‎GÖDEL, KURT.‎
‎Über eine bisher noch nicht benützte Erweiterung des finiten Standpunktes. (In: Dialectica, volume 12, pp.280-87). - [GÖDEL'S FINAL PAPER]‎

‎Neuchâtel, Dialectica, 1958. 8vo. Original printed wrappers. The entire issue 47/48 offered here. Uncut and unopened.‎

Reference : 35481

‎First edition of Gödel's 'Dialectica-paper' in which he presented his consistency proof for arithmetic. In 1931 Gödel formulated and proved his second incompleetness theorem" that the consistency of Peano arithmetic cannot be proved using Peano arithmetic itself or any of its direct extensions. The title of Gödel's famous 1931 paper (Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I) states that it is the first part of several papers. Gödel mentions, in a footnote, that the second part of his paper will deal with the source of the incompleteness of formal systems using the theory of types. But no actual continuation of Gödel's 1931 paper ever appeared. However, in his 1958 ""Dialectica-paper"" (the offered item) Gödel showed how type theory can be used to give a consistency proof for arithmetic. In this paper Gödel furthermore discussed some of the philosophical implications of his results. Paul Bernays thought highly of this paper, and planned to publish an English translation, but during the revision of the paper Gödel became dissatisfied with the philosophical introduction and rewrote it completely. When the proof sheets of the revised paper arrived from the printer, Gödel once again became unpleased with the sections concerning his philosophical views. He never returned the proof sheets. The issue offered, which is a festschrift on the occasion of Paul Bernay's 70th birthday, furthermore contains original contributions by Ackermann, Carnap, Curry, Fraenkel, Robinson, Skolem.‎