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The Four Sons of Penrose

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3835))

Abstract

We distill Penrose’s argument against the “artificial intelligence premiss”, and analyze its logical alternatives. We then clarify the different positions one can take in answer to the question raised by the argument, skirting the issue of introspection per se.

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References

  1. Avron, A.: Mishpete Gedel u-ve‘ayat ha-yesodot shel ha-matematikah (= Gödel’s Theorems and the Problem of the Foundations of Mathematics. Broadcast University, Ministry of Defence, Tel Aviv, Israel (1998) (In Hebrew)

    Google Scholar 

  2. Boker, U., Dershowitz, N.: Comparing computational power. Logic Journal of the IGPL (2006) (to appear) available at, http://www.cs.tau.ac.il/~nachum/papers/ComparingComputationalPower.pdf

  3. Chalmers, D. (ed.): Symposium on Roger Penrose’s Shadows of the Mind. Association for the Scientific Study of Consciousness, vol. 2 (1995), Available at, http://psyche.cs.monash.edu.au/psyche-index-v2.html (viewed September 2005).

  4. Chalmers, D.J.: Minds, machines, and mathematics: A review of Shadows of the Mind by Roger Penrose. Psyche: An Interdisciplinary Journal of Research on Consciousness, 2(9) (June 1995), Available at http://psyche.cs.monash.edu.au/v2/psyche-2-09-chalmers.html (viewed September 2005)

  5. Davis, M.: Engines of Logic: Mathematicians and the Origin of the Computer. W. W. Norton & Company, New York (2001)

    Google Scholar 

  6. Dershowitz, N.: Orderings for term-rewriting systems. Theoretical Computer Science 17(3), 279–301 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  7. Hofstadter, D.R.: Gödel, Escher, Bach: An Eternal Golden Braid. Basic Books (1979)

    Google Scholar 

  8. Kieu, T.D.: Quantum algorithm for Hilbert’s Tenth Problem. In: ArXiv Quantum Physics e-prints (October 2003) Available at, www.arXiv:quantph/0110136.com

  9. Kieu, T.D.: Hypercomputability of quantum adiabatic processes: Fact versus prejudices. In: ArXiv Quantum Physics e-prints (April 2005), Available at, arXiv.org:quantph/0504101

  10. LaForte, G., Hayes, P.J., Ford, K.M.: Why Gödel’s theorem cannot refute computationalism. Artificial Intelligence 104(1–2), 265–286 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  11. Lucas, J.R.: Minds, machines and Gödel. Philosophy XXXVI, 112–127 (1961)

    Article  Google Scholar 

  12. McCarthy, J.: Awareness and understanding in computer programs: A review of Shadows of the Mind by Roger Penrose. Psyche: An Interdisciplinary Journal of Research on Consciousness, 2(11) (July 1995), Available at, http://psyche.cs.monash.edu.au/v2/psyche-2-11-mccarthy.html (viewed September 2005)

  13. Newell, A., Simon, H.A.: Computer science as empirical enquiry. Communications of the ACM 19(3), 113–126 (1976)

    Article  MathSciNet  Google Scholar 

  14. Penrose, R.: The Emperor’s New Mind: Concerning Computers, Minds, and The Laws of Physics. Oxford University Press, New York (1989)

    Google Scholar 

  15. Penrose, R.: Shadows of the Mind: A Search for the Missing Science of Consciousness. Oxford University Press, Oxford (1994)

    Google Scholar 

  16. Putnam, H., Penrose, R.: Book review: Shadows of the Mind. Bulletin of the American Mathematical Society 32(3), 370–373 (1995), Available at, http://www.ams.org/bull/pre-1996-data/199507/199507015.pdf (viewed September 2005)

    Article  Google Scholar 

  17. Reingold, E.M., Shen, X.: More nearly optimal algorithms for unbounded searching, Part II: The transfinite case. SIAM J. Comput. 20(1), 184–208 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  18. Searle, J.: Minds, brains and programs. Behavioral and Brain Sciences 3, 417–424 (1980) Available at, http://members.aol.com/NeoNoetics/MindsBrainsPrograms.html (September 2005)

    Article  Google Scholar 

  19. Smith, W.D.: Three counterexamples refuting Kieu’s plan for “quantum adiabatic hypercomputation”; and some uncomputable quantum mechanical tasks. Journal of Applied Mathematics and Computation (2006) (to appear)

    Google Scholar 

  20. Takeuti, G.: Ordinal diagrams. II. J. Math. Soc. Japan 12, 385–391 (1960)

    Article  MATH  MathSciNet  Google Scholar 

  21. Tsirelson, B.: The quantum algorithm of Kieu does not solve the Hilbert’s Tenth Problem (November 2001), Available at, arXiv.org/abs/quant-ph/0111009

  22. Turing, A.M.: On computable numbers, with an application to the Entscheidungsproblem. Proceedings of the London Mathematical Society, Ser. 2(42), 230–265 (1936) Correction in vol. 43, pp. 544-546 (1937), Available at, http://www.abelard.org/turpap2/tp2-ie.asp (viewed September 2005)

    Google Scholar 

  23. Turing, A.M.: Lecture to the London Mathematical Society on 20 February 1947. In: Carpenter, B.E., Doran, R.W. (eds.) A. M. Turing’s ACE Report of 1946 and Other Papers. Charles Babbage Institute Reprint Series for the History of Computing, vol. 10. MIT Press, Cambridge (1986)

    Google Scholar 

  24. Zeilberger, D.: A 2-minute proof of the 2nd most important theorem of the 2nd millennium (October 1998) Available at, http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/halt.html (viewed September 2005)

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© 2005 Springer-Verlag Berlin Heidelberg

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Dershowitz, N. (2005). The Four Sons of Penrose. In: Sutcliffe, G., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2005. Lecture Notes in Computer Science(), vol 3835. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11591191_10

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  • DOI: https://doi.org/10.1007/11591191_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30553-8

  • Online ISBN: 978-3-540-31650-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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