George Boolos (boolos)

Contributions to Philosophie.ch

Bibliography

Boolos, George. 1969. “Effectiveness and Natural Languages.” in Language and Philosophy. A Symposium, edited by Sidney Hook, pp. 282–290. New York: New York University Press.
Boolos, George. 1970a. “On the Semantics of Constructible Levels.” Zeitschrift für mathematische Logik und Grundlagen der Mathematik 16: 139–148.
Boolos, George. 1970b. “A proof of the Löwenheim-Skolem theorem.” Notre Dame Journal of Formal Logic 11: 76–78.
Boolos, George. 1971. “The Iterative Conception of a Set.” The Journal of Philosophy 68: 215–232. Reprinted in Boolos (1998a, 13–29).
Boolos, George. 1973. “A Note on Beth’s Theorem.” Bulletin de l’Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques et Physiques 21(1–2).
Boolos, George. 1974a. “Arithmetical Functions and Minimization.” Zeitschrift für mathematische Logik und Grundlagen der Mathematik 20: 353–354.
Boolos, George. 1974b. “Reply to Parsons (1974).” in Logic, Logic, and Logic, pp. 30–36. Cambridge, Massachusetts: Harvard University Press. Introductions and afterword by John P. Burgess; edited by Richard Jeffrey, doi:10.1080/01445340051095856.
Boolos, George. 1975a. “On Second-Order Logic.” The Journal of Philosophy 72: 509–527. Reprinted in Shapiro (1996) and Boolos (1998a, 37–54).
Boolos, George. 1975b. “On Kalmar’s consistency proof and a generalization of the notion of omega-consistency.” Archiv für mathematische Logik und Grundlagenforschung 17: 3–7.
Boolos, George. 1975c. “Friedman’s 35th Problem Has an Affirmative Solution.” Notices of the American Mathematical Society 22: A–646.
Boolos, George. 1976. “On Deciding the Truth of Certain Statements Involving the Notion of Consistency.” The Journal of Symbolic Logic 41: 779–781.
Boolos, George. 1977. “On Deciding the Provability of Certain Fixed Point Statements.” The Journal of Symbolic Logic 42: 191–193.
Boolos, George. 1979a. The Unprovability of Consistency. Cambridge: Cambridge University Press.
Boolos, George. 1979b. “Reflection Principles and Iterated Consistency Assertions.” The Journal of Symbolic Logic 44: 33–45.
Boolos, George. 1980a. “Provability, Truth, and Modal Logic.” The Journal of Philosophical Logic 9(1): 1–7.
Boolos, George. 1980b. “Omega-Consistency and the Diamond.” Studia Logica: An International Journal for Symbolic Logic 39: 237–243.
Boolos, George. 1980c. “On Systems of Modal Logic with Provability Interpretations.” Theoria 46: 7–18.
Boolos, George. 1980d. “Provability in Arithmetic and a Schema of Grzegorczyk.” Fundamenta Mathematicae 106: 41–45.
Boolos, George. 1980e. “Review of Smullyan (1978).” The Philosophical Review 89: 467–470.
Boolos, George. 1981a. “For every \(A\) there is a \(B\).” Linguistic Inquiry 12: 465–466.
Boolos, George. 1981b. “Review of Solovay (1976).” The Journal of Symbolic Logic 46: 661–662.
Boolos, George. 1982a. “On the Nonexistence of Certain Normal Forms in the Logic of Provability.” The Journal of Symbolic Logic 47: 638–640.
Boolos, George. 1982b. “Extremely Undecidable Sentences.” The Journal of Symbolic Logic 47: 191–196.
Boolos, George. 1984a. “To Be is to Be Value of a Variable (or to Be Some Values of Some Variables).” The Journal of Philosophy 81(8): 430–449. Reprinted in Boolos (1998a, 54–72), doi:10.2307/2026308.
Boolos, George. 1984b. “Don’t Eliminate Cut.” The Journal of Philosophical Logic 13(4): 373–378. Reprinted in Boolos (1998a, 365–369).
Boolos, George. 1984c. “Trees and finite satisfiability: Proof of a conjecture of Burgess.” Notre Dame Journal of Formal Logic 25: 193–197.
Boolos, George. 1984d. “Nonfirstorderizability again.” Linguistic Inquiry 15: 343.
