Does vagueness underlie the mass/count distinction?

Abstract

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.

This is a preview of subscription content, access via your institution.

Notes

  1. 1.

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

  2. 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. 3.

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

  4. 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. 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. 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. 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. 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. 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. 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. 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. 12.

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

  13. 13.

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

  14. 14.

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

  15. 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. 16.

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

  17. 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. 18.

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

  19. 19.

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

  20. 20.

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

  21. 21.

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

  22. 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. 23.

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

References

  1. Barwise, J., & Cooper, R. (1981). Generalized quantifiers and natural language. Linguistics and Philosophy, 4(2), 159–219.

    Article  Google Scholar 

  2. Burge, T. (1972). Truth and mass terms. The Journal of Philosophy, 64(1), 263–282.

    Article  Google Scholar 

  3. Carlson, G. (1977). A unified analysis of the english bare plural. Linguistics and Philosophy, 1(3), 413–457.

    Article  Google Scholar 

  4. Chierchia, G. (1998). Plurality of mass nouns and the notion of semantic parameter. In S. Rothstein (Ed.), Events and grammar (pp. 53–103). Dordrecht: Kluwer.

    Google Scholar 

  5. Chierchia, G. (1998). Reference to kinds across language. Natural Language Semantics, 6(4), 339–405.

    Article  Google Scholar 

  6. Chierchia, G. (2010). Mass nouns. Vagueness and semantic variation. Synthese, 174(1), 99–149.

    Article  Google Scholar 

  7. Fox, D., & Hackl, M. (2006). The universal density of measurement. Linguistics and Philosophy, 29(5), 537–586.

    Article  Google Scholar 

  8. Hodes, H. (1984). Logicism and the ontological commitments of arithmetic. The Journal of Philosophy, 123–149.

  9. Hofweber, T. (2005). Number determiners, numbers, and arithmetic. The Philosophical Review, 179–225.

  10. Ionin, T., & Matushansky, O. (2006). The composition of complex cardinals. Journal of Semantics, 23(4), 315–360.

    Article  Google Scholar 

  11. Kennedy, C. (2013). A scalar semantics for scalar readings of number words. In I. Caponigro & C. Cecchetto (Eds.), From grammar to meaning: The spontaneous logicality of language. Cambridge University Press.

  12. Koslicki, K. (1999). The semantics of mass-predicates. Noûs, 33(1), 46–91.

  13. Landman, F. (2000). Events and plurality. Dordrecht: Kluwer Academic Publishers.

    Google Scholar 

  14. Lewis, D. (1993). Many, but almost one. In K. Cambell, J. Bacon, & L. Reinhardt (Eds.), Ontology, causality, and mind (pp. 23–38). Cambridge: Cambridge University Press.

    Google Scholar 

  15. Liebesman, D. (2015). We do not count by identity. Australasian Journal of Philosophy, 93(1), 123–142.

    Article  Google Scholar 

  16. Link, G. (1983). The logical analysis of plurals and mass terms. In C. S. R. Bauerle & A. von Stechow (Eds.), Meaning, use, and the interpretation of language (pp. 302–323). Berlin: Mouton de Gruyter.

    Google Scholar 

  17. Markosian, N. (1998). Brutal composition. Philosophical Studies, 92(3), 211–249.

    Article  Google Scholar 

  18. McGee, V. (1997). Kilimanjaro. Canadian Journal of Philosophy, 27(sup1), 141–163.

    Google Scholar 

  19. McGee, V., & McLaughlin, B. (2000). The lessons of the many. PhilosophicalTopics, 28(1), 129–151.

    Google Scholar 

  20. McKay, T. (2006). Plural predication. Oxford: Oxford University Press.

    Google Scholar 

  21. Parsons, T. (1979). An analysis of mass terms and amount terms. In F. J. Pelletier (Ed.), Mass terms: Some philosophical problems (pp. 137–166). Dordrecht: Kluwer.

    Google Scholar 

  22. Pelletier, F., & Schubert, L. (1989). Mass expressions. In Handbook of philosophical logic, 4, 327–407.

  23. Rothstein, S. (2010). Counting and the mass/count distinction. Journal of Semantics, 27(3), 343–397.

    Article  Google Scholar 

  24. Salmon, N. (1997). Wholes, parts, and numbers. In J. E. Tomberlin (Ed.), Philosophical Perspectives 11: Mind, Causation, and World. Ridgeview, 1–15.

  25. Unger, P. (1980). The problem of the many. Midwest Studies in Philosophy, 5(1), 411–468.

    Article  Google Scholar 

  26. Weatherson, B. (2009). The problem of the many. The stanford encyclopedia of philosophy. The Metaphysics Research Lab: Stanford University.

  27. Weatherson, B. (2010). Vagueness as indeterminacy. In R. Dietz & S. Moruzzi (Eds.), Cuts and clouds: Vagueness, its nature, and its logic. Oxford: Oxford University Press.

    Google Scholar 

Download references

Acknowledgments

Thanks to Jared Henderson and three referees for Synthese.

Author information

Affiliations

Authors

Corresponding author

Correspondence to David Liebesman.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Liebesman, D. Does vagueness underlie the mass/count distinction?. Synthese 193, 185–203 (2016). https://doi.org/10.1007/s11229-015-0752-y

Download citation

Keywords

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