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

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Ackermann, Wilhelm, 1928, “Zum Hilbertschen Aufbau der reellen Zahlen”, Mathematische Annalen, 99(1): 118–133. doi:10.1007/bf01459088 (Scholar)
Aharonov, Dorit and Umesh V. Vazirani, 2013, “Is Quantum Mechanics Falsifiable? A Computational Perspective on the Foundations of Quantum Mechanics”, in Copeland, Posy, and Shagrir 2013: 329–349 (ch. 11). (Scholar)
Andréka, Hajnal, István Németi, and Péter Németi, 2009, “General Relativistic Hypercomputing and Foundation of Mathematics”, Natural Computing, 8(3): 499–516. doi:10.1007/s11047-009-9114-3 (Scholar)
Baldwin, J. Mark, 1902, “Logical Machine”, in J. Mark Baldwin (ed.), Dictionary of Philosophy and Psychology, volume 2, New York: Macmillan, 28–30. (Scholar)
Barendregt, Henk, 1997, “The Impact of the Lambda Calculus in Logic and Computer Science”, Bulletin of Symbolic Logic, 3(2): 181–215. doi:10.2307/421013 (Scholar)
Barrett, Lindsay and Matthew Connell, 2005, “Jevons and the Logic ‘Piano’”, The Rutherford Journal, 1: article 3. [Barrett & Connell 2005 available online] (Scholar)
Barwise, Jon, 1977, “An Introduction to First-Order Logic”, in Jon Barwise (ed.), Handbook of Mathematical Logic, Amsterdam: North-Holland, 5–46. (Scholar)
Bausch, Johannes, Toby S. Cubitt, Angelo Lucia, and David Perez-Garcia, 2020, “Undecidability of the Spectral Gap in One Dimension”, Physical Review X, 10(3): 031038. doi:10.1103/physrevx.10.031038 (Scholar)
Bausch, Johannes, Toby S. Cubitt, and James D. Watson, 2019, “Uncomputability of Phase Diagrams”, arXiv:1910.01631. (Scholar)
–––, 2021, “Uncomputability of Phase Diagrams”, Nature Communications, 12(1): article 452. doi:10.1038/s41467-020-20504-6 (Scholar)
Behmann, Heinrich, 1921 [2015], “Entscheidungsproblem und Algebra der Logik”, Lecture, 10 May 1921, to the Göttingen Mathematical Society. In Mancosu and Zach 2015: 177–187, with a partial translation by Richard Zach in the same (2015: 173–177). (Scholar)
–––, 1922, “Beiträge zur Algebra der Logik, insbesondere zum Entscheidungsproblem”, Mathematische Annalen, 88(1–2): 168–168. doi:10.1007/bf01448447 (Scholar)
Bernays, Paul, 1918, “Beiträge zur axiomatischen Behandlung des Logik-Kalküls”, Habilitationsschrift, University of Göttingen. Bernays Papers, ETH Zurich (Hs 973.192). (Scholar)
Bernays, Paul and Moses Schönfinkel, 1928, “Zum Entscheidungsproblem der mathematischen Logik”, Mathematische Annalen, 99(1): 342–372. doi:10.1007/BF01459101 (Scholar)
Bernstein, Ethan and Umesh Vazirani, 1997, “Quantum Complexity Theory”, SIAM Journal on Computing, 26(5): 1411–1473. doi:10.1137/s0097539796300921 (Scholar)
Blum, Lenore, Felipe Cucker, Michael Shub, and Steve Smale, 1998, Complexity and Real Computation, New York: Springer. doi:10.1007/978-1-4612-0701-6 (Scholar)
Boolos, George and Richard C. Jeffrey, 1974, Computability and Logic, New York: Cambridge University Press. (Scholar)
Buss, Samuel R., Alexander S. Kechris, Anand Pillay, and Richard A. Shore, 2001, “The Prospects for Mathematical Logic in the Twenty-First Century”, Bulletin of Symbolic Logic, 7(2): 169–196. doi:10.2307/2687773 (Scholar)
