Ackermann, Wilhelm. “Die Widerspruchsfreiheit der allgemeinen Mengenlehre.” Mathematische Annalen 114 (1937), 305–315.
Aczel, Peter. “An Introduction to Inductive Definitions.” In Barwise, Handbook, pp. 739–782.
Barwise, Jon. Admissible Sets and Structures. Berlin: Springer, 1975.
Barwise, Jon, ed. Handbook of Mathematical Logic. Amsterdam: North-Holland, 1977.
Bealer, George. “Intuition.” In Borchert, Donald M. (editor in chief), The Encyclopedia of Philosophy Supplement, pp. 268–269. New York: Macmillan Reference USA, 1996. Reprinted in Borchert, Encyclopedia 2nd ed., IV, 732–733.
Bealer, George. “On the Possibility of Philosophical Knowledge.” Philosophical Perspectives 10 (1996), 1–34.
Beeson, Michael. Foundations of Constructive Mathematics. Berlin: Springer, 1985.
Benacerraf, Paul. “Mathematical Truth.” The Journal of Philosophy 70 (1973), 661–679. Reprinted in Benacerraf and Putnam, pp. 403–420. (Not in 1st ed.)
Benacerraf, Paul. “What Numbers Could Not Be.” Philosophical Review 74 (1965), 47–73. Reprinted in Benacerraf and Putnam, pp. 272–294. (Not in 1st ed.) Cited according to reprint.
Benacerraf, Paul, and Putnam, Hilary, eds. Philosophy of Mathematics: Selected Readings. Englewood Cliffs, NJ: Prentice Hall, 1964. 2nd ed. Cambridge University Press, 1983 (published 1984).
Bernays, Paul. Abhandlungen zur Philosophie der Mathematik. Darmstadt: Wissenschaftliche Buchgesellschaft, 1976.
Bernays, Paul. “Bemerkungen zum Paradoxon von Thoralf Skolem.” Avhandlingen uitgitt av Det Norske Videnskaps-Akademi i Oslo, I. Mat.-Naturv. Klasse, 1957, No. 5, 3–9. Reprinted in Abhandlungen, pp. 113–118.
Bernays, Paul. “Die Mathematik als ein zugleich Vertrautes und Unbekanntes.” Synthese 9 (1955), 465–471. Reprinted in Abhandlungen, pp. 107–112.
Bernays, Paul. “Mathematische Existenz und Widerspruchsfreiheit.” In Études de philosophie des sciences, en hommage à F. Gonseth à l'occasion de son soixantième anniversaire, pp. 11–25. Neuchâtel: Griffon, 1950. Reprinted in Abhandlungen, pp. 92–106.
Bernays, Paul. “Die Philosophie der Mathematik und die Hilbertsche Beweistheorie.” Blätter für deutsche Philosophie 4 (1930), 326–367. Reprinted with postscript in Abhandlungen, pp. 17–61.
Bernays, Paul. “Quelques points essentiels de la métamathématique.” L'enseignement mathématique 52 (1935), 70–95.
Bernays, Paul. “Quelques points de vue concernant le problème de l'évidence,” Synthese 5 (1946), 321–326. (The German translation in Abhandlungen is by Bernays but was evidently done in 1974.)
Bernays, Paul. “Sur le platonisme dans les mathématiques.” L'enseignement mathématique 52 (1935), 52–69. Translation in Benacerraf and Putnam, pp. 258–271 of 2nd ed. (The German version in Abhandlungen is a translation from the French.)
Bernays, Paul. “A System of Axiomatic Set Theory, Part II.” The Journal of Symbolic Logic 6 (1941), 1–17. Reprinted in Müller, Sets and Classes, pp. 14–30.
Bernays, Paul. “A System of Axiomatic Set Theory, Part VII.” The Journal of Symbolic Logic 19 (1954), 81–96. Reprinted in Müller, Sets and Classes, pp. 102–119.
Bernays, Paul. “Über Hilberts Gedanken zur Grundlegung der Arithmetik,” Jahresbericht der Deutschen Mathematiker-Vereinigung 31 (1922), 10–19.
Bernays, Paul. “Zur Frage der Unendlichkeitsschemata in deraxiomatischen Mengenlehre.” In Essays on the Foundations of Mathematics, dedicated to Professor A. A. Fraenkel on his 70th birthday, pp. 3–49. Jerusalem: Magnes Press, 1961. Translation, “partially revised,” in Müller, Sets and Classes, pp. 121–172.
Bernays, Paul. See also Hilbert and Bernays.
Black, Max. “The elusiveness of sets.” Review of Metaphysics 24 (1970–1971), 614–636.
Bolzano, Bernard. Paradoxien des Unendlichen. Ed. by Příhonský, F.. Leipzig 1851.
Bolzano, Bernard. Wissenschaftslehre. 4 vols. Sulzach 1837.
BonJour, Laurence. In Defense of Pure Reason. A Rationalist Account of a priori Justification. Cambridge University Press, 1998.
Boolos, George. “Iteration Again.” Philosophical Topics 17 (1989), 5–21. Reprinted in LLL.
Boolos, George. “The Iterative Conception of Set.” The Journal of Philosophy 68 (1971), 215–231. Reprinted in LLL. Also reprinted in Benacerraf and Putnam, 2nd ed.
Boolos, George. Logic, Logic, and Logic. Edited by Jeffrey, Richard. With Introductions and Afterword by John P. Burgess. Cambridge, MA: Harvard University Press, 1998. Hereafter LLL.
Boolos, George. The Logic of Provability. Cambridge University Press, 1993.
Boolos, George. “Must we believe in set theory?” In LLL, pp. 120–132. Also in Sher and Tieszen, pp. 257–268.
Boolos, George. “Nominalist Platonism.” Philosophical Review 94 (1985), 327–344. Reprinted in LLL.
Boolos, George. “Reply to Charles Parsons, ‘Sets and Classes’.” In LLL, pp. 30–36. (Written and presented in 1974.)
Boolos, George. “To Be is to be the Value of a Variable (or to be Some Values of Some Variables).” The Journal of Philosophy 81 (1984), 430–449. Reprinted in LLL.
Boolos, George, and Jeffrey, Richard C.. Computability and Logic. Cambridge University Press, 1974. 2nd ed., 1981. 3rd ed., 1990. 4th ed., with John P. Burgess, 2002.
Borchert, Donald M. (Editor in chief). The Encyclopedia of Philosophy, Second Edition. 10 vols. Detroit: Macmillan Reference USA, 2006. (For first edition, see Edwards.)
Brentano, Franz. Wahrheit und Evidenz. Erkenntnistheoretische Abhandlungen und Briefe. Edited by Kraus, Oskar. Leipzig: Meiner, 1930. Reprinted Hamburg: Meiner, 1962, 1974.
Bromberger, Sylvain. On What We Know We Don't Know. Explanation, Theory, Linguistics, and How Questions Shape Them. Chicago: University of Chicago Press, and Stanford: Center for the Study of Language and Information, 1992.
Bromberger, Sylvain. “Types and Tokens in Linguistics.” In George, Alexander (ed.), Reflections on Chomsky, pp. 58–89. Cambridge, Mass., MIT Press, 1989. Reprinted in On What We Know We Don't Know, pp. 170–208.
Bromberger, Sylvain, and Halle, Morris. “The Ontology of Phonology.” In Bromberger, On What We Know We Don't Know, pp. 209–228.
Brouwer, L. E. J. Collected Works, volume 1: Philosophy and Intuitionistic Mathematics. Edited by Heyting, Arend. Amsterdam: North-Holland, 1975.
Brouwer, L. E. J.. “Mathematik, Wissenschaft, und Sprache.” Monatshefte für Mathematik und Physik 36 (1929), 153–164. Reprinted, Collected Works, vol. 1.
Brouwer, L. E. J.. Over de grondslagen der wiskunde. Amsterdam and Leipzig: Maass and van Suchtelen, 1907. Critical edition in Dirk van Dalen (ed.), L. E. J. Brouwer en de grondslagen van de wiskunde (Utrecht: Epsilon, 2001), pp. 39–147. English translation (of the main text) in Collected Works, vol. 1.
