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Full Idea
If there were an object called 'not', it would follow that 'not-not-p' would say something different from what 'p' said, just because the one proposition would then be about 'not', and the other would not.
Gist of Idea
'Not' isn't an object, because not-not-p would then differ from p
Source
Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 5.44)
Book Ref
Wittgenstein,Ludwig: 'Tractatus Logico-Philosophicus (Pears)', ed/tr. Pears,D. /McGuinness,B. [RKP 1961], p.45
A Reaction
That is, the first proposition would be about not-p, and the second would be about p. Assuming we can say what such things are 'about'. A rather good argument that the connectives are not entities. P and double-negated P should be indistinguishable.