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References

[Bel62] Nuel D. Belnap. Tonk, plonk and plink. Analysis, 22:130-134, 1962. [ .pdf ]
[BP83] Paul Benacerraf and Hilary Putnam. Introduction. In Paul Benacerraf and Hilary Putnam, editors, Philosophy of Mathematics, pages 1-37. Cambridge University Press, Cambridge, England, second edition, 1983.
[Bur84] Tyler Burge. Semantical paradox. In Robert L. Martin, editor, Recent Essays on Truth and the Liar Paradox, pages 85-117. Oxford University Press, New York, 1984.
[Car95] Lewis Carroll. What the tortoise said to Achilles. Mind, n. s. 4:278-280, 1895. [ http ]
[Car94] Richard L. Cartwright. Speaking of everything. Nôus, 28:1-20, 1994.
[Die06] Patrick Dieveney. Quantification and Indispensable Ontology. PhD thesis, University of Arizona, 2006.
[Dra74] Frank R. Drake. Set Theory. North-Holland, Amsterdam, 1974.
[Dum63] Michael A. E. Dummett. The philosophical significance of Gödel's theorem. Ratio, 5:140-155, 1963. All page references are to the reprinting as pp. 186-201 [Dum78b].
[Dum78] Michael A. E. Dummett. Platonism. In Michael A. E. Dummett, editor, Truth and Other Enigmas, pages 202-214. Harvard University Press, Cambridge, Massachusetts, 1978. Invited address to the Third International Congress on Logic, Methodology and Philosophy of Science, Amsterdam, 29 August, 1967.
[Dum91] Michael A. E. Dummett. Frege: Philosophy of Mathematics. Gerald Duckworth & Co., London, 1991.
[Fef91] Solomon Feferman. Reflecting on incompleteness. Journal of Symbolic Logic, 56:1-49, 1991.
[Fie94] Hartry Field. Are our logical and mathematical concepts highly indeterminate? In Peter A. French, Theodore E. Uehling, Jr., and Howard K. Wettstein, editors, Philosophical Naturalism, number 19 in Midwest Studies in Philosophy, pages 391-429. University of Notre Dame Press, Notre Dame, Indiana, U. S. A., 1994.
[G47] Kurt Gödel. What is Cantor's continuum problem? American Mathematical Monthly, 54:515-525, 1947. Errata, vol. 55, p. 151. Revised and expanded for the first (1964) edition [BP83]. All page references are either to the reprinting of the revised and expanded version as pp. 470-485 [BP83] or to the reprinting of the original version as Vol. 2, pp. 176-187 [Göd90].
[Gol76] Alvin I. Goldman. Discrimination and perceptual knowledge. Journal of Philosophy, 73:771-791, 1976.
[Har82] J. H. Harris. What's so logical about the “logical” axioms? Studia Logica, 41:159-171, 1982.
[L60] Azriel Lévy. Axiom schemata of strong infinity in axiomatic set theory. Pacific Journal of Mathematics, 10:223-238, 1960.
[Lav94] Shaughan Lavine. Understanding the Infinite. Harvard University Press, Cambridge, Massachusetts, 1994. Paperback edition 1998. Spanish translation Comprendiendo el Infinito (Fondo de Cultura Economica USA, San Diego, California, 2006). Mathematical Reviews 95k:60009.
[Lav99] Shaughan Lavine. Skolem was wrong. Widely circulated but unpublished manuscript. 161 pages. Cited in print by Field, McGee, and Parsons, 1999.
[Lav00] Shaughan Lavine. Quantification and ontology. Synthese, 124:1-43, 2000. [ .pdf ]
[Lev79] Azriel Levy. Basic Set Theory. Perspectives in Mathematical Logic. Springer-Verlag, New York, 1979.
[Lew73] David K. Lewis. Counterfactuals. Blackwell Publishers, Oxford, 1973.
[Lew91] David K. Lewis. Parts of Classes. Basil Blackwell Publishers, Oxford, 1991. With an Appendix by John P. Burgess, A. P. Hazen, and David Lewis.
[Mad88] Penelope Maddy. Believing the axioms. I. Journal of Symbolic Logic, 53:481-511, 1988.
[McG97] Vann McGee. How we learn mathematical language. Philosophical Review, 106:35-68, 1997.
[McG00] Vann McGee. `Everything'. In Gila Sher and Richard Tieszen, editors, Between Logic and Intuition: Essays in Honor of Charles Parsons, pages 54-78. Cambridge University Press, New York, 2000.
[Par74a] Charles Parsons. The liar paradox. Journal of Philosophical Logic, 3:381-412, 1974. All page references are to the reprinting as pp. 221-251 [Par83], which has an added postscript, pp. 251-267.
[Par74b] Charles Parsons. Sets and classes. Noûs, 8:1-12, 1974. All page references are to the reprinting as pp. 209-220 [Par83].
[Par83] Charles Parsons. Sets and modality. In Mathematics in Philosophy; Selected Essays, pages 298-341. Cornell University Press, Ithaca, New York, 1983.
