'this sentance is either true or false'
Which is problematic - and yet it seems that it must have a truth value if the first sentance did.
Why is that a problem? It is a true sentence.
I take it the problem is that it doesn't unpack even though it does have a truth value. Or at least it isn't obvious how to unpack it. It's a false negative candidate.
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.