Buchholz, Wilfried, Feferman, Solomon, Pohlers, Wolfram, and Sieg, Wilfried, Iterated Inductive Definitions and Subsystems of Analysis. Lecture Notes in Mathematics 897. Berlin etc.: Springer, 1981.
Burgess, John P. “E pluribus unum: Plural Logic and Set Theory.” Philosophia Mathematica (III) 12 (2004), 193–221.
Burgess, John P.. Fixing Frege. Princeton University Press, 2005.
Burgess, John P.. “Mathematics and Bleak House.” Philosophia Mathematica (III) 12 (2004), 18–36.
Burgess, John P.. Review of Shapiro, Philosophy of Mathematics. Notre Dame Journal of Formal Logic 40 (1999), 283–291.
Burgess, John P., and Hazen, Allen. “Predicative Logic and Formal Arithmetic.” Notre Dame Journal of Formal Logic 39 (1998), 1–17.
Burgess, John P., and Rosen, Gideon. A Subject with no Object. Strategies for Nominalistic Interpretation of Mathematics. Oxford: Clarendon Press, 1997.
Cantor, Georg. Gesammelte Abhandlungen mathematischen und philosophischen Inhalts. Edited by Zermelo, Ernst. Berlin: Springer, 1932. Reprinted Hildesheim: Olms, 1962.
Carnap, Rudolf. Logische Syntax der Sprache. Vienna: Springer, 1934.
Carnap, Rudolf. Logical Syntax of Language. Translated by Amethe Smeation. London: Kegan Paul, 1937. (Contains two sections not in the German edition.)
Carson, Emily. “On realism in set theory.” Philosophia Mathematica (III) 4 (1996), 3–17.
Cartwright, Richard L. “Speaking of Everything.” NoÛs 28 (1994), 1–20.
Church, Alonzo. “Comparison of Russell's Solution of the Semantical Paradoxes with that of Tarski.” The Journal of Symbolic Logic 41 (1976), 747–760. Reprinted in Martin, Recent Essays.
Church, Alonzo. “A Formulation of the Logic of Sense and Denotation.” In Structure, Method, and Meaning: Essays in Honor of Henry M. Sheffer, pp. 3–24. New York: Liberal Arts Press, 1951.
Church, Alonzo. “A Formulation of the Simple Theory of Types.” The Journal of Symbolic Logic 5 (1940), 56–68.
Cohn-Vossen, S. See Hilbert and Cohn-Vossen.
Collins, George E., and Halpern, J. D.. “On the Interpretability of Arithmetic in Set Theory.” Notre Dame Journal of Formal Logic 11 (1970), 477–483.
Dales, H. G., and Oliveri, G. (eds.). Truth in Mathematics. Oxford: Clarendon Press, 1998.
Davidson, Donald. Inquiries into Truth and Interpretation. Oxford: Clarendon Press, 1984.
Davidson, Donald. “On Saying That.” Synthese 19 (1968), 130–146. Reprinted in Inquiries.
Davidson, Donald. “Radical Interpretation.” Dialectica 27 (1973), 313–328. Reprinted in Inquiries.
Dedekind, Richard. Gesammelte mathematische Werke. 3 vols. Edited by Fricke, Robert, Noether, Emmy, and Ore, Öystein. Braunschweig: Vieweg, 1930–32.
Dedekind, Richard. Was sind und was sollen die Zahlen?Braunschweig: Vieweg, 1888, 3rd ed. 1911. Translation in Ewald, II, 787–833.
Demopoulos, William (ed.). Frege's Philosophy of Mathematics. Cambridge, MA: Harvard University Press, 1995.
Descartes, René. The Philosophical Writings of Descartes. Translated by John Cottingham, Robert Stoothoff, and Dugald Murdoch. 2 vols. Cambridge University Press, 1985.
Donnellan, Keith. “Reference and Definite Descriptions.” Philosophical Review 75 (1966), 281–304.
Drake, F. R.Set Theory. An Introduction to Large Cardinals. Amsterdam: North-Holland, 1974.
Dummett, Michael. Frege: Philosophy of Language. London: Duckworth, 1973. 2nd ed., 1981.
Dummett, Michael. Frege: Philosophy of Mathematics. Cambridge, Mass.: Harvard University Press, 1991.
Dummett, Michael. “The Philosophical Basis of Intuitionistic Logic.” In Rose, H. E. and Shepherdson, J. C. (eds.), Logic Colloquium '73, pp. 5–40. Amsterdam: North-Holland, 1975. Reprinted in Truth and Other Enigmas, pp. 215–247, and in Benacerraf and Putnam (not in 1st ed.).
Dummett, Michael. “The Philosophical Significance of Gödel's Theorem.” Ratio 5 (1963), 140–155. Reprinted in Truth and Other Enigmas, pp. 186–201.
Dummett, Michael. “Platonism.” In Truth and Other Enigmas, pp. 202–214. (Text of an address given in 1967.)
Dummett, Michael. The Seas of Language. Oxford: Clarendon Press, 1993.
Dummett, Michael. Truth and Other Enigmas. London: Duckworth, 1978.
Dummett, Michael. “Wang's Paradox.” Synthese 30 (1975), 301–324. Reprinted in Truth and Other Enigmas, pp. 248–268.
Dummett, Michael. “What is Mathematics About?” In George, Mathematics and Mind, pp. 11–26. Also in The Seas of Language, pp. 429–445.
Edwards, Paul (ed.). The Encyclopedia of Philosophy. 7 vols. New York: Free Press/Macmillan, 1967. (For second edition, see Borchert.)
Evans, Gareth. “Can there be Vague Objects?” Analysis 38 (1978), 208. Reprinted in Collected Papers (Oxford: Clarendon Press, 1985), pp. 176–177.
Ewald, William (ed.). From Kant to Hilbert. A Source Book in the Foundations of Mathematics. 2 vols. Oxford: Clarendon Press, 1996.
Feferman, Solomon. “Definedness.” Erkenntnis 43 (1995), 295–320.
Feferman, Solomon. In the Light of Logic. Oxford University Press, 1998.
Feferman, Solomon. “Reflecting on Incompleteness.” The Journal of Symbolic Logic 56 (1991), 1–49.
Feferman, Solomon. “Systems of Predicative Analysis.” The Journal of Symbolic Logic 29 (1964), 1–30.
Feferman, Solomon. “Weyl vindicated. Das Kontinuum 70 years later.” In Cellucci, Carlo and Sambin, Giovanni (eds.), Temi e prospettive della logica e della scienza contemporanee, vol. 1, pp. 59–93. Bologna: CLUEB, 1988. Reprinted with corrrections and additions in In the Light of Logic.
See also Buchholz, Feferman, Pohlers, and Sieg.
See also Gödel.
Feferman, Solomon, and Hellman, Geoffrey. “Predicative Foundations of Arithmetic.” Journal of Philosophical Logic 22 (1995), 1–17.
Feferman, Solomon, and Geoffrey Hellman. “Challenges to Predicative Foundations of Arithmetic.” In Sher and Tieszen, pp. 317–335.
Ferreira, Fernando. “A Note on Finiteness in the Predicative Foundations of Arithmetic.” Journal of Philosophical Logic 28 (1999), 165–174.
Field, Hartry. “Are Our Logical and Mathematical Concepts Highly Indeterminate?” In French, Peter A., Uehling, Theodore E. Jr., and Wettstein, Howard K. (eds.), Midwest Studies in Philosophy, volume 19: Philosophical Naturalism, pp. 391–429. Minneapolis: University of Minnesota Press, 1994.
Field, Hartry. “Is Mathematical Knowledge Just Logical Knowledge?” Philosophical Review 93 (1984), 509–552. Reprinted, with revisions and postscript, in Realism, Mathematics, and Modality, pp. 79–124.
Field, Hartry. “On Conservativeness and Incompleteness.” The Journal of Philosophy 82 (1985), 239–260. Reprinted in Realism, Mathematics, and Modality, pp. 125–146.
