ShaughanLavine - 09 Mar 2010 - 19:26 - 1.26 " class="twikiLink">TWiki> TWiki Web>BibtexPlugin>BibFiles (15 Feb 2010, ShaughanLavine)EditAttach
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Jon Barwise. Admissible Sets and Structures. Perspectives in Mathematical Logic. Springer-Verlag, Berlin, 1975.
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Jon Barwise and Larry Moss. Vicious Circles: On the Mathematics of Non-Wellfounded Phenomena. Number 60 in CSLI Lecture Notes. CSLI Publications, Center for the Study of Language and Information, Leland Stanford Junior University, Stanford, 1996.
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K. J. Barwise, R. O. Gandy, and Y. N. Moschovakis. The next admissible set. Journal of Symbolic Logic, 36:108-120, 1971.
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Michael J. Beeson. Foundations of Constructive Mathematics. Number 6 in the 3rd Series in Ergebnisse der Mathematik und ihrer Grenzgebiete. Springer-Verlag, New York, 1985.
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E. T. Bell. Men of Mathematics. Simon and Schuster, New York, 1937.
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Paul Benacerraf. Mathematical truth. Journal of Philosophy, 70:661-679, 1973. All page references are to the reprinting as pp. 403-420 [BP83].
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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.
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Paul Benacerraf and Hilary Putnam, editors. Philosophy of Mathematics. Cambridge University Press, Cambridge, England, second edition, 1983.
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George Berkeley. A defence of free-thinking in mathematics. In answer to a pamphlet of Philalethes Cantabrigiensis, intituled, Geometry no friend to Infidelity, or a defence of Sir Isaac Newton, and the British Mathematicians. Also an appendix concerning Mr. Walton's Vindication of the principles of fluxions against the objections contained in the Analyst; wherein it is attempted to put this controversy in such a light as that every reader may be able to judge thereof. Printed by M. Rhames, for R. Gunne, Dublin, 1735. All page references are to the reprinting as Vol. 4, pp. 109-141 [Ber51].
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George Berkeley. The Works of George Berkeley Bishop of Cloyne. Thomas Nelson and Sons, 1951. Edited by A. A. Luce. Reprinted by Kraus Reprint (Nendeln, Liechtenstein) 1979.
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Paul Bernays. Die Bedeutung Hilberts für die Philosophie der Mathematik (Hilbert's significance for the philosophy of mathematics). Die Naturwissenschaften, 10:93-99, 1922. All page references are to the translation by Paolo Mancosu as pp. 189-197 Mancosu98.
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Paul Bernays. Die Philosophie der Mathematik und die Hilbertsche Beweistheorie (The philosophy of mathematics and Hilbert's proof theory). Blätter für deutsche Philosophie, 4:326-367, 1930-31. Reprinted as pp. 17-61 of Bernays76. All page references are to the translation by Paolo Mancosu as pp. 234-265 of Mancosu98.
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Paul Bernays. Sur le platonisme dans les mathématiques. L'Enseignement mathématique, 1st ser., 34:52-69, 1935. All page references are to the translation by Charles D. Parsons, pp. 258-271 [BP83].
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Paul Bernays. Abhandlungen zur Philosophie der Mathematik. Wissenschaftliche Buchgesellschaft, Darmstadt, 1976.
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Paul Bernays. A system of axiomatic set theory. In Gert H. Müller, editor, Sets and Classes; On the Work by Paul Bernays, number 84 in Studies in Logic and the Foundations of Mathematics, pages 1-119. North-Holland Publishing Company, New York, 1976. Originally published in the Journal of Symbolic Logic, 2:65-77, 1937; 6: 1-17, 1941; 7:65-89, 1942; 7:133-145, 1942; 8:89-106, 1943; 13:65-79, 1948; 19:81-96 1954.
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Errett Bishop and Douglas Bridges. Constructive Analysis. Number 279 in Grundlehren der mathematischen Wissenschaften. Springer-Verlag, New York, 1985.
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Patricia A. Blanchette. Logical consequence. In Lou Goble, editor, The Blackwell Guide to Philosophical Logic, Blackwell Philosophy Guides, chapter 6, pages 115-135. Blackwell Publishers Inc., 2001. [ http ]
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Lenore Blum, Mike Shub, and Steve Smale. On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines. Bulletin (New Series) of the American Mathematical Society, 21:1-46, 1989.
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Bernard Bolzano. Wissenschaftslehre. Scientia Verlag Aalen, Darmstadt, 1970. Reprint of the second edition (F. Meiner, Leipzig, 1929-1931).
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George Boolos. The iterative conception of set. Journal of Philosophy, 68:215-231, 1971. All page references are to the reprinting as pp. 486-502 [BP83].
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George S. Boolos and Richard C. Jeffrey. Computability and Logic. Cambridge University Press, New York, third edition, 1989. First edition, 1974; second edition, 1980.
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Egon Börger. Computability, Complexity, Logic. Number 128 in Studies in Logic and the Foundations of Mathematics. North-Holland, New York, 1989. Distributed by Elsevier Science Publishing.
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H. J. M. Bos. Differentials, higher-order differentials and the derivative in the Leibnizian calculus. Archive for History of Exact Sciences, 14:1-90, 1974.
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Umberto Bottazzini. The Higher Calculus: A History of Real and Complex Analysis from Euler to Weierstrass. Springer-Verlag, New York, 1986. Translation by Warren Van Egmond, with substantial corrections and revisions, of Il Calcolo sublime: storia dell'analisi matematica de Euler a Weierstrass. Editore Boringhieri, Turin, 1981.
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Carl B. Boyer. The Concepts of the Calculus, A Critical and Historical Discussion of the Derivative and the Integral. Hafner Publishing Company, 1949. All page references are to the reprinting as The History of the Calculus and Its Conceptual Development (Dover Publications, New York, 1959).
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Robert Brandom. Reference explained away. Journal of Philosophy, 81:469-492, 1984.
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Luitzen Egbertus Jan Brouwer. Über die Bedeutung des Satzes vom ausgeschlossenen Dritten in der Mathematik, insbesondere in der Funktionentheorie. Journal für die reine und angewandte Mathematik, 154:1-7, 1923. Translation by Stefan Bauer-Mengelberg and Jan van Heijenoort, pp. 335-341 [vH67].
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John Burgess and Douglas Miller. Remarks on invariant descriptive set theory. Fundamenta Mathematicae, 90:53-75, 1975.
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John P. Burgess. Why I am not a nominalist. Notre Dame Journal of Formal Logic, 24:93-105, 1983.
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Georg Cantor. Ueber unendliche, lineare Punktmannigfaltigkeiten, 5. Mathematische Annalen, 21:545-586, 1883. Reprinted as pp. 165-204 [Can32].
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Georg Cantor. Ueber unendliche, lineare Punktmannigfaltigkeiten, 6. Mathematische Annalen, 23:453-488, 1884. All page references are to the reprinting as pp. 210-244 [Can32b].
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Georg Cantor. Beiträge zur Begründung der transfiniten Mengenlehre, I. Mathematische Annalen, 46:481-512, 1895. Reprinted as pp. 282-311 [Can32b] and translated in [Can15].
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Georg Cantor. Beiträge zur Begründung der transfiniten Mengenlehre, II. Mathematische Annalen, 49:207-246, 1897. Reprinted as pp. 312-351 [Can32b] and translated in [Can15].
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Georg Cantor. Gesammelte Abhandlungen. Verlag von Julius Springer, Berlin, 1932. Edited by Ernst Zermelo.
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Rudolf Carnap. Introduction to Semantics. Harvard University Press, Cambridge, Mass., 1942.
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Michael A. E. Dummett. Truth and Other Enigmas. Harvard University Press, Cambridge, Massachusetts, 1978.
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Charles Parsons. Some remarks on Frege's conception of extension. In Matthias Schirn, editor, Studien zu Frege, volume 1, pages 265-277. Friedrich Frommann, Stuttgart, 1976.
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Charles Parsons. What is the iterative conception of set? In R. E. Butts and J. Hintikka, editors, Logic, Foundations of Mathematics, and Computability Theory. Proceedings of the Fifth International Congress of Logic, Methodology, and the Philosophy of Science (London, Ontario, 1975), Dordrecht, The Netherlands, 1977. Reidel. All page references are to the reprinting as pp. 503-529 [Par83a].
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Charles Parsons. Mathematical intuition. Proceedings of the Aristotelian Society, n.s. 80:145-168, 1979-1980.
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Charles Parsons. Mathematics in Philosophy; Selected Essays. Cornell University Press, Ithaca, New York, 1983.
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Charles Parsons. Quine on the philosophy of mathematics. In Mathematics in Philosophy; Selected Essays, pages 176-205. Cornell University Press, Ithaca, New York, 1983.
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Charles Parsons. Sets and modality. In Mathematics in Philosophy; Selected Essays, pages 298-341. Cornell University Press, Ithaca, New York, 1983.
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Charles Parsons. The structuralist view of mathematical objects. Synthese, 84:303-346, 1990.
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Charles Parsons. The uniqueness of the natural numbers. Iyyun, A Jerusalem Philosophical Quarterly, 39:13-44, 1990.
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Hilary Putnam. Mathematics, Matter and Method. Cambridge University Press, Cambridge, England, second edition, 1979.
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Hilary Putnam. What is mathematical truth? In Mathematics, Matter and Method, chapter 4, pages 60-78. Cambridge University Press, Cambridge, England, second edition, 1979. All page references are to the reprinting as pp. 49-65 [Tym86].
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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 ]
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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].
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Willard Van Orman Quine. On the logic of quantification. Journal of Symbolic Logic, 10:1-12, 1945. [ .pdf ]
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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 ]
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Willard Van Orman Quine. Identity, ostension, and hypostasis. Journal of Philosophy, 47:621-633, 1950. All page references are to the reprinting as pp. 65-79 of Quine61. [ http ]
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Willard Van Orman Quine. Main trends in recent philosophy: Two dogmas of empiricism. Philosophical Review, 60:20-43, 1951. [ http ]
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Willard Van Orman Quine. On Carnap's views on ontology. Philosophical Studies, 2:65-72, 1951. Reprinted as pp. 126-134 of Qui66. [ http ]
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Willard Van Orman Quine. Symposium: On what there is, III. Proceedings of the Aristotelian Society, supplementary volume 25:149-160, 1951. Joint Session of the Aristotelian Society and the Mind Association at the University of Edinburgh, 1951. Symposiasts: Peter Thomas Geach, Alfred Jules Ayer, Willard Van Orman Quine.
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Willard Van Orman Quine. Variables explained away. Proceedings of the American Philosophical Society, 104:343-347, 1960. All page references are to the reprinting as pp. 227-235 of [Qui66]. [ http ]
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Willard Van Orman Quine. Word and Object. M. I. T. Press, Cambridge, Massachusetts, 1960.
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Willard Van Orman Quine. From a Logical Point of View: Logico-Philosophical Essays. Harper Torchbooks, Harper & Row, New York, second, revised edition, 1961.
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Willard Van Orman Quine. Logic and the reification of universals. In From a Logical Point of View: Logico-Philosophical Essays, pages 102-129. Harper Torchbooks, Harper & Row, New York, second, revised edition, 1961.
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Willard Van Orman Quine. Reference and modality. In From a Logical Point of View: Logico-Philosophical Essays, pages 139-157. Harper Torchbooks, Harper & Row, New York, second, revised edition, 1961.
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Willard Van Orman Quine. Reply to Professor Marcus. Synthese, 13:323-330, 1961. All page references are to the reprinting as pp. 177-184 of [Qui76b].
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Willard Van Orman Quine. Set Theory and Its Logic. The Belknap Press of Harvard University Press, Cambridge, Mass., revised edition, 1963 and 1969.
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Willard Van Orman Quine. Ontological reduction and the world of numbers. Journal of Philosophy, 61:185-212, 1964. Reprinted as pp. 212-220 of the 2006 revised edition of [Qui66]. [ http ]
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Willard Van Orman Quine. Selected Logic Papers. Random House, New York, 1966.
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Willard Van Orman Quine. Symposium: The philosophy of Bertrand Russell: Russell's ontological development. Journal of Philosophy, 63:657-667, 1966. [ http ]
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Willard Van Orman Quine. Ways of Paradox and Other Essays. Random House, New York, 1966. Revised and enlarged editions issued by Harvard University Press, Cambridge, Mass. in 1976 and 2006.
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Willard Van Orman Quine. Ontological relativity. Journal of Philosophy, 65:185-212, 1968. Reprinted as pp. 26-68 of [Quine69c]. [ http ]
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Willard Van Orman Quine. Reply to Noam Chomsky. Synthese, 19:274-283, 1968. [ .pdf ]
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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.
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Willard Van Orman Quine. Ontological Relativity and Other Essays. Number 1 in John Dewey Essays in Philosophy. Columbia University Press, New York, 1969.
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Willard Van Orman Quine. Speaking of objects. In Ontological Relativity and Other Essays, pages 1-25. Columbia University Press, New York, 1969.
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Willard Van Orman Quine. Philosophy of Logic. Foundations of Philosophy Series. Prentice-Hall, Englewood Cliffs, New Jersey, 1970.
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Willard Van Orman Quine. Methods of Logic. Holt, Rinehart and Winston, Inc., New York, third edition, 1972. First edition, 1950, second edition 1959.
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Willard Van Orman Quine. Roots of Reference. Number 14 in Paul Carus Lectures. Open Court, La Salle, Illinois, 1973.
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Willard Van Orman Quine. Comment on Donald Davidson. Synthese, 27:325-329, 1974. Comment on Davidson, "Belief and the basis of meaning," 1974. [ .pdf ]
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Willard Van Orman Quine. Comment on Michael Dummett. Synthese, 27:399, 1974. Comment on Dummett, "The significance of Quine's Indeterminacy Thesis," 1974. [ .pdf ]
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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.
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Willard Van Orman Quine. Worlds away. Journal of Philosophy, 73:859-863, 1976.
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Willard Van Orman Quine. Review of Parsons's Mathematics in Philosophy. Journal of Philosophy, 81:783-794, 1984.
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Willard Van Orman Quine. Reply to Charles Parsons. In Lewis Edward Hahn and Paul Arthur Schilpp, editors, The Philosophy of W. V. Quine, number 18 in Library of Living Philosophers, pages 396-403. Open Court, La Salle, Illinois, 1986.
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Willard Van Orman Quine. Reply to Hilary Putnam. In Lewis Edward Hahn and Paul Arthur Schilpp, editors, The Philosophy of W. V. Quine, number 18 in Library of Living Philosophers, pages 427-432. Open Court, La Salle, Illinois, 1986.
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Willard Van Orman Quine. Indeterminacy of translation again. Journal of Philosophy, 84:5-10, 1987. [ http ]
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Willard Van Orman Quine. Quiddities: an intermittently philosophical dictionary. Belknap Press of Harvard University Press, Cambridge, Massachusetts, 1987.
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Willard Van Orman Quine. Pursuit of Truth. Harvard University Press, Cambridge, Mass., revised edition, 1990 and 1992.
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Willard Van Orman Quine and Rudolf Carnap. Dear Carnap, Dear Van. University of California Press, Berkeley, 1990. Edited and with an Introduction by Richard Creath.
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B. Rang and W. Thomas. Zermelo's discovery of the “Russell paradox”. Historia Mathematica, 8:15-22, 1981.
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Michael Resnik. Mathematics as a science of patterns: Ontology and reference. Noûs, 15:529-550, 1981. [ http ]
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Michael D. Resnik. Frege and the Philosophy of Mathematics. Cornell University Press, Ithaca, 1980.
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Michael D. Resnik. Mathematics as a Science of Patterns. Oxford University Press, Oxford, 1997.
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J. P. Ressayre. Models with compactness properties relative to an admissible language. Annals of Mathematical Logic, 11:31-55, 1977.
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Mark Richard. Inscrutability. Canadian Journal of Philosophy, supplementary volume 23:165-209, 1997.
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D. Rödding. Primitiv-rekursive Funktionen über einem Bereich endlicher Mengen. Archiv für mathematische Logik und Grundlagenforschung, 10:13-29, 1967.
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Bertrand Russell. On denoting. Mind, 14:479-493, 1905. [ http ]
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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].
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Bertrand Russell. Mathematical logic as based on the theory of types. American Journal of Mathematics, 30:222-262, 1908. All page references are to the reprinting as pp. 152-182 [vH67].
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Bertrand Russell. Introduction to Mathematical Philosophy. Macmillan, New York, 1919.
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Bertrand Russell. Letter to Frege. In Jean van Heijenoort, editor, From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931, pages 124-125. Harvard University Press, Cambridge, Massachusetts, 1967. Translated by Beverly Woodward.
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Heinrich Scholz and Gisbert Hasenjaeger. Grundzüge der Mathematischen Logik. Number 106 in Die Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, Berlin, 1961.
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Dana Scott. Axiomatizing set theory. In Thomas J. Jech, editor, Axiomatic Set Theory, number 13, part 2 in Proceedings of Symposia in Pure Mathematics, pages 207-214. American Mathematical Society, Providence, Rhode Island, 1974.
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John R. Searle. Indeterminacy, empiricism, and the first person. Journal of Philosophy, 84:123-146, 1987.
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Stewart Shapiro. Second-order languages and mathematical practice. Journal of Symbolic Logic, 50:714-742, 1985.
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Stewart Shapiro. Structure and ontology. Philosophical Topics, 17:145-171, 1989.
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Stewart Shapiro. Second-order logic, foundations, and rules. Journal of Philosophy, 87:234-261, 1990.
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Stewart Shapiro. Foundations without Foundationalism. Clarendon Press, Oxford, 1991.
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Stewart Shapiro. Modality and ontology. Mind, n.s. 102:455-481, 1993.
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Stewart Shapiro. Classical logic II-Higher-order logic. In Lou Goble, editor, The Blackwell Guide to Philosophical Logic, Blackwell Philosophy Guides, chapter 2, pages 33-54. Blackwell Publishers Inc., 2001. [ http ]
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Stewart Shapiro. All sets great and small: and I do mean all. Philosophical Perspectives, 17:467-489, 2003.
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Henry Maurice Sheffer. A set of five independent postulates for boolean algebras, with application to logical constants. Transactions of the American Mathematical Society, 14:481-488, 1913.
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Gila Sher. The Bounds of Logic: A Generalized Viewpoint. MIT Press, Cambridge, Mass., 1991.
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Gila Y. Sher. Did Tarski commit “Tarski's fallacy”? Journal of Symbolic Logic, 61(2):653-686, 1996. [ .pdf ]
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Joseph R. Shoenfield. Mathematical Logic. Addison-Wesley Series in Logic. Addison-Wesley Publishing Company, Reading, Massachusetts, 1967.
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Alan Sidelle. Is there a true metaphysics of material objects? Philosophical Issues, 36(Supplement 1):118-145, 2002.
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Theodore Sider. Neo-Fregeanism and quantifier variance I. Supplement to the Proceedings of The Aristotelian Society, 81:201-232, 2007. [ http ]
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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].
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Thoralf Skolem. Begründung der elementaren Arithmetik durch die rekurrierende Denkweise ohne Anwendung scheinbarer Veränderlichen mit unendlichem Ausdehnungsbereich. Skrifter, Videnskabsakademiet i Kristiania, (6), 1923. All page references are to the translation by Stefan Bauer-Mengelberg, pp. 303-333 [vH67].
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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].
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Thoralf Skolem. Über einige Grundlagenfragen der Mathematik, 1929. Reprinted as pp. 227-273 [Sko70].
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Thoralf Skolem. Einige Bemerkungen zu der Abhandlung von E. Zermelo: “Über die Definheit in der Axiomatik”. Fundamenta Mathematicae, 15:337-341, 1930.
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Thoralf Skolem. Über die Unmöglichkeit einer vollständigen Charakterisierung der Zahlenreihe mittels eines endlichen Axiomensystems. Norsk Matematisk Forenings, Skrifter, (10):73-82, 1933. Reprinted as pp. 345-354 [Sko70].
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Thoralf Skolem. Über die Nicht-charakterisierbarkeit der Zahlenreihe mittels endlich oder abzählbar unendlich vieler Aussagen mit ausschliesslich Zahlenvariablen. Fundamenta Mathematicae, 23:150-161, 1934. Reprinted as pp. 355-366 [Sko70].
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Thoralf Skolem. Sur la portée du théorèm de Löwenheim-Skolem. In Ferdinand Gonseth, editor, Les entretiens de Zurich sur les fondements et la méthode des sciences mathématique, 6-9 décembre 1938, pages 25-47, discussion pp. 47-52, Zurich, 1941. Leeman. Reprinted as pp. 455-482 [Sko70].
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Thoralf Skolem. Une relativisation des notions mathématiques fondamentales. In Colloques internationaux des Centre National de la Recherche Scientifique, pages 13-18, Paris, 1958. Reprinted as pp. 633-638 [Sko70].
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Thoralf Skolem. Selected Works in Logic. Skandinavian University Books, Boston, 1970. Edited by E. J. Fenstad.
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C. Smorynski. The incompleteness theorems. In Jon Barwise, editor, Handbook of Mathematical Logic, number 90 in Studies in Logic and the Foundations of Mathematics, chapter D.1, pages 821-865. North-Holland Publishing Company, Amsterdam, 1977.
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Raymond Smullyan. Languages in which self reference is possible. Journal of Symbolic Logic, 22:55-67, 1957. [ http ]
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Raymond Smullyan. Gödel's incompleteness theorem. In Lou Goble, editor, The Blackwell Guide to Philosophical Logic, Blackwell Philosophy Guides, chapter 4, pages 72-89. Blackwell Publishers Inc., 2001. [ http ]
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Elliott Sober. Mathematics and indispensability. Philosophical Review, 102:35-57, 1993.
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Robert M. Solovay. Injecting inconsistencies into Peano arithmetic. Annals of Pure and Applied Logic, 44:101-132, 1989. [ .pdf ]
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Roy A. Sorensen. Commentary: The epistemic conception of vagueness. In Terry Horgan, editor, Spindel Conference 1994: Vagueness, Supplement to The Southern Journal of Philosophy (1994), Vol. XXXIII, pages 161-170, Memphis, Tennessee, 1995. The Department of Philosophy, The University of Memphis.
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C. Spector. Hyperarithmetical quantifiers. Fundamenta Mathematicae, 48:313-320, 1960.
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Howard Stein. Logos, logic, and logistiké: Some philosophical remarks on nineteenth century transformation of mathematics. In William Aspray and Philip Kitcher, editors, History and Philosophy of Modern Mathematics, number 11 in Minnesota Studies in the Philosophy of Science, pages 238-259. University of Minnesota Press, Minneapolis, Minnesota, 1988.
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Mark Steiner. Mathematical Knowledge. Cornell University Press, Ithaca, New York, 1975.
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Peter F. Strawson. A logician's landscape. Philosophy (The Journal of the Royal Institute of Philosophy), 30:229-237, 1955.
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Barry Stroud. The Significance of Philosophical Scepticism. Clarendon Press, Oxford, 1984.
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William W. Tait. Finitism. Journal of Philosophy, 78:524-546, 1981.
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William W. Tait. The iterative hierarchy of sets. Iyyun, A Jerusalem Philosophical Quarterly, 39:65-79, 1990.
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Jamie Tappenden. The liar and Sorites paradoxes: Toward a unified treatment. Journal of Philosophy, 1993.
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Jamie Tappenden. Some remarks on vagueness and a dynamic conception of language. In Terry Horgan, editor, Spindel Conference 1994: Vagueness, Supplement to The Southern Journal of Philosophy (1994), Vol. XXXIII, pages 193-201, Memphis, Tennessee, 1995. The Department of Philosophy, The University of Memphis.
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Alfred Tarski. Über einige fundamentale Begriffe der Mathematik (On some fundamental concepts of metamathematics). Comptes Rendu des séances de la Société des Sciences et des Lettres de Varsovie, 23:22-29, 1930. In German. All page references are to the English translation that appears as pp. 30-37 of [Tar83].
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Alfred Tarski. Pojecie prawdy w jezykach nauk dedukcyjnych (On the concept of truth in languages of deductive sciences). Number 34 in Prace Towarzystwa Naukowego Warszawskiego Wydzial III-Nauk Matematyczno-fizycznych. Nakl. Tow. Naukowego Warszawskiego, Warsaw, 1933. In Polish. All page references are to the revised translation published as “The concept of truth in formalized languages,” pp. 152-278 of [Tar83].
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Alfred Tarski. Z badań metodologicznych nad definiowalnośca terminów (Some methodological investigations on the definability of concepts). Przeglad Filozoficzny, 37:438-460, 1934. In Polish. All page references are to the English translation that appears as pp. 296-319 of [Tar83].
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Alfred Tarski. O pojciu wynikania logicznego (On the concept of logical consequence). Przeglad Filozoficzny, 39:58-68, 1936. In Polish. All page references are to the English translation that appears as pp. 409-420 of [Tar83].
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Alfred Tarski. Einführung in die mathematische Logik und in die Methodologie der Mathematik. Julius Springer, Vienna, 1937. Translated into English as Introduction to Logic and to the Methodology of Deductive Science by O. Helmer (Oxford University Press, New York, 1941). All page references are to the third, revised, edition of the English translation (Oxford University Press, New York, 1965).
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Alfred Tarski. Über unerreichbare Kardinalzahlen. Fundamenta Mathematicae, 30:68-89, 1938.
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Alfred Tarski. Contributions to the theory of models, parts I and II. Indagationes Mathematicae, 16:572-588, 1954.
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Alfred Tarski. Contributions to the theory of models, part III. Indagationes Mathematicae, 17:56-64, 1955.
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Alfred Tarski. General principles of induction and recursion: The notion of rank in axiomatic set theory and some of its applications. Bulletin of the American Mathematical Society, 61:442-443, 1955. Two abstracts.
