You won't create anything worthwhile in math if you don't study it. To break your current system, consider the proposition "This proposition is either false, contradictory, or ambiguous".
You are absolutely correct. I haven't thought this through. Thank you for the lesson.
Edit: I did take the lesson that I should think more before making such a claim, however, I wanted to point out that your sentence poses no problem and was not the point.
this p. is false is contradictory this p. is condradictory/ambigous is false The conjunction of contradictory and false is contradictory so you have a unique solution. This is also what intuition tells us since the proposition cannot be true and cannot be false and that would be contradictory.
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.