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Chaospet, how about doing some jokes about the ontological argument? Suppose Nester argued that the ontological argument is sound, and the other guy responded with the perfect island objection, then Nester could concede that with an “awesome” remark, and say that he wants to go there, or something. Worth thinking about it, I think.

“I’m not convinced that any paradox cannot be resolved within classical logic. It seems one can just dispose of some set of self-referential propositions and the problem disappears.”

That sounds uncomfortably close to “if we ignore the problem, the problem disappears” to me. How exactly do we “dispose” of the problematic sentences? If they express propositions, as you think, and those propositions aren’t true or false (since either would would generate a contradiction), then we’ve reasoned our way out of the framework of classical logic and into some kind of three-valued framework. (Of course, like Priest with his “accept the contradictions and move on” approach, one could attempt a classical re-capture for reasoning about domains in which no truth-value gaps have been discovered, but that’s not quite the same as staying within the framework of classical logic.) If you’re going to say that they don’t express propositions, or are meaningless or whatever, then you both need to have something to say about revenge paradoxes like, for example….

“This sentence is either false or meaningless.”

….and you face the challenge of explaining *why* they’re meaningless. After all, there are clearly meaningful sentences, like (1) and (2) in the series below….

(1) Sentence (2) is false.
(2) Sentence (3) is true.
(3) Hitler won World War II.

….that aren’t about any subject above and beyond the truth-value of a sentence. There are also self-referential sentences, like (5) and (6)…..

(5) This sentence has seven words in it.
(6) This sentence has twenty words in it.

….that are clearly meaningful, and to which we have no problem assigning one or the other of the classical truth-values. Why, then, should we say that a sentence like the Liar that does both of these things isn’t meaningful? And even if we could come up with so since we have Liar-like paradoxes, like Yablo’s series of sentences that each assert of all the ones starting with the next one that they are false–that don’t even involve self-reference per se.

So….disposing….at least disposing in a remotely principled, persuasive way….is tricky.

That’s what Bertrand Russel thought. He spent years and years working on the Principia Mathematica, attempting to eliminate the paradoxes from math (and to a lesser extent from logic). Then Goedel came along… He proved in precise terms that any logical system strong enough to reason about the natural numbers was also inherently paradoxical.

In short, you can’t devise a formal system that can both express all truth and NOT contain contradictions.

-Wm