Letters on Logic to Max Newman (c.1940)

At the outbreak of war with Germany in September 1939, Turing left Cambridge to take up work as a codebreaker at Bletchley Park, the wartime headquarters of the Government Code and Cypher School (see ‘Enigma’, below). In the early months of 1940, Turing received a letter from the Cambridge mathematician M. H. A. Newman, his teacher, colleague, and friend. Turing replied on 23 March, writing from his lodgings at the Crown Inn (situated in the small village of Shenley Brook End): ‘Dear Newman, Very glad to get your letter, as I needed some stimulus to make me start thinking about logic.’ This was to be the first of five letters that Turing wrote to Newman during the seventeen months before Newman too left Cambridge for Bletchley Park. In his first letter Turing agreed (presumably at Newman’s request—Newman’s letters seem not to have been preserved) to ‘let [Newman] in on ... the tricks of the conversion calculus’. The conversion calculus, or ‘λ-calculus’, is due to Alonzo Church, with whom Turing studied in Princeton from 1936 to 1938 (see the introduction to Chapter 3). Turing’s letters consist for the most part of detailed remarks on the conversion calculus, often elucidating material from what Turing calls ‘Church’s notes’—a substantial typescript entitled ‘Mathematical Logic’ which was in circulation at Princeton and elsewhere and which Newman was evidently reading. Their correspondence on Church’s work issued in their joint paper ‘A Formal Theorem in Church’s Theory of Types’, which was submitted to Church’s Journal of Symbolic Logic in May 1941 and published in March 1942. The paper was written while Turing played a leading role in the battle to break Naval Enigma (see ‘Enigma’ and Chapters 5–8). Turing would spend his occasional nights off duty ‘coming in as usual ..., doing his own mathematical research at night, in the warmth and light of the office, without interrupting the routine of daytime sleep’. The two most interesting items of the correspondence, which are printed here, contain substantial passages in which Turing departs from his commentary on Church’s work and expounds his own views.

Academic and Historical Perspectives in Psychology · Computer Science · Mathematics · Philosophy · Philosophy, Science, and History