Abstract
Much of the recent countability research agrees on the idea that a satisfactory account of individuation in terms of what counts as “one” unit for counting is highly relevant for characterizing a semantics of the mass/count distinction. (What counts as “one” is not necessarily a formal atom in a Boolean algebra or a natural unit associated with natural kinds like cat.) Taking the most parsimonious stance, our main question is: If we have a full-fledged formal theory of individuation (what counts as “one”), what data would still remain to be explained for a formal theory of the mass/count distinction? Would classical mereology be sufficient to cover such data? And, if not, what minimal extensions would be required to classical mereology to do so? We conclude that, minimally, two dimensions of context sensitivity are needed to enrich a mereological semantics of count nouns denotations. The first kind of context sensitivity enables counting operations to apply by removing overlap from an overlapping set of individuated entities. The second kind of context sensitivity allows us to motivate how a set of individuated entities can sometimes be taken as a counts as “one” despite not being a formal atom or a natural unit associated with a natural kind.
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Notes
- 1.
Also see Pelletier (1979) and references therein.
- 2.
A notable omission from Table 1 are so-called “dual life” nouns such as stone \(_{+\mathrm {C}}\)/stone \(_{-\mathrm {C}}\) (\(+C\) abbreviates COUNT and \(-C\) abbreviates MASS). We leave these aside in this paper, given that it is unclear whether one should take either the mass or count sense to be primary, or, indeed, whether such nouns should be classified as being of some intermediary morphosyntactic category between count and mass.
- 3.
We do not rule out there being more than these four.
- 4.
We do not view this role for context as the same as that employed by Rothstein (2010) which specifies what is lexically accessible for counting in context.
- 5.
This would require taking the view that in Yudja, a more liberal view is taken on what counts as “one” such that nouns denoting, for example, mud would have non-empty \( Ind \) sets. This may be relative to some specific context only, however. The examples for counting with nouns denoting substances and liquids in Lima (2014) tend to be in contexts where there are clearly perceptual portions involved such as drops of blood.
- 6.
This is, again, not absolute. For example, table seems to behave closer to fence insofar as two tables pushed together can count as “one” table.
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Acknowledgements
This research was funded by the German Research Foundation (DFG) CRC991, project C09.
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Sutton, P.R., Filip, H. (2016). Countability: Individuation and Context. In: Foret, A., Morrill, G., Muskens, R., Osswald, R., Pogodalla, S. (eds) Formal Grammar. FG FG 2015 2016. Lecture Notes in Computer Science(), vol 9804. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53042-9_17
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