Boolos, George. 1984e. “The Logic of Provability.” American Mathematical Monthly 91: 470–480.
Boolos, George. 1984f. “On ‘Syllogistic Inference’ .” Cognition 17: 181–182.
Boolos, George. 1985a. “Nominalist Platonism.” The Philosophical Review 94(3): 327–344. Reprinted in Boolos (1998a, 73–88), doi:10.2307/2185003.
Boolos, George. 1985b. “Reading the Begriffsschrift.” Mind 94: 331–344. Reprinted in Demopoulos (1995, 163–181) and in Boolos (1998a).
Boolos, George. 1985c. “1-consistency and the diamond.” Notre Dame Journal of Formal Logic 26: 341–346.
Boolos, George. 1985d. “The Justification of Mathematical Induction.” in PSA 1984: Proceedings of the Biennial Meeting of the Philosophy of Science Association, Part II: Symposium Papers, edited by Peter D. Asquith and Philip Kitcher, pp. 469–475. East Lansing, Michigan: Philosophy of Science Association.
Boolos, George. 1986. “Review of Manin (1977).” The Journal of Symbolic Logic 51: 829–830.
Boolos, George. 1987a. “The Consistency of Frege’s Foundations of Arithmetic.” in On Being and Saying: Essays for Richard Cartwright, edited by Judith Jarvis Thomson, pp. 3–20. Cambridge, Massachusetts: The MIT Press. Reprinted in Demopoulos (1995, 211–233) and in Boolos (1998a, 183–201).
Boolos, George. 1987b. “Saving Frege From Contradiction.” Proceedings of the Aristotelian Society 87: 137–151. Reprinted in Demopoulos (1995, 438–452) and in Boolos (1998a, 171–182).
Boolos, George. 1987c. “A Curious Inference.” The Journal of Philosophical Logic 16(1): 1–12. Reprinted in Boolos (1998a, 376–382), doi:10.1007/bf00250612.
Boolos, George. 1987d. “On Notions of Provability in Provability Logic.” in Abstracts of the 8th International Congress of Logic, Methodology and Philosophy of Science, volume 5, pp. 236–238. Dordrecht: Kluwer Academic Publishers.
Boolos, George. 1988a. “Alphabetical Order.” Notre Dame Journal of Formal Logic 29: 214–215.
Boolos, George. 1988b. “Review of Smoryński (1985).” The Journal of Symbolic Logic 53: 306–309.
Boolos, George. 1989a. “Iteration Again.” Philosophical Topics 17(2): 5–21. Reprinted in Boolos (1998a, 88–104).
Boolos, George. 1989b. “A New Proof of the Gödel Incompleteness Theorem.” Notices of the American Mathematical Society 36: 388–390. Reprinted in Boolos (1998a, 383–388).
Boolos, George, ed. 1990a. Meaning and Method – Essays in Honour of Hilary Putnam. Cambridge: Cambridge University Press.
Boolos, George. 1990b. “The Standard of Equality of Numbers.” in Meaning and Method – Essays in Honour of Hilary Putnam, edited by George Boolos, pp. 261–277. Cambridge: Cambridge University Press. Reprinted in Demopoulos (1995, 234–254) and in Boolos (1998a, 202–219).
Boolos, George. 1990c. “On ‘Seeing’ the Truth of the Gödel Sentence [Commentary on Penrose (1989)].” Behavioral and Brain Sciences 13(4): 655–656. Reprinted in Boolos (1998a, 389–391).
Boolos, George. 1990d. “Review of Uspensky (1987).” The Journal of Symbolic Logic 55: 889–891.
Boolos, George. 1991. “Zooming Down the Slippery Slope.” Noûs 25: 695–706. Reprinted in Boolos (1998a, 354–364).
Boolos, George. 1993a. The Logic of Provability. Cambridge: Cambridge University Press.
Boolos, George. 1993b. “Whence the Contradiction?” Proceedings of the Aristotelian Society, Supplementary Volume 67: 213–233. Reprinted in Schirn (1996, 234–252) and in Boolos (1998a, 220–236).
Boolos, George. 1993c. “The Analytical Completeness of Dzhaparidze’s Polymodal Logics.” Annals of Pure and Applied Logic 61: 95–111.
