Linked bibliography for the SEP article "Gödel’s Incompleteness Theorems" by Panu Raatikainen

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Auerbach, David, 1985, “Intensionality and the Gödel theorems,” Philosophical Studies, 48 (3):337–51. (Scholar)
–––, 1992, “How to say things with formalisms,” in Proof, Logic, and Formalization, M. Detlefsen (ed.), London: Routledge, 77–93 [available online]. (Scholar)
Awodey, S. & A.W. Carus, 2003, “Carnap versus Gödel on Syntax and Tolerance,” in Logical Empiricism: Historical and Contemporary Perspectives, P. Parrini et al. (eds.), Pittsburgh: University of Pittsburgh Press, pp. 57–64 [available online]. (Scholar)
–––, 2004, “How Carnap Could Have Replied to Gödel,” in S. Awodey and C. Klein (eds.), Carnap Brought Home: The View from Jena, LaSalle, IL: Open Court, pp. 203–223 [available online]. (Scholar)
Barzin, M., 1940, “Sur la portée du théorème de M. Gödel,” Académie Royale de Belgique, Bulletin de la Classe des Sciences, Series 5, 26: 230–39. (Scholar)
Benacerraf, P., 1967, “God, the Devil, and Gödel,” The Monist, 51: 9–32 [available online]. (Scholar)
Bezboruah, A. and J.C. Shepherdson, 1976, “Gödel’s Second Incompleteness Theorem for Q,” The Journal of Symbolic Logic, 41: 503–512.
Boolos, G., 1968, “Review of ‘Minds, Machines and Gödel’, by J.R. Lucas, and ‘God, the Devil, and Gödel’,” Journal of Symbolic Logic, 33: 613–15. (Scholar)
–––, 1990, “On ‘Seeing’ the Truth of Gödel Sentence,” Behavioral and Brain Sciences, 13: 655–656. (Scholar)
–––, 1995, “Introductory Note to *1951,” in Gödel 1995: 290–304. (Scholar)
Boolos, G. and R. Jeffrey, 1989, Computability and logic, 3^rd revised edition, Cambridge: Cambridge University Press. (Scholar)
Carnap, R., 1934, Logische Syntax der Sprache, Vienna: Julius Springer. (Scholar)
Chihara, C., 1972, “On Alleged Refutations of Mechanism Using Gödel’s Incompleteness Results,” Journal of Philosophy, 69: 507–26. (Scholar)
Church, A., 1936a, “An Unsolvable Problem of Elementary Number Theory,” American Journal of Mathematics, 58: 354–363. Republished in Davis 1965, 89–107. (Scholar)
–––, 1936b, “A Note on Entscheidungsproblem,” Journal of Symbolic Logic, 1: 40–41; correction, ibid., 101–102. Republished in Davis 1965, 110–115. (Scholar)
Cohen, P. J., 1963, “The Independence of the Continuum Hypothesis I,” Proceedings of the National Academy of Sciences, (U.S.A.), 50(6): 1143–48. (Scholar)
–––, 1964, “The Independence of the Continuum Hypothesis II,” Proceedings of the National Academy of Sciences, (U.S.A.), 51(1): 105–110. (Scholar)
Crocco, G., 2003, “Gödel, Carnap, and the Fregean Heritage,” Synthese, 137: 21–41. (Scholar)
Davis, M., 1965, The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions, Hewlett, NY: Raven Press. (Scholar)
–––, 1973, “Hilbert’s Tenth Problem is Unsolvable,” The American Mathematical Monthly, 80: 233–269. (Scholar)
–––, 1977, “Unsolvable Problems,” in Handbook of Mathematical Logic, J. Barwise (ed.), Amsterdam: North-Holland, pp. 567–594. (Scholar)
–––, 1990, “Is Mathematical Insight Algorithmic?” Behavioral and Brain Sciences, 13: 659–660. (Scholar)
–––, 1993, “How Subtle is Gödel’s Theorem? More on Roger Penrose,” Behavioral and Brain Sciences, 16: 611–612. (Scholar)
Davis, M., H. Putnam, and J. Robinson, 1961, “The decision problem for exponential diophantine equations,” Annals of Mathematics (2), 74(3): 425–436. (Scholar)
