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    • Publisher:
      Cambridge University Press
      Publication date:
      05 February 2024
      29 February 2024
      ISBN:
      9781009241373
      9781009467858
      9781009241403
      DOI:
      https://doi.org/10.1017/9781009241373
      Dimensions:
      (229 x 152 mm)
      Weight & Pages:
      0.25kg, 68 Pages
      Dimensions:
      (229 x 152 mm)
      Weight & Pages:
      0.14kg, 68 Pages
      • Series:
      Elements in Metaphysics
      Subjects:
      Epistemology and Metaphysics, Philosophy: General Interest, Philosophy
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    Series:
    Elements in Metaphysics
    Subjects:
    Epistemology and Metaphysics, Philosophy: General Interest, Philosophy
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    Book description

    Philosophers often debate the existence of such things as numbers and propositions, and say that if these objects exist, they are abstract. But what does it mean to call something 'abstract'? And do we have good reason to believe in the existence of abstract objects? This Element addresses those questions, putting newcomers to these debates in a position to understand what they concern and what are the most influential considerations at work in this area of metaphysics. It also provides advice on which lines of discussion promise to be the most fruitful.

    References

    References

    Alston, W. (1958). Ontological commitments. Philosophical Studies, 9 (1/2), 8–17. https://doi.org/10.1007/BF00797866.
    Armstrong, D. M. (2004). Truth and Truthmakers. Cambridge: Cambridge University Press.
    Baker, A. (2003). Does the existence of mathematical objects make a difference? Australasian Journal of Philosophy, 81 (2), 246–64. https://doi.org/10.1080/713659635.
    Baker, A. (2005). Are there genuine mathematical explanations of physical phenomena? Mind, 114 (454), 223–38. https://doi.org/10.1093/mind/fzi223.
    Baker, L. R. (1987). Saving Belief: A Critique of Physicalism. Princeton: Princeton University Press.
    Balaguer, M. (1998a). Attitudes without propositions. Philosophy and Phenomenological Research, 58 (4), 805–26. https://doi.org/10.2307/2653723.
    Balaguer, M. (1998b). Platonism and Anti-Platonism in Mathematics. New York: Oxford University Press.
    Balaguer, M. (2009). Fictionalism, theft, and the story of mathematics. Philosophia Mathematica, 17 (2), 131–62. https://doi.org/10.1093/philmat/nkn019.
    Baras, D. (2022). Calling for Explanation. New York: Oxford University Press. https://doi.org/10.1093/oso/9780197633649.001.0001.
    Båve, A. (2015). A deflationist error theory of properties. Dialectica, 69 (1), 23–59. https://doi.org/10.1111/1746-8361.12086.
    Benacerraf, P. (1965). What numbers could not be. Philosophical Review, 74 (1), 47–73. https://doi.org/10.2307/2183530.
    Benacerraf, P. (1973). Mathematical truth. Journal of Philosophy, 70 (19), 661–79. https://doi.org/10.2307/2025075.
    Boyce, K. (2020). Mathematical surrealism as an alternative to easy-road fictionalism. Philosophical Studies, 177 (10), 2815–35. https://doi.org/10.1007/s11098-019-01340-x.
    Burgess, J. (1982). Epistemology and nominalism. In Irvine, A. D., ed., Physicalism in Mathematics. Dordrecht: Kluwer, pp. 1–15. https://doi.org/10.1007/978-94-009-1902-0_1.
    Burgess, J. and Rosen, G. (1997). A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics. Oxford: Clarendon Press. https://doi.org/10.1093/0198250126.001.0001.
    Chalmers, D. J. (2009). Ontological anti-realism. In Chalmers, D. J., Manley, D. and Wasserman, R., eds., Metametaphysics: New Essays on the Foundations of Ontology. Oxford: Oxford University Press, pp. 77–129.
    Chudnoff, E. (2013). Intuition. New York: Oxford University Press. https://doi.org/10.1093/acprof:oso/9780199683000.001.0001.