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{philos,cc,logic,qm}

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P.", ADDRESS = "New York", YEAR = 1999, EDITOR = "Klee, Robert" } @BOOK{kimsosmet, TITLE = "Metaphysics: {A}n Anthology", PUBLISHER = "Blackwell Publishers Inc.", ADDRESS = "Malden, Mass.", YEAR = 1999, SERIES = "Blackwell Philosophy Anthologies", EDITOR = "Kim, Jaegwon and Sosa, Ernest" } @ARTICLE{solinj, AUTHOR = "Solovay, Robert M.", TITLE = "Injecting Inconsistencies into {P}eano arithmetic", JOURNAL = "Annals of Pure and Applied Logic", YEAR = 1989, VOLUME = 44, PAGES = "101--132", URL = {http://www.sciencedirect.com.ezproxy2.library.arizona.edu/science?_ob=MImg&_imagekey=B6TYB-45G1M9K-8-1&_cdi=5614&_user=56761&_orig=browse&_coverDate=10%2F09%2F1989&_sk=999559998&view=c&wchp=dGLbVtb-zSkWb&md5=062a7aedc24e470c7a90cd94ef0fb732&ie=/sdarticle.pdf}} @ARTICLE{hirqua, AUTHOR = "Hirsch, Eli", TITLE = "Quantifier Variance and Realism", JOURNAL = "Philosophical Issues", YEAR = 2002, VOLUME = 36, NUMBER = "Supplement 1", PAGES = "51--73"} @ARTICLE{hortimcon, AUTHOR = {Horgan, Terry and Timmons, Mark}, TITLE = "Conceptual Relativity and Metaphysical Realism", JOURNAL = "Philosophical Issues", YEAR = 2002, VOLUME = 36, NUMBER = "Supplement 1", PAGES = "74--96"} @ARTICLE{moopro, AUTHOR = {Moore, George Edward}, TITLE = "Proof of an External World", JOURNAL = "Proceedings of the British Academy", YEAR = 1939, VOLUME = 25, PAGES = "273--300", NOTE = "Reprinted as pages 126--148 of ShaughanLavine - 15 Feb 2010 - 20:19 - 1.173 " class="twikiCurrentTopicLink twikiAnchorLink">Moore66.", URL = "http://www.hist-analytic.org/MooreExternalWorld.pdf" } @ARTICLE{shedid, AUTHOR = {Sher, Gila Y.}, TITLE = {Did {T}arski Commit ``{T}arski's Fallacy''?}, JOURNAL = jsl, YEAR = 1996, VOLUME = 61, NUMBER = "2", PAGES = "653--686", URL={http://www.jstor.org.ezproxy1.library.arizona.edu/stable/pdfplus/2275681.pdf} } @ARTICLE{sidist, AUTHOR = {Sidelle, Alan}, TITLE = "Is There a True Metaphysics of Material Objects?", JOURNAL = "Philosophical Issues", YEAR = 2002, VOLUME = 36, NUMBER = "Supplement 1", PAGES = "118--145"} @ARTICLE{yabdoe, AUTHOR = {Yablo, Stephen}, TITLE = " Does Ontology Rest on a Mistake? {I}", JOURNAL = "Supplement to the Proceedings of The Aristotelian Society", YEAR = 1998, VOLUME = 72, PAGES = "229-262"} @ARTICLE{galdoe, AUTHOR = {Gallois, Andre}, TITLE = "Does Ontology Rest on a Mistake? {II}", JOURNAL = "Supplement to the Proceedings of The Aristotelian Society", YEAR = 1998, VOLUME = 72, PAGES = "263-283"} @ARTICLE{sidneo, AUTHOR = {Sider, Theodore}, TITLE = "Neo-{F}regeanism and Quantifier Variance {I}", JOURNAL = "Supplement to the Proceedings of The Aristotelian Society", YEAR = 2007, VOLUME = 81, PAGES = "201--232", URL = {http://www.blackwell-synergy.com.ezproxy2.library.arizona.edu/toc/supa/81/1} } @ARTICLE{primet, AUTHOR = {Price, Huw}, TITLE = "Metaphysical Pluralism", JOURNAL = jop, YEAR = 1992, VOLUME = 89, PAGES = "387--409", URL = {http://ezproxy.library.arizona.edu/login?url=http://links.jstor.org/sici?sici=0022-362X%28199208%2989%3A8%3C387%3AMP%3E2.0.CO%3B2-O} } @ARTICLE{hofpuz, AUTHOR = {Hofweber, Thomas}, TITLE = "A Puzzle about Ontology", JOURNAL = "No\^{u}s", YEAR = 2005, VOLUME = 39, PAGES = "256--283", URL = {http://www.blackwell-synergy.com.ezproxy2.library.arizona.edu/toc/nous/39/2} } @ARTICLE{primet, AUTHOR = {Price, Huw}, TITLE = "Quining Naturalism", JOURNAL = jop, YEAR = 2007, VOLUME = 104, PAGES = "375--405", URL = {http://www.usyd.edu.au/time/price/preprints/QuiningNaturalism.pdf}, NOTE = "All page references are to the linked version." } @ARTICLE{pricar, AUTHOR = {Price, Huw}, TITLE = "Carnap, {Q}uine and the fate of metaphysics", JOURNAL = "The Electronic Journal of Analytic Philosophy (http://ejap.louisiana.edu/)", YEAR = 1997, NUMBER = 5, URL = {http://www.usyd.edu.au/time/price/preprints/CarnapQuine.pdf} } @ARTICLE{glanqua, AUTHOR = {Glanzberg, Michael}, TITLE = " Quantification and Realism", JOURNAL = "Philosophy and Phenomenological Research", YEAR = 2004, VOLUME = 69, URL = {http://poiesis.nlx.com/} } @INCOLLECTION{worfre, AUTHOR = "Worrall, John", TITLE = "Fresnel, {P}oisson, and the white spot: {T}he role of successful predictions in the acceptance of scientific theories", BOOKTITLE = "The Uses of Experiment", PUBLISHER = "Cambridge University Press", YEAR = 1989, PAGES = "135--157", EDITOR = "Gooding, David and Pinch, Trevor and Schaffer, Simon" } @BOOK{appdar, TITLE = "Darwin", PUBLISHER = "W. W. Norton and Company", ADDRESS = "New York", YEAR = 2001, SERIES = "Norton Critical Editions", EDITOR = "Appleman, Philip", EDITION = "Third" } @BOOK{colpingol, TITLE = "The Golem: {W}hat You Should Know about Science", PUBLISHER = "Cambridge University Press", ADDRESS = "Cambridge", YEAR = 1998, EDITION = "Second", AUTHOR = "Collins, Harry and Pinch, Trevor" } @BOOK{godthe, TITLE = "Theory and Reality: {A}n Introduction to the Philosophy of Science", PUBLISHER = "The University of Chicago Press", ADDRESS = "Chicago", YEAR = 2003, SERIES = "Science and Its Conceptual Foundations", AUTHOR = "Godfrey-Smith, Peter" } @INCOLLECTION{gobint, AUTHOR = "Goble, Lou", TITLE = "Introduction", BOOKTITLE = "The {B}lackwell Guide to Philosophical Logic", PUBLISHER = "Blackwell Publishers Inc.", YEAR = 2001, PAGES = "1--8", SERIES = "Blackwell Philosophy Guides", EDITOR = "Goble, Lou", URL = "http://www.blackwellreference.com.ezproxy2.library.arizona.edu/subscriber/tocnode?id=g9780631206934_chunk_g97806312069343" } @INCOLLECTION{hodcla, AUTHOR = "Hodges, Wilfrid", TITLE = "Classical Logic {I}---{F}irst-Order Logic", CHAPTER = 1, BOOKTITLE = "The {B}lackwell Guide to Philosophical Logic", PUBLISHER = "Blackwell Publishers Inc.", YEAR = 2001, PAGES = "9--32", SERIES = "Blackwell Philosophy Guides", EDITOR = "Goble, Lou", URL = "http://www.blackwellreference.com.ezproxy2.library.arizona.edu/subscriber/tocnode?id=g9780631206934_chunk_g97806312069344" } @INCOLLECTION{shacla, AUTHOR = "Shapiro, Stewart", TITLE = "Classical Logic {II}---{H}igher-Order Logic", CHAPTER = 2, BOOKTITLE = "The {B}lackwell Guide to Philosophical Logic", PUBLISHER = "Blackwell Publishers Inc.", YEAR = 2001, PAGES = "33--54", SERIES = "Blackwell Philosophy Guides", EDITOR = "Goble, Lou", URL = "http://www.blackwellreference.com.ezproxy2.library.arizona.edu/subscriber/tocnode?id=g9780631206934_chunk_g97806312069345" } @INCOLLECTION{burset, AUTHOR = "Burgess, John P", TITLE = "Set Theory", CHAPTER = 3, BOOKTITLE = "The {B}lackwell Guide to Philosophical Logic", PUBLISHER = "Blackwell Publishers Inc.", YEAR = 2001, PAGES = "55--71", SERIES = "Blackwell Philosophy Guides", EDITOR = "Goble, Lou", URL = "http://www.blackwellreference.com.ezproxy2.library.arizona.edu/subscriber/tocnode?id=g9780631206934_chunk_g97806312069346" } @INCOLLECTION{smugod, AUTHOR = "Smullyan, Raymond", TITLE = {G\"{o}del's Incompleteness Theorem}, CHAPTER = 4, BOOKTITLE = "The {B}lackwell Guide to Philosophical Logic", PUBLISHER = "Blackwell Publishers Inc.", YEAR = 2001, PAGES = "72--89", SERIES = "Blackwell Philosophy Guides", EDITOR = "Goble, Lou", URL = "http://www.blackwellreference.com.ezproxy2.library.arizona.edu/subscriber/tocnode?id=g9780631206934_chunk_g97806312069347" } @INCOLLECTION{guptru, AUTHOR = "Gupta, Anil", TITLE = "Truth", CHAPTER = 5, BOOKTITLE = "The {B}lackwell Guide to Philosophical Logic", PUBLISHER = "Blackwell Publishers Inc.", YEAR = 2001, PAGES = "90--114", SERIES = "Blackwell Philosophy Guides", EDITOR = "Goble, Lou", URL = "http://www.blackwellreference.com.ezproxy2.library.arizona.edu/subscriber/tocnode?id=g9780631206934_chunk_g97806312069348" } @INCOLLECTION{blalog, AUTHOR = "Blanchette, Patricia A.", TITLE = "Logical Consequence", CHAPTER = 6, BOOKTITLE = "The {B}lackwell Guide to Philosophical Logic", PUBLISHER = "Blackwell Publishers Inc.", YEAR = 2001, PAGES = "115--135", SERIES = "Blackwell Philosophy Guides", EDITOR = "Goble, Lou", URL = "http://www.blackwellreference.com.ezproxy2.library.arizona.edu/subscriber/tocnode?id=g9780631206934_chunk_g97806312069349" } @INCOLLECTION{cremod, AUTHOR = "Cresswell, M. J.", TITLE = "Modal Logic", CHAPTER = 7, BOOKTITLE = "The {B}lackwell Guide to Philosophical Logic", PUBLISHER = "Blackwell Publishers Inc.", YEAR = 2001, PAGES = "136--158", SERIES = "Blackwell Philosophy Guides", EDITOR = "Goble, Lou", URL = "http://www.blackwellreference.com.ezproxy2.library.arizona.edu/subscriber/tocnode?id=g9780631206934_chunk_g978063120693410" } @INCOLLECTION{hildeo, AUTHOR = "Hilpinen, Risto", TITLE = "Deontic Logic", CHAPTER = 8, BOOKTITLE = "The {B}lackwell Guide to Philosophical Logic", PUBLISHER = "Blackwell Publishers Inc.", YEAR = 2001, PAGES = "159--182", SERIES = "Blackwell Philosophy Guides", EDITOR = "Goble, Lou", URL = "http://www.blackwellreference.com.ezproxy2.library.arizona.edu/subscriber/tocnode?id=g9780631206934_chunk_g978063120693411" } @INCOLLECTION{meyepi, AUTHOR = "Meyer, J.-J. Ch.", TITLE = "Epistemic Logic", CHAPTER = 9, BOOKTITLE = "The {B}lackwell Guide to Philosophical Logic", PUBLISHER = "Blackwell Publishers Inc.", YEAR = 2001, PAGES = "183--202", SERIES = "Blackwell Philosophy Guides", EDITOR = "Goble, Lou", URL = "http://www.blackwellreference.com.ezproxy2.library.arizona.edu/subscriber/tocnode?id=g9780631206934_chunk_g978063120693412" } @INCOLLECTION{ventem, AUTHOR = "Venema, Yde", TITLE = "Temporal Logic", CHAPTER = 10, BOOKTITLE = "The {B}lackwell Guide to Philosophical Logic", PUBLISHER = "Blackwell Publishers Inc.", YEAR = 2001, PAGES = "203--223", SERIES = "Blackwell Philosophy Guides", EDITOR = "Goble, Lou", URL = "http://www.blackwellreference.com.ezproxy2.library.arizona.edu/subscriber/tocnode?id=g9780631206934_chunk_g978063120693413" } @INCOLLECTION{dalint, AUTHOR = "van Dalen, Dirk", TITLE = "Intuitionistic Logic", CHAPTER = 11, BOOKTITLE = "The {B}lackwell Guide to Philosophical Logic", PUBLISHER = "Blackwell Publishers Inc.", YEAR = 2001, PAGES = "224--257", SERIES = "Blackwell Philosophy Guides", EDITOR = "Goble, Lou", URL = "http://www.blackwellreference.com.ezproxy2.library.arizona.edu/subscriber/tocnode?id=g9780631206934_chunk_g978063120693414" } @INCOLLECTION{lamfre, AUTHOR = "Lambert, Karel", TITLE = "Free Logics", CHAPTER = 12, BOOKTITLE = "The {B}lackwell Guide to Philosophical Logic", PUBLISHER = "Blackwell Publishers Inc.", YEAR = 2001, PAGES = "258--279", SERIES = "Blackwell Philosophy Guides", EDITOR = "Goble, Lou", URL = "http://www.blackwellreference.com.ezproxy2.library.arizona.edu/subscriber/tocnode?id=g9780631206934_chunk_g978063120693415" } @INCOLLECTION{marmeyrel, AUTHOR = "Mares, Edwin D. and Meyer, Robert K.", TITLE = "Relevant Logics", CHAPTER = 13, BOOKTITLE = "The {B}lackwell Guide to Philosophical Logic", PUBLISHER = "Blackwell Publishers Inc.", YEAR = 2001, PAGES = "280--308", SERIES = "Blackwell Philosophy Guides", EDITOR = "Goble, Lou", URL = "http://www.blackwellreference.com.ezproxy2.library.arizona.edu/subscriber/tocnode?id=g9780631206934_chunk_g978063120693416" } @INCOLLECTION{malman, AUTHOR = "Malinowski, Grzegorz", TITLE = "Many-Valued Logics", CHAPTER = 14, BOOKTITLE = "The {B}lackwell Guide to Philosophical Logic", PUBLISHER = "Blackwell Publishers Inc.", YEAR = 2001, PAGES = "309--335", SERIES = "Blackwell Philosophy Guides", EDITOR = "Goble, Lou", URL = "http://www.blackwellreference.com.ezproxy2.library.arizona.edu/subscriber/tocnode?id=g9780631206934_chunk_g978063120693417" } @INCOLLECTION{hornon, AUTHOR = "Horty, John F.", TITLE = "Nonmonotonic Logic", CHAPTER = 15, BOOKTITLE = "The {B}lackwell Guide to Philosophical Logic", PUBLISHER = "Blackwell Publishers Inc.", YEAR = 2001, PAGES = "336--361", SERIES = "Blackwell Philosophy Guides", EDITOR = "Goble, Lou", URL = "http://www.blackwellreference.com.ezproxy2.library.arizona.edu/subscriber/tocnode?id=g9780631206934_chunk_g978063120693418" } @INCOLLECTION{hajpro, AUTHOR = "H\'{a}jek, Alan", TITLE = "Probability, Logic, and Probability Logic", CHAPTER = 16, BOOKTITLE = "The {B}lackwell Guide to Philosophical Logic", PUBLISHER = "Blackwell Publishers Inc.", YEAR = 2001, PAGES = "362--384", SERIES = "Blackwell Philosophy Guides", EDITOR = "Goble, Lou", URL = "http://www.blackwellreference.com.ezproxy2.library.arizona.edu/subscriber/tocnode?id=g9780631206934_chunk_g978063120693419" } @INCOLLECTION{edgcon, AUTHOR = "Edgington, Dorothy", TITLE = "Conditionals", CHAPTER = 17, BOOKTITLE = "The {B}lackwell Guide to Philosophical Logic", PUBLISHER = "Blackwell Publishers Inc.", YEAR = 2001, PAGES = "385--414", SERIES = "Blackwell Philosophy Guides", EDITOR = "Goble, Lou", URL = "http://www.blackwellreference.com.ezproxy2.library.arizona.edu/subscriber/tocnode?id=g9780631206934_chunk_g978063120693420" } @INCOLLECTION{wanneg, AUTHOR = "Wansing, Heinrich", TITLE = "Negation", CHAPTER = 18, BOOKTITLE = "The {B}lackwell Guide to Philosophical Logic", PUBLISHER = "Blackwell Publishers Inc.", YEAR = 2001, PAGES = "415--436", SERIES = "Blackwell Philosophy Guides", EDITOR = "Goble, Lou", URL = "http://www.blackwellreference.com.ezproxy2.library.arizona.edu/subscriber/tocnode?id=g9780631206934_chunk_g978063120693421" } @INCOLLECTION{wesqua, AUTHOR = "Westerst{\aa}hl, Dag", TITLE = "Quantifiers", CHAPTER = 19, BOOKTITLE = "The {B}lackwell Guide to Philosophical Logic", PUBLISHER = "Blackwell Publishers Inc.", YEAR = 2001, PAGES = "437--460", SERIES = "Blackwell Philosophy Guides", EDITOR = "Goble, Lou", URL = "http://www.blackwellreference.com.ezproxy2.library.arizona.edu/subscriber/tocnode?id=g9780631206934_chunk_g978063120693422" } @INCOLLECTION{meulog, AUTHOR = "ter Meulen, Alice", TITLE = "Logic and Natural Language", CHAPTER = 20, BOOKTITLE = "The {B}lackwell Guide to Philosophical Logic", PUBLISHER = "Blackwell Publishers Inc.", YEAR = 2001, PAGES = "461--483", SERIES = "Blackwell Philosophy Guides", EDITOR = "Goble, Lou", URL = "http://www.blackwellreference.com.ezproxy2.library.arizona.edu/subscriber/tocnode?id=g9780631206934_chunk_g978063120693423" } @BOOK{gobbla, TITLE = "The {B}lackwell Guide to Philosophical Logic", PUBLISHER = "Blackwell Publishers Inc.", YEAR = 2001, SERIES = "Blackwell Philosophy Guides", EDITOR = "Goble, Lou", URL = "http://www.blackwellreference.com.ezproxy2.library.arizona.edu/subscriber/book?id=g9780631206934_9780631206934" } @INCOLLECTION{quirephp, AUTHOR = quine, TITLE = "Reply to {H}ilary {P}utnam", BOOKTITLE = "The Philosophy of {W.} {V.} {Q}uine", PUBLISHER = {Open Court}, ADDRESS = {La Salle, Illinois}, YEAR = 1986, PAGES = "427--432", SERIES = "Library of Living Philosophers", NUMBER = 18, EDITOR = "Hahn, Lewis Edward and Schilpp, Paul Arthur" } @INCOLLECTION{benputint, AUTHOR = "Benacerraf, Paul and Putnam, Hilary", TITLE = "Introduction", BOOKTITLE = "Philosophy of Mathematics", PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge, England}, YEAR = 1983, EDITOR = "Benacerraf, Paul and Putnam, Hilary", PAGES = "1--37", EDITION = "second" } @BOOK{aussen, AUTHOR = {Austin, John Langshaw and Warnock, Geoffrey James}, TITLE = {Sense and Sensibilia}, PUBLISHER = {Clarendon Press}, ADDRESS = {Oxford}, YEAR = 1962, NOTE = {By J. L. Austin. Published posthumously. Reconstructed from the manuscript notes by G. J. Warnock.} } @BOOK{ayefou, AUTHOR = {Ayer, Alfred Jules}, TITLE = {The Foundations of Empirical Knowledge}, PUBLISHER = {Macmillan and Co., Limited}, ADDRESS = {London}, YEAR = {1940. Reprinted 1947, 1951} } @BOOK{quiqui, AUTHOR = quine, TITLE = "Quiddities: an intermittently philosophical dictionary", PUBLISHER = {Belknap Press of Harvard University Press}, ADDRESS = {Cambridge, Massachusetts}, YEAR = 1987 } @BOOK{antmot, AUTHOR = " Van Rooten, Luis d'Antin", TITLE = "Mots d'Heures: Gousses, Rames; The d'{A}ntin Manuscript (Mother Goose Rhymes)", PUBLISHER = {New York}, ADDRESS = {Grossman Publishers}, YEAR = 1967 } @BOOK{gloqui, AUTHOR = "Glock, Hans-Johann", TITLE = "Quine and Davidson on Language, Thought and Reality", PUBLISHER = {Cambridge U. P.}, ADDRESS = {New York}, YEAR = 2003, URL = "http://ezproxy.library.arizona.edu/login/up?url=http://site.ebrary.com/lib/arizona/Doc?id=10069853" } @BOOK{kanurt, AUTHOR = "Kant, Immanuel", TITLE = "Kritik der Urteilskraft", PUBLISHER = {Lagarde \& Friederich}, ADDRESS = {Berlin and Liebau}, YEAR = 1790, NOTE = "All page references are to the translation as Guyer00" } @BOOK{guypow, EDITOR = "Guyer, Paul", TITLE = "Immanuel Kant: Critique of the Power of Judgment", PUBLISHER = {Cambridge University Press}, ADDRESS = {New York}, YEAR = 2000, NOTE = "Translation by Paul Guyer and Eric Matthews of Kant90" } @BOOK{ammcla, EDITOR = "Ammerman, Robert R.", TITLE = "Classics of Analytic Philosophy", PUBLISHER = {McGraw-Hill}, ADDRESS = {New York}, YEAR = 1965, NOTE = {Reprinted by Hackett, Indianapolis, 1990.} } @BOOK{finrea, AUTHOR = "Fine, Kit", TITLE = "Reasoning with Arbitrary Objects", PUBLISHER = {Basil Blackwell}, ADDRESS = {New York}, YEAR = 1985 } @BOOK{wrifre, AUTHOR = "Wright, Crispin", TITLE = "Frege's Conception of Numbers as Objects", PUBLISHER = {Aberdeen University Press}, ADDRESS = {Aberdeen}, YEAR = 1983 } @BOOK{husphi, AUTHOR = "Husserl, Edmund G.", TITLE = "Philosophie der Arithmetik. Psychologische und logische Untersuchungen. (Philosophy of arithmetic. Psychological and logical investigations)", PUBLISHER = {C. E. M. Pfeffer (Robert Stricker)}, ADDRESS = {Halle-Saale}, YEAR = 1991, VOLUME = "First" } @BOOK{marphi, AUTHOR = "Martinich, A. P.", TITLE = "The Philosophy of Language", PUBLISHER = {Oxford University Press}, ADDRESS = {New York}, YEAR = 2001, EDITION = "Fourth", NOTE = "First edition, 1985" } @BOOK{manfro, EDITOR ="Mancosu, Paolo", TITLE = "From {B}rouwer to {H}ilbert: {T}he Debate on the Foundations of Mathematics in the 1920s", PUBLISHER = {Oxford University Press}, ADDRESS = {New York}, YEAR = 1998 } @BOOK{kriwit, AUTHOR ="Kripke, Saul A.", TITLE = "Wittgenstein on Rules and Private Language: {A}n Elementary Exposition", PUBLISHER = {Blackwell}, ADDRESS = {Oxford}, YEAR = 1982 } @BOOK{whiruspri, AUTHOR = "Whitehead, Alfred North and Russell, Bertrand A. W.", TITLE = "Principia Mathematica", PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge, England}, YEAR = 1925, VOLUME = 1, EDITION = "second", NOTE = "First edition, 1910. Second edition reprinted 1957" } @BOOK{quiwor, AUTHOR = quine, TITLE = "Word and Object", PUBLISHER = {M. I. T. Press}, ADDRESS = {Cambridge, Massachusetts}, YEAR = 1960 } @BOOK{mooinf, AUTHOR = "Moore, A. W.", TITLE = "The Infinite", PUBLISHER = {Routledge}, ADDRESS = {London}, YEAR = 1990, SERIES = "The Problems of Philosophy" } @BOOK{chiont, AUTHOR = "Chihara, Charles", TITLE = "Ontology and the Vicious Circle Principle", PUBLISHER = {Cornell University Press}, ADDRESS = "Ithaca", YEAR = 1973 } @BOOK{finlim, AUTHOR = "Fine, Kit", TITLE = "The Limits of Abstraction", PUBLISHER = {Clarendon Press}, ADDRESS = "Oxford", YEAR = 2002 } @BOOK{halwrirea, AUTHOR = "Hale, Bob and Wright, Crispin", TITLE = "The Reason's Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics", PUBLISHER = {Clarendon Press}, ADDRESS = "Oxford", YEAR = 2001 } @BOOK{dethil, AUTHOR = "Detlefsen, Michael", TITLE = "Hilbert's Program", PUBLISHER = {Reidel}, ADDRESS = {Boston}, YEAR = 1986, SERIES = "Synthese Library", NUMBER = 182 } @INCOLLECTION{lavobj, AUTHOR = sml, TITLE = "Objectivity: {T}he Justification for Extrapolation", BOOKTITLE = "One Hundred Years of Russell's Paradox. Papers from the Munich Centenary Conference", PUBLISHER = {Walter de Gruyter}, ADDRESS = {Berlin}, YEAR = 2004, EDITOR = "Link, Godehard", PAGES = "549--560" } @INCOLLECTION{lavsom, AUTHOR = sml, TITLE = "Something about everything: {U}niversal quantification in the universal sense of universal quantification", BOOKTITLE = "Absolute Generality", PUBLISHER = {Oxford University Press}, ADDRESS = {New York}, YEAR = 2007, EDITOR = "Rayo, Agustin and Uzquiano, Gabriel", PAGES = "98--148" } @INCOLLECTION{finrel, AUTHOR = {Fine, Kit}, TITLE = "Relatively Unrestricted Quantification", BOOKTITLE = "Absolute Generality", PUBLISHER = {Oxford University Press}, ADDRESS = {New York}, YEAR = 2007, EDITOR = "Rayo, Agustin and Uzquiano, Gabriel", PAGES = "20--44" } @INCOLLECTION{finour, AUTHOR = "Fine, Kit", TITLE = "Our Knowledge of Mathematical Objects", BOOKTITLE = "Oxford Studies in Epistemology", VOLUME = 1, PUBLISHER = {Clarendon Press}, ADDRESS = {Oxford}, YEAR = 2005, EDITOR = "Gendler, T. S. and Hawthorne, J.", PAGES = "89--110" } @BOOK{rayuzqsom, TITLE = "Absolute Generality", PUBLISHER = {Oxford University Press}, ADDRESS = {New York}, YEAR = 2007, EDITOR = "Rayo, Agustin and Uzquiano, Gabriel" } @INCOLLECTION{kripuz, AUTHOR = "Kripke, Saul", TITLE = "A Puzzle about Belief", BOOKTITLE = "Meaning and Use: {P}apers Presented at the Second {J}erusalem Philosophical Encounter {A}pril 1976", PUBLISHER = {D. Reidel}, ADDRESS = {Dordrecht}, YEAR = 1979, EDITOR = "Margalit, Avishai", PAGES = "239--283", SERIES = " Studies in Linguistics and Philosophy", VOLUME = 3, NOTE = "All page references are to the reprinting as 405--432 of ShaughanLavine - 15 Feb 2010 - 20:19 - 1.173 " class="twikiCurrentTopicLink twikiAnchorLink">Martinich01.", NOTE = "Reprinted as 405--432 of [Martinich01]." } @INCOLLECTION{wriphi, AUTHOR = "Wright, Crispin", TITLE = "On the Philosophical Significance of {F}rege's Theorem", BOOKTITLE = "Language, Thought, and Logic: Essays in Honour of Michael Dummett", PUBLISHER = {Oxford University Press}, ADDRESS = {New York}, YEAR = 1997, EDITOR = "Heck, Jnr., Richard G.", PAGES = "201--244", NOTE = "Reprinted as 272--306 of ShaughanLavine - 15 Feb 2010 - 20:19 - 1.173 " class="twikiCurrentTopicLink twikiAnchorLink">HaleWright01" } @INCOLLECTION{halwribur, AUTHOR = "Hale, Bob and Wright, Crispin", TITLE = {To Bury {C}aesar \dots}, BOOKTITLE = "The Reason's Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics", PUBLISHER = {Clarendon Press}, ADDRESS = "Oxford", EDITOR = {Hale, Bob and Wright, Crispin}, PAGES = {335--396}, YEAR = 2001 } @INCOLLECTION{manhil, AUTHOR = "Mancosu, Paolo", TITLE = "{H}ilbert and {B}ernays on Metamathematics", BOOKTITLE = "From {B}rouwer to {H}ilbert: {Th}e Debate on the Foundations of Mathematics in the 1920s", PUBLISHER = {Oxford University Press}, ADDRESS = {New York}, YEAR = 1998, EDITOR = "Mancosu, Paolo", PAGES = "149--188" } @INCOLLECTION{frecon, AUTHOR = "Frege, Gottlob", TITLE = "The Concept of Number", BOOKTITLE = "Philosophy of Mathematics", PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge, England}, YEAR = 1983, EDITOR = "Benacerraf, Paul and Putnam, Hilary", PAGES = "130--159", EDITION = "second", NOTE = "Translation by Michael Mahoney of pages 67–104, 115–119 of ShaughanLavine - 15 Feb 2010 - 20:19 - 1.173 " class="twikiCurrentTopicLink twikiAnchorLink">Frege84b" } @BOOK{benputphi, TITLE = "Philosophy of Mathematics", PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge, England}, YEAR = 1983, EDITOR = "Benacerraf, Paul and Putnam, Hilary", EDITION = "second" } @BOOK{carmea2, TITLE = "Meaning and Necessity: {A} Study in Semantics and Modal Logic", PUBLISHER = {University of Chicago Press}, ADDRESS = {Chicago}, YEAR = 1956, AUTHOR = "Carnap, Rudolf", EDITION = "second, enlarged" } @BOOK{hilges, TITLE = "Gesammelte Abhandlungen", PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = 1935, AUTHOR = "Hilbert, David", NOTE = "Reprint Chelsea, New York, 1965", VOLUME = {Dritter Band: Analysis, Grundlagen der Mathematik, Physik, Verschiedenes} } @BOOK{ewafro, TITLE = "From {K}ant to {H}ilbert: {R}eadings in the Foundations of Mathematics", PUBLISHER = {Oxford University Press}, ADDRESS = {Oxford}, YEAR = 1996, EDITOR = "Ewald, William Bragg" } @BOOK{berabh, TITLE = {Abhandlungen zur Philosophie der Mathematik}, PUBLISHER = {Wissenschaftliche Buchgesellschaft}, ADDRESS = {Darmstadt}, YEAR = 1976, AUTHOR = "Bernays, Paul" } @INCOLLECTION{dumfre, AUTHOR = dummett, TITLE = "Frege, {G}ottlob", EDITOR = "Edwards, Paul", BOOKTITLE = "The Encyclopedia of Philosophy", PUBLISHER = {Macmillan and The Free Press}, ADDRESS = {New York}, YEAR = 1967, VOLUME = 3, PAGES = "225--237" } @INCOLLECTION{hecfrefr, AUTHOR = {Heck, Jr., Richard G.}, TITLE = "Introduction au th\'{e}or\`{e}me de {F}rege", EDITOR = "Marion, M. and Voizard, A.", BOOKTITLE = "Frege: {L}ogique et philosophie", PUBLISHER = {Harmattan}, ADDRESS = {Montreal}, YEAR = 1998, PAGES = "33--61", NOTE = "Translated by L. Perrin" } @ARTICLE{putmod, AUTHOR = {Putnam, Hilary}, TITLE = "Models and Reality", JOURNAL = jsl, YEAR = 1980, VOLUME = 45, PAGES = "464--482", NOTE = {Presidential Address to the annual meeting of the Association for Symbolic Logic, December, 1977. All page references are to the reprinting as pp.~421--444 [BP83].