Name for statements with exhaustible meaning?

Question

I'm new to linguistics and I'm having trouble finding out if there's any existing literature on statements that have exhaustible meaning.

By exhaustible meaning, I'm trying to get at something like the following:

Professor X wants to recommend A and B for a job. To maximize the chance they are hired, X might want to say "A is the best student I've ever had," and the same for B.

If both statements are made together, there is a contradiction. I would say the honor of best student is exhausted (given both statements are made at the same time). Similarly, other statements might have exhaustible meaning. Compliments, especially rivalrous claims, become less meaningful with abundance, even coming from multiple speakers. The previous example just seems to be a special case of that.

So is there a name for this or anything else worth saying that might have already been said?

Answer 1

Here's a bag of random notes:

1. Superlatives of all sorts, which you mention, should have the uniqueness presupposition.

2. Focus often carries exhaustive meaning. See Katalin Kiss's seminal 1998 paper for a start. A GoogleScholar search for "exhaustification (operator)" gives a few interesting results.

3. Certain questions require a "list-all" (1) rather than "mention-some" (2) answers.

   (1) Who (all) came to the party?

   (2) Where on campus can I buy a newspaper?

And maybe somebody here can add to the list.