Doing Justice to the Imitation Game

A Farewell to Formalism
  • Jean Lassègue


My claim in this article is that the 1950 paper in which Turing describes the world-famous set-up of the Imitation Game is much richer and intriguing than the formalist ersatz coined in the early 1970s under the name “Turing Test”. Therefore, doing justice to the Imitation Game implies showing first, that the formalist interpretation misses some crucial points in Turing’s line of thought and second, that the 1950 paper should not be understood as the Magna Chartaof strong Artificial Intelligence (AI) but as a work in progressfocused on the notion of Form. This has unexpected consequences about the status of Mind, and from a more general point of view, about the way we interpret the notions of Science and Language.


Determinism formalism gender difference geometry mental processes 


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  1. Boden, M., ed., 1990, Introduction, in: The Philosophy of Artificial Intelligence, Oxford University Press, Oxford.Google Scholar
  2. Brouwer, L. E. J., 1913, Intuitionism and formalism, Bulletin of the American Mathematical Society 20: 81–96.MathSciNetGoogle Scholar
  3. Cantor, G., 1932, Gesammelte Abhandlungen mathematischen und philosophischen Inhalts. Mit erläuternden Anmerkungen sowie mit Ergänzungen aus dem Briefwechsel Cantor-Dedekind, E. Zermelo, ed., Springer, Berlin.Google Scholar
  4. Church, A., 1937, Review of Turing 1936, The Journal of Symbolic Logic 2: 42–43.CrossRefGoogle Scholar
  5. Dupuy, J.P., 2000, The Mechanization of the Mind: On the Origins of Cognitive Science, Princeton University Press, Princeton, NJ.Google Scholar
  6. Feferman, S., 1987, Weyl vindicated: “Das Kontinuum” 70 years later, in: Temi e Prospettiva della logica e della filosofia della scienza contemporanea, CLUEB, Bologna, pp. 59–93.Google Scholar
  7. French, R. M., 1990, Subcognition and the limits of the Turing Test, Mind 99: 53–65.CrossRefMathSciNetGoogle Scholar
  8. Frege, G., 1884, Grundlagen der Arithmetik, Marcus, Breslau.Google Scholar
  9. Gandy, R., 1988, The confluence of ideas in 1936, in: The Universal Turing Machine; a Half- Century Survey. R. Herken, ed., Oxford University Press, Oxford, pp. 55–111.Google Scholar
  10. Girard, J.Y., 2001, Locus solum, Mathematical Structures in Computer Science 11(3).Google Scholar
  11. Gödel K., 1931, Über formal entscheidbare sätze der principia mathematica und verwandter systeme, Monatshefte für Math. Physik, 38: 173–198; reprinted in 1986, Gödel’s Collected Works, S. Feferman, et al., eds., 1: 144–195.CrossRefGoogle Scholar
  12. Guillaume, M., 1994, La logique mathèmatique en sa jeunesse : Essai sur l’histoire de la logique dans la première moitiè du vingtième siècle, in: Development of Mathematics 1900–1950. J. P. Pier, ed., Birkhaüser Verlag, Basel.Google Scholar
  13. Hallett, M., 1994, Hilbert’s axiomatic method and the laws of thought, in: Mathematics and Mind, A. George, ed., Oxford University Press, Oxford, pp. 158–200.Google Scholar
  14. Haugeland, J., 1985, Artificial Intelligence, the Very Idea, MIT Press, Cambridge, MA.Google Scholar
  15. Hilbert, D., 1899, Grundlagen der Geometrie, Teubner, Berlin.Google Scholar
  16. Hilbert, D., 1917, Axiomatisches denken, Mathematische Annalen 78(1918): 405–415.zbMATHCrossRefMathSciNetGoogle Scholar
  17. Hilbert, D., 1923, Die logischen grundlagen der mathematik, Mathematische Annalen 88(1923): 151–165.MathSciNetGoogle Scholar
  18. Hilbert, D., 1925, Über das unendliche, Mathematische Annalen 95(1926): 161–190.zbMATHMathSciNetGoogle Scholar
  19. Hodges, A., 1988, Alan Turing and the Turing machine, The Universal Turing Machine, R. Herken, ed., Oxford University Press, Oxford, pp. 3–15.Google Scholar
  20. Hodges, A., 1997, Turing: A Natural Philosopher, Phoenix, London.Google Scholar
  21. Hofstadter, D. and Dennett, D., 1981, The Mind’s I, Basic Books, New York.zbMATHGoogle Scholar
  22. Lachterman, D. R., 1989, The Ethics of Geometry: A Genealogy of Modernity, Routledge, New York/London.Google Scholar
