Church–Turing thesis (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Church–Turing thesis" in English language version.

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Abramson, Darren (2011). "Philosophy of mind is (in part) philosophy of computer science". Minds and Machines. 21 (2): 203–219. doi:10.1007/s11023-011-9236-0. S2CID 32116031.

archive.org

Rosser 1939 in Davis 1965:225. Rosser, J. B. (1939). "An Informal Exposition of Proofs of Godel's Theorem and Church's Theorem". The Journal of Symbolic Logic. 4 (2): 53–60. doi:10.2307/2269059. JSTOR 2269059. S2CID 39499392. Davis, Martin, ed. (1965). The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions. New York: Raven Press. Includes original papers by Gödel, Church, Turing, Rosser, Kleene, and Post mentioned in this section.
cf. footnote 3 in Church 1936a An Unsolvable Problem of Elementary Number Theory in Davis 1965:89. Church, Alonzo (April 1936a). "An Unsolvable Problem of Elementary Number Theory" (PDF). American Journal of Mathematics. 58 (2): 345–363. doi:10.2307/2371045. JSTOR 2371045. S2CID 14181275. Archived from the original (PDF) on 2020-02-27. Davis, Martin, ed. (1965). The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions. New York: Raven Press. Includes original papers by Gödel, Church, Turing, Rosser, Kleene, and Post mentioned in this section.
Sieg 1997:160 quoting from the 1935 letter written by Church to Kleene, cf. Footnote 3 in Gödel 1934 in Davis 1965:44. Davis, Martin, ed. (1965). The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions. New York: Raven Press. Includes original papers by Gödel, Church, Turing, Rosser, Kleene, and Post mentioned in this section.
cf. Church 1936 in Davis 1965:105ff.. Davis, Martin, ed. (1965). The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions. New York: Raven Press. Includes original papers by Gödel, Church, Turing, Rosser, Kleene, and Post mentioned in this section.
Davis's commentary before Gödel 1934 in Davis 1965:40. Davis, Martin, ed. (1965). The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions. New York: Raven Press. Includes original papers by Gödel, Church, Turing, Rosser, Kleene, and Post mentioned in this section.
cf. Editor's footnote to Post 1936 Finite Combinatory Process. Formulation I. at Davis 1965:289. Davis, Martin, ed. (1965). The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions. New York: Raven Press. Includes original papers by Gödel, Church, Turing, Rosser, Kleene, and Post mentioned in this section.
Post 1936 in Davis 1965:291, footnote 8. Davis, Martin, ed. (1965). The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions. New York: Raven Press. Includes original papers by Gödel, Church, Turing, Rosser, Kleene, and Post mentioned in this section.
Turing 1936–1937 in Davis 1965:263ff.. Davis, Martin, ed. (1965). The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions. New York: Raven Press. Includes original papers by Gödel, Church, Turing, Rosser, Kleene, and Post mentioned in this section.
cf. Church 1934 in Davis 1965:100, also Turing 1939 in Davis 1965:160. Davis, Martin, ed. (1965). The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions. New York: Raven Press. Includes original papers by Gödel, Church, Turing, Rosser, Kleene, and Post mentioned in this section. Davis, Martin, ed. (1965). The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions. New York: Raven Press. Includes original papers by Gödel, Church, Turing, Rosser, Kleene, and Post mentioned in this section.
italics added, Rosser 1939 in Davis 1965:226. Rosser, J. B. (1939). "An Informal Exposition of Proofs of Godel's Theorem and Church's Theorem". The Journal of Symbolic Logic. 4 (2): 53–60. doi:10.2307/2269059. JSTOR 2269059. S2CID 39499392. Davis, Martin, ed. (1965). The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions. New York: Raven Press. Includes original papers by Gödel, Church, Turing, Rosser, Kleene, and Post mentioned in this section.
Kleene 1943, p. 60 in Davis 1965:274. Footnotes omitted. Kleene, Stephen Cole (1943). "Recursive Predicates and Quantifiers". Transactions of the American Mathematical Society. 53 (1): 41–73. doi:10.2307/1990131. JSTOR 1990131. Reprinted in The Undecidable, p. 255ff. Kleene refined his definition of "general recursion" and proceeded in his chapter "12. Algorithmic theories" to posit "Thesis I" (p. 274); he would later repeat this thesis (in Kleene 1952:300) and name it "Church's Thesis" (Kleene 1952:317) (i.e., the Church thesis). Davis, Martin, ed. (1965). The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions. New York: Raven Press. Includes original papers by Gödel, Church, Turing, Rosser, Kleene, and Post mentioned in this section.

