On 9/13/23, mailbombbin <[email protected]> wrote: > 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 —
[to help think of this we could say we explore the tree breadth-first to linearize it “fairly” but of course infinite things never complete anyway and the breadth brows exponentially
