The foundation of mathematics

Good presentation below. Math is internally consistent because it builds on first premises while expanding on them for more complex math. But what underlies its first premises? The answer is logic, a philosophical and not mathematical position. This philosophy is itself based on the first premise that logic is a complete generality of form, not content. I.e., a very Platonic idealism.

One of its axioms is the law of the excluded middle. You're either one thing or the other, either in a set or not. It's based on dualism. Within some contemporary math though this is not an assumed axiom, like via Graham Priest here, which has correlations with the Buddhist system of logic, much different that the Platonist version. They challenged both the axioms of the excluded middle and non-contradiction. Something similar happened in the West via plurivalent logic.