>if we ever found a contradiction in the ZFC axioms, we wouldn't throw out math, we'd just throw out ZFC. It's like saying: if we ever found a contradiction in

>if we ever found a contradiction in the ZFC axioms, we wouldn't throw out math, we'd just throw out ZFC. It's like saying: if we ever found a contradiction in the base case of a mathematical induction, we wouldn't throw out mathematical induction, we'd just throw out the base case. The indudction step remains sound. https://en.wikipedia.org/wiki/Mathematical_induction https://en.wikipedia.org/wiki/Mathematical_induction