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. (shrink)

Offers a text of mathematical logic on a sophisticated level, presenting the reader with several of the most significant discoveries, including the independence of the continuum hypothesis, the Diophantine nature of enumerable sets and the impossibility of finding an algorithmic solution for certain problems.