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"It's not important that I'm not on the bench."

Is it the same as saying: "It is important that I'm on the bench".

?

closed as off-topic by jobermark, Dave, jeroenk, Mitch, Conifold Sep 30 '16 at 17:33

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    It depends on the underlying logic of the "modifier" : important... "It's not important that I'm not on the bench" is clearly the negation of "It's important that I'm not on the bench." And the negation of "It is important that I'm on the bench" is clearly : "It is not important that I'm on the bench". – Mauro ALLEGRANZA Sep 27 '16 at 13:40
  • Now the issue is : are "It's important that I'm not on the bench" and "It is not important that I'm on the bench" the same ? – Mauro ALLEGRANZA Sep 27 '16 at 13:40
  • Compare with : "There exists a not even number" with "Does not exist an even number". – Mauro ALLEGRANZA Sep 27 '16 at 13:42
  • @MauroALLEGRANZA I'm inclined to say that "it's important that I'm not on the bench" IS NOT the same thing as "it's not important that I'm on the bench". I think intention, or intentionality seems to play a role here. On the first case, we are saying: "the fact that I'm not on the bench, is an important feature". (being on the bench has a meaning to me). On the other case, I'm saying a different thing, I'm saying that being on the bench has not a particular important meaning to me). My question is: is the "meaning" important for logic evaluation? – m3m Sep 27 '16 at 14:03
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    I'm voting to close this question as off-topic because it belongs in one of the Stack Exchanges about grammar and grammatical terminology EL&U or ELL – jobermark Sep 27 '16 at 18:37
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Consider the situation where it is of no importance whatsever whether I am on the bench or not. In that case

"It's not important that I'm not on the bench."
"It's not important that I'm on the bench."

are both true. And

"It's important that I'm on the bench."

is false.

There is one statement about my location - on the bench or not. There's another statement about the importance of the first fact. There is no reason why these would be related. Or take a company trying to hire a new employee:

"It's important that the new employee is honest". 
"It's not important that the new employee is dishonest". 

If heard the first being said, I've never heard the second.

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It's not double negation because the two not's are applied to different clauses within the sentence.

I break this sentence up as:

(It is not important) that (I am not on the bench)

here "that" is playing the role of (sort of) a conjunction connecting the subjective feeling/impression first clause with the state of the world that feeling/impression relates to. This is a pretty common usage pattern.

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    By definition of double negation, that's what I though. But it's not clear to me what are those clauses. Can you please point them out, as a) and b), so that I be more clear about it? – m3m Sep 27 '16 at 14:36
  • double negation is "not (not P(x))". your example is "not P (not Q (x))". Not double negation. – user20153 Sep 27 '16 at 19:57
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    This is basically correct, but I'd like just to point out that 'it is important that' does not have the form of a connective but rather is much closer to operators such as 'it is possible that'. – Eliran Sep 28 '16 at 10:38
  • This answer is way off the mark. "That" is certainly not playing the role of conjunction. @EliranH has the right idea. "It's important that..." is a modal operator, not a truth functional connective. – user22273 Sep 30 '16 at 4:13
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double negation is "not (not P (x))". your example is "not P (not Q (x))". Not double neg.

  • Thank you. I would upvote it. Because it helped. But I don't have enough reputation. – m3m Sep 28 '16 at 8:01

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