    Clarke-Doane, J. (2017). What is the Benacerraf problem? In Pataut, F., ed., New Perspectives on the Philosophy of Paul Benacerraf: Truth, Objects, Infinity. Dordrecht: Springer, pp. 17–43. https://doi.org/10.1007/978-3-319-45980-6_2.
    Cling, A. (1989). Eliminative materialism and self-referential inconsistency. Philosophical Studies, 56 (1), 53–75. https://doi.org/10.1007/BF00646209.
    Colyvan, M. (2001). The Indispensability of Mathematics. New York: Oxford University Press. https://doi.org/10.1093/019513754X.001.0001.
    Colyvan, M. (2010). There is no easy road to nominalism. Mind, 119 (474), 285–306. https://doi.org/10.1093/mind/fzq014.
    Cowling, S. (2017). Abstract Entities. London: Routledge.
    Daly, C. (2013). Psychology and indispensability. Monist, 96 (4), 561–81. https://doi.org/10.5840/monist201396426.
    Daly, C. and Liggins, D. (2010). In defence of error theory. Philosophical Studies, 149 (2), 209–30. https://doi.org/10.1007/s11098-009-9346-1.
    Daly, C. and Liggins, D. (2011). Deferentialism. Philosophical Studies, 156, 321–37. https://doi.org/10.1007/s11098-010-9596-y.
    Dever, J. (2008). Compositionality. In Lepore, E. and Smith, B., eds., The Oxford Handbook of Philosophy of Language. Oxford: Oxford University Press, pp. 633–66. https://doi.org/10.1093/oxfordhb/9780199552238.003.0026.
    Dorr, C. (2010). Of numbers and electrons. Proceedings of the Aristotelian Society, 110, 133–81. https://doi.org/10.1111/j.1467-9264.2010.00282.x.
    Edwards, D. (2014). Properties. Cambridge: Polity.
    Enoch, D. (2010). The epistemological challenge to metanormative realism: How best to understand it, and how to cope with it. Philosophical Studies, 148 (3), 413–38.
    Felappi, G. (2014). ‘In defence of sententialism’. Dialectica, 68 (4), 581–603. https://doi.org/10.1111/1746-8361.12085.
    Field, H. (1984). Review of Frege’s Conception of Numbers as Objects by Crispin Wright. Canadian Journal of Philosophy, 14 (4), 637–62. https://doi.org/doi:10.1080/00455091.1984.10716402.
    Field, H. (1989). Realism, Mathematics and Modality. Oxford: Blackwell.
    Field, H. (1998). Mathematical objectivity and mathematical objects. In Laurence, S. and MacDonald, C., eds., Contemporary Readings in the Foundations of Metaphysics. Oxford: Blackwell, pp. 387–403.
    Field, H. (2016). Science without Numbers: A Defence of Nominalism, 2nd ed. Oxford: Oxford University Press. https://doi.org/10.1093/acprof:oso/9780198777915.001.0001.
    Fodor, J. A. (1987). Psychosemantics: The Problem of Meaning in the Philosophy of Mind. Cambridge, MA: MIT Press. https://doi.org/10.7551/mitpress/5684.001.0001.
    Goldman, A. (1967). A causal theory of knowing. Journal of Philosophy, 64 (12), 357–72. https://doi.org/10.2307/2024268.
    Goodman, N. and Quine, W. V. (1947). Steps toward a constructive nominalism. Journal of Symbolic Logic, 12 (4), 105–22. https://doi.org/10.2307/2266485.
    Hale, B. (1987). Abstract Objects. Oxford: Blackwell.
    Hale, B. (2001a). Singular terms (1). In Hale, B. and Wright, C., eds., The Reason’s Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics. Oxford: Clarendon Press, pp. 31–47. https://doi.org/10.1093/0198236395.003.0002.
    Hale, B. (2001b). Singular terms (2). In Hale, B. and Wright, C., eds., The Reason’s Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics. Oxford: Clarendon Press, pp. 48–71. https://doi.org/10.1093/0198236395.003.0003.
