ABSTRACT Logical pluralism is the view according to which there is more than one relation of logical consequence, even within a given language. A recent articulation of this view has been developed in terms of quantification over different cases: classical logic emerges from consistent and complete cases; constructive logic from consistent and incomplete cases, and paraconsistent logic from inconsistent and complete cases. We argue that this formulation causes pluralism to collapse into either logical nihilism or logical universalism. In its place, we propose a modalist account of logical pluralism that is independently well motivated and that avoids these collapses. (..) Beall and Restall (2006) argue that by considering different types of cases the logical pluralist obtains different logics. For example, if the cases are consistent and complete (say, Tarskian models), the logics are classical. If the cases are consistent and incomplete (say, certain mathematical constructions), constructive logics emerge. If the cases are inconsistent and complete (say, certain databases), the logics are paraconsistent. In order to have a logic, however, Beall and Restall insist that the notion of logical consequence meet three familiar constraints: necessity, formality, and normativity. In this paper, we argue that, despite its intuitive appeal, the formulation of logical pluralism in terms of cases is ultimately inadequate. (..) we offer an alternative understanding of logical pluralism that couples modalism (the view that some modality is treated as primitive) and attention to the demands of different domains. We argue that this understanding of pluralism avoids the difficulties raised for pluralism via cases. An independently well-motivated form of logical pluralism emerges. (..) Their account of the necessity constraint on logics ends not in logical pluralism, but in logical nihilism. The source of the problem is the combination of (1) extending what counts as a case for evaluating the validity of an argument form so as to accommodate the background semantics for both classical and nonclassical logics, (2) keeping the standard semantics in the metatheory for the quantifier in the necessity constraint, (3) and keeping the metatheory’s domain of quantification fixed. (..) 3. From models to modality: modalist logical pluralism (..) To meet the necessity requirement, it is not good enough for ‘all cases’ to be simply all cases; ‘all cases’ need to be all possible cases. (..) To articulate what it is to satisfy the necessity requirement we need some background modal notion. (..) The modal notion is taken as primitive (..) An argument is valid if, and only if, the conjunction of its premisses with the negation of its conclusion is impossible. (..) When we cease to focus exclusively on what the world makes true, though, it is perfectly obvious that contradictions are possible. Note: possible, not possibly true. In fact, we are all quite familiar with the fact that contradictions abound. (..) The main point of inference is that it permits us to extend our knowledge, in the sense that it helps us realize some of the consequences of things we already know. (..) The paraconsistent logician effectively expands the domain of the possible. By allowing that certain inconsistencies might lurk among claims, the paraconsistent logician is in a position to reason about an inconsistent domain without the triviality that classical logic would impose. (..) Expanding the way we think about the domain of the possible is what the non-classical logician typically does and this is perfectly in line with modalism. (..) modalism and logical pluralism go hand in hand. (..) Having distinguished complete and consistent worlds from incomplete but consistent situations from potentially incomplete and inconsistent databases, focus not on the background semantic structures for the various logics under consideration (..) Different domains are just different subject matters along with various ways of conceptualizing those subject matters. Different domains or subject matters typically concern different objects. (..) Well-managed inference permits us to deduce what follows from some assumptions and, implicitly, rule out things that are not the case, if the assumptions hold. (..) classical inference is not suitable for thinking about intensional contexts, including degrees of doxastic certainty or epistemic warrant. (..) Focusing on domains rather than on cases puts the inferential horse before the modelling cart, just where it should be. Focusing on domains also has the advantage of yielding neither logical nihilism nor universalism. (..) We argued that if the quantification over cases is left unrestricted, we obtain logical nihilism and if it is restricted, the result is logical universalism - almost everything would count as an admissible consequence relation. (..) The fundamental work of warranting pluralism, for a modalist, are judgements about possibility, and these judgements are the basis for determining which arguments are valid or invalid. Those very judgements involve discriminating in familiar ways. Some inferences are judged valid; others are not. Both extremes of logical nihilism and universalism are avoided in a straightforward manner. Logical universalism is avoided precisely because some systems of inference fail straightforwardly to satisfy the necessity constraint, even if they preserve truth as things are, as in the inference that grass is green from the premisse that snow is white. As a result, not every system of inference counts as a logic. Logical nihilism is avoided because there are domains about which we reason for which several logics are ideally suited (for instance, different paraconsistent logics are adequate for the same inconsistent domain), and for different domains, distinct logics are adequate (e.g. classical logic for consistent and complete domains, and constructive logics for consistent and incomplete domains). (..) The preceding discussion makes it clear that we have four main alternatives in the debate about the range of logic: logical nihilism, monism, pluralism, and universalism. Just as Beall and Restall, we favour the logical pluralist option. As opposed to them, however, we favour a modalist conception of logical pluralism that, by emphasizing domains and a primitive modality, is able to avoid collapsing into the extremes of nihilism and universalism. With modalism in place, a genuine logical pluralism is possible. |