Abstract

This paper describes the enormous impact of Gödel's work on mathematical logic and recursion theory. After a brief description of the major theorems that Gödel proved, it focuses on subsequent work extending what he did, sometimes by quite different methods. The paper closes with a new result, applying Gödel's methods to show that if scientific epistemology could be completely represented by a particular Turing machine, then it would be impossible for us to know that fact