The Scandinavian Logic Society

NOL Seminar with Jan van Plato

The Nordic Online Logic Seminar is organised monthly over Zoom, with expository talks on topics of interest for the broader logic community. The seminar is open for professional or aspiring logicians and logic aficionados worldwide. If you wish to receive the Zoom ID and password for it, as well as further announcements, please subscribe here: https://listserv.gu.se/sympa/subscribe/nordiclogic.

Next talk: Monday, September 26, 16.00-17.30 CEST (UTC+2), on Zoom (details are provided to the seminar subscribers)

Speaker: Jan von Plato, University of Helsinki

Title: Gödel’s work in logic and foundations in the light of his shorthand notebooks

The study of Gödel’s shorthand notebooks in the ERC project GODELIANA has revealed two main aspects of his work: First, there is behind each of his relatively few published papers an enormous amount of notes. They typically reveal how he arrived at his results, as with the incompleteness theorem. An extreme case are Gödel’s 1938 results on set theory, preceded by some 700 pages of notes never studied before. Secondly, his threshold for publishing was by 1940 so high that some two thousand pages of developments and results remained unknown. One highlight here is a series of notebooks titled “Resultate Grundlagen” in which numerous anticipations of later results in set theory are found. A second main topic are the relations between modal and intuitionistic logic. In particular, Gödel gives a syntactic translation from S4 to intuitionistic logic by methods that are readily generalizable to any decent intermediate logics. These newly discovered methods are, even by today’s standards, a clear step ahead in the study of interrelations between systems of non-classical logics.