Doubt Accumulation and the Epistemic Validity of Logic

Amir Horowitz

Summary: 1. Multi premise closure. 2. Single premise closure. 3. Multi premise closure again.

Abstract: It seems natural to assume that deductive rules of inference preserve epistemic merits such as the justifiability or rationality of beliefs. This is the notion of the (logical or deductive) closure of justification. While this notion seems obvious to many philosophers, various arguments against it have been suggested. Some of them aim at undermining the closure of justification under specific inference rules (notably Modus Ponens and Conjunction Introduction), and some of them aim at undermining it under any inference rule, or under any multi premise inference rule. In part I of this paper I attempt to provide a precise presentation of an argument against the closure of justification under any multi premise inference rule. This argument is based on the idea of doubt accumulation. In part II I argue that, pace some philosophers, single premise closure can be said to founder on the rocks of doubt accumulation only under such an understanding of the closure that no one has ever wanted to endorse it. In part III I further pursue the significance of the failure of multi premise closure.

Keywords: Argumentation theory, Doubt Accumulation, Logic, Epistemic Validity.