Physical hypercomputation and the Church-Turing thesis

Minds and Machines

Volumn 13, Issue 1, 2003, Pages 87-101

  Shagrir, Oron ^a   Pitowsky, Itamar ^a  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

Church Turing thesis; Effective computation; Gandy's thesis; Physical hypercomputation; Supertasks

Indexed keywords

COMPUTABILITY AND DECIDABILITY; FUNCTION EVALUATION; PROBLEM SOLVING; THEOREM PROVING;

CHURCH-TURING THESIS; HYPERCOMPUTATION; HYPERCOMPUTER;

TURING MACHINES;

EID: 0037312546     PISSN: 09246495     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021365222692     Document Type: Article

References (36)

1. Church A. (1936a), 'An Unsolvable Problem of Elementary Number Theory', American Journal of Mathematics 58, pp. 345-363. Reprinted in Davis (1965), pp. 88-107.
2. Church A. (1936b), 'A Note on the Entscheidungsproblem', Journal of Symbolic Logic 1, pp. 40-41, Reprinted in Davis (1965), pp. 108-115.
3. Cleland C. (1993), 'Is the Church-Turing Thesis True?' Minds and Machines 3, pp. 283-312.
4. Copeland B.J. (1996), 'The Church-Turing Thesis', in Perry J. and Zalta E., eds., Stanford Encyclopedia of Philosophy [http://plato.stanford.edu].
5. Copeland B.J. (2002), 'Accelerating Turing Machines', Minds and Machines 12, pp. 281-301.
6. Copeland B.J. and Sylvan R. (1999), 'Beyond the Universal Turing Machine', Australasian Journal of Philosophy 77, pp. 46-67.
7. Davis M. (ed.) (1965), The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions, New York: Raven.
8. Earman J. (1986), A Primer of Determinism, Holland: Reidel.
9. Earman J. and Norton J.D. (1993), 'Forever is A Day: Supertasks in Pitowsky and Malament-Hogarth Spacetimes', Philosophy of Science 60, pp. 22-42.
10. Gandy R.O. (1980), 'Church's Thesis and Principles of Mechanisms', in Barwise J., Keisler J.J. and Kunen K., eds., The Kleene Symposium, Amsterdam: North-Holland, pp. 123-145.
11. Gandy R.O. (1988), 'The Confluence of Ideas in 1936', in Herken (1988), pp. 55-111.
12. Gödel K. (1931), 'On Formally Undecidable Propositions of Principia Mathematica and Related Systems I', Monatshefte für Mathematik und Physik 38, pp. 173-198. Translated and Reprinted in Davis (1965), pp. 5-38.
13. Goldstine H.H. (1972), The Computer from Pascal to Von Neumann, Princeton: Princeton University Press.
14. Herken R. (ed.) (1988), The Universal Turing Machine A Half-Century Survey, Oxford: Oxford University Press
15. Hilbert D. and Ackermann W. (1928), Grundzuge der Theoretischen Logic, Berlin: Springer-Verlag.
16. Hodges A. (1983), Alan Turing: The Enigma, New York: Touchstone, Simon and Schuster.
17. Hogarth M.L. (1992), 'Does General Relativity Allow an Observer to View an Eternity in a Finite Time?', Foundations of Physics Letters 5, pp. 173-181.
18. Hogarth M.L. (1994) 'Non-Turing Computers and Non-Turing Computability', Proceedings of the Philosophy of Science Association (PSA) 1, pp. 126-138.
19. Kleene S.C. (1936), 'General Recursive Functions of Natural Numbers', Mathematische Annalen 112, pp. 727-742. Reprinted in Davis (1965), pp. 236-253.
20. Kleene S.C. (1988), 'Turing's Analysis of Computability, and Major Applications of It', in Herken (1988), pp. 17-54.
21. Laraudogoitia J.P. (1999), 'Supertasks', in Perry J. and Zalta E., eds., Stanford Encyclopedia of Philosophy [http://plato.stanford.edu].
22. Moore C. (1990), 'Unpredictability and Undecidability in Dynamical Systems', Physical Review Letters 64, pp. 2354-2357.
23. Penrose R. (1994), Shadows of the Mind, New York and Oxford: Oxford University Press.
24. Pitowsky I. (1990), 'The Physical Church Thesis and Physical Computational Complexity', Iyyun 39, pp. 81-99.
25. Pitowsky I. (1996), 'Laplace's Demon Consults an Oracle: The Computational Complexity of Prediction', Studies in History and Philosophy of Physics 27, pp. 161-180.
26. Post E.L. (1936), 'Finitary Combinatory Processes - Formulation I', Journal of Symbolic Logic 1, pp. 103-105. Reprinted in Davis (1965) pp. 288-291.
27. Pour-El M.B. and Richards I. (1981), 'The Wave Equation with Computable Initial Data such that its Unique Solution is not Computable', Advances in Mathematics 39, pp. 215-239.
28. Shagrir O. (1997), 'Two Dogmas of Computationalism', Minds and Machines 7, pp. 321-344.
29. Shapiro S. (1983), 'Remarks on the Development of Computability', History and Philosophy of Logic 4, pp. 203-220.
30. Sieg W. (1994), 'Mechanical Procedures and Mathematical Experience', in George A., ed., Mathematics and Mind, Oxford: Oxford University Press.
31. Sieg W. and Byrnes J. (1999), 'An Abstract Model for Parallel Computations: Gandy's Thesis', The Monist 82, pp. 150-164.
32. Siegelmann H.T. (1995), 'Computation Beyond Turing Limit', Science 268, pp. 545-548.
33. Turing A.M. (1936), 'On Computable Numbers, with an Application to the Entscheidungsproblem', Proceedings of the London Mathematical Society (2) 42, pp. 230-265. A correction in 43 (1937), pp. 544-546. Reprinted in Davis (1965), pp. 115-154.
34. Turing A.M. (1939), 'Systems of Logic Based on Ordinals', Proceedings of the London Mathematical Society 45 (2), pp. 161-228. Reprinted in Davis (1965), pp. 154-222.
35. Wald R.M. (1984), General Relativity, Chicago: University of Chicago Press.
36. Wolfarm S. (1985), 'Undecidability and Intractability in Theoretical Physics', Physical Review Letters 54, pp. 735-738.