Linked bibliography for the SEP article "The Church-Turing Thesis" by B. Jack Copeland

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Abramson, F.G., 1971, “Effective Computation over the Real Numbers”, Twelfth Annual Symposium on Switching and Automata Theory, Northridge, CA: Institute of Electrical and Electronics Engineers. (Scholar)
Andréka, H., I. Németi, and P. Németi, 2009, “General Relativistic Hypercomputing and Foundation of Mathematics”, Natural Computing, 8: 499–516. (Scholar)
Boden, M.A., 1988, Computer Models of Mind, Cambridge: Cambridge University Press. (Scholar)
Boolos, G.S. and R.C. Jeffrey, 1980, Computability and Logic, 2^nd edition, Cambridge: Cambridge University Press. (Scholar)
Cantor, G., 1874, “Ueber eine Eigenschaft des Inbegriffs aller reellen algebraischen Zahlen”, Journal für die reine und angewandte Mathematik, 77: 258–262. (Scholar)
Church, A., 1932, “A Set of Postulates for the Foundation of Logic”, Annals of Mathematics (Second Series), 33: 346–366. (Scholar)
–––, 1936a, “An Unsolvable Problem of Elementary Number Theory”, American Journal of Mathematics, 58: 345–363. (Scholar)
–––, 1936b, “A Note on the Entscheidungsproblem”, Journal of Symbolic Logic, 1: 40–41. (Scholar)
–––, 1937a, Review of Turing 1936, Journal of Symbolic Logic, 2: 42–43. (Scholar)
–––, 1937b, Review of Post 1936, Journal of Symbolic Logic, 2: 43. (Scholar)
–––, 1941, The Calculi of Lambda-Conversion, Princeton: Princeton University Press. (Scholar)
Churchland, P.M. and P.S. Churchland, 1983, “Stalking the Wild Epistemic Engine”, Noûs, 17: 5–18. (Scholar)
–––, 1990, “Could a Machine Think?”, Scientific American, 262 (Jan.): 26–31. (Scholar)
Copeland, B.J., 1997, “The Broad Conception of Computation”, American Behavioral Scientist, 40: 690–716. (Scholar)
–––, 1998a, “Even Turing Machines Can Compute Uncomputable Functions”, in C. Calude, J. Casti, and M. Dinneen (eds.) 1998, Unconventional Models of Computation, London: Springer-Verlag: 150–164. (Scholar)
–––, 1998b, “Super Turing-Machines”, Complexity, 4: 30–32. (Scholar)
–––, 1998c, “Turing’s O-machines, Penrose, Searle, and the Brain”, Analysis, 58: 128–138. (Scholar)
–––, 2000, “Narrow Versus Wide Mechanism”, Journal of Philosophy, 97: 5–32. (Scholar)
–––, 2002a, “Accelerating Turing Machines”, Minds and Machines, 12: 281–300. (A special issue on the Church-Turing thesis, edited by C. Cleland) (Scholar)
–––, 2002b, “Hypercomputation”, Minds and Machines, 12: 461–502. (Scholar)
–––, 2004a, “Hypercomputation: Philosophical Issues”, Theoretical Computer Science, 317: 251–267. (Scholar)
–––, 2004b, The Essential Turing: Seminal Writings in Computing, Logic, Philosophy, Artificial Intelligence, and Artificial Life, Oxford: Oxford University Press. (Scholar)
–––, 2006, “Turing’s Thesis”, in Olszewski, Wolenski, and Janusz 2006: 147–174. (Scholar)
Copeland, B.J., C. Posy, and O. Shagrir (eds), 2013, Computability: Turing, Gödel, Church and Beyond, Cambridge, MA: MIT Press. (Scholar)
Copeland, B.J. and D. Proudfoot, 1999a, “Alan Turing’s Forgotten Ideas in Computer Science”, Scientific American, 280 (April): 76–81. (Scholar)
–––, 1999b, “The Legacy of Alan Turing”, Mind, 108: 187–195. (Scholar)
–––, 2000, “What Turing Did After He Invented the Universal Turing Machine”, Journal of Logic, Language, and Information, 9: 491–509. (Scholar)
–––, 2012, “Artificial Intelligence”, in E. Margolis, R. Samuels, and S.P. Stich (eds), 2012, Oxford Handbook of Philosophy of Cognitive Science, New York: Oxford University Press: 147–182. (Scholar)
Copeland, B.J. and O. Shagrir, 2007, “Physical Computation: How General are Gandy’s Principles for Mechanisms”, Minds and Machines, 17: 217–231. (Scholar)
–––, 2011, “Do Accelerating Turing Machines Compute the Uncomputable?”, Minds and Machines, 21: 221–239. (Scholar)