Dawson, J., 1985, “The Reception of Gödel’s Incompleteness Theorems,” PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1984, vol. II, pp. 253–271. (Scholar)
–––, 1997, Logical Dilemmas: The Life and Work of Kurt Gödel, Natick, MA: A. K. Peters. (Scholar)
Detlefsen, M., 1979, “On Interpreting Gödel’s Second Theorem,” Journal of Philosophical Logic, 8(1): 297–313. (Scholar)
–––, 1986, Hilbert’s Program: An Essay in Mathematical Instrumentalism, Dordrecht: Reidel. (Scholar)
–––, 1990, “On an Alleged Refutation of Hilbert’s Program Using Gödel’s First Incompleteness Theorem,” Journal of Philosophical Logic, 19(4): 343–377. (Scholar)
–––, 1995, “Wright on the Non-mechanizability of Intuitionist Reasoning,” Philosophia Mathematica, 3(1): 103–118. (Scholar)
–––, 2001, “What Does Gödel’s Second Theorem Say?” Philosophia Mathematica, 9: 37–71. (Scholar)
Dyson, V., J.P. Jones, and J.C. Shepherdson, 1982, “Some Diophantine Forms of Gödel’s Theorem,” Archiv für Mathematische Logik und Grundlagenforschung, 22: 51–60. (Scholar)
Ehrenfeucht, A. and S. Feferman, 1960, “Representability of recursively enumerable sets in formal theories”, Arch. Math. Logik Grundlag., 5(1–2), 37–41. (Scholar)
Feferman, S., 1960, “Arithmetization of Metamathematics in a General Setting,” Fundamenta Mathematicae, 49: 35–92. (Scholar)
–––, 1982, “Inductively Presented Systems and the Formalization of Meta-mathematics,” in Logic Colloquium ’80, D. van Dalen et al. (eds.), Amsterdam: North-Holland, pp. 95–128. (Scholar)
–––, 1989a, “Finitary Inductively Presented Logics,” in Logic Colloquium ‘88, R. Ferro, et al. (eds.), Amsterdam: North-Holland, pp. 191–220. [available online] (Scholar)
–––, 1989b, “Infinity in Mathematics: Is Cantor Necessary?” Philosophical Topics, 17(2): 23–45. (Scholar)
–––, 1995, “Penrose’s Gödelian argument: A Review of Shadows of Mind, by Roger Penrose,” Psyche, 2 (7). (Scholar)
–––, 1997, “My Route to Arithmetization,” Theoria, 63: 168–181. (Scholar)
Finsler, P., 1926, “Formale Beweise und die Entscheidbarkeit,” Mathematische Zeitschrift, 25: 676–82. (Scholar)
Fitting, M., 2007, Incompleteness in the land of sets, London: College Publications. Series: Studies in logic ; v. 5. (Scholar)
Franks, C., 2009, The Autonomy of Mathematical Knowledge. Hilbert’s Program Revisited, Oxford: Oxford University Press. (Scholar)
Gaifman, H., 2006, “Naming and Diagonalization, From Cantor to Gödel to Kleene,” Logic Journal of the IGPL, 14: 709–728. [available online] (Scholar)
Gentzen, G., 1936, “Die Widerspruchsfreiheit der reinen Zahlentheorie,” Mathematische Annalen, 112: 493–565. (Scholar)
Gödel, K., 1931, “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I,” Monatshefte für Mathematik Physik, 38: 173–198. English translation in van Heijenoort 1967, 596–616, and in Gödel 1986, 144–195. (Scholar)
–––, 1932, “Über Vollständigkeit und Widerspruchsfreiheit,” Ergebnisse eines mathematischen Kolloquiums, 3: 12–13. English translation “On Completeness and Consistency” in Gödel 1986: 235–7. (Scholar)
–––, 1933, “The Present Situation in Foundations of Mathematics,” in Gödel 1995: 45–53. (Scholar)
–––, 1934, “On Undecidable Propositions of Formal Mathematical Systems” (mimeographed lecture notes; taken by S. Kleene and J. Rosser), reprinted with corrections in Davis 1965, 41–81, and Gödel 1986, 346–371. (Scholar)
–––, 1935, “Review of Carnap 1934,” in Gödel 1986: 389. (Scholar)
–––, 1941, “In What Sense is Intuitionistic Logic Constructive?” in Gödel 1995: 189–200. (Scholar)
