Reactions to the discovery of the incompleteness phenomenon

Roman Murawski

pp. 213-227

in: Jaakko Hintikka, Tadeusz Czarnecki, Tomasz Placek, Artur Rojszczak (eds), Philosophy and logic in search of the Polish tradition, Berlin, Springer, 2003

Abstract

Gödel's incompleteness theorems belong to the most important results of logic and the foundations of mathematics. They indicated the phenomenon of incompleteness of first order systems and in this way struck Hilbert's program of clarification and justification of the classical (infinite) mathematics by finitistic methods. They showed that this program cannot be fully realized in the original form by indicating some limitations of the axiomatic-deductive method.¹