Linked bibliography for the SEP article "Abstract Objects" by José L. Falguera, Concha Martínez-Vidal and Gideon Rosen
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- Burgess, John P., and Rosen, Gideon, 1997, A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics, Oxford: Oxford University Press. (Scholar)
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- Colyvan, Mark, and Zalta, Edward N., 1999, “Mathematics: Truth and Fiction?” Philosophia Mathematica, 7(3): 336–349. doi:10.1093/philmat/7.3.336 (Scholar)
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- Dedekind, Richard, 1888 [1963], Was Sind Und Was Sollen Die Zahlen, Braunschweig: Vieweg und Sohn; English translation, “The Nature and Meaning of Numbers”, in R. Dedekind, Essays on the Theory of Numbers, Wooster Woodruff Beman (trans.), New York: Dover, 1963, pp. 29–115. (Scholar)
- Donato-Rodríguez, Xavier, and Falguera, José L., 2020, “The Nature of Scientific Models: Abstract Artifacts That Determine Fictional Systems,” in Falguera & Martínez-Vidal (eds.) 2020, pp. 151–171. (Scholar)
- Dummett, Michael, 1973, Frege: Philosophy of Language, London: Duckworth. (Scholar)
- Enoch, David, 2011, Taking Morality Seriously: A Defense of Robust Realism, Oxford: Oxford University Press. doi:10.1093/acprof:oso/9780199579969.001.0001 (Scholar)
- –––, 2016, “Indispensability Arguments in Metaethics: Even Better Than in Mathematics?” in Uri D. Leibowitz & Neil Sinclair (eds.), Explanation in Ethics and Mathematics, Oxford: Oxford University Press. (Scholar)
- Falguera, José L., and Martínez-Vidal, Concha (eds.), 2020, Abstract Objects: For and Against (Synthese Library: Volume 422), Cham, Switzerland: Springer. (Scholar)
- Field, Hartry, 1980, Science Without Numbers, Princeton: Princeton University Press. (Scholar)
- –––, 1989, Realism, Mathematics and Modality, Oxford: Basil Blackwell. (Scholar)
- Fine, Kit, 1994, “Essence and Modality,” Philosophical Perspectives, 8: 1–16. doi:10.2307/2214160 (Scholar)
- –––, 2002, The Limits of Abstraction, Oxford; New York: Clarendon Press. (Scholar)
- –––, 2005, “Our Knowledge of Mathematical Objects,” in Oxford Studies in Epistemology: Volume 1, pp. 89–110, Oxford: Oxford University Press. (Scholar)
- Frege, Gottlob, 1884, Grundlagen Der Arithmetik, Breslau: W. Koebner. (Scholar)
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- Goodman, Nelson, and Quine, W. V. O., 1947, “Steps Toward a Constructive Nominalism,” The Journal of Symbolic Logic, 12(4): 105–122. (Scholar)
- Gödel, Kurt, 1964, “What Is Cantor’s Continuum Problem?” in P. Benacerraf & H. Putnam (eds.), Philosophy of Mathematics: Selected Readings, 2nd edition, pp. 254–270, Cambridge: Cambridge University Press. (Scholar)
- Hale, Bob, 1987, Abstract Objects, Oxford: Blackwell. (Scholar)
- Hale, Bob, and Wright, Crispin, 2001, The Reason’s Proper Study: Essays Towards a Neo-Fregean Philosophy of Mathematics, Oxford: Oxford University Press. (Scholar)
- –––, 2009, “The Metaontology of Abstraction,” in D. Chalmers, D. Manley, & R. Wasserman (eds.), Metametaphysics, pp. 178–212, New York: Oxford University Press. (Scholar)
- Hellman, Geoffrey, 1989, Mathematics Without Numbers: Towards a Modal-Structural Interpretation, Oxford: Clarendon Press. (Scholar)
- Hirsch, Eli, 2002, “Quantifier Variance and Realism,” Philosophical Issues, 12(1): 51–73. doi:10.1111/j.1758-2237.2002.tb00061.x (Scholar)
- –––, 2011, Quantifier Variance and Realism: Essays in Metaontology, New York: Oxford University Press. (Scholar)
- Inwagen, Peter van, 1977, “Creatures of Fiction,” American Philosophical Quarterly, 14(4): 299–308. (Scholar)
- –––, 1983, “Fiction and Metaphysics,” Philosophy and Literature, 7(1): 67–77. doi:10.1353/phl.1983.0059 (Scholar)
