Philosophy of logic and mathematics in Warsaw School

The aim of the talk is to analyze main trends and tendencies, main standpoints and views in the philosophical reflection on mathematics and logic in Warsaw School between the wars. This was the time of intensive development of mathematics (Polish Mathematical School) and of logic (Warsaw Logical School, Lvov-Warsaw Philosophical School) in Poland. Hence a natural question arises whether this development of mathematics and logic was accompanied by philosophical reflection on those disciplines, whether the researches were founded on and stimulated by certain fixed philosophical presuppositions. On the other hand philosophy of mathematics and logic is based on and uses certain results of metamathematics, of the foundations of mathematics and of logic. Did logical achievements influence the philosophical reflection?
The philosophical views of main logicians and mathematician (among them of Tarski and Mostowski) will be presented and analyzed.
We come to the conclusion that Polish logicians and mathematicians being convinced of the importance of philosophical problems and knowing quite well the current philosophical trends treated logic and mathematics as autonomous disciplines independent of philosophical reflection on them, independent of any philosophical presuppositions. Therefore they sharply separated mathematical and logical research practice and philosophical discussions concerning logic and mathematics. Philosophical views and opinions were treated as "private" matter that should not influence the mathematical and metamathematical investigations. On the contrary, in the latter all correct methods could and should be used. This "methodological Platonism" enabled Polish logicians and mathematicians to work in various areas without being preoccupied by philosophical dogmas. In controversial cases, as for example in the case of the axiom of choice in set theory, their attitude can be characterized as neutral - without making any philosophical declarations they simply considered and studied various mathematical consequences of both accepting and rejecting the controversial principles and investigated their role in mathematics.