Calude, Cristian S. and Karl Svozil, 2008, “Quantum Randomness and Value Indefiniteness”, Advanced Science Letters, 1(2): 165–168. doi:10.1166/asl.2008.016 (Scholar)
Calude, Cristian S., Michael J. Dinneen, Monica Dumitrescu, and Karl Svozil, 2010, “Experimental Evidence of Quantum Randomness Incomputability”, Physical Review A, 82(2): 022102. doi:10.1103/physreva.82.022102 (Scholar)
Cantor, Georg, 1874, “Ueber eine Eigenschaft des Inbegriffs aller reellen algebraischen Zahlen”, Journal für die reine und angewandte Mathematik, 77: 258–262. doi:10.1515/crll.1874.77.258 (Scholar)
Carnap, Rudolf, 1935, “Ein Gültigkeitskriterium für die Sätze der klassischen Mathematik”, Monatshefte für Mathematik und Physik, 42: 163–190. doi:10.1007/bf01733289 (Scholar)
Cassirer, Ernst, 1929, Philosophie der symbolischen Formen (Volume 3: Phänomenologie der Erkenntnis), Berlin: Bruno Cassirer. (Scholar)
Church, Alonzo, 1932, “A Set of Postulates for the Foundation of Logic”, Annals of Mathematics, second series 33(2): 346–366. doi:10.2307/1968337 (Scholar)
–––, 1933, “A Set of Postulates For the Foundation of Logic (2)”, Annals of Mathematics, second series 34(4): 839–864. doi:10.2307/1968702 (Scholar)
–––, 1935a, “An Unsolvable Problem of Elementary Number Theory, Preliminary Report” (abstract), Bulletin of the American Mathematical Society, 41(6): 332–333. Full paper in Church 1936b. (Scholar)
–––, 1935b, letter to Kleene, 29 November 1935. Excerpt in Davis 1982: 9. (Scholar)
–––, 1935c, “A Proof of Freedom from Contradiction”, Proceedings of the National Academy of Sciences, 21(5): 275–281. doi:10.1073/pnas.21.5.275 (Scholar)
–––, 1936a, “An Unsolvable Problem of Elementary Number Theory”, American Journal of Mathematics, 58(2): 345–363. doi:10.2307/2371045 (Scholar)
–––, 1936b, “A Note on the Entscheidungsproblem”, The Journal of Symbolic Logic, 1(1): 40–41. doi:10.2307/2269326 (Scholar)
–––, 1937a, Review of Turing 1936, The Journal of Symbolic Logic, 2(1): 42–43. doi:10.1017/S002248120003958X (Scholar)
–––, 1937b, Review of Post 1936, The Journal of Symbolic Logic, 2(1): 43. doi:10.1017/S0022481200039591 (Scholar)
–––, 1941, The Calculi of Lambda-Conversion, Princeton, NJ: Princeton University Press. (Scholar)
Church, Alonzo and J. Barkley Rosser, 1936, “Some Properties of Conversion”, Transactions of the American Mathematical Society, 39(3): 472–482. doi:10.1090/s0002-9947-1936-1501858-0 (Scholar)
Copeland, B. Jack, 1998a, “Even Turing Machines Can Compute Uncomputable Functions”, in Unconventional Models of Computation, Proceedings of the 1st International Conference, New Zealand, Christian S. Calude, John Casti, and Michael J. Dinneen (eds), London: Springer-Verlag, 150–164. (Scholar)
–––, 1998b, “Super Turing-Machines”, Complexity, 4(1): 30–32. doi:10.1002/(sici)1099-0526(199809/10)4:1<30::AID-CPLX9>3.0.CO;2-8 (Scholar)
–––, 2000, “Narrow versus Wide Mechanism: Including a Re-Examination of Turing’s Views on the Mind-Machine Issue”, The Journal of Philosophy, 97(1): 5–32. doi:10.2307/2678472 (Scholar)
