More powerful formal systems are not more powerful because they know more stuff. They’re more powerful because they have more confidence.
That’s an awesome way of putting it, thanks!
PA proves that PA+Con(PA) proves Con(PA)
Duh, PA proves that PA+X proves X for any X, because X is one of the axioms of PA+X. Did you mean some less trivial example?
No. I meant to include a trivial example. I believed that it would help clarify the point.
That’s an awesome way of putting it, thanks!
Duh, PA proves that PA+X proves X for any X, because X is one of the axioms of PA+X. Did you mean some less trivial example?
No. I meant to include a trivial example. I believed that it would help clarify the point.