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Nick_Tarleton comments on Anime Explains the Epimenides Paradox - Less Wrong
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Video may be a wee bit longer than needed to get the point across. And by wee bit, I mean you could cut 7.5 minutes off of it, and it runs for 7:40.
I've always (after a fun paper on this!) thought of this in modal terms. Self-referential statements are not truths about the world; they're truths about ill-defined universes. "This statement is false" doesn't refer to anything; it's its own little world, and consequently truth has no meaning.
Similarly, "This statement is true" really doesn't provide any information. What if it's a false statement? Is there a difference? How can we tell? It's its own self-referential world, and it's unclear what truth even means in that little world, though it's very clear that it does not make the least bit of difference in any world I care about.
This is also how I've always thought about self-referential statements; is there a name for this position? Is it even a position?
Modal logic, from what I remember of it, deals with "worlds" of sorts, so it might be possible to express it with modal logic; I don't remember well enough, and I certainly don't recall this being a named position. It does seem like a position, though.