Boolos, George. 1994a. “The Advantages of Honest Toil over Theft.” in Mathematics and Mind, edited by Alexander George, pp. 27–44. Oxford: Oxford University Press. Reprinted in Boolos (1998a, 255–274).
Boolos, George. 1994b. “1879?” in Reading Putnam, edited by Peter Clark and Robert Hale, pp. 31–48. Philosophers and Their Critics. Oxford: Blackwell Publishers. Reprinted in Boolos (1998a, 237–254).
Boolos, George. 1994c. “Gödel’s Second Incompleteness Theorem Explained in Words of One Syllable.” Mind 103: 1–3. Reprinted in Boolos (1998a, 411–414).
Boolos, George. 1995a. “Frege’s Theorem and the Peano Postulates.” The Bulletin of Symbolic Logic 1: 317–326. Reprinted in Boolos (1998a, 291–300).
Boolos, George. 1995b. “Quotational Ambiguity.” in On Quine – New Essays, edited by Paolo Leonardi and Marco Santambrogio, pp. 283–296. Cambridge: Cambridge University Press. Reprinted in Boolos (1998a, 392–405).
Boolos, George. 1995c. “Introductory Note to Kurt Gödel’s ‘Some Basic Theorems on the Foundations of Mathematics and their Implications’ .” in Logic, Logic, and Logic, pp. 105–119. Cambridge, Massachusetts: Harvard University Press. Introductions and afterword by John P. Burgess; edited by Richard Jeffrey, doi:10.1080/01445340051095856.
Boolos, George. 1996a. “On the Proof of Frege’s Theorem.” in Benacerraf and His Critics, edited by Adam Morton and Stephen P. Stich, pp. 143–159. Philosophers and Their Critics. Oxford: Blackwell Publishers. Reprinted in Boolos (1998a, 275–290).
Boolos, George. 1996b. “The Hardest Logical Puzzle Ever.” The Harvard Review of Philosophy 6: 62–65. Reprinted in Boolos (1998a, 406–410).
Boolos, George. 1997a. “Is Hume’s Principle Analytic?” Notre Dame Journal of Formal Logic 38: 6–30. Reprinted in Heck (1997, 245–261), in Boolos (1998a, 301–314) and in Cook (2007, 3–16).
Boolos, George. 1997b. “Constructing Cantorian Counterexamples.” The Journal of Philosophical Logic 26(3): 237–239. Reprinted in Boolos (1998a, 339–341).
Boolos, George. 1998a. Logic, Logic, and Logic. Cambridge, Massachusetts: Harvard University Press. Introductions and afterword by John P. Burgess; edited by Richard Jeffrey, doi:10.1080/01445340051095856.
Boolos, George. 1998b. “Must We Believe in Set Theory?” in Logic, Logic, and Logic, pp. 120–132. Cambridge, Massachusetts: Harvard University Press. Reprinted in Sher and Tieszen (2000, 257–268), doi:10.1080/01445340051095856.
Boolos, George. 1998c. “Gottlob Frege and the Foundations of Arithmetic.” in Logic, Logic, and Logic, pp. 143–154. Cambridge, Massachusetts: Harvard University Press. Introductions and afterword by John P. Burgess; edited by Richard Jeffrey, doi:10.1080/01445340051095856.
Boolos, George. 1998d. “Reply to Parsons (1974).” in Logic, Logic, and Logic, pp. 30–36. Cambridge, Massachusetts: Harvard University Press. Introductions and afterword by John P. Burgess; edited by Richard Jeffrey, doi:10.1080/01445340051095856.
Boolos, George. 2020. “Logicism and Second-Order Logic.” in Logic, Language, and Mathematics. Themes from the Philosophy of Crispin Wright, edited by Alexander Miller, pp. 96–115. Oxford: Oxford University Press, doi:10.1093/oso/9780199278343.001.0001.
Boolos, George, Burgess, John P. and Jeffrey, Richard C. 2002. Computability and Logic. 4th ed. Cambridge: Cambridge University Press. First edition: Boolos and Jeffrey (1974).
Boolos, George, Burgess, John P. and Jeffrey, Richard C. 2007. Computability and Logic. 5th ed. Cambridge: Cambridge University Press. First edition: Boolos and Jeffrey (1974), doi:10.1017/cbo9780511804076.
