Comment on SUNS OUT GUNS OUT
someacnt@sh.itjust.works 3 days agoI am sure there was a typo, it’s Gödel’s incompleteness theorem which proves that consistent systems are incomplete.
Consistency means likely what you expect: it’s that you cannot reach contradiction from very axioms.
The result is insane in my opinion, it means any sensible math system with basic arithmetic has a proposition that you cannot prove. AND you cannot also prove that the system is contradiction-free.
It is completionist’s worst nightmare.
exasperation@lemm.ee 2 days ago
Stated more precisely, it has true propositions that you cannot prove to be true. Obviously it has false propositions that can’t be proven, too, but that’s not interesting.