Well, “classical logic is based on set theory” seems off too… In fact, a theory can always be formulated using a minimum number of axioms, so none requires som

Well, “classical logic is based on set theory” seems off too… In fact, a theory can always be formulated using a minimum number of axioms, so none requires some other theory as its base. For example, the system of real numbers can be built starting from the natural numbers, but what this achieves is, this just gives a “proof of existence” of the reals, i.e of consistency of the definition of the reals as a complete ordered field.