FRANCESCO BERTO. There's Something about Godel. Malden, Mass., and Oxford: Wiley-Blackwell, 2009. ISBN 978-1-4051-9766-3 (hbk); 978-1-4051-9767-0 (pbk). Pp. xx + 233. English translation of Tutti pazzi per Godel! (Rome: Gius, Laterza & Figli, 2008)

Abstract

There's Something about Gödel is a bargain: two books in one. The first half is a gentle but rigorous introduction to the incompleteness theorems for the mathematically uninitiated. The second is a survey of the philosophical, psychological, and sociological consequences people have attempted to derive from the theorems, some of them quite fantastical. The first part, which stays close to Gödel's original proofs, strikes a nice balance, giving enough details that the reader understands what is going on in the proofs, without giving so many that the reader feels overburdened. Perhaps he skimps too much on details, as when he decides not to explain how to convert recursive definitions into explicit ones. Also, I wish he had talked about Löb's theorem. But these are small complaints. The second half discusses a sampling of what one reads about Gödel's theorems in philosophy journals and in the popular press, and here Berto often finds himself exasperated, especially by the postmodernists. One only has to set what Gödel proved alongside what the postmodernist philosophers say Gödel proved to share his sense of bewilderment. Berto's ally in the effort to separate the real content of Gödel's theorem from the cultural chaff that clings to it is Torkel Franzén [2005], on whose ideas Berto frequently relies.