberg were Jews, but Leśniewski and Sobociński (later also Łukasiewicz) were radical anti-Semites.

The years 1939–1945 were tragic for Poland. Many young and promising scholars and students lost their lives. Among the logicians, Leśniewski died in 1939, a few months before the outbreak of the Second World War, Chwistek in 1944, few months before its end. Lindenbaum, Presburger, Salamucha and Wajsberg were killed by the Nazis (some dates are uncertain, hence the question marks), Hetper perished in the Soviet Union. The war also had other sad consequences for logic: Tarski left Poland in August 1939, Łukasiewicz in 1944, and the same happened during the war or shortly after its end to Hiż, Lejewski and Sobociński; Bocheński remained abroad. Zawirski died in 1948. Poland restored its academic life very soon after 1945 and logic returned in this country as a very respectable subject of research and teaching.

The series of papers about logic in Poland included in this issue of European Review begins with Katarzyna Kijania-Placek’s paper on Twardowski’s theory of presentations. This theory is a pattern of philosophical analysis as practised in the Lvov-Warsaw School. Peter Simons focuses on Łukasiewicz’s approach to the concept of possibility based on many-valued logic. Rafał Urbaniak discusses the prospects of Leśniewski’s ideas concerning the foundations of mathematics, a topic that is usually considered as secondary compared with the logical systems of Leśniewski. The papers by Cezary Cieśliński and Leon Horsten concern Tarski’s theory of truth, doubtless the most important result coming from ‘Polish logic’; I use quotation marks, because logic is not national, but international. As Tarski said once ‘Religion [you can also say ‘ideology’ – JW] divides people, logic brings them together.’ The final paper, by Victor Marek and myself, provides some details about the situation of logic in Poland after 1945. Although the material covered by the particular contributions is quite selective, I hope that they form a general picture of the Polish school of logic and its achievements.