If you know something implies something else, and it really does, do you know that too?

The principle of epistemic closure says knowledge is preserved across known logical implication: if you know P, and know P implies Q, then you know Q. It sounds obvious, but has sharp teeth — if you know you have hands, and know that implies you're not a handless brain in a vat, closure says you know you're not a brain in a vat, a claim sceptics deny we can know. Robert Nozick argued the principle should be rejected rather than accept that conclusion.

— Robert Nozick, Philosophical Explanations — Harvard University Press, 1981