# George Boolos, 1940-1996

faculty resolution, submitted by Judith Thomson, Richard Cartwright, and Joshua Cohen

### 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.