–––, 2002a, “Accelerating Turing Machines”, Minds and Machines, 12(2): 281–300. (In a special issue on the Church-Turing thesis, edited by Carol Cleland.) doi:10.1023/a:1015607401307 (Scholar)
––– (ed.), 2004, The Essential Turing: Seminal Writings in Computing, Logic, Philosophy, Artificial Intelligence, and Artificial Life, Oxford: Clarendon Press. doi:10.1093/oso/9780198250791.001.0001 (Scholar)
Copeland, B. Jack and Zhao Fan, 2022, “Did Turing Stand on Gödel’s Shoulders?”, The Mathematical Intelligencer, 44: 308–319. doi:10.1007/s00283-022-10177-y (Scholar)
–––, 2023, “Turing and von Neumann: From Logic to the Computer”, Philosophies, 8(2): 1–30. (Scholar)
Copeland, B. Jack, Carl J. Posy, and Oron Shagrir (eds), 2013, Computability: Turing, Gödel, Church, and Beyond, Cambridge, MA: The MIT Press. (Scholar)
Copeland, B. Jack and Oron Shagrir, 2007, “Physical Computation: How General Are Gandy’s Principles for Mechanisms?”, Minds and Machines, 17(2): 217–231. doi:10.1007/s11023-007-9058-2 (Scholar)
–––, 2011, “Do Accelerating Turing Machines Compute the Uncomputable?”, Minds and Machines, 21(2): 221–239. doi:10.1007/s11023-011-9238-y (Scholar)
–––, 2013, “Turing versus Gödel on Computability and the Mind”, in Copeland, Posy, and Shagrir 2013: 1–33 (ch. 1). (Scholar)
–––, 2019, “The Church-Turing Thesis: Logical Limit or Breachable Barrier?”, Communications of the ACM, 62(1): 66–74. doi:10.1145/3198448 (Scholar)
–––, 2020, “Physical Computability Theories”, in Quantum, Probability, Logic: The Work and Influence of Itamar Pitowsky, Meir Hemmo and Orly Shenker (eds), Cham: Springer: 217–231. (Scholar)
Copeland, B. Jack, Oron Shagrir, and Mark Sprevak, 2018, “Zuse’s Thesis, Gandy’s Thesis, and Penrose’s Thesis”, in Physical Perspectives on Computation, Computational Perspectives on Physics, Michael E. Cuffaro and Samuel C. Fletcher (eds), Cambridge: Cambridge University Press, 39–59. doi:10.1017/9781316759745.003 (Scholar)
Copeland, B. Jack and Richard Sylvan, 1999, “Beyond the Universal Turing Machine”, Australasian Journal of Philosophy, 77(1): 46–66. doi:10.1080/00048409912348801 (Scholar)
Couturat, Louis (ed.), 1903, Opuscules et Fragments Inédits de Leibniz, Paris: Alcan. Facsimile of the 1903 edition, Hildesheim: G. Olms, 1961. (Scholar)
Cubitt, Toby S., David Perez-Garcia, and Michael M. Wolf, 2015, “Undecidability of the Spectral Gap”, Nature, 528(7581): 207–211. doi:10.1038/nature16059 (Scholar)
Curry, Haskell B., 1929, “An Analysis of Logical Substitution”, American Journal of Mathematics, 51(3): 363–384. doi:10.2307/2370728 (Scholar)
–––, 1930a, “Grundlagen der kombinatorischen Logik, Teil 1”, American Journal of Mathematics, 52(3): 509–536. doi:10.2307/2370619 (Scholar)
–––, 1930b, “Grundlagen der kombinatorischen Logik, Teil 2”, American Journal of Mathematics, 52(4): 789–834. doi:10.2307/2370716 (Scholar)
–––, 1932, “Some Additions to the Theory of Combinators”, American Journal of Mathematics, 54(3): 551–558. doi:10.2307/2370900 (Scholar)
Curry, Haskell B. and Robert Feys, 1958, Combinatory Logic, Amsterdam: North-Holland. (Scholar)