Field, Hartry. “Realism, Mathematics, and Modality.” Philosophical Topics 19 (1988), 57–107. Reprinted in Realism, Mathematics, and Modality, pp. 227–281.
Field, Hartry. Realism, Mathematics, and Modality. Oxford: Blackwell, 1989.
Field, Hartry. Science without Numbers: A Defense of Nominalism. Princeton University Press, 1980.
Field, Hartry. Truth and the Absence of Fact. Oxford: Clarendon Press, 2001.
Field, Hartry. “Which Undecidable Mathematical Sentences have Determinate Truth Values?” In Dales and Oliveri, pp. 291–310. Reprinted with Postscript in Truth and the Absence of Fact, pp. 332–360.
Fraenkel, (Abraham) Adolf. Einleitung in die Mengenlehre. Berlin: Springer, 1919. 2nd ed., revised and enlarged, 1923. 3d ed., further revised and enlarged, 1928.
Frege, Gottlob. Begriffschrift. Eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Halle: Nebert, 1879. Reprinted in Begriffschrift und andere Aufsätze. Translation in van Heijenoort.
Frege, Gottlob. Begriffschrift und andere Aufsätze. Edited by Angelelli, Ignacio. Hildesheim: Olms, 1964.
Frege, Gottlob. Collected Papers on Mathematics, Logic, and Philosophy. Edited by McGuinness, Brian. Translated by Max Black and others. Oxford: Blackwell, 1984.
Frege, Gottlob. Frege on the Foundations of Geometry and Formal Theories in Arithmetic. Translated and edited by Eike-Henner W. Kluge. New Haven: Yale University Press, 1971.
Frege, Gottlob. “Der Gedanke: Eine logische Untersuchung.” Beiträge zur Philosophie des deutschen Idealismus 1 (1918–19), 58–77. Reprinted in Kleine Schriften. Translation in Collected Papers.
Frege, Gottlob. The Foundations of Arithmetic. Translated by J. L. Austin. Contains the German text. Oxford: Blackwell, 1950. 2nd ed. 1953. (The pagination of the German text is exactly the same as that of the original, and thus that of the translation is very close.)
Frege, Gottlob. Funktion und Begriff. Jena: Pohle, 1891. Reprinted in Kleine Schriften. Translation in Collected Papers.
Frege, Gottlob. Grundgesetze der Arithmetik. Jena: Pohle. Vol. I, 1893. Vol. II, 1903. Reprinted Hildesheim: Olms, 1962, 1998.
Frege, Gottlob. Die Grundlagen der Arithmetik. Breslau: Koebner, 1884. Centenary edition, with amplifying texts, critically edited by Christian Thiel. Hamburg: Meiner, 1986. English translation Foundations.
Frege, Gottlob. Kleine Schriften. Edited by Angelelli, Ignacio. Hildesheim: Olms, 1967. Translated as Collected Papers.
Frege, Gottlob. Logical Investigations. Edited by Geach, Peter. Translated by Geach and R. H. Stoothoff. Oxford: Blackwell, 1977.
Frege, Gottlob. Nachgelassene Schriften. Edited by Hermes, Hans, Kambartel, Friedrich, and Kaulbach, Friedrich. Hamburg: Meiner, 1969. 2nd. ed., revised, with an appendix (lecture notes) ed. with an introduction by Lothar Kreiser. Hamburg: Meiner, 1983.
Frege, Gottlob. Review of Husserl, Philosophie der Arithmetik. Zeitschrift für Philosophie und philosophische Kritik 103 (1894), 313–332. Reprinted in Kleine Schriften. Translation in Collected Papers.
Frege, Gottlob. Wissenschaftlicher Briefwechsel. Edited by Gabriel, Gottfried, Hermes, Hans, Kambartel, Friedrich, Thiel, Christian, and Veraart, Albert. Hamburg: Meiner, 1976.
Friedman, Michael. Kant and the Exact Sciences. Cambridge, MA: Harvard University Press, 1992.
Gallin, Daniel. Intensional and Higher-Order Modal Logic. Amsterdam: North-Holland, 1975.
Gandy, Robin O. “Limitations to Mathematical Knowledge.” In Dalen, D., Lascar, D., and Smiley, T. J. (eds.), Logic Colloquium ′80, pp. 129–145. Amsterdam: North-Holland, 1982.
George, Alexander. “The Imprecision of Impredicativity.” Mind N. S. 96 (1987), 514–518.
George, Alexander,(ed.). Mathematics and Mind. Oxford University Press, 1994.
George, Alexander, and Daniel J. Velleman. “Two Conceptions of Natural Number.” In Dales and Oliveri, pp. 311–327.
Givant, Steven, and Tarski, Alfred. “Peano Arithmetic and the Zermelo-like Theory of Sets with Finite Ranks.” Abstract 77T-E51. Notices of the Americal Mathematical Society 24 (1977), A-437.
See also Tarski and Givant.
Gödel, Kurt. Collected Works. Volume I, Publications 1929–1936. Edited by Feferman, Solomon, Dawson, John W. Jr., Kleene, Stephen C., Moore, Gregory H., Solovay, Robert M., and Heijenoort, Jean. New York and Oxford: Oxford University Press, 1986.
Gödel, Kurt. Collected Works. Volume II, Publications 1938–1974. Edited by Feferman, Solomon, Dawson, John W. Jr., Kleene, Stephen C., Moore, Gregory H., Solovay, Robert M., and Heijenoort, Jean. New York and Oxford: Oxford University Press, 1990.
Gödel, Kurt. Collected Works. Volume III, Unpublished Essays and Lectures. Edited by Feferman, Solomon, Dawson, John W. Jr., Goldfarb, Warren, Parsons, Charles, and Solovay, Robert M.. New York and Oxford: Oxford University Press, 1995.
Gödel, Kurt. Collected Works. Volume IV, Correspondence, A-G. Edited by Feferman, Solomon, Dawson, John W. Jr., Goldfarb, Warren, Parsons, Charles, and Sieg, Wilfried. Oxford: Clarendon Press, 2003.
Gödel, Kurt. Collected Works. Volume V, Correspondence, H-Z. Edited by Feferman, Solomon, Dawson, John W. Jr., Goldfarb, Warren, Parsons, Charles, and Sieg, Wilfried. Oxford: Clarendon Press, 2003.
Gödel, Kurt. The Consistency of the Continuum Hypothesis. Princeton University Press, 1940. Reprinted in Collected Works, II, 33–101.
Gödel, Kurt. “Is Mathematics Syntax of Language?” Unfinished paper written between 1953 and 1959. Versions III and V in Collected Works, III, 334–362.
Gödel, Kurt. “On an Extension of Finitary Mathematics which has not yet been Used.” Revised English version, with additional notes, of “Über eine noch nicht benützte Erweiterung.” In Collected Works, II, 271–280.
Gödel, Kurt. “The Present Situation in the Foundations of Mathematics.” Lecture to the Mathematical Association of America, 1933. In Collected Works, III, 45–53.
Gödel, Kurt. “Russell's Mathematical Logic.” In Schilpp, P. A. (ed.), The Philosophy of Bertrand Russell (Evanston: Northwestern University, 1944), pp. 125–153. Reprinted in Collected Works, II, 119–141. Also reprinted in Benacerraf and Putnam, pp. 442–470.
Gödel, Kurt. “Some Basic Theorems on the Foundations of Mathematics and their Philosophical Implications.” Josiah Willard Gibbs Lecture, American Mathematical Society, 1951. In Collected Works, III, 304–323. (The word ‘philosophical’ was omitted from the title of the published version. See Collected Works, IV, 636.)
Gödel, Kurt. “Über eine bisher noch nicht benützte Erweiterung des finiten Standpunktes.” Dialectica 12 (1958), 280–287. Reprinted, with English translation, in Collected Works, II, 240–251.
Gödel, Kurt. “Vortrag bei Zilsel.” Lecture to an informal circle, Vienna, 1938. In Collected Works, III, 86–113. With English translation.
