When I studied math, I learned that not all math truths were provable which was disappointing. When I studied computer science, I learned that not everything was computable which was even worse. Basically, I no longer believe that all truths are discoverable using science alone.
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But, unlike the Epimenides paradox ("This sentence is false"), it seems intuitively true that the Godel sentence IS TRUE -- "This sentence cannot be proven true" IS TRUE, you just can't prove it Godel used this intuition to justify his own Platonism
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Extremely counterintuitively, assuming the opposite is actually consistent and AIUI you get a system that "thinks," "incorrectly," that it proves a contradiction
End of conversation
New conversation -
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*any sufficiently powerful logical system, ie any system that can express the notion of true-in-that-system, which surprisingly turns out to be any logical system that includes arithmetic
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