The Question of the Non-validity of the Law of Excluded Middle in the Intuitionistic Prepositional Calculus

Abstract

The paper discusses the problem of whether the law of excluded middle is valid or not, a question that has been posed in the intuitionistic propositional calculus. Accordingly, the author investigates how the intuitionists understood the law of excluded middle and the reasons for its refutation. The relationship between the intuitionistic law of excluded middle and its classical equivalent has been established. Moreover, the author sought to answer the main questions which the representatives of intuitionistic logic pose (and answer). The final part of the paper addresses the issue of constructivism as the key element of intuitionistic philosophy.