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Does vagueness underlie the mass/count distinction?


Does vagueness underlie the mass/count distinction? My answer is no. I motivate this answer in two ways. First, I argue against Chierchia’s (Synthese 174:99–149, 2010) recent attempt to explain the distinction in terms of vagueness. Second, I give a more general argument that no such account will succeed.

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  1. All page references to Chierchia’s work are to Chierchia (2010).

  2. Chierchia relies on a number of assumptions about the nature of plurality and vagueness. This reliance is largely incidental. Nonetheless, presenting Chierchia’s view complete with his own assumptions allows for a better understanding of the view.

  3. Among many others, including Chierchia (1998a, (1998b).

  4. There is plenty one may worry about with regard to this understanding of plurality. Philosophically, the most troubling worry is what McKay (2006) calls “singularism”. I’ll argue that Chierchia’s account fails even given his own understanding of plurality, so I’ll set aside anti-singularist scruples.

  5. Taking plurals to be true of atoms is controversial. In earlier work (1998b), Chierchia rejects this. His change of mind stems from the fact that the sentence “No cats are on the mat,” is intuitively false if there is just one cat on the mat. This is hard to account for if single cats are not in the denotation of “cats”.

  6. Following Chierchia, I’ll take AT to apply to sets, properties, predicates, and individuals. If we take the set case as fundamental, then AT applies to properties by applying to the sets that model them, and AT applies to predicates by applying to the sets that capture their domains.

  7. For simplicity, I am skipping a number of complications and innovations in presenting this framework. Most notably, Chierchia takes the ‘uppermost’ elements in domains to be kinds. Following Carlson (1977), among many others, we can then take kinds to be the referents of a number of occurrences of terms, e.g. bare occurrences of plural count nouns.

  8. Note that it is problematic to take non-overlap as a constraint on the set of atoms relative to some property. This is due to the fact that, for instance, we may wish to both count Spot as an atom, as well as Spot’s left leg.

  9. Perhaps this is settled by the existence of a soul, or something of the sort. If so, feel free to change the example to chairs.

  10. There are difficult questions about whether modelling vague predicates as partial functions suffices for capturing the essence of their vagueness. In particular, we may wish to distinguish between vagueness, which seems to require that there are borderline cases of the sort that lead to the Sorites paradox, and indeterminacy, which seems merely to require that there are cases left open. For a discussion of these issues see Weatherson (2010). I’ll set this aside and grant Chierchia the adequacy of his model, at least for his purposes.

  11. Chierchia (119) does give a technical definition of “ground context”: they are contexts, in a given model, that are minimal with respect to \(\propto \). This definition, in an of itself, doesn’t determine which contexts are ground without an independent means to determine which models are under discussion. Since we are attempting to explain the ordinary behaviour of mass and count nouns, it stands to reason that among the ground contexts are ordinary conversational contexts. Note, also, that in at least one place he refers to them as “base contexts”.

  12. There is substantial disagreement about this, both in philosophy, e.g. Hodes (1984) and Hofweber (2005), and linguistics, e.g. Kennedy (2013).

  13. McGee and McLaughlin present their determinacy-based solution in their (2000).

  14. Compare Chierchia’s discussion of “heap” on pg. 122. These issues are also discussed in Rothstein (1998) and (2010).

  15. In particular, a brutalist view as developed by Markosian (1998) may fit better since there will be the intuitive number of stable atoms for count nouns. However, even Brutalism will not be compatible with Chierchia’s view if we combine Brutalism with an epistemic view of vagueness. Furthermore, given Brutalism an epistemic view is particularly plausible.

  16. These remaining peaks are stable universe atoms, but not stable mountain atoms.

  17. Chierchia clearly allows the possibility of such contexts, as he treats vague predicates as predicates with entities that are neither in their extension nor ant-extension.

  18. See Salmon (1997), Fox and Hackl (2006), and Liebesman (2015) for a discussion of these issues.

  19. For some criticisms of such a solution, see Pelletier and Schubert (1989) and Rothstein (2010).

  20. See Koslicki (1999) for a discussion of these issues.

  21. See Burge (1972) for an example of the pragmatic strategy.

  22. It is worth noting that the two envisioned semantic explanations may be notational variants of one another if there are multiple equally good ways to type expressions for various purposes. On the other hand, if our typing system is not so conventional, then the sorts of explanations may be genuinely distinct.

  23. Landman (2004) also pursues an adjectival theory, though he takes adjectives to be first-order predicates.


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Thanks to Jared Henderson and three referees for Synthese.

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Liebesman, D. Does vagueness underlie the mass/count distinction?. Synthese 193, 185–203 (2016).

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  • Vagueness
  • Mass/count
  • Philosophy of language
  • Semantics