[Par90] Charles Parsons. The uniqueness of the natural numbers. Iyyun, A Jerusalem Philosophical Quarterly, 39:13-44, 1990.
[Put80] Hilary Putnam. Models and reality. Journal of Symbolic Logic, 45:464-482, 1980. Presidential Address to the annual meeting of the Association for Symbolic Logic, December, 1977. Reprinted as pp. 421-444 [BP83]. [ http ]
[Qui36] Willard Van Orman Quine. Truth by convention. In Otis H. Lee, editor, Philosophical Essays for Alfred North Whitehead, pages 90-124. Longmans, Green, New York, 1936. All page references are to the corrected reprinting as pp. 329-354 of [BP83].
[Qui45] Willard Van Orman Quine. On the logic of quantification. Journal of Symbolic Logic, 10:1-12, 1945. [ .pdf ]
[Qui48] Willard Van Orman Quine. On what there is. Review of Metaphysics, 2:21-38, 1948. The article was reprinted, with minor changes and added footnotes, as 1–19 of Quine61. That, later, version is the one that is commonly reprinted and referenced, but, so far as I know, it is not available on-line, and so I have referenced the original. [ http ]
[Qui60] Willard Van Orman Quine. Word and Object. M. I. T. Press, Cambridge, Massachusetts, 1960.
[Qui61] Willard Van Orman Quine. From a Logical Point of View: Logico-Philosophical Essays. Harper Torchbooks, Harper & Row, New York, second, revised edition, 1961.
[Qui68] Willard Van Orman Quine. Reply to Noam Chomsky. Synthese, 19:274-283, 1968. [ .pdf ]
[Qui69a] Willard Van Orman Quine. Existence and quantification. In Ontological Relativity and Other Essays, number 1 in John Dewey Essays in Philosophy, pages 91-113. Columbia University Press, New York, 1969.
[Qui69b] Willard Van Orman Quine. Ontological Relativity and Other Essays. Number 1 in John Dewey Essays in Philosophy. Columbia University Press, New York, 1969.
[Qui76] Willard Van Orman Quine. The variable. In Ways of Paradox and Other Essays, pages 272-282. Harvard University Press, Cambridge, Massachusetts, revised and enlarged edition, 1976.
[Rus05a] Bertrand Russell. On denoting. Mind, 14:479-493, 1905. [ http ]
[Rus05b] Bertrand Russell. On some difficulties in the theory of transfinite numbers and order types. Proceedings of the London Mathematical Society, 2nd series, 4:29-53, 1905. Reprinted as pp. 135-164 [Rus73].
[Rus73] Bertrand Russell. Essays in Analysis. George Braziller, New York, 1973. Edited by Douglas Lackey.
[Sha91] Stewart Shapiro. Foundations without Foundationalism. Clarendon Press, Oxford, 1991.
[Sha03] Stewart Shapiro. All sets great and small: and I do mean all. Philosophical Perspectives, 17:467-489, 2003.
[Sko20] Thoralf Skolem. Logische-kombinatorische Untersuchungen über die Erfüllbarkeit und Beweisbarkeit mathematischen Sätze nebst einem Theoreme über dichte Mengen (Logico-combinatorial investigations in the satisfiability or provability of mathematical propositions: A simplified proof of a theorem by L. Löwenheim and generalizations of the theorem). Skrifter, Videnskabsakademiet i Kristiania, I, (4):1-36, 1920. All page references are to the translation of 1 by Stefan Bauer-Mengelberg printed as pp. 254-263 of [vH67].
[Sko23] Thoralf Skolem. Einige Bemerkungen zur axiomatischen Begründung der Mengenlehre (Some remarks on axiomatised set theory). In Matematikerkongressen i Helsingfors den 4-7 Juli 1922, Den femte skandinaviska matematikerkongressen, Redogörelse, pages 217-232, Helsinki, 1923. Akademiska Bokhandeln. All page references are to the translation by Stefan Bauer-Mengelberg, pp. 291-301 [vH67].
[vH99] Jean van Heijenoort, editor. From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931. Source Books in the History of the Sciences. Harvard University Press, reprinted by iUniverse, Cambridge, Massachusetts, 1967, reprinted 1999. Series editor, Edward H. Madden.
[Wil98] Timothy Williamson. Indefinite extensibility. In Johannes L. Brandl and Peter Sullivan, editors, New Essays on the Philosophy of Michael Dummett, volume 55 of Grazer Philosophische Studien, pages 1-24. Rodopi, Atlanta, Georgia, 1998.
[Wil99] Timothy Williamson. Existence and contingency. Proceedings of the Aristotelian Society, n.s. 100:117-139, 1999.
[Wil03] Timothy Williamson. Everything. Philosophical Perspectives, 17:415-465, 2003.

-- ShaughanLavine - 16 Jan 2009

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