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Kaj_Sotala comments on How to write a mathematical formula on the fear of death? - Less Wrong
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I'm not sure if this helps, but: you can think of it this way
Dying = Someone dies.
Not-dying = It is not so that someone dies.
Not-not-dying = It is not so that (it is not so that someone dies).
The first "it is not so that" cancels out the second "it is not so that".
Similarly, if someone said (in ordinary speech) "I'm not ungrateful", that would mean that they were grateful, while "I'm not grateful" or "I'm ungrateful" would mean that they weren't. "I'm not-not-grateful = I'm grateful."
Be careful with ordinary speech ;-)