Abstract

The article deals with the evolution of the foundations of arithmetic: from the auspicious beginnings with Frege and Dedekind through the cataclysm of Russell’s antinomy to the late writings of Hilbert and the work of Paul Lorenzen . The proposed historical and dialectic reconstruction does not consist in ad hoc attempts to overcome formal difficulties of the systems in question. It rather shows how Frege’s and Dedekind’s original intentions are to be understood and can partly be justified. For this, Gödel’s famous results are of great importance