What we humans do is store our underlying representations as contingent networks and only "round them off" to categorical propositions when we reason explicitly about them.
That is, "This sentence is in English" is a categorical proposition, but if I trace it down to the cognitive structures that motivated me to generate it, I won't find any categorical representations, just contingent ones: spreading networks of activation. Ditto for "This sentence is true" and "This sentence is false" and everything else I might say.
In other words, 0 and 1 are not probabilities.
If what we want to accomplish is to design a system that can use inconsistent information like we humans do, without suddenly discovering that it believes everything, then the thing to do is move away from representing categorical propositions at all.
Also, it's interesting.
Now that makes perfect sense to me. If it's interesting, by all means continue doing it with my blessing (not that you need it)... but if it has something to do with using inconsistent information the way humans do, then I've completely failed to understand.
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 se...
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.