User:Tiiba is correct. Math (after mapping to real-world predicates) allows me to more quickly form reliable expectations about the world. The claim that "this sentence is false" does not. Therefore, I can leave beliefs about the latter unassigned without epistemic or instrumental penalty.
Graham Priest discusses The Liar's Paradox for a NY Times blog. It seems that one way of solving the Liar's Paradox is defining dialethei, a true contradiction. Less Wrong, can you do what modern philosophers have failed to do and solve or successfully dissolve the Liar's Paradox? This doesn't seem nearly as hard as solving free will.
This post is a practice problem for what may become a sequence on unsolved problems in philosophy.