If it's meaningless, it doesn't assert anything.
A sharper formulation of the paradox just came to my mind. Consider the statements X = "X is not true" and Y = "X isn't true". (The difference in spelling is intentional.) If X is meaningless, then X isn't true, therefore Y is true. But it's a very weird state of affairs if replacing "isn't" by "is not" can make a true sentence meaningless!
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.