George Boolos: List of Publications

1. (with Hilary Putnam) "Degrees of unsolvability of constructible sets of integers." Journal of Symbolic Logic 33 (1968): 497-513.

2. "Effectiveness and natural languages." In S. Hook, ed., Language and Philosophy. New York University Press, 1969.

3. "On the semantics of the constructible levels." Zeitschrift für mathematische Logik und Grundlagen der Mathematik 16 (1970): 139-148.

4. "A proof of the Löwenheim-Skolem theorem." Notre Dame Journal of Formal Logic 11 (1970): 76-78.

5. "The iterative conception of set." Journal of Philosophy 68 (1971) 215-231. Reprinted in Logic, Logic, and Logic and in Benacerraf, P. and Putnam, H., eds. Philosophy of Mathematics: Selected Readings, second ed. Cambridge: Cambridge University Press, 1984, pp. 486-502.

6. "A note on Beth's theorem." Bulletin de l'Academie Polonaise des Sciences 21 (1973): 1-2.

7. "Arithmetical functions and minimization." Zeitschrift für mathematische Logik und Grundlagen der Mathematik 20 (1974): 353-354.

8. "Reply to Charles Parsons' 'Sets and classes' (1974)" First published in Logic, Logic, and Logic.

9. (with Richard Jeffrey) Computability and Logic. Cambridge: Cambridge University Press, 1974.

10. "Friedman's 35th problem has an affirmative solution." Notices of the American Mathematical Society 22 (1975): A-646.

11. "On Kalmar's consistency proof and a generalization of the notion of omega-consistency." Archiv für Mathematische Logik und Grundlagenforschung 17 (1975): 3-7.

12. "On second-order logic." Journal of Philosophy 72 (1975): 509-527. Reprinted in Logic, Logic, and Logic.

13. "On deciding the truth of certain statements involving the notion of consistency." Journal of Symbolic Logic 41 (1976): 779-781.

14. "On deciding the provability of certain fixed point statements." Journal of Symbolic Logic 42 (1977): 191-193.

15. "Reflection principles and iterated consistency assertions." Journal of Symbolic Logic 44 (1979): 33-35.

16. The Unprovability of Consistency: An Essay in Modal Logic. Cambridge: Cambridge University Press, 1979.

17. "Omega-consistency and the diamond." Studia Logica 39 (1980): 237-243.

18. "On systems of modal logic with provability interpretations." Theoria 46 (1980): 7-18.

19. "Provability in arithmetic and a schema of Grzegorczyk." Fundamenta Mathematicae 106 (1980): 41-45.

20. "Provability, truth, and modal logic." Journal of Philosophical Logic 9 (1980): 1-7.

21. "Review of Raymond M. Smullyan, What is the Name of This Book?"" The Philosophical Review 89 (1980): 467-470.

22. "For every A there is a B." Linguistic Inquiry 12 (1981): 465-466.

23. "Review of Robert M. Solovay, Provability Interpretations of Modal Logic." Journal of Symbolic Logic 46 (1981): 661-662.

24. "Extremely undecidable sentences." Journal of Symbolic Logic 47 (1982): 191-196.

25. "On the nonexistence of certain normal forms in the logic of provability." Journal of Symbolic Logic 47 (1982): 638-640.

26. "Don't eliminate cut." Journal of Philosophical Logic 13 (1984): 373-378. Reprinted in Logic, Logic, and Logic.

27. "The logic of provability." American Mathematical Monthly 91 (1984): 470-480.

28. "Nonfirstorderizability again." Linguistic Inquiry 15 (1984): 343.

29. "On 'Syllogistic inference'." Cognition 17 (1984): 181-182.

30. "To be is to be the value of a variable (or some values of some variables)." Journal of Philosophy 81 (1984): 430-450. Reprinted in Logic, Logic, and Logic.

31. "Trees and finite satisfiability: Proof of a conjecture of Burgess." Notre Dame Journal of Formal Logic 25 (1984): 193-197.

32. "1-consistency and the diamond." Notre Dame Journal of Formal Logic 26 (1985): 341-347.

33. "The justification of mathematical induction." PSA 1984 2 (1985): 469-475. Reprinted in Logic, Logic, and Logic.

34. "Nominalist Platonism." The Philosophical Review 94 (1985): 327-344. Reprinted in Logic, Logic, and Logic.

35. "Reading the Begriffsschrift." Mind 94 (1985): 331-334. Reprinted in Logic, Logic, and Logic and in Demopoulos, W., ed., Frege's Philosophy of Mathematics. Cambridge, Mass: Harvard University Press, 1995, pp. 163-181.

36. (with Giovanni Sambin) "An incomplete system of modal logic." Journal of Philosophical Logic 14 (1985): 351-358.

37. "Review of Yuri Manin, A Course in Mathematical Logic." Journal of Symbolic Logic 51 (986): 829-830.

38. "Saving Frege from contradiction." Proceedings of the Aristotelian Society 87 (1986-87): 137-151. Reprinted in Logic, Logic, and Logic and in Demopoulos, W., ed., Frege's Philosophy of Mathematics. Cambridge, Mass: Harvard University Press, 1995, pp. 438-452.

39. "The consistency of Frege's Foundations of Arithmetic." In J. J. Thomson, ed., On Being and Saying: Essays for Richard Cartwright, pp. 3-20. Cambridge, Mass.: MIT Press, 1987. Reprinted in Logic, Logic, and Logic and in Demopoulos, W., ed., Frege's Philosophy of Mathematics. Cambridge, Mass: Harvard University Press, 1995, pp. 211-233.

