Publications

Books

Ontology and the Vicious-Circle Principle (Cornell University Press, Ithaca and London: 1973), 257 pages.

Constructibility and Mathematical Existence (Oxford University Press, Oxford: 1990), 282 pages. 2nd Printing: Oxford University Press, Oxford: 1991. Paperback edition: Oxford University Press, Oxford, 1991.

The Worlds of Possibility: Modal Realism and the Semantics of Modal Logic (Oxford University Press, Oxford: l998), 342 pages. Paperback edition: Oxford University Press, Oxford, 2001.

A Structural Account of Mathematics (Oxford University Press, Oxford: 2004), 380 pages. Paperback edition: Oxford University Press, Oxford, 2007.

Articles

“Wittgenstein and Logical Compulsion,” Analysis, Vol. 21, No. 6, June 1961, pp. 136 - 140. Reprinted in Wittgenstein: The Philosophical Investigations, edited by George Pitcher (Doubleday: Garden City, NY., 1966). Also reprinted in The Philosophy of Wittgenstein, Vol. 10: Logical Necessity and Rules, edited by John Canfield (Garland Publishing Inc.: New York and London, 1986).

“Mathematical Discovery and Concept Formation,” The Philosophical Review, Vol. 72, No. l, January 1963, pp. 17 - 34. Reprinted in Wittgenstein: The Philosophical Investigations, edited by George Pitcher (Doubleday: Garden City, NY., 1966). Also reprinted in the Bobbs-Merrill Reprint Series in Philosophy. Also reprinted in The Philosophy of Wittgenstein, Vol. 11: Philosophy of Mathematics, edited by John Canfield (Garland Publishing Inc.: New York and London, 1986).

“On the Possibility of Completing an Infinite Process,” The Philosophical Review, Vol. 74, No. 1, January 1965, pp. 74 - 87.

“Operationalism and Ordinary Language: A Critique of Wittgenstein,” co-authored with J. A. Fodor, American Philosophical Quarterly, Vol. 2, No. 4, October 1965, pp. 281 - 295. Reprinted in Wittgenstein: The Philosophical Investigations, edited by George Pitcher (Doubleday: Garden City, NY., 1966). Also reprinted in the Bobbs-Merrill Reprint Series in Philosophy. Also reprinted in Contemporary Essays on Dreaming: Philosophical and Psychological Perspectives, edited by Charles Dunlop (Cornell University Press: Ithaca, NY. and London, 1977). Also reprinted in Representations: Philosophical Essays on the Foundations of Cognitive Science, by J.A. Fodor (M.I.T. Press: Cambridge, Massachusetts, 1981). Also reprinted in The Philosophy of Wittgenstein, Vol. 7: Criteria, edited by John Canfield (Garland Publishing Inc.: New York and London, 1986). Also reprinted in The Nature of Mind, edited by David M. Rosenthal (Oxford University Press: Oxford, 1991).

“What Dreams are Made On,” Theoria, Vol. 31, No. 3, 1965. Reprinted in Contemporary Essays on Dreaming: Philosophical and Psychological Perspectives, edited by Charles Dunlop (Cornell University Press: Ithaca, NY. and London, 1977), pp. 145 - 158.

“Our Ontological Commitment to Universals,” Noûs, Vol. 2, February, 1968, No. l, pp. 25 - 46.

“Russell’s Theory of Types,” in Bertrand Russell: A Collection of Critical Essays, edited by David Pears (Doubleday: Garden City, NY., 1972), pp. 245 - 289.

“On Alleged Refutations of Mechanism Using Gödel’s Incompleteness Results,” The Journal of Philosophy, Vol. 69, No. 17, September 1972, pp. 507 - 536.

“Operationalism and Ordinary Language Revisited: A Reply to Cook,” Philosophical Studies, Vol. 24, No. 3, May 1973, pp. 137 - 157. Reprinted in The Philosophy of Wittgenstein, Vol. 7: Criteria, edited by John Canfield (Garland Publishing Inc.: New York and London, 1986).

“On Criteria of Ontological Commitment,” in Ontological Commitment, edited by Richard Severns (University of Georgia Press: Athens, Georgia, 1974), pp. 69 - 90.

“An Improvement on Zabludowski’s Critique of Goodman’s Theory of Projection,” co-authored with Ralph Kennedy, The Journal of Philosophy, Vol. 72, No. 5, March 1975, pp. 137 - 141.

“The Surprise Examination Paradox,” co-authored with James McLelland, Journal of Philosophical Logic, Vol. 4, No. l, February 1975, pp. 71 - 89.