–––, 2013, “Turing versus Gödel on Computability and the Mind”, in Copeland, Posy, and Shagrir 2013: 1–33. (Scholar)
Copeland, B.J. and R. Sylvan, 1999, “Beyond the Universal Turing Machine”, Australasian Journal of Philosophy, 77: 46–66. (Scholar)
Curry, H.B., 1929, “An Analysis of Logical Substitution”, American Journal of Mathematics, 51: 363–384. (Scholar)
–––, 1930, “Grundlagen der kombinatorischen Logik”, American Journal of Mathematics, 52: 509–536, 789–834. (Scholar)
–––, 1932, “Some Additions to the Theory of Combinators”, American Journal of Mathematics, 54: 551–558. (Scholar)
da Costa, N.C.A. and F.A. Doria, 1991, “Classical Physics and Penrose’s Thesis”, Foundations of Physics Letters, 4: 363–374. (Scholar)
–––, 1994, “Undecidable Hopf Bifurcation with Undecidable Fixed Point”, International Journal of Theoretical Physics, 33: 1913–1931. (Scholar)
Davis, M., 1958, Computability and Unsolvability, New York: McGraw-Hill. (Scholar)
––– (ed.), 1965, The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions, New York: Raven. (Scholar)
Dennett, D.C., 1978, Brainstorms: Philosophical Essays on Mind and Psychology, Brighton: Harvester. (Scholar)
–––, 1991, Consciousness Explained, Boston: Little, Brown. (Scholar)
Dershowitz, N. and Y. Gurevich, 2008, “A Natural Axiomatization of Computability and Proof of Church’s Thesis”, Bulletin of Symbolic Logic, 14: 299–350. (Scholar)
Deutsch, D., 1985, “Quantum Theory, the Church-Turing Principle and the Universal Quantum Computer”, Proceedings of the Royal Society (Series A), 400: 97–117. (Scholar)
Doyle, J., 1982, “What is Church’s Thesis? An Outline”, Laboratory for Computer Science, MIT. (Scholar)
–––, 2002, “What is Church’s Thesis? An Outline”, Minds and Machines, 12: 519–520. (Scholar)
Etesi, G. and I. Németi, 2002, “Non-Turing Computations via Malament-Hogarth Space-Times”, International Journal of Theoretical Physics, 41: 341–370. (Scholar)
Feferman, S. et al. (eds.) 1990, Kurt Gödel: Collected Works (Volume 2), Oxford: Oxford University Press. (Scholar)
Feferman, S. et al. (eds.) 1995, Kurt Gödel: Collected Works (Volume 3), Oxford: Oxford University Press. (Scholar)
Fodor, J.A., 1981, “The Mind-Body Problem”, Scientific American, 244 (Jan.): 124–32. (Scholar)
Gandy, R., 1980, “Church’s Thesis and Principles for Mechanisms”, in J. Barwise, H.J. Keisler, and K. Kunen (eds.), 1980, The Kleene Symposium, Amsterdam: North-Holland: 123–148. (Scholar)
–––, 1988, “The Confluence of Ideas in 1936”, in R. Herken (ed.), 1988, The Universal Turing Machine: A Half-Century Survey, Oxford: Oxford University Press: 51–102. (Scholar)
Geroch, R. and, J.B. Hartle, 1986, “Computability and Physical Theories”, Foundations of Physics, 16: 533–550. (Scholar)
Gödel, K., 1934, “On Undecidable Propositions of Formal Mathematical Systems”, Lecture notes taken by Kleene and Rosser at the Institute for Advanced Study; reprinted in Davis 1965: 39–74. (Scholar)
–––, 1936, “Über die Lange von Beweisen”, Ergebnisse eines mathematischen Kolloquiums, 7: 23–24. (Scholar)
–––, 193?, “Undecidable Diophantine Propositions”, in Feferman et al. 1995: 164–175. (Scholar)
–––, 1946, “Remarks Before the Princeton Bicentennial Conference”, in Feferman et al. 1990: 150–153. (Scholar)
–––, 1951, “Some Basic Theorems on the Foundations of Mathematics and Their Implications”, in Feferman et al. 1995: 304–323. (Scholar)
Gregory, R.L., 1987, The Oxford Companion to the Mind, Oxford: Oxford University Press. (Scholar)
Guttenplan, S., 1994, A Companion to the Philosophy of Mind, Oxford: Blackwell. (Scholar)
Henry, G.C., 1993, The mechanism and freedom of logic, Lanham: University Press of America. (Scholar)
Herbrand, J., 1932, “Sur la non-contradiction de l’arithmetique”, Journal fur die reine und angewandte Mathematik, 166: 1–8. (Scholar)
Hilbert, D. and W. Ackermann, 1928, Grundzüge der Theoretischen Logik, Berlin: Springer. (Scholar)
