Gödel's theorems presuppose the meaningfulness of infinitary processes. Zeilberger and I touch briefly on it in this interview: https://www.youtube.com/watch?v=uNYRUUkuhuo
YouTube Ep. 97 - Math Heresy: Ultrafinitism | Dr. Doron Zeilberger Dr. Doron Zeilberger is the Distinguished Professor of Mathematics at Rutgers University. He's also a math heretic who thoroughly rejects the orthodox concep...