Addo_Of_Nex
Fuck of Death
I'm talking more about the amusing little trick of language.
"This sentence is false."
What do you do with something like that? Is it false? well then it's true, so fuck. Maybe instead you want to say it's true? Well if it's true, then it's false, so also fuck.
I was actually talking to a graduate student a few months ago who was focusing on constructing a formal system of truth that tackled things like the liar/barber paradox and pretty much anything bearing resemblance to the infinite regress you find with the true-but-unprovable statements of the form "P is true, but the incompleteness of the system (read: necessity of introducing a new axiom into the system) renders it unprovable" that Godel's theorems tackle. He described a syntax that treats these as a special class of statements that are assigned some particular truth value in a different way than "standard" propositions. I have no idea of knowing how much he actually achieved, as it was the only time I've ever seen him and it was a conversation that took place after my beer count had reached double digits.
Come to think of it, this method sort of resembles Cesaro summation and other non-conventional methods of attacking infinite series in mathematics. For instance, Grandi's series diverges with respect to the typical definition of convergence found in real analysis, but the Cesaro sum is 1/2, as it is the "average" of the constituent terms, in some sense. Basically, it states that such a series doesn't actually converge, but that if it did, it should converge to this particular limit. Granted, the comparison is simply a non-rigorous analogous case that's probably only interesting on an armchair level. I'm out of my league with the metamathematical details of Godel's work, let alone its rigorous connection with non-standard methods of analysis.