Derivative normativity and logical pluralism

Abstract

In a much-discussed article, Gillian Russell claimed that “logic isn’t normative”: according to her, the usual bridge principles for logic are just derived from general principles for truth and falsity, such as “believe the truth” or “avoid falsity.” For example, we ought to believe tautologies just because we ought to believe the truth. Russell argues that this rejection of logical normativity can avoid the collapse objection for logical pluralism, which typically presupposes the normativity. In the last part of his new book Logical Pluralism and Logical Consequence, Erik Stei responds that even if logic is normative in this weak derivative sense, the collapse objection re-emerges. His main point is that the collapse argument can still work even if the bridge principles are derivative (they just need to be true). In this paper I will argue against Stei’s point. I will show that there is a possible strategy which maintains the derivative normativity of logic and provides a non-trivial logical pluralism. The key to my approach is the possibility of having different normative sources for different logics. I will argue that the distinction between classical and relevant logic can be understood in this way.