On 9/13/23, mailbombbin <[email protected]> wrote: > On 9/13/23, mailbombbin <[email protected]> wrote: >> Godel’s first theorem claims there are statements in every formal >> system that are neither provable nor unprovable. >> >> Boolos made a short proof, but it hinges in agreeing on a different >> expression of the theorem: “There is no algorithm whose output contains >> all >> true sentences of arithmetic and no false ones." >> >> I think I’d be willing to accept that those two expressions are >> sufficiently comparable challenges for now. > > demonstration of equivalence: if every statement can be proven or > disproven, we can enumerate every possible proof to enumerate every > true sentence
[bug in math? this is a fractal tree with infinitely many branches each infinitely deep so an iterative algorithm would never exhaust it since no branch of the tree can ever be complete —
