Logic and Set Theory

Abstract

In mathematics, our formation of sets is quite often of the form ‘the set of all satisfying x certain property’. Since logic is the calculus about the property, the nature of logic plays an intrinsic role in set theory. Here we take the classical logic, the intuitionistic logic, and the quantum logic and discuss the relation between each of them and set theory. Let us say a few words on these logic. The classical logic is the logic of the absolute. The intuitionistic logic is the logic of the mind. The quantum logic is the logic of the particles. The precise definition of the quantum logic is the logic of the closed linear subspaces of a Hilbert space.