“Davidson’s Extensional Theory of Meaning,” Philosophical Studies, Vol. 28, No. l, July 1975, pp. 1 - 15.

“A Formalization of a Nominalistic Set Theory,” co-authored with Yutang Lin and Thomas Schaffter, Journal of Philosophical Logic, Vol. 4, No. 2, May 1975, pp. 155 - 169.

“Church’s Thesis Misconstrued,” co-authored with Jonathan Berg, Philosophical Studies, Vol. 28, 1975, pp. 357 - 362.

“Truth, Meaning and Paradox,” Noûs, Vol. 10, No. 3, September 1976, pp. 305 - 311.

“Cohen’s Defense of Cook,” Philosophical Studies, Vol. 29, No. 5, May 1976, pp. 353 - 355.

“Wittgenstein’s Analysis of the Paradoxes in His Lectures on the Foundations of Mathematics,” The Philosophical Review, Vol. 86, No. 3, July 1977, pp. 365 - 381. Also reprinted in The Philosophy of Wittgenstein, Vol. 11: Philosophy of Mathematics, edited by John Canfield (Garland Publishing Inc.: New York and London, 1986).

“The Principle of Wanton Embedding,” co-authored with Ralph Kennedy, The Journal of Philosophy, Vol. 74, No. 9, September 1977, pp. 539 - 540.

“Beyond Zabludowskian Competitors: A New Theory of Projectibility,” co-authored with Ralph Kennedy, Philosophical Studies, Vol. 33, No. 3, April 1978, pp. 229 - 253.

“A Diagnosis of the Liar and Other Semantical Vicious Circle Paradoxes,” in Bertrand Russell Memorial Volume, edited by George Roberts (Allen & Unwin: London, 1978) and (Humanities Press: Atlantic Highlands, NY., 1978), pp. 52 - 80.

“The Dutch Book Argument: Its Logical Flaws, Its Subjective Sources,” co-authored with Ralph Kennedy, Philosophical Studies, Vol. 36, 1979, pp. 19 - 33.

“The Semantic Paradoxes: A Diagnostic Investigation,” The Philosophical Review, Vol. 88, No. 4, October 1979, pp. 590 - 618.

“Ramsey’s Theory of Types: Suggestions for a Return to Fregean Sources,” in Prospects for Pragmatism: Essays in Memory of F.P. Ramsey, edited by H. Mellor (Cambridge University Press: Cambridge, 1980), pp. 21 - 47.

“Quine and the Confirmational Paradoxes,” in Midwest Studies in Philosophy, Vol. 6, 1981, edited by P. French, T. Uehling Jr., and H. Wettstein. (University of Minnesota Press: Minneapolis, 1981), pp. 425 - 454.

“The Wright-Wing Defense of Wittgenstein’s Philosophy of Logic,” The Philosophical Review, Vol. 91, No. 1, January 1982, pp. 99 - 108. Reprinted in The Philosophy of Wittgenstein, Vol. 11: Philosophy of Mathematics, edited by John Canfield (Garland Publishing Inc.: New York and London, 1986).

“A Gödelian Thesis Regarding Mathematical Objects: Do They Exist? And Can We Perceive Them?” The Philosophical Review, Vol. 91, No. 2, April 1982, pp. 211 - 227. Reprinted in Mathematical Objects and Mathematical Knowledge, edited by Michael Resnik, in the series The International Research Library of Philosophy (Dartmouth Publishing Company: Aldershot, England, 1995). Also translated and published in Japanese (see below).

“The Semantic Paradoxes: Some Second Thoughts,” Philosophical Studies, Vol. 45, No. 2, March 1984, pp. 223 - 229.

“Priest, the Liar, and Gödel,” Journal of Philosophical Logic, Vol. 13, No. 2, May 1984, pp. 117 - 124.

“A Simple Type Theory Without Platonic Domains,” Journal of Philosophical Logic, Vol. 13, 1984, pp. 249 - 283.

“Horwich’s Justification of Induction,” Philosophical Studies, Vol. 48, 1985, pp. 107 - 110.

“Some Problems for Bayesian Confirmation Theory,” The British Journal for the Philosophy of Science, Vol. 38, 1987, pp. 551 - 560.

“Quine’s Indeterminacy,” in On Being and Saying: Essays for Richard Cartwright, ed. by Judith Jarvis Thompson (M.I.T. Press, Cambridge, MA., and London: 1987), pp. 41 - 55.