}, NOTE = {Presidential Address to the annual meeting of the Association for Symbolic Logic, December, 1977. Reprinted as pp.~421--444 [BP83].}, URL = {http://ezproxy.library.arizona.edu/login?url=http://links.jstor.org/sici?sici=0022-4812%28198009%2945%3A3%3C464%3AMAR%3E2.0.CO%3B2-I} } } @ARTICLE{kosstrlog, AUTHOR = {Koslow, Arnold}, TITLE = "Structuralist Logic: Implications, Inferences, and Consequences", JOURNAL = "Logica Universalis", YEAR = 2007, VOLUME = 1, PAGES = "167--181", URL = {http://www.springerlink.com.ezproxy.library.arizona.edu/content/b7115xg144h521g1/fulltext.pdf} } @ARTICLE{fierealism, AUTHOR = field, TITLE = "Realism and Anti-Realism about Mathematics", JOURNAL = "Philosophical Topics", YEAR = 1982, VOLUME = 13, PAGES = "45--69", NOTE = "Reprinted as 53--78 of ShaughanLavine - 15 Feb 2010 - 20:19 - 1.173 " class="twikiCurrentTopicLink twikiAnchorLink">Field89" } @ARTICLE{lavarc, AUTHOR = sml, TITLE = "The Architecture of a Person", JOURNAL = "Interfaces", YEAR = 2004, VOLUME = {21/22}, PAGES = "351--355" } @ARTICLE{lavmar, AUTHOR = sml, TITLE = "Review of {R}uth {B}arcan {M}arcus's {M}odalities", JOURNAL = "British Journal of the Philosophy of Science", YEAR = 1995, VOLUME = 46, PAGES = "267--274" } @ARTICLE{lavfer, AUTHOR = sml, TITLE = {Review of {J}os\'e {F}erreir\'{o}s's {L}abyrinth of {T}hought: {A} {H}istory of {S}et {T}heory and {I}ts {R}ole in {M}odern {M}athematics}, JOURNAL = "Metascience", YEAR = 2001, VOLUME = 10 } @ARTICLE{jenkno, AUTHOR = "Jenkins, C. S.", TITLE = "Knowledge of Arithmetic", JOURNAL = "British Journal for the Philosophy of Science", YEAR = 2005, VOLUME = 56, PAGES = "727--747", URL = {http://bjps.oxfordjournals.org/cgi/reprint/56/4/727} } @ARTICLE{fiecri, AUTHOR = field, TITLE = "Critical Notice of {C}rispin {W}right: {F}rege's Conception of Numbers as Objects", JOURNAL = "Canadian Journal of Philosophy", YEAR = 1984, VOLUME = 14, PAGES = "637--662", NOTE = {Reprinted with the title ``Platonism for cheap? Crispin Wright on Frege's context principle'' as 147--170 of ShaughanLavine - 15 Feb 2010 - 20:19 - 1.173 " class="twikiCurrentTopicLink twikiAnchorLink">Field89} } @ARTICLE{halgru, AUTHOR = {Hale, Bob}, TITLE = { {\em Grundlagen\/} §64}, JOURNAL = {Proceedings of the Aristotelian Society}, YEAR = 1997, VOLUME = 97, PAGES = "243--261", NOTE = {Reprinted as 91--116 of ShaughanLavine - 15 Feb 2010 - 20:19 - 1.173 " class="twikiCurrentTopicLink twikiAnchorLink">HaleWright01.}, URL = {http://www.blackwell-synergy.com.ezproxy.library.arizona.edu/doi/pdf/10.1111/1467-9264.00015} } @ARTICLE{berbed, AUTHOR = {Bernays, Paul}, TITLE = {Die {B}edeutung {H}ilberts f\"{u}r die {P}hilosophie der {M}athematik ({H}ilbert's Significance for the Philosophy of Mathematics)}, JOURNAL = {Die Naturwissenschaften}, YEAR = 1922, VOLUME = 10, PAGES = "93--99", NOTE = {All page references are to the translation by Paolo Mancosu as pp.~189--197 ShaughanLavine - 15 Feb 2010 - 20:19 - 1.173 " class="twikiCurrentTopicLink twikiAnchorLink">Mancosu98.} } @ARTICLE{berphi, AUTHOR = {Bernays, Paul}, TITLE = {Die {P}hilosophie der {M}athematik und die {H}ilbertsche {B}eweistheorie ({T}he Philosophy of Mathematics and {H}ilbert's Proof Theory)}, JOURNAL = {Bl\"{a}tter f\"{u}r deutsche {P}hilosophie}, YEAR = "1930--31", VOLUME = 4, PAGES = "326--367", NOTE = {Reprinted as pp.~17--61 of ShaughanLavine - 15 Feb 2010 - 20:19 - 1.173 " class="twikiCurrentTopicLink twikiAnchorLink">Bernays76. All page references are to the translation by Paolo Mancosu as pp.~234--265 of ShaughanLavine - 15 Feb 2010 - 20:19 - 1.173 " class="twikiCurrentTopicLink twikiAnchorLink">Mancosu98.} } @ARTICLE{wriish, AUTHOR = {Wright, Crispin}, TITLE = {Is {H}ume's Principle Analytic?}, JOURNAL = {Notre Dame Journal of Formal Logic}, YEAR = 1999, VOLUME = 40, PAGES = "6--30", URL = {http://projecteuclid.org.ezproxy.library.arizona.edu/Dienst/Repository/1.0/Disseminate/euclid.ndjfl/1039096303/body/pdf}, NOTE = {Reprinted as pp.~307--332 of ShaughanLavine - 15 Feb 2010 - 20:19 - 1.173 " class="twikiCurrentTopicLink twikiAnchorLink">HaleWright01.} } @ARTICLE{hilneu, AUTHOR = {Hilbert, David}, TITLE = {Neubegr\"{u}ndung der {M}athematik. {E}rste {M}itteilung ({T}he New Grounding of Mathematics. {F}irst Report)}, JOURNAL = {Abhandlungen aus dem Mathematischen Seminar der Hamburgischen Universit\"{a}t}, YEAR = 1922, VOLUME = 1, PAGES = "157--177", NOTE = {Reprinted with notes by Paul Bernays in ShaughanLavine - 15 Feb 2010 - 20:19 - 1.173 " class="twikiCurrentTopicLink twikiAnchorLink">Hilbert35. Translated by William Ewald, Ewald96. All page references are to the reprinting of the Ewald translation as pp.~198--214 of ShaughanLavine - 15 Feb 2010 - 20:19 - 1.173 " class="twikiCurrentTopicLink twikiAnchorLink">Mancosu98.} } @ARTICLE{carmea, AUTHOR = {Carnap, Rudolf}, TITLE = "Empiricism, Semantics, and Ontology", JOURNAL = "Revue Internationale de Philosophie", YEAR = 1950, VOLUME = 4, PAGES = "20--40", NOTE = "Reprinted in ShaughanLavine - 15 Feb 2010 - 20:19 - 1.173 " class="twikiCurrentTopicLink twikiAnchorLink">Carnap56", URL = "http://www.ditext.com/carnap/carnap.html" } @ARTICLE{hecfre, AUTHOR = {Heck, Jr., Richard G.}, TITLE = "Frege's Theorem: An Introduction", JOURNAL = "Harvard Review of Philosophy", YEAR = 1999, VOLUME = 7, PAGES = "56–73", NOTE = "Originally published, in French, as ShaughanLavine - 15 Feb 2010 - 20:19 - 1.173 " class="twikiCurrentTopicLink twikiAnchorLink">Heck98", URL = "http://hcs.harvard.edu/~hrp/issues/1999/Heck.pdf", URL = "http://frege.brown.edu/heck/pdf/published/FregesTheoremIntro.pdf" } @ARTICLE{carwha, AUTHOR = {Carroll, Lewis}, TITLE = "What the Tortoise Said to {A}chilles", JOURNAL = "Mind", YEAR = 1895, VOLUME = "n. s. 4", PAGES = "278--280", URL = "http://ezproxy.library.arizona.edu/login?url=http://links.jstor.org/sici?sici=0026-4423%28189504%292%3A4%3A14%3C278%3AWTTSTA%3E2.0.CO%3B2-" } @ARTICLE{davver, AUTHOR = {Davidson, Donald}, TITLE = "On the Very Idea of a Conceptual Scheme", JOURNAL = "Proceedings and Addresses of the American Philosophical Association", YEAR = {1973--1974}, VOLUME = 47, PAGES = "5--20", NOTE = "Presidential Address", URL = "http://ezproxy.library.arizona.edu/login?url=http://links.jstor.org/sici?sici=0065-972X%281973%2F1974%2947%3C5%3AOTVIOA%3E2.0.CO%3B2-%23" } @ARTICLE{carwha, AUTHOR = {Smullyan, Raymond}, TITLE = "Languages in Which Self Reference is Possible", JOURNAL = jsl, YEAR = 1957, VOLUME = 22, PAGES = "55--67", URL = "http://ezproxy.library.arizona.edu/login?url=http://links.jstor.org/sici?sici=0022-4812%28195703%2922%3A1%3C55%3ALIWSRI%3E2.0.CO%3B2-E" }

@ARTICLE{quiind, AUTHOR = quine, TITLE = "Indeterminacy of Translation Again", JOURNAL = jop, YEAR = 1987, VOLUME = 84, PAGES = "5-10", URL = "http://ezproxy.library.arizona.edu/login?url=http://links.jstor.org/sici?sici=0022-362X%28198701%2984%3A1%3C5%3AIOTA%3E2.0.CO%3B2-K" } @ARTICLE{pivhus, AUTHOR = {Pivcevic, E.}, TITLE = "Husserl versus {F}rege", JOURNAL = "Mind", YEAR = 1967, VOLUME = "n. s. 76", PAGES = "155--165", NOTE = "A translation of excerpts of Chapter~7 (Definitions of numbers based on the concept of equivalence) of ShaughanLavine - 15 Feb 2010 - 20:19 - 1.173 " class="twikiCurrentTopicLink twikiAnchorLink">Husserl91", URL = "http://ezproxy.library.arizona.edu/login?url=http://links.jstor.org/sici?sici=0026-4423%28196704%292%3A76%3A302%3C155%3AHVF%3E2.0.CO%3B2-F" } @ARTICLE{wilfre, AUTHOR = {Wilson, Mark}, TITLE = "Frege: {T}he Royal Road from Geometry", JOURNAL = "No\^{u}s", YEAR = 1992, VOLUME = "26", PAGES = "149--180", URL = "http://ezproxy.library.arizona.edu/login?url=http://links.jstor.org/sici?sici=0029-4624%28199206%2926%3A2%3C149%3AFTRRFG%3E2.0.CO%3B2-9" } @ARTICLE{quirus, AUTHOR = quine, TITLE = "Symposium: {T}he Philosophy of {B}ertrand {R}ussell: {R}ussell's Ontological Development", JOURNAL = jop, YEAR = 1966, VOLUME = "63", PAGES = "657--667", URL = "http://ezproxy.library.arizona.edu/login?url=http://links.jstor.org/sici?sici=0022-362X%2819661110%2963%3A21%3C657%3AROD%3E2.0.CO%3B2-P" } @ARTICLE{putmea, AUTHOR = {Putnam, Hilary}, TITLE = "Meaning and Reference", JOURNAL = jop, YEAR = 1973, VOLUME = 70, PAGES = "699--711", URL = "http://www.jstor.org.ezproxy1.library.arizona.edu/view/0022362x/di973057/97p0342b/0?frame=noframe&userID=9687ef61@arizona.edu/01cce440610050b2650&dpi=3&config=jstor" } @ARTICLE{kenmat, AUTHOR = {Kennedy, Hubert C.}, TITLE = "The Mathematical Philosophy of {G}iuseppe {P}eano", JOURNAL = "Philosophy of Science", YEAR = 1963, VOLUME = 30, PAGES = "262--266", URL = "http://ezproxy.library.arizona.edu/login?url=http://links.jstor.org/sici?sici=0031-8248%28196307%2930%3A3%3C262%3ATMPOGP%3E2.0.CO%3B2-3" } @ARTICLE{margod, AUTHOR = {Martin, Donald A.}, TITLE = {G\"{o}del's Conceptual Realism}, JOURNAL = "Bulletin of Symbolic Logic", YEAR = 2005, VOLUME = 11, PAGES = "207-224", URL = "http://ezproxy.library.arizona.edu/login?url=http://links.jstor.org/sici?sici=1079-8986%28200506%2911%3A2%3C207%3AGCR%3E2.0.CO%3B2-W" } @Misc{moneng, author = {Monger, Christopher}, title = {The {E}nglishman Who Went Up a Hill But Came Down a Mountain}, year = {1995}, note = {Movie}, } @Article{fincan, author = {Fine, Kit}, title = {Cantorian Abstraction: {A} Reconstruction and Defense}, journal = jop, year = {1998}, volume = {95}, pages = {599--634}, url = {http://ezproxy.library.arizona.edu/login?url=http://links.jstor.org/sici?sici=0022-362X%28199812%2995%3A12%3C599%3ACAARAD%3E2.0.CO%3B2-2} } @Article{shamod, author = {Shapiro, Stewart}, title = {Modality and Ontology}, journal = {Mind}, year = {1993}, volume = {n.s. 102}, pages = {455-481}, } @ARTICLE{ungpro, AUTHOR = {Unger, Peter}, TITLE = "The Problem of the Many", JOURNAL = "Midwest Studies in Philosophy", YEAR = 1980, VOLUME = 5, PAGES = "411--467" } @INCOLLECTION{godrus, AUTHOR = {G\"{o}del, Kurt}, TITLE = "Russell's Mathematical Logic", BOOKTITLE = "The Philosophy of Bertrand Russell", SERIES = "Library of Living Philosophers", NUMBER = 5, PUBLISHER = "Northwestern University Press", ADDRESS = "Evanston, Illinois", YEAR = 1944, EDITOR = "Schilpp, Paul Arthur", PAGES = "123--153", NOTE = "All page references are to the reprinting as pp.~447--469 [BP83]"} @ARTICLE{godwha, AUTHOR = {G\"{o}del, Kurt}, TITLE = "What Is {C}antor's Continuum Problem?", JOURNAL = "American Mathematical Monthly", YEAR = 1947, VOLUME = 54, PAGES = "515--525", NOTE = {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 [G\"{o}d90]} } @INPROCEEDINGS{parwha, AUTHOR = "Parsons, Charles", TITLE = "What Is the Iterative Conception of Set?", BOOKTITLE = "Logic, Foundations of Mathematics, and Computability Theory. Proceedings of the Fifth International Congress of Logic, Methodology, and the Philosophy of Science (London, Ontario, 1975)", PART = 1, PUBLISHER = {Reidel}, ADDRESS = {Dordrecht, The Netherlands}, YEAR = 1977, EDITOR = "Butts, R. E. and Hintikka, J.", NOTE = "All page references are to the reprinting as pp.~503--529 [Par83a]" } @ARTICLE{quirepnc, AUTHOR = quine, TITLE = "Reply to {N}oam {C}homsky", JOURNAL = "Synthese", VOLUME = 19, YEAR = 1968, PAGES = "274--283", URL = "http://www.springerlink.com.ezproxy.library.arizona.edu/content/m4827782513ql233/fulltext.pdf" } @ARTICLE{hilinf, AUTHOR = "Hilbert, David", TITLE = {\"{U}ber das {U}nendliche ({O}n the Infinite)}, JOURNAL = {Mathematische Annalen}, YEAR = 1926, VOLUME = 95, PAGES = "161--190", NOTE = "Translation by Stefan Bauer-Mengelberg, pp.~369--392 [vH67]. Partial translation by Erna Putnam and Gerald J. Massey, 1964. All page references are to the second edition of the Putnam and Massey translation, pp.~183--201 [BP83]", NOTE = " Partial translation by Erna Putnam and Gerald J. Massey, 1964, pp.~183--201 of the second edition of ShaughanLavine - 15 Feb 2010 - 20:19 - 1.173 " class="twikiCurrentTopicLink twikiAnchorLink">BenacerrafEtal83. All page references are to the translation by Stefan Bauer-Mengelberg, pp.~369--392 of ShaughanLavine - 15 Feb 2010 - 20:19 - 1.173 " class="twikiCurrentTopicLink twikiAnchorLink">Heijenoort67. " } @ARTICLE{mycmea, AUTHOR = "Mycielski, Jan", TITLE = "The Meaning of Pure Mathematics", JOURNAL = "Journal of Philosophical Logic", YEAR = 1989, VOLUME = 18, PAGES = "315--320" } @ARTICLE{mycqua, AUTHOR = "Mycielski, Jan", TITLE = "Quantifier-free Versions of First-Order Logic and Their Psychological Significance", JOURNAL = "Journal of Philosophical Logic", YEAR = 1992, VOLUME = 21, PAGES = "125--147" } @ARTICLE{berpla, AUTHOR = "Bernays, Paul", TITLE = "Sur le platonisme dans les math\'{e}matiques", JOURNAL = "L'Enseignement math\'{e}matique, 1st ser.", YEAR = 1935, VOLUME = 34, PAGES = "52--69", NOTE = "All page references are to the translation by Charles D. Parsons, pp.~258--271 [BP83]" } @ARTICLE{taifin, AUTHOR = "Tait, William W.", TITLE = "Finitism", JOURNAL = jop, YEAR = 1981, VOLUME = 78, PAGES = "524--546" } @ARTICLE{madroo, AUTHOR = maddy, TITLE = "The Roots of Contemporary {P}latonism", JOURNAL = jsl, YEAR = 1989, VOLUME = 54, PAGES = "1121--1144" } @INCOLLECTION{quispe, AUTHOR = quine, TITLE = "Speaking of Objects", BOOKTITLE = "Ontological Relativity and Other Essays", PUBLISHER = {Columbia University Press}, ADDRESS = {New York}, YEAR = 1969, PAGES = "1--25"} @BOOK{resfre, AUTHOR = "Resnik, Michael D.", TITLE = "Frege and the Philosophy of Mathematics", PUBLISHER = {Cornell University Press}, ADDRESS = {Ithaca}, YEAR = 1980 } @INCOLLECTION{dumpla, AUTHOR = dummett, TITLE = "Platonism", BOOKTITLE = "Truth and Other Enigmas", PAGES = "202--214", PUBLISHER = "Harvard University Press", ADDRESS = "Cambridge, Massachusetts", YEAR = 1978, EDITOR = dummett, NOTE = {Invited address to the Third International Congress on Logic, Methodology and Philosophy of Science, Amsterdam, 29 August, 1967.} } @BOOK{skosel, AUTHOR = "Skolem, Thoralf", TITLE = "Selected Works in Logic", PUBLISHER = "Skandinavian University Books", ADDRESS = {Boston}, YEAR = 1970, NOTE = {Edited by E. J. Fenstad.} } @BOOKLET{skoein, AUTHOR = "Skolem, Thoralf", TITLE = {\"{U}ber einige {G}rundlagenfragen der {M}athematik}, JOURNAL = {Skrifter, Vitenskapsakademiet i Oslo}, SERIES = "I", NUMBER = 4, PAGES = "1--49", NOTE = {Reprinted as pp. 227--273 [Sko70].}, YEAR = 1929 } @INPROCEEDINGS{skorel, AUTHOR = "Skolem, Thoralf", TITLE = {Une relativisation des notions math\'{e}matiques fondamentales}, YEAR = 1958, BOOKTITLE = {Colloques internationaux des Centre National de la Recherche Scientifique}, ADDRESS = "Paris", PAGES = "13--18", NOTE = {Reprinted as pp. 633--638 [Sko70].} } @INPROCEEDINGS{skopor, AUTHOR = "Skolem, Thoralf", TITLE = {Sur la Port\'{e}e du Th\'{e}or\`{e}m de {L\"{o}wenheim-Skolem} }, BOOKTITLE = {Les entretiens de Zurich sur les fondements et la m\'{e}thode des sciences math\'{e}matique, 6--9 d\'{e}cembre 1938}, PUBLISHER = "Leeman", YEAR = 1941, PAGES = "25--47, discussion pp. 47--52", EDITOR = "Gonseth, Ferdinand", ADDRESS = {Zurich}, NOTE = {Reprinted as pp. 455--482 [Sko70].} } @BOOK{hilcohgeo, AUTHOR = {Hilbert, David and Cohn-Vossen, Stephan}, TITLE = "Geometry and the Imagination", PUBLISHER = {Chelsea}, ADDRESS = {New York}, YEAR = 1952, NOTE = "This work is a translation by P. Nemenyi of {\em Anschauliche Geometrie,\/} Verlag von Julius Springer, Berlin, 1932"} @MISC{fefmat, AUTHOR = "Feferman, Solomon", TITLE = "Mathematics as Objective Subjectivity", YEAR = 1977, HOWPUBLISHED = "Text of a talk to the Columbia University Philosophy Colloquium, 9 December"} @BOOK{madrea, AUTHOR = maddy, TITLE = "Realism in Mathematics", PUBLISHER = {Clarendon Press of Oxford University Press}, ADDRESS = {Oxford}, YEAR = 1990 } @ARTICLE{madbel1, AUTHOR = maddy, TITLE = "Believing the Axioms. {I}", JOURNAL = jsl, YEAR = 1988, VOLUME = 53, PAGES = "481--511" } @ARTICLE{madbel2, AUTHOR = maddy, TITLE = "Believing the Axioms. {II}", JOURNAL = jsl, YEAR = 1988, VOLUME = 53, PAGES = "736--764" } @BOOK{berdef, AUTHOR = "Berkeley, George", TITLE = "A defence of free-thinking in mathematics. In answer to a pamphlet of Philalethes Cantabrigiensis, intituled, {\em Geometry no friend to Infidelity, or a defence of Sir Isaac Newton, and the British Mathematicians.\/} Also an appendix concerning Mr. Walton's {\em Vindication of the principles of fluxions against the objections contained in\/} the Analyst; wherein it is attempted to put this controversy in such a light as that every reader may be able to judge thereof", PUBLISHER = {Printed by M. Rhames, for R. Gunne}, YEAR = 1735, ADDRESS = "Dublin", NOTE = "All page references are to the reprinting as Vol.~4, pp.~109--141 [Ber51]" } @BOOK{belmen, AUTHOR = "Bell, E. T.", TITLE = "Men of Mathematics", PUBLISHER = {Simon and Schuster}, ADDRESS = {New York}, YEAR = 1937 } @BOOK{klimat, AUTHOR = "Kline, Morris", TITLE = "Mathematical Thought from Ancient to Modern Times", PUBLISHER = {Oxford University Press}, ADDRESS = {Oxford}, YEAR = 1972 } @BOOK{cajhis, AUTHOR = "Cajori, Florian", TITLE = "A History of Mathematics", PUBLISHER = {Chelsea}, ADDRESS = {New York}, YEAR = 1985, EDITION = "fourth" } @BOOK{strcon, AUTHOR = "Struik, Dirk J.", TITLE = "A Concise History of Mathematics", PUBLISHER = {Dover Publications}, ADDRESS = {New York}, YEAR = 1987, EDITION = "fourth" } @BOOK{gracal, EDITOR = "Grattan-Guiness, I.", TITLE = "From the Calculus to Set Theory, 1630--1910", PUBLISHER = duckworth, ADDRESS = {London}, YEAR = 1980 } @INCOLLECTION{pedtec, AUTHOR = "Pedersen, Kirsti M\oller", TITLE = "Techniques of the Calculus, 1630--1660", CHAPTER = 1, PAGES = "10--48", EDITOR = "Grattan-Guiness, I.", BOOKTITLE = "From the Calculus to Set Theory, 1630--1910", PUBLISHER = duckworth, ADDRESS = {London}, YEAR = 1980 } @INCOLLECTION{bosnew, AUTHOR = "Bos, H. J. M.", TITLE = "Newton, {L}eibniz, and the {L}eibnizian Tradition", CHAPTER = 2, PAGES = "49--93", EDITOR = "Grattan-Guiness, I.", BOOKTITLE = "From the Calculus to Set Theory, 1630--1910", PUBLISHER = duckworth, ADDRESS = {London}, YEAR = 1980 } @INCOLLECTION{graeme, AUTHOR = "Grattan-Guiness, I.", TITLE = "The Emergence of Mathematical Analysis and Its Foundational Progress, 1780--1880", CHAPTER = 3, PAGES = "94--148", EDITOR = "Grattan-Guiness, I.", BOOKTITLE = "From the Calculus to Set Theory, 1630--1910", PUBLISHER = duckworth, ADDRESS = {London}, YEAR = 1980 } @INCOLLECTION{hawori, AUTHOR = "Hawkins, Thomas", TITLE = "The Origins of Modern Theories of Integration", CHAPTER = 4, PAGES = "149--180", EDITOR = "Grattan-Guiness, I.", BOOKTITLE = "From the Calculus to Set Theory, 1630--1910", PUBLISHER = duckworth, ADDRESS = {London}, YEAR = 1980 } @INCOLLECTION{daudev, AUTHOR = "Dauben, Joseph Warren", TITLE = "The Development of {C}antorian Set Theory", CHAPTER = 5, PAGES = "181--219", EDITOR = "Grattan-Guiness, I.", BOOKTITLE = "From the Calculus to Set Theory, 1630--1910", PUBLISHER = duckworth, ADDRESS = {London}, YEAR = 1980 } @INCOLLECTION{bundev, AUTHOR = "Bunn, R.", TITLE = "Developments in the Foundations of Mathematics, 1870--1910", CHAPTER = 6, PAGES = "220--255", EDITOR = "Grattan-Guiness, I.", BOOKTITLE = "From the Calculus to Set Theory, 1630--1910", PUBLISHER = duckworth, ADDRESS = {London}, YEAR = 1980 } @BOOK{lewpar, AUTHOR = "Lewis, David K.", TITLE = "Parts of Classes", PUBLISHER = {Basil Blackwell Publishers}, ADDRESS = {Oxford}, YEAR = 1991, NOTE = "With an Appendix by John P. Burgess, A. P. Hazen, and David Lewis" } @BOOK{ruspri, AUTHOR = "Russell, Bertrand", TITLE = "Principles of Mathematics", PUBLISHER = {George Allen and Unwin}, ADDRESS = {London}, YEAR = 1903, NOTE = "Second edition (1938) reprinted by W. W. Norton and Company (New York, no date)" } @ARTICLE{dautri, AUTHOR = "Dauben, Joseph Warren", TITLE = "The Trigonometric Background to {G}eorg {C}antor's Theory of Sets", JOURNAL = "Archive for History of Exact Sciences", YEAR = 1971, VOLUME = 7, PAGES = "181--216" } @BOOK{daucan, AUTHOR = "Dauben, Joseph Warren", TITLE = "{G}eorg {C}antor: His Mathematics and Philosophy of the Infinite", PUBLISHER = {Princeton University Press}, ADDRESS = {Princeton, New Jersey}, YEAR = 1979 } @BOOK{halcan, AUTHOR = "Hallett, Michael", TITLE = "Cantorian Set Theory and Limitation of Size", PUBLISHER = {Clarendon Press}, ADDRESS = {Oxford}, YEAR = 1984 } @BOOK{encphi, EDITOR = "Edwards, Paul", TITLE = "The Encyclopedia of Philosophy", PUBLISHER = {Macmillan and The Free Press}, ADDRESS = {New York}, YEAR = 1967 } @ARTICLE{gracor, AUTHOR = "Grattan-Guiness, I.", TITLE = "The Correspondence between {G}eorg {C}antor and {P}hilip {J}ourdain", JOURNAL = dmv, YEAR = 1971, VOLUME = 73, PAGES = "111--130" } @ARTICLE{grared, AUTHOR = "Grattan-Guiness, I.", TITLE = "The Rediscovery of the {C}antor-{D}edekind Correspondence", JOURNAL = dmv, YEAR = 1974, VOLUME = 76, PAGES = "104--139" } @BOOK{heifro, EDITOR = "van Heijenoort, Jean", TITLE = {From {F}rege to {G}\"{o}del: A Source Book in Mathematical Logic, 1879--1931}, SERIES = "Source Books in the History of the Sciences", NOTE = "Series editor, Edward H. Madden", PUBLISHER = {Harvard University Press, reprinted by iUniverse}, ADDRESS = {Cambridge, Massachusetts}, YEAR = "1967, reprinted 1999"} @INCOLLECTION{canlet, AUTHOR = "Cantor, Georg", TITLE = "Cantor an {D}edekind", PAGES = "443--447, 451", NOTE = "Includes Zermelo's editorial comments. All page references are to the translation by Stefan Bauer-Mengelberg and Jean van Heijenoort, pp.~113--117 [vH67]", EDITOR = "Zermelo, Ernst", BOOKTITLE = "Gesammelte Abhandlungen", PUBLISHER = {Verlag von Julius Springer}, ADDRESS = {Berlin}, YEAR = 1932 } @BOOKLET{peapri, AUTHOR = "Guiseppe Peano", TITLE = "Arithmetices principia, nova methodo exposita", YEAR = 1889, NOTE = "Reprinted in {\em Opera scelte,\/} volume 2, pages 20--55. Edizioni cremonese, Rome, 1958. All page references are to the excerpt translated from the Latin by Jean van Heijenoort, pp.~85--97 and to the translator's preface, pages 83--85. ShaughanLavine - 15 Feb 2010 - 20:19 - 1.173 " class="twikiCurrentTopicLink twikiAnchorLink">Heijenoort67", ADDRESS = {Turin} } @ARTICLE{gritie, AUTHOR = "Griffin, Nicholas", TITLE = "The {T}iergarten Programme", PAGES = "19--34", JOURNAL = "Russell", YEAR = 1988, VOLUME = "n.s. 8" } @ARTICLE{mooroo, AUTHOR = "Moore, Gregory H.", TITLE = "The Roots of {R}ussell's Paradox", PAGES = "46--56", JOURNAL = "Russell", YEAR = 1988, VOLUME = "n.s. 8" } @BOOK{rusaut, AUTHOR = "Russell, Bertrand", TITLE = "The Autobiography of {B}ertrand {R}ussell", PUBLISHER = {Little, Brown and Company}, ADDRESS = {Boston}, YEAR = 1967 } @ARTICLE{moogarbur, AUTHOR = "Moore, Gregory H. and Garciadiego, Alejandro", TITLE = "{B}urali-{F}orti's Paradox: A Reappraisal of Its Origins", PAGES = "319--350", JOURNAL = "Historia Mathematica", YEAR = 1981, VOLUME = 8 } @ARTICLE{cofhum, AUTHOR = "Coffa, J. Alberto", TITLE = "The Humble Origins of {R}ussell's Paradox", PAGES = "31--37", JOURNAL = "Russell", YEAR = 1979, VOLUME = "33--34" } @INCOLLECTION{ruslet, AUTHOR = "Russell, Bertrand", TITLE = "Letter to {F}rege", PAGES = "124--125", NOTE = "Translated by Beverly Woodward", EDITOR = "van Heijenoort, Jean", BOOKTITLE = {From {F}rege to {G}\"{o}del: A Source Book in Mathematical Logic, 1879--1931}, PUBLISHER = {Harvard University Press}, ADDRESS = {Cambridge, Massachusetts}, YEAR = 1967} @INCOLLECTION{frelet, AUTHOR = "Frege, Gottlob", TITLE = "Letter to {R}ussell", PAGES = "127--128", NOTE = "Translated by Beverly Woodward", EDITOR = "van Heijenoort, Jean", BOOKTITLE = {From {F}rege to {G}\"{o}del: A Source Book in Mathematical Logic, 1879--1931}, PUBLISHER = {Harvard University Press}, ADDRESS = {Cambridge, Massachusetts}, YEAR = 1967} @BOOK{frephi, AUTHOR = "Frege, Gottlob", TITLE = "Philosophical and Mathematical Correspondence", PUBLISHER = {University of Chicago Press}, ADDRESS = {Chicago}, YEAR = 1980, NOTE = "Abridged from the German edition by Brian McGuinness , translated by Hans Kaal, and edited by Gottfried Gabriel {\em et al.\/}"} @BOOK{kenpea, AUTHOR = "Kennedy, Hubert C.", TITLE = "Peano, Life and Works of Guiseppe Peano", PUBLISHER = {Reidel}, ADDRESS = {Boston}, YEAR = 1980} @BOOK{moozer, AUTHOR = "Moore, Gregory H.", TITLE = "Zermelo's Axiom of Choice, Its Origins, Development, and Influence", PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = 1982, SERIES = "Studies in the History of Mathematics and Physical Sciences", NUMBER = 8} @ARTICLE{conrus, AUTHOR = "Consuegra, Francisco Rodr\'{\i}guez", TITLE = "Russell's Logicist Definitions of Numbers, 1898--1913: {C}hronology and Significance", PAGES = "141--169", JOURNAL = "History and Philosophy of Logic", YEAR = 1987, VOLUME = 8 } @ARTICLE{lanrus, AUTHOR = "Landini, Gregory", TITLE = "Russell's Substitutional Theory of Classes and Relations", PAGES = "171--200", JOURNAL = "History and Philosophy of Logic", YEAR = 1987, VOLUME = 8 } @ARTICLE{lannew, AUTHOR = "Landini, Gregory", TITLE = "New Evidence Concerning {R}ussell's Substitutional Theory of Classes", PAGES = "26--42", JOURNAL = "Russell", YEAR = 1989, VOLUME = "n.s. 9" } @ARTICLE{urqrus, AUTHOR = "Urquhart, Alasdair", TITLE = "Russell's Zigzag Path to the Ramified Theory of Types", PAGES = "82--91", JOURNAL = "Russell", YEAR = 1988, VOLUME = "n.s. 8" } @ARTICLE{rusmat, AUTHOR = "Russell, Bertrand", TITLE = "Mathematical Logic as Based on the Theory of Types", PAGES = "222--262", JOURNAL = "American Journal of Mathematics", VOLUME = 30, YEAR = 1908, NOTE = "All page references are to the reprinting as pp.