Yes, truth values of paradoxes cannot be determined, but it's you who called it a paradox. On its face, it isn't a paradox.
If we're being pedantic, which your initial response struck me as, there are again true statements with no proof, and this isn't a paradox, it's Gödel's first incompleteness theorem (which is specifically different from the liar's paradox you mentioned, precisely in the difference between what is true and what is provable).
