Is "you know everything" the (using sentential logic) logical negation of "you know nothing"? My friend and I are trying to settle a debate here. Someone joked that they're "not Jon Snow" when debating a yes/no question, and I retorted that the logical negation of "you know nothing, Jon Snow" is not "you know everything, Jon Snow", but my other friend claims that it is. The question, as reduced, stands:
Is "you know everything" the (using S.L.) logical negation of "you know nothing"?

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.