~152--182 [vH67]"} @BOOK{rusint, AUTHOR = "Russell, Bertrand", TITLE = "Introduction to Mathematical Philosophy", PUBLISHER = {Macmillan}, ADDRESS = {New York}, YEAR = 1919 } @ARTICLE{ranthozer, AUTHOR = "Rang, B. and Thomas, W.", TITLE = "Zermelo's Discovery of the ``{R}ussell Paradox''", PAGES = "15--22", JOURNAL = "Historia Mathematica", YEAR = 1981, VOLUME = 8 } @INCOLLECTION{parsom, AUTHOR = "Parsons, Charles", TITLE = "Some Remarks on {F}rege's Conception of Extension", PAGES = "265--277", EDITOR = "Schirn, Matthias", BOOKTITLE = {Studien zu Frege}, VOLUME = 1, PUBLISHER = {Friedrich Frommann}, ADDRESS = {Stuttgart}, YEAR = 1976} @ARTICLE{canele, AUTHOR = "Cantor, Georg", TITLE = {\"{U}ber eine elementare {F}rage der {M}annigfaltigkeitslehre}, PAGES = "75--78", JOURNAL = dmv, YEAR = "1890--1891", VOLUME = 1, NOTE = "Reprinted as pp.~278--280 [Can32b] and translated as Appendix B to Chapter IV of this book" } @BOOK{canges, AUTHOR = "Cantor, Georg", TITLE = "Gesammelte Abhandlungen", PUBLISHER = {Verlag von Julius Springer}, ADDRESS = {Berlin}, YEAR = 1932, NOTE = "Edited by Ernst Zermelo"} @ARTICLE{canfou, AUTHOR = "Cantor, Georg", TITLE = "Foundations of a General Theory of Manifolds", JOURNAL = "Campaigner, Journal of the National Caucus of Labor Committees", YEAR = 1976, VOLUME = 9, PAGES = "69--96", NOTE = "Translation by Uwe Parpart of [Can83]", NOTE = "Translation by Uwe Parpart of Cantor83" } @BOOK{cangru, AUTHOR = "Cantor, Georg", TITLE = {Grundlagen einer allgemeinen {M}annigfaltigkeitslehre. {E}in mathematische-philosophischer {V}ersuch in der {L}ehre des {U}nendlichen}, PUBLISHER = {B. G. Teubner}, ADDRESS = {Leipzig}, YEAR = 1883, NOTE = "All page references are to the reprinting as pp.~165--208 [Can32b]. Translated as [Can76]", NOTE = "Translated as Cantor76" } @BOOK{gosphi, AUTHOR = "Gosling, J. C. B.", TITLE = "Plato: Philebus", PUBLISHER = {Clarendon Press}, ADDRESS = {Oxford}, YEAR = 1975 } @ARTICLE{lavmad, AUTHOR = sml, TITLE = "Penelope {M}addy: {R}ealism in Mathematics", JOURNAL = jop, YEAR = 1992, VOLUME = 89, PAGES = "321--326", NOTE = "Book review" } @ARTICLE{madind, AUTHOR = maddy, TITLE = "Indispensability and Practice", JOURNAL = jop, YEAR = 1992, VOLUME = 89, PAGES = "275--289" } @ARTICLE{mooori, AUTHOR = "Moore, Gregory H.", TITLE = "The Origins of {Z}ermelo's Axiomatization of Set Theory", PAGES = "305--329", JOURNAL = "Journal of Philosophical Logic", YEAR = 1978, VOLUME = 7 } @ARTICLE{baiborcin, AUTHOR = "Baire, Ren\'{e} and Borel, Emile and Hadamard, Jacques and Lebesgue, Henri", TITLE = "Cinq Lettres sur la Th\'{e}orie des Ensembles", JOURNAL = "Bulletin de la Soci\'{e}t\'{e} Math\'{e}mathique de France", YEAR = 1905, VOLUME = 33, PAGES = "261--273", NOTE = "All page references are to the translation by G. H. Moore, pp.~311--320 [Moo82]" } @BOOK{gradea, AUTHOR = "Grattan-Guiness, I.", TITLE = "Dear {R}ussell--{D}ear {J}ourdain", PUBLISHER = {Columbia University Press}, ADDRESS = {New York}, YEAR = 1977 } @ARTICLE{frazer, AUTHOR = "Fraenkel, A.", TITLE = {\"{U}ber die {Z}ermelosche {B}egr\"{u}ndung der {M}engenlehre}, JOURNAL = "Jahresbericht der Deutschen Mathematiker-Vereinigung (Angelegenheiten)", YEAR = 1921, VOLUME = 30, PAGES = "97--98" } @INPROCEEDINGS{skosom, AUTHOR = "Skolem, Thoralf", TITLE = {Einige {B}emerkungen zur axiomatischen {B}egr\"{u}ndung der {M}engenlehre ({S}ome remarks on axiomatised set theory)}, PAGES = "217--232", NOTE = "All page references are to the translation by Stefan Bauer-Mengelberg, pp.~291--301 [vH67]", BOOKTITLE = {Matematikerkongressen i Helsingfors den 4--7 Juli 1922, Den femte skandinaviska matematikerkongressen, Redog\"{o}relse}, PUBLISHER = {Akademiska Bokhandeln}, ADDRESS = {Helsinki}, YEAR = 1923} @ARTICLE{fragru, AUTHOR = "Fraenkel, A.", TITLE = {Zu den {G}rundlagen der {C}antor-{Z}ermeloschen {M}engenlehre}, JOURNAL = "Mathematische Annalen", YEAR = 1922, VOLUME = 86, PAGES = "230--237" } @ARTICLE{mirant, AUTHOR = "Mirimanoff, D.", TITLE = {Les Antinomies de {R}ussell et de {B}urali-{F}orti et le Probl\`{e}me Fondamental de la Th\'{e}orie des Ensembles}, JOURNAL = "L'Enseignement Math\'{e}matique", YEAR = 1917, VOLUME = 19, PAGES = "37--52" } @ARTICLE{neuaxi, AUTHOR = "von Neumann, John", TITLE = "Eine {A}xiomatisierung der {M}engenlehre", PAGES = "219--240", NOTE = "Errata 155:128. Reprinted as pp.~34--56 [vN61]. All page references are to the translation by Stefan Bauer-Mengelberg and Dagfin F{\o}llesdal, pp.~394--413 [vH67]", JOURNAL = {Journal f\"{u}r die reine und angewandte {M}athematik}, VOLUME = 154, YEAR = 1925, NOTE = "Errata 155:128. Reprinted as pp.~34--56 Neumann61. All page references are to the translation by Stefan Bauer-Mengelberg and Dagfin F{\o}llesdal, pp.~394--413 Heijenoort67",} @ARTICLE{neuint, AUTHOR = "von Neumann, John", TITLE = {Zur {E}inf\"{u}hrung der transfiniten {Z}ahlen}, PAGES = "199--208", NOTE = "Reprinted as pp.~24--33 [vN61]. All page references are to the translation by Jean van Heijenoort, pp.~347--354 [vH67]", VOLUME =1, JOURNAL = {Acta litterarum ac scientiarum Regiae Universitatis Hungaricae Francisco-Josephinae, Sectio scientiarum mathematicarum}, YEAR = 1923} @INCOLLECTION{klewor, AUTHOR = "Kleene, Stephen C.", TITLE = {The Work of {K}urt {G}\"{o}del}, PAGES = "48--71", EDITOR = "Stuart G. Shanker", BOOKTITLE = {G\"{o}del's Theorem in Focus}, PUBLISHER = {Routledge}, ADDRESS = {New York}, YEAR = 1988} @INPROCEEDINGS{franot, AUTHOR = "Fraenkel, A.", TITLE = {Der {B}egriff ``definit'' und die {U}nabh\"{a}ngigkeit des {A}uswahlsaxioms}, PAGES = "253--257", NOTE = "All page references are to the translation by Beverly Woodward, pp.~285--289 [vH67]", BOOKTITLE = {Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-mathematische Klasse}, YEAR = 1922} @ARTICLE{zerstu, AUTHOR = "Zermelo, Ernst", TITLE = {\"{U}ber {S}tufen der {Q}uantifikation und die {L}ogik des {U}nendlichen}, JOURNAL = "Jahresbericht der Deutschen Mathematiker-Vereinigung (Angelegenheiten)", YEAR = 1932, VOLUME = 41, PAGES = "85--88" } @ARTICLE{moobey, AUTHOR = "Moore, Gregory H.", TITLE = "Beyond First-order Logic: The Historical Interplay between Mathematical Logic and Axiomatic Set Theory", PAGES = "95--137", JOURNAL = "History and Philosophy of Logic", YEAR = 1980, VOLUME = 1 } @BOOK{heahis, AUTHOR = "Heath, Sir Thomas", TITLE = "A History of Greek Mathematics", PUBLISHER = {Dover Publications}, ADDRESS = {New York}, YEAR = 1981, NOTE = "Reprinting with corrections of the original Clarendon Press edition (Oxford, 1921)" } @BOOK{eucele, AUTHOR = "Euclid", TITLE = "Euclid; {T}he Thirteen Books of {T}he {E}lements", PUBLISHER = {Dover Publications}, ADDRESS = {New York}, YEAR = "Early 3rd century {\sc BCE}", NOTE = "Edited by Sir Thomas Heath. 1956 Reprinting of the second edition (Cambridge University Press, Cambridge, England, 1925)" } @BOOK{newmat, EDITOR = "Whiteside, Derek T.", TITLE = "The Mathematical Works of Isaac Newton", PUBLISHER = {Johnson Reprint}, ADDRESS = {New York}, YEAR = 1967 } @BOOK{gauqui, AUTHOR = "Gaudet, Eve", TITLE = "Quine on Meaning", PUBLISHER = {Continuum International Publishing Group}, ADDRESS = {New York}, YEAR = 2006 } @ARTICLE{bosdif, AUTHOR = "Bos, H. J. M.", TITLE = "Differentials, Higher-Order Differentials and the Derivative in the {L}eibnizian Calculus", PAGES = "1--90", JOURNAL = "Archive for History of Exact Sciences", YEAR = 1974, VOLUME = 14 } @BOOK{graravfou, AUTHOR = "Grattan-Guiness, I. and Ravetz, J. R.", TITLE = "Joseph Fourier 1768--1830", PUBLISHER = {MIT Press}, ADDRESS = {Cambridge, Massachusetts}, YEAR = 1972 } @ARTICLE{booite, AUTHOR = "Boolos, George", TITLE = "The Iterative Conception of Set", JOURNAL = jop, YEAR = 1971, VOLUME = 68, PAGES = "215--231", NOTE = "All page references are to the reprinting as pp.~486--502 [BP83]" } @INCOLLECTION{parset, AUTHOR = "Parsons, Charles", TITLE = "Sets and Modality", BOOKTITLE = "Mathematics in Philosophy; Selected Essays", PUBLISHER = {Cornell University Press}, ADDRESS = {Ithaca, New York}, YEAR = 1983, PAGES = "298--341" } @INCOLLECTION{parint, AUTHOR = "Parsons, Charles", TITLE = "Introduction", BOOKTITLE = "Mathematics in Philosophy; Selected Essays", PUBLISHER = {Cornell University Press}, ADDRESS = {Ithaca, New York}, YEAR = 1983, PAGES = "15--34" } @ARTICLE{parsets, AUTHOR = "Parsons, Charles", TITLE = "Sets and Classes", JOURNAL = "No\^{u}s", YEAR = 1974, VOLUME = 8, PAGES = "1--12", NOTE = "All page references are to the reprinting as pp.~209--220 [Par83]" } @ARTICLE{parlia, AUTHOR = "Parsons, Charles", TITLE = "The Liar Paradox", JOURNAL = "Journal of Philosophical Logic", YEAR = 1974, VOLUME = 3, PAGES = "381--412", NOTE = "All page references are to the reprinting as pp.~221--251 [Par83], which has an added postscript, pp.~251--267" } @ARTICLE{pardif, AUTHOR = "Parsons, Charles", TITLE = "On Some Difficulties Concerning Intuition and Intuitive Knowledge", JOURNAL = "Mind", YEAR = 1993, VOLUME = "n.s. 102", PAGES = "233-246" } @ARTICLE{paront, AUTHOR = "Parsons, Charles", TITLE = "Ontology and Mathematics", JOURNAL = "Philosophical Review", YEAR = 1971, PAGES = "151--176", VOLUME = 80, NOTE = "All page references are to the reprinting as pp.~37--62 [Par83a]" } @ARTICLE{quitwo, AUTHOR = quine, TITLE = "Main Trends in Recent Philosophy: Two Dogmas of Empiricism", JOURNAL = "Philosophical Review", YEAR = 1951, PAGES = "20--43", VOLUME = 60, URL = "http://ezproxy.library.arizona.edu/login?url=http://links.jstor.org/sici?sici=0031-8108%28195101%2960%3A1%3C20%3AMTIRPT%3E2.0.CO%3B2-P" } @BOOK{wancon, AUTHOR = "Wang, Hao", TITLE = "From Mathematics to Philosophy", PUBLISHER = {Routledge and Kegan Paul}, ADDRESS = {London}, YEAR = 1974, NOTE = "All page references are to the reprinting of Chapter 6, ``The concept of set,'' as pp.~530--570 [BP83]" } @BOOK{paldis, AUTHOR = "Yourgrau, Palle", TITLE = {The Disappearance of Time---{K}urt {G}\"{o}del and the Idealistic Tradition in Philosophy}, PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge, England}, YEAR = 1991 } @BOOK{dumele, AUTHOR = dummett, TITLE = {Elements of Intuitionism}, PUBLISHER = {Clarendon Press}, ADDRESS = {Oxford}, YEAR = 1977, SERIES = "Oxford Logic Guides" } @BOOK{dumsea, AUTHOR = dummett, TITLE = {The Seas of Language}, PUBLISHER = {Clarendon Press}, ADDRESS = {Oxford}, YEAR = 1993 } @INPROCEEDINGS{dumphi, AUTHOR = dummett, TITLE = "The Philosophical Basis of Intuitionistic Logic", BOOKTITLE = "Logic Colloquium '73. Proceedings of the Logic Colloquium (Bristol, 1973)", PUBLISHER = {North-Holland Publishing Company}, ADDRESS = {New York}, YEAR = 1975, EDITOR = "Rose, H. E. and Shepherdson, J. C.", PAGES = "5--40", SERIES = sil, NUMBER = 80, NOTE = "All page references are to the reprinting as pp.~97--129 [BP83]. Also reprinted as pp.~215--247 [Dum78b]"} @ARTICLE{dumgod, AUTHOR = dummett, TITLE = {The Philosophical Significance of {G}\"{o}del's Theorem}, JOURNAL = "Ratio", YEAR = 1963, VOLUME = 5, PAGES = "140--155", NOTE = "All page references are to the reprinting as pp. 186--201 [Dum78b]"} @INCOLLECTION{dumpre, AUTHOR = dummett, TITLE = "Preface", BOOKTITLE = "Truth and Other Enigmas", PUBLISHER = {Harvard University Press}, ADDRESS = {Cambridge, Massachusetts}, YEAR = 1978, PAGES = "ix--li" } @BOOK{dumtru, AUTHOR = dummett, TITLE = "Truth and Other Enigmas", PUBLISHER = {Harvard University Press}, ADDRESS = {Cambridge, Massachusetts}, YEAR = 1978 } @ARTICLE{mccint, AUTHOR = "McCarty, Charles", TITLE = "Intuitionism: {A}n Introduction to a Seminar", JOURNAL = "Journal of Philosophical Logic", YEAR = 1983, VOLUME = 12, PAGES = "105--149", URL = "http://www.springerlink.com.ezproxy.library.arizona.edu/content/k877m6274v523360/fulltext.pdf" } @ARTICLE{benmat, AUTHOR = "Benacerraf, Paul", TITLE = "Mathematical Truth", JOURNAL = jop, YEAR = 1973, VOLUME = 70, PAGES = "661--679", NOTE = "All page references are to the reprinting as pp.~403--420 [BP83]" } @BOOK{tilphi, AUTHOR = "Tiles, Mary", TITLE = "The Philosophy of Set Theory: {A}n Introduction to {C}antor's Paradise", PUBLISHER = {Basil Blackwell Publishers}, ADDRESS = {New York}, YEAR = 1989 } @BOOK{curout, AUTHOR = "Curry, Haskell B.", TITLE = "Outlines of a Formalist Philosophy of Mathematics", PUBLISHER = {North-Holland Publishing Company}, ADDRESS = {New York}, YEAR = 1951 } @ARTICLE{hilfou, AUTHOR = "Hilbert, David", TITLE = "Die {G}rundlagen der Mathematik", PAGES = "65--85", YEAR = 1928, JOURNAL = {Abhandlungen aus dem mathematischen {S}eminar der {H}amburgischen {U}niversit\"{a}t}, VOLUME = 6, NOTE = "All references are to the translation by Stefan Bauer-Mengelberg and Dagfinn F{\o}llesdal, pp.~464--479 [vH67]" } @ARTICLE{frasin, AUTHOR = "van Fraassen, Bas C.", TITLE = "Singular Terms, Truth-Value Gaps, and Free Logic", JOURNAL = jop, YEAR = 1966, VOLUME = 63, PAGES = "481--495" } @BOOK{stemat, AUTHOR = "Steiner, Mark", TITLE = "Mathematical Knowledge", PUBLISHER = {Cornell University Press}, ADDRESS = {Ithaca, New York}, YEAR = 1975 } @BOOK{quifro, AUTHOR = quine, TITLE = "From a Logical Point of View: Logico-Philosophical Essays", PUBLISHER = {Harper Torchbooks, Harper \& Row}, ADDRESS = {New York}, EDITION = "second, revised", YEAR = 1961 } @ARTICLE{quiide, AUTHOR = quine, TITLE = "Identity, Ostension, and Hypostasis", JOURNAL = jop, YEAR = 1950, VOLUME = 47, PAGES = "621--633", NOTE = "All page references are to the reprinting as pp.~65--79 of [Qui61].", NOTE = "All page references are to the reprinting as pp.~65--79 of Quine61.", URL = {http://ezproxy.library.arizona.edu/login?url=http://links.jstor.org/sici?sici=0022-362X%2819501026%2947%3A22%3C621%3AIOAH%3E2.0.CO%3B2-U} } @BOOK{putmat, AUTHOR = "Putnam, Hilary", TITLE = "Mathematics, Matter and Method", PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge, England}, EDITION = "second", YEAR = 1979 } @ARTICLE{putmath, AUTHOR = "Putnam, Hilary", TITLE = "Mathematics without Foundations", JOURNAL = jop, YEAR = 1967, PAGES = "5--22", NOTE = "All page references are to the reprinting as pp.~295--311 [BP83]"} @INCOLLECTION{parqui, AUTHOR = "Parsons, Charles", TITLE = "Quine on the Philosophy of Mathematics", BOOKTITLE = "Mathematics in Philosophy; Selected Essays", PUBLISHER = {Cornell University Press}, ADDRESS = {Ithaca, New York}, YEAR = 1983, PAGES = "176--205" } @ARTICLE{burwhy, AUTHOR = "Burgess, John P.", TITLE = "Why {I} Am Not a Nominalist", JOURNAL = "Notre Dame Journal of Formal Logic", YEAR = 1983, VOLUME = 24, PAGES = "93--105" } @BOOK{fierea, AUTHOR = field, TITLE = "Realism, Mathematics and Modality", PUBLISHER = {Basil Blackwell Publishers}, ADDRESS = {Oxford}, YEAR = 1989 } @INCOLLECTION{fiereaint, AUTHOR = field, TITLE = "Introduction: {F}ictionalism, Epistemology and Modality", BOOKTITLE = "Realism, Mathematics and Modality", PUBLISHER = {Basil Blackwell Publishers}, ADDRESS = {Oxford}, YEAR = 1989, EDITOR = field, PAGES = "1--52" } @ARTICLE{quipar, AUTHOR = quine, TITLE = "Review of {P}arsons's {M}athematics in {P}hilosophy", JOURNAL = jop, YEAR = 1984, VOLUME = 81, PAGES = "783--794"} @INCOLLECTION{quirep, AUTHOR = quine, TITLE = "Reply to {C}harles {P}arsons", BOOKTITLE = "The Philosophy of {W.} {V.} {Q}uine", PUBLISHER = {Open Court}, ADDRESS = {La Salle, Illinois}, YEAR = 1986, PAGES = "396--403", SERIES = "Library of Living Philosophers", NUMBER = 18, EDITOR = "Hahn, Lewis Edward and Schilpp, Paul Arthur" } @ARTICLE{parmat, AUTHOR = "Parsons, Charles", TITLE = {Mathematical Intuition}, PAGES = "145--168", JOURNAL = "Proceedings of the Aristotelian Society", YEAR = "1979--1980", VOLUME = "n.s. 80" } @BOOK{shafou, AUTHOR = "Shapiro, Stewart", TITLE = "Foundations without Foundationalism", PUBLISHER = {Clarendon Press}, ADDRESS = {Oxford}, YEAR = 1991 } @BOOK{quiphi, AUTHOR = quine, TITLE = "Philosophy of Logic", PUBLISHER = {Prentice-Hall}, ADDRESS = {Englewood Cliffs, New Jersey}, YEAR = 1970, SERIES = "Foundations of Philosophy Series" } @ARTICLE{bensko, AUTHOR = "Benacerraf, Paul", TITLE = {Skolem and the Skeptic}, PAGES = "85--115", JOURNAL = "Proceedings of the Aristotelian Society", YEAR = "1985", VOLUME = "supplementary volume 59" } @ARTICLE{brosig, AUTHOR = "Brouwer, Luitzen Egbertus Jan", TITLE = {\"{U}ber die {B}edeutung des {S}atzes vom ausgeschlossenen {D}ritten in der {M}athematik, insbesondere in der {F}unktionentheorie}, PAGES = "1--7", JOURNAL = {Journal f\"{u}r die reine und angewandte {M}athematik}, YEAR = "1923", VOLUME = "154", NOTE = {Translation by Stefan Bauer-Mengelberg and Jan van Heijenoort, pp. 335--341 [vH67].} } @ARTICLE{wrisko, AUTHOR = "Wright, Crispin", TITLE = {Skolem and the Skeptic}, PAGES = "117--137", JOURNAL = "Proceedings of the Aristotelian Society", YEAR = "1985", VOLUME = "supplementary volume 59" } @ARTICLE{shamat, AUTHOR = "Shapiro, Stewart", TITLE = "Second-Order Languages and Mathematical Practice", JOURNAL = jsl, YEAR = 1985, VOLUME = 50, PAGES = "714--742" } @ARTICLE{shasec, AUTHOR = "Shapiro, Stewart", TITLE = "Second-Order Logic, Foundations, and Rules", JOURNAL = jop, YEAR = 1990, VOLUME = 87, PAGES = "234--261" } @BOOK{helmat, AUTHOR = "Hellman, Geoffrey", TITLE = "Mathematics without Numbers: {T}owards a Modal-Structural Interpretation", PUBLISHER = {Clarendon Press}, ADDRESS = {Oxford}, YEAR = 1989 } @BOOK{fiesci, AUTHOR = "Field, Hartry", TITLE = "Science without Numbers", PUBLISHER = {Princeton University Press}, ADDRESS = {Princeton, New Jersey}, YEAR = 1980 } @INPROCEEDINGS{pozlib, AUTHOR = "Pozsgay, Lawrence", TITLE = "Liberal Intuitionism as a Basis for Set Theory", BOOKTITLE = "Axiomatic Set Theory", PUBLISHER = {American Mathematical Society}, ADDRESS = {Providence, Rhode Island}, YEAR = 1971, EDITOR = "Scott, Dana S.", PAGES = "321--330", SERIES = "Proceedings of Symposia in Pure Mathematics", NUMBER = "13, part 1" } } @INCOLLECTION{benwha1, AUTHOR = "Benacerraf, Paul", TITLE = "What Mathematical Truth Could Not Be---{I}", BOOKTITLE = "Benacerraf and His Critics", PUBLISHER = {Blackwell Publishers Ltd.}, ADDRESS = {Oxford}, YEAR = 1996, EDITOR = "Morton, Adam and Stich, Stephen P.", PAGES = "9--59", SERIES = "Philosophers and Their Critics" } @INPROCEEDINGS{kreobs, AUTHOR = "Kreisel, Georg", TITLE = "Observations on Popular Discussions of Foundations", BOOKTITLE = "Axiomatic Set Theory", PUBLISHER = {American Mathematical Society}, ADDRESS = {Providence, Rhode Island}, YEAR = 1971, EDITOR = "Scott, Dana S.", PAGES = "189--198", SERIES = "Proceedings of Symposia in Pure Mathematics", NUMBER = "13, part 1" } @ARTICLE{paruni, AUTHOR = "Parsons, Charles", TITLE = {The Uniqueness of the Natural Numbers}, PAGES = "13--44", JOURNAL = "Iyyun, A Jerusalem Philosophical Quarterly", YEAR = 1990, VOLUME = 39 } @ARTICLE{knephi, AUTHOR = "Kneebone, G. T.", TITLE = {The philosophical basis of mathematical rigour}, PAGES = "204--223", JOURNAL = "The Philosophical Quarterly", YEAR = 1957, VOLUME = 7, URL = "http://ezproxy.library.arizona.edu/login?url=http://links.jstor.org/sici?sici=0031-8094%28195707%297%3A28%3C204%3ATPBOMR%3E2.0.CO%3B2-4" } @BOOK{kitnat, AUTHOR = "Kitcher, Philip", TITLE = "The Nature of Mathematical Knowledge", PUBLISHER = {Oxford University Press}, ADDRESS = {New York}, YEAR = 1983 } @BOOK{desgeo, AUTHOR = "Descartes, Ren\'{e}", TITLE = "The Geometry", PUBLISHER = {Dover Publications}, ADDRESS = {New York}, YEAR = 1637, NOTE = "Printed 1954 with a facsimile of the first (1637) edition. Translated by David Eugene Smith and Marcia L. Latham. Reprinting of the 1925 Open Court edition" } @INCOLLECTION{grodes, AUTHOR = "Grosholz, E.", TITLE = "Descartes' Unification of Algebra and Geometry", BOOKTITLE = "Descartes, Mathematics and Physics", PUBLISHER = {Harvester}, ADDRESS = {Hassocks, England}, YEAR = 1980, EDITOR = "Gaukroger, Stephen" } @BOOK{mahmat, AUTHOR = "Mahoney, M. S.", TITLE = "The Mathematical Career of Pierre de Fermat", PUBLISHER = {Princeton University Press}, ADDRESS = {Princeton}, YEAR = 1973 } @INCOLLECTION{dauabr, AUTHOR = "Dauben, Joseph W.", TITLE = "Abraham {R}obinson and Nonstandard Analysis: {H}istory, Philosophy, and Foundations of Mathematics", BOOKTITLE = "History and Philosophy of Modern Mathematics", PUBLISHER = {University of Minnesota Press}, ADDRESS = {Minneapolis, Minnesota}, YEAR = 1988, PAGES = "177--200", SERIES = "Minnesota Studies in the Philosophy of Science", NUMBER = 11, EDITOR = "Aspray, William and Kitcher, Philip" } @INCOLLECTION{stelog, AUTHOR = "Stein, Howard", TITLE = "{\em Logos,\/} Logic, and {\em Logistik\'{e}:\/} {S}ome Philosophical Remarks on Nineteenth Century Transformation of Mathematics", BOOKTITLE = "History and Philosophy of Modern Mathematics", PUBLISHER = {University of Minnesota Press}, ADDRESS = {Minneapolis, Minnesota}, YEAR = 1988, PAGES = "238--259", SERIES = "Minnesota Studies in the Philosophy of Science", NUMBER = 11, EDITOR = "Aspray, William and Kitcher, Philip" } @BOOK{dedste, AUTHOR = "Dedekind, Richard", TITLE = "Stetigkeit und irrationale {Z}ahlen", PUBLISHER = {Viewig}, ADDRESS = {Braunschweig}, YEAR = 1872, NOTE = "All page references are to the translation by Wooster Woodruff Beman, pp.~1--27 of ShaughanLavine - 15 Feb 2010 - 20:19 - 1.173 " class="twikiCurrentTopicLink twikiAnchorLink">Dedekind01" } @INCOLLECTION{kitmat, AUTHOR = "Kitcher, Philip", TITLE = "Mathematical Naturalism", BOOKTITLE = "History and Philosophy of Modern Mathematics", PUBLISHER = {University of Minnesota Press}, ADDRESS = {Minneapolis, Minnesota}, YEAR = 1988, PAGES = "293--325", SERIES = "Minnesota Studies in the Philosophy of Science", NUMBER = 11, EDITOR = "Aspray, William and Kitcher, Philip" } @INCOLLECTION{edwkro, AUTHOR = "Edwards, Harold", TITLE = "Kronecker's Place in History", BOOKTITLE = "History and Philosophy of Modern Mathematics", PUBLISHER = {University of Minnesota Press}, ADDRESS = {Minneapolis, Minnesota}, YEAR = 1988, PAGES = "139--144", SERIES = "Minnesota Studies in the Philosophy of Science", NUMBER = 11, EDITOR = "Aspray, William and Kitcher, Philip" } @BOOK{dedwas, AUTHOR = "Dedekind, Richard", TITLE = "Was sind und was sollen die {Z}ahlen?", PUBLISHER = {Viewig}, ADDRESS = {Braunschweig}, YEAR = 1888, EDITION = "1911, third edition; 1893, second edition; 1888, original edition", NOTE = "All page references are to the translation of the second edition by Wooster Woodruff Beman, pp.~28--115 in ShaughanLavine - 15 Feb 2010 - 20:19 - 1.173 " class="twikiCurrentTopicLink twikiAnchorLink">Dedekind01" } @BOOK{dedess, AUTHOR = "Dedekind, Richard", TITLE = "Essays on the Theory of Numbers", PUBLISHER = {Open Court}, ADDRESS = {La Salle, Illinois}, YEAR = 1901, NOTE = "Reprinted in 1963 by Dover Publications, New York" } @INCOLLECTION{hyllog, AUTHOR = "Hylton, Peter", TITLE = "Logic in {R}ussell's Logicism", BOOKTITLE = "The Analytic Tradition: Meaning, Thought and Knowledge", PUBLISHER = {Basil Blackwell Publishers}, ADDRESS = {Oxford}, YEAR = 1990, EDITOR = "Bell, David and Cooper, Neil", PAGES = "137--172", CHAPTER = 7, SERIES = "Philosophical Quarterly Monographs", NUMBER = 1 } @INCOLLECTION{mooeme, AUTHOR = "Moore, Gregory H.", TITLE = "The Emergence of First-Order Logic", BOOKTITLE = "History and Philosophy of Modern Mathematics", PUBLISHER = {University of Minnesota Press}, ADDRESS = {Minneapolis, Minnesota}, YEAR = 1988, PAGES = "95--135", SERIES = "Minnesota Studies in the Philosophy of Science", NUMBER = 11, EDITOR = "Aspray, William and Kitcher, Philip" } @BOOK{quicardea, AUTHOR = "Quine, Willard Van Orman and Carnap, Rudolf", TITLE = "Dear Carnap, Dear Van", PUBLISHER = {University of California Press}, ADDRESS = {Berkeley}, YEAR = 1990, NOTE = "Edited and with an Introduction by Richard Creath" } @ARTICLE{lavisq, AUTHOR = sml, TITLE = {Is Quantum Mechanics an Atomistic Theory?}, JOURNAL = {Synthese}, YEAR = 1991, VOLUME = 89, PAGES = "253--271" } @PHDTHESIS{evaund, AUTHOR = "Evans, Diane Wilkinson", TITLE = "Understanding Zero and Infinity in the Early School Years", SCHOOL = "University of Pennsylvania", YEAR = 1983 } @BOOK{boyhis, AUTHOR = "Boyer, Carl B.", TITLE = "The Concepts of the Calculus, A Critical and Historical Discussion of the Derivative and the Integral", PUBLISHER = {Hafner Publishing Company}, YEAR = 1949, NOTE = "All page references are to the reprinting as {\em The History of the Calculus and Its Conceptual Development\/} (Dover Publications, New York, 1959)" } @INCOLLECTION{lakcau, AUTHOR = "Lakatos, Imre", TITLE = "Cauchy and the Continuum: {T}he Significance of Nonstandard Analysis for the History and Philosophy of Mathematics (edited by {J}. {P.