Intuition Mongering: Iterable Plurals? June 16, 2008
Posted by Colin in Language, Logic.trackback
I’ve written about plurals before. In the meanwhile I’ve come to see things more in line with the standard view of those like Yi (“The Logic and Meaning of Plurals I & II” 2005, 2006), and Oliver & Smiley (“A Modest Logic of Plurals” 2006) who take plural reference to be irreducible to singular reference enriched with, e.g. set theory or mereology. Plural referring expressions are much like their familiar singular cousins except that they are, well, plural. We model singular reference in classical first-order set theory by letting the domain of any interpretation be a set and letting the denotation function assign to each term one member of that set. Plural reference can be modeled similarly, with the exception that the denotation function assigns to each term some members of the domain (possibly more than one). Standard singular referring expressions: Bertrand Russell, the Solar System, the empty set. Standard plural referring expressions: Russell and Whitehead, the planets of the Solar System, the (pure) sets.
Question for my readers: do plurals iterate? Forms of singular collective reference certainly do. ”The set of sets whose members are primes greater than 100″ is well-formed. ”The fusion of fusions of cats or dogs” is well-formed. Iterating plurals seems a lot more awkward to me, but it is entirely possible that I just haven’t hit on the right vocabulary to do it. A common way to talk about a plurality in Enligsh is to use the plural “some” as in “some critics”. Can we iterate this like we can with sets-of-sets or fusions-of-fusions? Suppose that we have some bicycles and we have some canoes. Is it well-formed to refer to what we have as ”some some things” or “two some things” or “more than one of some things”?
Since lists can be plural, like ‘Russell and Whitehead’, you would have thought you could have things like:
“John and Mary, and Philip and Louise play doubles together.”
Similarly, instead of nested lists, you could just have lists of any old plural expressions
“The science books, the maths books, and the computing books need to be reshelved separately”
Then you’d probably need to check whether these are irreducibly superplural expressions.
Also, lets not forget plural predicates. So ‘knows one another’, and ’surrounds the building’ are plural predicates, not reducible to singular predication, so must have semantic values that are higher order plurals.
Andrew, thanks I think my question was a bit ill-formed to begin with. Your lists are starting to get at the issue. What seems interesting to me is something like this: when we aggregate singular reference we get plurals reference, but when we aggregate plurals reference we just get more plural reference. In other words, I think that what you mean by “superplural expressions” don’t exist. The reason? Plurals refer to some individuals, so a superplural would have to be referring to some individuals, e.g. some pluralities, but a plurality is not an individual at all. Does this make sense?
Yeah, I can see where you’re coming from. We seem to be able to make sense of a singular term referring to an individual, and a plural term referring to individuals. So do superplurals refer to individualses?
Instead of thinking of a superplural expression as (singularly) referring to a super plurality of things, or plurally referring to some pluralities of things, I find it best to think of them superplurally referring to the individuals. As a separate kind of reference irreducible and distinct from the first two kinds.
BTW, note that in the lists I gave, it’s not clear that they are functioning as ordinary plurals. Compare:
“John and Mary, and Philip and Louise play doubles together.”
“Philip and Mary, and John and Louise play doubles together.”
Also, let the A-M books and the N-Z books refer the the science or maths books that begin with A-M, and N-Z respectively. Then
“The science books and the maths booksneed to be reshelved separately”
“The A-M books and the N-Z books need to be reshelved separately”
The obvious plural analysis doesn’t seem to work here, yet the superplural does.
I’m not sure I get your primitive superplurals.
Let me take a stab at one of your sentences.
“John and Mary, and Phillip and Louise play doubles together.”
Let e’s be variables quantifying over events, let D be “playing doubles”, let T be “at the same time”, and let A be “the agents of” relation.
Hi Colin,
I was thinking of games like tennis, where in one playing you have two teams, each team consisting of two people. I have no doubt you could write the truth conditions for this sentence in a non-third order language. But can this be done systematically?
But most importantly, taking the expression “John and Mary, and Phillip and Louise” at face value it is a noun phrase. So the next question is: is it a singular or a plural noun phrase. I claim neither. Clearly its not a singular term. If it were a plural term then “John and Mary, and Phillip and Louise” would have the same semantic value as “Phillip and Mary, and John and Louise”. But the sentences I gave were supposed to show they couldn’t be. The only way I can make sense of this is if we can have superplural terms.
I see what you mean, but there might be another answer. An easy way to form plurals is with the “and” that Yi calls a term connective, as in your “John and Mary”. Now if we take two terms joined by the plural term connective “and” and two other terms joined by the plural term connective “and” and put an “and” between them, Yi considers this just another plural term. We basically go from four singular terms each referring to one thing, to two plural terms each referring to two things, to one plural term referring to four things. What then makes the difference between “John and Mary, and Phillip and Louise” and “Phillip and Mary, and John and Louise” is simply order. Now you might argue that this is implausible in the kinds of examples you were giving because there is further structure on the individuals involved, but what kind of structure would that be?