da Costa, Newton C. A. and Francisco A. Doria, 1991, “Classical Physics and Penrose’s Thesis”, Foundations of Physics Letters, 4(4): 363–373. doi:10.1007/bf00665895 (Scholar)
–––, 1994, “Undecidable Hopf Bifurcation with Undecidable Fixed Point”, International Journal of Theoretical Physics, 33(9): 1885–1903. doi:10.1007/bf00671031 (Scholar)
Davies, E. Brian, 2001, “Building Infinite Machines”, The British Journal for the Philosophy of Science, 52(4): 671–682. doi:10.1093/bjps/52.4.671 (Scholar)
Davis, Martin, 1958, Computability and Unsolvability, New York: McGraw-Hill. (Scholar)
––– (ed.), 1965, The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions, Hewlett, NY: Raven Press. (Scholar)
–––, 1982, “Why Gödel Didn’t Have Church’s Thesis”, Information and Control, 54(1–2): 3–24. doi:10.1016/S0019-9958(82)91226-8 (Scholar)
Davis, Martin and Wilfried Sieg, 2015, “Conceptual Confluence in 1936: Post and Turing”, in Turing’s Revolution, Giovanni Sommaruga and Thomas Strahm (eds), Cham: Birkhäuser, 3–27. doi:10.1007/978-3-319-22156-4_1 (Scholar)
Dawson, John W., 2006, “Gödel and the Origins of Computer Science”, in Logical Approaches to Computational Barriers, Arnold Beckmann, Ulrich Berger, Benedikt Löwe, and John V. Tucker (eds), (Lecture Notes in Computer Science 3988), Berlin/Heidelberg: Springer, 133–136. doi:10.1007/11780342_14 (Scholar)
Dedekind, Richard, 1888, Was Sind und was Sollen die Zahlen? Braunschweig: Vieweg. (Scholar)
Dershowitz, Nachum and Yuri Gurevich, 2008, “A Natural Axiomatization of Computability and Proof of Church’s Thesis”, Bulletin of Symbolic Logic, 14(3): 299–350. doi:10.2178/bsl/1231081370 (Scholar)
Deutsch, David, 1985, “Quantum Theory, the Church–Turing Principle and the Universal Quantum Computer”, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 400(1818): 97–117. doi:10.1098/rspa.1985.0070 (Scholar)
Doyle, Jon, 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(4): 519–520. doi:10.1023/a:1021126521437 (Scholar)
Earman, John, 1986, A Primer on Determinism, Dordrecht: Reidel. (Scholar)
Eisert, Jens, Markus P. Müller, and Christian Gogolin, 2012, “Quantum Measurement Occurrence Is Undecidable”, Physical Review Letters, 108(26): 260501 (5 pages). doi:10.1103/physrevlett.108.260501 (Scholar)
Engeler, Erwin, 1983 [1993], Metamathematik der Elementarmathematik, Berlin: Springer. Translated as Foundations of Mathematics: Questions of Analysis, Geometry & Algorithmics, Charles B. Thomas (trans.), Berlin/New York: Springer-Verlag. (Scholar)
Etesi, Gábor and István Németi, 2002, “Non-Turing Computations via Malament-Hogarth Space-Times”, International Journal of Theoretical Physics, 41(2): 341–370. doi:10.1023/a:1014019225365 (Scholar)
Frankena, William and Arthur W. Burks, 1964, “Cooper Harold Langford 1895–1964”, Proceedings and Addresses of the American Philosophical Association, 38: 99–101. (Scholar)
Gandy, Robin, 1980, “Church’s Thesis and Principles for Mechanisms”, in The Kleene Symposium, Jon Barwise, H. Jerome Keisler, and Kenneth Kunen (eds), Amsterdam: North-Holland, 123–148. doi:10.1016/s0049-237x(08)71257-6 (Scholar)
–––, 1988, “The Confluence of Ideas in 1936”, in The Universal Turing Machine: A Half-Century Survey, Rolf Herken (ed.), New York: Oxford University Press, 51–102. (Scholar)
