Classical reasoning in the justification paradigm

Abstract

Abstract Artemov, building upon a tradition beginning with Kolmogorov and Gödel, developed a paradigm for understanding Constructive Reasoning in terms of classical proofs. Kolmogorov–Gödel–Artemov constructivism flies in the face of the usual understanding of Constructive Reasoning as being distinguished from Classical Reasoning in terms of its theory of truth. Is there something that stands to traditional Classical Reasoning as Kolmogorov–Gödel–Artemov constructivism stands to Constructive Reasoning? In this paper, we develop an affirmative answer to this question by presenting a justification account of Classical Reasoning in terms of explicit justification. The traditional truth paradigm account of Classical Reasoning leads to the well-known paradoxes of material implication. We show that the justification account of Classical Reasoning avoids this problem.1