Philosophical reflection on mathematics in Poland in the interwar period

AbstractIn the paper the views and tendencies in the philosophical reflection on mathematics in Poland between the wars are analyzed. Views of most outstanding representatives of Lvov–Warsaw Philosophical School and of Polish Mathematical School are presented. Their influence on logical and mathematical researches is considered

Troubles with (the concept of) truth in mathematics

In the paper the problem of definability and undefinability of the concept of satisfaction and truth is considered. Connections between satisfaction and truth on the one hand and consistency of certain systems of omega-logic and transfinite induction on the other are indicated

Church's thesis and its epistemological status

The aim of this paper is to present the origin of Church's thesis and the main arguments in favour of it as well as arguments against it. Further the general problem of the epistemological status of the thesis will be considered, in particular the problem whether it can be treated as a definition and whether it is provable or has a definite truth-value

Związki Szkoły Lwowsko-Warszawskiej i Uniwersytetu w Poznaniu

The Lvov-Warsaw School in Philosophy – as the very name suggests – was connected mainly with two academic centers: universities in Lvov and Warsaw. However, it had a broader impact. The members of this school were active also at other universities, in particular in Cracow, Vilnius and Poznań. The aim of the paper is to present and analyze the connections of Lvov-Warsaw School with the university in Poznań.Szkoła Lwowsko-Warszawska – jak wskazuje sama nazwa – związana była glównie z dwoma ośrodkami akademickimi: uniwersytetami we Lwowie i w Warszawie. Jednakże jej wpływ był znacznie szerszy, uczeni będący członkami tej szkoły byli aktywni także w innych uniwersytetach, w szczególności w Krakowie, Wilnie i Poznaniu. Celem tej pracy jest prezentacja i analiza związków Szkoły Lwowsko-Warszawskiej i uniwersytetu w Poznaniu

Decidability vs. undecidability. Logico-philosophico-historical remarks

The aim of the paper is to present the decidability problems from a philosophical and historical perspective as well as to indicate basic mathematical and logical results concerning (un)decidability of particular theories and problems

Truth vs. provability – philosophical and historical remarks

Since Plato, Aristotle and Euclid the axiomatic method was considered as the best method to justify and to organize mathematical knowledge. The first mature and most representative example of its usage in mathematics were Elements of Euclid. They established a pattern of a scientific theory and in particular a paradigm in mathematics

Badania logiczne prowadzone w Uniwersytecie Poznańskim w latach 1945 - 1955

This paper is a synopsis of a more comprehensive work presented at the conference 50 years of Studia Logica in 2003. The full English version of the text will be published elsewhere. The text below is devoted to the presentation of logical investigations carried out at the University of Poznań in the first decade after its reopening in 1945, i.e. at the time when and at the place where Studia Logica came into existence. This paper is a synopsis of a more comprehensive work presented at the conference 50 years of Studia Logica in 2003. The full English version of the text will be published elsewhere. The text below is devoted to the presentation of logical investigations carried out at the University of Poznań in the first decade after its reopening in 1945, i.e. at the time when and at the place where Studia Logica came into existence.

Stanisław Piątkiewicz and the Beginnings of Mathematical Logic in Poland

AbstractThis paper presents information on the life and work of Stanisław Piątkiewicz (1849–?). HisAlgebra w logice(Algebra in Logic) of 1888 contains an exposition of the algebra of logic and its use in representing syllogisms. This was the first original Polish publication on symbolic logic. It appeared 20 years before analogous works by Łukasiewicz and Stamm.In dem Aufsatz werden Informationen zu Leben und Werk von Stanisław Piątkiewicz (1849–?) gegeben. SeinAlgebra w logice(Algebra in der Logik) von 1888 enthält eine Darstellung der Algebra der Logik und ihre Anwendung auf die Syllogistik. Piątkiewicz' Schrift war die erste polnische Publikation über symbolische Logik. Sie erschien 20 Jahre vor ähnlichen Arbeiten von Łukasiewicz und Stamm.W pracy przedstawiono osobę i dzieło Stanisława Piątkiewicza (1849–?). W szczególności analizuje się jego rozprawęAlgebra w logicez roku 1888, w której zajmował się on nowymi nówczas ideami algebry logiki oraz ich zastosowaniami do sylogistyki. Praca ta jest pierwszą oryginalną polską publikacją z zakresu logiki symbolicznej. Ukazała się 20 lat przed analogicznymi pracami Łukasiewicza i Stamma

What do mathematicians dispute about, or on the ontological status of the objects of mathematics

In this article the author considers various conceptions concerning ontological status of the objects of mathematics. The relation is show between these problems and a dispute over universals, and then Platonism, conceptualism and nominalism as the fundamental standpoints on the question o f mathematical objects are presented. Examples are given of concrete (specific) theories w ith in these standpoints and their implications (also epistemological ones) are shown.In this article the author considers various conceptions concerning ontological status of the objects of mathematics. The relation is show between these problems and a dispute over universals, and then Platonism, conceptualism and nominalism as the fundamental standpoints on the question o f mathematical objects are presented. Examples are given of concrete (specific) theories w ith in these standpoints and their implications (also epistemological ones) are shown