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The Daily Mirror recently used the phrase "Pentagon experts on Friday said it was impossible to imagine that the missile could not have been fired without Russian help". This exact phrase has appeared in other news stories as well, likely spread from the original Pentagon press release via newswire.

Is the "not" a mistake or idiomatic English? Without the "not" the phrase makes sense to me and the meaning is consistent with the context. With the "not" I don't even know what it means.

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    I imagine most people think that "the missile could not have been fired without Russian help". So it's hardly impossible, is it? I can believe as many as six impossible things before breakfast along with the best of 'em, but I can't believe OP's supposedly commonplace sentence makes any sense at all. – FumbleFingers Jul 21 '14 at 22:03
  • @FumbleFingers it's just exaggeration. You may disagree, but you wouldn't think there's anything unidiomatic about the not. – curiousdannii Jul 21 '14 at 22:08
  • @curiousdannii: Possibly it's intended to be reinforcingly emphatic, but the fact remains that what's actually being said is nonsense. I'd prefer to hope whoever wrote/said that was just making a careless mistake, rather than actually thinking his usage was credible/defensible. – FumbleFingers Jul 21 '14 at 22:14
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    It's overnegated, all right. Impossible, not, and without are all negatives (and imagine is an added hypothetical note). As Larry Horn puts it, "Simplex negatio negat, duplex negatio affirmat, triplex negatio confundit." – John Lawler Jul 21 '14 at 23:22
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    it's just a typo, no big deal – Fattie Jul 31 '14 at 11:42
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If I understand the Pentagon's attitude correctly, the sentence should say "Pentagon experts on Friday said it was impossible to imagine that the missile could have been fired without Russian help," without the not. This is an example of misnegation (or overnegation), which Mark Liberman of Language Log describes as "the confusions arising from our poor monkey brain's inability to deal with combinations of negations, modals, and scalar expressions." See that link for examples and further explanations.

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