Gödel, Kurt. “What is Cantor's Continuum Problem?” American Mathematical Monthly 54 (1947), 515–525. Revised and expanded in Benacerraf and Putnam, 1st ed., pp. 258–271, also in 2nd ed., pp. 470–485. Both versions reprinted in Collected Works, II, 176–187 and 254–270 respectively.
Gödel, Kurt. “Zur intuitionistischen Arithmetik und Zahlentheorie.” Ergebnisse eines mathematischen Kolloquiums 4 (1933), 34–38. Reprinted, with English translation, in Collected Works, I, 286–295.
Goldfarb, Warren. See Gödel.
Goldfarb, Warren, and Thomas Ricketts. “Carnap and the Philosophy of Mathematics.” In Bell, David and Vossenkuhl, Wilhelm (eds.), Wissenschaft und Subjektivität, pp. 61–78. Berlin: Akademie-Verlag, 1992.
Goodman, Nelson. Fact, Fiction, and Forecast. Cambridge, MA: Harvard University Press, 1955. 4th ed., 1983.
Goodman, Nelson. Problems and Projects. Indianapolis: Bobbs-Merrill, 1972.
Goodman, Nelson. “Sense and Certainty.” The Philosophical Review 61 (1952), 160–167. Reprinted in Problems and Projects, pp. 60–68.
Goodman, Nelson. The Structure of Appearance. Cambridge, MA: Harvard University Press, 1951. 3rd ed. Dordrecht: Reidel, 1977.
Goodman, Nelson, and Quine, W. V.. “Steps towards a Constructive Nominalism.” The Journal of Symbolic Logic 12 (1947), 105–122. Reprinted in Goodman, Problems and Projects, pp. 173–198.
Goodman, Nicolas D. “The Knowing Mathematician.” Synthese 60 (1984), 21–38.
Goodstein, R. L.Recursive Number Theory. Amsterdam: North-Holland, 1957.
Gottlieb, Dale. Ontological Economy. Substitutional Quantification and Mathematics. Oxford: Clarendon Press, 1980.
Grossmann, Reinhardt. “Meinong's Doctrine of the Aussersein of the Pure Object.” NoÛs 8 (1974), 67–82.
Hájek, Petr, and Pudlák, Pavel. Metamathematics of First-Order Arithmetic. Berlin, Heidelberg, New York: Springer-Verlag, 1993.
Hale, Bob. “Structuralism's Unpaid Epistemological Debts.” Philosophia Mathematica (III) 4 (1996), 124–147.
Hale, Bob, and Wright, Crispin. The Reason's Proper Study. Essays towards a Neo-Fregean Philosophy of Mathematics. Oxford: Clarendon Press, 2001.
Hale, Bob, and Wright, Crispin. “Benacerraf's Dilemma Revisited.” European Journal of Philosophy 10 (2002), 101–129.
Halle, Morris. See Bromberger and Halle.
Hart, W. D. “Benacerraf's Dilemma.” Crítica 23 (1991), 87–103.
Hart, W. D.. Review of Steiner, Mathematical Knowledge. The Journal of Philosophy 74 (1977), 118–129.
Hart, W. D.. “Skolem's Promises and Paradoxes.” The Journal of Philosophy 67 (1970), 98–109.
Hauser, Kai. “Is Cantor's Continuum Problem Inherently Vague?” Philosophia Mathematica (III) 10 (2002), 257–285.
Heck, Richard G. Jr. “The consistency of predicative fragments of Frege's Grundgesetze der Arithmetik.” History and Philosophy of Logic 17 (1996), 209–220.
Hellman, Geoffrey. Mathematics without Numbers: Toward a Modal-Structural Interpretation. Oxford: Clarendon Press, 1989.
See also Feferman and Hellman.
Higginbotham, James. “Linguistic Theory and Davidson's Program in Semantics.” In Lepore, Ernest (ed.), Truth and Interpretation. Oxford: Blackwell, 1986.
Higginbotham, James. “On Higher-Order Logic and Natural Language.” Proceedings of the British Academy 95 (1998), 1–27. Somewhat abridged version in Sher and Tieszen, pp. 75–99.
Hilbert, David. Grundlagen der Geometrie. Leipzig: Teubner, 1899. 11th ed., ed. by Bernays, Paul, Stuttgart: Teubner, 1972. English translation of 10th ed. by Leo Unger, La Salle, Ill.: Open Court, 1971, 2nd ed. 1992.
Hilbert, David. “Neubegründung der Mathematik (Erste Mitteilung).” Abhandlungen aus dem mathematischen Seminar der Hamburgischen Universität 1 (1922), 157–177. Translation in Mancosu.
Hilbert, David. “Über das Unendliche.” Mathematische Annalen 95 (1926), 161–190. Translation in van Heijenoort. Partial translation in Benacerraf and Putnam. (Citations of a translation are of the one in van Heijenoort.)
Hilbert, David, and Bernays, Paul. Grundlagen der Mathematik. Berlin: Springer, vol. I, 1934; vol. II, 1939. 2nd ed., vol. I, 1968; vol. II, 1970.
Hilbert, David, and Cohn-Vossen, S.. Anschauliche Geometrie. Berlin: Springer, 1932.
Hodes, Harold T. “Logicism and the Ontological Commitments of Arithmetic.” The Journal of Philosophy 81 (1984), 123–149.
Husserl, Edmund. Erfahrung und Urteil. Edited by Landgrebe, Ludwig. Hamburg: Claassen, 1948.
Husserl, Edmund. Formale und transzendentale Logik. Halle: Niemeyer, 1929; reprinted Tübingen: Niemeyer, 1981. Critical edition edited by Paul Janssen. Husserliana, vol. 17. The Hague: Nijhoff, 1974.
Husserl, Edmund. Logical Investigations. Translated by J. N. Findlay. London: Routledge and Kegan Paul, 1970. Translation of second edition of Logische Untersuchungen.
Husserl, Edmund. Logische Untersuchungen. Halle: Niemeyer, 1900–01, 2nd ed. 1913–20. Critical edition of volume 1 edited by Elmar Holenstein. Husserliana, vol. 18. The Hague: Nijhoff, 1975. Critical edition of volume 2 edited by Ursula Panzer. Husserliana, vol. 19. The Hague: Nijhoff, 1984. Page references prefixed A are to the 1st ed., B to the 2nd ed., with the subscript indicating the part of volume 2 in the 2nd ed.
Husserl, Edmund. Philosophie der Arithmetik, mit ergänzenden Texten (1890–1901). Edited by Eley, Lothar. Hussserliana, vol. 12. The Hague: Nijhoff, 1970. (Philosophie der Arithmetik first published Halle: Pfeffer, 1891.)
Isles, David. “What Evidence Is There that 265536 Is a Natural Number?” Notre Dame Journal of Formal Logic 33 (1992), 465–480.
Jeffrey, Richard C. See Boolos and Jeffrey.
Kant, Immanuel. Critique of Pure Reason. Translated by Norman Kemp Smith. London: Macmillan, 1929. 2nd ed., 1933.
Kant, Immanuel. Critique of Pure Reason. Translated by Paul Guyer and Allen W. Wood. Cambridge University Press, 1997.
Kant, Immanuel. Gesammelte Schriften. Edited by the Preussische Akademie der Wissenschaften and its successors. Berlin: Reimer, later de Gruyter, 1902–. Cited as Ak.
Kant, Immanuel. Kritik der reinen Vernunft. Edited by Timmermann, Jens. Hamburg: Meiner, 1998.
Kant, Immanuel. Prolegomena to any Future Metaphysics. Translated by Lewis White Beck (revising earlier translations). New York: Liberal Arts Press, 1956.
Kaufman, E. L., Lord, M. W., Reese, T. W., and Volkmann, J.. “The Discrimination of Visual Number.” American Journal of Psychology 62 (1949), 498–525.
Keränen, Jukka. “The Identity Problem for Realist Structuralism.” Philosophia Mathematica (III) 9 (2001), 308–330.
