Is logic normative for belief? A standard approach to answering this question has been to investigate bridge principles relating claims of logical consequence to norms for belief. Although the question is naturally an epistemic one, bridge principles have typically been investigated in isolation from epistemic debates over the correct norms for belief. In this paper we tackle the question of whether logic is normative for belief by proposing a Kripkean model theory accounting for the interaction between logical, doxastic, epistemic and (...) deontic notions and using this model theory to show which bridge principles are implied by epistemic norms that we have independent reason to accept, for example, theknowledge normand thetruth norm. We propose a preliminary theory of the interaction between logical, doxastic, epistemic and deontic notions that has among its commitments bridge principles expressing how logic is normative for belief. We also show how our framework suggests that logic is exceptionally normative. (shrink)

Logical pluralism is a general idea that there is more than one correct logic. Carnielli and Rodrigues [2019a] defend an epistemic interpretation of the paraconsistent logic N4, according to which an argument is valid in this logic just in case it necessarily preserves evidence. The authors appeal to this epistemic interpretation to briefly motivate a kind of logical pluralism: “different accounts of logical consequence may preserve different properties of propositions”. The aim of this paper is to study the prospect of (...) a logical pluralism based on different interpretations of logical systems. First, we give our analysis of what it means to interpret a logic – and make some hopefully useful distinctions along the way. Second, we present what we call an interpretational logical pluralism: there is more than one correct logic and a logic is correct only if it has some adequate interpretation. We consider four variants of this idea, bring up some possible objections, and try to find plausible solutions on behalf of the pluralist. We will argue that interpretations of logical systems provide a promising – albeit not unproblematic – route to logical pluralism. (shrink)

Many philosophers have argued that logical pluralism is not compatible with the normativity of logic. They developed different versions of the collapse argument: if two logics are correct, then the weaker one will be normatively irrelevant. In this paper, I argue that the collapse argument is based on a controversial premise: the assumption that every logic can be characterized by the same bridge principle. I provide a solution to the collapse argument based on the modification of this premise, maintaining both (...) logical pluralism and the normativity of logic. (shrink)

We will present all the mixed and impure disjoint three-valued logics based on the Strong Kleene schema. Some, but not all of them, are (inferentially) empty logics. We will also provide a recipe to build philosophical interpretations for each of these logics, and show why the kind of permeability that characterized them is not such a bad feature.