    Hart, W. D. (1991). Benacerraf’s dilemma. Crítica: Revista Hispanoamericana de Filosofía, 28 (68), 87–103.
    Hellman, G. (1989). Mathematics without Numbers. Oxford: Clarendon Press. https://doi.org/10.1093/0198240341.001.0001.
    Hellman, G. (1998). Maoist Mathematics? Philosophia Mathematica, 6 (3), 334–45. https://doi.org/10.1093/philmat/6.3.334.
    Hellman, G. and Shapiro, S. (2019). Mathematical Structuralism (Cambridge Elements: Elements in the Philosophy of Mathematics). Cambridge: Cambridge University Press.
    Huber, F. (2008). Assessing theories, Bayes style. Synthese, 161, 89–118. https://doi.org/10.1007/s11229-006-9141-x.
    Huemer, M. (2009). When is parsimony a virtue? Philosophical Quarterly, 59 (235), 216–36. https://doi.org/10.1111/j.1467-9213.2008.569.x.
    Jackson, F. (1977). Statements about universals. Mind, 86 (343), 427–9.
    Keller, J. A. (2017). Paraphrase and the symmetry objection. Australasian Journal of Philosophy, 95 (2), 365–78. https://doi.org/10.1080/00048402.2016.1168457.
    Kim, J. (2001). Lonely souls: Causality and substance dualism. In Corcoran, K. J., ed., Soul, Body, and Survival: Essays on the Metaphysics of Human Persons. New York: Cornell University Press, pp. 30–43. https://doi.org/10.7591/9781501723520-004.
    Knowles, R. and Liggins, D. (2015). Good weasel hunting. Synthese, 192 (10), 3397–412. https://doi.org/10.1007/s11229-015-0711-7.
    Kovacs, D. (2021). How to be an uncompromising revisionary ontologist. Synthese, 198, 2129–52. https://doi.org/10.1007/s11229-019-02196-8.
    Lange, M. (2017). Because without Cause: Non-Causal Explanations in Science and Mathematics. New York: Oxford University Press.
    Leng, M. (2010). Mathematics and Reality. Oxford: Oxford University Press. https://doi.org/10.1093/acprof:oso/9780199280797.001.0001.
    Lewis, D. (1973). Counterfactuals. Malden: Blackwell.
    Lewis, D. (1986). On the Plurality of Worlds. Malden: Blackwell.
    Lewis, D. (1991). Parts of Classes. Oxford: Oxford University Press.
    Liggins, D. (2008). Quine, Putnam, and the ‘Quine–Putnam’ indispensability argument. Erkenntnis, 68 (1), 113–27. https://doi.org/10.1007/s10670-007-9081-y.
    Liggins, D. (2010a). Epistemological objections to platonism. Philosophy Compass, 5 (1), 67–77. https://doi.org/10.1111/j.1747-9991.2009.00259.x.
    Liggins, D. (2010b). The autism objection to pretence theories. Philosophical Quarterly, 60 (241), 764–82. https://doi.org/10.1111/j.1467-9213.2010.656.x.
    Liggins, D. (2014). Abstract expressionism and the communication problem. British Journal for the Philosophy of Science, 65 (3), 599–620. https://doi.org/10.1093/bjps/axt012.
    Liggins, D. (2020). Against hermeneutic fictionalism. In Armour-Garb, B. and Kroon, F., eds., Fictionalism in Philosophy, Oxford: Oxford University Press, pp. 81–102. https://doi.org/10.1093/oso/9780190689605.003.0005.
    Liggins, D. (2021). Should a higher-order metaphysician believe in properties? Synthese, 199, 10017–37. https://doi.org/10.1007/s11229-021-03234-0.
    Lyon, A. (2012). Mathematical explanations of empirical facts, and mathematical realism. Australasian Journal of Philosophy, 90 (3), 559–78. https://doi.org/10.1080/00048402.2011.596216.