Kim, Jaegwon. “The Role of Perception in A Priori Knowledge.” Philosophical Studies 40 (1981), 339–354.
Kirby, Laurence. “Finitary Set Theory.” Notre Dame Journal of Formal Logic, forthcoming.
Kitcher, Philip. The Nature of Mathematical Knowledge. New York and Oxford: Oxford University Press, 1983.
Kitcher, Philip. “The Plight of the Platonist.” NoÛs 12 (1978), 119–136.
Kleene, Stephen Cole. Introduction to Metamathematics. New York: Van Nostrand, 1952.
See also Gödel.
Kluge, Eike-Henner W. See Frege.
Koellner, Peter. “On the Question of Absolute Undecidability.” Philosophia Mathematica (III) 14 (2006), 153–188.
Kreisel, G. “Informal Rigour and Completeness Proofs.” In Lakatos, Imre (ed.), Problems in the Philosophy of Mathematics, pp. 138–186. Amsterdam: North-Holland, 1967.
Kreisel, G.. “Mathematical Logic.” In Saaty, T. L. (ed.), Lectures on Modern Mathematics, vol. III, pp. 95–195. New York: John Wiley and Sons, 1965.
Kreisel, G.. “Ordinal logics and the characterization of informal concepts of proof.” In Proceedings of the International Congress of Mathematicians, Edinburgh 1958, pp. 289–299. Cambridge University Press, 1960.
Kripke, Saul A. “Is There a Problem about Substitutional Quantification?” In Evans, Gareth and and McDowell, John (eds.). Truth and Meaning, pp. 325–419. Oxford: Clarendon Press, 1976.
Kripke, Saul A.. “Naming and Necessity.” In Davidson, Donald and Harman, Gilbert, eds., Semantics of Natural Language, pp. 253–355, 763–769. Dordrecht: Reidel, 1972. 2nd ed.: Naming and Necessity. Cambridge, MA: Harvard University Press, 1980.
Krivine, Jean-Louis. Introduction to Axiomatic Set Theory. Translated by David Miller. Dordrecht: Reidel, 1971.
Ladyman, James. See Leitgeb and Ladyman.
Lambek, Joachim, and Scott, P. J.. Introduction to Higher-Order Categorical Logic. Cambridge University Press, 1986.
Lambert, Karel. Meinong and the Principle of Independence: Its Place in Meinong's Theory of Objects and its Significance in Contemporary Philosophical Logic. Cambridge University Press, 1983.
Lavine, Shaughan. “Something about Everything: Universal Quantification in the Universal Sense of Universal Quantification.” In Rayo and Uzquiano, pp. 98–148.
Lavine, Shaughan. Understanding the Infinite. Cambridge, MA: Harvard University Press, 1994.
Leibniz, Gottfried Wilhelm. Philosophical Essays. Translated and edited by Ariew, Roger and Garber, Daniel. Indianapolis: Hackett, 1989.
Leitgeb, Hannes, and James Ladyman. “Criteria of Identity and Structuralist Ontology.” Analysis, forthcoming.
Lévy, Azriel. Basic Set Theory. Berlin: Springer, 1979.
Lewis, David. “Mathematics is Megethology.” Philosophia Mathematica (III) 1 (1993), 3–23. Reprinted in Papers in Philosophical Logic (Cambridge University Press, 1998), pp. 203–229.
Lewis, David. On the Plurality of Worlds. Oxford: Blackwell, 1986.
Lewis, David. Parts of Classes. Oxford: Blackwell, 1991.
Linnebo, Øystein. “Epistemological Challenges to Mathematical Platonism.” Philosophical Studies 129 (2006), 545–574.
Linnebo, Øystein . “Plural Quantification.” In Stanford Encyclopedia of Philosophy, 2004. Online at http://plato.stanford.edu.
Lorenzen, Paul. Einführung in die operative Logik und Mathematik. Berlin: Springer, 1955.
Lorenzen, Paul. “Logical Reflection and Formalism.” The Journal of Symbolic Logic 23 (1958), 241–249.
Lorenzen, Paul, and Myhill, John. “Constructive Definition of Certain Analytic Sets of Numbers.” Ibid. 24 (1959), 37–49.
MacBride, Fraser. “Structuralism Reconsidered.” In Shapiro, Oxford Handbook, pp. 563–589.
Maddy, Penelope. “Believing the Axioms.” The Journal of Symbolic Logic 53 (1988), 481–511, 736–764.
Maddy, Penelope. “Indispensability and Practice.” The Journal of Philosophy 89 (1992), 275–289.
Maddy, Penelope. Naturalism in Mathematics. Oxford: Clarendon Press, 1997.
Maddy, Penelope. “Perception and Mathematical Intuition.” Philosophical Review 89 (1980), 163–196.
Maddy, Penelope. Realism in Mathematics. Oxford: Clarendon Press, 1990.
Majer, Ulrich. “Geometrie und Erfahrung: Ein Vergleich der Auffassungen von Hilbert und Kant.” Report no. 17/93 of the Research Group on Semantical Aspects of Space-Time Theories. Bielefeld: Zentrum für interdisziplinäre Forschung, 1993.
Majer, Ulrich. “Geometry, intuition, and experience: From Kant to Husserl.” Erkenntnis 42 (1995), 261–285. Revised English version of “Geometrie und Erfahrung.”
Martin, Donald A. “Descriptive Set Theory: Projective Sets.” In Barwise, Handbook, pp. 783–815.
Martin, Donald A.. “Mathematical Evidence.” In Dales and Oliveri, pp. 214–231.
Martin, Robert L. (ed.). Recent Essays on Truth and the Liar Paradox. New York and Oxford: Oxford University Press.
Martin-Löf, Per. Intuitionistic Type Theory. Naples: Bibliopilis, 1984.
McCarthy, Timothy. “Platonism and Possibility.” The Journal of Philosophy 83 (1986), 275–290.
McGee, Vann. “How we Learn Mathematical Language.” Philosophical Review 107 (1997), 35–68.
McGee, Vann. “Truth by Default.” Philosophia Mathematica (III) 9 (2001), 5–20.
Meinong, Alexius. Gesamtausgabe. Edited by Chisholm, Roderick M., Haller, Rudolf, and Kindlinger, Rudolf. Graz: Akademische Druck- und Verlagsanstalt, 1968–78.
Meinong, Alexius. “Über Gegenstandstheorie.” In Meinong, (ed.), Untersuchungen zur Gegenstandstheorie und Psychologie, pp. 1–50. Leipzig: Barth, 1904. Reprinted in Gesamtausgabe, II.
Meinong, Alexius. Über die Stellung der Gegenstandstheorie im System der Wissenschaften. Leipzig: Voigtländer, 1907. Reprinted in Gesamtausgabe, V.
Meyer, Robert K. “In Memoriam: Richard (Routley) Sylvan, 1935–1996.” The Bulletin of Symbolic Logic 4 (1998), 338–340.
Montagna, Franco, and Mancini, Antonella. “A Minimal Predicative Set Theory.” Notre Dame Journal of Formal Logic 35 (1994), 186–203.
Moore, Gregory H. “Beyond First-Order Logic: The Historical Interplay between Mathematical Logic and Axiomatic Set Theory.” History and Philosophy of Logic 1 (1980), 95–137.
See also Gödel.
Moschovakis, Yiannis N.Descriptive Set Theory. Amsterdam: North-Holland, 1980.
Mostowski, Andrzej. See Tarski, Mostowski, and Robinson.
Müller, Gert H. “Framing Mathematics.” Epistemologia 4 (1981), 253–286.
Müller, Gert H. (ed.). Sets and Classes: On the Work by Paul Bernays. Amsterdam: North-Holland, 1976.
Myhill, John. “The Undefinability of the Set of Natural Numbers in the Ramified Principia.” In Nakhnikian, George (ed.), Bertrand Russell's Philosophy, pp. 19–27. New York: Barnes and Noble, 1974.
See also Lorenzen and Myhill.
Nagel, Thomas. The Last Word. New York and Oxford: Oxford University Press, 1997.
