The author discusses Gödel’s Incompleteness Theorem and its implications for formal systems. They explain that no powerful enough system can be both complete and consistent. They introduce Rosser’s Theorem as a way to strengthen Gödel’s original argument. The author then presents a Turing-machine-based proof of Rosser’s Theorem, highlighting the connection between Gödel’s Theorem and Turing’s Theorem on the unsolvability of the halting problem. This article challenges the traditional view of Gödel’s Theorem and suggests that the importance of Turing machines in understanding these concepts cannot be overstated. The use of Rosser’s Theorem in place of Gödel’s is innovative and thought-provoking.
https://scottaaronson.blog/?p=710