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Jack comments on The Last Number - Less Wrong
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I'm familiar with "anything statement can be derived from an inconsistent theory" but I really am confused by how any such derivation could be a proof of consistency. If proofs of consistency are possible for inconsistent theories then how exactly are they proofs of consistency?
It's a "proof" in that it follows the formal rules of the proof system. You can "prove" anything if your rules are sufficiently ridiculous, but that doesn't mean the proof actually means anything.
Thanks.
If I tell the truth, I cannot say: "I lie".
But if I lie, I can say: "I tell the truth".