On Mathematicians Who Liked Logic

The Case of Max Newman
  • Ivor Grattan-Guinness
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7318)

Abstract

The interaction between mathematicians and (formal) logicians has always been much slighter than one might imagine. After a brief review of examples of very partial contact in the period 1850-1930, the case of Max Newman is reviewed in some detail. The rather surprising origins and development of his interest in logic are recorded; they included a lecture course at Cambridge University, which was attended in 1935 by Alan Turing.

Keywords

London Mathematical Society Vienna Circle Logical Pluralism Biographical Memoir Sophical Society 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aspray, W.: Oswald Veblen and the Origins of Mathematical Logic at Princeton. In: Drucker, T. (ed.) Perspectives on the History Of Mathematical Logic, pp. 54–70. Birkhäuser, Boston (1991)Google Scholar
  2. Bottazzini, U.: The Higher Calculus. A History of Real and Complex Analysis from Euler to Weierstrass. Springer, New York (1986)MATHCrossRefGoogle Scholar
  3. Gardiner, M.: A Scatter of Memories. Free Association Books, London (1988)Google Scholar
  4. Gödel, K.: Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme. Monatshefte fu ̈r Mathematik und Physik 38, 173–198 (1931); Many reprs. and transs. Google Scholar
  5. Grattan-Guinness, I.: The Search For Mathematical Roots, 1870-1940. Logics, Set Theories and the Foundations of Mathematics from Cantor through Russell to Gödel. Princeton University Press, Princeton (2000)Google Scholar
  6. Grattan-Guinness, I.: Re-interpreting “\(\rotatebox[origin=c]{180}{\textsf{Y}}\)”: Kempe on Multisets and Peirce on Graphs, 1886-1905. Transactions of the C. S. Peirce Society 38, 327–350 (2002)MathSciNetGoogle Scholar
  7. Grattan-Guinness, I.: The Reception of Gödel’s 1931 Incompletability Theorems by Mathematicians, and Some Logicians, up to the Early 1960s. In: Baaz, M., Papadimitriou, C.H., Putnam, H.W., Scott, D.S., Harper, C.L. (eds.) Kurt Gödel and the Foundations of Mathematics. Horizons of Truth, pp. 55–74. Cambridge University Press, Cambridge (2011)Google Scholar
  8. Grattan-Guinness, I.: Discovering the Logician Max Newman (in preparation, 2012a)Google Scholar
  9. Grattan-Guinness, I.: Logic, Topology and Physics: Max Newman to Bertrand Russell (1928) (in preparation, 2012b) Google Scholar
  10. Hallett, M.: Cantorian Set Theory and Limitation of Size. Clarendon Press, Oxford (1984)Google Scholar
  11. Harris, H.: Lionel Sharples Penrose. Biographical Memoirs of Fellows of the Royal Society 19, 521–561 (1973); Repr. in Journal of Medical Genetics 11, 1–24 (1974)Google Scholar
  12. Hilbert, D.: Die logischen Grundlagen der Mathematik. Mathematische Annalen 88, 151–165 (1922); Repr. in Gesammelte Abhandlungen, vol. 3, pp. 178-191. Springer, Berlin (1935)MathSciNetMATHCrossRefGoogle Scholar
  13. Hodges, A.: Alan Turing: the Enigma. Burnett Books and Hutchinson, London (1983)Google Scholar
  14. Jahnke, N.H.: A History of Analysis. American Mathematical Society, Providence (2003)MATHGoogle Scholar
  15. Kleene, S.C.: Introduction to Metamathematics. van Nostrand, Amsterdam (1952)MATHGoogle Scholar
  16. Kuratowski, K.: A Half Century of Polish Mathematics. Polish Scientific Publishers, Oxford (1980)MATHGoogle Scholar
  17. Medvedev, F.A.: Scenes from the History of Real Functions. Birkhäuser, Basel (1991); translated by R. CookeMATHCrossRefGoogle Scholar
