"Allah is God"
My knowledge of the Arabic language is only good enough to recognize that this is a tautology.
...and now that I think about it, it doesn't appear that the first part of
There is no god but God, and Mohammed is His prophet
is actually an existence claim!
~exist(God)
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.