–––, 1944, “Russell’s Mathematical Logic,” in The Philosophy of Bertrand Russell, P. A. Schilpp (ed.), Evanston, Il.: Northwestern University, pp. 125–153. Reprinted in Gödel 1990: 119–141. (Scholar)
–––, 1951, “Some Basic Theorems on the Foundations of Mathematics and their Implications” (Gibbs Lecture), in Gödel 1995: 304–323. (Scholar)
–––, 1953/9, “Is Mathematics a Syntax of Language?,” lecture manuscript (two versions), in Gödel 1995: 334–362. (Scholar)
–––, 1963, “Note added 28 August 1963” (to Gödel 1931), in Gödel 1986: 195. (Scholar)
–––, 1986, Collected Works I. Publications 1929–1936, S. Feferman et al. (eds.), Oxford: Oxford University Press. (Scholar)
–––, 1990, Collected Works II. Publications 1938–1974, S. Feferman et al. (eds.), Oxford: Oxford University Press. (Scholar)
–––, 1995, Collected Works III. Unpublished Essays and Lectures, S. Feferman et al. (eds.), Oxford: Oxford University Press. (Scholar)
Goldfarb, W., 1995, “Introductory Note to *1953/9,” in Gödel 1995: 324–334. (Scholar)
Goldfarb, W. and T. Ricketts, 1992, “Carnap and the Philosophy of Mathematics,” in Science and Subjectivity, D. Bell and W. Vossenkuhl (eds.), Berlin: Akademie Verlag, pp. 61–78. (Scholar)
Gómez Torrente, M., 2004, “The Indefinability of Truth in the Wahrheitsbegriff,” Annals of Pure and Applied Logic, 126(1–3): 27–37. [available online] (Scholar)
Goodstein, R., 1944, “On the Restricted Ordinal Theorem,” The Journal of Symbolic Logic, 9: 33–41. (Scholar)
Grelling, K., 1937, “Gibt es eine Gödelsche Antinomie?,” Theoria, 3: 297–306. (Scholar)
Hanson, W.H., 1971, “Mechanism and Gödel’s theorems,” The British Journal for the Philosophy of Science, 22: 9–16. (Scholar)
Hellman, G., 1981, “How to Gödel a Frege-Russell: Gödel’s Incompleteness Theorems and Logicism,” Nous, 15: 451–468. (Scholar)
Helmer, O., 1938, “Perelman versus Gödel,” Mind, 46: 58–60. (Scholar)
Henkin, L., 1952, “Problem,” The Journal of Symbolic Logic, 17: 160. (Scholar)
–––, 1962, “Are Mathematics and Logic Identical?” Science, 138: 788–794. (Scholar)
Hilbert, D., 1928, “Die Grundlagen der Mathematik,” Abhandlungen aus dem Mathematischen Seminar der Hamburgischen Universität, 6: 65–85. English translation in van Heijenoort 1967. (Scholar)
Hilbert, D. and P. Bernays, 1939, Grundlagen der Mathematik, vol. 2, Berlin: Springer. (Scholar)
Jeroslow, R., 1973, “Redundancies in the Hilbert-Bernays Derivability Conditions for Gödel’s Second Incompleteness Theorem,” Journal of Symbolic Logic, 38: 359–367. (Scholar)
Kaye, R., 1991, Models of Peano Arithmetic, (Oxford Logic Guides), Oxford: Clarendon Press. (Scholar)
Kirby, L. and J. Paris, 1982, “Accessible Independence Results for Peano Arithmetic,” Bull. London. Math. Soc., 14: 285–93. (Scholar)
Kleene, S.C., 1936, “General recursive functions of natural numbers,”, Mathematische Annalen 112(1): 727–742. (Scholar)
–––,1937a, “Review of Perelman 1936,” Journal of Symbolic Logic, 2: 40–41. (Scholar)
–––, 1937b, “Review of Helmer 1937,” Journal of Symbolic Logic, 2: 48–49. (Scholar)
–––, 1986, “Introductory note to 1930b, 1931 and 1932b”, in Gödel 1986, pp. 126–141. (Scholar)
Kreisel, G., 1953, “On a Problem of Henkin’s,” Proc. Netherlands Acad. Sci. 56: 405–406. (Scholar)
–––, 1958, “Mathematical significance of consistency proofs,” The Journal of Symbolic Logic, 23: 159–182. (Scholar)
–––, 1967, “Mathematical Logic: What Has it Done For the Philosophy of Mathematics?” in Bertrand Russell: Philosopher of the Century, R. Schoenman (ed.), London: George Allen and Unwin. (Scholar)