books.google.com

Gödel, Kurt (1995) [193?]. "Undecidable Diophantine Propositions". In Feferman, Solomon (ed.). Collected Works. Vol. 3. New York: Oxford University Press. p. 168. ISBN 978-0-19-507255-6. OCLC 928791907.

chalmers.se

cse.chalmers.se

Turing, Alan (2004). The essential Turing : seminal writings in computing, logic, philosophy, artificial intelligence, and artificial life, plus the secrets of Enigma (PDF). Oxford: Clarendon Press. p. 44. ISBN 9780198250791. Retrieved 2021-12-06.

claymath.org

"Official Problem Description" (PDF). Archived from the original (PDF) on 2005-11-24.

doi.org

Soare, Robert I. (September 1996). "Computability and Recursion". Bulletin of Symbolic Logic. 2 (3): 284–321. CiteSeerX 10.1.1.35.5803. doi:10.2307/420992. JSTOR 420992. S2CID 5894394.
Church 1936a Church, Alonzo (April 1936a). "An Unsolvable Problem of Elementary Number Theory" (PDF). American Journal of Mathematics. 58 (2): 345–363. doi:10.2307/2371045. JSTOR 2371045. S2CID 14181275. Archived from the original (PDF) on 2020-02-27.
Kleene 1936 Kleene, Stephen Cole (1936). "Lambda-Definability and Recursiveness". Duke Mathematical Journal. 2 (2): 340–353. doi:10.1215/s0012-7094-36-00227-2.
Turing 1937a Turing, A. M. (1937a) [Delivered to the Society November 1936], "On Computable Numbers, with an Application to the Entscheidungsproblem" (PDF), Proceedings of the London Mathematical Society, 2, vol. 42, pp. 230–265, doi:10.1112/plms/s2-42.1.230, S2CID 73712 and Turing, A. M. (1938). "On Computable Numbers, with an Application to the Entscheidungsproblem: A correction". Proceedings of the London Mathematical Society. 2. Vol. 43 (published 1937). pp. 544–546. doi:10.1112/plms/s2-43.6.544. (See also: Davis 1965:115ff.)
Kleene 1936 Kleene, Stephen Cole (1936). "Lambda-Definability and Recursiveness". Duke Mathematical Journal. 2 (2): 340–353. doi:10.1215/s0012-7094-36-00227-2.
Turing 1937b. Proof outline on p. 153: $\lambda {\mbox{-definable}}$ ${\stackrel {triv}{\implies }}$ $\lambda {\mbox{-}}K{\mbox{-definable}}$ ${\stackrel {160}{\implies }}$ ${\mbox{Turing computable}}$ ${\stackrel {161}{\implies }}$ $\mu {\mbox{-recursive}}$ ${\stackrel {Kleene}{\implies }}$ ^[10] $\lambda {\mbox{-definable}}$ Turing, Alan Mathison (December 1937b). "Computability and λ-Definability" (PDF). Journal of Symbolic Logic. 2 (4): 153–163. doi:10.2307/2268280. JSTOR 2268280. S2CID 2317046. Archived from the original (PDF) on 2020-08-09.
Rosser 1939 in Davis 1965:225. Rosser, J. B. (1939). "An Informal Exposition of Proofs of Godel's Theorem and Church's Theorem". The Journal of Symbolic Logic. 4 (2): 53–60. doi:10.2307/2269059. JSTOR 2269059. S2CID 39499392. Davis, Martin, ed. (1965). The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions. New York: Raven Press. Includes original papers by Gödel, Church, Turing, Rosser, Kleene, and Post mentioned in this section.
cf. footnote 3 in Church 1936a An Unsolvable Problem of Elementary Number Theory in Davis 1965:89. Church, Alonzo (April 1936a). "An Unsolvable Problem of Elementary Number Theory" (PDF). American Journal of Mathematics. 58 (2): 345–363. doi:10.2307/2371045. JSTOR 2371045. S2CID 14181275. Archived from the original (PDF) on 2020-02-27. Davis, Martin, ed. (1965). The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions. New York: Raven Press. Includes original papers by Gödel, Church, Turing, Rosser, Kleene, and Post mentioned in this section.
