The value of ambiguous speech

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This was going to be a reply in a discussion between ChristianKl and MattG in another thread about conlangs, but their discussion seemed to have enough significance, independent of the original topic, to deserve a thread of its own.  If I'm doing this correctly (this sentence is an after-the-fact update), then you should be able to link to the original comments that inspired this thread here: http://lesswrong.com/r/discussion/lw/n0h/linguistic_mechanisms_for_less_wrong_cognition/cxb2

Is a lack of ambiguity necessary for clear thinking?  Are there times when it's better to be ambiguous?  This came up in the context of the extent to which a conlang should discourage ambiguity, as a means of encouraging cognitive correctness by its users.  It seems to me that something is being taken for granted here, that ambiguity is necessarily an impediment to clear thinking.  And I certainly agree that it can be.  But if detail or specificity are the opposites of ambiguity, then surely maximal detail or specificity is undesirable when the extra information isn't relevant, so that a conlang would benefit from not requiring users to minimize ambiguity.

Moving away from the concept of conlangs, this opens up some interesting (at least to me) questions.  Exactly what does "ambiguity" mean?  Is there, for each speech act, an optimal level of ambiguity, and how much can be gained by achieving it?  Are there reasons why a certain, minimal degree of ambiguity might be desirable beyond avoiding irrelevant information?