Linked bibliography for the SEP article "Abstract Objects" by José L. Falguera, Concha Martínez-Vidal and Gideon Rosen

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Armstrong, David, 1978, Universals and Scientific Realism (Volume I: Nominalism and Realism; Volume II: A Theory of Universals), New York: Cambridge University Press. (Scholar)
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Azzouni, Jody, 1997a, “Applied Mathematics, Existential Commitment and the Quine-Putnam Indispensability Thesis,” Philosophia Mathematica, 3(5): 193–209. (Scholar)
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–––, 2010, Talking About Nothing: Numbers, Hallucinations and Fictions, Oxford: Oxford University Press. (Scholar)
Baker, Alan, 2005, “Are There Genuine Mathematical Explanations of Physical Phenomena?” Mind, 114(454): 223–238. (Scholar)
–––, 2009, “Mathematical Explanation in Science,” British Journal for the Philosophy of Science, 60(3): 611–633. (Scholar)
–––, 2017, “Mathematics and Explanatory Generality,” Philosophia Mathematica, 25(2): 194–209. doi:10.1093/philmat/nkw021 (Scholar)
Balaguer, Mark, 1995, “A Platonist Epistemology,” Synthese, 103(3): 303–325. (Scholar)
–––, 1996, “A Fictionalist Account of the Indispensable Applications of Mathematics,” Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition, 83(3): 291–314. (Scholar)
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–––, 2020, “Moral Folkism and the Deflation of (Lots of) Normative and Metaethics,” in José Falguera & Martínez-Vidal (eds.) 2020, pp. 297–318. (Scholar)
Baron, Samuel, 2016, “Explaining Mathematical Explanation,” The Philosophical Quarterly, 66(264): 458–480. doi:10.1093/pq/pqv123 (Scholar)
–––, 2020, “Purely Physical Explananda: Bistability in Perception,” in Falguera & Martínez-Vidal (eds.) 2020, pp. 17–34. (Scholar)
Bealer, George, 1993, “Universals,” The Journal of Philosophy, 90(1): 5–32. doi:10.2307/2940824 (Scholar)
Benacerraf, Paul, 1965, “What Numbers Could Not Be,” Philosophical Review, 74(1): 47–73. (Scholar)
–––, 1973, “Mathematical Truth,” Journal of Philosophy, 70(19): 661–679. (Scholar)
Berto, Francesco, and Plebani, Matteo, 2015, Ontology and Metaontology: A Contemporary Guide, London; New York: Bloomsbury Academic. (Scholar)
Bolzano, Bernard, 1837, Wissenschaftslehre, Sulzbach: J. E. v. Seidel. (Scholar)
Brentano, Franz, 1874, Psychologie Vom Empirischen Standpunkt, Leipzig: Duncker & Humblot. (Scholar)
Bueno, Otávio, 2008a, “Nominalism and Mathematical Intuition,” Protosociology, 25: 89–107. (Scholar)
–––, 2008b, “Truth and Proof,” Manuscrito, 31(1): 419–440. (Scholar)
–––, 2020, “Contingent Abstract Objects,” in Falguera & Martínez-Vidal (eds.) 2020, pp. 91–109. (Scholar)
Burgess, John P., 2005, Fixing Frege, Princeton: Princeton University Press. (Scholar)
Burgess, John P., and Rosen, Gideon, 1997, A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics, Oxford: Oxford University Press. (Scholar)
Carnap, Rudolf, 1950 [1956], “Empiricism, Semantics, and Ontology,” Revue Internationale de Philosophie, 4(11): 20–40; reprinted with revisions in Rudolf Carnap, Meaning and Necessity, expanded edition, Chicago: Chicago University Press, 1956, pp. 205–221. (Scholar)
Chalmers, David, 1996, The Conscious Mind, Oxford: Oxford University Press. (Scholar)
Colyvan, Mark, 2001, The Indispensability of Mathematics, Oxford: Oxford University Press. (Scholar)
–––, 2010, “There Is No Easy Road to Nominalism,” Mind, 119(474): 285–306. doi:10.1093/mind/fzq014 (Scholar)
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)
Cook, Roy, 2003, “Iteration One More Time,” Notre Dame Journal of Formal Logic, 44(2): 63–92. (Scholar)
Cowling, Sam, 2017, Abstract Entities, London: Routledge. (Scholar)
Crane, Tim, and Mellor, D. H., 1990, “There Is No Question of Physicalism,” Mind, 99(394): 185–206. (Scholar)
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)
–––, 1918, “Der Gedanke: Eine Logische Untersuchung,” Beiträge Zur Philosophie Des Deutschen Idealismus, I: 58–77. (Scholar)
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)
–––, 1986b, “Events”, in D. Lewis, Philosophical Papers (Volume II), Oxford: Oxford University Press, pp. 241–269. (Scholar)
–––, 2007, “Events,” in Philosophical Papers: Volume Ii, pp. 241–269, Oxford: Oxford University Press. (Scholar)
Linnebo, 2012, “Metaontological Minimalism,” Philosophy Compass, 7(2): 139–151. doi:10.1111/j.1747-9991.2011.00471.x (Scholar)
–––, 2018, Thin Objects: An Abstractionist Account, Oxford: Oxford University Press. doi:10.1093/oso/9780199641314.001.0001 (Scholar)
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)
Meinong, Alexius, 1904, “Über Gegenstandstheorie,” in A. Meinong (ed.), Untersuchungen Zur Gegenstandstheorie Und Psychologie [Investigations in Theory of Objects and Psychology], pp. 1–51, Leipzig: Barth. (Scholar)