For a detailed discussion of Gödel's adoption of Turing's machines as models of computation, see Shagrir, Oron (2006-06-15). "Gödel on Turing on Computability" (PDF). Church's Thesis After 70 Years. De Gruyter. pp. 393–419. doi:10.1515/9783110325461.393. ISBN 978-3-11-032494-5. Archived from the original (PDF) on 2015-12-17. Retrieved 2016-02-08.
Turing 1937a. Turing, A. M. (1937a) [Delivered to the Society November 1936], "On Computable Numbers, with an Application to the Entscheidungsproblem" (PDF), Proceedings of the London Mathematical Society, 2, vol. 42, pp. 230–265, doi:10.1112/plms/s2-42.1.230, S2CID 73712 and Turing, A. M. (1938). "On Computable Numbers, with an Application to the Entscheidungsproblem: A correction". Proceedings of the London Mathematical Society. 2. Vol. 43 (published 1937). pp. 544–546. doi:10.1112/plms/s2-43.6.544. (See also: Davis 1965:115ff.)
Church 1937. Church, Alonzo (March 1937). "Review: A. M. Turing, On Computable Numbers, with an Application to the Entscheidungsproblem". Journal of Symbolic Logic. 2 (1): 42–43. doi:10.2307/2268810. JSTOR 2268810.
italics added, Rosser 1939 in Davis 1965:226. Rosser, J. B. (1939). "An Informal Exposition of Proofs of Godel's Theorem and Church's Theorem". The Journal of Symbolic Logic. 4 (2): 53–60. doi:10.2307/2269059. JSTOR 2269059. S2CID 39499392. Davis, Martin, ed. (1965). The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions. New York: Raven Press. Includes original papers by Gödel, Church, Turing, Rosser, Kleene, and Post mentioned in this section.
Kleene 1943, p. 60 in Davis 1965:274. Footnotes omitted. Kleene, Stephen Cole (1943). "Recursive Predicates and Quantifiers". Transactions of the American Mathematical Society. 53 (1): 41–73. doi:10.2307/1990131. JSTOR 1990131. Reprinted in The Undecidable, p. 255ff. Kleene refined his definition of "general recursion" and proceeded in his chapter "12. Algorithmic theories" to posit "Thesis I" (p. 274); he would later repeat this thesis (in Kleene 1952:300) and name it "Church's Thesis" (Kleene 1952:317) (i.e., the Church thesis). Davis, Martin, ed. (1965). The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions. New York: Raven Press. Includes original papers by Gödel, Church, Turing, Rosser, Kleene, and Post mentioned in this section.
Piccinini, Gualtiero (January 2007). "Computationalism, the Church–Turing Thesis, and the Church–Turing Fallacy" (PDF). Synthese. 154 (1): 97–120. CiteSeerX 10.1.1.360.9796. doi:10.1007/s11229-005-0194-z. S2CID 494161. Archived (PDF) from the original on 2008-04-24.
Abramson, Darren (2011). "Philosophy of mind is (in part) philosophy of computer science". Minds and Machines. 21 (2): 203–219. doi:10.1007/s11023-011-9236-0. S2CID 32116031.

eatcs.org

Eberbach & Wegner 2003, p. 287. Eberbach, E.; Wegner, P. (October 2003). "Beyond Turing Machines" (PDF). Bulletin of the European Association for Theoretical Computer Science (81): 279–304. CiteSeerX 10.1.1.61.9759. Archived (PDF) from the original on 2016-03-15.

huji.ac.il

moon.cc.huji.ac.il

For a detailed discussion of Gödel's adoption of Turing's machines as models of computation, see Shagrir, Oron (2006-06-15). "Gödel on Turing on Computability" (PDF). Church's Thesis After 70 Years. De Gruyter. pp. 393–419. doi:10.1515/9783110325461.393. ISBN 978-3-11-032494-5. Archived from the original (PDF) on 2015-12-17. Retrieved 2016-02-08.

