Hypercomputation: Philosophical issues

Theoretical Computer Science

Volumn 317, Issue 1-3, 2004, Pages 251-267

  Copeland, B Jack ^a  

^a UNIVERSITY OF CANTERBURY   (New Zealand)

Author keywords

Church; Mind; Oracle; Super Turing; Turing

Indexed keywords

COMPUTATION THEORY; HUMAN ENGINEERING; LEARNING SYSTEMS; TURING MACHINES;

HUMAN COMPUTERS; HYPERCOMPUTATION; MIND;

COMPUTER SCIENCE;

EID: 2442519284     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2003.12.014     Document Type: Conference Paper

References (60)

1. Ambrose A. Finitism in mathematics (I and II). Mind. 35:1935;186-203; 317-340.
2. Bechtel W., Richardson R.C. Discovering Complexity: Decomposition and Localization as Strategies in Scientific Research. 1993;Princeton University Press, Princeton.
3. Burgin M.S. Inductive Turing machines. Soviet Math. Dokl. 270:1983;1289-1293.
4. Burgin M.S. How we know what technology can do. Comm. ACM. 44:2001;82-88.
5. M.S. Burgin, From neural networks to grid automata, in: Proc. IASTED Internat. Conf. Modeling and Simulation, Palm Springs, California, 2003, pp. 307-312.
6. Calude C.S., Pavlov B. Coins, quantum measurements, and Turing's barrier. Quantum Inform. Process. 1:2002;107-127.
7. Church A. Review. J. Symbolic Logic. 2:1937;42-43.
8. Church A. On the concept of a random sequence. American Math. Soc. Bull. 46:1940;130-135.
9. B.J. Copeland, The Church-Turing thesis, in: E. Zalta (Ed.), Stanford Encyclopedia of Philosophy, http://plato.stanford.edu.
10. Copeland B.J. The broad conception of computation. Amer. Behavioral Sci. 40:1997;690-716.
11. Copeland B.J. Super Turing-machines. Complexity. 4:1998;30-32.
12. Copeland B.J. Even Turing machines can compute uncomputable functions. Calude C., Casti J., Dinneen M. Unconventional Models of Computation. 1998;Springer, London.
13. B.J. Copeland (Ed.), A lecture and two radio broadcasts on machine intelligence by Alan Turing, in: K. Furukawa, D. Michie, S. Muggleton (Eds.), Machine Intelligence, Vol. 15, Oxford University Press, Oxford, 1999.
14. Copeland B.J. Narrow versus wide mechanism. J. Phil. 96:2000;5-32.
15. Copeland B.J. Colossus and the dawning of the computer age. Erskine R., Smith M. Action This Day. 2001;Bantam Books, London.
16. B.J. Copeland, Modern history of computing, in: E. Zalta (Ed.), Stanford Encyclopedia of Philosophy, http://plato.stanford.edu.
17. Copeland B.J. Accelerating Turing machines. Minds Mach. 12:2002;281-301.
18. Copeland B.J. Hypercomputation. Minds Mach. 12:2002;461-502.
19. Copeland B.J., Sylvan R. Beyond the universal Turing machine. Austral. J. Phil. 77:1999;46-66.
20. Davis M. Computability and Unsolvability. 1958;McGraw-Hill, New York.
21. M. Davis, The myth of hypercomputation (February 2003), in: C. Teuscher (Ed.), Alan Turing: Life and Legacy of a Great Thinker, Springer, Berlin, 2003, to appear.
22. Doyle J. What is Church's thesis? An outline. Minds Mach. 12:2002;519-520.
23. Freyvald R.V. Functions and functionals computable in the limit. Trans. Latvijas Vlasts Univ. Zinatn. Raksti. 210:1974;6-19.
24. Gold E.M. Limiting recursion. J. Symbolic Logic. 30:1965;28-48.
25. Harvey I., Bossomaier T. Time out of joint: attractors in asynchronous random boolean networks. Husbands P., Harvey I. Fourth European Conf. on Artificial Life. 1997;MIT Press, Cambridge, MA.
26. J. Hintikka, A. Mutanen, An alternative concept of computability, in: Language, Truth, and Logic in Mathematics, Kluwer, Dordrecht, 1998.
27. Hodges A. Alan Turing: The Enigma. 1992;Vintage, London.
28. Hodges A. Turing. 1997;Phoenix, London.
29. A. Hodges, What would Alan Turing have done after 1954? in: C. Teuscher (Ed.), Alan Turing: Life and Legacy of a Great Thinker, Springer, Berlin, 2003, to appear, http://www.turing.org.uk/philosophy/lausanne1.html .
30. Hogarth M.L. Does general relativity allow an observer to view an eternity in a finite time? Found. Phys. Lett. 5:1992;173-181.
31. M.L. Hogarth, Non-Turing computers and non-Turing computability, Vol. 1, PSA, 1994.
