Re:What Gödel Discovered (2020)
by qnleigh on Thursday April 02, 2026 @10:48AM
(#47615251)
> We can't prove that the axioms of arithmetic are consistent
using the axioms themselves. We can prove consistency using a stronger set of axioms, but those axioms have their own liar sentence, and so they can't prove their own consistency. And without knowing if the stronger set of axioms is consistent, we can't be sure that we have really proved the consistency of arithmetic.
using the axioms themselves. We can prove consistency using a stronger set of axioms, but those axioms have their own liar sentence, and so they can't prove their own consistency. And without knowing if the stronger set of axioms is consistent, we can't be sure that we have really proved the consistency of arithmetic.