Godel, Tarski, and a Typo

I think it was two winters ago I decided to read Godel's On Formally Undecidable Propositions of Principia Mathematica and Related Systems one more time for comprehension. I pushed the project through in less than two weeks. I gained a greater appreciation of how recursive relations create the bridge between the formal and metamathematical worlds.

However, I felt I had arrived when I discovered a nasty type on page 59 of the Dover edition, right in the heart of the proof of Proposition VI leading to the first incompleteness theorem. I wrote an outline of the paper for later reference.

I had been studying the logic papers of Alfred Tarski for several years. If anyone could claim to be a peer of Kurt Godel, it would be Tarski. His logic papers are the most elegant writing about logic you will ever find. I decided to reread several of his papers to see how it felt in retrospect of my last reading of Godel. As usual, I picked up new insights from reading them.

After I finished reading the papers, I decided to read the article Tarski wrote in the June, 1969, issue of Scientific American, Truth and Proof. The article is pure Tarski. You can't find a better explanation about what is going on in the mathematical logic game. His discussion of incompleteness, delivered in a short section at the end of the article, is stunningly simple, yet profound at the same time.

I felt I had hiked a ways into the forest and mountains with two geniuses. I was glad that life had afforded me the means to do it.