Logical pluralism, indeterminacy and the normativity of logic

Abstract

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 Restall'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 Restall's logical pluralism as a thesis of semantic indeterminacy of our concept of logical consequence -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 Restall's indeterminacy logical pluralism. Third, in Section 6, following Beall and Restall'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 Restall'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.

Proof-theoretic pluralism

“…However, before concluding, we would like to mention an advantage that the version of proof-theoretic pluralism sketched in this paper has over the model-theoretic pluralism defended in [1]. As argued in [13], model-theoretic pluralism suffers from a variety of challenges concerning the normative role that the notion of 'follows from' plays in connection with (deductive) reasoning. The source of these challenges resides in the fact that they take the English expression 'follows from' to be semantically indeterminate -they explicitly draw a parallel with the vagueness debate [1, p. 27].…”

“…By doing so, we replace the model-theoretic notions of truth and evaluation with the proof-theoretic notion of following from. 13 12 The notion of 'cases' employed in the proof-theoretic reading of sequents is the intuitive, pre-theoretic, notion which is standard in mathematical reasoning -see, for instance, [24] -and as such should not be conflated with the model-theoretic notion of cases often used to refer to possible worlds, situations, or entities of the like rather than formulas (or propositions). In particular, it should not be conflated with the notion of casex employed in [1].…”

“…In particular, it should not be conflated with the notion of casex employed in [1]. 13 Another possibility would be to adopt a form of bilateralism [29] and read Γ ∆ as 'the non-co-deniability of the members of ∆ follows from the acceptance of the members of Γ '. We prefer the reading given in ( ) -which is based on Gentzen's [14] denotational interpretation of sequents, cf.…”

Inductive Metaphysics

“…So, for example, new work on anti-exceptionalism in the philosophy of logic suggests that an abductive methodology is also fruitfully applied there (cf. Ferrari & Moruzzi 2017). By this and many other investigations we hope that the programme of inductive metaphysics can be established as a fruitful and progressive research programme.…”

Normative Alethic Pluralism

“…This ultimately depends on whether we can have a normatively inert truth property operating locally, in some areas of discourse. 42 XI. Conclusions I have outlined a pluralist framework for understanding the normativity of truthnormative alethic pluralism-that promises to score better than normative alethic monism in addressing the variability in the normative significance of disagreement discussed above.…”