— so one idea is maybe to have two different kinds of disproofs. one where it is shown the axioms of the statements are not together true, and another where it is shown the axioms of the statements and those of the logic system are not together true
the difference is that in the first, stating the inverse of the statements together is true whereas in the second, different logical conclusions are implied so if you say “this statement is not provable” and you also say “all true statements are provable” then you can derive “this statement is false” from “this statement is not provable”, this makes a contradiction and disproves it in the second manner, not the first it’s not mathematically rigorous, needs changes to be so.
