Jan Woleński

The foundations of mathematics cover mathematical as well as philosophical problems. At the turn of the 20th century logicism, formalism and intuitionism, main foundational schools were developed. A natural problem arose, namely of how much the foundations of mathematics influence the real practice of mathematicians. Although mathematics was and still is declared to be independent of philosophy, various foundational controversies concerned some mathematical axioms, e.g. the axiom of choice, or methods of proof (particularly, non-constructive ones) and sometimes qualified them as admissible (or not) in mathematical practice, relatively to their philosophical (and foundational) content. Polish Mathematical School was established in the years 1915–1920. Its research program was outlined by Zygmunt Janiszewski (the Janiszewski program) and suggested that Polish mathematicians should concentrate on special branches of studies, including set theory, topology and mathematical logic. In this way, the foundations of mathematics became a legitimate part of mathematics. In particular, the foundational investigations should be conducted independently of philosophical assumptions and apply all mathematically accepted methods, finitary or not, and the same concerns other branches of mathematics. This scientific ideology contributed essentially to the remarkable development of logic, set theory and topology in Poland.

Legal theory was the main field of Leon Petrażycki’s investigations. However, his interests also included philosophy, methodology, psychology and sociology. His views in these fields were non-trivial, not only as far as the cognitive horizon of his time was concerned, but also with regard to the present epoche. Particularly significant is the idea of politics of law, i.e. the investigation and prediction of social effects of legal systems.

The aim of this article is to analyse Radbruch’'s formula (lex iniustissima non est lex) with regard to the notions it contains and to indicate that it expresses a basic problem of philosophy of law linked to the discussion between legal positivism and the doctrines of natural law. That analysis underpins the proposal for a possible  rational compromise between the two standpoints. The main problem in the dispute between the rival doctrines amounts to the adoption of some material criterion for defining gross injustice, whilst the background to the dispute is the functioning of the principle which states that law is not retroactive.

This paper describes the philosophy of logic and mathematics in Poland in the years 1918‒1939. The special attention is attributed to the views developed in the Polish Mathematical School and the Warsaw School of Logic. The paper indicates various differences between mathematical circles in Warszawa, Lvov and Kraków.

This paper presents the reception of mathematical logic (semantics and methodology of science are entirely omitted, but the foundations of mathematics are included) in Poland in the years 1870–1920. Roughly speaking, Polish logicians, philosophers and mathematicians mainly followed Boole’s algebraic ideas in this period. Logic as shaped by works of Gottlob Frege and Bertrand Russell became known in Poland not earlier than about 1905. The foundations for the subsequent rapid development of logic in Poland in the interwar period were laid in the years 1915–1920. The rise of Polish Mathematical School and its program (the Janiszewski program) played the crucial role in this context. Further details can be found in [8]. This paper uses the material published in [20‒24].