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Part of the book series: International Mathematical Series ((IMAT,volume 4))

The author would like to acknowledge the support of E.P.S.R.C. Research Grant No. EP/C001389/1, Extensions of Embeddings in the Turing Universe.

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References

  1. H. Broch, The Sleepwalkers (trans. W. and E. Muir). New York, Vintage Intern., 1996.

    Google Scholar 

  2. J. Brockman (ed.), The Third Culture: Beyond the Scientific Revolution, New York-London, Simon and Schuster, 1995.

    Google Scholar 

  3. F. Capra, The Web of Life: A New Scientific Understanding of Living Systems, London, Harper Collins, 1996.

    Google Scholar 

  4. S. B. Cooper, Clockwork or Turing U/universe? — remarks on causal determinism and computability, In: S. B. Cooper and J. K. Truss (eds.), Models and Computability London Math. Soc. Lect. Note Ser. 259 (1999), pp. 63–116.

    Google Scholar 

  5. S. B. Cooper, Computability Theory, New York-London, Chapman & Hall/ CRC Press, 2004.

    MATH  Google Scholar 

  6. S. B. Cooper, The incomputable Alan Turing, In: Proceedings of Turing 2004: A celebration of his life and achievements [To be electronically published by the British Computer Society, 2005].

    Google Scholar 

  7. S. B. Cooper, and P. Odifreddi, Incomputability in nature, In: S. B. Cooper and S. S. Goncharov (eds.), Computability and Models: Perspectives East and West, New York etc., Kluwer Academic/ Plenum Publishers, 2003, pp. 137–160.

    Google Scholar 

  8. J. Copeland, Turing’s O-machines, Penrose, Searle, and the brain, Analysis, 58 (1998), 128–38.

    Article  MATH  MathSciNet  Google Scholar 

  9. J. Copeland, Narrow versus wide mechanism: Including a reexamination of Turing’s views on the mind-machine issue, J. Phil. 96 (2000), 5–32.

    Article  MathSciNet  Google Scholar 

  10. J. Copeland and D. Proudfoot, On Alan Turing’s anticipation of connectionism. Synthese, 108 (1996), 361–377, Reprinted in: R. Chrisley (ed.), Artificial Intelligence: Critical Concepts in Cognitive Science. Vol. 2: Symbolic AI, London, Routledge, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  11. J. Copeland and D. Proudfoot, Alan Turing’s forgotten ideas in computer science. Scientific American, 253:4 (1996), 98–103.

    Google Scholar 

  12. M. Davis, The Universal Computer: The Road from Leibniz to Turing, New York, W. W. Norton, 2000.

    Google Scholar 

  13. M. Davis, The myth of hypercomputation, In: Teuscher (2004), 195–211.

    Google Scholar 

  14. A. Einstein, Out of My Later Years. New York, Phil. Library, 1950.

    MATH  Google Scholar 

  15. A. Einstein, B. Podolsky, and N. Rosen, Can quantum mechanical description of physical reality be considered complete?. Phys. Rev. 47 (1935), 777–780.

    Article  MATH  Google Scholar 

  16. G. Etesi, and I. Németi, Non-Turing computations via Malament-Hogarth space-times. Int. J. Theoretical Phys. 41 (2002), 341–370.

    Article  MATH  Google Scholar 

  17. R. P. Feynman, Simulating physics with computers, Int. J. Theoretical Phys. 21 (1982), 467–488.

    MathSciNet  Google Scholar 

  18. T. Franzen, Inexhaustibility — A Non-Exhaustive Treatment. Association for Symbolic Logic/ A K Peters, Wellesley, Mass. 2004.

    MATH  Google Scholar 

  19. R. O. Gandy and C. E. M. Yates (eds.), Collected Works of A. M. Turing: Mathematical Logic, Amsterdam etc., North-Holland, 2001.

    MATH  Google Scholar 

  20. R. Geroch and J. B. Hartle, Computability and physical theories, Foundations Phys. 16 (1986), 533–550.

    Article  MathSciNet  Google Scholar 

  21. D. Goldin, S. Smolka, and P. Wegner (eds.) Interactive Computation: the New Paradigm, Springer-Verlag [To appear].

    Google Scholar 

  22. D. Goldin and P. Wegner, Computation Beyond Turing Machines, Communications of the ACM, 2003.

    Google Scholar 

  23. A. H. Guth, The Inflationary Universe — The Quest for a New Theory of Cosmic Origins, New York etc., Addison-Wesley, 1997.

    Google Scholar 

  24. J. Hadamard, The Psychology of Invention in the Mathematical Field, Princeton, Princeton Univ. Press, 1945.

    MATH  Google Scholar 

  25. A. Hodges, Alan Turing: The Enigma, London etc., Vintage, 1992.

    Google Scholar 

  26. J. H. Holland, Emergence — From Chaos to Order. Oxford etc. Oxford Univ. Press, 1998.

    MATH  Google Scholar 

  27. D. Hume, An Enquiry Concerning Human Understanding (1748), (L. A. Selby-Bigge and P. H. Nidditch, Eds.). Oxford, Oxford Univ. Press, 1975 edn.