jstor.org

Soare, Robert I. (September 1996). "Computability and Recursion". Bulletin of Symbolic Logic. 2 (3): 284–321. CiteSeerX 10.1.1.35.5803. doi:10.2307/420992. JSTOR 420992. S2CID 5894394.
Church 1936a Church, Alonzo (April 1936a). "An Unsolvable Problem of Elementary Number Theory" (PDF). American Journal of Mathematics. 58 (2): 345–363. doi:10.2307/2371045. JSTOR 2371045. S2CID 14181275. Archived from the original (PDF) on 2020-02-27.
Turing 1937b. Proof outline on p. 153: $\lambda {\mbox{-definable}}$ ${\stackrel {triv}{\implies }}$ $\lambda {\mbox{-}}K{\mbox{-definable}}$ ${\stackrel {160}{\implies }}$ ${\mbox{Turing computable}}$ ${\stackrel {161}{\implies }}$ $\mu {\mbox{-recursive}}$ ${\stackrel {Kleene}{\implies }}$ ^[10] $\lambda {\mbox{-definable}}$ Turing, Alan Mathison (December 1937b). "Computability and λ-Definability" (PDF). Journal of Symbolic Logic. 2 (4): 153–163. doi:10.2307/2268280. JSTOR 2268280. S2CID 2317046. Archived from the original (PDF) on 2020-08-09.
Rosser 1939 in Davis 1965:225. Rosser, J. B. (1939). "An Informal Exposition of Proofs of Godel's Theorem and Church's Theorem". The Journal of Symbolic Logic. 4 (2): 53–60. doi:10.2307/2269059. JSTOR 2269059. S2CID 39499392. Davis, Martin, ed. (1965). The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions. New York: Raven Press. Includes original papers by Gödel, Church, Turing, Rosser, Kleene, and Post mentioned in this section.
cf. footnote 3 in Church 1936a An Unsolvable Problem of Elementary Number Theory in Davis 1965:89. Church, Alonzo (April 1936a). "An Unsolvable Problem of Elementary Number Theory" (PDF). American Journal of Mathematics. 58 (2): 345–363. doi:10.2307/2371045. JSTOR 2371045. S2CID 14181275. Archived from the original (PDF) on 2020-02-27. Davis, Martin, ed. (1965). The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions. New York: Raven Press. Includes original papers by Gödel, Church, Turing, Rosser, Kleene, and Post mentioned in this section.
Church 1937. Church, Alonzo (March 1937). "Review: A. M. Turing, On Computable Numbers, with an Application to the Entscheidungsproblem". Journal of Symbolic Logic. 2 (1): 42–43. doi:10.2307/2268810. JSTOR 2268810.
italics added, Rosser 1939 in Davis 1965:226. Rosser, J. B. (1939). "An Informal Exposition of Proofs of Godel's Theorem and Church's Theorem". The Journal of Symbolic Logic. 4 (2): 53–60. doi:10.2307/2269059. JSTOR 2269059. S2CID 39499392. Davis, Martin, ed. (1965). The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions. New York: Raven Press. Includes original papers by Gödel, Church, Turing, Rosser, Kleene, and Post mentioned in this section.
Kleene 1943, p. 60 in Davis 1965:274. Footnotes omitted. Kleene, Stephen Cole (1943). "Recursive Predicates and Quantifiers". Transactions of the American Mathematical Society. 53 (1): 41–73. doi:10.2307/1990131. JSTOR 1990131. Reprinted in The Undecidable, p. 255ff. Kleene refined his definition of "general recursion" and proceeded in his chapter "12. Algorithmic theories" to posit "Thesis I" (p. 274); he would later repeat this thesis (in Kleene 1952:300) and name it "Church's Thesis" (Kleene 1952:317) (i.e., the Church thesis). Davis, Martin, ed. (1965). The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions. New York: Raven Press. Includes original papers by Gödel, Church, Turing, Rosser, Kleene, and Post mentioned in this section.