    Lyon, A. and Colyvan, M. (2008). The explanatory power of phase spaces. Philosophia Mathematica, 16 (2), 227–43. https://doi.org/10.1093/philmat/nkm025.
    MacBride, F. (1999). Listening to fictions: A study of Fieldian nominalism. British Journal for the Philosophy of Science, 50 (3), 431–55. https://doi.org/10.1093/bjps/50.3.431.
    Maddy, P. (1997). Naturalism in Mathematics. Oxford: Oxford University Press. https://doi.org/10.1093/0198250754.001.0001.
    Maddy, P. (2005). Three forms of naturalism. In Shapiro, S., ed., Oxford Handbook of Philosophy of Mathematics and Logic. New York: Oxford University Press, pp. 437–59. https://doi.org/10.1093/oxfordhb/9780195325928.003.0013.
    Magidor, O. (2013). Category Mistakes. Oxford: Oxford University Press. https://doi.org/10.1093/acprof:oso/9780199572977.001.0001.
    Malament, D. (1982). Review of Science without Numbers by Field, Hartry H.. Journal of Philosophy, 79 (9), 523–34. https://doi.org/10.5840/jphil198279913.
    Markosian, N. (2004). A defence of presentism. In Zimmerman, D., ed., Oxford Studies in Metaphysics. Vol. 1. Oxford: Oxford University Press, pp. 47–82.
    McCain, K. and Poston, T. (eds.) (2017). Best Explanations: New Essays on Inference to the Best Explanation. Oxford: Oxford University Press.
    Melia, J. (1995). On what there’s not. Analysis, 55 (4), 223–9. https://doi.org/10.2307/3328390.
    Melia, J. (1998). Field’s programme: Some interference. Analysis, 58 (2), 63–71. https://doi.org/10.1093/analys/58.2.63.
    Melia, J. (2000). Weaseling away the indispensability argument. Mind, 109 (435), 455–79. https://doi.org/10.1093/mind/109.435.455.
    Miller, K. (2012). Mathematical contingentism. Erkenntnis, 77 (3), 335–59. https://doi.org/10.1007/s10670-012-9404-5.
    Morrison, J. (2010). Just how controversial is evidential holism? Synthese, 173 (3), 335–52. https://doi.org/10.1007/s11229-008-9440-5.
    Morrison, J. (2012). Evidential holism and indispensability arguments. Erkenntnis, 76 (2), 263–278. https://doi.org/10.1007/s10670-011-9300-4.
    Nolan, D. (1997). Quantitative parsimony. British Journal for the Philosophy of Science, 48 (3), 329–43. https://doi.org/10.1093/bjps/48.3.329.
    Nolan, D. (2016). Method in analytic metaphysics. In Cappelen, H., Gendler, T. S. and Hawthorne, J., eds., The Oxford Handbook of Philosophical Methodology. Oxford: Oxford University Press, pp. 159–78. https://doi.org/10.1093/oxfordhb/9780199668779.013.16.
    Oliver, A. (1996). The metaphysics of properties. Mind, 105 (417), 1–80. https://doi.org/10.1093/mind/105.417.1.
    Parsons, T. (1980). Nonexistent Objects. New Haven: Yale University Press.
    Paseau, A. (2005). Naturalism in mathematics and the authority of philosophy. British Journal for the Philosophy of Science, 56 (2), 377–96. https://doi.org/10.1093/bjps/axi123.
    Pettigrew, R. (2008). Platonism and aristotelianism in mathematics. Philosophia Mathematica, 16 (3), 310–32. https://doi.org/10.1093/philmat/nkm035.
    Quine, W. V. (1960). Word and Object. Cambridge, MA: MIT Press.
    Quine, W. V. (1969). Existence and quantification. In Quine, W. V., ed., Ontological Relativity and Other Essays. New York: Columbia University Press, pp. 91–113.
    Quine, W. V. (1970). Philosophy of Logic. Englewood Cliffs: Prentice-Hall.