- Jackson, Frank, 1982, “Epiphenomenal Qualia,” The Philosophical Quarterly, 32(127): 127–136. doi:10.2307/2960077 (Scholar)
- Kalderon, Mark Eli, 2005, Fictionalism in Metaphysics, Oxford: Oxford University Press. (Scholar)
- Katz, Jerrold, 1980, Language and Other Abstract Objects, Lanham, MD: Rowman & Littlefield. (Scholar)
- Knowles, Robert, and Saatsi, Juha, 2019, “Mathematics and Explanatory Generality: Nothing but Cognitive Salience,” Erkenntnis. doi:10.1007/s10670-019-00146-x (Scholar)
- Kripke, Saul, 1973 [2013], Reference and Existence: The John Locke Lectures, Oxford: Oxford University Press, 2013. [These lectures were given in 1973 but remained unpublished until 2013.] (Scholar)
- Leibowitz, Uri D., and Sinclair, Neil (eds.), 2016, Explanation in Ethics and Mathematics: Debunking and Dispensability, Oxford: Oxford University Press. doi:10.1093/acprof:oso/9780198778592.001.0001 (Scholar)
- Leng, Mary, 2010, Mathematics and Reality, Oxford: Oxford University Press. (Scholar)
- –––, 2020, “Is There a Fact of the Matter About the Existence of Abstract Objects?” in Falguera & Martínez-Vidal (eds.) 2020, pp. 111–130. (Scholar)
- Lewis, David, 1986a, On the Plurality of Worlds, Oxford: Blackwell. (Scholar)
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- Linnebo, 2012, “Metaontological Minimalism,” Philosophy Compass, 7(2): 139–151. doi:10.1111/j.1747-9991.2011.00471.x (Scholar)
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- Linsky, Bernard, and Zalta, Edward N., 1995, “Naturalized Platonism Versus Platonized Naturalism,” The Journal of Philosophy, 92(10): 525–555. doi:10.2307/2940786 (Scholar)
- Locke, John, 1689, An Essay Concerning Human Understanding, Oxford: Clarendon Press. (Scholar)
- Maddy, Penelope, 1990, Realism in Mathematics, New York; London: Clarendon Press. (Scholar)
- –––, 1995, “Naturalism and Ontology,” Philosophia Mathematica, 3(3): 248–270. doi:10.1093/philmat/3.3.248 (Scholar)
- –––, 1997, Naturalism in Mathematics, Oxford: Oxford University Press. (Scholar)
- –––, 2011, Defending the Axioms: On the Philosophical Foundations of Set Theory, Oxford: Oxford University Press. (Scholar)
- Malament, David, 1982, “Review of Field (1980),” The Journal of Philosophy, 79: 523–34. (Scholar)
- Mally, Ernst, 1912, Gegenstandstheoretische Grundlagen Der Logik Und Logistik, Leipzig: Barth. (Scholar)
- Martínez-Vidal, Concha, and Rivas-de-Castro, Navia, 2020, “Description, Explanation and Ontological Commitment,” in Falguera & Martínez-Vidal (eds.) 2020, pp. 35–57. (Scholar)
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- Moltmann, Friederike, 2013, Abstract Objects and the Semantics of Natural Language, Oxford: Oxford University Press. (Scholar)
- –––, 2020, “Abstract Objects and the Core-Periphery Distinction in the Ontological and the Conceptual Domain of Natural Language,” in Falguera & Martínez-Vidal (eds.) 2020, pp. 255–276. (Scholar)
- Nodelman, Uri, and Zalta, Edward N., 2014, “Foundations for Mathematical Structuralism,” Mind, 123(489): 39–78. doi:10.1093/mind/fzu003 (Scholar)
- Parsons, Charles, 1990, “The Structuralist View of Mathematical Objects,” Synthese, 84(3): 303–346. (Scholar)
- Parsons, Terence, 1980, Nonexistent Objects, New Haven: Yale University Press. (Scholar)
- Popper, Karl, 1968, “Epistemology Without a Knowing Subject,” in Logic, Methodology, and Philosophy of Science Iii, pp. 333–373, Amsterdam: North Holland. (Scholar)
- Putnam, Hilary, 1967, “Mathematics Without Foundations,” The Journal of Philosophy, 64(1): 5–22. (Scholar)
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- Rosen, Gideon, 1994, “Objectivity and Modern Idealism: What Is the Question?” in M. Michael & J. O’Leary-Hawthorne (eds.), Philosophy in Mind, pp. 277–319, Dordrecht: Springer. (Scholar)
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