i'm thinking now that godel is right. [interesting personal similar behavior here, serial consideration of alternatives, started doing heavily when lost mind] On 9/13/23, mailbombbin <mailbombbin@gmail.com> wrote:
so “this statement is unprovable” becomes a false expanded statement. given in the logic, the expanded statement is false, and provability is equivalent to truth, this statement sounds true. one could even write "the expanded statement of this statement in karl's 9/13/23 system of logic, is false" to make the contradiction more clear [of course you could add an axiom countering that]
expanded: “[axioms of logic] provability is equivalent to truth. [axioms of statements] this statement is true. [statement] this statement is unprovable.”
this expanded statement looks false. additionally, the expanded statement "[axioms] this statement is true. [statement] this statement is false." also looks false (self-contradictory), if the labels are removed. however, it looks correct (to me) to form the second expanded statement from the first.
we can then derive a contradiction from the expanded statement and prove it false.
one of the expressions on the internet around the incompleteness theorem was around the lines of "all logics contain unprovable statements that are true". this isn't exactly countered by what i say here. we'd have to precisely define "statement", "provable", and "truth" to make that not true. given we make the logic ourselves, that's totally doable.