It would not. If a system can prove (I know sufficiently rich systems can’t do this but suppose it could) its own consistency you still can't conclude it is consistent.
EDIT: I'm working under the hypothetical situation in which PA could prove its consistency. I know it can't but assuming that it could prove it's own consistency you still couldn't conclude that it was consistent since an inconsistent system can prove it's consistency.
GP is (I think correctly) stating that a system that can "prove" its own consistency is definitely inconsistent. Inconsistent systems can "prove" anything; if a system can appear to prove its own consistency, it isn't.
skhunted|1 year ago
EDIT: I'm working under the hypothetical situation in which PA could prove its consistency. I know it can't but assuming that it could prove it's own consistency you still couldn't conclude that it was consistent since an inconsistent system can prove it's consistency.
roywiggins|1 year ago