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Naturalness, Vagueness, and Sortals

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Metaphysica

Abstract

In the past few years, deflationary positions in the debate on the nature of composite material objects have become prominent. According to Ted Sider these include the thesis of quantifier variance, against which he has defended ontological realism. Recently, Sider has considered the possibility of rejecting his arguments against the vagueness of the unrestricted quantifiers in terms of translation functions. Against this strategy, he has presented an intuitive complaint and has argued that it can only be resisted if quantifier variance is accepted. But this is false. In this paper I argue, against Sider, that there is a coherent way to combine the rejection of quantifier variance with the vagueness of the unrestricted quantifiers. I sketch a model to show this, and then I consider, on the basis of it, several versions of the indeterminacy argument against the vagueness of the unrestricted quantifiers that Sider has formulated over the years.

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Notes

  1. In a mereological sense which we can assume is the usual one: x is a sum of the zs = df The zs are all parts of x and every part of x has a part in common with at least one of the zs.

  2. Among them, (1) Equivocation according to which the participants express different propositions with ‘there exist the sum of the Sun and the Moon’ and each one makes claims that are true given what he means; so the debate is merely verbal; (2) Indeterminacy according to which the participants do not express a unique proposition with ‘there exists the sum of the Sun and the Moon’; when they use the sentence, it is semantically indeterminate over various candidates, some of which make one of the participant’s claims true, others of which make another participant’s claims true. So the debate is ill-formulated; (3) Obviousness according to which all the participants express the same proposition with ‘There exists the sum of the Sun and the Moon’ but it is obvious through linguistic/conceptual reflection what its truth value is, so the debate is silly.

  3. Sider considers some other possible refinements in (Sider 2009a, pp. 391–392).

  4. Now, what are these ‘candidate meanings’? Sider (2009a) considers different possibilities, but there does not seem to be one best option. We could consider the idea that they result from different choices of a domain for the quantifiers to range over. Or we could consider the idea of characterizing them by using translations—see Hirsch (2002); or, for another way to proceed (even if the author is not a deflationist himself), see Dorr (2005). Or we could consider the idea of characterizing them by describing what they are supposed to do, etc.

  5. The ‘ideology of the theory’, in Quine’s (1951) terminology.

  6. In the paper, (Sider 2009a), Sider reconstructs the argument in nominalist terms.

  7. See Lewis (1983, 1984, and 1986); Lewis sees natural properties and relations as similarity determiners as well. Moreover, he connects naturalness to nomic and causal notions (see Lewis 1994). Sider adds that structure has an evaluative component (the goal of inquiry is to discover it) and that it allows us to make sense of claims according to which certain features are projected onto the world. It would be, as well, central to metaphysics and sciences.

  8. As Sider says, he is assuming here that the naturalness of EXISTENCE overcomes any mismatch between it and the use of ‘there exists’. This may be wrong. In that case, deflationism may be correct about the English quantifiers but then the ontologists can recast their debate directly in terms of EXISTENCE introducing a new language for this purpose.

  9. See, for example, Fine (1975) or Lewis (1993, 1986).

  10. Defended by Braun and Sider himself (see Braun and Sider 2007).

  11. Here we should take into account the so-called ‘penumbral connections’.

  12. Even if it is not relevant for our present purposes, let me mention that this is understood in every theory of vagueness accepting precisifications in a slightly different way.

  13. David Lewis’s condensed argument against vague unrestricted quantifiers, in Lewis (1986), also appeals to this seemingly impossibility of finding different adequate precisifications for the unrestricted quantifiers (given a semantic theory of vagueness): ‘The only intelligible account of vagueness locates it in our thought and language […] Vagueness is semantic indecision. But not all of language is vague. The truth-functional connectives are not, for instance. Nor are the words for identity and difference, and for the partial identity of overlap. Nor are the idioms of quantification, so long as they are unrestricted. How could any of these be vague? What would be the alternatives between which we have not chosen?’ (Lewis 1986, p. 212).

  14. Not that Sider or Eklund or Liebesman accept that this is so.

  15. See, for example, Koslicki (2008) or Wiggins (2001) for further developments.

  16. Sider understands temporal part in the following way:

    (TP) x is an instantaneous temporal part of y at instant t=def. (i) x exists at, but only at, t, (ii) x is part of y at t, and (iii) x overlaps at t everything that is part of y at t.

    (where two objects overlap at a time iff something is part of each then.)

  17. For an excellent summary of this, see Varzi (2005).

  18. For example, we can resist Sider’s argument endorsing mereological essentialism (see, e.g., Chisholm 1973).

  19. Relative to penumbral connections.

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Acknowledgements

I would very much like to thank all the members of the LOGOS group for their invaluable comments on previous versions of this paper. Special thanks are due to Fabrice Correia, Manuel García-Carpintero, Dan López de Sa, Sònia Roca, Pablo Rychter, Gabriel Uzquiano and Achille Varzi. The research leading to these results has received funding from the European Community's Seventh Framework Programme FP7/2007-2013 under grant agreement no. 238128, and also from the DGI, Spanish Government, research project HUM2006-08236 and Consolider-Ingenio project CSD2009-00056. Thanks also to Michael Maudsley for his linguistic revisions.

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Correspondence to Marta Campdelacreu.

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Campdelacreu, M. Naturalness, Vagueness, and Sortals. Int Ontology Metaphysics 11, 79–91 (2010). https://doi.org/10.1007/s12133-010-0060-4

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