Abstract
So far, we have said very little about what a “group” of objects is. And, to a large extent, it hardly matters exactly what groups are like; we have come a long way making just minimal assumptions. Specifically, our assumptions so far (stated in Section 7.1) are just that a model for the interpretation of English must contain a set I of individuals and a set G of groups, and that for any subset X of I of cardinality 2 or greater, there is a group +X in G. (In the case of singletons, +{x} was defined as equal to x, hence not a group; + Ø was undefined.)
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Notes
In Schwarzschild (1992a), he called these approaches the “sums” theory and the “groups” theory, following the terminology of Link (1984). Because we have been using groups in a somewhat different sense, I prefer to avoid this terminology here.
See Landman also for responses to those arguments of Link’s which are not based on concerns about abstractness.
For Link, even pluralities of objects count as a species of “individual” — a regrettable use of terminology, in my opinion, regardless of one’s position on whether pluralities of individuals are type-theoretically distinct from single individuals. (It should be noted that this terminology goes back at least to Leonard and Goodman 1940 and is not original with Link, of course.) I will refrain from this rather unintuitive usage here. The point is that single objects correspond to atoms, while pluralities of objects may correspond to non-atomic elements in the algebra.
Or “groups,” as Link also calls them. The “sum”/“group” distinction of Link (1984) has been perpetuated in much of the subsequent literature, although Link himself uses the term group rather differently in later articles (e.g. Link 1987). The use of group specifically for impure atoms conflicts with the way this term has been used throughout the present book — namely as a general, more-or-less pretheoretic term for the referents of plural noun phrases, whatever these may turn out to be like. Therefore, I will not follow Link in reserving the term group for elements of G.
This second part is presented mainly in Schwarzschild (1991), and receives much less attention in Schwarzschild (1992a).
The versions here are from Schwarzschild (1991) p. 71 and p. 77. Schwarzschild (1992) uses somewhat different wording, but the essential content is the same.
Despite the rather poor arguments of Lasersohn (1988, p. 139), which he rightly criticizes.
Or, strictly speaking, of the domain of discourse as a whole. Problems with using covers of the entire domain rather than the set denoted by the subject were outlined in Section 8.2 above.
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© 1995 Springer Science+Business Media Dordrecht
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Lasersohn, P. (1995). On the Structure of Groups. In: Plurality, Conjunction and Events. Studies in Linguistics and Philosophy, vol 55. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8581-1_9
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