} {C}leave)", BOOKTITLE = "Mathematics, Science, and Epistemology", PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge, England}, YEAR = 1978, PAGES = "43--60", EDITOR = "Worrall, John and Currie, Gregory", NOTE = "Volume 2 of Lakatos's unpublished papers"} @ARTICLE{taiite, AUTHOR = "Tait, William W.", TITLE = {The Iterative Hierarchy of Sets}, PAGES = "65--79", JOURNAL = "Iyyun, A Jerusalem Philosophical Quarterly", YEAR = 1990, VOLUME = 39 } @ARTICLE{corcat, AUTHOR = "Corcoran, John", TITLE = "Categoricity", PAGES = "187--207", JOURNAL = "History and Philosophy of Logic", YEAR = 1980, VOLUME = 1 } @ARTICLE{corcon, AUTHOR = "Corcoran, John", TITLE = "Conceptual Structure of Classical Logic", PAGES = "25--47", JOURNAL = "Philosophy and Phenomenological Research", YEAR = 1972, VOLUME = 33, URL = "http://ezproxy.library.arizona.edu/login/up?url=http://links.jstor.org/sici?sici=0031-8205%28197209%2933%3A1%3C25%3ACSOCL%3E2.0.CO%3B2-E" } @ARTICLE{taplia, AUTHOR = "Tappenden, Jamie", YEAR = "1993", TITLE = "The Liar and {S}orites Paradoxes: {T}oward a Unified Treatment", JOURNAL = jop } @ARTICLE{lavfin, AUTHOR = sml, TITLE = "Finite Mathematics", JOURNAL = "Synthese", YEAR = "1995", PAGES = "389--420", VOLUME = 103, NOTE = "Mathematical Reviews 96k:03115" } @INCOLLECTION{monset, AUTHOR = "Montague, Richard", TITLE = "Set Theory and Higher-Order Logic", BOOKTITLE = "Formal Systems and Recursive Functions", PUBLISHER = "North-Holland Publishing Company", ADDRESS = "Amsterdam", YEAR = 1965, EDITOR = "Crossley, J. N. and Dummett, Michael A. E.", PAGES = "131--148", SERIES = sil } @ARTICLE{kleint, AUTHOR = "Klenk, Virginia", TITLE = {Intended Models and the {L}\"{o}wenheim-{S}kolem Theorem}, JOURNAL = "Journal of Philosophical Logic", YEAR = 1976, VOLUME = 5, PAGES = "475-489", URL = "http://www.springerlink.com.ezproxy.library.arizona.edu/content/l5676g04nn414210/fulltext.pdf" } @INCOLLECTION{halphy, AUTHOR = "Hallett, Michael", TITLE = "Physicalism, Reductionism \& {H}ilbert", BOOKTITLE = "Physicalism in Mathematics", PUBLISHER = {Kluwer Academic Publishers}, ADDRESS = {Dordrecht, The Netherlands}, YEAR = 1990, PAGES = "183--257", SERIES = "The University of Western Ontario Series in Philosophy of Science", NUMBER = 45, EDITOR = "Irvine, A. D." } @INCOLLECTION{wanthe, AUTHOR = "Wang, Hao", TITLE = "Theory and Practice in Mathematics", BOOKTITLE = "New Directions in the Philosophy of Mathematics", PUBLISHER = {Birkh\"{a}user}, ADDRESS = {Boston}, YEAR = 1986, EDITOR = "Tymoczko, Thomas", PAGES = "131--152" } @BOOK{bothig, AUTHOR = {Bottazzini, Umberto}, TITLE = "The Higher Calculus: {A} History of Real and Complex Analysis from {E}uler to {W}eierstrass", PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = 1986, NOTE = "Translation by Warren Van Egmond, with substantial corrections and revisions, of {\em Il Calcolo sublime: storia dell'analisi matematica de Euler a Weierstrass.\/} Editore Boringhieri, Turin, 1981" } @ARTICLE{youcon, AUTHOR = "Youschkevitch, A. P.", TITLE = "The Concept of Function up to the Middle of the 19th Century", JOURNAL = "Archive for History of Exact Sciences", YEAR = 1976, VOLUME = 16, PAGES = "37--85" } @BOOK{hawles, AUTHOR = "Hawkins, Thomas", TITLE = " Lebesgue's Theory of Integration: {I}ts Origins and Development", PUBLISHER = {Chelsea Publishing}, ADDRESS = {New York}, YEAR = 1975, EDITION = "second" } @ARTICLE{volges, AUTHOR = "Volkert, Klaus", TITLE = "Die {G}eschichte der pathologischen {F}unktionen---{E}in {B}eitrag zur {E}ntstehung der mathematischen {M}ethodologie", JOURNAL = "Archive for History of Exact Sciences", YEAR = 1986, VOLUME = 37, PAGES = "193--232" } @INCOLLECTION{parnot, AUTHOR = "Parsons, Charles", TITLE = "Introductory Note to 1944", BOOKTITLE = {Kurt G\"{o}del: Collected Works}, PUBLISHER = {Oxford University Press}, ADDRESS = {New York}, YEAR = 1986, VOLUME = 2, PAGES = "102--118", EDITOR = "Feferman, Solomon and Dawson, Jr., John W. and Kleene, Stephen C. and Moore, Gregory H. and Solovay, Robert M. and van Heijenoort, Jean"} @ARTICLE{leaset, AUTHOR = "Lear, Jonathan", TITLE = "Sets and Semantics", JOURNAL = jop, YEAR = 1977, VOLUME = 74, PAGES = "86--102", URL = "http://ezproxy.library.arizona.edu/login/up?url=http://links.jstor.org/sici?sici=0022-362X%28197702%2974%3A2%3C86%3ASAS%3E2.0.CO%3B2-5" } @ARTICLE{velcon, AUTHOR = "Velleman, Daniel J.", TITLE = "Constructivism Liberalized", JOURNAL = "Philosophical Review", YEAR = 1993, VOLUME = 102, PAGES = "59--84" } @INCOLLECTION{putwha, AUTHOR = "Putnam, Hilary", TITLE = "What Is Mathematical Truth?", BOOKTITLE = "Mathematics, Matter and Method", PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge, England}, EDITION = "second", YEAR = 1979, PAGES = "60--78", CHAPTER = 4, NOTE = "All page references are to the reprinting as pp.~49--65 [Tym86]" } @BOOK{tymnew, EDITOR = "Tymoczko, Thomas", TITLE = "New Directions in the Philosophy of Mathematics", PUBLISHER = {Birkh\"{a}user}, ADDRESS = {Boston}, YEAR = 1986 } @ARTICLE{manbet, AUTHOR = "Mancosu, Paolo", TITLE = "Between {R}ussell and {H}ilbert: {B}ehmann on the Foundations of Mathematics", JOURNAL = "Bulletin of Symbolic Logic", YEAR = 1999, VOLUME = 5, PAGES = "303--330", URL = "http://ezproxy.library.arizona.edu/login?url=http://links.jstor.org/sici?sici=1079-8986%28199909%295%3A3%3C303%3ABRAHBO%3E2.0.CO%3B2-0" } @ARTICLE{manmet, AUTHOR = "Mancosu, Paolo", TITLE = "The Metaphysics of the Calculus: {A} Foundational Debate in the {P}aris {A}cademy of {S}ciences 1700--1706", JOURNAL = "Historia Mathematica", YEAR = 1989, VOLUME = 16, PAGES = "224--248" } @ARTICLE{geosko, AUTHOR = "George, Alexander", TITLE = {Skolem and the {L}\"{o}wenheim-{S}kolem Theorem: {A} Case Study of the Philosophical Significance of Mathematical Results}, PAGES = "75--89", JOURNAL = "History and Philosophy of Logic", YEAR = 1985, VOLUME = 6 } @BOOK{medsce, AUTHOR = "Medvedev, Fyodor A.", TITLE = "Scenes from the History of Real Functions", PUBLISHER = {Birkh\"{a}user}, ADDRESS = {Boston}, YEAR = 1991, SERIES = "Science Networks---Historical Studies", NUMBER = 7, NOTE = "Translated from the Russian work of 1975 by Roger Cooke, with corrections and new references supplied by the author"} @ARTICLE{benfou, AUTHOR = "Van Bendegem, Jean Paul", TITLE = "Foundations of Mathematics Or Mathematical Practice: {I}s One Forced to Choose", JOURNAL = "Philosophica", YEAR = 1989, VOLUME = 43, PAGES = "197--213" } @ARTICLE{geogol, AUTHOR = "George, Alexander", TITLE = {Goldbach's Conjecture Can Be Decided in One Minute: {O}n an Alleged Problem for Intuitionism}, PAGES = "187--189", JOURNAL = "Proceedings of the Aristotelian Society", YEAR = "1990--1991", VOLUME = "91, Part 2" } @BOOK{vopmat, AUTHOR = {Vop\v{e}nka, Petr}, TITLE = "Mathematics in the Alternative Set Theory", PUBLISHER = {Teubner Verlagsgesellschaft}, ADDRESS = {Leipzig}, YEAR = 1979 } @BOOK{cancon, AUTHOR = "Cantor, Georg", TITLE = "Contributions to the Founding of the Theory of Transfinite Numbers", PUBLISHER = {Open Court Publishing Company}, ADDRESS = {Chicago}, YEAR = 1915, NOTE = {Translation of [Can95] and [Can97] by Philip E. B. Jourdain. With an introduction by the translator. Reprinted by Dover Publications (New York, 1955)} } @MISC{jouint, AUTHOR = "Jourdain, Philip E. B.", YEAR = 1915, PAGES = "1--85", HOWPUBLISHED = "Introduction to [Can15]" } @ARTICLE{canbei1, AUTHOR = "Cantor, Georg", TITLE = {Beitr\"{a}ge zur {B}egr\"{u}ndung der transfiniten {M}engenlehre, {I} }, JOURNAL = "Mathematische Annalen", YEAR = 1895, VOLUME = 46, PAGES = "481--512", NOTE = "Reprinted as pp.~282--311 [Can32b] and translated in [Can15]" } @ARTICLE{canbei2, AUTHOR = "Cantor, Georg", TITLE = {Beitr\"{a}ge zur {B}egr\"{u}ndung der transfiniten {M}engenlehre, {II} }, JOURNAL = "Mathematische Annalen", YEAR = 1897, VOLUME = 49, PAGES = "207--246", NOTE = "Reprinted as pp.~312--351 [Can32b] and translated in [Can15]" } @ARTICLE{canmit, AUTHOR = "Cantor, Georg", TITLE = {Mitteilungen zur {L}ehre vom {T}ransfiniten}, PAGES = "81--125", JOURNAL = {Zeitschrift f\"{u}r {P}hilosophie und philosophische {K}ritik}, YEAR = "1887", VOLUME = 91, NOTE = "All page references are to the reprinting in [Can32b]" } @ARTICLE{canune3, AUTHOR = "Cantor, Georg", TITLE = {Ueber unendliche, lineare {P}unktmannigfaltigkeiten, 3}, PAGES = "113--121", JOURNAL = {Mathematische Annalen}, YEAR = "1882", VOLUME = 20, NOTE = "All page references are to the reprinting as pp.~149--157 [Can32b]" } @ARTICLE{canune6, AUTHOR = "Cantor, Georg", TITLE = {Ueber unendliche, lineare {P}unktmannigfaltigkeiten, 6}, PAGES = "453--488", JOURNAL = {Mathematische Annalen}, YEAR = 1884, VOLUME = 23, NOTE = "All page references are to the reprinting as pp.~210--244 [Can32b]" } @BOOK{frecol, AUTHOR = "Frege, Gottlob", TITLE = "Collected Papers on Mathematics, Logic, and Philosophy", PUBLISHER = {Basil Blackwell Publishers}, ADDRESS = {New York}, YEAR = 1984, NOTE = "Edited by Brian McGuinness " } @Book{fregru, author = {Frege, Gottlob}, title = {Die Grundlagen der Arithmetik. Eine logisch-mathematische Untersuchung \"{u}ber den Begriff der Zahlen}, publisher = {W. Kochner}, year = {1884}, address = {Breslau}, note = {Translated in bilingual edition as {\em The Foundations of Arithmetic\/} by John L. Austin (Basil Blackwell, Oxford, 1950).} } @article{frekri, AUTHOR = "Frege, Gottlob", TITLE = {Kritische {B}eleuchtung einiger {P}unkte in {E}. {S}chr\"{o}der's { {V}orlesungen \"{u}ber die {A}lgebra der {L}ogik\/} }, PAGES = "433--456", JOURNAL = {Archiv f\"{u}r systematische {P}hilosophie}, YEAR = 1895, VOLUME = 1, NOTE = "All page references are to the translation by Peter Thomas Geach, pp.~210--228 [Fre84]"} @ARTICLE{godmet, AUTHOR = {G\"{o}del, Kurt}, TITLE = {Einige metamathematische {R}esultate \"{u}ber {E}ntscheidungsdefinitheit und {W}iderspruchsfreiheit}, JOURNAL = "Anzeiger der Akademie der Wissenschaften in Wien", YEAR = 1930, VOLUME = 67, PAGES = "214--215", NOTE = "Translated by Stefan Bauer-Mengelberg as pp.~595--596 [vH67]" } @ARTICLE{godsko, AUTHOR = {G\"{o}del, Kurt}, TITLE = {Review of [{S}ko33]}, JOURNAL = {Zentralblatt f\"{u}r Mathematik und ihre Grenzgebiete}, YEAR = 1934, VOLUME = 7, PAGES = "193--194", NOTE = {Translated as Vol. 1, pp.~379, 381 [G\"{o}d90]} } @BOOK{parsel, AUTHOR = "Parsons, Charles", TITLE = "Mathematics in Philosophy; Selected Essays", PUBLISHER = {Cornell University Press}, ADDRESS = {Ithaca, New York}, YEAR = 1983 } @BOOK{rusess, AUTHOR = "Russell, Bertrand", PAGES = "135--164", TITLE = {Essays in Analysis}, PUBLISHER = {George Braziller}, ADDRESS = {New York}, YEAR = 1973, NOTE = "Edited by Douglas Lackey" } @ARTICLE{russom, AUTHOR = "Russell, Bertrand", TITLE = "On Some Difficulties in the Theory of Transfinite Numbers and Order Types", PAGES = "29--53", JOURNAL = "Proceedings of the London Mathematical Society", YEAR = 1905, VOLUME = "2nd series, 4", NOTE = "Reprinted as pp.~135--164 [Rus73]"} @BOOK{berwor, AUTHOR = "Berkeley, George", TITLE = "The Works of George Berkeley Bishop of Cloyne", PUBLISHER = {Thomas Nelson and Sons}, YEAR = 1951, NOTE = "Edited by A. A. Luce. Reprinted by Kraus Reprint (Nendeln, Liechtenstein) 1979" } @BOOKLET{berana, AUTHOR = "Berkeley, George", TITLE = "The Analyst", YEAR = 1734, ADDRESS = "London and Dublin", NOTE = "All page references are to the reprinting as Vol.~4, pp.~65--102 [Ber51]" } @BOOK{lavund, AUTHOR = sml, TITLE = "Understanding the Infinite", PUBLISHER = {Harvard University Press}, ADDRESS = {Cambridge, Massachusetts}, YEAR = 1994, NOTE = "Paperback edition 1998. Spanish translation {\em Comprendiendo el Infinito\/} (Fondo de Cultura Economica USA, San Diego, California, 2006). Mathematical Reviews 95k:60009." } @MISC{norson, AUTHOR = "Martin, Norman L.", YEAR = "1989--1991", TITLE = "The Song that Doesn't End", HOWPUBLISHED = "Norman Martin Music (BMI)"} @INCOLLECTION{fieare, AUTHOR = field, TITLE = "Are Our Logical and Mathematical Concepts Highly Indeterminate? ", BOOKTITLE = "Philosophical Naturalism", PUBLISHER = {University of Notre Dame Press}, ADDRESS = {Notre Dame, Indiana, U. S. A.}, YEAR = 1994, EDITOR = "French, Peter A. and Uehling, Jr., Theodore E. and Wettstein, Howard K.", PAGES = "391--429", SERIES = "Midwest Studies in Philosophy", NUMBER = 19 } @BOOK{carphi, AUTHOR = "Carnap, Rudolf", TITLE = "Philosophy and Logical Syntax", PUBLISHER = {Kegan Paul, Trench, Trubner \& Co.}, ADDRESS = {London}, YEAR = 1935, SERIES = "Psyche Miniatures, General Series", NUMBER = 70} @BOOK{carint, AUTHOR = "Carnap, Rudolf", TITLE = "Introduction to Semantics", PUBLISHER = {Harvard University Press}, ADDRESS = {Cambridge, Mass.}, YEAR = 1942} @BOOK{quiset, AUTHOR = quine, TITLE = "Set Theory and Its Logic", PUBLISHER = {The Belknap Press of Harvard University Press}, ADDRESS = {Cambridge, Mass.}, YEAR = "1963 and 1969", EDITION = "revised"} @BOOK{schhasgru, AUTHOR = "Scholz, Heinrich and Hasenjaeger, Gisbert", TITLE = {Grundz\"{u}ge der Mathematischen Logik}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = 1961, SERIES = "Die Grundlehren der Mathematischen Wissenschaften", NUMBER = 106} @BOOK{tarlog, AUTHOR = "Tarski, Alfred", TITLE = "Logic Semantics, Metamathematics", PUBLISHER = {Hackett Publishing Co.}, ADDRESS = {Indianapolis, Ind.}, YEAR = "1983", EDITION = "second", NOTE = "Translated by J. H. Woodger. Second edition edited and introduced by John Corcoran"} @BOOK{tartru, AUTHOR = "Tarski, Alfred", TITLE = { {\em Poj\c{e}cie prawdy w j\c{e}zykach nauk dedukcyjnych\/} (On the concept of truth in languages of deductive sciences)}, ADDRESS = {Warsaw}, YEAR = "1933", PUBLISHER = {Nak\l .\t{\ }{T}ow. Naukowego Warszawskiego}, SERIES = {Prace Towarzystwa Naukowego Warszawskiego Wydzia\l \ {III}---Nauk Matematyczno-fizycznych}, NUMBER = 34, NOTE = "In Polish. All page references are to the revised translation published as ``The concept of truth in formalized languages,'' pp. 152--278 of [Tar83]"} @BOOK{prifor, AUTHOR = "Prior, A. N.", TITLE = {Formal Logic}, PUBLISHER = {Oxford at the Clarendon Press}, ADDRESS = {London}, YEAR = "1955"} @BOOK{shebou, AUTHOR = "Sher, Gila", TITLE = "The Bounds of Logic: {A} Generalized Viewpoint", PUBLISHER = {MIT Press}, ADDRESS = {Cambridge, Mass.}, YEAR = 1991 } @BOOK{haaphi, AUTHOR = "Haack, Susan", TITLE = "Philosophy of Logics", PUBLISHER = {Cambridge University Press}, ADDRESS = {New York}, YEAR = 1978 } @BOOK{kosstr, AUTHOR = "Koslow, Arnold", TITLE = "A Structuralist Theory of Logic", PUBLISHER = {Cambridge University Press}, ADDRESS = {New York}, YEAR = 1992 } NUMBER = 70} @BOOK{carlog, AUTHOR = "Carnap, Rudolf", TITLE = "Logische Syntax der Sprache", PUBLISHER = {Verlag von Julius Springer}, ADDRESS = {Vienna}, YEAR = 1934, SERIES = "Schriften zur wissenschaftlichen Weltauffassung", NUMBER = 8, NOTE = "In German. An English translation forms the bulk of Carnap (1937). Carnap (1935) discusses many of the same ideas in a less technical way"} @BOOK{carloge, AUTHOR = "Carnap, Rudolf", TITLE = "Logical Syntax of Language", PUBLISHER = {Kegan Paul}, ADDRESS = {London}, YEAR = 1937, SERIES = "International Library of Psychology, Philosophy, and Scientific Method", NOTE = "An English translation, with additions, of Carnap (1934) by Amethe Smeaton (Countess von Zeppelin)"} @ARTICLE{tarcon, AUTHOR = "Tarski, Alfred", TITLE = "O pojciu wynikania logicznego ({O}n the Concept of Logical Consequence)", JOURNAL = "Przegl\c{a}d Filozoficzny", YEAR = 1936, VOLUME = 39, PAGES = "58--68", NOTE = "In Polish. All page references are to the English translation that appears as pp. 409--420 of [Tar83]"} @BOOK{bolwis, AUTHOR = "Bolzano, Bernard", TITLE = "Wissenschaftslehre", PUBLISHER = {Scientia Verlag Aalen}, ADDRESS = {Darmstadt}, YEAR = 1970, NOTE = "Reprint of the second edition (F. Meiner, Leipzig, 1929--1931)"} @BOOK{marmod, AUTHOR = "Marcus, Ruth Barcan", TITLE = "Modalities: Philosophical Essays", PUBLISHER = {Oxford University Press}, ADDRESS = {New York}, YEAR = 1993 } @ARTICLE{marint, AUTHOR = {Marcus, Ruth Barcan}, TITLE = "Modalities and Intensional Languages", JOURNAL = "Synthese", YEAR = 1961, VOLUME = 13, PAGES = "303--322", NOTE = {All page references are to the reprinting of the corrected version as pp.~5--23 of [Mar93]} } @BOOK{quipur, AUTHOR = quine, TITLE = "Pursuit of Truth", PUBLISHER = {Harvard University Press}, ADDRESS = {Cambridge, Mass.}, YEAR = "1990 and 1992", EDITION = "revised"} @ARTICLE{marquikridis, AUTHOR = {Marcus, Ruth Barcan and Quine, Willard Van Orman and Kripke, Saul A. and McCarthy , J. and F{\o}llesdal, Dagfin}, TITLE = "Modalities and Intensional Languages: Discussion", JOURNAL = "Synthese", YEAR = 1962, VOLUME = 14, PAGES = "132--143", NOTE = {All page references are to the reprinting as pp.~24--35 [Mar93]}, URL = "http://www.springerlink.com.ezproxy.library.arizona.edu/content/x367445012t2337n/fulltext.pdf" } @ARTICLE{marpos, AUTHOR = {Marcus, Ruth Barcan}, TITLE = "Possibilia and Possible Worlds", JOURNAL = "Grazer Philosophische Studien", YEAR = "1985--1986", VOLUME = "25/26", PAGES = "107--133", NOTE = {All page references are to the reprinting of the corrected version as pp.~190--213 of [Mar93]} } @INCOLLECTION{marbac, AUTHOR = "Marcus, Ruth Barcan", TITLE = "A Backward Look at {Q}uine's Animadversions on Modalities", BOOKTITLE = "Perspectives on Quine", PUBLISHER = {Basil Blackwell Publishers}, ADDRESS = {Cambridge, Massachusetts}, YEAR = 1990, EDITOR = "Barrett, Robert B. and Gibson, Roger F.", PAGES = "230--243", NOTE = {Proceedings of the conference, ``Perspectives on Quine,'' organized by Robert B. Barrett and Roger F. Gibson, April 1988, Washington University in St. Louis. All page references are to the reprinting as pp.~216--232 of [Mar93]} } @ARTICLE{jacont, AUTHOR = {Jackson, Frank}, TITLE = "Ontological Commitment and Paraphrase", JOURNAL = "Philosophy: The Journal of the Royal Institute of Philosophy", YEAR = 1980, VOLUME = 55, PAGES = "303--315", URL = "http://ezproxy.library.arizona.edu/login/up?url=http://links.jstor.org/sici?sici=0031-8191%28198007%2955%3A213%3C303%3AOCAP%3E2.0.CO%3B2-U" } @INCOLLECTION{quirei, AUTHOR = quine, TITLE = "Logic and the Reification of Universals", BOOKTITLE = "From a Logical Point of View: Logico-Philosophical Essays", PUBLISHER = {Harper Torchbooks, Harper \& Row}, ADDRESS = {New York}, EDITION = "second, revised", YEAR = 1961, EDITION = "second, revised", PAGES = "102--129" } @ARTICLE{quionw, AUTHOR = quine, TITLE = "On What There Is", JOURNAL = "Review of Metaphysics", YEAR = "1948", VOLUME = "2", PAGES = "21--38", URL = {http://www.jstor.org.ezproxy1.library.arizona.edu/stable/20123117}, NOTE = {All page references are to the reprinting with minor changes as pp.~1--19 of [Qui61a]} , NOTE = {The article was reprinted, with minor changes and added footnotes, as 1–19 of ShaughanLavine - 15 Feb 2010 - 20:19 - 1.173 " class="twikiCurrentTopicLink twikiAnchorLink">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.}, } @ARTICLE{quilog, AUTHOR = quine, TITLE = "On the Logic of Quantification", JOURNAL = jsl, YEAR = "1945", VOLUME = "10", PAGES = "1--12", URL={http://www.jstor.org.ezproxy1.library.arizona.edu/stable/pdfplus/2267200.pdf} } @ARTICLE{quisym, AUTHOR = quine, TITLE = {Symposium: On What There Is, {III} }, PAGES = "149--160", JOURNAL = "Proceedings of the Aristotelian Society", YEAR = "1951", VOLUME = "supplementary volume 25", NOTE = "Joint Session of the Aristotelian Society and the Mind Association at the University of Edinburgh, 1951. Symposiasts: Peter Thomas Geach, Alfred Jules Ayer, Willard Van Orman Quine", PUBLISHER = "Harrison and Sons, Ltd.", ADDRESS = "London" } @BOOK{sexadv, AUTHOR = "Sextus Empiricus", TITLE = "Against the Logicians", PUBLISHER = {Harvard University Press}, ADDRESS = {Cambridge, Massachusetts}, YEAR = 1935, SERIES = "Loeb Classical Library", VOLUME = 2, NOTE = "Translated by the Reverend R. G. Bury" } @BOOK{gearef, AUTHOR = geach, TITLE = "Reference and Generality: An Examination of Some Medieval and Modern Theories", PUBLISHER = {Cornell University Press}, ADDRESS = {Ithaca, New York}, YEAR = 1980, EDITION = "third", NOTE = "First edition 1962, emended edition 1968" } @INCOLLECTION{oreexp, AUTHOR = "Orenstein, Alex", TITLE = "On Explicating Existence in Terms of Quantification", BOOKTITLE = "Logic and Ontology", PUBLISHER = {New York University Press}, ADDRESS = {New York}, YEAR = 1973, EDITOR = "Munitz, Milton K.", PAGES = "59--84" } @BOOK{quiroo, AUTHOR = quine, TITLE = "Roots of Reference", PUBLISHER = {Open Court}, ADDRESS = {La Salle, Illinois}, YEAR = 1973, SERIES = "Paul Carus Lectures", NUMBER = 14 } @ARTICLE{quivarexp, AUTHOR = quine, TITLE = "Variables Explained Away", JOURNAL = "Proceedings of the American Philosophical Society", YEAR = "1960", VOLUME = "104", PAGES = "343--347", NOTE = {All page references are to the reprinting as pp.~227--235 of [Qui66]}, URL= "http://ezproxy.library.arizona.edu/login?url=http://links.jstor.org/sici?sici=0003-049X%2819600615%29104%3A3%3C343%3AVEA%3E2.0.CO%3B2-W" } @BOOK{quisel, AUTHOR = quine, TITLE = "Selected Logic Papers", PUBLISHER = {Random House}, ADDRESS = {New York}, YEAR = 1966 } @ARTICLE{tarfun, AUTHOR = "Tarski, Alfred", TITLE = {\"{U}ber einige fundamentale {B}egriffe der {M}athematik ({O}n Some Fundamental Concepts of Metamathematics)}, JOURNAL = "Comptes Rendu des s\'{e}ances de la Soci\'{e}t\'{e} des Sciences et des Lettres de Varsovie", YEAR = 1930, VOLUME = 23, PAGES = "22--29", NOTE = "In German. All page references are to the English translation that appears as pp. 30--37 of [Tar83]"} @ARTICLE{tarsom, AUTHOR = "Tarski, Alfred", TITLE = "Z bada\'{n} metodologicznych nad definiowalno\'{s}c\c{a} termin\'{o}w ({S}ome Methodological Investigations on the Definability of Concepts)", JOURNAL = "Przegl\c{a}d Filozoficzny", YEAR = 1934, VOLUME = 37, PAGES = "438--460", NOTE = "In Polish. All page references are to the English translation that appears as pp. 296--319 of [Tar83]"} @INCOLLECTION{lavpre, AUTHOR = sml, TITLE = "Predicate Calculus", EDITOR = "Craig {\em et al.\/}, Edward", BOOKTITLE = "Routledge Encyclopedia of Philosophy", PUBLISHER = {Routledge}, ADDRESS = {New York}, YEAR = "1998" } @INCOLLECTION{lavsec, AUTHOR = sml, TITLE = "Second and Higher-Order Logics", EDITOR = "Craig {\em et al.\/}, Edward", BOOKTITLE = "Routledge Encyclopedia of Philosophy", PUBLISHER = {Routledge}, ADDRESS = {New York}, YEAR = "1998" } @ARTICLE{quimar, AUTHOR = quine, TITLE = "Reply to {P}rofessor {M}arcus", JOURNAL = "Synthese", YEAR = 1961, VOLUME = 13, PAGES = "323--330", NOTE = {All page references are to the reprinting as pp.~177--184 of [Qui76b]} } @ARTICLE{quionc, AUTHOR = quine, TITLE = "On {C}arnap's Views on Ontology", JOURNAL = "Philosophical Studies", YEAR = 1951, VOLUME = 2, PAGES = "65--72", NOTE = {Reprinted as pp.~126--134 of ShaughanLavine - 15 Feb 2010 - 20:19 - 1.173 " class="twikiCurrentTopicLink twikiAnchorLink">Qui66}, URL = {http://www.jstor.org.ezproxy1.library.arizona.edu/stable/4318118} } @BOOK{quiway, AUTHOR = quine, TITLE = "Ways of Paradox and Other Essays", PUBLISHER = {Random House}, ADDRESS = {New York}, YEAR = 1966, NOTE = "Revised and enlarged editions issued by {H}arvard {U}niversity {P}ress, {C}ambridge, {M}ass. in 1976 and 2006"} @INCOLLECTION{quivar, AUTHOR = quine, TITLE = "The Variable", BOOKTITLE = "Ways of Paradox and Other Essays", PUBLISHER = {Harvard University Press}, ADDRESS = {Cambridge, Massachusetts}, YEAR = 1976, EDITION = "revised and enlarged", PAGES = "272--282" } @INCOLLECTION{quiexi, AUTHOR = quine, TITLE = "Existence and Quantification", BOOKTITLE = "Ontological Relativity and Other Essays", PUBLISHER = {Columbia University Press}, ADDRESS = {New York}, YEAR = 1969, SERIES = "John Dewey Essays in Philosophy", NUMBER = 1, PAGES = "91--113" } @BOOK{quiont, AUTHOR = quine, TITLE = "Ontological Relativity and Other Essays", PUBLISHER = {Columbia University Press}, ADDRESS = {New York}, YEAR = 1969, SERIES = "John Dewey Essays in Philosophy", NUMBER = 1 } @BOOK{gotont, AUTHOR = "Gottlieb, Dale", TITLE = "Ontological Economy: {S}ubstitutional Quantification and Mathematics", PUBLISHER = {Oxford University Press}, ADDRESS = {New York}, YEAR = 1980 } @BOOK{gealog, AUTHOR = geach, TITLE = "Logic Matters", PUBLISHER = {University of California Press}, ADDRESS = {Berkeley, California}, YEAR = 1972 } @BOOKLET{geahis, AUTHOR = geach, TITLE = "History of the Corruptions of Logic: {A}n Inaugural Lecture", NOTE = "All page references are to the reprinting as pp. 44--61 of [Gea72]", YEAR = 1968, PUBLISHER = "Leeds University Press", ADDRESS = "Leeds" } @ARTICLE{geanom, AUTHOR = geach, TITLE = "Nominalism", JOURNAL = "Sophia: A Journal for Discussion in Philosophical Theology", YEAR = 1964, VOLUME = 3, PAGES = "3--14", NOTE = {Journal subtitle varies. All page references are to the reprinting as pp.