Member Rara Avis
LOL @ Grinch. That's exactly why the Liar Paradox has persisted to fascinate for these few thousand years; it calls into question the very existence of Truth or, at least, our ability to perceive it.
Stephen, I think Prior's proposed solution has a few problems, starting with it's initial assertion. "Every statement includes an implicit assertion of its own truth" can be disproved in several ways, though of course only one is necessary to invalidate the assertion. Remember the roomful of monkeys typing away for a thousand years and producing the entire collected work of Shakespeare? Or imagine twirling your spoon in a bowl of alphabet soup, then looking down to discover the letters had spelled out "bad soup." I don't think anyone would argue that such random statements assert their own truth. Don't want random? The common phrase "willing suspension of disbelief," I think, lends lie to Prior's assertion. The artist, and especially the performing artist, tell his audience he is going to lie and then he lies with absolutely no assertion of truth (except perhaps below the surface and rarely in direct relation to the lie being told).
Bertrand Russell formulated the Liar Paradox in terms of set there, correctly recognizing that self-reference lies at the heart of the paradox, and indeed, at the heart of most logical paradoxes. In joining Prior's implied statement with the direct statement, the referents are subtly changed. "This statement is true and this statement is false" are no longer clearly self-referencing. "This statement" can't unambiguously be applied to two statements. The appearance of non-contradiction is directly the result of removing (or at least greatly diluting) the self-referential characteristic of the paradox.
Finally, Prior's solution doesn't apply to versions of the Liar Paradox that are not directly self-referential (it can't since it relies on removing the self-reference), such as multi-sentence versions.
The next sentence is false.
The preceding sentence is true.
Change those sentence per Prior's version ...
This sentence is true and the next sentence is false.
This sentence is true and the preceding sentence is true.
... and you find yourself stuck right back in the paradoxical loop. Indeed, I think one of the characteristics of the Liar Paradox is that any time a solution looks like it might work, a simple rephrasing of the Paradox leads us right back into the same conundrum.