logicmatters.net

In his review of Church's Thesis after 70 Years edited by Adam Olszewski et al. 2006, Peter Smith's criticism of a paper by Muraswski and Wolenski suggests 4 "lines" re the status of the Church–Turing Thesis: (1) empirical hypothesis (2) axiom or theorem, (3) definition, (4) explication. But Smith opines that (4) is indistinguishable from (3), cf. Smith (2007-07-11) Church's Thesis after 70 Years at http://www.logicmatters.net/resources/pdfs/CTT.pdf
A collection of papers can be found in Olszewski, Woleński & Janusz (2006). Also a review of this collection: Smith, Peter (2007-07-11). "Church's Thesis after 70 Years" (PDF). Olszewski, Adam; Woleński, Jan; Janusz, Robert, eds. (2006). Church's Thesis After 70 Years. Frankfurt: Ontos. ISBN 978-3-938793-09-1. OCLC 909679288.

merriam-webster.com

See also "effective". Merriam-Webster's Online Dictionary (11th ed.). Retrieved 2014-07-26, which also gives these definitions for "effective" – the first ["producing a decided, decisive, or desired effect"] as the definition for sense "1a" of the word "effective", and the second ["capable of producing a result"] as part of the "Synonym Discussion of EFFECTIVE" there, (in the introductory part, where it summarizes the similarities between the meanings of the words "effective", "effectual", "efficient", and "efficacious").

ox.ac.uk

comlab.ox.ac.uk

Turing 1937a Turing, A. M. (1937a) [Delivered to the Society November 1936], "On Computable Numbers, with an Application to the Entscheidungsproblem" (PDF), Proceedings of the London Mathematical Society, 2, vol. 42, pp. 230–265, doi:10.1112/plms/s2-42.1.230, S2CID 73712 and Turing, A. M. (1938). "On Computable Numbers, with an Application to the Entscheidungsproblem: A correction". Proceedings of the London Mathematical Society. 2. Vol. 43 (published 1937). pp. 544–546. doi:10.1112/plms/s2-43.6.544. (See also: Davis 1965:115ff.)
Turing 1937a. Turing, A. M. (1937a) [Delivered to the Society November 1936], "On Computable Numbers, with an Application to the Entscheidungsproblem" (PDF), Proceedings of the London Mathematical Society, 2, vol. 42, pp. 230–265, doi:10.1112/plms/s2-42.1.230, S2CID 73712 and Turing, A. M. (1938). "On Computable Numbers, with an Application to the Entscheidungsproblem: A correction". Proceedings of the London Mathematical Society. 2. Vol. 43 (published 1937). pp. 544–546. doi:10.1112/plms/s2-43.6.544. (See also: Davis 1965:115ff.)

princeton.edu

findingaids.princeton.edu

Correspondence between Max Newman and Church in Alonzo Church papers

webspace.princeton.edu

Turing, A. M. (1938). Systems of Logic Based on Ordinals (PDF) (PhD). Princeton University. p. 8. Archived from the original (PDF) on 2012-10-23. Retrieved 2012-06-23.

cs.princeton.edu

Arora, Sanjeev; Barak, Boaz (2009). Complexity Theory: A Modern Approach. Cambridge University Press. ISBN 978-0-521-42426-4. Sections 1.4, "Machines as strings and the universal Turing machine" and 1.7, "Proof of theorem 1.9".

psu.edu

citeseerx.ist.psu.edu

Soare, Robert I. (September 1996). "Computability and Recursion". Bulletin of Symbolic Logic. 2 (3): 284–321. CiteSeerX 10.1.1.35.5803. doi:10.2307/420992. JSTOR 420992. S2CID 5894394.
Piccinini, Gualtiero (January 2007). "Computationalism, the Church–Turing Thesis, and the Church–Turing Fallacy" (PDF). Synthese. 154 (1): 97–120. CiteSeerX 10.1.1.360.9796. doi:10.1007/s11229-005-0194-z. S2CID 494161. Archived (PDF) from the original on 2008-04-24.
Eberbach & Wegner 2003, p. 287. Eberbach, E.; Wegner, P. (October 2003). "Beyond Turing Machines" (PDF). Bulletin of the European Association for Theoretical Computer Science (81): 279–304. CiteSeerX 10.1.1.61.9759. Archived (PDF) from the original on 2016-03-15.

