I'm still not convinced that truth is to do with language, though. Consider a squirrel trying to get nuts out of a bird-feeder, say. The squirrel believes that the feeder contains nuts, that there's a small hole in the feeder, and that it can eat the nuts by suspending itself upside down from a branch to access the hole. The squirrel does actually possess those beliefs, in the sense that it has a state of mind which enables it to anticipate the given outcome from the given conditions. The beliefs are true, but I'm certain that the squirrel is not using a language to formulate those beliefs in.
That sounds right. I think if we describe a sentence as being "true" then we're really saying that it induces a possibly-nonverbal mental model of reality that is true (or very accurate), but we can say the same about mental models that were nonverbal to begin with.
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.