Gödel for Goldilocks: A Rigorous, Streamlined Proof of Gödel’s First Incompleteness Theorem, Requiring Minimal Background by Dan Gusfield.
Abstract:
Most discussions of Gödel’s theorems fall into one of two types: either they emphasize perceived philosophical “meanings” of the theorems, and maybe sketch some of the ideas of the proofs, usually relating Gödel’s proofs to riddles and paradoxes, but do not attempt to present rigorous, complete proofs; or they do present rigorous proofs, but in the traditional style of mathematical logic, with all of its heavy notation and difficult definitions, and technical issues which reflect Gödel’s original exposition and needed extensions by Gödel’s contemporaries. Many non-specialists are frustrated by these two extreme types of expositions and want a complete, rigorous proof that they can understand. Such an exposition is possible, because many people have realized that Gödel’s first incompleteness theorem can be rigorously proved by a simpler middle approach, avoiding philosophical discussions and hand-waiving at one extreme; and also avoiding the heavy machinery of traditional mathematical logic, and many of the harder detail’s of Gödel’s original proof, at the other extreme. This is the just-right Goldilocks approach. In this exposition we give a short, self-contained Goldilocks exposition of Gödel’s first theorem, aimed at a broad audience.
Proof that even difficult subjects can be explained without “hand=waiving” or “heavy machinery of traditional mathematical logic.”
I first saw this in a tweet by Lars Marius Garshol.