It also seems to be governed by the principle that proof yields knowledge: Consider however the sentence: Assume for reductio ad absurdum that (K) is known.
Since, given the diagonal lemma, every sufficiently strong theory will have to accept something like (K), absurdity can only be avoided either by rejecting one of the two principles of knowledge (KF) and (PK) or by rejecting classical logic (which validates the reasoning from (KF) and (PK) to absurdity).
One approach takes its inspiration from the hierarchy of truth predicates familiar from Alfred Tarski's work on the Liar paradox and constructs a similar hierarchy of knowledge predicates.
One approach rejects the law of excluded middle and consequently reductio ad absurdum.
[7] Another approach upholds reductio ad absurdum and thus accepts the conclusion that (K) is both not known and known, thereby rejecting the law of non-contradiction.