32. Kieu T.D. Quantum hypercomputation. Minds Mach. 12:2002;541-561.
33. Komar A. Undecidability of macroscopically distinguishable states in quantum field theory. Phys. Rev. Ser. 2. 133B:1964;542-544.
34. Kripke S. Wittgenstein on Rules and Private Language: an Elementary Exposition. 1982;Blackwell, Oxford.
35. G.J. Lokhorst, Why I am not a super-Turing machine, Hypercomputation Workshop, University College, London, 24 May 2000.
36. Newman E. Memories of the Pilot Ace. Resurrection. 9:1994;11-14.
37. Penrose R. Shadows of the Mind: A Search for the Missing Science of Consciousness. 1994;Oxford University Press, Oxford.
38. Piccinini G. Alan Turing and the mathematical objection. Minds Mach. 13:2003;23-48.
39. Pitowsky I. The physical Church thesis and physical computational complexity. Iyyun. 39:1990;81-99.
40. Putnam H. Trial and error predicates and the solution of a problem of Mostowski. J. of Symbolic Logic. 30:1965;49-57.
41. Putnam H. Renewing Philosophy. 1992;Harvard University Press, Cambridge, MA.
42. Russell B.A.W. The limits of empiricism. Proc. Aristotelian Soc. 36:1936;131-150.
43. B. Scarpellini, Zwei Unentscheitbare Probleme der Analysis [Two undecidable problems of analysis], Z. Math. Logik Grundlagen Math. 9 (1963) 265-289, Minds Mach. 13 (2003) (in English).
44. B. Scarpellini, Zwei Unentscheitbare Probleme der Analysis [Two undecidable problems of analysis], Z. Math. Logik Grundlagen Math. 9 (1963) 265-289, Minds Mach. 13 (2003) (in English).
45. Scarpellini B. Comments on 'Two undecidable problems of analysis'. Minds Mach. 13:2003.
46. Sieg W. Mechanical procedures and mathematical experience. George A. Mathematics and Mind. 1994;Oxford University Press, Oxford.
47. Siegelmann H.T. Neural and super-Turing computing. Minds Mach. 13:2003;103-114.
48. Siegelmann H.T., Sontag E.D. Analog computation via neural networks. Theoret. Comput. Sci. 131:1994;331-360.
49. Stannett M. X-machines and the halting problem. building a super-Turing machine Formal Aspects Comput. 2:1990;331-341.
50. Stannett M. Computation and hypercomputation. Minds Mach. 13:2003;115-153.
51. Turing A.M. On computable numbers, with an application to the Entscheidungsproblem. Proc. London Math. Soc., Ser. 2. 42:1936-1937;230-265.
52. Turing A.M. Systems of logic based on ordinals. Proc. London Math. Soc., Ser. 2. 45:1939;161-228.
53. Turing A.M. Lecture to the London Mathematical Society on 20 February 1947. Carpenter B.E., Doran R.W. A.M. Turing's ACE Report of 1946 and Other Papers. 1986;MIT Press, Cambridge, MA.
54. Turing A.M. Intelligent Machinery, National Physical Laboratory, London, 1948. Meltzer B., Michie D. Machine Intelligence. Vol. 5:1969;Edinburgh University Press, Edinburgh. A digital facsimile of the original document is in The Turing Archive for the History of Computing, http://www.AlanTuring.net/ intelligent_machinery.
55. Turing A.M. Computing machinery and intelligence. Mind. 59:1950;433-460.
56. A.M. Turing, Can digital computers think? (1951), in: B.J. Copeland, A lecture and two radio broadcasts on machine intelligence by Alan Turing, in: K. Furukawa, D. Michie, S. Muggleton (Eds.), Machine Intelligence, Vol. 15, Oxford University Press, Oxford, 1999.
57. A.M. Turing, Intelligent machinery, a heretical theory (c.1951), in: B.J. Copeland, A lecture and two radio broadcasts on machine intelligence by Alan Turing, in: K. Furukawa, D. Michie, S. Muggleton (Eds.), Machine Intelligence, Vol. 15, Oxford University Press, Oxford, 1999.
58. A.M. Turing et al., Can automatic calculating machines be said to think? (1952), in: B.J. Copeland, A lecture and two radio broadcasts on machine intelligence by Alan Turing, in: K. Furukawa, D. Michie, S. Muggleton (Eds.), Machine Intelligence, Vol. 15, Oxford University Press, Oxford, 1999.
59. A.M. Turing, Chess, in: B.V. Bowden (Ed.), Faster Than Thought (part of Chapter 25), Sir Isaac Pitman & Sons, London, 1953.
60. Wegner P. Why interaction is more powerful than algorithms. Commun. ACM. 40:1997;80-91.