  23. Lassègue, J., 1993, Le test de Turing et l’ènigme de la diffèrence des sexes, in: Les Contenants de Pensèe, D. Anzieu et al., ed., Dunod, Paris, pp. 145–195.Google Scholar
  24. Lassègue, J., 1996, What kind of Turing Test did Turing have in mind? Tekhnema; Journal of Philosophy and Technology 3: 37–58; Google Scholar
  25. Lassègue, J., 1998a, Turing, l’ordinateur et la morphogenèse”, La Recherche 305(Jan): 76–77.Google Scholar
  26. Lassègue, J., 1998b, Turing, Les Belles Lettres, Paris, published, (2003), as De la logique du mental à la morphogenèse de l’idèe, dossier Les constructivismes in: Intellectica, M. -J. Durand, ed., Paris; Google Scholar
  27. Leiber J., 1991, An Invitation to Cognitive Science, Basil Blackwell, Oxford.Google Scholar
  28. Longo, G., 1999, The difference between clocks and Turing machines, in: Functional Models of Cognition, Kluwer, Boston, MA;
  29. Longo, G., 2001, Laplace in Locus Solum (see Girard J. Y.);
  30. Longo, G., 2005, The reasonable effectiveness of mathematics and its cognitive roots, in: Geometries of Nature, Living Systems and Human Cognition: New Interactions of Mathematics with Natural Sciences, L. Boi, ed., World Scientific.Google Scholar
  31. Longo, G., 2008, Laplace, Turing and the “Imitation Game”. In R. Epstein, G. Roberts and G. Beber, eds., Parsing the Turing Test, Springer, Dortrecht, The Netherlands.Google Scholar
  32. McCulloch W. S. and Pitts W. H., 1943, A logical calculus of the ideas immanent in nervous activity, Bulletin of Mathematical Biophysics, 5: 115–133.zbMATHCrossRefMathSciNetGoogle Scholar
  33. Michie, D., 1974, On Machine Intelligence, Wiley New York.Google Scholar
  34. Peano, G., 1899, Arithmetices principia, nova methodo exposita, Augustae Taurinorum, ed., Bocca, Turin.Google Scholar
  35. Penrose, R., 1989, The Emperor’s New Mind : Concerning Computers, Minds and the Laws of Physics, Oxford University Press, Oxford.Google Scholar
  36. Poincarè, H., 1913, Dernières pensèes, Flammarion, Paris.Google Scholar
  37. Riemann, B., 1854, Über die hypothesen, welche der geometrie zu grunde liegen, Abhandlungen der königlichen Gesellschaft der Wissenschaften, in: Göttingen 13: 133–150;
  38. Stewart, J., 2000, Teleology in biology, Tekhnema; Journal of Philosophy and Technology 6: 14–33.Google Scholar
  39. Turing, A. M., 1936, On computable numbers with an application to the Entscheidung’s problem, Proceedings of the London Mathematical Society 42: 230–265; reprinted in: R. O. Gandy and C. E. M Yates,eds., Collected Works of A. M. Turing, vol. 4, Mathematical Logic 4:
  40. Turing, A. M., 1939, Systems of logic based on ordinals, Proceedings of the London Mathematical Society 45(ser 2): 161–228; reprinted in: R. O. Gandy and C. E. M. Yates, , eds., Collected Works of A. M. Turing, vol. 4, Mathematical Logic 4.Google Scholar
  41. Turing, A. M., 1949, The word problem in semi-groups with cancellation, Annals of Mathematics 52(2): 491–505; reprinted in: J. L. Britton, ed., Collected Works of A. M. Turing, vol. 2, Pure Mathematics 2.Google Scholar
  42. Turing, A. M., 1950, Computing machinery and intelligence, Mind 59(236): 433–460.CrossRefMathSciNetGoogle Scholar
  43. Turing, A. M., 1952, The Chemical basis of morphogenesis, Philosophical transactions of the Royal Society of London. Series B, Biological sciences 237: 37–72; reprinted in: P. T Saunders, ed., Collected Works of A. M. Turing, vol. 3, Morphogenesis 2: 1–36.Google Scholar
  44. Wagner, P., 1994, Machine et pensèe: l’importance philosophique de l’informatique et de l’intelligence artificielle, Doctoral thesis, Universitè Paris 1.Google Scholar
  45. Weyl, H., 1918, Das Kontinuum: Kritische Untersuchungen über die Grundlagen der Analysis, Veit Verlag, Leipzig.Google Scholar

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© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Jean Lassègue
    • 1
  1. 1.Laboratoire CREA-CNRSEcole PolytechniqueParisFrance

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