Proof Sketch

Having acquired the necessary knowledge in Chap. 2 to comprehend both the formal details and the philosophical dimensions of the incompleteness theorems, the time has come to return to Gödel’s work. In the few passages quoted so far, Gödel had taken stock of the mathematics of the early twentieth century. With the Principia Mathematica and the Zermelo-Fraenkel set theory, he mentioned two of the predominant axiomatic systems of that era. While these terms were still empty shells towards the end of Chap. 1 , they appear in bright colors before our mind’s eye after our historical excursion. We are now well-equipped to master the rest of Gödel’s work. So let us listen again!