Kruskal, J.B., 1960, “Well-quasi-ordering, the Tree Theorem, and Vazsonyi’s Conjecture,” Transactions of the American Mathematical Society, 95 (2): 210–225. (Scholar)
Lindström, P., 2001, “Penrose’s New Argument,” Journal of Philosophical Logic, 30(3): 241–250. (Scholar)
Lucas, J. R., 1961, “Minds, Machines, and Gödel,” Philosophy, 36(137): 112–137 [available online]. (Scholar)
–––, 1996, “Minds, Machines, and Gödel: A Retrospect,” in Machines and Thought. The Legacy of Alan Turing, Vol. 1, P.J.R. Millican and A. Clark (eds.), Oxford: Oxford University Press, 103–124. (Scholar)
Löb, M. H., 1955, “Solution of a Problem of Leon Henkin,” Journal of Symbolic Logic, 20: 115–118. (Scholar)
Mancosu, P., 1999, “Between Vienna and Berlin: The Immediate Reception of Gödel’s Incompleteness Theorems,” History and Philosophy of Logic, 20: 33–45. (Scholar)
Martin, D., 1977, “Descriptive Set Theory: Projective Sets,” in Handbook of Mathematical Logic, J. Barwise (ed.), Amsterdam: North-Holland, 783–815. (Scholar)
Martin, D. and Steel, J., 1988, “Projective Determinacy,” Proceedings of the National Academy of Sciences, (U.S.A.), 85: 6582–86. (Scholar)
–––, 1989, “A Proof of Projective Determinacy,” Journal of the A.M.S., 2: 71–125. (Scholar)
Matiyasevich, Y., 1970, “Diofantovost’ perechislimykh mnozhestv,” Dokl. Akad. Nauk SSSR, 191(2): 297–282 (Russian). (English translation, 1970, “Enumerable sets are Diophantine,” Soviet Math. Dokl., 11(2): 354–358.) (Scholar)
–––, 1993, Hilbert’s Tenth Problem, Cambridge, MA: MIT Press. (Scholar)
Milne, P., 2007, “On Gödel Sentences and What They Say,” Philosophia Mathematica, 15: 193–226. (Scholar)
Montague, R., 1962, “Theories Incomparable with Respect to Relative Interpretability,” The Journal of Symbolic Logic, 27: 195–211. (Scholar)
Murawski, R., 1998, “Undefinability of Truth. The Problem of Priority: Tarski vs. Gödel,” History and Philosophy of Logic, 19: 153–160. (Scholar)
–––, 1999, Recursive Functions and Metamathematics: Problems of Completeness and Decidability, Gödel’s Theorems, Dordrecht: Kluwer. (Scholar)
Musgrave, A., 1977, “Logicism Revisited,” British Journal for the Philosophy of Science, 28: 99–127. (Scholar)
Nagel, E. and J.R. Newman, 1958, Gödel’s Proof, New York: New York University Press.
Paris, J. and L. Harrington, 1977, “A Mathematical Incompleteness in Peano Arithmetic,” in Handbook of Mathematical Logic, J. Barwise (ed.), Amsterdam: North-Holland, pp. 1133–1142 [available online]. (Scholar)
Paris, J. and L. Kirby, 1978, “\(S_n\) Collection Schema in Arithmetic,” in Logic Colloquium ’77, A. McIntyre et al. (eds.), Amsterdam: North-Holland, pp. 199–209. (Scholar)
Parsons, C., 1970, “On Number Choice Schema and its Relation to Induction,” in Intuitionism and Proof Theory, Kino et al. (eds.), Amsterdam: North-Holland, pp. 459–473. (Scholar)
Penrose, R., 1989, The Emperor’s New Mind: Concerning Computers, Minds, and the Laws of Physics, New York: Oxford University Press. (Scholar)
–––, 1994, Shadows of the Mind: A Search for the Missing Science of Consciousness, New York: Oxford University Press (Scholar)
–––, 1995, “Beyond the Doubting of a Shadow: A Reply to Commentaries of Shadows of the Mind,” Psyche, Vol 2. (Scholar)
–––, 1997, “On understanding understanding”, International Studies in the Philosophy of Science, 11: 7–20. (Scholar)
Perelman, C., 1936, “L’Antinomie de M. Gödel,” Académie Royale de Belgique. Bulletin de la Classe des Sciences (Series 5), 22: 730–36.