    Quine, W. V. (1980). Logic and the reification of universals, In Quine, W. V., ed., From a Logical Point of View. 2nd ed. Cambridge, MA: Harvard University Press, pp. 102–29.
    Raven, M. J. (2022). Metaphysical grounding. Oxford Bibliographies Online. https://doi.org/10.1093/OBO/9780195396577-0389.
    Rosen, G. (1993). The refutation of nominalism (?). Philosophical Topics, 21 (2), 149–86. https://doi.org/10.5840/philtopics199321221.
    Rosen, G. (1999). Review of Naturalism in Mathematics by Penelope Maddy. British Journal for the Philosophy of Science, 50 (3), 467–74. https://doi.org/10.1093/bjps/50.3.467.
    Rosen, G. (2002). A study in modal deviance. In Gendler, T. S. and Hawthorne, J., eds., Conceivability and Possibility. Oxford: Clarendon Press, pp. 283–307.
    Rosen, G. (2009). Abstract objects. In E. N. Zalta, ed., The Stanford Encyclopedia of Philosophy. (Fall 2009 ed.). https://plato.stanford.edu/archives/fall2009/entries/abstract-objects/.
    Rosen, G. (2010). Metaphysical dependence: Grounding and reduction. In Hale, B. and Hoffman, A., eds., Modality: Metaphysics, Logic, and Epistemology. Oxford: Oxford University Press, pp. 109–36. https://doi.org/10.1093/acprof:oso/9780199565818.003.0007.
    Rosen, G. and Burgess, J. (2005). Nominalism reconsidered. In Shapiro, S., ed., The Oxford Handbook of Philosophy of Mathematics and Logic. New York: Oxford University Press, pp. 515–35. https://doi.org/10.1093/oxfordhb/9780195325928.003.0016.
    Saatsi, J. (2016). On the ‘indispensable explanatory role’ of mathematics. Mind, 125 (500), 1045–70. https://doi.org/10.1093/mind/fzv175.
    Schiffer, S. (2003). The Things We Mean. Oxford: Clarendon Press. https://doi.org/10.1093/0199257760.001.0001.
    Sennet, A. and Fisher, T. (2014). Quine on paraphrase and regimentation. In Harman, G. and Lepore, E., eds., A Companion to W. V. O. Quine. Oxford: Wiley-Blackwell, pp. 89–113. https://doi.org/10.1002/9781118607992.ch5.
    Shapiro, L. (ed. and trans.) (2007) The Correspondence between Princess Elisabeth of Bohemia and René Descartes. Chicago: University of Chicago Press.
    Sider, T. (1999). Presentism and ontological commitment. Journal of Philosophy, 96 (7), 325–47. https://doi.org/10.2307/2564601.
    Sider, T. (2013). Against parthood. In Bennett, K. and Zimmerman, D. W., eds., Oxford Studies in Metaphysics. Vol. 8. Oxford: Oxford University Press, pp. 236–93. https://doi.org/10.1093/acprof:oso/9780199682904.003.0006.
    Sjölin Wirling, Y. (forthcoming). Neutrality and force in Field’s epistemological objection to platonism. Inquiry. https://doi.org/10.1080/0020174X.2022.2048689.
    Skiba, L. (2021). Higher-order metaphysics. Philosophy Compass, 16, 1–11. https://doi.org/10.1111/phc3.12756.
    Sober, E. (1981). Evolutionary theory and the ontological status of properties. Philosophical Studies, 40 (2), 147–76. https://doi.org/10.1007/BF00353787.
    Sober, E. (2000). Quine’s two dogmas. Proceedings of the Aristotelian Society, suppl. vol. 74 (1), 237–80. https://doi.org/10.1111/1467-8349.00071.
    Stanley, J. (2001). Hermeneutic fictionalism. Midwest Studies in Philosophy, 25 (1), 36–71. https://doi.org/10.1111/1475-4975.00039.
