A comment on my earlier post on type-shift:

Here’s something I was thinking about in semantics class today. I haven’t asked Elena about it, and it might just be stupid. But I’m going to take the comments form of this blog post as an opportunity to write it down and thus maybe sort it out in my head a bit.

We’re using the Heim & Kratzer textbook and the system described therein, so we say that the denotation of a verb like ’smokes’ is a function from individuals to truth values (returning 1 in this specific example iff the person smokes). We write something like the following:

[[smokes]] = lambda(x) . x smokes

While that may look illuminating, it’s really just a clever label for the function itself, which is e.g. the following set:

{(Mary, 1), (John, 0), (Lisa, 1)}

Now I understand that one of the prime assumptions of the whole theory is that we as native speakers don’t have to know the actual truth value of an utterance, but rather only the truth conditions — what would be required to make it true. So the fact that the function is that specific set in this specific world is immaterial; what matters is that we know how to judge whether any particular set would work out for the given utterance and state of affairs.

So then isn’t it sort of a contradiction to say that the denotation of ’smokes’ is the function described in lambda notation above? Because if that’s what we are saying, then we are also saying that the denotation of ’smokes’ is that set:

[[smokes]] = {(Mary, 1), (John, 0), (Lisa, 1)}

But we said that we don’t have to know (and in many cases *can’t* know) the actual composition of sets like this. So how can the set be the denotation of the word we’re using? If we’re to say that there is any sort of psychological reality to our compositional theory of function application, shouldn’t we actually be able to *know* (in some epistemological sense I apparently can’t quite articulate) the objects we are talking about?

Perhaps I’m misunderstanding the meaning of the term ‘denotation’.

First, a clarification on ‘denotation’. I’m at home and don’t have the Heim & Kratzer handy, but at least from your interpretation of ‘denotation’, it seems as if they’re using this in the same way that others use the term ‘extension’. That means that these values are world-specific. An intensional value for a verb such as smokes would be the set of triples, from worlds to individuals to truth values (or if you curry/schönfinkel that function, the function from worlds to a function from individuals to truth values). So all of these values are world-dependent. The 1’s and 0’s in each ordered pair are dependent upon which world you’re in, and you need not know what world you’re in to evaluate an utterance. Once you know what world you’re in (and everything about that world), then you are in a position to know who smokes and who doesn’t, yes? I’m not entirely sure that this is the best answer to your question (it seems to me that even taking the extension of ’smokes’ doesn’t necessarily require you to know whether certain individuals get mapped to 1 or 0; just that the speaker understands the relation that would map individuals to 1 or 0 is what matters), but I think the picture gets clearer when you take world-dependency into account.

emma :: Feb.03.2007 :: semantics, linguistics :: 8 Comments »