The philosophical problem of implicit commitment can be roughly stated in the form:
(*) What are we implicitly committed to, in accepting a theory S? Which principles and inferences can we justifiably accept?
As is well-known, (*) has its roots in work by Georg Kreisel in the fifties. Solomon Feferman proposed systematic solutions over the years, starting already in the sixties and the early seventies with the work on Predicative Analysis, and culminating in 1991 with the investigation of self-referential truth. This approach was eventually transformed by Feferman himself, in cooperation with Thomas Strahm in 2000, and by Strahm alone in 2017, also with his student Sebastian Eberhard. Additional contributions are to be found in Ulrik Buchholtz’s Ph.D. thesis (Stanford 2013).
While the first route – reflecting – directly leads into the land of truth theories, the second route – unfolding – is more mathematical in spirit and drives us to the very notion of operation. Our talk will address the opening question, focusing mainly upon unfolding and in the light of possible formal implementations.
Meetings will be online, via Zoom. To request the access link for the meetings, please write to Daniel Isaacson
Philosophy of Mathematics Seminar Convenors: Daniel Isaacson, Volker Halbach and James Studd