The Everett Solution to Paradoxes
Good points! I've always been suspicious of claims of so-called quantum weirdness, an interpretation that can trace it roots to the Schrödinger's cat gedankenexperiment. I only surmise this connection as highly probable.
However, as great a mind as Schrödinger's was of the view that the best translation of his equations was, macroscopically rendered, that a cat
is both dead
and alive. In other words, given the stature of the man who made the claim, quantum paradoxes should be taken seriously (as true paradoxes).
Anyway, the MWI seems to, whether deliberately or not is up for debate, rather cleverly resolve the Schrödinger's cat contradiction by proposing that the cat is alive in one universe and dead in the other.
From this it follows that any contradiction (p & ~p) can be compared to an observation in a quantum experiment vis-à-vis MWI - essentially causing the universe to divide into two, one in which p and the other in which ~p. As with Schrödinger's cat, the, any, contradiction melts away as the two incompatible propositions are now in two separate, logically independent universes. Picture two inimical men being housed in different rooms (violence, which, being mutually annihilatory, contradictions are, is averted).
How do I use Everett's technique on an actual paradox like the Liar sentence? Well, assume it is true - this is one universe. Then you reason (this is the counterpart of observation in quantum experiments) and conclude it is false - this is another universe. The same logic applies to all subsequent true and false sequences in the chain of reasoning. Either there are only two universes and you go back and forth between them OR it's a branching tree-like universe with every true and false state birthing daughter universes.