526 | NOTES TO PAGES 438–441
- See W. Aspray, ‘Oswald Veblen and the origins of mathematical logic at Princeton’, in T. Drucker (ed.),
Perspectives on the History of Mathematical Logic, Birkhäuser (1991), 54–70. - See I. Grattan-Guinness, ‘Re-interpreting “λ”: Kempe on multisets and Peirce on graphs, 1886–1905’,
Transactions of the C. S. Peirce Society, 38 (2002), 327–50. - See M. Hallett, Cantorian Set Theory and Limitation of Size, Clarendon Press (1984), Chapter 8.
- A. Tarski, Introduction to Logic and to the Methodology of the Deductive Sciences (transl. O. Helmer),
1st edn, Oxford University Press (1941), 125–30. - See I. Grattan-Guinness, ‘The reception of Gödel’s 1931 incompletability theorems by mathemati-
cians, and some logicians, up to the early 1960s’, in M. Baaz, C. H. Papadimitriou, H. W. Putnam, D.
S. Scott, and C. L. Harper (eds), Kurt Gödel and the Foundations of Mathematics. Horizons of Truth,
Cambridge University Press (2011), 55–74. - Hodges (1983), pp. 109–14.
- Turing (1936).
- See I. Grattan-Guinness, ‘The mentor of Alan Turing: Max Newman (1897–1984) as a logician’,
Mathematical Intelligencer, 35(3) (September 2013), 54–63. - See also B. J. Copeland, ‘From the Entscheidungsproblem to the Personal Computer’, in M. Baaz, C. H.
Papadimitriou, H. W. Putnam, D. S. Scott, and C. L. Harper (eds), Kurt Gödel and the Foundations of
Mathematics. Horizons of Truth, Cambridge University Press (2011), 151–84. - The Newman Archive is in St John’s College, Cambridge; thanks to David Anderson much of it is
available in digital form at http://www.cdpa.co.uk/Newman/. Individual items are cited in the style
‘NA, [box] a- [folder] b- [document] c’; here 2–12–3. - A Mathematical Tripos course in ‘logic’ was launched in 1944 by S. W. P. Steen; the Moral Sciences
Tripos continued to offer its long-running course on the more traditional parts of ‘logic’. - For Turing’s teaching, see Hodges (1983), pp. 153, 157, and the Faculty Board minutes for 29 May 1939.
- M. H. A. Newman, ‘Stratified systems of logic’, Proceedings of the Cambridge Philosophical Society,
39 (1943), 69–83; M. H. A. Newman and A. Turing, ‘A formal theorem in Church’s theory of types’,
Journal of Symbolic Logic, 7 (1943), 28–33. - M. H. A. Newman, ‘On theories with a combinatorial definition of “equivalence” ’, Annals of
Mathematics, 43 (1942), 223–43. For a discussion see J. R. Hindley, ‘M. H. Newman’s typability algo-
rithm for lambda-calculus’, Journal of Logic and Computation, 18 (2008), 229–38. - W. Newman, ‘Max Newman—mathematician, codebreaker, and computer pioneer’, in Copeland et al.
(2006), 176–88. - See J. F. Adams, ‘Maxwell Herman Alexander Newman, 7 February 1897–22 February 1984’,
Biographical Memoirs of Fellows of the Royal Society, 31 (1985), 436–52. - M. Gardiner, A Scatter of Memories, Free Association Books (1988), pp. 61–8.
- The Wirtinger letter is in the Newman Archive (Note 15), item 2–1–2.
- K. Gödel, ‘Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I’,
Monatshefte für Mathematik und Physik, 38 (1931), 173–98. - For the Vienna Circle see F. Stadler, The Vienna Circle, Springer (2001). For Hahn see K. Sigmund,
‘A philosopher’s mathematician: Hans Hahn and the Vienna Circle’, Mathematical Intelligencer, 17(4)
(1995), 16–19. - M. H. A. Newman, ‘On approximate continuity’, Transactions of the Cambridge Philosophical Society,
23 (1923), 1–18. For the context see F. A. Medvedev, Scenes from the History of Real Functions (transl.
R. Cooke), Birkhäuser (1991). - M. H. A. Newman, ‘The foundations of mathematics from the standpoint of physics’, manuscript
dated 1923, Newman Archive (Note 15), item F 33.1. - D. Hilbert, ‘Die logischen Grundlagen der Mathematik’, Mathematische Annalen, 88 (1922), 151–65
(also in Gesammelte Abhandlungen, Vol. 3, Springer (1935), 178–91). - L. E. J. Brouwer, ‘Begründung der Mengenlehre unabhängig vom logischen Satz von ausgeschloss-
enen Dritten’ Erster Teil, Allgemeine Mengenlehre, Verhandlingen der Koninklijke Akademie
van Wetenschappen te Amsterdam, 12(5) (1918), 1–43; Zweite Teil, Theorie der Punktmengen, 7
(1919), 1–33; also in Collected Works, Vol. 1, North-Holland (1975), 150–221; C. H. H. Weyl. ‘Über