Nelson, Edward. Predicative Arithmetic. Mathematical Notes, 32. Princeton University Press, 1986.
Page, James. “Parsons on Mathematical Intuition.” Mind N. S. 102 (1993), 223–232.
Parsons, Charles. “Arithmetic and the Categories.” Topoi 3 (1984), 109–121.
Parsons, Charles. “Developing Arithmetic in Set Theory without the Axiom of Infinity: Some Historical Remarks.” History and Philosophy of Logic 8 (1987), 201–213.
Parsons, Charles. “Finitism and intuitive knowledge.” In Schirn, The Philosophy of Mathematics Today, pp. 249–270.
Parsons, Charles. “Genetic Explanation in The Roots of Reference.” In Barrett, Robert B. and Gibson, Roger F. (eds.), Perspectives on Quine, pp. 273–290. Oxford: Blackwell, 1990.
Parsons, Charles. “The Impredicativity of Induction.” In Cauman, Leigh S., Levi, Isaac, Parsons, Charles, and Schwartz, Robert (eds.), How Many Questions? Essays in Honor of Sidney Morgenbesser, pp. 132–153. Indianapolis: Hackett, 1983. Revised and expanded version in Michael Detlefsen (ed.), Proof, Logic, and Formalization, pp. 139–161. London: Routledge, 1992.
Parsons, Charles. “Intuition and Number.” In George, Mathematics and Mind, pp. 141–157.
Parsons, Charles. “Intuition in Constructive Mathematics.” In Butterfield, Jeremy (ed.). Language, Mind, and Logic, pp. 211–229. Cambridge University Press, 1986.
Parsons, Charles. “Mathematical Intuition.” Proceedings of the Aristotelian Society N. S. 80 (1979–1980), 145–168.
Parsons, Charles. Mathematics in Philosophy: Selected Essays. Ithaca, NY: Cornell University Press, 1983. Paperback edition with corrections and short preface, 2005.
Parsons, Charles. “On Some Difficulties concerning Intuition and Intuitive Knowledge.” Mind N. S. 102 (1993), 233–245.
Parsons, Charles. “Paul Bernays' Later Philosophy of Mathematics.” In Dimitracopoulos, Costa, Newelski, Ludomir, and Normann, Dag (eds.), Logic Colloquium 2005, pp. 129–150. Lecture Notes in Logic, 28. Urbana, Association for Symbolic Logic, and Cambridge University Press, 2007.
Parsons, Charles. “Platonism and Mathematical Intuition in Kurt Gödel's Thought.” The Bulletin of Symbolic Logic 1 (1995), 44–74.
Parsons, Charles. “Realism and the Debate on Impredicativity, 1917–1944.” In Sieg, Sommer, and Talcott, pp. 372–389.
Parsons, Charles. “Reason and Intuition.” Synthese 125 (2000), 299–315.
Parsons, Charles. Review of Kitcher, The Nature of Mathematical Knowledge. Philosophical Review 95 (1986), 129–137.
Parsons, Charles. “The Structuralist View of Mathematical Objects.” Synthese 84 (1990), 303–346.
Parsons, Charles. “Substitutional Quantification and Mathematics. Review of Gottlieb, Ontological Economy.” British Journal for the Philosophy of Science 33 (1982), 409–421.
Parsons, Charles. “The Transcendental Aesthetic.” In Guyer, Paul (ed.), The Cambridge Companion to Kant, pp. 62–100. Cambridge University Press, 1992.
Parsons, Charles. “The Uniqueness of the Natural Numbers.” Iyyun 39 (1990), 13–44.
Parsons, Charles. “What Can We Do ‘In Principle’?” In Chiara, Maria Luisa Dalla, Doets, Kees, Mundici, Daniele, and Benthem, Johan (eds.), Logic and Scientific Methods, pp. 335–354. Volume One of the Tenth International Congress of Logic, Methodology, and Philosophy of Science, Florence, August 1995. Dordrecht: Kluwer, 1997.
See also Gödel.
Parsons, Terence. “The Methodology of Nonexistence.” The Journal of Philosophy 76 (1979), 639–662.
Parsons, Terence. Nonexistent Objects. New Haven: Yale University Press, 1980.
Plantinga, Alvin. The Nature of Necessity. Oxford: Clarendon Press, 1974.
Pohlers, Wolfram. See Buchholz, Feferman, Pohlers, and Sieg.
Poincaré, Henri. Dernières Pensées. Paris: Flammarion, 1913. 2nd ed., 1926.
Poincaré, Henri. “Réflexions sur les deux notes précédentes,” Acta Mathematica 32 (1909), 195–200.
Previale, Flavio. “Induction and Foundation in the Theory of Hereditarily Finite Sets.” Archive for Mathematical Logic 33 (1994), 213–241.
Pudlák, Pavel. See Hájek and Pudlák.
Putnam, Hilary. Mathematics, Matter, and Method. Collected Philosophical Papers, Volume 1. Cambridge University Press, 1975. 2nd ed. 1980.
Putnam, Hilary. “Mathematics without Foundations.” The Journal of Philosophy 64 (1967), 5–22. Reprinted in Mathematics, Matter, and Method, pp. 43–59, and in Benacerraf and Putnam, pp. 295–311 (not in 1st ed.). Cited according to Mathematics, Matter, and Method.
Putnam, Hilary. “Models and Reality.” The Journal of Symbolic Logic 45 (1980), 464–482. Reprinted in Realism and Reason, pp. 1–25, and in Benacerraf and Putnam, pp. 421–444 (not in 1st ed.). Cited according to Realism and Reason.
Putnam, Hilary. Realism and Reason: Collected Philosophical Papers, Volume 3. Cambridge University Press, 1983.
Putnam, Hilary. “The Thesis that Mathematics is Logic.” In Schoenman, Ralph ed., Bertrand Russell: Philosopher of the Century, pp. 273–303. London: Allen & Unwin, 1967. Reprinted in Mathematics, Matter, and Method, pp. 12–42.
See also Benacerraf and Putnam.
Quine, W. V.Methods of Logic. New York: Holt, 1950. 3rd ed., 1972. 4th ed. Cambridge, MA: Harvard University Press, 1982.
Quine, W. V.. “Ontological Relativity.” The Journal of Philosophy 65 (1968), 185–212. Reprinted in Ontological Relativity and Other Essays, pp. 26–68.
Quine, W. V.. Ontological Relativity and Other Essays. New York: Columbia University Press, 1969.
Quine, W. V.. Philosophy of Logic. Englewood Cliffs, N.J.: Prentice-Hall, 1970. 2nd ed., Cambridge, MA.: Harvard University Press, 1986.
Quine, W. V.. The Roots of Reference. La Salle, IL: Open Court, 1974.
Quine, W. V.. Set Theory and its Logic. Cambridge, MA: The Belknap Press, Harvard University Press, 1963. Revised edition, 1969.
See also Goodman and Quine.
Rawls, John. Collected Papers. Edited by Freeman, Samuel. Cambridge, MA: Harvard University Press, 1999.
Rawls, John. “The Independence of Moral Theory.” Proceedings and Addresses of the American Philosophical Association 48 (1974–75), 5–22. Reprinted in Collected Papers, pp. 286–302.
Rawls, John. Political Liberalism. New York: Columbia University Press, 1993.
Rawls, John. A Theory of Justice. Cambridge, MA: The Belknap Press of Harvard University Press, 1971.
Rayo, Agustín. “Word and Objects.” NoÛs 36 (2002), 436–464.
Rayo, Agustín, and Uzquiano, Gabriel (eds.). Absolute Generality. Oxford: Clarendon Press, 2006.
Reinhardt, W. N. “Epistemic Theories and the Interpretation of Gödel's Incompleteness Theorems.” Journal of Philosophical Logic 15 (1986), 427–484.
Resnik, Michael D.Frege and the Philosophy of Mathematics. Ithaca, NY: Cornell University Press, 1980.