semanticscholar.org

api.semanticscholar.org

Soare, Robert I. (September 1996). "Computability and Recursion". Bulletin of Symbolic Logic. 2 (3): 284–321. CiteSeerX 10.1.1.35.5803. doi:10.2307/420992. JSTOR 420992. S2CID 5894394.
Church 1936a Church, Alonzo (April 1936a). "An Unsolvable Problem of Elementary Number Theory" (PDF). American Journal of Mathematics. 58 (2): 345–363. doi:10.2307/2371045. JSTOR 2371045. S2CID 14181275. Archived from the original (PDF) on 2020-02-27.
Turing 1937a Turing, A. M. (1937a) [Delivered to the Society November 1936], "On Computable Numbers, with an Application to the Entscheidungsproblem" (PDF), Proceedings of the London Mathematical Society, 2, vol. 42, pp. 230–265, doi:10.1112/plms/s2-42.1.230, S2CID 73712 and Turing, A. M. (1938). "On Computable Numbers, with an Application to the Entscheidungsproblem: A correction". Proceedings of the London Mathematical Society. 2. Vol. 43 (published 1937). pp. 544–546. doi:10.1112/plms/s2-43.6.544. (See also: Davis 1965:115ff.)
Turing 1937b. Proof outline on p. 153: $\lambda {\mbox{-definable}}$ ${\stackrel {triv}{\implies }}$ $\lambda {\mbox{-}}K{\mbox{-definable}}$ ${\stackrel {160}{\implies }}$ ${\mbox{Turing computable}}$ ${\stackrel {161}{\implies }}$ $\mu {\mbox{-recursive}}$ ${\stackrel {Kleene}{\implies }}$ ^[10] $\lambda {\mbox{-definable}}$ Turing, Alan Mathison (December 1937b). "Computability and λ-Definability" (PDF). Journal of Symbolic Logic. 2 (4): 153–163. doi:10.2307/2268280. JSTOR 2268280. S2CID 2317046. Archived from the original (PDF) on 2020-08-09.
Rosser 1939 in Davis 1965:225. Rosser, J. B. (1939). "An Informal Exposition of Proofs of Godel's Theorem and Church's Theorem". The Journal of Symbolic Logic. 4 (2): 53–60. doi:10.2307/2269059. JSTOR 2269059. S2CID 39499392. Davis, Martin, ed. (1965). The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions. New York: Raven Press. Includes original papers by Gödel, Church, Turing, Rosser, Kleene, and Post mentioned in this section.
cf. footnote 3 in Church 1936a An Unsolvable Problem of Elementary Number Theory in Davis 1965:89. Church, Alonzo (April 1936a). "An Unsolvable Problem of Elementary Number Theory" (PDF). American Journal of Mathematics. 58 (2): 345–363. doi:10.2307/2371045. JSTOR 2371045. S2CID 14181275. Archived from the original (PDF) on 2020-02-27. Davis, Martin, ed. (1965). The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions. New York: Raven Press. Includes original papers by Gödel, Church, Turing, Rosser, Kleene, and Post mentioned in this section.
Turing 1937a. Turing, A. M. (1937a) [Delivered to the Society November 1936], "On Computable Numbers, with an Application to the Entscheidungsproblem" (PDF), Proceedings of the London Mathematical Society, 2, vol. 42, pp. 230–265, doi:10.1112/plms/s2-42.1.230, S2CID 73712 and Turing, A. M. (1938). "On Computable Numbers, with an Application to the Entscheidungsproblem: A correction". Proceedings of the London Mathematical Society. 2. Vol. 43 (published 1937). pp. 544–546. doi:10.1112/plms/s2-43.6.544. (See also: Davis 1965:115ff.)
italics added, Rosser 1939 in Davis 1965:226. Rosser, J. B. (1939). "An Informal Exposition of Proofs of Godel's Theorem and Church's Theorem". The Journal of Symbolic Logic. 4 (2): 53–60. doi:10.2307/2269059. JSTOR 2269059. S2CID 39499392. Davis, Martin, ed. (1965). The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions. New York: Raven Press. Includes original papers by Gödel, Church, Turing, Rosser, Kleene, and Post mentioned in this section.
Piccinini, Gualtiero (January 2007). "Computationalism, the Church–Turing Thesis, and the Church–Turing Fallacy" (PDF). Synthese. 154 (1): 97–120. CiteSeerX 10.1.1.360.9796. doi:10.1007/s11229-005-0194-z. S2CID 494161. Archived (PDF) from the original on 2008-04-24.
Abramson, Darren (2011). "Philosophy of mind is (in part) philosophy of computer science". Minds and Machines. 21 (2): 203–219. doi:10.1007/s11023-011-9236-0. S2CID 32116031.

