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orthonormal comments on An Introduction to Löb's Theorem in MIRI Research - Less Wrong
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I am stuck at part 2.2: "So in particular, if we could prove that mathematics would never prove a contradiction, then in fact mathematics would prove that contradiction"
I've spend 15 minutes on this, but still cannot see relation to löb's theorem. Even though it seems like it should be obvious to attentive reader.
Could anyone please explain or link me to an explanation?
Thanks for asking! I should add another sentence in that paragraph; the key step, as Kutta and Quill noted, is that "not A" is logically equivalent to "if A, then False", and in particular the statement "2+2=5 is not provable" is logically equivalent to "if 2+2=5 were provable, then 2+2=5", and then we can then run Löb's Theorem.