Piccinini, G., 2003, “Alan Turing and the Mathematical Objection,” Minds and Machines, 13: 23–48. (Scholar)
Post, E., 1941, “Absolutely Unsolvable Problems and Relatively Unsolvable Propositions: Account of an Anticipation,” published in Davis 1965, 338–433. (Scholar)
Presburger, M., 1929, “Über die Vollständigkeit eines gewissen Systems der Arithmetik ganzer Zahlen, in welchem die Addition als einzige Operation hervortritt,” Sprawozdanie z I Kongresu Matematyków Krajów Slowiańskich, (= Comptes-rendus du I Congrès Mathématiciens des Pays Slaves), Warsaw, pp. 92–101. English translation, 1991,“On the completeness of a certain system of arithmetic of whole numbers in which addition occurs as the only operation,” History and Philosophy of Logic, 12(2): 225–232. (Scholar)
Pudlák, P., 1996, “On the Length of Proofs of Consistency,” Collegium Logicum, Annals of the Kurt-Gödel-Society, 2: 65–86. (Scholar)
–––, 1999, “A Note on Applicability of the Incompleteness Theorem to Human Mind,” Annals of Pure and Applied Logic, 96: 335–342. (Scholar)
Putnam, H., 1960, “Minds and machines,” in Dimensions of Mind, S. Hook (ed.), New York: New York University Press. Reprinted in H. Putnam, 1975, Mind, Language, and Reality. Philosophical Papers, Vol 2, Cambridge: Cambridge University Press, pp. 325–341. (Scholar)
–––, 1975, “What is Mathematical Truth?” Historia Mathematica, 2: 529–545. Reprinted in H. Putnam, 1975, Mathematics, Matter and Method. Philosophical Papers, Vol 1, Cambridge: Cambridge University Press, pp. 60–78. (Scholar)
Quine, W.V. and J.S. Ullian, 1978, The Web of Belief, 2^nd ed., New York: Random House. (Scholar)
Raatikainen, P., 2005, “On the Philosophical Relevance of Gödel’s Incompleteness Theorems,” Revue Internationale de Philosophie, 59: 513–534. (Scholar)
Ramsey, F. P., 1930, “On a Problem of Formal Logic,” Proceedings of the London Mathematical Society, series 2, 30: 264–286. (Scholar)
Ricketts, T., 1995, “Carnap’s Principle of Tolerance, Empiricism, and Conventionalism,” in Reading Putnam, P. Clark & B. Hale (eds.), Cambridge: Blackwell, pp. 176–200. (Scholar)
Rodríguez-Consuegra, F., 1993, “Russell, Gödel and Logicism,” in Philosophy of Mathematics, J. Czermak (ed.), Vienna: Hölder-Pichler-Tempsky, pp. 233–42. Reprinted in, 1998, Bertrand Russell: Critical Assessments, A. Irvine (ed.), vol. 2: Logic and mathematics, London: Routledge, pp. 320–29. (Scholar)
Roeper, P., 2003, “Giving an Account of Provability within a Theory,” Philosophia Mathematica, 11: 332–340. (Scholar)
Rosser, J. B., 1936, “Extensions of Some Theorems of Gödel and Church,” Journal of Symbolic Logic, 1: 87–91. (Scholar)
–––, 1938, “Review: Kurt Grelling, Gibt es eine Godelsche Antinomie? [Grelling 1937/8],” Journal of Symbolic Logic, 3(2): 86. (Scholar)
Searle, J., 1997, “Roger Penrose, Kurt Gödel, and the Cytoskeletons,” in J. Searle: Mystery of Consciousness, New York: New York Review of Books, pp. 55–93. (Scholar)
Shapiro, S., 1998, “Incompleteness, Mechanism, and Optimism,” Bulletin of Symbolic Logic, 4: 273–302. (Scholar)
–––, 2003, “Mechanism, Truth and Penrose’s New Argument,” Journal of Philosophical Logic, 32(1): 19–42. (Scholar)