Hogarth, M.L., 1994, “Non-Turing Computers and Non-Turing Computability”, Proceedings of the Philosophy of Science Association, 1: 126–138. (Scholar)
–––, 2004, “Deciding Arithmetic Using SAD Computers”, British Journal for the Philosophy of Science, 55: 681–691. (Scholar)
Johnson-Laird, P., 1987, “How Could Consciousness Arise from the Computations of the Brain?”, in C. Blakemore and S. Greenfield (eds.) 1987, Mindwaves, Oxford: Basil Blackwell: 247–257. (Scholar)
Kalmár, L., 1959, “An Argument Against the Plausibility of Church’s Thesis”, in A. Heyting (ed.), 1959, Constructivity in Mathematics, Amsterdam: North-Holland: 72–80. (Scholar)
Kennedy, J., 2013, “On Formalism Freeness: Implementing Gödel’s 1946 Princeton Bicentennial Lecture”, Bulletin of Symbolic Logic, 19: 351–393. (Scholar)
Kleene, S.C., 1935, “A Theory of Positive Integers in Formal Logic”, American Journal of Mathematics, 57: 153–173, 219–244. (Scholar)
–––, 1936, “Lambda-Definability and Recursiveness”, Duke Mathematical Journal, 2: 340–353. (Scholar)
–––, 1952, Introduction to Metamathematics, Amsterdam: North-Holland. (Scholar)
–––, 1967, Mathematical Logic, New York: Wiley. (Scholar)
–––, 1981, “Origins of Recursive Function Theory”, Annals of the History of Computing, 3: 52–67. (Scholar)
Kreisel, G., 1967, “Mathematical Logic: What Has it Done For the Philosophy of Mathematics?”, in R. Schoenman (ed.) 1967, Bertrand Russell: Philosopher of the Century, London: George Allen and Unwin: 201–272. (Scholar)
–––, 1974, “A Notion of Mechanistic Theory”, Synthese, 29: 11–26. (Scholar)
–––, 1982, Review of Pour-El and Richards 1979 and 1981, Journal of Symbolic Logic, 47: 900–902. (Scholar)
Kripke, S.A., 2013, “The Church-Turing ‘Thesis’ as a Special Corollary of Gödel’s Completeness Theorem”, in Copeland, Posy, and Shagrir 2013: 77–104. (Scholar)
Langton, C.R., 1989, “Artificial Life”, in C.R. Langton (ed.), 1989, Artificial Life, Redwood City, CA: Addison-Wesley: 1–47. (Scholar)
Markov, A.A., 1960, “The Theory of Algorithms”, American Mathematical Society Translations (Series 2), 15: 1–14. (Scholar)
Mendelson, E., 1963, “On Some Recent Criticism of Church’s Thesis”, Notre Dame Journal of Formal Logic, 4: 201–205. (Scholar)
–––, 1964, Introduction to Mathematical Logic, New York: Van Nostrand. (Scholar)
Newell, A., 1980, “Physical Symbol Systems”, Cognitive Science, 4: 135–183. (Scholar)
Németi, I. and G. Dávid, 2006, “Relativistic Computers and the Turing Barrier”, Applied Mathematics and Computation, 178: 118–142. (Scholar)
Odifreddi, P., 1989, Classical recursion theory, Amsterdam: North-Holland. (Scholar)
Olszewski, A., J. Wolenski, and R. Janusz (eds.), 2006, Church’s Thesis After 70 Years, Frankfurt: Ontos Verlag. (Scholar)
Pitowsky, I., 1990, “The Physical Church Thesis and Physical Computational Complexity”, Iyyun, 39: 81–99. (Scholar)
Post, E.L., 1936, “Finite Combinatory Processes – Formulation 1”, Journal of Symbolic Logic, 1: 103–105. (Scholar)
–––, 1943, “Formal Reductions of the General Combinatorial Decision Problem”, American Journal of Mathematics, 65: 197–215. (Scholar)
–––, 1946, “A Variant of a Recursively Unsolvable Problem”, Bulletin of the American Mathematical Society, 52: 264–268. (Scholar)
Pour-El, M.B. and I. Richards, 1979, “A Computable Ordinary Differential Equation Which Possesses No Computable Solution”, Annals of Mathematical Logic, 17: 61–90. (Scholar)
–––, 1981, “The Wave Equation with Computable Initial Data such that its Unique Solution is not Computable”, Advances in Mathematics, 39: 215–239. (Scholar)
Scarpellini, B., 1963, “Zwei Unentscheitbare Probleme der Analysis”, Zeitschrift fur mathematische Logik und Grundlagen der Mathematik, 9: 265–289. (Scholar)
–––, 2003, “Comments on ‘Two Undecidable Problems of Analysis’”, Minds and Machines, 13: 79–85. (Scholar)
