Racjonalność bez granic. Dwie próby odpowiedzi

Abstract

In the history of the human knowledge the question about the principles of rationality has always been very important. One of the main aspects of this question is the problem of the limits of rational thinking. The way of thinking typical for mathematics has always been taken as a model of rationality. In the present paper I try to describe two attempts in the philosophy of mathematics which tried to form this branch of science as a strict, consistent domain. These attempts were: logicism created by B. Russell and A. N. Whitehead and the program of formalism proposed by D. Hilbert. Both logicism and formalism met many difficulties. In 1931 Kurt Gödel published his famous theorem that showed that the limits of rational thinking are based on the principles of this very thinking. This and others theorems, as for example theorems of Church or Skolem-Löwenheim, though they deal with meta-theoretical properties of formal systems, have their importance for every kind of rational thinking.