Soundness arguments for consistency and their epistemic value: A critical note

Abstract

Abstract Soundness Arguments for the consistency of a (mathematical) theory S aim to show that S is consistent by first showing or employing the fact that S is sound, i.e., that all theorems of S are true. Although soundness arguments are virtually unanimously accepted as valid and sound for most of our accepted theories, philosophers disagree about their epistemic value, i.e., about whether such arguments can be employed to improve our epistemic situation concerning questions of consistency. This article provides a (partial) negative answer to this question and argues that soundness arguments cannot be employed to justify their conclusion. Additionally, soundness arguments are unconvincing; they cannot be employed to overcome reasonable open-mindedness about their conclusion.