Resnik, Michael D.. “Mathematics as a Science of Patterns: Ontology and Reference.” NoÛs 15 (1981), 529–550.
Resnik, Michael D.. Mathematics as a Science of Patterns. Oxford: Clarendon Press, 1997.
Resnik, Michael D.. “Parsons on Mathematical Intuition and Obviousness.” In Sher and Tieszen, pp. 219–231.
Resnik, Michael D.. “Quine and the Web of Belief.” In Shapiro, Oxford Handbook, pp. 412–436.
Resnik, Michael D.. “Second-order Logic Still Wild.” The Journal of Philosophy 85 (1988), 75–87.
Rheinwald, Rosemarie. Der Formalismus und seine Grenzen. Untersuchungen zur neueren Philosophie der Mathematik. Königstein/Ts.: Hain, 1984.
Ricketts, Thomas. See Goldfarb and Ricketts.
Robinson, Raphael M. See Tarski, Mostowski, and Robinson.
Rödding, Dieter. “Primitiv-rekursive Funktionen über einem Bereich endlicher Mengen.” Archiv für mathematische Logik und Grundlagenforschung 10 (1967), 13–29.
Rosen, Gideon. See Burgess and Rosen.
Rorty, Richard. “Intuition.” In Edwards, Encyclopedia, III, 204–212, and with addenda by George Bealer and Bruce Russell in Borchert, Encyclopedia 2nd ed., IV, 722–735.
Routley, Richard. Exploring Meinong's Jungle and Beyond. Departmental Monograph #3, Philosophy Department, Research School of Social Sciences, Australian National University, Canberra, 1980.
Routley, Richard, and Routley, Valerie. “Rehabilitating Meinong's Theory of Objects.” Revue internationale de philosophie 27 (1973), 224–254.
Russell, Bertrand. Essays in Analysis. Edited by Lackey, Douglas. New York: Braziller, 1973.
Russell, Bertrand. Logic and Knowledge. Edited by Marsh, Robert C.. London: Allen and Unwin, 1956.
Russell, Bertrand. “Mathematical Logic as Based on the Theory of Types.” American Journal of Mathematics 30 (1908), 222–262. Reprinted in Logic and Knowledge, pp. 59–102, and in van Heijenoort, pp. 150–182 (with introductory note by W. V. Quine).
Russell, Bertrand. “The Philosophy of Logical Atomism.” The Monist 28 (1918), 495–527; 29 (1919), 32–63, 190–222, 345–380. Reprinted in Logic and Knowledge, pp. 175–281, and in The Philosophy of Logical Atomism and Other Essays, 1914–19, pp. 157–244. Cited according to Logic and Knowledge.
Russell, Bertrand. The Philosophy of Logical Atomism and Other Essays, 1914–19. Edited by Slater, John G.. The Collected Papers of Bertrand Russell, Vol. 8. London: Allen and Unwin, 1986.
Russell, Bertrand. The Principles of Mathematics. Cambridge University Press, 1903. 2nd ed. London: Allen and Unwin, 1937.
Russell, Bertrand. The Problems of Philosophy. London: Williams and Norgate, and New York: Holt, 1912. Later reprints Oxford University Press. (That of 1997 adds an introduction by John Perry.)
See also Whitehead and Russell.
Saunders, Simon. “Are Quantum Particles Objects?” Analysis 66 (2006), 52–63.
Schirn, Matthias (ed.). The Philosophy of Mathematics Today. Oxford: Clarendon Press, 1998.
Schütte, Kurt. Beweistheorie. Berlin: Springer, 1960.
Schütte, Kurt. “Logische Abgrenzungen des Transfiniten.” In Käsbauer, Max and Kutschera, Franz (eds.), Logik und Logikkalkül, pp. 105–114. Freiburg: Alber, 1962.
Schütte, Kurt. Proof Theory. Revised and expanded translation of Beweistheorie. Berlin: Springer, 1977.
Scott, Dana. “Axiomatizing Set Theory.” In Jech, Thomas J. (ed.), Axiomatic Set Theory, part 2, pp. 207–214. Proceedings of Symposia in Pure Mathematics, vol. 13, part 2. Providence, RI: American Mathematical Society, 1974.
Shapiro, Stewart (ed.). Intensional Mathematics. Amsterdam: North-Holland, 1985.
Shapiro, Stewart, (ed.). The Oxford Handbook of Philosophy of Mathematics and Logic. New York and Oxford: Oxford University Press, 2005.
Shapiro, Stewart. Philosophy of Mathematics. Structure and Ontology. New York and Oxford: Oxford University Press, 1997.
Shapiro, Stewart. “Space, Number, and Structure: A Tale of Two Debates.” Philosophia Mathematica (III) 4 (1996), 148–173.
Sharvy, Richard. “Why a Class Can't Change its Members.” NoÛs 2 (1968), 303–314.
Sher, Gila, and Tieszen, Richard (eds.). Between Logic and Intuition. Essays in honor of Charles Parsons. Cambridge University Press, 2000.
Shoenfield, J. R. “Axioms of Set Theory.” In Barwise, Handbook, pp. 321–344.
Sieg, Wilfried. “Fragments of Arithmetic.” Annals of Pure and Applied Logic 28 (1985), 33–71.
Sieg, Wilfried, Sommer, Richard, and Talcott, Carolyn (eds.). Reflections on the Foundations of Mathematics. Essays in honor of Solomon Feferman. Lecture Notes in Logic, 15. Urbana, IL: Association for Symbolic Logic, and Natick, MA: A. K. Peters, 2002.
See also Buchholz, Feferman, Pohlers, and Sieg.
Simons, Peter. Parts. A Study in Ontology. Oxford: Clarendon Press, 1987.
Simpson, Stephen G. “Predicativity: The Outer Limits.” In Sieg, Sommer, and Talcott, pp. 130–136.
Simpson, Stephen G.. “Reverse Mathematics.” In Nerode, Anil and Shore, Richard A. (eds.), Recursion Theory, pp. 261–271. Proceedings of Symposia in Pure Mathematics, 42. Providence, RI: American Mathematical Society, 1985.
Simpson, Stephen G.. Subsystems of Second-Order Arithmetic. Springer-Verlag, 1999.
Skolem, Thoralf. Abstract Set Theory. Notre Dame Mathematical Lectures, 8. University of Notre Dame, 1962.
Skolem, Thoralf. “Begründung der elementaren Zahlentheorie durch die rekurrierende Denkweise ohne Anwendung scheinbarer Veränderlichen mit unendlichem Ausdehnungsbereich.” Skrifter, Videnskabsakadmiet i Kristiania I, no. 6 (1923). Reprinted in Selected Works, pp. 153–188. Translation in van Heijenoort, pp. 303–333.
Skolem, Thoralf. “Einige Bermerkungen zur axiomatischen Begründung der Mengenlehre.” In Matematikerkongressen i Helsingfors den 4–7 Juli 1922, Den femte skandinaviska matematikerkongressen, Redogörelse, pp. 217–232. Helsinki: Akademiska Bokhandeln, 1923. Reprinted in Selected Works, pp. 137–152. Translation in van Heijenoort, pp. 290–301.
Skolem, Thoralf. Selected Works in Logic. Edited by Fenstad, Jens Erik. Oslo: Universitetsforlaget, 1970.
Sommer, Richard. See Sieg, Sommer, and Talcott.
Steiner, Mark. Mathematical Knowledge. Ithaca, NY: Cornell University Press, 1975.
Sylvan, Richard. See Routley.
Szmielew, Wanda, and Tarski, Alfred. “Mutual Interpretability of some Essentially Undecidable Theories” (abstract). In Proceedings of the International Congress of Mathematicians, Cambridge, Massachusetts, U.S.A., August 30–September 6, 1950, vol. 1, p. 734. Providence, RI: American Mathematical Society, 1952.
Tait, William (W. W.). “Against Intuitionism: Constructive Mathematics is Part of Classical Mathematics.” Journal of Philosophical Logic 12 (1983), 173–195.
Tait, William (W. W.). “Constructing Cardinals from Below.” In The Provenance, pp. 133–154.