Schönfinkel, M., 1924, “Uber die Bausteine der mathematischen”, Mathematische Annalen, 92: 305–316. (Scholar)
Searle, J., 1992, The Rediscovery of the Mind, Cambridge, MA: MIT Press. (Scholar)
–––, 1997, The Mystery of Consciousness, New York: New York Review of Books. (Scholar)
Shagrir, O., 2006, “Gödel on Turing on Computability”, in Olszewski, Wolenski, and Janusz 2006: 393–419. (Scholar)
Shagrir, O. and I. Pitowsky, 2003, “Physical Hypercomputation and the Church-Turing Thesis”, Minds and Machines, 13: 87–10. (Scholar)
Shepherdson, J.C. and H.E. Sturgis, 1963, “Computability of Recursive Functions”, Journal of the Association of Computing Machinery, 10: 217–255. (Scholar)
Sieg, W., 2002, “Calculations by man and machine: Conceptual analysis”, in W. Sieg, R. Sommer, and C. Talcott (eds), 2002, Reflections on the Foundations of Mathematics. Essays in Honor of Solomon Feferman (Lecture Notes in Logic: Volume 15), Natick, MA: Association for Symbolic Logic: 396–415. (Scholar)
–––, 2008, “Church Without Dogma: Axioms for Computability”, in B. Lowe, A. Sorbi, and B. Cooper (eds), 2008, New Computational Paradigms, New York: Springer Verlag: 139–152. (Scholar)
–––, 2013, “Gödel’s Philosophical Challenge (to Turing)”, in Copeland, Posy, and Shagrir 2013: 183–202.
Siegelmann, H.T., 2003, “Neural and Super-Turing Computing”, Minds and Machines, 13: 103–114. (Scholar)
Siegelmann, H.T. and E.D. Sontag, 1992, “On the Computational Power of Neural Nets”, Proceedings of the 5th Annual ACM Workshop on Computational Learning Theory, 440–449. (Scholar)
–––, 1994, “Analog Computation via Neural Networks”, Theoretical Computer Science, 131: 331–360. (Scholar)
Smolensky, P., 1988, “On the Proper Treatment of Connectionism”, Behavioral and Brain Sciences, 11: 1–23. (Scholar)
Stannett, M., 1990, “X-Machines and the Halting Problem: Building a Super-Turing Machine”, Formal Aspects of Computing, 2: 331–341. (Scholar)
Stewart, I., 1991, “Deciding the Undecidable”, Nature, 352: 664–5. (Scholar)
Syropoulos, A., 2008, Hypercomputation, New York: Springer. (Scholar)
Turing, A.M., 1936, “On Computable Numbers, with an Application to the Entscheidungsproblem”, Proceedings of the London Mathematical Society (Series 2), 42 (1936–37): 230–265; reprinted in Copeland 2004b: 58–90 (page references in the text are to this edition). (Scholar)
–––, 1937, “Computability and λ-Definability”, Journal of Symbolic Logic, 2: 153–163. (Scholar)
–––, 1939, “Systems of Logic Based on Ordinals”, Proceedings of the London Mathematical Society (Series 2), 45: 161–228; reprinted in Copeland 2004b: 146–204. (Scholar)
–––, 1945, “Proposed Electronic Calculator”, in B.J. Copeland 2005, Alan Turing’s Automatic Computing Engine, Oxford: Oxford University Press: 369–454. (Scholar)
–––, 1947, “Lecture on the Automatic Computing Engine”, in Copeland 2004b: 378–394. (Scholar)
–––, 1948, “Intelligent Machinery”, National Physical Laboratory Report, in Copeland 2004b: 410–432. (Scholar)
–––, 1950, “Computing Machinery and Intelligence”, Mind, 59: 433–460; reprinted in Copeland 2004b: 441–464 (page references in the text are to this edition). (Scholar)
–––, c1950, Programmers’ Handbook for Manchester Electronic Computer Mark II, Computing Machine Laboratory, University of Manchester. [Turing c1950 available online in The Turing Archive for the History of Computing] (Scholar)
–––, 1954, “Solvable and Unsolvable Problems”, Science News, 31: 7–23; reprinted in Copeland 2004b: 582–595 (page references in the text are to this edition). (Scholar)
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–––, 1996, A Logical Journey: From Gödel to Philosophy, Cambridge, MA: MIT Press. (Scholar)
Wittgenstein, L., 1947 [1980], Remarks on the Philosophy of Psychology (Volume 1), G.E.M. Anscombe, H. Nyman, and G.H. von Wright (eds), Oxford: Blackwell, 1980. (Scholar)

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