I was thinking a little

I was thinking a little about quantifiers for various reasons last night, and I ended up being so confused I had to write a blog entry about it.

If you listened to what some philosophers, yours truly included, taught their undergraduates, you’d think we spoke a language in which (1) and (2) were synonymous.

(1) Some cat is beautiful

(2) *Some beautiful is cat.

Some days it is amazing that philosophers can make any useful contribution to linguistics.

So let’s try and get a little clearer about just what role ‘some’ plays. It isn’t a quantifier, as philosophers normally think of that term. Rather, it’s a determiner, which combines with an NP (or other phrases?) to form a quantifier phrase. The quantifier in (1) is the phrase ‘some cat’. And the QP, as is widely known, can be treated as being the same type as a name – a function from predicates to truth-values.

So is there any such thing as unrestricted quantification? Possibly yes, in one sense, and possibly no, in another. The yes sense first.

None of the dogmatic assertions in the previous sentence were meant to be inconsistent with the idea that (1) is an unrestricted quantification over cats. For all I asserted, an utterance (1) could be true just in case some cat somewhere in the universe is beautiful. It’s agreed on all sides (I think!) that this is rarely the speaker meaning of (1). The speaker meaning of (1) is usually that some salient cat is beautiful. When pushed I usually agree with those who say this is also part of the semantic meaning, but for present purposes I want to bracket that issue. Let’s agree with those who say that the semantic meaning of (1) is just that some cat is beautiful. (That looks so plausible written like that!) It’s still the case that the quantifier in (1) is restricted to cats. All cats now, but still cats. The question is could there be an utterly unrestricted quantifier?

Some may think that the quantifier in (3) is such a quantifier, but I doubt it. The problem is that (3) is too similar to (4), and (4) looks like it is restricted to quantification over things, and I rather doubt that ‘thing’ in English is an utterly trivial noun.

(3) Something is beautiful.

(4) Some thing is beautiful.

So I conclude, somewhat hastily, that quantifier phrases in subject position are always restricted. This is hardly a new conclusion, which is why I feel safe moving at such speed. What though of QPs in subject position, as in (5)?

(5) There is a cat who can play the piano.

To start with, this ‘there is’ construction is very hard to get a handle on. Here’s a relatively simple question about it that I don’t know if anyone has solved. (I don’t know if anyone’s noticed it before, though I suspect they have. As I may have mentioned, I’m away from my books right now.) I assume for now that the prepositional phrase ‘who can play the piano’ is part of the quantifier phrase. We will come back to that below.

We can make all kinds of sentences using the construction ‘There’ + copula + QP. Focus for now on such sentences where the QP has ‘no’ at its head. In some of these sentences the copula is most naturally singular. In others it is most naturally plural. For example, (6) is more natural than (7), but (9) is more natural than (8).

(6) There is no way to rescue the princess.

(7) ?There are no ways to rescue the princess

(8) ??There is no Bengals supporter in Sydney.

(9) There are no Bengals supporters in Sydney.

I have no idea why this would be so. Here was one thought I had that doesn’t seem to work. Imagine an atheist using the problem of evil to argue against the existence of any gods. She would probably use (10) when addressing a monotheist, but (11) when addressing a polytheist. (Bracket for now concerns about the problem of evil as an argument against multiple gods.)

(10) The famine in Africa is yet more proof that there is no god.

(11) The famine in Africa is yet more proof that there are no gods.

So, I thought to myself, maybe the difference is that we use ‘is’ when the audience expects that if there is any, there is one, and ‘are’ when they expect that if there is any, there are many. But this can’t be right. American football fans are thin on the ground in Sydney, and Bengals fans are thin on the ground wherever one looks. If there are any there, there is probably just one. And if there is one way to rescue the princess, it wouldn’t be surprising at all if there is some relatively minor alternative to that plan. So I don’t really know what to make of this. Any suggestions would be most appreciated. Philosophers are notoriously weak on issues to do with plurality in language, so I might leave this one to the experts.

What I was originally interested in was whether the ‘There’ + copula + QP construction could be used to get an utterly unrestricted quantifier. At first glance, it is plausible that (5) contains an utterly unrestricted quantifier – it says the world contains a cat that is capable of playing the piano. As we might put it in formalese:

(12) Ex (Cat(x) & Can-play-the-piano(x))

But if that’s right, then (13) should be a fine sentence, and at least in discourse-initial position it is very odd.

(13) There is a cat.

We can say that in the middle of a conversation. Imagine we are looking through the normal directories for animal pianists. After I’ve ruled out all the monkeys, whales, giraffes, pandas and antelopes, you might say ‘There is a cat’, (speaker) meaning (5). But it would be odd to start a conversation.

Now there are good pragmatic explanations for why this would be odd. But in the spirit of early morning experimentation, let me propose a (bad?) semantic explanation. I suggest (13), despite being a somewhat well-formed sentence, does not express a complete proposition. Rather, I think, the proposition expressed by a sentence ‘There’ + copula + QP + PP is generated by replacing the ‘there’ in subject position by the QP, and dropping the copula and the head of the PP. So (5) expresses exactly the same proposition as (14).

(14) A cat can play the piano.

And (13) expresses the same proposition as (15).

(15) A cat.

What advantages does this have? Well, not many, but it does explain why (13) is odd in discourse-initial position, and after all we have to try and find some way of writing a semantic entry for these ‘There is’ sentences. There are also some disadvantages – including some potential counterexamples hidden on this page – but for now that’s my morning suggestion.

I would try and write more, including about the differences between using ‘there’ as a null subject and ‘there’ as a demonstrative – the stress patterns in the two are notably different I think – but I’ve probably made enough blunders for one entry.