Abstract

The Hangman Paradox has a simple solution. The amazing refutation of the judge's decree rests on the axiom of knowledge-conservation. This axiom is false under unfavourable conditions. You can have a perfect piece of knowledge in the ordinary sense, i.e. a true justified conviction, and yet be unable to conserve it. More interesting than its solution is the element of self-reference, connecting the Hangman via Moore's Paradox and Buridan's Epistemic Paradox with the Liar. This one, I think, has also a natural solution, but less simple. The basic idea is given here, but the technical treatment goes far beyond this paper. It requires a strong, but conservative, extension of classical and three-valued logic to a six-valued logic with infinitely many levels of reflection.