    Stoljar, D. (2017). Philosophical Progress: In Defence of a Reasonable Optimism. Oxford: Oxford University Press. https://doi.org/10.1093/oso/9780198802099.001.0001.
    Stump, E. and Kretzmann, N. (1981). Eternity. Journal of Philosophy, 78 (8), 429–58. https://doi.org/10.2307/2026047.
    Swain, M. (1998). Causal theory of knowledge. In Craig, E., ed., Routledge Encyclopedia of Philosophy. Vol. 5. London: Routledge, pp. 263–6. https://doi.org/10.4324/9780415249126-P004-1.
    Swoyer, C. (1996). Theories of properties: From plenitude to paucity. Philosophical Perspectives, 10, 243–64. https://doi.org/10.2307/2216246.
    Szabó, Z. G. (2003). Nominalism. In Loux, M. J. and Zimmerman, D. W., eds., The Oxford Handbook of Metaphysics. Oxford: Oxford University Press, pp. 11–45. https://doi.org/10.1093/oxfordhb/9780199284221.001.0001.
    Tarski, A. (1983). On the concept of logical consequence. In Corcoran, J., ed., Logic, Semantics, Metamathematics: Papers from 1923 to 1938. Indianapolis: Hackett, pp. 409–20.
    Topey, B. (2021). Realism, reliability, and epistemic possibility: On modally interpreting the Benacerraf–Field challenge. Synthese, 199, 4415–36. https://doi.org/10.1007/s11229-020-02984-7.
    van Elswyk, P. (2022). The linguistic basis for propositions. In Tillman, C. and Murray, A., eds., The Routledge Handbook of Propositions. New York: Routledge, pp. 57–78. https://doi.org/10.4324/9781315270500-3.
    von Solodkoff, T. (2014). Paraphrase strategies in metaphysics. Philosophy Compass, 9 (8), 570–82. https://doi.org/10.1111/phc3.12150.
    Walton, K. L. (1993). Metaphor and prop oriented make-believe. European Journal of Philosophy, 1 (1), 39–57. https://doi.org/10.1111/j.1468-0378.1993.tb00023.x.
    Wetzel, L. (2009). Types and Tokens. Cambridge, MA: MIT Press.
    Williamson, T. (2007). The Philosophy of Philosophy. Malden: Blackwell.
    Williamson, T. (2016). Abductive philosophy. Philosophical Forum, 47 (3–4), 263–80. https://doi.org/10.1111/phil.12122.
    Williamson, T. (2017). Semantic paradoxes and abductive methodology. In Armour-Garb, B., ed., Reflections on the Liar. Oxford: Oxford University Press. pp. 325–46. https://doi.org/10.1093/oso/9780199896042.003.0013.
    Wright, C. (2001). On the philosophical significance of Frege’s theorem. In Hale, B. and Wright, C., eds., The Reason’s Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics. Oxford: Oxford University Press, pp. 272–306. https://doi.org/10.1093/0198236395.003.0013.
    Yablo, S. (1998). Does ontology rest on a mistake? Proceedings of the Aristotelian Society, supp vol. 72 (1), 229–61.
    Yablo, S. (2000). Apriority and existence. In Boghossian, P. and Peacocke, C., eds., New Essays on the a Priori. Oxford: Clarendon Press, pp. 197–228. https://doi.org/10.1093/0199241279.003.0009.
    Yablo, S. (2001). Go figure: A path through fictionalism. Midwest Studies in Philosophy, 25 (1), 72–102. https://doi.org/10.1111/1475-4975.00040.
    Yablo, S. (2002). Abstract objects: A case study. Philosophical Issues, 12 (1), 220–40. https://doi.org/10.1111/j.1758-2237.2002.tb00068.x.
    Yablo, S. (2005). The myth of the seven. In Kalderon, M., ed., Fictionalism in Metaphysics. New York: Oxford University Press, pp. 88–115.
    Yablo, S. (2014). Aboutness. Princeton: Princeton University Press. https://doi.org/10.2307/j.ctt2tt8rv.

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