Today, 1978, Vintage Books Edition, New York, 1980. His chapter describes Turing machines in the terms of the simpler Post–Turing machine, then proceeds onward with descriptions of Turing's first proof and Chaitin's contributions. Andrew Hodges, Alan Turing: The Enigma, Simon and Schuster, New York. Cf Chapter "The Spirit of Truth" for a history leading to, and a discussion of, his proof. Hans Reichenbach, Elements of Symbolic Logic, Dover Publications Inc., New York, 1947. A reference often cited by other authors. Ernest Nagel and James Newman, Gödel's Proof, New York University Press, 1958. Edward Beltrami, What is Random? Chance and Order in Mathematics and Life, Springer-Verlag New York, Inc., 1999. Torkel Franzén, Godel's Theorem, An Incomplete Guide to Its Use and Abuse, A.K. Peters, Wellesley Mass, 2005. A recent take on Gödel's Theorems and the abuses thereof. Not so simple a read as the author believes it is. Franzén's (blurry) discussion of Turing's 3rd proof is useful because of his attempts to clarify terminology. Offers discussions of Freeman Dyson's, Stephen Hawking's, Roger Penrose's and Gregory Chaitin's arguments (among others) that use Gödel's theorems, and useful criticism of some philosophic and metaphysical Gödel-inspired dreck that he's found on the web. Pavel Pudlák, Logical Foundations of Mathematics and Computational Complexity. A Gentle Introduction, Springer 2013. (See Chapter 4 "Proofs of impossibility".) Mathematical logic Mathematical proofs Methods of proof Possibility