    Google Scholar 

  28. S._A. Kauffman, The Origins of Order — Self-Organisation and Selection in Evolution. Oxford-New York, Oxford Univ. Press, 1993.

    Google Scholar 

  29. T. Kieu, Quantum algorithm for the Hilbert’s Tenth Problem, Int. J. Theoretical Phys. 42 (2003), 1461–1478.

    Article  MATH  MathSciNet  Google Scholar 

  30. G. Kreisel, Church’s Thesis: a kind of reducibility axiom for constructive mathematics, In: A. Kino, J. Myhill, and R. E. Vesley (eds.), Intuitionism and Proof Theory: Proceedings of the Summer Conference at Buffalo N.Y. 1968 Amsterdam etc., North-Holland, 1970, pp. 121–150.

    Google Scholar 

  31. P. S. de Laplace, Essai philosophique sur les probabilit’es (1819); English translation by F. W. Truscott and F. L. Emory, New York, Dover, 1951.

    Google Scholar 

  32. G. W. Leibniz, The Monadology (1714), In: L. E. Loemker (ed.), Gottfried Wilhelm Leibniz: Philosophical Papers and Letters, Dordrecht, 1969.

    Google Scholar 

  33. W. McCulloch and W. Pitts, A logical calculus of the ideas immanent in nervous activity, Bull. Math. Biophys. 5 (2003), 115–133.

    MathSciNet  Google Scholar 

  34. P. Odifreddi, Classical Recursion Theory, Amsterdam etc., North-Holland, 1989.

    MATH  Google Scholar 

  35. R. Penrose, Quantum physics and conscious thought, In: B. J. Hiley and F. D. Peat (eds.), Quantum Implications: Essays in Honour of David Bohm, London-New York, Routledge & Kegan Paul, 1987, pp. 105–120.

    Google Scholar 

  36. R. Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness, Oxford, Oxford Univ. Press, 1994.

    Google Scholar 

  37. E. L. Post, Absolutely unsolvable problems and relatively undecidable propositions — Account of an anticipation (1941), In: M. Davis (ed.), Collected Works of Post, 1994, pp. 375–441.

    Google Scholar 

  38. E. L. Post, Recursively enumerable sets of positive integers and their decision problems, Bull. Am. Math. Soc. 50 (1944), 284–316.

    Article  MATH  MathSciNet  Google Scholar 

  39. E. L. Post, Degrees of recursive unsolvability: preliminary report (abstract), Bull. Am. Math. Soc. 54 (1948), 641–642.

    Google Scholar 

  40. D. G. Saari and Z. Xia (Jeff), Off to infinity in finite time, Notices Am. Math. Soc. 42 (1995), 538–546.

    MATH  MathSciNet  Google Scholar 

  41. R. Shaw, The Dripping Faucet as a Model Chaotic System, Santa Cruz, CA, Aerial Press, 1984.

    Google Scholar 

  42. P. Smolenskyo, On the proper treatment of connectionism, Behavioral and Brain Sciences 11 (1988), 1–74.

    Article  Google Scholar 

  43. R. I. Soare, Computability theory and differential geometry, Bull. Symbolic Logic 10 (2004), 457–486.

    Article  MATH  MathSciNet  Google Scholar 

  44. S. Strogatz, Sync: The Emerging Science of Spontaneous Order. Hyperion Press, 2003.

    Google Scholar 

  45. C. Teuscher (ed.), Alan Turing: Life and Legacy of a Great Thinker, Berlin-Heidelberg, Springer-Verlag, 2004.

    MATH  Google Scholar 

  46. A. M. Turing, On computable numbers, with an application to the Entscheidungsproblem, Proc. London Math. Soc. (2) 42 (1936–7), 230–265, Reprinted in: A. M. Turing, Collected Works: Mathematical Logic, pp. 18-53.

    MATH  Google Scholar 

  47. A. M. Turing, Systems of logic based on ordinals, Proc. London Math. Soc. (2) 45 (1939), 161–228, Reprinted in: A. M. Turing, Collected Works: Mathematical Logic, pp. 81-148.

    MATH  Google Scholar 

  48. A. M. Turing, Intelligent machinery (1948), In: B. Meltzer and D. Michie (eds.), Machine Intelligence 5 Edinburgh, Edinburgh Univ. Press, 1969, pp. 3–23, Reprinted in: A. M. Turing, Collected Works: Mechanical Intelligence, Amsterdam etc., North-Holland, 1992.

    Google Scholar 

  49. A. M. Turing, The chemical basis of morphogenesis. Phil. Trans. Royal Soc. London, 237 (1952), 37–72, Reprinted in: A. M. Turing, Collected Works: Morphogenesis, Amsterdam etc., North-Holland, 1992.

    Google Scholar 

  50. A. M. Turing, Collected Works: Mathematical Logic Amsterdam etc., North-Holland, 2001

    MATH  Google Scholar 

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Cooper, S.B. (2006). Computability and Emergence. In: Gabbay, D.M., Goncharov, S.S., Zakharyaschev, M. (eds) Mathematical Problems from Applied Logic I. International Mathematical Series, vol 4. Springer, New York, NY. https://doi.org/10.1007/0-387-31072-X_4

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