pdfs.semanticscholar.org

Church 1936a Church, Alonzo (April 1936a). "An Unsolvable Problem of Elementary Number Theory" (PDF). American Journal of Mathematics. 58 (2): 345–363. doi:10.2307/2371045. JSTOR 2371045. S2CID 14181275. Archived from the original (PDF) on 2020-02-27.
Turing 1937b. Proof outline on p. 153: $\lambda {\mbox{-definable}}$ ${\stackrel {triv}{\implies }}$ $\lambda {\mbox{-}}K{\mbox{-definable}}$ ${\stackrel {160}{\implies }}$ ${\mbox{Turing computable}}$ ${\stackrel {161}{\implies }}$ $\mu {\mbox{-recursive}}$ ${\stackrel {Kleene}{\implies }}$ ^[10] $\lambda {\mbox{-definable}}$ Turing, Alan Mathison (December 1937b). "Computability and λ-Definability" (PDF). Journal of Symbolic Logic. 2 (4): 153–163. doi:10.2307/2268280. JSTOR 2268280. S2CID 2317046. Archived from the original (PDF) on 2020-08-09.
cf. footnote 3 in Church 1936a An Unsolvable Problem of Elementary Number Theory in Davis 1965:89. Church, Alonzo (April 1936a). "An Unsolvable Problem of Elementary Number Theory" (PDF). American Journal of Mathematics. 58 (2): 345–363. doi:10.2307/2371045. JSTOR 2371045. S2CID 14181275. Archived from the original (PDF) on 2020-02-27. Davis, Martin, ed. (1965). The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions. New York: Raven Press. Includes original papers by Gödel, Church, Turing, Rosser, Kleene, and Post mentioned in this section.

stanford.edu

plato.stanford.edu

Copeland, B. Jack (2017-11-10). "The Church-Turing Thesis". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.

turing.org.uk

See also Hodges, Andrew (2005). "Did Church and Turing Have a Thesis about Machines?" (PDF). Archived from the original (PDF) on 2016-03-04. Retrieved 2014-07-27.

uchicago.edu

people.cs.uchicago.edu

Robert Soare, "Turing Oracle Machines, Online Computing, and Three Displacements in Computability Theory"

umsl.edu

Piccinini, Gualtiero (January 2007). "Computationalism, the Church–Turing Thesis, and the Church–Turing Fallacy" (PDF). Synthese. 154 (1): 97–120. CiteSeerX 10.1.1.360.9796. doi:10.1007/s11229-005-0194-z. S2CID 494161. Archived (PDF) from the original on 2008-04-24.

videolectures.net

Rabin, Michael O. (June 2012). Turing, Church, Gödel, Computability, Complexity and Randomization: A Personal View. Event occurs at 9:36. Retrieved 2021-12-05.

