"Know jack" vs. "Don't know jack." [duplicate]
Solution 1:
That this and similar slang expressions set up the apparent paradox of x = not x has a particular fascination for linguists. The logic, however, is easy to grasp.
If jack is a quantity of absolutely no value, i. e. zero, then the difference between
He knows zero.
and
He doesn't know zero.
is basically zero.
Both expressions are "correct" in the descriptive sense that native speakers use both.