~289--301 of [Gea72]}, PUBLISHER = "Department of Philosophy, University of Melbourne", Address= "Parkville, Victoria, Australia"} @ARTICLE{geaper, AUTHOR = geach, TITLE = "Perils of {P}auline", JOURNAL = "Review of Metaphysics", YEAR = 1969, VOLUME = 23, PAGES = "287--300", NOTE = {All page references are to the reprinting as pp.~153--165 of [Gea72]} } @ARTICLE{geaide, AUTHOR = geach, TITLE = "Identity", JOURNAL = "Poiesis", YEAR = 1967, VOLUME = 21, PAGES = "3--13", NOTE = {Reprinted as pp.~238--247 of [Geach72]}, URL = "http://poiesis.nlx.com.ezproxy.library.arizona.edu/display.cfm?&clientID=167694&advquery=toc.sect.rvm.21.1&infobase=postoc.nfo&softpage=GetClient42&view=browse&toString=function%20()%20{%20%20%20%20result%20=%20%22%22;%20%20%20%20firstItem%20=%20true;%20%20%20%20for%20(prop%20in%20this)%20{%20%20%20%20%20%20%20%20if%20(firstItem)%20{%20%20%20%20%20%20%20%20%20%20%20%20result%20+=%20%22,%20%22;%20%20%20%20%20%20%20%20}%20else%20{%20%20%20%20%20%20%20%20%20%20%20%20firstItem%20=%20false;%20%20%20%20%20%20%20%20}%20%20%20%20%20%20%20%20result%20+=%20prop%20+%20%22=%22%20+%20this[prop];%20%20%20%20}%20%20%20%20return%20result;}" } @ARTICLE{geaqua, AUTHOR = geach, TITLE = "Quantification Theory and the Problem of Identifying Objects of Reference", JOURNAL = "Acta Philosophica Fennica", YEAR = 1963, VOLUME = 16, PAGES = "41--52", NOTE = {Proceedings of a Colloquium on Modal and Many-Valued Logics, Helsinki, 23--26 August, 1962. All page references are to the slightly rewritten reprinting as pp.~139--146 and 205--209 of [Gea72]} } @BOOK{fraqua, AUTHOR = "van Fraasen, Bas C.", TITLE = "Quantum Mechanics: {A}n Empiricist View", PUBLISHER = {Clarendon Press}, ADDRESS = {Oxford}, YEAR = 1991 } @ARTICLE{hugsayqua, AUTHOR = "Hugly, Philip and Sayward, Charles", TITLE = "Quantifying over the Reals", JOURNAL = "Synthese", YEAR = 1994, VOLUME = 101, PAGES = "53--64" } @BOOK{luslog, AUTHOR = "Luschei, E. C.", TITLE = " The Logical Systems of Le\'{s}niewski", PUBLISHER = {North-Holland Publishing Company}, ADDRESS = {Amsterdam}, YEAR = 1962 } @INCOLLECTION{kriist, AUTHOR = "Kripke, Saul A.", TITLE = "Is There a Problem about Substitutional Quantification?", BOOKTITLE = "Truth and Meaning: {E}ssays in Semantics", PUBLISHER = {Clarendon Press}, ADDRESS = {Oxford}, YEAR = 1976, EDITOR = "Evans, Gareth and McDowell , John", PAGES = "325--419" } @ARTICLE{walfra, AUTHOR = "Wallace, John", TITLE = "On the Frame of Reference", JOURNAL = "Synthese", YEAR = 1970, VOLUME = 22, PAGES = "117--150" } @ARTICLE{parstr, AUTHOR = {Parsons, Charles}, TITLE = "The Structuralist View of Mathematical Objects", JOURNAL = "Synthese", YEAR = 1990, VOLUME = 84, PAGES = "303--346" } @BOOK{krinam, AUTHOR = "Kripke, Saul A.", TITLE = " Naming and Necessity", PUBLISHER = {Basil Blackwell Publishers}, ADDRESS = {Oxford}, YEAR = 1980 } @ARTICLE{geasym, AUTHOR = geach, TITLE = {Symposium: On What There Is, {I} }, PAGES = "125--136", JOURNAL = "Proceedings of the Aristotelian Society", YEAR = "1951", VOLUME = "supplementary volume 25", NOTE = "Joint Session of the Aristotelian Society and the Mind Association at the University of Edinburgh, 1951. Symposiasts: Peter Thomas Geach, Alfred Jules Ayer, Willard Van Orman Quine", PUBLISHER = "Harrison and Sons, Ltd.", ADDRESS = "London" } @BOOK{chicon, AUTHOR = "Chihara, Charles S.", TITLE = {Constructibility and Mathematical Existence}, PUBLISHER = {Clarendon Press and Oxford University Press}, ADDRESS = {Oxford and New York}, YEAR = "1990"} @INCOLLECTION{quiref, AUTHOR = quine, TITLE = "Reference and Modality", PAGES = "139--157", BOOKTITLE = "From a Logical Point of View: Logico-Philosophical Essays", PUBLISHER = {Harper Torchbooks, Harper \& Row}, ADDRESS = {New York}, EDITION = "second, revised", YEAR = 1961 } @Article{fiemet, author = field, title = {Metalogic and Modality}, journal = {Philosophical Studies}, year = {1991}, volume = {62}, pages = {1--22}, url = {http://www.springerlink.com.ezproxy.library.arizona.edu/content/m420547877625433/fulltext.pdf} } @INCOLLECTION{kreinf, AUTHOR = "Kreisel, Georg", TITLE = "Informal Rigour and Completeness Proofs", BOOKTITLE = "Problems in the Philosophy of Mathematics", PUBLISHER = {North Holland}, ADDRESS = {Amsterdam}, YEAR = 1967, EDITOR = "Lakatos, Imre", PAGES = "138--186" } @ARTICLE{mcghow, AUTHOR = {McGee, Vann}, TITLE = {How We Learn Mathematical Language}, JOURNAL = {Philosophical Review}, VOLUME = 106, PAGES = {35--68}, YEAR = 1997 } @ARTICLE{lavqua, AUTHOR = sml, TITLE = {Quantification and Ontology}, JOURNAL = {Synthese}, VOLUME = 124, PAGES = {1--43}, YEAR = 2000, URL = "http://www.springerlink.com.ezproxy.library.arizona.edu/content/tq14591523275132/fulltext.pdf"} @ARTICLE{canune5, AUTHOR = "Cantor, Georg", TITLE = {Ueber unendliche, lineare {P}unktmannigfaltigkeiten, 5}, PAGES = "545--586", JOURNAL = {Mathematische Annalen}, YEAR = "1883", VOLUME = 21, NOTE = "Reprinted as pp.~165--204 [Can32]" } @ARTICLE{fefdoe, AUTHOR = {Feferman, Solomon}, TITLE = {Does Mathematics Need New Axioms?}, JOURNAL = {American Mathematical Monthly}, VOLUME = 106, PAGES = {99-111}, YEAR = 1999 } @ARTICLE{harqui1, AUTHOR = {Harman, Gilbert}, TITLE = "Quine on Meaning and Existence, {I}", JOURNAL = "Review of Metaphysics", YEAR = "1967", VOLUME = "21", PAGES = "124--152", URL = "http://poiesis.nlx.com.ezproxy.library.arizona.edu/display.cfm?&clientID=167694&advquery=toc.sect.rvm.21.1&infobase=postoc.nfo&softpage=GetClient42&view=browse&toString=function%20()%20{%20%20%20%20result%20=%20%22%22;%20%20%20%20firstItem%20=%20true;%20%20%20%20for%20(prop%20in%20this)%20{%20%20%20%20%20%20%20%20if%20(firstItem)%20{%20%20%20%20%20%20%20%20%20%20%20%20result%20+=%20%22,%20%22;%20%20%20%20%20%20%20%20}%20else%20{%20%20%20%20%20%20%20%20%20%20%20%20firstItem%20=%20false;%20%20%20%20%20%20%20%20}%20%20%20%20%20%20%20%20result%20+=%20prop%20+%20%22=%22%20+%20this[prop];%20%20%20%20}%20%20%20%20return%20result;}" } @ARTICLE{harqui2, AUTHOR = {Harman, Gilbert}, TITLE = "Quine on Meaning and Existence, {II}", JOURNAL = "Review of Metaphysics", YEAR = "1967", VOLUME = "21", PAGES = "343--367", URL = "http://poiesis.nlx.com.ezproxy.library.arizona.edu/display.cfm?&clientID=167512&advquery=toc.sect.rvm.21.2&infobase=postoc.nfo&softpage=GetClient42&view=browse&toString=function%20()%20{%20%20%20%20result%20=%20%22%22;%20%20%20%20firstItem%20=%20true;%20%20%20%20for%20(prop%20in%20this)%20{%20%20%20%20%20%20%20%20if%20(firstItem)%20{%20%20%20%20%20%20%20%20%20%20%20%20result%20+=%20%22,%20%22;%20%20%20%20%20%20%20%20}%20else%20{%20%20%20%20%20%20%20%20%20%20%20%20firstItem%20=%20false;%20%20%20%20%20%20%20%20}%20%20%20%20%20%20%20%20result%20+=%20prop%20+%20%22=%22%20+%20this[prop];%20%20%20%20}%20%20%20%20return%20result;}" }

@BOOK{thosym, AUTHOR = "Thomason, Richmond H.", TITLE = {Symbolic Logic: {A}n Introduction}, PUBLISHER = {The Macmillan Company}, ADDRESS = {Toronto, Ontario, Canada}, YEAR = "1970"} @ARTICLE{balint, AUTHOR = "Baldwin, Thomas", TITLE = "Interpretations of Quantifiers", PAGES = "215--240", JOURNAL = "Mind", YEAR = 1979, VOLUME = "n.s. 88" } @ARTICLE{finmcctru, AUTHOR = "Fine, Kit and McCarthy , Timothy", TITLE = "Truth without Satisfaction", JOURNAL = "Journal of Philosophical Logic", YEAR = 1984, VOLUME = 13, PAGES = "397--421", URL = "http://www.springerlink.com.ezproxy.library.arizona.edu/content/k4m956060m625u12/fulltext.pdf" } @BOOK{dumfrelan, AUTHOR = dummett, TITLE = {Frege: {P}hilosophy of Language}, PUBLISHER = {Harvard University Press}, ADDRESS = {Cambridge, Massachusetts}, EDITION = "second", YEAR = "1981"} @BOOK{dumfremat, AUTHOR = dummett, TITLE = {Frege: {P}hilosophy of Mathematics}, PUBLISHER = duckworth, ADDRESS = {London}, YEAR = "1991"} @INCOLLECTION{orepla, AUTHOR = "Orenstein, Alex", TITLE = "Plato's Beard, {Q}uine's Stubble, and {L}e\'{s}niewski's Razor", BOOKTITLE = "Knowledge, Language and Logic: Questions for Quine", PUBLISHER = {Kluwer Academic Publishers}, ADDRESS = {Dordrecht, The Netherlands}, YEAR = 1999, EDITOR = "Orenstein, Alex and Kotatko, Petr", SERIES = "Boston Studies in the Philosophy of Science", NUMBER = 210 } @ARTICLE{gotmccsub, AUTHOR = "Gottlieb, Dale and McCarthy , Timothy", TITLE = "Substitutional Quantification and Set Theory", JOURNAL = "Journal of Philosophical Logic", YEAR = 1979, VOLUME = 8, PAGES = "315--331", URL = "http://www.springerlink.com.ezproxy.library.arizona.edu/content/rq1h2754854v7856/fulltext.pdf" } @ARTICLE{gotmccsub, AUTHOR = "McCarthy, Timothy", TITLE = "Representation, intentionality, and quantifiers", JOURNAL = "Synthese", YEAR = 1984, VOLUME = 60, PAGES = "369--411", URL = "http://www.springerlink.com.ezproxy.library.arizona.edu/content/r84886211k536141/fulltext.pdf" } @ARTICLE{oreref, AUTHOR = "Orenstein, Alex", TITLE = "Referential and Nonreferential Substitutional Quantifiers", JOURNAL = "Synthese", VOLUME = 60, YEAR = 1984, PAGES = "145--157"} @ARTICLE{orehow, AUTHOR = "Orenstein, Alex", TITLE = {How to Get Something from Nothing}, PAGES = "93--112", JOURNAL = "Proceedings of the Aristotelian Society", YEAR = "1994--1995", VOLUME = "n.s. 95" } @ARTICLE{strlog, AUTHOR = "Strawson, Peter F.", TITLE = {A Logician's Landscape}, PAGES = "229--237", JOURNAL = "Philosophy (The Journal of the Royal Institute of Philosophy)", YEAR = "1955", VOLUME = "30" } @BOOK{matele, AUTHOR = {Mates, Benson}, TITLE = {Elementary Logic}, PUBLISHER = {Oxford University Press}, ADDRESS = {New York}, EDITION = "second", YEAR = "1972"} @BOOK{harcon, AUTHOR = {Hart, H. L. A.}, TITLE = {The Concept of Law}, SERIES = {Clarendon Law Series}, PUBLISHER = {Clarendon Press}, ADDRESS = {Oxford}, EDITION = "second", YEAR = "1994", NOTE = "Reissue with minor corrections of the 1961 edition with a new postscript edited by Penelope A. Bulloch and Joseph Raz."} @BOOK{etccon, AUTHOR = {Etchemendy, John}, TITLE = {The Concept of Logical Consequence}, PUBLISHER = {Harvard University Press}, ADDRESS = {Cambridge, Massachusetts}, YEAR = "1990"} @INCOLLECTION{orequa, AUTHOR = {Orenstein, Alex}, TITLE = "Quality, Not Quantitity, Determines Existential Import", BOOKTITLE = "Logique en perspective. M\'{e}langes offerts au professeur Gochet", PUBLISHER = {\'{E}ditions Ousia}, ADDRESS = {Brussels}, YEAR = "forthcoming", EDITOR = "Beets, Fran\c{c}ois and Gillet, Eric" } @BOOK{katrea, TITLE = "Realistic Rationalism", PUBLISHER = {A Bradford Book, MIT Press}, ADDRESS = {Cambridge, Massachusetts}, YEAR = 1998, AUTHOR = "Katz, Jerrold J.", SERIES = "Representation and Mind series" } @INCOLLECTION{musari, AUTHOR = "Musgrave, Alan", TITLE = "Arithmetical {P}latonism: {I}s {W}right wrong or must {F}ield yield?", PAGES = "90--110", EDITOR = "M. Fricke", BOOKTITLE = {Essays in Honor of Bob Durrant}, PUBLISHER = {Otago University Press}, ADDRESS = {Dunedin, New Zealand}, YEAR = 1986} @ARTICLE{sobmat, AUTHOR = "Sober, Elliott", TITLE = {Mathematics and Indispensability}, PAGES = "35--57", JOURNAL = "Philosophical Review", YEAR = "1993", VOLUME = "102" } @INCOLLECTION{mcgeve, AUTHOR = "McGee, Vann", TITLE = {`{E}verything'}, PAGES = "54--78", EDITOR = "Sher, Gila and Tieszen, Richard", BOOKTITLE = {Between Logic and Intuition: Essays in Honor of Charles Parsons}, PUBLISHER = {Cambridge University Press}, ADDRESS = {New York}, YEAR = 2000} @ARTICLE{quionta, AUTHOR = quine, TITLE = "Ontological Relativity", JOURNAL = jop, YEAR = 1968, VOLUME = 65, PAGES = "185--212", NOTE = {All page references are to the reprinting as pp.~26--68 of [Qui69c]}, NOTE = {Reprinted as pp.~26--68 of [Quine69c]}, URL = {http://ezproxy.library.arizona.edu/login?url=http://links.jstor.org/sici?sici=0022-362X%2819680404%2965%3A7%3C185%3AOR%3E2.0.CO%3B2-G} } @ARTICLE{quiontw, AUTHOR = quine, TITLE = "Ontological Reduction and the World of Numbers", JOURNAL = jop, YEAR = 1964, VOLUME = 61, PAGES = "185--212", NOTE = {Reprinted as pp.~212--220 of the 2006 revised edition of [Qui66]}, URL = {http://ezproxy.library.arizona.edu/login?url=http://links.jstor.org/sici?sici=0022-362X%2819640326%2961%3A7%3C209%3AORATWO%3E2.0.CO%3B2-U} } @ARTICLE{skolog, AUTHOR = "Skolem, Thoralf", TITLE = {Logische-kombinatorische {U}ntersuchungen \"{u}ber die {E}rf\"{u}llbarkeit und {B}eweisbarkeit mathematischen {S}\"{a}tze nebst einem {T}heoreme \"{u}ber dichte {M}engen ({L}ogico-combinatorial investigations in the satisfiability or provability of mathematical propositions: {A} simplified proof of a theorem by {L}. {L}\"{o}wenheim and generalizations of the theorem)}, JOURNAL = {Skrifter, Videnskabsakademiet i Kristiania, {I} }, YEAR = 1920, NUMBER = 4, PAGES = "1--36", NOTE = {All page references are to the translation of \S 1 by Stefan Bauer-Mengelberg printed as pp.~254--263 of [vH67]} } @INCOLLECTION{quitru, AUTHOR = quine, TITLE = {Truth by Convention}, PAGES = "90--124", EDITOR = "Lee, Otis H.", BOOKTITLE = {Philosophical Essays for Alfred North Whitehead}, PUBLISHER = {Longmans, Green}, ADDRESS = {New York}, YEAR = 1936, NOTE = "All page references are to the corrected reprinting as pp.~329--354 of [BP83]"} @INCOLLECTION{bursem, AUTHOR = "Burge, Tyler", TITLE = {Semantical Paradox}, PAGES = "85--117", EDITOR = "Martin, Robert L.", BOOKTITLE = {Recent Essays on Truth and the Liar Paradox}, PUBLISHER = {Oxford University Press}, ADDRESS = {New York}, YEAR = 1984 } @ARTICLE{goldis, AUTHOR = "Goldman, Alvin I.", TITLE = "Discrimination and Perceptual Knowledge", JOURNAL = jop, YEAR = 1976, VOLUME = 73, PAGES = "771--791" } @ARTICLE{belton, AUTHOR = "Belnap, Nuel D.", TITLE = "Tonk, Plonk and Plink", JOURNAL = "Analysis", YEAR = 1962, VOLUME = 22, PAGES = "130--134", URL = {http://www.jstor.org.ezproxy2.library.arizona.edu/stable/pdfplus/3326862.pdf} } @BOOK{lewcou, TITLE = "Counterfactuals", PUBLISHER = {Blackwell Publishers}, ADDRESS = {Oxford}, YEAR = 1973, AUTHOR = "Lewis, David K." } @ARTICLE{quiwa, AUTHOR = quine, TITLE = "Worlds Away", JOURNAL = jop, YEAR = 1976, VOLUME = 73, PAGES = "859--863" } @INCOLLECTION{madleg, AUTHOR = "Maddy, Penelope", TITLE = "The Legacy of `Mathematical Truth'", BOOKTITLE = "Benacerraf and His Critics", PUBLISHER = {Blackwell Publishers Ltd.}, ADDRESS = {Oxford}, YEAR = 1996, EDITOR = "Morton, Adam and Stich, Stephen P.", PAGES = "60--72", SERIES = "Philosophers and Their Critics" } @INPROCEEDINGS{mcgmcldis, AUTHOR = "McGee, Vann and McLaughlin , Brian", TITLE = "Distinctions Without a Difference", BOOKTITLE = "Spindel Conference 1994: Vagueness", PUBLISHER = {The Department of Philosophy, The University of Memphis}, ADDRESS = { Memphis, Tennessee}, YEAR = 1995, EDITOR = "Horgan, Terry", PAGES = "203--251", SERIES = "Supplement to The Southern Journal of Philosophy (1994), Vol. XXXIII" } @MISC{mcgles, AUTHOR = "McGee, Vann and McLaughlin , Brian", TITLE = "The Lessons of the Many", JOURNAL = "Philosophical Topics", YEAR = 2000, VOLUME = 28, PAGES = "129--151"} @INPROCEEDINGS{wriepi, AUTHOR = "Wright, Crispin", TITLE = "The Epistemic Conception of Vagueness", BOOKTITLE = "Spindel Conference 1994: Vagueness", PUBLISHER = {The Department of Philosophy, The University of Memphis}, ADDRESS = { Memphis, Tennessee}, YEAR = 1995, EDITOR = "Horgan, Terry", PAGES = "133--159", SERIES = "Supplement to The Southern Journal of Philosophy (1994), Vol. XXXIII" } @ARTICLE{shaall, AUTHOR = "Shapiro, Stewart", TITLE = " All Sets Great and Small: and {I} Do Mean All", JOURNAL = "Philosophical Perspectives", YEAR = 2003, VOLUME = 17, PAGES = "467--489" } @ARTICLE{wileve, AUTHOR = "Williamson, Timothy", TITLE = "Everything", JOURNAL = "Philosophical Perspectives", YEAR = 2003, VOLUME = 17, PAGES = "415--465" } @BOOK{wilvag, TITLE = "Vagueness", PUBLISHER = {Routledge}, ADDRESS = {New York}, YEAR = 1994, AUTHOR = "Williamson, Timothy" } @INPROCEEDINGS{wildef, AUTHOR = "Williamson, Timothy", TITLE = "Definiteness and Knowability", BOOKTITLE = "Spindel Conference 1994: Vagueness", PUBLISHER = {The Department of Philosophy, The University of Memphis}, ADDRESS = { Memphis, Tennessee}, YEAR = 1995, EDITOR = "Horgan, Terry", PAGES = "171--191", SERIES = "Supplement to The Southern Journal of Philosophy (1994), Vol. XXXIII" } @INPROCEEDINGS{sorcom, AUTHOR = "Sorensen, Roy A.", TITLE = "Commentary: {T}he Epistemic Conception of Vagueness", BOOKTITLE = "Spindel Conference 1994: Vagueness", PUBLISHER = {The Department of Philosophy, The University of Memphis}, ADDRESS = {Memphis, Tennessee}, YEAR = 1995, EDITOR = "Horgan, Terry", PAGES = "161--170", SERIES = "Supplement to The Southern Journal of Philosophy (1994), Vol. XXXIII" } @BOOK{resmatb, TITLE = "Mathematics as a Science of Patterns", PUBLISHER = {Oxford University Press}, ADDRESS = {Oxford}, YEAR = 1997, AUTHOR = "Resnik, Michael D." } @ARTICLE{benwha, AUTHOR = "Benacerraf, Paul", TITLE = "What Numbers Could Not Be", JOURNAL = "Philosophical Review", YEAR = 1965, VOLUME = 74, PAGES = "47--73", NOTE = "All references are to the reprinting as pp.~272--294 of [BP83]", NOTE = "Reprinted as pp.~272--294 of ShaughanLavine - 15 Feb 2010 - 20:19 - 1.173 " class="twikiCurrentTopicLink twikiAnchorLink">BenacerrafEtal83", URL = {http://ezproxy.library.arizona.edu/login?url=http://links.jstor.org/sici?sici=0031-8108(196501)74%3A1%3C47%3AWNCNB%3E2.0.CO;2-7} } @MISC{mcgman, AUTHOR = "McGee, Vann", TITLE = "The Many Lives of {E}benezer {W}ilkes {S}mith", YEAR = 2001, HOWPUBLISHED = "Text of a talk at One Hundred Years of Russell's Paradox: International Conference in Logic and Philosophy, 2--5 June", ADDRESS = "University of Munich"} @INPROCEEDINGS{tapsom, AUTHOR = "Tappenden, Jamie", TITLE = "Some Remarks on Vagueness and a Dynamic Conception of Language", BOOKTITLE = "Spindel Conference 1994: Vagueness", PUBLISHER = {The Department of Philosophy, The University of Memphis}, ADDRESS = { Memphis, Tennessee}, YEAR = 1995, EDITOR = "Horgan, Terry", PAGES = "193--201", SERIES = "Supplement to The Southern Journal of Philosophy (1994), Vol. XXXIII" } @ARTICLE{evacan, AUTHOR = "Evans, Gareth", TITLE = "Can There Be Vague Objects?", JOURNAL = "Analysis", YEAR = 1978, VOLUME = 38, PAGES = "208" } @ARTICLE{mcgkil, AUTHOR = "McGee, Vann", TITLE = {`{K}ilimanjaro'}, PAGES = "141--163", JOURNAL = "Canadian Journal of Philosophy", YEAR = "1997", EDITOR = "Kazmi, Ali A.", VOLUME = "supplementary volume 23" } @ARTICLE{fieind, AUTHOR = field, TITLE = {Indeterminacy, Degree of Belief, and Excluded Middle}, PAGES = "1--30", JOURNAL = "N\^{o}us", YEAR = "2000", VOLUME = "34" } @ARTICLE{brasig, AUTHOR = "Brandom, Robert", TITLE = {The Significance of Complex Numbers for {F}rege's Philosophy of Mathematics}, PAGES = "293--315", JOURNAL = "Proceedings of the Aristotelian Society", YEAR = "1996", VOLUME = "96" } @ARTICLE{braref, AUTHOR = "Brandom, Robert", TITLE = {Reference Explained Away}, PAGES = "469--492", JOURNAL = jop, YEAR = "1984", VOLUME = "81" } @ARTICLE{resmat, AUTHOR = "Resnik, Michael", TITLE = {Mathematics as a Science of Patterns: {O}ntology and Reference}, PAGES = "529--550", JOURNAL = "No\^{u}s", YEAR = "1981", VOLUME = "15", URL = "http://ezproxy.library.arizona.edu/login?url=http://links.jstor.org/sici?sici=0029-4624%28198111%2915%3A4%3C529%3AMAASOP%3E2.0.CO%3B2-M" } @BOOK{wolart, TITLE = "Art and Its Objects", PUBLISHER = {Harper \& Row}, ADDRESS = {New York}, YEAR = 1963, AUTHOR = "Wollheim, Richard" } @MISC{romemp, TITLE = "Roman Emperors--{T}he Imperial Index", YEAR = 2002, URL = "http://www.roman-emperors.org/impindex.htm", author = {Weigel, Richard and e, e and i, i and a, b and a, b and a, b and a, b} } @MISC{phimuc, TITLE = "Much Ado about {P}luto", YEAR = 1999, URL = "http://science.nasa.gov/newhome/headlines/ast17feb99_1.htm", author = {Phillips, Tony} } @ARTICLE{burqui, AUTHOR = "Burgess, John P.", TITLE = { {\em {Q}uinus ab {O}mni {N}\ae vo {V}indicatus\/} }, PAGES = "25--65", JOURNAL = "Canadian Journal of Philosophy", YEAR = "1997", EDITOR = "Kazmi, Ali A.", VOLUME = "supplementary volume 23" } @INCOLLECTION{ackder, AUTHOR = "Ackerman, Diana", TITLE = { {\em De re\/} Propositional Attitudes Toward Integers}, BOOKTITLE = "Essays on the Philosophy of W. V. Quine", PUBLISHER = {University of Oklahoma Press}, ADDRESS = {Norman, Oklahoma}, YEAR = 1979, EDITOR = "Shahan, R. W. and Swoyer, Christopher", PAGES = "???" } @ARTICLE{fiequi, AUTHOR = field, TITLE = "Quine and the Correspondence Theory", PAGES = "200--228", JOURNAL = "Philosophical Review", YEAR = 1974, VOLUME = 83 } @ARTICLE{goomat, AUTHOR = "Goodman, Nicolas D.", TITLE = "Mathematics as Natural Science", JOURNAL = jsl, VOLUME = 55, YEAR = 1990, PAGES = "182--193"} @ARTICLE{tymmat, AUTHOR = "Tymoczko, Thomas", TITLE = "Mathematics, Science and Ontology", JOURNAL = "Synthese", VOLUME = 88, YEAR = 1991, PAGES = "201--228"} @BOOK{fietru, AUTHOR = field, TITLE = "Truth and the Absence of Fact", PUBLISHER = {Clarendon Press of Oxford University Press}, ADDRESS = {Oxford}, YEAR = 2001 } @MISC{parcom, AUTHOR = "Parsons, Charles", TITLE = "Communication and the uniqueness of the natural numbers", YEAR = 2001, HOWPUBLISHED = "Unpublished revised and expanded version of a talk given to the First Seminar in the Philosophy of Mathematics in Iran, Shahid Beheshti University, Tehran, 17 October 2001"} @ARTICLE{evaide, AUTHOR = "Evans, Gareth", TITLE = "Identity and Predication", JOURNAL = jop, YEAR = 1975, VOLUME = 72, PAGES = "343--363" } @ARTICLE{fiedis, AUTHOR = field, TITLE = "Disquotational Truth and Factually Defective Discourse", JOURNAL = "Philosophical Review", YEAR = 1994, VOLUME = 103, PAGES = "405--452", URL = "http://ezproxy.library.arizona.edu/login?url=http://links.jstor.org/sici?sici=0300-7162%28198621%2916%3A1%3C65%3AMSDADO%3E2.0.CO%3B2-7" } @ARTICLE{fiedef, AUTHOR = field, TITLE = "Deflationist Views of Meaning and Content", PAGES = "249--285", JOURNAL = "Mind", YEAR = 1994, VOLUME = "103 n.s.", URL = "http://ezproxy.library.arizona.edu/login?url=http://links.jstor.org/sici?sici=0026-4423%28199407%292%3A103%3A411%3C249%3ADVOMAC%3E2.0.CO%3B2-%23" } @ARTICLE{fiethe, AUTHOR = field, TITLE = "Theory Change and the Indeterminacy of Reference", PAGES = "462--481", JOURNAL = jop, YEAR = 1973, VOLUME = "70" } @ARTICLE{finvag, AUTHOR = "Fine, Kit", TITLE = "Vagueness, Truth and Logic", JOURNAL = "Synthese", VOLUME = 30, YEAR = 1975, PAGES = "265--300"} @ARTICLE{shastr, AUTHOR = "Shapiro, Stewart", TITLE = "Structure and Ontology", JOURNAL = "Philosophical Topics", YEAR = 1989, VOLUME = 17, PAGES = "145--171" } @ARTICLE{wagari, AUTHOR = "Wagner, Steven", TITLE = "Arithmetical Fiction", JOURNAL = "Pacific Philosophical Quarterly", YEAR = 1982, VOLUME = 63, PAGES = "255--269" } @INCOLLECTION{fiewhi, AUTHOR = field, TITLE = "Which Undecidable Mathematical Sentences Have Determinate Truth Values?", BOOKTITLE = "Truth in Mathematics", PUBLISHER = {Oxford University Press}, ADDRESS = {Oxford}, YEAR = 1998, EDITOR = "Dales, H. Garth and Oliveri, Gianluigi", PAGES = "291--310", REMARK = "All page references are to the reprinting with an added postscript (pp.~351--360) as pp.~332--360 of [Fie01]." } @MISC{lavsko, AUTHOR = "Lavine, Shaughan", TITLE = "Skolem Was Wrong", YEAR = 1999, HOWPUBLISHED = "Widely circulated but unpublished manuscript. 