Jan Wolenski´

CHWISTEK-TARSKI COMPETITION IN LVOV

A Contribution to Social History of Logic

Kazimierz Twardowski became professor of philosophy at the Lvov Univer- sity in 1895 (see Skolimowski 1967, Wolenski´ 1989 for detailed accounts of Twardowski’s activity and the school created by him); although there is a prob- lem whether one should use ›Lvov‹ or ›Lviv‹ (English version of name of this city in Ukrainian), I choose the first possibility, because the paper concerns the period when the city was Polish. Twardowski’s metaphilosophical pro- gram favored logic sensu largo (semiotics plus formal logic plus methodology of science) and he trained several philosophers strongly interested in logic and working in it. Jan Łukasiewicz was the first logician who studied with Twar- dowski. He started to teach logic in 1906 and essentially contributed to formation of the Lvov circle of logicians consisting of Kazimierz Ajdukiewicz, Tadeusz Czezowski,˙ Tadeusz Kotarbinski,´ Stanisław Lesniewski´ and Zygmunt Zawirski as major figures. Although all Lvov logicians in the years 1900–1918 graduated in philosophy, they knew mathematics quite well; in particular, they were influ- enced by Wacław Sierpinski´ and his courses and seminars in set theory (since 1909). The interests of logicians in Lvov were quite extensively stratified and comprised problems from diversified mathematical logic to philosophy of sci- ence and semiotic, for example, logical paradoxes (Ajdukiewicz, Czezowski,˙ Lesniewski,´ Łukasiewicz), existential sentences (Lesniewski),´ the logic of rela- tions (Łukasiewicz), causality (Łukasiewicz), the concept of truth (Twardowski, Łukasiewicz, Lesniewski),´ induction and probability (Łukasiewicz), the principles of contradiction and excluded middle (Lesniewski,´ Łukasiewicz) the criticism of psychologism (Łukasiewicz), modalities (Zawirski), the problem of statements about the future (Kotarbinski,´ Lesniewski).´ The end of World War I brought ’s independence. It also meant that Poles had to build their own academic systems. The renewal of the University became a national enterprise; in fact, it was reopened in 1915, but the war prevented its full activity. Many professors and younger fellows from Lvov, including Kotarbinski,´ Lesniewski,´ Łukasiewicz and Sierpinski´ were called to Warsaw. In 1916 the Committee of the Mianowski Fund, a special institution 230 Jan Wolenski´ supporting Polish science, initiated a discussion about needs of the Polish science. Invited scholars from various fields prepared 44 papers. The needs of mathematics in Poland were reviewed by contributions of Stanisław Zaremba (Krakow) and Zygmunt Janiszewski (Warsaw, formerly Lvov). Although the former paper is almost entirely forgotten, Janiszewski’s contribution (Janiszewski 1918) became extremely important and famous. This paper contains an outline of the future development of mathematics in Poland, called the Janiszewski program. The main idea of the program consisted in promoting various activities for achieving an autonomous position by Polish mathematics. Let me quote the end of Janiszewski 1918 (p. 18): If we do not like to always »to lag behind«, we must apply radical means and go to the fundamentals of what is wrong. We must create a [mathematical] »workshop« at home! However, we may achieve this by concentrating the majority of our mathematicians on working on one selected branch of mathematics. In fact, this takes place automatically nowadays, but we have to help this process. Doubtless, establishing in Poland a special journal devoted to the only selected branch of mathematics, will attract many to research in this field. Yet there is also another advantage of such a journal in building the mentioned »workshop« in ourselves: we would became a technical center for publications in the related field. Others would send manuscripts of new works and have relations with us. If we want to capture the proper position in the world of science, let us come with our own initiative. Although these words are cryptic to some extent, his project became understood univocally: Polish mathematicians should concentrate on set theory and topology as well as their applications to other branches of mathematics. The new journal very soon materialized as Fundamenta Mathematica andwasdevotedtothisarea of mathematical studies. According to the Janiszewski, program logic and the foundations belonged to the hearts of mathematics. This was documented by the fact that the Editorial Board of the journal consisted of two mathematicians (Sierpinski,´ Mazurkiewicz; Janiszewski died in 1920, before the first volume appeared) and two logicians (Lesniewski,´ Łukasiewicz). The first volume of (1920) included eight papers, namely by Stefan Banach (Lvov), Janiszewski (Warsaw), (Warsaw), Stefan Mazurkiewicz (Warsaw), Stanisław Ruziewicz (Lvov), Hugo Steinhaus (Lvov), Sierpinski´ (Warsaw) and Witold Wilkosz (Cracow). This group of authors presents how the map of the Polish mathematical school looked like as far as the involvement into the Janiszewski program is concerned. There were two centers: Lvov and Warsaw, represented by 3 and 4 people, respectively. Yet, although mathematicians working in Lvov and Warsaw accepted the basic points of Janiszewski’s program, there was a considerable difference in scientific interests in both centers of Polish mathematical school. Generally speaking, the Warsaw circle specialized in set theory, topology and mathematical logic, whereas the