The Provability of Consistency. Sergei Artemov

We revisit the foundational question “Can consistency of a theory T be established by means of T?” The usual answer “No, by Gödel’s Second Incompleteness Theorem” is based on two assumptions:

1. Gödel’s internalized consistency formula is the only way to represent consistency.
2. Any contentual reasoning within T internalizes as a formal derivation in T.

We show that already for Peano arithmetic PA both of these assumptions are false: (1) does not cover such legitimate mode of presentation as schemes (think of the Induction scheme), (2) fails for schemes. Based on these observations, we offer a proof of PA-consistency by means of PA and discuss its potential impact.

Logic & Metaphysics Workshop

September 2 GC Closed NO MEETING

September 9 Yael Sharvit, UCLA

September 16  Ole Hjortland and Ben Martin, Bergen

September 23 Alessandro Rossi, StAndrews

September 30 GC Closed NO MEETING

October 7 Dongwoo Kim, GC

October 14 GC Closed NO MEETING

October 21 Rohit Parikh, GC

October 28 Barbara Montero, GC

November 4 Sergei Aretmov, GC

November 11 Martin Pleitz, Muenster

November 18

November 25
December 2 Jessica Wilson, Toronto

December 9 Mark Colyvan, Sydney

December 16  MAYBE A MEETING; MAYBE NOT