–––, 1915, Über Möglichkeit Und Wahrscheinlichkeit. Beiträge Zur Gegenstandstheorie Und Erkenntnistheorie [on Possibility and Probability. Contributions to Object Theory and Epistemology], Leipzig: Barth. (Scholar)
Melia, Joseph, 2000, “Weaseling Away the Indispensability Argument,” Mind, 109(435): 455–479. (Scholar)
–––, 2002, “Response to Colyvan,” Mind, 111(441): 75–79. (Scholar)
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)
–––, 1971, Philosophy of Logic, London: Harper; Row. (Scholar)
–––, 1987, The Many Faces of Realism, La Salle: Open Court. (Scholar)
–––, 1990, Realism with a Human Face, Cambridge, MA: Harvard University Press. (Scholar)
Quine, W. V. O., 1948, “On What There Is,” The Review of Metaphysics, 2(5): 21–38. (Scholar)
–––, 1960, Word and Object, Cambridge, MA: The MIT Press. (Scholar)
–––, 1969, Ontological Relativity and Other Essays, New York: Columbia University Press. (Scholar)
–––, 1976, The Ways of Paradox and Other Essays, Cambridge, MA: Harvard University Press. (Scholar)
Rayo, Agustín, 2013, The Construction of Logical Space, Oxford: Oxford University Press. (Scholar)
Resnik, Michael D., 1982, “Mathematics as a Science of Patterns: Epistemology,” Noûs, 16(1): 95–105. doi:10.2307/2215419 (Scholar)
–––, 1997, Mathematics as a Science of Patterns p. 290, Oxford: Oxford University Press. doi:10.1093/0198250142.001.0001 (Scholar)
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)
–––, 2011, “The Reality of Mathematical Objects,” in J. Polkinghorne (ed.), Meaning in Mathematics, pp. 113–131, Oxford: Oxford University Press. (Scholar)
Rosen, Gideon, and Yablo, Stephen, 2020, “Solving the Caesar Problem – with Metaphysics,” in A. Miller (ed.), Logic, Language and Mathematics: Themes from the Philosophy of Crispin Wright, pp. 116–131, Oxford: Oxford University Press. (Scholar)
Saatsi, Juha, 2011, “The Enhanced Indispensability Argument: Representational Versus Explanatory Role of Mathematics in Science,” The British Journal for the Philosophy of Science, 62(1): 143–154. (Scholar)
Sainsbury, Mark, 2009, Fiction and Fictionalism, London: Routledge. (Scholar)
Shapiro, Stewart, 1997, Philosophy of Mathematics: Structure and Ontology, New York: Oxford University Press. doi:10.1093/0195139305.001.0001 (Scholar)
Sider, Theodore, 2007, “Parthood,” The Philosophical Review, 116(1): 51–91. doi:10.1215/00318108-2006-022 (Scholar)
–––, 2009, “Ontological Realism,” in D. Chalmers, D. Manley, & R. Wasserman (eds.), Metametaphysics, pp. 384–423, Oxford: Oxford University Press. (Scholar)
–––, 2013, “Against Parthood,” in Karen Bennett and Dean W. Zimmerman (eds.), Oxford Studies in Metaphysics, vol. 8, Oxford: Oxford University Press, pp. 237–93. (Scholar)
Steiner, Mark, 1975, Mathematical Knowledge, Ithaca: Cornell University Press. (Scholar)
Swoyer, Chris, 2007, “Abstract Entities,” in T. Sider, J. Hawthorne, & D. W. Zimmerman (eds.), Contemporary Debates in Metaphysics, pp. 11–31, Malden, MA: Wiley-Blackwell. (Scholar)
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Thomasson, Amie L., 1999, Fiction and Metaphysics, Cambridge: Cambridge University Press. (Scholar)
–––, 2015, Ontology Made Easy, Oxford: Oxford University Press. (Scholar)
Wetzel, Linda, 2009, Types and Tokens: On Abstract Objects, Cambridge, MA: The MIT Press. (Scholar)
Wright, Crispin, 1983, Frege’s Conception of Numbers as Objects, Aberdeen: Aberdeen University Press. (Scholar)
Yablo, Stephen, 1998, “Does Ontology Rest on a Mistake?” Proceedings of the Aristotelian Society (Supplementary Volume), 72(1): 229–262. doi:10.1111/1467-8349.00044 (Scholar)
–––, 2001, “Go Figure: A Path Through Fictionalism,” Midwest Studies in Philosophy, 25: 72–102. doi:10.1111/1475-4975.00040 (Scholar)
–––, 2002, “Abstract Objects: A Case Study,” Philosophical Issues, 12(1): 220–240. (Scholar)
–––, 2009, Thoughts: Papers on Mind, Meaning, and Modality, New York: Oxford University Press. (Scholar)
–––, 2010, “The Myth of the Seven,” in Things: Papers on Objects, Events, and Properties, pp. 233–245, Oxford: Oxford University Press. (Scholar)
–––, 2014, Aboutness, Princeton: Princeton University Press. (Scholar)
Zalta, Edward N., 1983, Abstract Objects: An Introduction to Axiomatic Metaphysics, Dordrecht: D. Reidel. (Scholar)
–––, 1988, Intensional Logic and Metaphysics of Intentionality, Cambridge, MA: The MIT Press. (Scholar)
–––, 1993, “Twenty-Five Basic Theorems in Situation and World Theory,” Journal of Philosophical Logic, 22: 385–428. (Scholar)
–––, 2006, “Essence and Modality,” Mind, 115(459): 659–693. (Scholar)
–––, 2020, “Typed Object Theory,” in Falguera & Martínez-Vidal (eds.) 2020, pp. 59–88. (Scholar)

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