40. "A curious inference." Journal of Philosophical Logic 16 (1987): 1-12. Reprinted in Logic, Logic, and Logic.

41. "On notions of provability in provability logic." Abstracts of the 8th International Congress of Logic, Methodology and Philosophy of Science 5 (1987): 236-238.

42. (with Vann McGee) "The degree of the set of sentences of predicate provability logic that are true under every interpretation." Journal of Symbolic Logic 52 (1987): 165-171.

43. "Alphabetical order." Notre Dame Journal of Formal Logic 29 (1988): 214-215.

44. 1988b. "Review of Craig Smorynski, Self-Reference and Modal Logic." Journal of Symbolic Logic 53, 306-309.

45. "Iteration again." Philosophical Topics 17 (1989): 5-21. Reprinted in Logic, Logic, and Logic.

46. "A new proof of the Gödel incompleteness theorem." Notices of the American Mathematical Society 36 (1989): 388-390. An afterword appeared under the title "A letter from George Boolos," ibid., p. 676. Both are reprinted in Logic, Logic, and Logic.

47. Ed., Meaning and Method: Essays in Honor of Hilary Putnam. Cambridge: Cambridge University Press, 1990.

48. "On 'seeing' the truth of the Gödel sentence." Behavioral and Brain Sciences 13 (1990): 655-656. Reprinted in Logic, Logic, and Logic.

49. "Review of Jon Barwise and John Etchemendy, Turing's World and Tarski's World." Journal of Symbolic Logic 55 (1990) 370-371.

50. "Review of V. A. Uspensky, Gödel's IncompletenessTheorem." Journal of Symbolic Logic 55 (1990) 889-891.

51. "The standard of equality of numbers." In Meaning and Method, op. cit. pp. 261-278. Reprinted in Logic, Logic, and Logic and in William Demopoulos, ed., Frege's Philosophy of Mathematics Cambridge, Mass: Harvard University Press, 1995, pp. 234-254.

52. "Zooming down the slippery slope." NOUS 25 (1991): 695-706. Reprinted in Logic, Logic, and Logic.

53. (with Giovanni Sambin) "Provability: The emergence of a mathematical modality." Studia Logica 50 (1991): 1-23.

54. "The analytical completeness of Dzhaparidze's polymodal logics." Annals of Pure and Applied Logic 61 (1993): 95-111.

55. The Logic of Provability. Cambridge: Cambridge University Press, 1993.

56. "Whence the contradiction?" Aristotelian Society Supplementary Volume 67 (1993): 213-233. Reprinted in Logic, Logic, and Logic.

57. "1879?" In P. Clark and B. Hale, eds., Reading Putnam, pp. 31-48. Oxford: Blackwell, 1994. Reprinted in Logic, Logic, and Logic.

58. "The advantages of honest toil over theft." In A. George, ed., Mathematics and Mind, pp. 27-44. Oxford: Oxford University Press, 1994. Reprinted in Logic, Logic, and Logic.

59. "Gödel's second incompleteness theorem explained in words of one syllable." Mind 103 (1994): 1-3. Reprinted in Logic, Logic, and Logic.

60. "Frege's theorem and the Peano postulates." Bulletin of Symbolic Logic 1 (1995) 317-326. Reprinted in Logic, Logic, and Logic.

61. "Introductory note to *1951." In Feferman, S. et al., eds., Kurt Gödel, Collected Works vol. 3. Oxford: Oxford University Press, 1995, pp. 290-304. [Item *1951 is the 1951 Gibbs lecture by Gödel, "Some basic theorems on the foundations of mathematics and their implications."] Reprinted in Logic, Logic, and Logic.

62. "Quotational ambiguity." In Leonardi, P. and Santambrogio, M., eds., On Quine. Cambridge: Cambridge University Press, 1995, pp. 283-296. Reprinted in Logic, Logic, and Logic.

63. "The hardest logical puzzle ever." Harvard Review of Philosophy 6 (1996): 62-65. Reprinted in Logic, Logic, and Logic. An Italian translation by Massimo Piattelli-Palmarini, "L'indovinello piu difficile del mondo," appeared in La Repubblica 16 April 1992, pp. 36-37.

64. "On the proof of Frege's theorem." In A. Morton and S. P. Stich, eds., Benacerraf and his Critics. Cambridge, Mass.: Blackwell, 1996. Reprinted in Logic, Logic, and Logic.

65. "Constructing Cantorian counterexamples." Journal of Philosophical Logic 26 (1997): 237-239. Reprinted in Logic, Logic, and Logic.

66. "Gottlob Frege and the Foundations of Arithmetic." First published in Logic, Logic, and Logic. A French translation appeared in Mathieu Marion and Alain Voizard eds., Frege. Logique et philosophie, pp. 17-32, Montréal and Paris: L'Harmattan, 1998.

67. "Is Hume's principle analytic?" In Richard G. Heck, Jr., ed., Language, Thought, and Logic: Essays in Honour of Michael Dummett, pp. 245-261, Oxford: Clarendon Press. Reprinted in Logic, Logic, and Logic.

68. "Must we believe in set theory?" In Gila Sher and Richard Tieszen, eds., Between Logic and Intuition: Essays in Honour of Charles Parsons, Cambridge: Cambridge University Press, 2000. First published in Logic, Logic, and Logic.

69. (with Richard Heck) "Die Grundlagen der Arithmetik, §§82-83" In Matthias Schirn, ed., Philosophy of Mathematics Today, Oxford: Clarendon Press. Reprinted in Logic, Logic, and Logic.

70. Logic, Logic, and Logic. Cambridge, Mass: Harvard University Press, 1998.


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