Is "you know everything" the (using sentential logic) logical negation of "you know nothing"?

No, the negation of "you know nothing" is "you know something". "You know nothing" is of the form $(\forall x) \: \neg P(x)$, where $P(x)$ is "you know $x$". So its negation is $(\exists x) \: P(x)$, which is "you know something" or slightly more precisely "you know at least one thing".


The negation of "You know nothing." is "You do not know nothing." Which implies that your knowledge is non-zero; not that it is necessarily absolute.

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Predicate Logic

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