The Cardinality of Logical Consequence

Abstract

In previous chapters, I construed logical pluralism as the view that there are multiple correct theories of extra-systematic logical consequence. Against this background, it may be tempting to think that logical pluralists are committed to the postulation of a plurality of extra-systematic logical consequence relations. In this chapter I argue that further options are available. I first show that, depending on the underlying notion of correctness, logical pluralism is compatible with any account of the cardinality of extra-systematic logical consequence. I then identify readings of the plurality thesis that give rise to the revisionist reading of logical pluralism that is the target of this book. The most obvious one is genuine plurality—the view that there is more than one extra-systematic consequence relation. A less obvious one acknowledges monism about extra-systematic consequence but argues that there cannot be a single precise theory that captures this relation. I propose a monist approach to logic in both the theory sense and the subject of investigation sense that rejects revisionist logical pluralism.