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I guess it's just me, but this kind of sentence:

"All the elephant trainers have not been informed of this decision."

...seems misleading to me; what is meant (which can be deduced from the context) is:

"Not all the elephant trainers have been informed of this direction."

So why isn't the (to me) clearer way of stating it used? From my perspective, the first statement:

"All the elephant trainers have not been informed of this decision."

...is logically saying that none of the elephant trainers have been informed. After all, by beginning with, "All the elephant trainers" that is what is being discussed: the entirety of them. Now, what about them? They have not been informed about the decision.

It seems ambiguous at best to me, whereas the second statement:

"Not all the elephant trainers have been informed of this direction."

...makes it clear that there are at least some elephant trainers who have not been informed, and implies that some have.] been.

If the first, and common, way of expressing this thought is truly correct, can somebody explain to me how to understand it?

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    It's English. It's supposed to be ambiguous. (In many cases you must assume the role of "any reasonable person", and interpret it as "any reasonable person" would. You must assume this role, since "any reasonable person" has never actually been spotted anywhere, so you can't ask him directly.) – Hot Licks Mar 5 '16 at 14:08
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    Asking why people do strange / illogical ... things isn't really a linguistics question. // There is a whole body of English (idioms) defined as having non-standard word senses, grammar, or both. I'd certainly not use "All the elephant trainers have not been informed of this decision.", choosing "Not all the elephant trainers have been informed of this direction." or "None of the elephant trainers have been informed ..." as appropriate. But I use say 'He insisted that the children went to school' in place of 'He insisted that the children go to school' (where context disambiguates). – Edwin Ashworth Mar 5 '16 at 14:25
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    When we write mathematical arguments, of course this ambiguous wording must be avoided. But of course in normal speech it is common. It cannot be called incorrect. But if you wish, you may always use the non-ambiguous form. (Just ignore the funny looks that result.) – GEdgar Mar 5 '16 at 14:30
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    "All of the parents have not yet been informed." perhaps packs less baggage as an example. – Edwin Ashworth Mar 5 '16 at 14:54
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    i) (lexically-encoded) presuppositions, or (ii) Gricean Maxim-induced implicatures. >> I'd argue that ambiguities that are truly (rather than surface- , like 'Your grandma's wicked – she can still dance the tango) ambiguous may be labelled 'incorrect'. Agreed grammar is not the only standard of acceptability. // The above link should, in the first instance, have been to user177 over on Linguistics beta; they provide the analysis / summary. – Edwin Ashworth Mar 5 '16 at 15:12
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In ordinary predicate logic, both "all" and "not" are sentence operators -- items which combine with a sentence to make another sentence. Diagrammatically, not(...) and all(...). When both occur together, there are potentially two interpretations:

NEG-Q: not(all(...))
NEG-V: all(not(...))

Evidently, there is no particular reason to adopt one interpretation over the other, and some English speakers do it one way, some the other, some either, some neither (these speakers don't accept "all" before "not" when there might be an ambiguity).

The terms NEG-Q and NEG-V are those used by Guy Carden, who first studied the phenomenon. If you do a web search on "neg-q dialect", you'll find many references. Here is a good one: Sociolinguistic Patterns.

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    This is ordinary predicate logic. Not all - Some! All not - None. Some not? Some did, some didn't. No some? All in the opposite context. – Sakatox Mar 5 '16 at 17:07
  • I was trying to enumerate some examples of what translates to what with predicates. Excuse my arbitrary formatting in comments. (As a sort of answer aid, my two cents.) – Sakatox Mar 5 '16 at 19:27
  • @Sakatox I can't follow what you're trying to say. I used parentheses to surround sentences (or "well formed formulas"). Some parentheses are often omitted in logic notation, but that doesn't matter tp where the sentences are. – Greg Lee Mar 5 '16 at 20:06
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The example given is a perfectly good response to the claim "All trainers have been notified...". Otherwise, I think all competent speakers would prefer to say "Not all trainers have been notified...", but in the email age, perhaps we begin a sentence one way and can't be bothered to rephrase it. We might not even have been less lazy in a bygone age, but perhaps we thought more before before putting pen to paper?

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