Simpson, S.G., 1985, “Nonprovability of Certain Combinatorial Properties of Finite Trees,” in Harvey Friedman’s Research on the Foundations of Mathematics, L. Harrington et al. (eds.), Studies in Logic and the Foundations of Mathematics, Amsterdam: North-Holland, pp. 87–117 (Scholar)
–––, 1999, Subsystems of Second Order Arithmetic, Berlin: Springer. (Scholar)
Skolem, T., 1930, “Über einige Satzfunktionen in der Arithmetik,” Skrifter utgitt av Det Norske Videnskaps-Akademi i Oslo, I, no. 7, 1–28. Reprinted in T. Skolem, 1970, Selected Works in Logic, (J. Fenstad, editor), Oslo: Universitetsforlaget, pp. 281–306. (Scholar)
Smoryński, C., 1977, “The Incompleteness Theorems,” in Handbook of Mathematical Logic, J. Barwise (ed.), Amsterdam: North-Holland, pp. 821–865. (Scholar)
–––, 1981, “Fifty Years of Self-reference in Arithmetic,” Notre Dame Journal of Formal Logic, 22(4): 357–374. (Scholar)
–––, 1991, “The Development of Self-reference: Löb’s Theorem,” in Perspectives on the History of Mathematical Logic, T. Drucker (ed.), Birkhauser, pp. 111–133. (Scholar)
Smullyan, R., 1992, Gödel’s Incompleteness Theorems, Oxford: Oxford University Press.
Solovay, R.M., 1970, “A Model of Set Theory in which Every Set of Reals is Lebesgue Measurable,” Annals of Mathematics, 92: 1–56. (Scholar)
Sternfeld, R., 1976, “The Logistic Thesis,” in Studien zu Frege/Studies on Frege I, M. Schirn (ed.), Stuttgart-Bad Cannstatt: Frommann-Holzboog, pp. 139–160. (Scholar)
Tarski, A., 1948, A Decision Method for Elementary Algebra and Geometry, manuscript. Santa Monica, CA: RAND Corp., 1948. Republished as A Decision Method for Elementary Algebra and Geometry, 2nd ed. Berkeley, CA: University of California Press, 1951. (Scholar)
Tarski, A., A. Mostowski, and R.M. Robinson, 1953, Undecidable Theories, Amsterdam: North-Holland. (Scholar)
Tennant, Neil, 2008, “Carnap, Gödel, and the Analyticity of Arithmetic”, Philosophia Mathematica, 16: 100–112. (Scholar)
Turing, A.M., 1936–7, “On Computable Numbers, with an Application to the Entscheidungsproblem,” Proceedings of the London Mathematical Society, Series 2, 42: 230–265; correction, ibid., 43: 544–546. Republished in Davis 1965, 115–154. (Scholar)
Van Heijenoort, J. (ed.), 1967, From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931, Cambridge, MA: Harvard University Press. (Scholar)
Visser, A., 2011, “Can We Make the Second Incompleteness Theorem Coordinate Free,” Journal on Logic and Computation, 21(4): 543–560. (Scholar)
Woodin, H., 1988, “Supercompact Cardinals, Sets of Reals, and Weakly Homogeneous Trees,” Proceedings of the National Academy of Sciences, (U.S.A.), 85: 6587–91. (Scholar)
Wright, C., 1994, “About ‘The Philosophical Significance of Gödel’s Theorem’: Some Issues,” in The Philosophy of Michael Dummett, B. McGuinness and G. Oliveri (eds.) Dordrecht: Kluwer, pp. 167–202. (Scholar)
–––, 1995, “Intuitionists are not (Turing) Machines,” Philosophia Mathematica, 3: 86–102. (Scholar)
Zach, R., 2005, “Paper on the Incompleteness Theorems,” in Landmark Writings in Western Mathematics, I. Grattan-Guinness (ed.), Amsterdam: Elsevier, pp. 917–25 [available online]. (Scholar)

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