> And yet.. quantum mechanics managed to break the most certain of all principles.
Though natural language logic remains the same.
> Or actually.. the man who says "I always lie", does he belong to the group of people who always lie, or does he not belong to it?
The Russell-type paradox is more interesting than the liar-type paradoxes since it is not susceptible to the same resolutions (though can be avoided with a theory of types).
Similar to liar's paradox, may be "this page was intentionally left blank" paradox. Since the page contains this writing, it is not blank. So whoever wrote on that page "this page was intentionally left blank" was lying.
So, Aristotle holds, because the page is not "blank" and "not blank" at the same time.
That is an interesting parallel I hadn't thought about in that context. (It's better if we change the tense so that it's "this page is intentionally left blank", otherwise it could be trivially resolvable.) The "this sentence is false" type can be explained away, to an extent, but appealling to the fact that 'this sentence' mixes 'object language' and 'meta language' and we could say the paradox arises from self-reference (in a somewhat problematic recursion fashion). For "this page is intentionally left blank", 'this page' doesn't refer to itself, but indeed to the page, so it's doesn't seem susceptible to quite the same approach. (Though I suppose we could take 'this page' as elliptical for 'this page with this writing on it'.)
Though natural language logic remains the same.
> Or actually.. the man who says "I always lie", does he belong to the group of people who always lie, or does he not belong to it?
The Russell-type paradox is more interesting than the liar-type paradoxes since it is not susceptible to the same resolutions (though can be avoided with a theory of types).