Depends on what sort of metaphysics of propositions you accept, whether you want to deal with an extensional or an intensional language, and a whole bunch of other stuff that generally only philosophers and some mathematicians have cared about.

If you're interested, though, let me know and I'll see what I can dig up for you from back when I was studying this stuff.

Either, and occasionally both, my favorite example being 'this sentence no verb'. There's a big difference between being able to find a way out of a given paradox and in being able to generalize that insight to makes statements about computability (or proofs, in the context of mathematics).