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Stuart_Armstrong comments on Probabilistic Löb theorem - Less Wrong Discussion
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We don't - generally we build systems where we can show "system X is consistent iff Peano Arithmetic is consistent". And we assume that PA is consistent (or we panic).
Sorry my phrasing was bad; I actually do know that much about logic. But how do you know that this system is consistent iff Peano Arithmetic is consistent?
We don't have that system yet! Just that that is what we generally do with the systems we have.