161 pages. Cited in print by Field, McGee , and Parsons"} @MISC{lavhow, AUTHOR = "Lavine, Shaughan", TITLE = "How to Talk with Strangers", YEAR = 2005, HOWPUBLISHED = "Colloquium talk, University of Arizona, September, 2005.", URL="http://zillion.philosophy.arizona.edu/twiki/bin/view/Discussion/HowtoTalkwithStrangers" } @ARTICLE{hauobj, AUTHOR = "Hauser, Kai", TITLE = "Objectivity Over Objects: {A} Case Study in Theory Formation", JOURNAL = "Synthese", VOLUME = 128, YEAR = 2001, PAGES = "245--285", URL = "http://www.springerlink.com.ezproxy.library.arizona.edu/content/ng5027788217l208/fulltext.pdf" } @BOOK{balpla, AUTHOR = "Balaguer, Mark", TITLE = "Platonism and Anti-Platonism in Mathematics", PUBLISHER = {Oxford University Press}, ADDRESS = "New York", YEAR = 1998 } @MISC{camthy, AUTHOR = "Campbell, C.", TITLE = "The Thylacine Museum", YEAR = 2002, URL = "http://www.naturalworlds.org/thylacine/"} @ARTICLE{davstr, AUTHOR = "Davidson, Donald", TITLE = "The Structure and Content of Truth", JOURNAL = jop, YEAR = 1990, VOLUME = 87, PAGES = "279--328", URL = "http://ezproxy.library.arizona.edu/login?url=http://links.jstor.org/sici?sici=0022-362X%28199006%2987%3A6%3C279%3ATSACOT%3E2.0.CO%3B2-H" } @ARTICLE{ricins, AUTHOR = "Richard, Mark", TITLE = {Inscrutability}, PAGES = "165--209", JOURNAL = "Canadian Journal of Philosophy", YEAR = "1997", EDITOR = "Kazmi, Ali A.", VOLUME = "supplementary volume 23" } @BOOK{davinq, AUTHOR = "Davidson, Donald", TITLE = "Inquiries into Truth and Interpretation", PUBLISHER = {Oxford University Press}, ADDRESS = {New York}, YEAR = 1984 } @INCOLLECTION{davnic, AUTHOR = "Davidson, Donald", TITLE = "A Nice Derangement of Epitaphs", BOOKTITLE = "Truth and Interpretation: {P}erspectives on the Philosophy of {D}onald {D}avidson", PUBLISHER = {Blackwell Publishers}, ADDRESS = {New York}, YEAR = 1986, EDITOR = "Le{P}ore, Ernest", PAGES = "433--446" } @BOOK{kanhig, AUTHOR = "Kanamori, Akihiro", TITLE = {The Higher Infinite: {L}arge Cardinals in Set Theory from Their Beginnings}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = 1994, SERIES = "Perspectives in Mathematical Logic" } @BOOK{draset, AUTHOR = "Drake, Frank R.", TITLE = {Set Theory}, PUBLISHER = {North-Holland}, ADDRESS = {Amsterdam}, YEAR = 1974 } @ARTICLE{barind, AUTHOR = "Bar-{O}n, Dorit", TITLE = "Indeterminacy of Translation---{T}heory and Practice", JOURNAL = "Philosophy and Phenomenological Research", VOLUME = 53, YEAR = 1993, PAGES = "781--810"} @BOOK{oed, KEY = {OED71}, TITLE = {The Compact Edition of the Oxford English Dictionary}, PUBLISHER = {Oxford University Press}, ADDRESS = {New York}, YEAR = 1971 } @ARTICLE{kinana, AUTHOR = {King, Jeffrey C.}, TITLE = "Anaphora and Operators", JOURNAL = "Philosophical Perspectives", YEAR = 1994, VOLUME = 8, PAGES = "221--250", NOTE = "Issue on Logic and Language" } @INCOLLECTION{horpsy, AUTHOR = "Horgan, Terence", TITLE = "Psychologistic Semantics, Robust Vagueness, and The Philosophy of Language", BOOKTITLE = "Meanings and Prototypes: {S}tudies in Linguistic Categorization", PUBLISHER = {Routledge}, ADDRESS = {London}, YEAR = 1990, EDITOR = "Tsohatzidis, S. L.", PAGES = "???" } @ARTICLE{altpro, AUTHOR = { {a}ltieri, {j}oan {t}aber}, TITLE = "Singular They: {T}he Pronoun That Came in from the Cold", JOURNAL = "Vocabula Review", YEAR = 2003, MONTH = "September", URL = "http://www.vocabula.com" } @ARTICLE{macimp, AUTHOR = {MacArthur, John R.}, TITLE = "Impeach {B}ush Now", JOURNAL = "Globe and Mail", YEAR = 2003, MONTH = "October", ADDRESS = "Toronto, Ontario, Canada", URL = "http://www.commondreams.org/views03/1009-06.htm" } @ARTICLE{litacc, AUTHOR = {Lithwick, Dahlia}, TITLE = "The Accidental Tourist", JOURNAL = "Slate", YEAR = 2003, URL = "http://slate.msn.com/id/2091143" } @ARTICLE{rasvag, AUTHOR = {Rasmussen, Stig Alstrup}, TITLE = "Vague Identity", PAGES = "81--91", JOURNAL = "Mind", YEAR = 1986, VOLUME = "95 n.s." } @ARTICLE{zemvag, AUTHOR = {Zemach, Eddy M.}, TITLE = "Vague Objects", PAGES = "323--340", JOURNAL = "N\^{o}us", YEAR = 1991, VOLUME = "25" } @ARTICLE{carspe, AUTHOR = "Cartwright, Richard L.", TITLE = "Speaking of Everything", JOURNAL = "N\^{o}us", YEAR = 1994, VOLUME = 28, PAGES = "1--20" } @INCOLLECTION{wilind, AUTHOR = "Williamson, Timothy", TITLE = "Indefinite Extensibility", BOOKTITLE = "New Essays on the Philosophy of Michael Dummett", SERIES = "Grazer Philosophische Studien", EDITOR = "Brandl, Johannes L. and Sullivan, Peter", VOLUME = 55, YEAR = 1998, PUBLISHER = {Rodopi}, ADDRESS = {Atlanta, Georgia}, PAGES = "1--24"} @ARTICLE{wilexi, AUTHOR = "Williamson, Timothy", TITLE = {Existence and Contingency}, PAGES = "117--139", JOURNAL = "Proceedings of the Aristotelian Society", YEAR = "1999", VOLUME = "n.s. 100" } @ARTICLE{chaast, AUTHOR = "Chang, Kenneth and Overbye, Dennis", TITLE = {Astronomers Find Another Planet in Solar System}, JOURNAL = " New York Times", YEAR = "29 July 2005", URL ="www.nytimes.com/2005/07/29/science/29cnd-planet.html?hp&ex=1122696000&en=041567292ccf323b&ei=5094&partner=homepage" } @ARTICLE{rusden, AUTHOR = "Russell, Bertrand", TITLE = "On Denoting", PAGES = "479--493", JOURNAL = "Mind", VOLUME = 14, YEAR = 1905, URL = "http://ezproxy.library.arizona.edu/login?url=http://links.jstor.org/sici?sici=0026-4423%28190510%292%3A14%3A56%3C479%3AOD%3E2.0.CO%3B2-P" } @PHDTHESIS{diequa, AUTHOR = "Dieveney, Patrick", TITLE = "Quantification and Indispensable Ontology", SCHOOL = "University of Arizona", YEAR = 2006 } @ARTICLE{fierev, AUTHOR = "Field, Hartry", TITLE = "A Revenge-Immune Solution to the Paradoxes", JOURNAL = "Journal of Philosophical Logic", YEAR = 2003, VOLUME = 32, PAGES = "139--177", URL = "http://www.springerlink.com.ezproxy1.library.arizona.edu/content/pcffl51n2a49/?p=05902578b3d44c278be608b5abbb0563&pi=25" } @ARTICLE{fierepmcg, AUTHOR = "Field, Hartry", TITLE = "Reply to {M}c{G}ee", JOURNAL = "Philosophical Studies", YEAR = 2005, VOLUME = 124, PAGES = "118--128", URL = "http://www.springerlink.com.ezproxy.library.arizona.edu/content/u144375381285782/fulltext.pdf" } @ARTICLE{ketdef, AUTHOR = "Ketland, Jeffrey", TITLE = {Deflationism and the {G}\"{o}del Phenomena: {R}eply to {T}ennant}, JOURNAL = "Mind", YEAR = 2005, VOLUME = 114, PAGES = "75--88", URL = "http://www.jstor.org.ezproxy.library.arizona.edu/view/00264423/di015164/01p0095y/0?currentResult=00264423%2bdi015164%2b01p0095y%2b0%2cDF7FDF07&searchUrl=http%3A%2F%2Fwww.jstor.org%2Fsearch%2FBasicResults%3Fhp%3D25%26si%3D1%26gw%3Djtx%26jtxsi%3D1%26jcpsi%3D1%26artsi%3D1%26Query%3Dketland%2Bdeflationism" } @ARTICLE{mcgtwo, AUTHOR = "McGee, Vann", TITLE = "Two Conceptions of Truth?---{C}omment", JOURNAL = "Philosophical Studies", YEAR = 2005, VOLUME = 124, PAGES = "71--104", URL = "http://www.springerlink.com.ezproxy1.library.arizona.edu/content/q17508h801w83424/fulltext.pdf" } @INCOLLECTION{devmet, AUTHOR = "Devitt, Michael", TITLE = "The Metaphysics of Truth", BOOKTITLE = "The Nature of Truth", EDITOR = "Michael Lynch", YEAR = 2001, PUBLISHER = {MIT Press}, ADDRESS = {Cambridge, Massachusetts}, PAGES = "579--611"} @ARTICLE{gupmarfie, AUTHOR = "Gupta, Anil and Mart\'{i}nez-Fern\'{a}ndez, Jos\'{e}", TITLE = "Field on The Concept of Truth---{C}omment", JOURNAL = "Philosophical Studies", YEAR = 2005, VOLUME = 124, PAGES = "45--58", URL = "http://www.springerlink.com.ezproxy.library.arizona.edu/content/u123105p00t3h118/fulltext.pdf" } @ARTICLE{seaind, AUTHOR = "Searle, John R.", TITLE = "Indeterminacy, Empiricism, and the First Person", JOURNAL = jop, YEAR = 1987, VOLUME = 84, PAGES = "123--146" }

@STRING{zfm = {Zeitschrift f\"{u}r Mathematische Logik und Grundlagen der Mathematik} } @STRING{bams = "Bulletin (New Series) of the American Mathematical Society"} @ARTICLE{lgsom, AUTHOR = "Lov\'{a}sz, L. and G\'{a}cs, P.", TITLE = "Some Remarks on Generalized Spectra", JOURNAL = zfm, YEAR = 1977, VOLUME = 23, PAGES = "547--554" } @INPROCEEDINGS{immlan, AUTHOR = "Immerman, Neil", TITLE = "Languages Which Capture Complexity Classes", BOOKTITLE = "Proceedings of the Fifteenth Annual ACM Symposium on Theory of Computing", PUBLISHER = "Association for Computing Machinery", ADDRESS = "New York", YEAR = 1983, PAGES = "347--354" } @PHDTHESIS{fagdis, AUTHOR = "Fagin, Ronald", TITLE = "Contributions to the Model Theory of Finite Structures", SCHOOL = "University of California, Berkeley", YEAR = 1973 } @BOOK{hopullint, AUTHOR = "Hopcroft, John E. and Ullman, Jeffrey D.", TITLE = "Introduction to Automata Theory, Languages, and Computation", PUBLISHER = "Addison--Wesley", ADDRESS = "Reading, Massachusetts", YEAR = 1979 } @INPROCEEDINGS{faggen, AUTHOR = "Fagin, Ronald", TITLE = "Generalized First-Order Spectra and Polynomial-Time Recognizable Sets", BOOKTITLE = "Complexity of Computation", YEAR = 1974, PAGES = "27--41", EDITOR = "Karp, Richard", NUMBER = 7, SERIES = "SIAM-AMS Proceedings" } @BOOK{garjohcom, AUTHOR = "Garey, Michael R. and Johnson, David S.", TITLE = "Computers and Intractability: A Guide to the Theory of NP-Completeness", PUBLISHER = "W. H. Freeman", ADDRESS = "San Francisco", YEAR = 1979 } @ARTICLE{bssthe, AUTHOR = "Blum, Lenore and Shub, Mike and Smale, Steve", TITLE = "On a Theory of Computation and Complexity over the Real Numbers: {\em NP\/}-completeness, Recursive Functions and Universal Machines", JOURNAL = bams, YEAR = 1989, VOLUME = 21, PAGES = "1--46" } @BOOK{borcom, AUTHOR = {B\"{o}rger, Egon}, TITLE = "Computability, Complexity, Logic", PUBLISHER = "North-Holland", ADDRESS = "New York", YEAR = 1989, SERIES = "Studies in Logic and the Foundations of Mathematics", NUMBER = 128, NOTE = "Distributed by Elsevier Science Publishing." } @BOOK{dregoldec, AUTHOR = {Dreben, Burton and Goldfarb, Warren D.}, TITLE = "The Decision Problem: Solvable Classes of Quantificational Formulas", PUBLISHER = "Addison-Wesley Advanced Book Program", ADDRESS = "Reading, Mass.", YEAR = 1979 }

@BOOK{dirpri, AUTHOR = "Dirac, P. A. M.", TITLE = "The Principles of Quantum Mechanics", PUBLISHER = "Oxford U. P.", ADDRESS = {London}, YEAR = "1958, revised 1967", EDITION = "fourth" } @ARTICLE{teldis, AUTHOR = "Teller, Paul", TITLE = "Discussion: Quantum Physics, the Identity of Indiscernibles and Some Unanswered Questions", JOURNAL = "Philosophy of Science", YEAR = 1983, VOLUME = 50, PAGES = "309--319" } @ARTICLE{feialblavtwo, AUTHOR = "Feinberg, Gerald and Albert, David Z. and Lavine, Shaughan", TITLE = "Two types of prediction in {N}ewtonian and quantum mechanics", JOURNAL = "Physics Letters A", YEAR = 1989, VOLUME = 138, PAGES = "454--458" } @ARTICLE{feialblavkno, AUTHOR = "Feinberg, Gerald and Albert, David Z. and Lavine, Shaughan", TITLE = "Knowledge of the Past and Future", JOURNAL = jop, YEAR = 1992, VOLUME = 89, PAGES = "607--642" } @INCOLLECTION{frapro, AUTHOR = "van Fraassen, Bas C.", TITLE = "Probabilities and the Problem of Individuation", BOOKTITLE = "Probabilities, Problems, and Paradoxes", PUBLISHER = "Dickenson", ADDRESS = {Encino, California}, YEAR = 1972, EDITOR = "Luckenbach, Sidney A.", CHAPTER = 6, PAGES = "121--138" } @BOOK{feyqed, AUTHOR = "Feynman, Richard P.", TITLE = "QED", PUBLISHER = "Princeton U. P.", ADDRESS = {Princeton, New Jersey}, YEAR = 1985 } @ARTICLE{ginpar, AUTHOR = "Ginsberg, Allen", TITLE = "On a Paradox in Quantum Mechanics", JOURNAL = "Synthese", YEAR = 1984, VOLUME = 61, PAGES = "325--349" } @ARTICLE{frqua, AUTHOR = "French, Steven and Redhead, Michael", TITLE = "Quantum Physics and the Identity of Indiscernibles", JOURNAL = "British Journal of the Philosophy of Science", YEAR = 1988, VOLUME = 39, PAGES = "233--246" }

@STRING{lnm = "Lecture Notes in Mathematics"} @STRING{aml = "Annals of Mathematical Logic"} @STRING{jsl = "Journal of Symbolic Logic"} @STRING{fm = "Fundamenta Mathematicae"} @STRING{mams = "Memoirs of the American Mathematical Society"} @STRING{pml = "Perspectives in Mathematical Logic"} @STRING{sil = "Studies in Logic and the Foundations of Mathematics"} @STRING{abs = "Abstracts of Papers Presented to the American Mathematical Society"} @STRING{ind = "Indagationes Mathematicae"} @STRING{me = "Lavine, Shaughan"} @BOOK{baradm, AUTHOR = "Barwise, Jon", TITLE = "Admissible Sets and Structures", PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = 1975, SERIES = pml } @ARTICLE{adaadm, AUTHOR = "Adamson, Alan", TITLE = "Admissible Sets and the Saturation of Structures", JOURNAL = aml, YEAR = 1978, VOLUME = 14, PAGES = "111--157" } @MISC{vaupcm, AUTHOR = "Vaught, Robert", YEAR = 1977, HOWPUBLISHED = "Personal communication" } @ARTICLE{makpcd, AUTHOR = "Makkai, M.", TITLE = "On {${\text{PC}}_{\Delta}$}-classes in the Theory of Models", JOURNAL = {A Magyar Tudom\'{a}nyos Akad\'{e}mia Matematikai Kutat\'{o} Int\'{e}zet\'{e}nek K\"{o}zlem\'{e}nyei (Budapest) }, YEAR = 1964, VOLUME = 9, PAGES = "159--194" } @ARTICLE{nadstapph, AUTHOR = "Nadel, Mark and Stavi, Jonathan", TITLE = "The Pure Part of {$\text{HYP}({\cal M})$}", JOURNAL = jsl, YEAR = 1977, VOLUME = 42, PAGES = "33--46" } @ARTICLE{sfrste, AUTHOR = "Friedman, Sy D.", TITLE = "Steel Forcing and {B}arwise Compactness", JOURNAL = aml, YEAR = 1982, VOLUME = 22, PAGES = "31--46" } @INCOLLECTION{nadlwo, AUTHOR = "Nadel, M.", TITLE = "{${\cal L}_{\omega _{1}\omega }$} and Admissible Fragments", BOOKTITLE = "Model-Theoretic Logics", PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = 1985, EDITOR = "Barwise, J. and Feferman, S.", CHAPTER = "VIII", PAGES = "271--316", SERIES = pml } @ARTICLE{spehyp, AUTHOR = "Spector, C.", TITLE = "Hyperarithmetical Quantifiers", JOURNAL = fm, YEAR = 1960, VOLUME = 48, PAGES = "313--320" } @ARTICLE{bgmnex, AUTHOR = "Barwise, K. J. and Gandy, R. O. and Moschovakis, Y. N.", TITLE = "The Next Admissible Set", JOURNAL = jsl, YEAR = 1971, VOLUME = 36, PAGES = "108--120" } @ARTICLE{resmod, AUTHOR = "Ressayre, J. P.", TITLE = "Models with Compactness Properties Relative to an Admissible Language", JOURNAL = aml, YEAR = 1977, VOLUME = 11, PAGES = "31--55" } @ARTICLE{cvfin, AUTHOR = "Craig, W. and Vaught, R.", TITLE = "Finite Axiomatizability Using Additional Predicates", JOURNAL = jsl, YEAR = 1958, VOLUME = 23, PAGES = "289--308" } @ARTICLE{klefin, AUTHOR = "Kleene, S.", TITLE = "Finite Axiomatizability of Theories in the Predicate Calculus Using Additional Predicate Symbols", JOURNAL = mams, YEAR = 1952, VOLUME = 10, PAGES = "27--68" } @INCOLLECTION{makinf, AUTHOR = "Makkai, M.", TITLE = "Admissible Sets and Infinitary Logic", BOOKTITLE = "Handbook of Mathematical Logic", PUBLISHER = "North-Holland Publishing Company", ADDRESS = "Amsterdam", YEAR = 1977, EDITOR = "Barwise, Jon", CHAPTER = "A.7", PAGES = "233--281", SERIES = sil, NUMBER = 90 } @ARTICLE{ganmos, AUTHOR = "Gandy, R. O.", TITLE = "Proof of {M}ostowski's Conjecture", JOURNAL = "Polska Akademia Nauk Instytut Matematczny Rozprawy Matematyczne", YEAR = 1960, VOLUME = 18, PAGES = "571--575" } @BOOK{hinrec, AUTHOR = "Hinman, Peter G.", TITLE = "Recursion-Theoretic Hierarchies", PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = 1978, SERIES = pml } @BOOK{mosdes, AUTHOR = "Moschovakis, Yiannis Nicholas", TITLE = "Descriptive Set Theory", PUBLISHER = {North-Holland Publishing Company}, ADDRESS = {Amsterdam}, YEAR = 1980, SERIES = sil, NUMBER = 100 } @ARTICLE{malmod, AUTHOR = "Mal${}'$cev (Maltsev), A. I.", TITLE = "Model Correspondences", JOURNAL = "Isvestiia Akademiia Nauk SSSR Seriia Matematicheskaia", YEAR = 1959, VOLUME = 23, PAGES = "313--336", NOTE = "In Russian. See E. Mendelson, {\em Mathematical Reviews\/} 22, no. 10909, 1961" } @ARTICLE{kursep, AUTHOR = "Kuratowski, K.", TITLE = "Sur les Th\'{e}or\`{e}mes de S\'{e}paration dans la Th\'{e}orie des Ensembles", JOURNAL = fm, YEAR = 1936, VOLUME = 26, PAGES = "183--191" } @BOOK{kurtop, AUTHOR = "Kuratowski, K.", TITLE = "Topology", VOLUME = 1, PUBLISHER = {Academic Press}, ADDRESS = {New York}, YEAR = 1966, NOTE = "Translated from French by J. Jaworowski" } @ARTICLE{kreaxi, AUTHOR = "Kreisel, G.", TITLE = "The Axiom of Choice and the Class of Hyperarithmetic Functions", JOURNAL = ind, YEAR = 1962, VOLUME = 24, PAGES = "307--319" } @ARTICLE{lavgen, AUTHOR = me, TITLE = "Generalized Reduction for Complements of {${\mathrm{PC}}_{\delta }$} Classes", JOURNAL = abs, YEAR = 1984, VOLUME = 5, PAGES = 388, NOTE = "Abstract" } @ARTICLE{lavspe, AUTHOR = me, TITLE = "A {S}pector--{G}andy Theorem for Model Classes that are {${\mathrm{cPC}}_{d}$} over an Admissible Set", JOURNAL = jsl, YEAR = 1985, VOLUME = 50, PAGES = 1096, NOTE = "Abstract" } @INPROCEEDINGS{vaupcd, AUTHOR = "Vaught, Robert", TITLE = "On {${\mathrm{PC}}_{d}({\cal A})$}-Classes for an Admissible Set {${\cal A}$}", BOOKTITLE = "Mathematical Logic in Latin America", YEAR = 1980, EDITOR = "Arruda, A. I. and Chuaqui, R. and da Costa, N. C. A.", PAGES = "377--392", PUBLISHER = {North-Holland Publishing Company}, ADDRESS = {Amsterdam} } @BOOK{ckmod, AUTHOR = "Chang, C. C. and Keisler, H. Jerome", TITLE = "Model Theory", PUBLISHER = {North-Holland Publishing Company}, ADDRESS = {Amsterdam}, YEAR = 1973, SERIES = sil, NUMBER = 73 } @BOOK{chakeimod3, AUTHOR = "Chang, C. C. and Keisler, H. Jerome", TITLE = "Model Theory", PUBLISHER = {North-Holland Publishing Company}, ADDRESS = {Amsterdam}, YEAR = 1990, SERIES = sil, NUMBER = 73, EDITION = "3rd", NOTE = "First edition, 1973." } @INCOLLECTION{davuns, AUTHOR = "Davis, Martin", TITLE = "Unsolvable Problems", PAGES = "567--594", CHAPTER = "C.2", BOOKTITLE = "Handbook of Mathematical Logic", EDITOR = "Barwise, Jon", SERIES = sil, NUMBER = 90, PUBLISHER = {North-Holland Publishing Company}, ADDRESS = {Amsterdam}, YEAR = 1977} @INCOLLECTION{aczint, AUTHOR = "Aczel, Peter", TITLE = "An Introduction to Inductive Definitions", PAGES = "739--782", CHAPTER = "C.7", BOOKTITLE = "Handbook of Mathematical Logic", EDITOR = "Barwise, Jon", SERIES = sil, NUMBER = 90, PUBLISHER = {North-Holland Publishing Company}, ADDRESS = {Amsterdam}, YEAR = 1977} @BOOK{mosele, AUTHOR = "Moschovakis, Yiannis N.", TITLE = "Elementary Induction on Abstract Structures", YEAR = "1974", PUBLISHER = {North-Holland Publishing Company}, ADDRESS = {Amsterdam}, SERIES = sil, NUMBER = 77} @ARTICLE{burmilrem, AUTHOR = "Burgess, John and Miller, Douglas", TITLE = "Remarks on Invariant Descriptive Set Theory", JOURNAL = fm, YEAR = 1975, VOLUME = 90, PAGES = "53--75" } @PHDTHESIS{milthe, AUTHOR = "Miller, Douglas", TITLE = "Invariant Descriptive Set Theory and the Topological Approach to Model Theory", SCHOOL = "University of California, Berkeley", YEAR = 1976 } @BOOK{endmat, AUTHOR = "Enderton, Herbert B.", TITLE = "A Mathematical Introduction to Logic", PUBLISHER = {Academic Press}, ADDRESS = {Orlando, Florida}, YEAR = 1972 } @BOOK{endmat2, AUTHOR = "Enderton, Herbert B.", TITLE = "A Mathematical Introduction to Logic", EDITION = "2nd", PUBLISHER = {Harcourt/Academic Press}, ADDRESS = {Burlington, Mass.}, YEAR = 2001 } @ARTICLE{tarcon1, AUTHOR = "Tarski, Alfred", TITLE = "Contributions to the Theory of Models, Parts {I} and {II}", JOURNAL = ind, YEAR = 1954, VOLUME = 16, PAGES = "572--588" } @ARTICLE{tarcon2, AUTHOR = "Tarski, Alfred", TITLE = "Contributions to the Theory of Models, Part {III}", JOURNAL = ind, YEAR = 1955, VOLUME = 17, PAGES = "56--64" } @INCOLLECTION{lintarlim, AUTHOR = "Lindenbaum, A. and Tarski, Alfred", TITLE = "On the Limitations of the Means of Expression of Deductive Theories", BOOKTITLE = "Logic, Semantics, and Metamathematics", PUBLISHER = "Clarendon Press", ADDRESS = "Oxford", YEAR = 1956, EDITOR = "Tarski, Alfred", PAGES = "384--392" } @PHDTHESIS{sherdiss, AUTHOR = "Sher, Gila", TITLE = "Generalized Logic---A Philosophical Perspective with Linguistic Applications", SCHOOL = "Columbia University", YEAR = 1989 } @PHDTHESIS{lavdiss, AUTHOR = "Shaughan Lavine (Michael A. Lavine)", TITLE = "{S}pector--{G}andy and Generalized Reduction Theorems for Model-Theoretic Analogs of the Class of Coanalytic Sets", SCHOOL = "University of California, Berkeley", YEAR = 1988 } @ARTICLE{lavsg, AUTHOR = me, TITLE = "A {S}pector--{G}andy Theorem for {${\mathrm{cPC}}_{d}({\Bbb A})$} Classes", JOURNAL = jsl, YEAR = 1992, VOLUME = 57, PAGES = "478--500", NOTE = "Mathematical Reviews 93h:03053" } @ARTICLE{lavgr, AUTHOR = me, TITLE = "Dual Easy Uniformization and Model-Theoretic Descriptive Set Theory", JOURNAL = jsl, YEAR = 1991, VOLUME = 56, PAGES = "1290--1316", NOTE = "Mathematical Reviews 93h:03069" } @ARTICLE{lavnor, AUTHOR = me, TITLE = "Generalized Reduction Theorems for Model-Theoretic Analogs of the Class of Coanalytic Sets", JOURNAL = jsl, YEAR = 1993, VOLUME = 58, PAGES = "81--98" } @ARTICLE{mycloc, AUTHOR = "Mycielski, Jan", TITLE = "Locally Finite Theories", JOURNAL = jsl, YEAR = 1986, VOLUME = 51, PAGES = "59--62" } @ARTICLE{mycfin, AUTHOR = "Mycielski, Jan", TITLE = "Finitistic Real Analysis", JOURNAL = "Real Analysis Exchange", YEAR = "1980--1981", VOLUME = 6, PAGES = "127--130" } @ARTICLE{mycana, AUTHOR = "Mycielski, Jan", TITLE = "Analysis without Actual Infinity", JOURNAL = jsl, YEAR = 1981, VOLUME = 46, PAGES = "625--633" } @ARTICLE{pawrem, AUTHOR = "Pawlikowski, Janusz", TITLE = "Remark on Locally Finite Theories", JOURNAL = abs, YEAR = 1989, VOLUME = 10, PAGES = 172, NOTE = "Abstract" } @BOOK{bisbricon, AUTHOR = "Bishop, Errett and Bridges, Douglas", TITLE = "Constructive Analysis", PUBLISHER = "Springer-Verlag", ADDRESS = "New York", YEAR = 1985, SERIES = "Grundlehren der mathematischen Wissenschaften", NUMBER = 279 } @BOOK{beefou, AUTHOR = "Beeson, Michael J.", TITLE = "Foundations of Constructive Mathematics", PUBLISHER = "Springer-Verlag", ADDRESS = "New York", YEAR = 1985, SERIES = "Ergebnisse der Mathematik und ihrer Grenzgebiete", NUMBER = "6 in the 3rd Series" } @BOOK{targivfor, AUTHOR = "Tarski, Alfred and Givant, Steve", TITLE = "A Formalization of Set Theory without Variables", PUBLISHER = "American Mathematical Society", ADDRESS = "Providence, Rhode Island", YEAR = 1987, SERIES = "American Mathematical Society Colloquium Publications", NUMBER = 41 } @ARTICLE{ackwid, AUTHOR = "Ackermann, Wilhelm", TITLE = "Die {W}iderspruchsfreiheit der allgemeinen {M}engenlehre", JOURNAL = "Mathematische Annalen", YEAR = 1937, VOLUME = 114, PAGES = "305--315" } @BOOK{vauset, AUTHOR = "Vaught, Robert L.", TITLE = "Set Theory, An Introduction", PUBLISHER = {Birkh\"{a}user}, ADDRESS = "Boston", YEAR = 1985 } @ARTICLE{vauaxi, AUTHOR = "Vaught, Robert L.", TITLE = "Axiomatizability by a Schema", JOURNAL = jsl, YEAR = 1967, VOLUME = 32, PAGES = "473--479", URL = "http://www.jstor.org.ezproxy1.library.arizona.edu/stable/pdfplus/2270175.pdf" } @BOOK{jecset, AUTHOR = "Jech, Thomas", TITLE = "Set Theory", PUBLISHER = "Academic Press", ADDRESS = "New York", YEAR = 1978, SERIES = "Pure and Applied Mathematics" } @ARTICLE{ersadm, AUTHOR = "Ershov, Yu. L.", TITLE = "{$\Sigma $}-Admissible Sets", JOURNAL = "Akademiya Nauk SSSR Sibirskoe Otdelenie Institut Matematiki Vychislitelnye Sistemy Sbornik Trudov", YEAR = 1986, VOLUME = 138, PAGES = "35--39", NOTE = "In Russian. See M. S. Burgin, {\em Mathematical Reviews\/} 88k:03080" } @PHDTHESIS{herinv, AUTHOR = "Herbrand, Jacques", TITLE = "Recherches sur la th\'{e}orie de la d\'{e}monstration", SCHOOL = "University of Paris", YEAR = 1930, NOTE = "All page references are to the translation of Chapter 5 by Burton Dreben and Jean van Heijenoort, pp.~529--579 [vH67]" } @ARTICLE{frihig, AUTHOR = "Friedman, Harvey", TITLE = "Higher Set Theory and Mathematical Practice", JOURNAL = aml, YEAR = 1971, VOLUME = 2, PAGES = "326--357" } @ARTICLE{marbor, AUTHOR = "Martin, Donald A.", TITLE = "Borel Determinacy", JOURNAL = "Annals of Mathematics", YEAR = 1975, VOLUME = 102, PAGES = "363--371" } @ARTICLE{skonic, AUTHOR = "Skolem, Thoralf", TITLE = {\"{U}ber die {N}icht-charakterisierbarkeit der {Z}ahlenreihe mittels endlich oder abz\"{a}hlbar unendlich vieler {A}ussagen mit ausschliesslich {Z}ahlenvariablen}, JOURNAL = fm, YEAR = 1934, VOLUME = 23, PAGES = "150--161", NOTE = "Reprinted as pp. 355--366 [Sko70]." } @ARTICLE{skounm, AUTHOR = "Skolem, Thoralf", TITLE = {\"{U}ber die {U}nm\"{o}glichkeit einer vollst\"{a}ndigen {C}harakterisierung der {Z}ahlenreihe mittels eines endlichen {A}xiomensystems}, JOURNAL = {Norsk Matematisk Forenings, Skrifter}, SERIES = 2, YEAR = 1933, NUMBER = 10, PAGES = "73--82", NOTE = "Reprinted as pp. 345--354 [Sko70]." } @ARTICLE{mirrem, AUTHOR = "Mirimanoff, D.", TITLE = {Remarques sur la Th\'{e}orie des Ensembles et les Antinomies {C}antoriennes. {I} }, JOURNAL = "L'Enseignement Math\'{e}matique", YEAR = 1917, VOLUME = 19, PAGES = "209--217" } @BOOK{weyges, AUTHOR = "Weyl, Hermann", TITLE = "Gesammelte Abhandlungen", PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = 1968, NOTE = "Edited by K. Chandrasekharan"} @BOOK{weykon, AUTHOR = "Weyl, Hermann", TITLE = "Das Kontinuum", PUBLISHER = {Veit}, ADDRESS = {Leipzig}, YEAR = 1918 } @ARTICLE{fraunt, AUTHOR = "Fraenkel, A.", TITLE = {Unterzuchen \"{u}ber die {G}rundlagen der {M}engenlehre}, JOURNAL = "Mathematische Zeitschrift", YEAR = 1925, VOLUME = 22, PAGES = "250--273" } @ARTICLE{frauntii, AUTHOR = "Fraenkel, A.", TITLE = {Axiomatische Theorie der geordneten {M}engen (Unterzuchen \"{u}ber die {G}rundlagen der {M}engenlehre {II})}, JOURNAL = {Journal f\"{u}r die reine und angewandte {M}athematik}, YEAR = 1926, VOLUME = 155, PAGES = "129--158" } @ARTICLE{frauntiii, AUTHOR = "Fraenkel, A.", TITLE = {Axiomatische Theorie der {W}ohlordnung (Unterzuchen \"{u}ber die {G}rundlagen der {M}engenlehre {III})}, JOURNAL = {Journal f\"{u}r die reine und angewandte {M}athematik}, YEAR = 1932, VOLUME = 167, PAGES = "1--11" } @BOOK{fraeinii, AUTHOR = "Fraenkel, A.", TITLE = "Einleitung in die {M}engenlehre", PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = 1923, EDITION = "2nd" } @BOOK{fraeiniii, AUTHOR = "Fraenkel, A.", TITLE = "Einleitung in die {M}engenlehre", PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = 1928, EDITION = "3rd" } @BOOK{neucol, AUTHOR = "von Neumann, John", TITLE = "Collected Works", PUBLISHER = {Pergamon Press}, ADDRESS = {New York}, YEAR = 1961, NOTE = "Edited by A. H. Taub"} @BOOK{godcol, AUTHOR = {G\"{o}del, Kurt}, TITLE = "Collected Works", PUBLISHER = {Oxford University Press}, ADDRESS = {New York}, YEAR = " Vol. 1, 1986; Vol. 2, 1990", NOTE = "Edited by Solomon Feferman, John W. Dawson, Jr., Stephen C. Kleene, Gregory H. Moore, Robert M. Solovay, and Jean van Heijenoort"} @PHDTHESIS{hendis, AUTHOR = "Henkin, Leon", TITLE = "The Completeness of Formal Systems", SCHOOL = "Princeton University", YEAR = 1947 } @ARTICLE{zerbeg, AUTHOR = "Zermelo, Ernst", TITLE = {\"{U}ber den {B}egriff der {D}efinheit in der {A}xiomatik}, JOURNAL = fm, YEAR = 1929, VOLUME = 14, PAGES = "339--344" } @ARTICLE{zergre, AUTHOR = "Zermelo, Ernst", TITLE = {\"{U}ber {G}renzzahlen und {M}engenbereiche}, JOURNAL = fm, YEAR = 1930, VOLUME = 16, PAGES = "29--47" } @ARTICLE{skobem, AUTHOR = "Skolem, Thoralf", TITLE = {Einige {B}emerkungen zu der {A}bhandlung von {E}. {Z}ermelo: ``\"{U}ber die {D}efinheit in der {A}xiomatik''}, JOURNAL = fm, YEAR = 1930, VOLUME = 15, PAGES = "337--341" } @ARTICLE{tarune, AUTHOR = "Tarski, Alfred", TITLE = {\"{U}ber unerreichbare {K}ardinalzahlen}, JOURNAL = fm, YEAR = 1938, VOLUME = 30, PAGES = "68--89" } @ARTICLE{zergru, AUTHOR = "Zermelo, Ernst", TITLE = {Grundlagen einer allgemeinen {T}heorie der mathematischen {S}atzsysteme}, JOURNAL = fm, YEAR = 1935, VOLUME = 25, PAGES = "136--146" } @ARTICLE{zerpro, AUTHOR = "Zermelo, Ernst", TITLE = "Beweis, da\ss\ jede {Menge} wohlgeordnet werden kann", JOURNAL = "Mathematische Annalen", VOLUME = 59, PAGES = "514--516", NOTE = "All page references are to the translation by Stefan Bauer-Mengelberg, pp.