Geroch, Robert and James B. Hartle, 1986, “Computability and Physical Theories”, Foundations of Physics, 16(6): 533–550. doi:10.1007/bf01886519 (Scholar)
Gödel, Kurt, 1930, “Die Vollständigkeit der Axiome des logischen Funktionenkalküls”, Monatshefte für Mathematik und Physik, 37: 349–360. doi:10.1007/bf01696781 (Scholar)
–––, 1931, “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I”, Monatshefte für Mathematik und Physik, 38: 173–198. doi:10.1007/bf01700692 (Scholar)
–––, 1933, “Zum Entscheidungsproblem des logischen Funktionenkalküls”, Monatshefte für Mathematik und Physik, 40: 433–443. doi:10.1007/bf01708881 (Scholar)
–––, 1934 [1965], “On Undecidable Propositions of Formal Mathematical Systems”, Lecture notes taken by Stephen Kleene and J. Barkley Rosser at the Institute for Advanced Study, in Davis 1965: 39–74. (Scholar)
–––, 1936, “Über die Länge von Beweisen”, Ergebnisse eirtes mathematischen Kolloquiums, 7: 23–24. (Scholar)
–––, 193?, “Undecidable Diophantine Propositions”, in Gödel 1995: 164–175. (Scholar)
–––, 1946, “Remarks Before the Princeton Bicentennial Conference”, in Gödel 1990: 150–153. (Scholar)
–––, 1951, “Some Basic Theorems on the Foundations of Mathematics and Their Implications”, in Gödel 1995: 304–323. (Scholar)
–––, 1965a, “Postscriptum” to Gödel 1934, in Davis 1965: 71–73. (Scholar)
–––, 1965b, letter to Davis, 15 February 1965. Excerpt in Davis 1982: 8. (Scholar)
–––, Kurt Gödel: Collected Works, 5 volumes, Solomon Feferman et al. (eds), Oxford: Clarendon Press.
- 1986, Volume 1: Publications 1929–1936 (Scholar)
- 1990, Volume 2: Publications 1938–1974
- 1995, Volume 3: Unpublished Essays and Lectures
Gurevich, Yuri, 2012, “What Is an Algorithm?”, in SOFSEM 2012: Theory and Practice of Computer Science, Mária Bieliková, Gerhard Friedrich, Georg Gottlob, Stefan Katzenbeisser, and György Turán (eds), (Lecture Notes in Computer Science 7147), Berlin/Heidelberg: Springer, 31–42. doi:10.1007/978-3-642-27660-6_3 (Scholar)
Guttenplan, Samuel D. (ed.), 1994, A Companion to the Philosophy of Mind, Oxford/Cambridge, MA: Blackwell Reference. doi:10.1002/9781405164597. (Scholar)
Hardy, G. H., 1929, “Mathematical Proof”, Mind, 38(149): 1–25. doi:10.1093/mind/xxxviii.149.1 (Scholar)
Harel, David, 1992, Algorithmics: The Spirit of Computing, second edition, Reading, MA: Addison-Wesley. (Scholar)
Herbrand, Jacques, 1930a, Recherches sur la Théorie de la Démonstration, doctoral thesis, University of Paris. In Herbrand 1968. (Scholar)
–––, 1930b, “Les bases de la logique Hilbertienne”, Revue de Métaphysique et de Morale, 37(2): 243–255. (Scholar)
–––, 1931a, “Sur le Problème Fondamental de la Logique Mathématique”, Sprawozdania z Posiedzeń Towarzystwa Naukowego Warszawskiego, Wydział III, 24: 12–56. (Scholar)
–––, 1931b, Precis of Herbrand 1930a, Annales de l’Université de Paris, 6: 186–189. In Herbrand 1968. (Scholar)
–––, 1932, “Sur la non-contradiction de l’Arithmétique”, Journal für die reine und angewandte Mathematik, 166: 1–8. doi:10.1515/crll.1932.166.1 (Scholar)