Tait, William (W. W.). “Constructive Reasoning.” In Rootselaar, B. and Staal, J. F. (eds.), Logic, Methodology, and Philosophy of Science III, pp. 185–198. Amsterdam: North-Holland, 1968.
Tait, William (W. W.). “Critical Notice: Charles Parsons' Mathematics in Philosophy.” Philosophy of Science 53 (1986), 588–607.
Tait, William (W. W.). “Finitism.” The Journal of Philosophy 78 (1981), 524–546. Reprinted in The Provenance, pp. 21–42.
Tait, William (W. W.). “Frege versus Cantor and Dedekind: On the Concept of Number.” In Tait, W. W. (ed.), Early Analytic Philosophy, Frege, Russell, Wittgenstein: Essays in honor of Leonard Linsky, pp. 213–248. Chicago and La Salle, IL: Open Court, 1997. Reprinted in The Provenance, pp. 212–251.
Tait, William (W. W.). The Provenance of Pure Reason. Essays in the Philosophy of Mathematics and its History. Oxford University Press, 2005.
Tait, William W. W.). “Truth and Proof: The Platonism of Mathematics.” Synthese 69 (1986), 341–370. Reprinted with some additional notes in The Provenance, pp. 61–88.
Takeuti, Gaisi. “Construction of the Set Theory from the Theory of Ordinal Numbers.” Journal of the Mathematical Society of Japan 6 (1954), 196–220.
Talcott, Carolyn. See Sieg, Sommer, and Talcott.
Tarski, Alfred. “Sur les ensembles finis.” Fundamenta Mathematicae 6 (1924), 45–95.
Tarski, Alfred. “What is Elementary Geometry?” In Henkin, Leon, Suppes, Patrick, and Tarski, Alfred (eds.), The Axiomatic Method, with Special Reference to Geometry and Physics, pp. 16–29. Proceedings of an International Symposium held at the University of California, Berkeley, December 26, 1957–January 4, 1958. Amsterdam: North-Holland, 1959.
Tarski, Alfred, Mostowski, Andrzej, and Robinson, Raphael M.. Undecidable Theories. Amsterdam: North-Holland, 1953.
Tarski, Alfred, and Givant, Steven. A Formalization of Set Theory without Variables. American Mathematical Society Colloquium Publications, 41. Providence, RI: American Mathematical Society, 1987.
See also Givant and Tarski and Szmielew and Tarski.
Taylor, R. Gregory. “Mathematical Definability and the Paradoxes.” Dissertation, Columbia University, 1983.
Taylor, R. Gregory. “Zermelo, Reductionism, and the Philosophy of Mathematics.” Notre Dame Journal of Formal Logic 34 (1993), 539–563.
Thomason, Richmond H. “Modal Logic and Metaphysics.” In Lambert, Karel (ed.), The Logical Way of Doing Things, pp. 119–146. New Haven: Yale University Press, 1969.
Tieszen, Richard L.Mathematical Intuition: Phenomenology and Mathematical Knowledge. Dordrecht: Kluwer, 1989.
See also Sher and Tieszen.
Troelstra, A. S., and Dalen, Dirk. Constructivism in Mathematics: An Introduction. 2 vols. Amsterdam: North-Holland, 1988.
James, Aken. “Axioms for the Set-Theoretic Hierarchy.” The Journal of Symbolic Logic 51 (1986), 992–1004.
van Dalen, Dirk. See Troelstra and van Dalen and also Brouwer.
D[avid], Dantzig. “Is 101010 a Finite Number?” Dialectica 9 (1955–56), 272–277.
Jean, Heijenoort, ed. From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931. Cambridge, MA: Harvard University Press, 1967.
See also Gödel.
Velleman, Daniel J. See George and Velleman.
Johann, Neumann. “Eine Axiomatisierung der Mengenlehre.” Journal für die reine und angewandte Mathematik 154 (1925), 219–240. Berichtigung, ibid. 155, 128. Translation in van Heijenoort, pp. 393–413.
Wang, Hao. “Between Number Theory and Set Theory.” Mathematische Annalen 126 (1953), 385–409. Reprinted as chapter XIX of A Survey.
Wang, Hao. A Logical Journey: From Gödel to Philosophy. Cambridge, MA: MIT Press, 1996.
Wang, Hao. From Mathematics to Philosophy. London: Routledge and Kegan Paul, 1974.
Wang, Hao. “Ordinal Numbers and Predicative Set Theory.” Zeitschrift für mathematische Logik und Grundlagen der Mathematik 5 (1959), 216–239. Reprinted as Chapter XXV of Survey.
Wang, Hao. A Survey of Mathematical Logic. Peking: Science Press, and Amsterdam: North-Holland, 1962. Reprinted as Logic, Computers, and Sets. New York: Chelsea, 1970.
Wang, Hao. “What is an Individual?” Philosophical Review 62 (1953), 413–420. Reprinted as Appendix 5 to From Mathematics to Philosophy.
Wetzel, Linda. “Expressions vs. Numbers.” Philosophical Topics 17 (1989), 173–196.
Weyl, Hermann. Das Kontinuum. Leipzig: Veit, 1918.
Weyl, Hermann. “Der circulus vitiosus in der heutigen Begründung der Analysis.” Jahresbericht der deutschen Mathematiker-Vereinigung 28 (1919), 85–92.
Whitehead, A. N., and Russell, Bertrand. Principia Mathematica. 3 vols. Cambridge University Press, 1910–13. 2nd ed., 1925–27.
Williamson, Timothy. “Everything.” In Hawthorne, John and Zimmerman, Dean (eds.), Philosophical Perspectives 17: Language and Philosophical Linguistics, pp. 415–465. Oxford: Blackwell, 2003.
Wollheim, Richard. Art and its Objects. New York: Harper and Row, 1968. 2nd ed. with six suppelementary essays. Cambridge University Press, 1980.
Woodin, W. Hugh. “The Continuum Hypothesis, part I.” Notices of the American Mathematical Society 48 (2001), 567–576.
Woodin, W. Hugh. “The Continuum Hypothesis, part II.” Ibid., 681–690.
Woodin, W. Hugh. “The Continuum Hypothesis.” In Cori, René, Razborov, Alexander, Todorcevic, Stevo, and Wood, Carol (eds.), Logic Colloquium 2000, pp. 143–197. Lecture Notes in Logic, 19. Urbana, IL: Association for Symbolic Logic, and Wellesley, MA: A. K. Peters, 2005.
Woodin, W. Hugh. “Set Theory after Russell: The Journey Back to Eden.” In Link, Godehard (ed.), One Hundred Years of Russell's Paradox: Mathematics, Logic, Philosophy, pp. 29–47. Berlin: de Gruyter, 2004.
Wright, Crispin. Frege's Conception of Numbers as Objects. Aberdeen University Press, 1983.
See also Hale and Wright.
Yi, Byeong-Uk. “Is Two a Property?”The Journal of Philosophy 96 (1999), 163–190.
Yi, Byeong-Uk. “The Logic and Meaning of Plurals. Part I.” Journal of Philosophical Logic 34 (2005), 459–506.
Yi, Byeong-Uk. “The Logic and Meaning of Plurals. Part II.” Journal of Philosophical Logic 35 (2006), 239–288.
Zach, Richard. “The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert's Program.” Synthese 137 (2003), 211–259.
Zermelo, Ernst. “Sur les ensembles finis et le principe de l'induction complète,” Acta Mathematica 32 (1909), 183–193.
Zermelo, Ernst. “Über den Begriff der Definitheit in der Axiomatik.” Fundamenta Mathematicae 14 (1929), 339–344.
Zermelo, Ernst. “Über Grenzzahlen und Mengenbereiche.” Ibid. 16 (1930), 29–47. Translation in Ewald, II, 1219–1233.
Zermelo, Ernst. “Untersuchungen über die Grundlagen der Mengenlehre I.” Mathematische Annalen 65 (1908), 261–281. Translation in van Heijenoort, pp. 199–215.
See also Cantor.
