Well, not "the way humans do," specifically - the fact that humans do it is just a way to motivate making logical systems that can do it too. Hopefully we can find how to do it better than humans do it by standards like consistency.
In other words, 0 and 1 are not probabilities.
Well, the problem with probabilities of 0 and 1 is more complicated than "they're not probabilities." But I see your point.
the thing to do is move away from representing categorical propositions at all.
That seems tricky. All the input into our brains seems to be translatable into categorical propositions with one extra parameter of probability. But we want to make our logical system deterministic, so that probability is just an ordinary extra parameter, which we've already seen doesn't help resolve the liar's paradox in simple applications. So are you just proposing making a system that's like the human brain in that we can't pick out the influence of individual parts? I think this would be a bad approach, even ignoring the appeal of simplicity, since it likely wouldn't solve the problem, it would just prevent us from knowing what the problems with the system were.
Well, not "the way humans do," specifically - the fact that humans do it is just a way to motivate making logical systems that can do it too. Hopefully we can find how to do it better than humans do it by standards like consistency.
Fair enough.
If you're not actually trying to build a system that interprets the Liar's Paradox the way humans do, but rather a system that (for example) interprets the Liar's Paradox as a categorical probabilistic proposition without immediately believing everything (perhaps using human cognition as an inspiration,...
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.