web.archive.org

Church 1936a Church, Alonzo (April 1936a). "An Unsolvable Problem of Elementary Number Theory" (PDF). American Journal of Mathematics. 58 (2): 345–363. doi:10.2307/2371045. JSTOR 2371045. S2CID 14181275. Archived from the original (PDF) on 2020-02-27.
Turing 1937b. Proof outline on p. 153: $\lambda {\mbox{-definable}}$ ${\stackrel {triv}{\implies }}$ $\lambda {\mbox{-}}K{\mbox{-definable}}$ ${\stackrel {160}{\implies }}$ ${\mbox{Turing computable}}$ ${\stackrel {161}{\implies }}$ $\mu {\mbox{-recursive}}$ ${\stackrel {Kleene}{\implies }}$ ^[10] $\lambda {\mbox{-definable}}$ Turing, Alan Mathison (December 1937b). "Computability and λ-Definability" (PDF). Journal of Symbolic Logic. 2 (4): 153–163. doi:10.2307/2268280. JSTOR 2268280. S2CID 2317046. Archived from the original (PDF) on 2020-08-09.
Turing, A. M. (1938). Systems of Logic Based on Ordinals (PDF) (PhD). Princeton University. p. 8. Archived from the original (PDF) on 2012-10-23. Retrieved 2012-06-23.
cf. footnote 3 in Church 1936a An Unsolvable Problem of Elementary Number Theory in Davis 1965:89. Church, Alonzo (April 1936a). "An Unsolvable Problem of Elementary Number Theory" (PDF). American Journal of Mathematics. 58 (2): 345–363. doi:10.2307/2371045. JSTOR 2371045. S2CID 14181275. Archived from the original (PDF) on 2020-02-27. Davis, Martin, ed. (1965). The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions. New York: Raven Press. Includes original papers by Gödel, Church, Turing, Rosser, Kleene, and Post mentioned in this section.
For a detailed discussion of Gödel's adoption of Turing's machines as models of computation, see Shagrir, Oron (2006-06-15). "Gödel on Turing on Computability" (PDF). Church's Thesis After 70 Years. De Gruyter. pp. 393–419. doi:10.1515/9783110325461.393. ISBN 978-3-11-032494-5. Archived from the original (PDF) on 2015-12-17. Retrieved 2016-02-08.
See also Hodges, Andrew (2005). "Did Church and Turing Have a Thesis about Machines?" (PDF). Archived from the original (PDF) on 2016-03-04. Retrieved 2014-07-27.
Piccinini, Gualtiero (January 2007). "Computationalism, the Church–Turing Thesis, and the Church–Turing Fallacy" (PDF). Synthese. 154 (1): 97–120. CiteSeerX 10.1.1.360.9796. doi:10.1007/s11229-005-0194-z. S2CID 494161. Archived (PDF) from the original on 2008-04-24.
"Official Problem Description" (PDF). Archived from the original (PDF) on 2005-11-24.
Eberbach & Wegner 2003, p. 287. Eberbach, E.; Wegner, P. (October 2003). "Beyond Turing Machines" (PDF). Bulletin of the European Association for Theoretical Computer Science (81): 279–304. CiteSeerX 10.1.1.61.9759. Archived (PDF) from the original on 2016-03-15.

worldcat.org

search.worldcat.org

Kleene 1952:300. Kleene, Stephen Cole (1952). Introduction to Metamathematics. North-Holland. OCLC 523942.
Kleene 1952:376. Kleene, Stephen Cole (1952). Introduction to Metamathematics. North-Holland. OCLC 523942.
Kleene 1952:382, 536 Kleene, Stephen Cole (1952). Introduction to Metamathematics. North-Holland. OCLC 523942.
A collection of papers can be found in Olszewski, Woleński & Janusz (2006). Also a review of this collection: Smith, Peter (2007-07-11). "Church's Thesis after 70 Years" (PDF). Olszewski, Adam; Woleński, Jan; Janusz, Robert, eds. (2006). Church's Thesis After 70 Years. Frankfurt: Ontos. ISBN 978-3-938793-09-1. OCLC 909679288.
Gödel, Kurt (1995) [193?]. "Undecidable Diophantine Propositions". In Feferman, Solomon (ed.). Collected Works. Vol. 3. New York: Oxford University Press. p. 168. ISBN 978-0-19-507255-6. OCLC 928791907.
Horsten in Olszewski, Woleński & Janusz 2006:256. Olszewski, Adam; Woleński, Jan; Janusz, Robert, eds. (2006). Church's Thesis After 70 Years. Frankfurt: Ontos. ISBN 978-3-938793-09-1. OCLC 909679288.
For a good place to encounter original papers see Chalmers, David J., ed. (2002). Philosophy of Mind: Classical and Contemporary Readings. New York: Oxford University Press. ISBN 978-0-19-514581-6. OCLC 610918145.
cf. Penrose, Roger (1990). "Algorithms and Turing machines". The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics. Oxford: Oxford University Press. pp. 47–49. ISBN 978-0-19-851973-7. OCLC 456785846.
Also the description of "the non-algorithmic nature of mathematical insight", Penrose, Roger (1990). "Where lies the physics of mind?". The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics. Oxford: Oxford University Press. pp. 416–418. ISBN 978-0-19-851973-7. OCLC 456785846.
Burgin, Mark (2005). Super-Recursive Algorithms. Monographs in Computer Science. New York: Springer. ISBN 978-0-387-95569-8. OCLC 990755791.