That's like saying 2 + 2 is not limited by being 4. You can "know" that 2 + 2 is 5. You're just wrong.
The human mind could be meta-rational so it can generate new consistent axioms that cannot be derived from the existing known axioms. The history of mathematical progress seems to be pretty good evidence our minds can do this.
The human mind could be meta-rational so it can generate new consistent axioms that cannot be derived from the existing known axioms. The history of mathematical progress seems to be pretty good evidence our minds can do this.