On 9/13/23, mailbombbin <mailbombbin@gmail.com> wrote:
On 9/13/23, mailbombbin <mailbombbin@gmail.com> 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 —