Well, sort of. You might say I'm advocating acknowledging that it's a paradox and considering that the end of it. Remember, I'm using the term meaningless (perhaps I should have said "useless") to mean that it tells us nothing. Not in the sense that it makes no claims, but in the sense that it contains no information. It's not clear to me that this kick starts the paradoxical loop like you're implying.
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.