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I think it is important to distinguish between the number of counterexamples that are easily proven to be counterexamples versus the number of counterexamples that exist. There are ##\aleph_1## transcendental numbers, but far fewer proven ones.Feynstein100 said:I've been meaning to ask about that. It seems to me that what Gödel actually discovered is that self-reference is different kind of thing that isn't compatible with normal everyday logic i.e. the pattern of true/false doesn't necessarily apply to self-referential statements. I have yet to see an example of it in a non-self-referential context i.e. a statement that isn't self-referential and not true/false. It seems that as long as you stay away from self-reference, you should be fine.
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