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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?

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    I'm not sure this "exhaustible meaning" is such a unique phenomenon, and limited to words like "best", etc. It seems to me that the same kind of FOL expression is just as applicable to natural number'ed quantifiers as well. For example, the FOL expression for "five" in "five apples were red" limits the applicability of "red" to just 5 "apple" entities. – prash Jun 20 '14 at 12:22
  • @prash In a proper context (e.g., 5 red apples being a relevant minimum) and with a proper intonation (e.g., pitch on the verb) that is defeasible. So, it can be continued: In fact, a dozen were. I'm not sure the same is true for superlatives. – Ivan Kapitonov Jun 21 '14 at 6:37
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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.

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    "Who knows how to build a house?" could also have the mention-some interpretation. Is the list-all vs mention-some interpretation just governed by pragmatics? – Russell Richie Jun 22 '14 at 17:47

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