 Assume for the sake of argument that \(k\) is known. Then, presuming that knowledge entails truth, \(k\) is true. But \(k\) says that \(k\) is unknown. So \(k\) is unknown. Consequently, \(k\) is both known and unknown. But then our assumption (i.e., that \(k\) is known) is false, and provably so. And, granting that a proven falsehood is known to be false, it follows that it is known that \(k\) is unknown. That is to say, it is known that \(k\). But we have already shown that if it is known that \(k\) then \(k\) is both known and unknown. So it is proven that \(k\) is both known and unknown. It is provably the case that the full description of our knowledge includes both \(K(k)\) and \(\neg K(k)\). That is the knower paradox.