I 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.
The result is insane in my opinion, it means any sensible math system with basic arithmetic has a proposition that you cannot prove.
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.
I 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.
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.