~139--141 [vH67]", YEAR = 1904} @ARTICLE{zernew, AUTHOR = "Zermelo, Ernst", TITLE = {Neuer {B}eweis f\"{u}r die {M}\"{o}glichkeit einer {W}ohlordnung}, JOURNAL = "Mathematische Annalen", VOLUME = 65, PAGES = "107--128", NOTE = "All page references are to the translation by Stefan Bauer-Mengelberg, pp.~183--198 [vH67]", YEAR = 1908} @ARTICLE{zerinv, AUTHOR = "Zermelo, Ernst", TITLE = {Untersuchungen \"{u}ber die {G}rundlagen der {M}engenlehre {I} }, JOURNAL = "Mathematische Annalen", VOLUME = 65, PAGES = "261--281", NOTE = "All page references are to the translation by Stefan Bauer-Mengelberg, pp.~200--215 [vH67]", YEAR = 1908} @BOOK{acznon, AUTHOR = {Aczel, Peter}, TITLE = "Non-Well-Founded Sets", PUBLISHER = {Center for the Study of Language and Information, Leland Stanford Junior University}, ADDRESS = {Stanford}, YEAR = 1988, SERIES = "CSLI Lecture Notes", NUMBER = 14 } @INCOLLECTION{levdef, AUTHOR = "L\'{e}vy, Azriel", TITLE = "The Definability of Cardinal Numbers", BOOKTITLE = {Foundations of Mathematics: {S}ymposium Papers Commemorating the Sixtieth Birthday of Kurt G\"{o}del}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = 1969, EDITOR = "Bulloff, Jack J. and Holyoke, Thomas C. and Hahn, S. W.", PAGES = "15--38" } @BOOK{frabarlevfou, AUTHOR = {Fraenkel, A. and Bar-Hillel, Yehoshua and Levy, Azriel}, TITLE = "Foundations of Set Theory", EDITION = "second revised", PUBLISHER = {North-Holland Publishing Company}, ADDRESS = {Amsterdam}, YEAR = 1973, SERIES = sil, NUMBER = 67 } @INCOLLECTION{scoaxi, AUTHOR = "Scott, Dana", TITLE = "Axiomatizing Set Theory", BOOKTITLE = "Axiomatic Set Theory", PUBLISHER = {American Mathematical Society}, ADDRESS = {Providence, Rhode Island}, YEAR = 1974, EDITOR = "Jech, Thomas J.", PAGES = "207--214", SERIES = "Proceedings of Symposia in Pure Mathematics", NUMBER = "13, part 2" } @INCOLLECTION{bersys, AUTHOR = "Bernays, Paul", TITLE = "A System of Axiomatic Set Theory", BOOKTITLE = "Sets and Classes; {O}n the Work by {P}aul {B}ernays", PUBLISHER = {North-Holland Publishing Company}, ADDRESS = {New York}, YEAR = 1976, EDITOR = {M\"{u}ller, Gert H.}, PAGES = "1--119", SERIES = sil, NUMBER = 84, NOTE = "Originally published in the {\em Journal of Symbolic Logic,\/} 2:65--77, 1937; 6: 1--17, 1941; 7:65--89, 1942; 7:133--145, 1942; 8:89--106, 1943; 13:65--79, 1948; 19:81--96 1954"} @ARTICLE{levvon, AUTHOR = "L\'{e}vy, Azriel", TITLE = "On von {N}eumann's Axiom System for Set Theory", JOURNAL = "American Mathematical Monthly", YEAR = 1968, VOLUME = 75, PAGES = "762--763" } @ARTICLE{levaxi, AUTHOR = "L\'{e}vy, Azriel", TITLE = "Axiom Schemata of Strong Infinity in Axiomatic Set Theory", JOURNAL = "Pacific Journal of Mathematics", YEAR = 1960, VOLUME = 10, PAGES = "223--238" } @ARTICLE{harwha, AUTHOR = "Harris, J. H.", TITLE = "What's So Logical about the ``Logical'' Axioms?", JOURNAL = "Studia Logica", YEAR = 1982, VOLUME = 41, PAGES = "159--171" } @BOOK{edm, EDITOR = "Iyanaga, Sh\^{o}kichi and Kawada, Yukiyosi", TITLE = "Encyclopedic Dictionary of Mathematics", PUBLISHER = {MIT Press}, ADDRESS = {Cambridge, Massachusetts}, YEAR = 1980, NOTE = "Translated by the Mathematical Society of Japan with the cooperation of the American Mathematical Society" } @BOOK{trodalcon, AUTHOR = "Troelstra, Anne Sjerp and Dalen, Dirk van", TITLE = "Constructivism in Mathematics: {A}n Introduction", PUBLISHER = {North-Holland Publishing Company}, ADDRESS = {New York}, YEAR = 1988, SERIES = sil, NUMBER = 121, NOTE = "Two volumes" } @BOOK{nelpre, AUTHOR = "Nelson, Edward", TITLE = "Predicative Arithmetic", PUBLISHER = {Princeton University Press}, ADDRESS = {Princeton, New Jersey}, YEAR = 1986, SERIES = "Mathematical Notes", NUMBER = 32 } @ARTICLE{skofou, AUTHOR = "Skolem, Thoralf", TITLE = {Begr\"{u}ndung der elementaren {A}rithmetik durch die rekurrierende {D}enkweise ohne {A}nwendung scheinbarer {V}er\"{a}nderlichen mit unendlichem {A}usdehnungsbereich}, YEAR = 1923, JOURNAL = {Skrifter, Videnskabsakademiet i Kristiania}, SERIES = "I", NUMBER = 6, NOTE = "All page references are to the translation by Stefan Bauer-Mengelberg, pp.~303--333 [vH67]" } @BOOK{hilbergru, AUTHOR = "Hilbert, David and Bernays, Paul", TITLE = "Grundlagen der {M}athematik", PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = "1968 and 1970", SERIES = "Die {G}rundlehren der mathematischen {W}issenschaften in {E}inzeldarstellungen", NUMBER = "40 and Number 50", EDITION = "second", NOTE = "Two volumes. First edition, 1934 and 1939" } @BOOK{goorec, AUTHOR = "Goodstein, Reuben Louis", TITLE = "Recursive Number Theory", PUBLISHER = {North-Holland Publishing Company}, ADDRESS = {Amsterdam}, YEAR = 1957, SERIES = sil } @ARTICLE{assrek, AUTHOR = {Asser, G\"{u}nter}, TITLE = {Rekursive {W}ortfunktionen}, JOURNAL = {Zeitschrift f\"{u}r mathematische Logik und Grundlagen der Mathematik}, YEAR = 1960, VOLUME = 6, PAGES = "258--278" } @ARTICLE{rodpri, AUTHOR = {R\"{o}dding, D.}, TITLE = {Primitiv-rekursive {F}unktionen \"{u}ber einem {B}ereich endlicher {M}engen}, JOURNAL = {Archiv f\"{u}r mathematische Logik und Grundlagenforschung}, YEAR = 1967, VOLUME = 10, PAGES = "13--29" } @ARTICLE{mahpri, AUTHOR = {Mahn, F.-K.}, TITLE = {Zu den Primitiv-rekursive {F}unktionen \"{u}ber einem {B}ereich endlicher {M}engen}, JOURNAL = {Archiv f\"{u}r mathematische Logik und Grundlagenforschung}, YEAR = 1967, VOLUME = 10, PAGES = "30--33" } @INCOLLECTION{jenkarpri, AUTHOR = "Jensen, Ronald B. and Karp, Carol", TITLE = "Primitive Recursive Set Functions", BOOKTITLE = "Axiomatic Set Theory", PUBLISHER = {American Mathematical Society}, ADDRESS = {Providence, Rhode Island}, YEAR = 1971, EDITOR = "Scott, Dana", PAGES = "143--176", SERIES = "Proceedings of Symposia in Pure Mathematics", NUMBER = "13, part 1" } @INCOLLECTION{fefthe, AUTHOR = "Feferman, Solomon", TITLE = "Theories of Finite Type Related to Mathematical Practice", BOOKTITLE = "Handbook of Mathematical Logic", PUBLISHER = "North-Holland Publishing Company", ADDRESS = "Amsterdam", YEAR = 1977, EDITOR = "Barwise, Jon", CHAPTER = "D.4", PAGES = "913--971", SERIES = sil, NUMBER = 90 } @BOOK{harmorscesimhar, EDITOR = "Harrington, Leo A. and Morley, Michael D. and \v{S}\v{c}edrov, A. and Simpson, Stephen G.", TITLE = "Harvey Friedman's Research on the Foundations of Mathematics", PUBLISHER = {North-Holland Publishing Company}, ADDRESS = {Amsterdam}, YEAR = 1985 } @BOOK{malmet, AUTHOR = "Maltsev, Anatolii Ivanovich", TITLE = "The Metamathematics of Algebraic Systems: Collected Papers 1936--1967", PUBLISHER = {North-Holland Publishing Company}, ADDRESS = {Amsterdam}, YEAR = 1971, NOTE = "Edited and translated by Benjamin F. Wells III. The author's name is also transliterated Mal${}'$cev" } @ARTICLE{lowmog, AUTHOR = {L\"{o}wenheim, Leopold}, TITLE = {\"{U}ber {M}\"{o}glichkeiten im {R}elativkalk\"{u}l}, JOURNAL = "Mathematische Annalen", VOLUME = 76, PAGES = "447--470", NOTE = "All page references are to the translation by Stefan Bauer-Mengelberg, pp.~232--251 [vH67]", YEAR = 1915} @BOOK{levbas, AUTHOR = {Levy, Azriel}, TITLE = "Basic Set Theory", PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = 1979, SERIES = pml } @INCOLLECTION{zaruni, AUTHOR = "Zarach, Andrzej", TITLE = "Unions of {ZF\({}^{-}\)}-Models Which Are Themselves {ZF\({}^{-}\)}-Models", BOOKTITLE = "Logic Colloquium '80", PUBLISHER = "North-Holland Publishing Company", ADDRESS = "Amsterdam", YEAR = 1982, EDITOR = "van Dalen, D. and Lascar, D. and Smiley, T. J.", PAGES = "315--342", SERIES = sil, NUMBER = 108 } @ARTICLE{fefref, AUTHOR = "Feferman, Solomon", TITLE = "Reflecting on Incompleteness", JOURNAL = jsl, YEAR = 1991, VOLUME = 56, PAGES = "1--49" } @ARTICLE{davmatrobhil, AUTHOR = "Davis, Martin and Matijacevi\v{c}, Yuri and Robinson, Julia", TITLE = "Hilbert's Tenth Problem. {D}iophantine Equations: {P}ositive Aspects of a Negative Solution", JOURNAL = "Proceedings of Symposia in Pure Mathematics", YEAR = 1976, VOLUME = 28, PAGES = "223--378" } @BOOK{shomat, AUTHOR = "Shoenfield, Joseph R.", TITLE = "Mathematical Logic", PUBLISHER = {Addison-Wesley Publishing Company}, ADDRESS = {Reading, Massachusetts}, YEAR = 1967, SERIES = "Addison-Wesley Series in Logic" } @ARTICLE{golher, AUTHOR = "Goldfarb, Warren", TITLE = {Herbrand's Theorem and the Incompleteness of Arithmetic}, PAGES = "45--64", JOURNAL = "Iyyun, A Jerusalem Philosophical Quarterly", YEAR = 1990, VOLUME = 39 } @INCOLLECTION{smoinc, AUTHOR = "Smorynski, C.", TITLE = "The Incompleteness Theorems", BOOKTITLE = "Handbook of Mathematical Logic", PUBLISHER = "North-Holland Publishing Company", ADDRESS = "Amsterdam", YEAR = 1977, EDITOR = "Barwise, Jon", CHAPTER = "D.1", PAGES = "821--865", SERIES = sil, NUMBER = 90 } @BOOK{knusur, AUTHOR = "Knuth, Donald Ervin", TITLE = "Surreal Numbers: How Two Ex-Students Turned On to Pure Mathematics and Found Total Happiness: A Mathematical Novelette", PUBLISHER = {Addison-Wesley Publishing Company}, ADDRESS = {Reading, Massachusetts}, YEAR = 1974 } @BOOK{frazeh, AUTHOR = "Fraenkel, A.", TITLE = {Zehn Vorlesungen \"{u}ber die Grundlegung der Mengenlehre}, PUBLISHER = {B. G. Teubner}, ADDRESS = {Leipzig and Berlin}, YEAR = 1927 } @INCOLLECTION{vauint, AUTHOR = {Vaught, Robert}, TITLE = {Introductory Note to 1934c and 1935}, BOOKTITLE = {Kurt G\"{o}del, Collected Works}, PUBLISHER = {Oxford University Press}, ADDRESS = {New York}, YEAR = 1986, PAGES = "Vol. 1, 376--379", NOTE = "Edited by Solomon Feferman, John W. Dawson, Jr., Stephen C. Kleene, Gregory H. Moore, Robert M. Solovay, and Jean van Heijenoort"} @INCOLLECTION{moonot, AUTHOR = {Moore, Gregory H.}, TITLE = {Note to 1947 and 1964}, BOOKTITLE = {Kurt G\"{o}del, Collected Works}, PUBLISHER = {Oxford University Press}, ADDRESS = {New York}, YEAR = 1986, PAGES = "Vol. 2, 154--175", NOTE = "Edited by Solomon Feferman, John W. Dawson, Jr., Stephen C. Kleene, Gregory H. Moore, Robert M. Solovay, and Jean van Heijenoort"} @BOOK{godcon, AUTHOR = {G\"{o}del, Kurt}, TITLE = "The Consistency of the Axiom of Choice and of the Generalized Continuum Hypothesis with the Axioms of Set Theory", PUBLISHER = {Princeton University Press}, ADDRESS = {Princeton, New Jersey}, YEAR = 1940, SERIES = "Annals of Mathematics Studies", NUMBER = 3, NOTE = {Lecture notes by George W. Brown. Reprinted with additions in 1951 and 1966. All page references are to the reprinting as Vol. 2, pp.~33--101 [G\"{o}d90]} } @BOOK{herlog, AUTHOR = "Herbrand, Jacques", TITLE = {Jacques Herbrand: Logical Writings}, PUBLISHER = {Harvard University Press}, ADDRESS = {Cambridge, Massachusetts}, YEAR = 1971, NOTE = "Edited and translated by Warren D. Goldfarb" } @ARTICLE{heruns, AUTHOR = "Herbrand, Jacques", TITLE = "Unsigned Note on {H}erbrand's Thesis", JOURNAL = "Annales de l'Universit\'{e} de Paris", YEAR = 1931, VOLUME = 6, PAGES = "186--189", NOTE = "All page references are to the translation as pp.~272--276 [Her71]" } @ARTICLE{malunt, AUTHOR = {Maltsev, Anatolii Ivanovich}, TITLE = {Untersuchungen aus dem {G}ebiete der mathematischen {L}ogik}, JOURNAL = "Matematicheskii sbornik", VOLUME = 1, PAGES = "323--336", NOTE = "Translated as pp.~1--14 of [Mal71]. The author's name is also transliterated Mal${}'$cev", YEAR = 1936 } @ARTICLE{malgen, AUTHOR = {Maltsev, Anatolii Ivanovich}, TITLE = {On a General Method for Obtaining Local Theorems in Group Theory}, JOURNAL = "Ivanovskii Gosudarstvennii Pedagogicheskii Institut im. D. A. Furmanova. Ivanovskoye matematicheskoye obshchestvo. Ucheniye zapiski", VOLUME = 1, PAGES = "3--9", NOTE = "In Russian. Translated as pp.~15--21 of [Mal71]. The author's name is also transliterated Mal${}'$cev", YEAR = 1936 } @ARTICLE{weymat, AUTHOR = "Weyl, Hermann", TITLE = {Mathematics and Logic. {A} brief survey serving as a preface to a review of ``{T}he {P}hilosophy of {B}ertrand {R}ussell''}, JOURNAL = "American Mathematical Monthly", YEAR = 1946, VOLUME = 53, PAGES = "2--13", NOTE = "Reprinted as Vol. 4, pp.~268--279 [Wey68]" } @ARTICLE{neudef, AUTHOR = "von Neumann, John", TITLE = {\"{U}ber die {D}efinition durch transfinite {I}nduktion und verwandte {F}ragen der allgemeinen {M}engenlehre}, JOURNAL = "Mathematische Annalen", YEAR = 1928, VOLUME = 99, PAGES = "373--391", NOTE = "All page references are to the reprinting as Vol. 1, pp.~320--338 [vN61]" } @ARTICLE{neuwid, AUTHOR = "von Neumann, John", TITLE = {\"{U}ber eine {W}iderspruchfreiheitsfrage in der axiomatischen {M}engenlehre}, JOURNAL = {Journal f\"{u}r die reine und angewandte {M}athematik}, YEAR = 1929, VOLUME = 160, PAGES = "227--241", NOTE = "All page references are to the reprinting as Vol. 1, pp.~494--508 [vN61]" } @BOOK{brocol, AUTHOR = "Brouwer, Luitzen Egbertus Jan", TITLE = "Collected Works", PUBLISHER = {North-Holland Publishing Company}, ADDRESS = {Amsterdam}, YEAR = 1975, NOTE = "Edited by Arend Heyting" } @ARTICLE{brohis, AUTHOR = "Brouwer, Luitzen Egbertus Jan", TITLE = "Historical Background, Principles and Methods of Intuitionism", JOURNAL = "South African Journal of Science", YEAR = 1952, VOLUME = 49, PAGES = "139--146", NOTE = "All page references are to the reprinting as Vol.~1, pp.~508--515 [Bro75]" } @INCOLLECTION{yesult, AUTHOR = "Yessenin-Volpin, A. S.", TITLE = "The Ultra-Intuitionistic Criticism and the Antitraditional Program for Foundations of Mathematics", BOOKTITLE = "Intuitionism and Proof Theory. Proceedings of the Summer Conference at Buffalo, New York, 1968", PUBLISHER = {North-Holland Publishing Company}, ADDRESS = {Amsterdam}, YEAR = 1970, EDITOR = "Kino, A. and Myhill, John and Vesley, Richard Eugene", PAGES = "3--45", NOTE = "The author's name is also transliterated Esenin-Vol${}'$pin" } @ARTICLE{weydef, AUTHOR = "Weyl, Hermann", TITLE = {\"{U}ber die {D}efinitionen der mathematischen {G}rundbegriffe}, JOURNAL = {Mathematish-naturwissenschaftliche Bl\"{a}tter}, YEAR = 1910, VOLUME = 7, PAGES = "93--95, 109--113", NOTE = "Reprinted as Vol.~1 , pp.~298--304 [Wey68]" } @INCOLLECTION{fefwey, AUTHOR = "Feferman, Solomon", TITLE = "Weyl Vindicated: ``{D}ass {K}ontinuum'' 70 Years Later", BOOKTITLE = "Temi e prospettive della logica e della filosofia contemporanee: {A}tti del congresso, {C}esena 7--10 gennaio, 1987", PUBLISHER = {CLUEB}, ADDRESS = {Bologna}, YEAR = 1988, VOLUME = 1, PAGES = "59--93" } @BOOK{ebbfluthomat, AUTHOR = {Ebbinghaus, Heinz-Dieter and Flum, J\"{o}rg and Thomas, Wolfgang}, TITLE = "Mathematical Logic", PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = 1984, SERIES = "Undergraduate Texts in Mathematics" } @BOOK{monmat, AUTHOR = {Monk, J. Donald}, TITLE = "Mathematical Logic", PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = 1976, SERIES = "Graduate Texts in Mathematics", NUMBER = 37 } @BOOK{chuint, AUTHOR = {Church, Alonzo}, TITLE = "Introduction to Mathematical Logic", PUBLISHER = {Princeton University Press}, ADDRESS = {Princeton, New Jersey}, YEAR = 1956 } @BOOK{hilackgru, AUTHOR = {Hilbert, David and Ackermann, Wilhelm}, TITLE = {Grundz\"{u}ge der Theoretischen Logic}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = 1938, SERIES = {Die Grundlehren der Mathematischen Wissenschaften}, NUMBER = 27, EDITION = "second", NOTE = "First edition 1928. In German. English translation by Lewis M. Hammond, George G. Leckie, and F. Steinhardt, {\em Principles of Mathematical Logic\/} (Chelsea Publishing Company, New York, 1950). Translation edited and with notes by Robert E. Luce." } @ARTICLE{zylsom, AUTHOR = "\.{Z}yli\'{n}ski, E.", TITLE = "Some Remarks Concerning the Theory of Deduction", JOURNAL = fm, YEAR = 1925, VOLUME = 7, PAGES = "203--209" } @ARTICLE{sheset, AUTHOR = "Sheffer, Henry Maurice", TITLE = "A Set of Five Independent Postulates for Boolean Algebras, With Application to Logical Constants", JOURNAL = "Transactions of the American Mathematical Society", YEAR = 1913, VOLUME = 14, PAGES = "481--488" } @BOOK{peicol, AUTHOR = "Peirce, Charles Sanders", TITLE = "Collected Papers", PUBLISHER = {Harvard University Press}, ADDRESS = {Cambridge, Mass.}, YEAR = "1931--1958", NOTE = "Eight volumes. Volumes 1--6 edited by Charles Hartshorne and Paul Weiss. Volumes 7--8 edited by Arthur W. Burks" } @ARTICLE{wercom, AUTHOR = "Wernick, William", TITLE = "Complete Sets of Logical Functions", JOURNAL = "Transactions of the American Mathematical Society", YEAR = 1942, VOLUME = 51, PAGES = "117--132" } @BOOK{postwo, AUTHOR = "Post, Emil L.", TITLE = "The Two-Valued Iterative Systems of Mathematical Logic", PUBLISHER = {Princeton University Press}, ADDRESS = {Princeton, New Jersey}, YEAR = 1941, SERIES = "Annals of Mathematics Studies", NUMBER = 5 } @BOOK{klemet, AUTHOR = "Kleene, Stephen Cole", TITLE = "Introduction to Metamathematics", PUBLISHER = {Wolters-Noordhoff Publishing and North-Holland Publishing Company and American Elsevier Publishing Company}, ADDRESS = {Groningen and Amsterdam and New York}, YEAR = 1952, SERIES = "Bibliotheca Mathematica: A Series of Monographs on Pure and Applied Mathematics", NUMBER = 1 } @ARTICLE{hasbem, AUTHOR = "Hasenjaeger, Gisbert", TITLE = {Eine {B}emerkung zu {H}enkin's {B}eweis f\"{u}r die {V}ollst\"{a}ndigkeit das {P}r\"{a}dikatenkalk\"{u}ls der ersten {S}tufe}, JOURNAL = jsl, YEAR = 1953, VOLUME = 18, PAGES = "42--48" } @BOOK{quimet, AUTHOR = "Quine, Willard Van Orman", TITLE = "Methods of Logic", PUBLISHER = {Holt, Rinehart and Winston, Inc.}, ADDRESS = {New York}, YEAR = 1972, EDITION = "third", NOTE = "First edition, 1950, second edition 1959" } @INPROCEEDINGS{prevol, AUTHOR = "Presburger, M.", TITLE = {\"{U}ber die {V}ollst\"{a}ndigkeit eines gewissen {S}ystems der {A}rithmetik ganzer {Z}ahlen, in welchem die {A}ddition als einzige {O}peration hervortritt}, BOOKTITLE = {Sprawozdanie z I Kongresu Matematyk\'{o}w Kraj\'{o}w S\l owia\'{n}skich}, YEAR = 1930, PAGES = "92--101, 395", ADDRESS = {Warsaw}, NOTE = "Transactions of the First Congress of Mathematicians of the Slavic Countries, Warsaw, 1929. English translation with commentary: D. Jacquette (translator). On the completeness of a certain system of arithmetic of whole numbers in which addition occurs as the only operation. {\em History and Philosophy of Logic,\/} 12:225--233, 1991." } @BOOK{boojefcom, author = {Boolos, George S. and Jeffrey, Richard C.}, title = {Computability and Logic}, publisher = {Cambridge University Press}, year = {1989}, address = {New York}, edition = {third}, note = {First edition, 1974; second edition, 1980} } @BOOK{barmosvic, AUTHOR = {Barwise, Jon and Moss, Larry}, TITLE = "Vicious Circles: {O}n the Mathematics of Non-Wellfounded Phenomena", PUBLISHER = {CSLI Publications, Center for the Study of Language and Information, Leland Stanford Junior University}, ADDRESS = {Stanford}, YEAR = 1996, SERIES = "CSLI Lecture Notes", NUMBER = 60 } @BOOK{devjoy, AUTHOR = {Devlin, Keith}, TITLE = "The Joy of Sets: {F}undamentals of Contemporary Set Theory", PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = 1993, SERIES = "Undergraduate Texts in Mathematics", EDITION = "second" } @ARTICLE{godfor, AUTHOR = {G\"{o}del, Kurt}, TITLE = {\"{U}ber formal unentscheidbare {S}\"{a}tze der { {\em Principia Mathematica\/} } und verwandter {S}ysteme {I} }, PAGES = "173--198", JOURNAL = {Monatshefte f\"{u}r {M}athematik und {P}hysik}, YEAR = 1931, VOLUME = 38, NOTE = {All page references are to the translation by John Dawson, revised in consultation with Stefan Bauer-Mengelberg and Jean van Heijenoort, published on pages facing a reprinting of the article, vol. 1, pp.~144--195 [G\"{o}d90]} } @ARTICLE{targen, AUTHOR = "Tarski, Alfred", TITLE = {General Principles of Induction and Recursion: {T}he Notion of Rank in Axiomatic Set Theory and Some of Its Applications}, PAGES = "442--443", JOURNAL = "Bulletin of the American Mathematical Society", YEAR = 1955, VOLUME = 61, NOTE = {Two abstracts} } @ARTICLE{monwel, AUTHOR = "Montague, Richard", TITLE = {Well-Founded Relations; {G}eneralizations of Principles of Induction and Recursion}, PAGES = "442", JOURNAL = "Bulletin of the American Mathematical Society", YEAR = 1955, VOLUME = 61, NOTE = {abstract} } @ARTICLE{benque, AUTHOR = "Bendixson, I.", TITLE = {Quelques th\'{e}oremes de la th\'{e}orie des ensembles de points}, PAGES = "4415--429", JOURNAL = "Acta Mathematica", YEAR = 1983, VOLUME = 2 } @BOOK{feflig, AUTHOR = "Feferman, Solomon", TITLE = "In the Light of Logic", PUBLISHER = {Oxford University Press}, ADDRESS = {New York}, YEAR = 1998 } @INPROCEEDINGS{fefinf, AUTHOR = "Feferman, Solomon", TITLE = {Infinity in Mathematics: {I}s {C}antor Necessary?}, BOOKTITLE = {L'infinito nella scienza (Infinity in Science)}, YEAR = 1987, PAGES = "151--209", ADDRESS = {Rome}, EDITOR = {Toraldo di Francia, G.}, NOTE = "All page references are to the reprinting with minor additions and corrections as pp.~28--73, 229--248 of [Fef98]." } @INPROCEEDINGS{fefgod, AUTHOR = "Feferman, Solomon", TITLE = {G\"{o}del's Program for New Axioms: {W}hy, Where, How and What?}, YEAR = 1996, PAGES = "1--32", BOOKTITLE = {G\"{o}del '96; Logical Foundations of Mathematics, Computer Science and Physics; Kurt G\"{o}del's Legacy. Brno, Czech Republic, August 1996, Proceedings.}, ADDRESS = "Urbana, Illinois", PUBLISHER = "Association for Symbolic Logic", SERIES = "Lecture Notes in Logic", NUMBER = 6, EDITOR = "P. Hajek" } @INPROCEEDINGS{fefwha, AUTHOR = "Feferman, Solomon", TITLE = "What Rests on What? {T}he Proof-Theoretic Analysis of Mathematics", BOOKTITLE = "Philosophy of Mathematics. {P}roceedings of the Fifteenth International {W}ittgenstein Symposium", PART = 1, YEAR = 1993, EDITOR = "Czermak, J.", PAGES = "147--171", PUBLISHER = {Verlag H\"{o}lder-Pichler-Tempsky}, ADDRESS = {Vienna}, NOTE = "All page references are to the reprinting with minor additions and corrections as pp.~187--208 of [Fef98]." } @INPROCEEDINGS{fefwhy, AUTHOR = "Feferman, Solomon", TITLE = {Why a Little Bit Goes a Long Way: {L}ogical Foundations of Scientifically Applicable Mathematics}, PAGES = "442--455", BOOKTITLE = "PSA; {P}roceedings of the Biennial Meeting of the Philosophy of Science Association", YEAR = 1993, VOLUME = 2, ADDRESS = "East Lansing, Michigan", PUBLISHER = "Philosophy of Science Association" } @ARTICLE{fefstrunf, AUTHOR = "Feferman, Solomon and Strahm, Thomas", TITLE = {The Unfolding of Non-Finitist Arithmetic}, YEAR = "20xx", PAGES = "xxxx--xxxx", JOURNAL = "Annals of Pure and Applied Logic", VOLUME = "xxx" } @BOOK{takpro, AUTHOR = "Takeuti, Gaisi", TITLE = "Proof Theory", PUBLISHER = {North-Holland}, ADDRESS = {Amsterdam}, YEAR = 1987, EDITION = "2nd" } @INCOLLECTION{simsub, AUTHOR = "Simpson, S. G.", TITLE = "Subsystems of ${Z}_{2}$ and Reverse Mathematics", BOOKTITLE = "Proof Theory", PUBLISHER = {North-Holland}, ADDRESS = {Amsterdam}, YEAR = 1987, BOOKAUTHOR = "Takeuti, Gaisi", CHAPTER = "Appendix", PAGES = "432--446" } @Book{pranat, author = {Prawitz, Dag}, title = {Natural Deduction: {A} Proof-Theoretical Study}, publisher = {Almqvist \& Wiksell}, year = {1965}, volume = {3}, series = {Stockholm Studies in Philosophy}, address = {Stockholm}, }

-- ShaughanLavine - 16 Aug 2006
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