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    Göhner, Julia Friederike and Steinbrink, Lukas 2018. Peter van Inwagen. Vol. 4, Issue. , p. 41.

  • Print publication year: 2014
  • Online publication date: June 2014

Chapter 8 - A theory of properties


It would be better not to believe in abstract objects if we could get away with it

In their book A Subject without an Object: Strategies for the Nominalistic Interpretation of Mathematics (the main topic of the book is well conveyed by its subtitle), John Burgess and Gideon Rosen suggest that – in fact, they argue at some length for the conclusion that – the motivation for undertaking nominalistic reconstructions of mathematics has not been clearly and persuasively formulated. This seems to me to be wrong. At any rate, it seems to me that it is not hard to formulate the motivation (or a sufficient motivation) for this project clearly and persuasively. Suppose one could show this: it would be better not to believe in abstract objects if one could get away with it. Or this, if it is not the same: it would be philosophically desirable to accept only philosophical positions that do not require their adherents to affirm the existence of abstract objects. I will take it that it is evident why someone who accepted this conclusion (or either of them, if they are different) would have a strong motivation for wishing that a nominalistic reconstruction or interpretation of mathematics were available.

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  • Online ISBN: 9781107111004
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Thomasson, Amie views, see her book Fiction and Metaphysics (Cambridge University Press, 1999)
Wolterstorff, Nicholas, see his Worlds and Works of Art (Oxford University Press, 1980)
Quine, W. V., “On What There Is,” in From a Logical Point of View (Cambridge, MA: Harvard University Press, 1961), pp. 1–19
Quine, W. V., Word and Object (Cambridge, MA: MIT Press, 1960)
Goodman, Nelson and Quine, W. V., “Steps toward a Constructive Nominalism,” Journal of Symbolic Logic 12 (1947): 105–122
, David and Lewis, Stephanie, “Holes,” in David Lewis, Philosophical Papers, volume I (Oxford University Press, 1983), pp. 3–9
Putnam, Hilary, Philosophy of Logic (New York: Harper & Row, 1971)
Laurence, Stephen and Macdonald, Cynthia, eds., Contemporary Readings in the Foundations of Metaphysics (Oxford: Blackwell, 1998), pp. 404–434
Melia, Joseph, “On What There's Not,” Analysis 55 (1995): 223–229
Cohen, R. S., Feyerabend, P. K., and Wartofsky, M. W., eds., Essays in Memory of Imre Lakatos (Dordrecht: Reidel, 1976), pp. 497–504
van Inwagen, Peter, “Why I Don't Understand Substitutional Quantification,” Philosophical Studies 39 (1981)
Lycan, William G. fine paper, “Semantic Competence and Funny Functors,” Monist 64 (1979)
“Why I Don't Understand Substitutional Quantification” is reprinted in my Ontology, Identity, and Modality: Essays in Metaphysics (Cambridge University Press, 2001)
Quine, W. V.Philosophy of Logic (Englewood Cliffs, NJ: Prentice-Hall, 1970)
Lewis, David, On the Plurality of Worlds (Oxford: Blackwell, 1986), section 1.5
Lewis, David, “New Work for a Theory of Universals,” Papers on Metaphysics and Epistemology (Cambridge University Press, 1999), pp. 8–55
Australasian Journal of Philosophy, 1983). See especially the section entitled “Universals and Properties,” pp. 10–24 in Papers on Metaphysics and Epistemology
Parsons, Terence, Non-Existent Objects (New Haven, CT: Yale University Press, 1980)
Lewis, David, “Noneism or Allism?,” Papers in Metaphysics and Epistemology, pp. 152–163 (originally published in Mind, 1990)
“Two Concepts of Possible Worlds,” Midwest Studies in Philosophy 11 (1986): 185–213
Crisp, Thomas M., Davidson, Matthew, and Laan, David Vander, eds., Knowledge and Reality: Essays in Honor of Alvin Plantinga (Dordrecht: Springer, 2006), pp. 15–34