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–––, 1930a, “Probleme der Grundlegung der Mathematik”, Mathematische Annalen, 102(1): 1–9. doi:10.1007/bf01782335 (Scholar)
–––, 1930b, “Naturerkennen und Logik”, Die Naturwissenschaften, 18(47–49): 959–963. doi:10.1007/bf01492194 (Scholar)
Hilbert, David and Wilhelm Ackermann, 1928, Grundzüge der Theoretischen Logik, Berlin: Springer. (Scholar)
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–––, 1939, Grundlagen der Mathematik, Volume 2, Berlin: Springer. (Scholar)
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Hogarth, Mark, 1994, “Non-Turing Computers and Non-Turing Computability”, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 1994(1): 126–138. doi:10.1086/psaprocbienmeetp.1994.1.193018 (Scholar)
–––, 2004, “Deciding Arithmetic Using SAD Computers”, The British Journal for the Philosophy of Science, 55(4): 681–691. doi:10.1093/bjps/55.4.681 (Scholar)
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Kalmár, László, 1959, “An Argument Against the Plausibility of Church’s Thesis”, in Constructivity in Mathematics: Proceedings of the colloquium held at Amsterdam 1957, Arend Heyting (ed.), Amsterdam: North-Holland: 72–80. (Scholar)
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Ketner, Kenneth L. and Arthur F. Stewart, 1984, “The Early History of Computer Design: Charles Sanders Peirce and Marquand’s Logical Machines”, The Princeton University Library Chronicle, 45(3): 187–224. doi:10.2307/26402393 (Scholar)
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Kleene, Stephen C., 1934, “Proof by Cases in Formal Logic”, Annals of Mathematics, second series 35(3): 529–544. doi:10.2307/1968749 (Scholar)
–––, 1935a, “A Theory of Positive Integers in Formal Logic. Part I”, American Journal of Mathematics, 57(1): 153–173. doi:10.2307/2372027 (Scholar)
–––, 1935b, “A Theory of Positive Integers in Formal Logic. Part II”, American Journal of Mathematics, 57(2): 219–244. doi:10.2307/2371199 (Scholar)
–––, 1936a, “General Recursive Functions of Natural Numbers”, Mathematische Annalen, 112(1): 727–742. doi:10.1007/bf01565439 (Scholar)
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–––, 1987, “Reflections on Church’s Thesis”, Notre Dame Journal of Formal Logic, 28(4): 490–498. doi:10.1305/ndjfl/1093637645 (Scholar)
Kleene, Stephen C. and J. Barkley Rosser, 1935, “The Inconsistency of Certain Formal Logics”, Annals of Mathematics, second series 36(3): 630–636. doi:10.2307/1968646 (Scholar)
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–––, 1974, “A Notion of Mechanistic Theory”, Synthese, 29(1–4): 11–26. doi:10.1007/bf00484949 (Scholar)
–––, 1982, Review of Pour-El and Richards 1979 and 1981, The Journal of Symbolic Logic, 47(4): 900–902. doi:10.2307/2273108 (Scholar)
Kripke, Saul A., 2013, “The Church-Turing ‘Thesis’ as a Special Corollary of Gödel’s Completeness Theorem”, in Copeland, Posy, and Shagrir 2013: 77–104 (ch. 4). (Scholar)
Langford, C. Harold, 1926a, “Some Theorems on Deducibility”, Annals of Mathematics, second series 28(1/4): 16–40. doi:10.2307/1968352 (Scholar)
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