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Penrose’s Philosophical Error

  • L. J. Landau
Part of the Perspectives in Neural Computing book series (PERSPECT.NEURAL)

Abstract

Computer learning techniques, as embodied in neural networks, are modelled on the way we learn and make decisions. With the ever greater power of computers, one may wonder if a point might be reached when it could be said that the computer has become conscious, that it behaves in the way that a thinking human being behaves. In his book Shadows of the Mind, Roger Penrose argues that our conscious mentality cannot be fully understood in terms of computational models, using mathematical theorems due to Gödel and Turing. The mathematics of computation and formal systems is developed in some detail, and it is shown that Penrose’s argument does not work.

Keywords

True Statement Formal System Function Symbol Mathematical Belief Arithmetical Procedure 
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.

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Bibliography

  1. [1]
    M.A. Boden, Escaping from the Chinese Room, in The Philosophy of Artificial Intelligence, ed. M.A.Boden, (Oxford University Press, 1990), pp.40–66Google Scholar
  2. [2]
    L. Boltzmann and B. McGuinness, Theoretical Physics and Philosophical Problems, vol.5 (D. Reidel Publishing Company, 1974) p.57CrossRefGoogle Scholar
  3. [3]
    L.E.J. Brouwer, Life, Art and Mysticism 1905 exerpts; in Collected Works 1, ed. A.Heyting, (North-Holland, 1975)Google Scholar
  4. [4]
    J.N. Crossley, et.al., What is Mathematical Logic?, (Oxford University Press, 1978)Google Scholar
  5. [5]
    G. Chaitin, Gödel’s Theorem and Information, International Journal of Theoretical Physics 22 (Plenum Publishing Corp., 1982) pp.941–954; reprinted in G.J. Chaitin,Information, Randomness, and Incompleteness (World Scientific, 1987)Google Scholar
  6. [6]
    P.J. Cohen, Comments on the Foundations of Set Theory, in Proceedings of the Symposia in Pure Mathematics Volume XIII Part I, (American Mathematical Society, 1971)Google Scholar
  7. [7]
    N.J. Cutland, Computability, (Cambridge University Press, 1980)zbMATHGoogle Scholar
  8. [8]
    D.C. Dennett, Brainstorms, (Harvester Wheatsheaf, 1981)Google Scholar
  9. [9]
    K. Fulves, Self-Working Number Magic (Dover, 1983)Google Scholar
  10. [10]
    J. Kalckar, Niels Bohr and his youngest disciples; in S. Rozental, ed., Niels Bohr: His life and work as seen by his friends and colleagues, (North-Holland, 1967)Google Scholar
  11. [11]
    R. Kirk, Mental Machinery and Gödel, Synthese 66 (D. Reidel Publishing Company, 1986) pp.437–452Google Scholar
  12. [12]
    M. Kline, Mathematics: The Loss of Certainty, (Oxford University Press, 1982)Google Scholar
  13. [13]
    J. Lucas, Minds, Machines and Gödel, Philosophy, Vol.XXXVI (Cambridge University Press, 1961); reprinted in Minds and Machines, ed. A.R. Anderson, (Prentice Hall, 1964)Google Scholar
  14. [14]
    R. Penrose, Shadows of the Mind, (Vintage, 1995)zbMATHGoogle Scholar
  15. [15]
    R. Penrose, Psyche, Volume 2, Number 1 (1996) pp.89–129Google Scholar
  16. [16]
    H. Putnam, The Best of all Possible Brains (Review of Shadows of the Mind by R. Penrose), New York Times, 20 November 1994.Google Scholar
  17. [17]
    H. Putnam, Mathematics without foundations, Journal of Philosophy 64 (Journal of Philosophy Inc., 1967) pp.5–22; reprinted in Philosophy of Mathematics, edited by P. Benacerraf and H. Putnam, (Cambridge University Press, 1985)Google Scholar
  18. [18]
    D. Ruelle, Chance and Chaos, (Princeton University Press, 1991)Google Scholar
  19. [19]
    B. Russell, Portraits from Memory, Bertrand Russell Peace Foundation (George Allen and Unwin, 1956)Google Scholar
  20. [20]
    B. Russell, My Philosophical Development (Unwin, 1975).Google Scholar
  21. [21]
    A. Scott, Stairway to the Mind, (Copernicus, 1995)Google Scholar
  22. [22]
    J.R. Searle, Minds, Brains, and Programs, Behavioral and Brain Sciences 3 (Cambridge University Press, 1980) 417–24, reprinted in The Philosophy of Artificial Intelligence, ed. M.A. Boden, (Oxford University Press, 1990), pp.67–88Google Scholar
  23. [23]
    J.C. Shepherdson and H.E.Sturgis, ‘Computability of Recursive Functions’, J. Assoc. Computing Machinery 10 (1963) 217–255MathSciNetzbMATHCrossRefGoogle Scholar
  24. [24]
    A. Turing, Computing Machinery and Intelligence, Mind 59 No.236 (Oxford University Press, 1950) 433–460, reprinted in The Philosophy of Artificial Intelligence, ed. M.A. Boden, (Oxford University Press, 1990), pp.40–66Google Scholar
  25. [25]
    A. Turing, Systems of Logic Based on Ordinals, P. Lond. Math. Soc. (2) 45 (1939) 161–228CrossRefGoogle Scholar
  26. [26]
    J. von Neumann, The Mathematician. “Works of the Mind.” in Collected Works Volume 1, ed. A.H. Taub, (Pergamon Press, 1961)Google Scholar
  27. [27]
    J. von Neumann, The Computer and the Brain, (Yale University Press, 1958)zbMATHGoogle Scholar
  28. [28]
    K. Warwick, March of the Machines, (Century, 1997)Google Scholar

Copyright information

© Springer-Verlag London Limited 1998

Authors and Affiliations

  • L. J. Landau
    • 1
  1. 1.Department of MathematicsKing’s College LondonUK

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