I'm comfortable (mostly, it's a bit of a bullet bite) saying 'all sentences are either true or false' doesn't have a truth value, since to determine one you have to reference the sentence itself and that function doesn't terminate. You can say in English or a Meta-language that all well-formed formulas in some system are either true or false. But you can't say this in the object language.
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.