“An Interchange on the Popper-Miller Argument,” co-authored with Donald Gillies, Philosophical Studies, Vol. 54, 1988, pp. 1 - 8.

“Tharp’s ‘Myth and Mathematics’,” Synthese, Vol. 81, November, 1989, pp. 153 - 165.

“Mathematical Structuralism and the Controversy Over Mathematical Objects,” in Controvérsies Científicas E Filosóficas, edited by Fernando Gil (Editorial Fragmentos: Lisbon, 1990), pp. 325 - 335.

“A Biological Objection to Constructive Empiricism,” co-authored with Carol Chihara, The British Journal for the Philosophy of Science 44 (1993), 653 - 58.

“Modality Without Worlds,” in Philosophy Of Mathematics: the Proceedings of the Fifteenth International Wittgenstein Symposium (part 1), edited by Johannes Czermak, (Verlag Hölder-Pichler-Tempsky: Vienna, 1993), pp. 253 - 268.

“The Howson-Urbach Proofs of Bayesian Principles,” in Probability and Conditionals: Belief Revision and Rational Decision, edited by Ellery Eells and Brian Skyrms (Cambridge University Press, Cambridge, 1994), pp. 161 - 178.

“The Many Persons Problem,” Philosophical Studies, Volume 76, 1994, pp. 45 - 49.

“The Mystery of Julius: A Paradox in Decision Theory,” Philosophical Studies, Volume 80, 1995, pp. 1-16.

“Poincaré and Logicism,” Henri Poincaré Science et philosophie, edited by Jean-Louis Greffe, Gerhard Heinzmann and Kuno Lorenz (Akademie Verlag, Berlin, and Albert Blanchard, Paris, 1996), pp. 435-447.

“Tarski’s Thesis and the Ontology of Mathematics,” Philosophy of Mathematics Today, edited by Matthias Schirn, (Oxford University Press, 1998), pp. 157-172.

“The Rationalist Conception of Mathematics of Frege and Bolzano,” Revue d’Histoire des Sciences, Volume 52, 1999, pp. 343-361..

“Five Puzzles About Mathematics In Search of Solutions,” in Proceedings of the 7th and 8th Asian Logic Conferences, edited by Downey, R., Decheng, D., Ping, T. S., Hui, Q. Y., Yasugi, M., and Wu, G. (Singapore University Press and World Scientific Publishing Co., 2003), pp. 11-38.

“Nominalism,” in The Oxford Handbook of Philosophy of Mathematics and Logic, edited by Stewart Shapiro (Oxford University Press: Oxford, 2005), pp. 483-514.

Review of Alvin Plantinga’s Essays in the Metaphysics of Modality, Notre Dame Philosophical Reviews, June, 2003.

“Modal Realism and Its Roots in Mathematical Realism,” Philosophy of Logic, edited by Dale Jacquette. (Elsevier, 2007), pp. 997-1022.

“Burgess’s “Scientific” Argument for the Existence of Mathematical Objects,” Philosophia Mathematica, Volume 14, 2006, pp. 318-337.

“The Burgess-Rosen Critique of Nominalistic Reconstructions”, Philosophia Mathematica, Volume 15, 2007, pp. 54-78.

“Five Questions on Philosophy of Mathematics,” in Philosophy of Mathematics: Five Questions, edited by Vincent Hendricks and Hannes Leitgeb. (Automatic Press, 2008), pp. 51-74.

“Quine’s Lecture on Nominalism From the Perspective of a Nominalist,” Edited by Dean Zimmerman. Oxford Studies in Metaphysics, Volume. 4, 2008, pp. 79-98.

“The Existence of Mathematical Objects”, in Proof & Other Dilemmas: Mathematics and Philosophy, edited by Bonnie Gold and Roger Simons. (The Mathematical Association of America, 2008), pp. 131-56.

Works Edited

The Leslie Tharp Memorial Issue of Synthese, co-edited with Brian Skyrms, Synthese, Vol. 81, November, 1989.

The special Philosophy of Mathematics issue of Taiwanese Journal for Philosophy & History of Science, Number 10, 1998.

Works That Have Been Translated and Published

“A Gödelian Thesis Regarding Mathematical Objects: Do They Exist? And Can We Perceive Them?” Translated into Japanese by H. Kurokaw and published in Sugaku no Tetsugaku: Gödel Igo (which can be translated: Readings in the Philosophy of Mathematics: After Gödel) edited by IIDA Takashi (Keiso Shobo, 1996).