The Law of Excluded Middle and Intuitionistic Logic

Abstract

The paper deals with the question of the validity of the Law of Excluded Middle in intuitionistic logic. Because of a different interpretation of the logical connectives, intuitionists reject the intuitionistic (constructive) counterpart of the Law of Excluded Middle. In the intuitionistic approach the meta-linguistic Law of Excluded Middle is not valid, which results in a replacement of a classical definition of truth with an <> definition, which sees the essence of truth in the relation of a sentence to the result of a certain cognitive efforts. A true sentence is a sentence which satisfies the criterion of truth, i.e. is (constructively) provable. Thus, a dispute between classical logic and intuitionistic logic can be described as a dispute between the <> and the <>.