  18. Menzler-Trott, E.: Gentzens Problem. Birkhäuser, Basel (2001); English ed.: Logic’s Lost Genius: the Life of Gerhard Gentzen. American Mathematical Society and London Mathematical Society, Providence (2007)Google Scholar
  19. Moore, G.H.: Zermelo’s Axiom of Choice. Springer, New York (1982)MATHCrossRefGoogle Scholar
  20. Moore-Colyer, R.J.: Rolf Gardiner, English Patriot and the Council for the Church and Countryside. The Agricultural History Review 49, 187–209 (2001)Google Scholar
  21. Newman, M.H.A.: On Approximate Continuity. Transactions of the Cambridge Philosophical Society 23, 1–18 (1923a)Google Scholar
  22. Newman, M.H.A.: The Foundations of Mathematics from the Standpoint of Physics (1923b) manuscript, Saint John College Archives, item F 33.1Google Scholar
  23. Newman, M.H.A.: Mr. Russell’s “Causal Theory of Perception”. Mind 37, 137–148 (1928)CrossRefGoogle Scholar
  24. Newman, M.H.A.: On Theories with a Combinatorial Definition of “Equivalence”. Annals of Mathematics 43, 223–243 (1942)MathSciNetMATHCrossRefGoogle Scholar
  25. Newman, M.H.A.: Stratified Systems of Logic. Proceedings of the Cambridge Philosophical Society 39, 69–83 (1943)MATHCrossRefGoogle Scholar
  26. Newman, M.H.A.: Alan Mathison Turing. Biographical Memoirs of Fellows of the Royal Society 1, 253–263 (1955)CrossRefGoogle Scholar
  27. Newman, M.H.A., Turing, A.: A Formal Theorem in Church’s Theory of Types. Journal of Symbolic Logic 7, 28–33 (1943)MathSciNetGoogle Scholar
  28. Peckhaus, V.: Hilbert, Zermelo und die Institutionalisierung der mathematischen Logik. Deutschland. Berichte zur Wissenschaftsgeschichte 15, 27–38 (1992)MathSciNetMATHCrossRefGoogle Scholar
  29. Peckhaus, V.: Logic in Transition: the Logical Calculi of Hilbert (1905) and Zermelo (1908). In: Prawitz, D., Westerståhl, D. (eds.) Logic and Philosophy of Science in Uppsala, pp. 311–323. Kluwer, Dordrecht (1994)Google Scholar
  30. Roero, C.S., Luciano, E.: La scuola di Giuseppe Peano. In: Roero (ed.) Peano e la sua scuola, Fra matematica, logica e interlingua, Atti del Congresso internazionale di studi, Torino, October 6-7, 2008, vol. xi–xviii, pp. 1–212. Deputazione Subalpina di Storia Patria (2010)Google Scholar
  31. Rosenthal, A.: Neuere Untersuchungen über Funktionen reeller Veränderlichen. In: Encyklopädie der mathematischen Wissenschaften, vol. 2, pt. C, (article IIC9), pp. 851–1187. Teubner, Leipzig (1923)Google Scholar
  32. Russell, B.A.W.: The Analysis of Matter. Kegan Paul, London (1927)Google Scholar
  33. Sieg, W.: Hilbert Programs: 1917-1922. Bulletin of Symbolic Logic 5, 1–44 (1999)MathSciNetMATHCrossRefGoogle Scholar
  34. Sigmund, K.: A Philosopher’s Mathematician: Hans Hahn and the Vienna Circle. The Mathematical Intelligencer 17(4), 16–19 (1995)MathSciNetMATHCrossRefGoogle Scholar
  35. Stadler, F.: The Vienna Circle. Springer, Vienna (2001)Google Scholar
  36. Tarski, A.: Introduction to Logic and to the Methodology of the Deductive Sciences. Oxford University Press, New York (1941); (1st edn., translated by O. Helmer)Google Scholar
  37. Turing, A.M.: On Computable Numbers, with an Application to the Entscheidungsproblem. Proceedings of the London Mathematical Society 42(2), 230–265 (1936)Google Scholar
  38. Weyl, C.H.H.: Über die neue Grundlagenkrise der Mathematik. Mathematische Zeitschrift 10, 39–79 (1921); Repr. in Gesammelte Abhandlungen, vol. 2, pp. 143-180. Springer, Berlin (1968)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ivor Grattan-Guinness
    • 1
  1. 1.Business SchoolMiddlesex UniversityLondonEngland

Personalised recommendations