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Jack comments on Unsolved Problems in Philosophy Part 1: The Liar's Paradox - Less Wrong
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What about
'all sentances are either true or false'.
This sounds like the sort of sentance we'd want to assign a truth value to. Yet we can instanciate it into
'this sentance is either true or false'
Which is problematic - and yet it seems that it must have a truth value if the first sentance did.
I'm comfortable (mostly, it's a bit of a bullet bite) saying 'all sentences are either true or false' doesn't have a truth value, since to determine one you have to reference the sentence itself and that function doesn't terminate. You can say in English or a Meta-language that all well-formed formulas in some system are either true or false. But you can't say this in the object language.