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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Gödel sentences don’t have to be truths, they can be false on some interpretations too. But if you fix an interpretation then they’re definitely knowable
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Yeah, Gödel doesn't justify the op's "alone". ;)
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Exactly! It's like saying "physics says we can't travel faster than light, therefore I learned to not rely on physics for understanding the world".
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It’s not provable by any mathematical system; metamathematics is necessary to reach this conclusion.
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naah lmao you can actually prove both of Gödel's Incompleteness Theorems within Peano Arithmetic.
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