G\"odel's Natural Deduction

Abstract

This is a companion to a paper by the authors entitled "G\"odel on deduction", which examined the links between some philosophical views ascribed to G\"odel and general proof theory. When writing that other paper, the authors were not acquainted with a system of natural deduction that G\"odel presented with the help of Gentzen's sequents, which amounts to Ja\'skowski's natural deduction system of 1934, and which may be found in G\"odel's unpublished notes for the elementary logic course he gave in 1939 at the University of Notre Dame. Here one finds a presentation of this system of G\" odel accompanied by a brief reexamination in the light of the notes of some points concerning his interest in sequents made in the preceding paper. This is preceded by a brief summary of G\"odel's Notre Dame course, and is followed by comments concerning G\"odel's natural deduction system.