Boolos, George and Heck, Richard Kimberley. 1998. “Die Grundlagen der Arithmetik, \(\S\S\)82-3.” in The Philosophy of Mathematics Today, edited by Matthias Schirn, pp. 407–428. Oxford: Oxford University Press. Reprinted in Boolos (1998a, 315–338); originally published under the names “George Boolos” and “Richard G. Heck, Jr.” , doi:10.1093/oso/9780198236542.001.0001.
Boolos, George and Jeffrey, Richard C. 1974. Computability and Logic. 1st ed. Cambridge: Cambridge University Press.
Boolos, George and Jeffrey, Richard C. 1989. Computability and Logic. 3rd ed. Cambridge: Cambridge University Press. First edition: Boolos and Jeffrey (1974).
Boolos, George and McGee, Vann. 1987. “The Degree of the Set of Sentences of Predicate Provability Logic that are True under every Interpretation.” The Journal of Symbolic Logic 52: 165–171.
Boolos, George and Putnam, Hilary. 1968. “Degrees of Unsolvability of Constructible Sets of Integers.” The Journal of Symbolic Logic 33: 497–513.
Boolos, George and Sambin, Giovanni. 1985. “An Incomplete System of Modal Logic.” The Journal of Philosophical Logic 14(4): 351–358.
Boolos, George and Sambin, Giovanni. 1991. “Provability: The Emergence of a Mathematical Modality.” Studia Logica: An International Journal for Symbolic Logic 50(1): 1–23.

Further References

Cook, Roy T., ed. 2007. The Arché Papers on the Mathematics of Abstraction. The University of Western Ontario Series in Philosophy of Science n. 71. Dordrecht: Springer, doi:10.1007/978-1-4020-4265-2.
Demopoulos, William, ed. 1995. Frege’s Philosophy of Mathematics. Cambridge, Massachusetts: Harvard University Press.
Heck, Richard Kimberley, ed. 1997. Language, Thought and Logic. Essays in Honour of Michael Dummett. Oxford: Oxford University Press. Originally published under the name “Richard G. Heck, Jr.” .
Manin, Yuri I. 1977. A Course in Mathematical Logic for Mathematicians. New York: Springer.
Parsons, Charles. 1974. “Sets and Classes.” Noûs 8(1): 1–12. Reprinted in Parsons (1983, 209–220).
Parsons, Charles. 1983. Mathematics in Philosophy: Selected Essays. Ithaca, New York: Cornell University Press.
Penrose, Roger. 1989. The Emperor’s New Mind. Concerning Computers, Minds and the Laws of Physics. Oxford: Oxford University Press. Second edition: Penrose (1999).
Penrose, Roger. 1999. The Emperor’s New Mind. Concerning Computers, Minds and the Laws of Physics. 2nd ed. Oxford: Oxford University Press. Foreword by Martin Gardner; first edition: Penrose (1989).
Schirn, Matthias, ed. 1996. Frege: Importance and Legacy. Perspektiven der analytischen Philosophie / Perspectives in Analytic Philosophy n. 13. Berlin: de Gruyter.
Shapiro, Stewart. 1996. The Limits of Logic: Second-Order Logic and the Löwenheim-Skolem Theorem. Brookfield, Vermont: Aldershot.
Sher, Gila Y. and Tieszen, Richard, eds. 2000. Between Logic and Intuition: Essays in Honor of Charles Parsons. Cambridge: Cambridge University Press.
Smoryński, Craig. 1985. Self-Reference and Modal Logic. Berlin: Springer.
Smullyan, Raymond M. 1978. What is the Name of this Book? The Riddle of Dracula and Other Logical Puzzles. Englewood Cliffs, New Jersey: Prentice-Hall, Inc.
Solovay, Robert M. 1976. “Provability Interpretations of Modal Logic.” Israel Journal of Mathematics 25: 287–304.
Uspensky, Vladimir A. 1987. Gödel’s Incompleteness Theorem. Moscow: Mir Publishers. Reprinted as Uspensky (1994).
Uspensky, Vladimir A. 1994. “Gödel’s Incompleteness Theorem.” Theoretical Computer Science 130: 239–319. Reprint of Uspensky (1987).