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The vagueness argument against abstract artifacts

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Notes

  1. For representative defenses of creationism, see Levinson (1980) on musical works, Bealer (1993, §7) on modes of presentation, Thomasson (1999) and Kripke (2013) on fictional characters and literary works, Sainsbury and Tye (2012) on words and concepts, Irmak (forthcoming) on software, and Rohrbaugh (2003) and Walters (forthcoming) on various kinds of repeatable artworks.

  2. Thanks to Ned Markosian for helpful discussion here. See Parsons (1980, p. 188) for an alternative account of our creationist intuitions.

  3. To say that there is an exact cut-off is to say that there are a pair of adjacent cases in the series such that some given abstract artifact exists in one but not the other.

  4. See Dawkins (1976).

  5. See, e.g., Williamson (1994), Fara (2000), Sorensen (2001), and Kearns and Magidor (2008).

  6. Moreover, whichever precisification of ‘∀’ is associated with the smaller domain arguably is not an admissible precisification of ‘∀’, since any candidate for being a precisification of ‘∀’ would have to range over absolutely everything. See Sider (2001, pp. 128–129).

  7. See Lewis (1986, pp. 212–213) and Sider (2001, §4.9.1).

  8. See Sider (2001, pp. 126–130).

  9. Put another way, one would then have no grounds for resisting Markosian’s (1998, §5) “brutal” response to the argument for universalism.

  10. Cf. Thomasson (2007, Chap. 6) on the B-argument.

  11. Cf. Hirsch (1999) and Barnes (forthcoming) on the B-argument.

  12. Thanks to Bryan Pickel and Richard Woodward for helpful discussion of this strategy.

  13. Thanks to Michaela McSweeney, Rohan Sud, and Ryan Wasserman for helpful discussion. See Fiocco (forthcoming) for discussion of this sort of “atemporal becoming”.

  14. Similar problems arise for structurally similar strategies for resisting B6. See Korman (2010, p. 895) in response to Baker (2007, pp. 130–132) and Donnelly (2009, pp. 73–76).

  15. In fact, this is simply an adaptation of a strategy for securing B9 against the complaint that there are borderline cases of concreteness; see Sider (2001, p. 127) and Korman (2010, p. 893). One might worry that this introduces an equivocation into the argument, insofar as ‘A’ in the numerical sentences no longer means abstract artifact. But this is cause for concern only if understanding ‘A’ in this new way weakens or undermines the support for one of the premises, and as far as I can tell it does not. Thanks to Meghan Sullivan for helpful discussion.

  16. Thanks to Ted Sider, Raúl Saucedo, and Ryan Wasserman for helpful discussion of this strategy. See Sider (2011) for more on fundamental quantifiers.

  17. See Korman (forthcoming).

  18. Cf. Dorr (2005), Cameron (2010), and Rettler (ms).

  19. Cf. Lewis (1983, p. 372) on their unnaturalness.

  20. The usual four-dimensionalist picture on which there is an object corresponding to every filled region of spacetime delivers just such a plenitude, so four-dimensionalists like Lewis and Sider are already well-positioned to adopt this plenitudinous account of generation. But it is equally open to three-dimensionalists to embrace the plenitude; see Miller (2005, §3), Lowe (2005), and Kurtsal Steen (2010).

  21. Fundamental particles may be an exception here. Assuming that their generation is governed by physical laws that do not admit of vagueness, one can account for how they are generated at exact points in a principled (non-arbitrary) way without postulating a generational plenitude. Thanks to Matti Eklund for helpful discussion here.

  22. Thanks to Dave Liebesman, Meghan Sullivan, Raúl Saucedo, Mary Beth Willard, Jonathan Schaffer, Lina Jansson, and Jason Turner for helpful discussion here.

  23. How long is that? Here the plenitudinous creationist faces another problem. She can say that they have always existed, but it would certainly be odd to treat the words of a language but not the letters of its alphabet as artifacts. And yet she will be hard pressed to identify a remarkable, non-arbitrary exact point at which the letters begin to exist. Thus, the problems raised in the text for words are going to arise for letters as well.

  24. Cf. Sider himself on vagueness-based arguments against ordinary objects (2001, p. 188): “At present, the theory of vagueness is in flux, with none of the prominent theories being perfectly acceptable. If paradoxical conclusions emerge in the area, it is hard to justify attributing them to the postulation of ordinary objects … rather than to an inadequate understanding of vagueness.” Mutatis mutandis, I say, for postulating restrictions on composition.

  25. See, e.g., Lewis (1991, §3.6) and Hudson (2001, pp. 107–108) respectively.

  26. See, e.g., Kaplan (1990) and Wetzel (2009) on words, Yagisawa (2001), Everett (2005) and Hayaki (2009) on fictional characters, Renear and Wickett (2009) on documents, Wickett et al. (2012) on data sets, and Caplan and Matheson (2006), Dodd (2007), Cameron (2008), and Tillman (2011) on musical works.

  27. Thanks to Laurie Paul for the example.

  28. See Barnes (2007).

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Acknowledgments

Many thanks to Chad Carmichael, Louis deRosset, Matti Eklund, Dave Liebesman, Dan López de Sa, Bryan Pickel, Ryan Wasserman, Richard Woodward, my commentators at the Bellingham Summer Philosophy Conference—Meghan Sullivan and Raúl Saucedo—and audience members who offered helpful suggestions and objections even at the cost of their pink and red cards: Mark Balaguer, Sara Bernstein, Heather Demarest, Lina Jansson, Karen Lewis, Ned Markosian, Michaela McSweeney, Laurie Paul, Michelle Saint, Jonathan Schaffer, Ted Sider, Rohan Sud, Jason Turner, and Mary Beth Willard. This paper was inspired in part by Elizabeth Barnes’s (2007) observation that sparse property ontologies give rise to vague existence.

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  1. Department of Philosophy, University of Illinois, Urbana, IL, USA

    Daniel Z. Korman

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Korman, D.Z. The vagueness argument against abstract artifacts. Philos Stud 167, 57–71 (2014). https://doi.org/10.1007/s11098-013-0232-5

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