Logical pluralism, indeterminacy and the normativity of logic

According to the form of logical pluralism elaborated by Beall and Restall there is more than one relation of logical consequence. Since they take the relation of logical consequence to reside at the very heart of a logical system, different relations of logical consequence yield different logics. In this paper, we are especially interested in understanding what are the consequences of endorsing Beall and Restallâ s version of logical pluralism vis-à-vis the normative guidance that logic is taken to provide to reasoners. In particular, the aim of this paper is threefold. First, in Sections 2 and 3, we offer an exegesis of Beall and Restallâ s logical pluralism as a thesis of semantic indeterminacy of our concept of logical consequence â i.e. understood as indeterminacy logical pluralism. Second, in Sections 4 and 5, we elaborate and critically scrutinize three models of semantic indeterminacy that we think are fit to capture Beall and Restallâ s indeterminacy logical pluralism. Third, in Section 6, following Beall and Restallâ s assumption that the notion of logical consequence has normative significance for deductive reasoning, we raise a series of normative problems for indeterminacy logical pluralism. The overall conclusion that we aim to establish is that Beall and Restallâ s indeterminate logical pluralism cannot offer an adequate account of the normative guidance that logic is taken to provide us with in ordinary contexts of reasoning.