In this paper I argue that Beall and Restall's claim that there is one true logic of metaphysical modality is incompatible with the formulation of logical pluralism that they give. I investigate various ways of reconciling their pluralism with this claim, but conclude that none of the options can be made to work.

I was quite excited when I first read Restall and Russell’s (2010) paper. For two reasons. First, because the paper provides rigorous formulations and formal proofs of implication barrier the- ses, namely “theses [which] deny that one can derive sentences of one type from sentences of another”. Second (and primarily), because the paper proves a general theorem, the Barrier Con- struction Theorem, which unifies implication barrier theses concerning four topics: generality, necessity, time, and normativity. After thinking about the paper, (...) I am satisfied with its treatment of the first three topics, namely generality, necessity, and time. But I am not satisfied with its treatment of normativity, so my comments are exclusively on that topic. (shrink)

Some think that logic concerns the “laws of truth”; others that logic concerns the “laws of thought.” This paper presents a way to reconcile both views by building a bridge between truth-maker theory, à la Fine, and normative bilateralism, à la Restall and Ripley. The paper suggests a novel way of understanding consequence in truth-maker theory and shows that this allows us to identify a common structure shared by truth-maker theory and normative bilateralism. We can thus transfer ideas from (...) normative bilateralism to truth-maker theory, such as non-transitive solutions to paradox, and vice versa, such as notions of factual equivalence and containment. (shrink)

Logical pluralism is the view that there is more than one logic. Logical normativism is the view that logic is normative. These positions have often been assumed to go hand-in-hand, but we show that one can be a logical pluralist without being a logical normativist. We begin by arguing directly against logical normativism. Then we reformulate one popular version of pluralism—due to Beall and Restall—to avoid a normativist commitment. We give three non-normativist pluralist views, the most promising of which (...) depends not on logic’s normativity but on epistemic goals. (shrink)

In this paper I investigate how differences in approach to truth and logic (in particular, a deflationist vs. a substantivist approach to these fields) affect philosophers’ views concerning pluralism and normativity in these fields. My perspective on truth and logic is largely epistemic, focusing on the role of truth in knowledge (rather than on the use of the words “true” and “truth” in natural language), and my reference group includes Carnap (1934), Harman (1986), Horwich (1990), Wright (1992), Beall and (...) class='Hi'>Restall (2006), Field (2009), Lynch (2009), and Sher (2016a).1 Whenever possible, I focus on positive rather than negative views on the issues involved, although in some cases this is not possible. (shrink)

Logical pluralism is the view that there is more than one correct logic. This very general characterization gives rise to a whole family of positions. I argue that not all of them are stable. The main argument in the paper is inspired by considerations known as the “collapse problem”, and it aims at the most popular form of logical pluralism advocated by JC Beall and Greg Restall. I argue that there is a more general argument available that challenges all (...) variants of logical pluralism that meet the following three conditions: that there are at least two correct logical systems characterized in terms of different consequence relations, that there is some sort of rivalry among the correct logics, and that logical consequence is normative. The hypothesis I argue for amounts to conditional claim: If a position satisfies all these conditions, then that position is unstable in the sense that it collapses into competing positions. (shrink)

Beall and Restall 2000; 2001; 2006 advocate a comprehensive pluralist approach to logic, which they call Logical Pluralism, according to which there is not one true logic but many equally acceptable logical systems. They maintain that Logical Pluralism is compatible with monism about metaphysical modality, according to which there is just one correct logic of metaphysical modality. Wyatt 2004 contends that Logical Pluralism is incompatible with monism about metaphysical modality. We first suggest that if Wyatt were right, Logical Pluralism (...) would be strongly implausible because it would get upside down a dependence relation that holds between metaphysics and logic of modality. We then argue that Logical Pluralism is prima facie compatible with monism about metaphysical modality. (shrink)

It is regrettably common for theorists to attempt to characterize the Humean dictum that one can’t get an ‘ought’ from an ‘is’ just in broadly logical terms. We here address an important new class of such approaches which appeal to model-theoretic machinery. Our complaint about these recent attempts is that they interfere with substantive debates about the nature of the ethical. This problem, developed in detail for Daniel Singer’s and Gillian Russell and Greg Restall’s accounts of Hume’s dictum, is (...) of a general type arising for the use of model-theoretic structures in cashing out substantive philosophical claims: the question of whether an abstract model-theoretic structure successfully interprets something often involves taking a stand on non-trivial issues surrounding the thing. In the particular case of Hume’s dictum, given reasonable conceptual or metaphysical claims about the ethical, Singer’s and Russell and Restall’s accounts treat obviously ethical claims as descriptive and vice versa. Consequently, their model-theoretic characterizations of Hume’s dictum are not metaethically neutral. This encourages skepticism about whether model-theoretic machinery suffices to provide an illuminating distinction between the ethical and the descriptive. (shrink)

Inferentialism is a theory in the philosophy of language which claims that the meanings of expressions are constituted by inferential roles or relations. Instead of a traditional model-theoretic semantics, it naturally lends itself to a proof-theoretic semantics, where meaning is understood in terms of inference rules with a proof system. Most work in proof-theoretic semantics has focused on logical constants, with comparatively little work on the semantics of non-logical vocabulary. Drawing on Robert Brandom’s notion of material inference and Greg (...) class='Hi'>Restall’s bilateralist interpretation of the multiple conclusion sequent calculus, I present a proof-theoretic semantics for atomic sentences and their constituent names and predicates. The resulting system has several interesting features: (1) the rules are harmonious and stable; (2) the rules create a structure analogous to familiar model-theoretic semantics; and (3) the semantics is compositional, in that the rules for atomic sentences are determined by those for their constituent names and predicates. (shrink)

Recent years have seen a surge of attention to the problem of logical pluralism; most of which has been a reaction to Beall and Restall’s account of logical pluralism as the existence of more than one equally correct semantic relation of logical consequence. The underlying thesis is that the indeterminacy of the notion of validity goes beyond what the inductive-deductive distinction can precisify. The notion of deductive validity itself is indeterminate as well and this indeterminacy has its roots in (...) the indeterminacy of the more fundamental notion of case. Cases are what make the premisses and the conclusion of an argument true; the most notable example being Tarskian models for classical logic. Deductive validity is the preservation of truth across all cases. This paper argues that unless this account of logical pluralism is supplemented with an argument in favor of the equal legitimacy of the purported cases it becomes merely a semi-controversial exposition of how different logics can be generated. (shrink)

This paper provides a proof-theoretic account of imperative logical consequence by generalising Greg Restall’s multiple conclusion bilateralism for declarative logic. According to imperative bilateralism, a sequent Γ ⊢ Δ is valid iff jointly commanding all the imperatives Φ ∈ Γ and prohibiting all the imperatives Ψ ∈ Δ clashes. This account has three main virtues: (1) it provides a proof-theoretic account of imperatives; (2) it does not rely on the controversial notion of imperative inference; and (3) it is neutral (...) regarding cognitivism about imperatives. (shrink)

I was quite excited when I first read Restall and Russell’s (2010) paper. For two reasons. First, because the paper provides rigorous formulations and formal proofs of implication barrier theses, namely “theses [which] deny that one can derive sentences of one type from sentences of another”. Second (and primarily), because the paper proves a general theorem, the Barrier Construction Theorem, which unifies implication barrier theses concerning four topics: generality, necessity, time, and normativity. After thinking about the paper, I am (...) satisfied with its treatment of the first three topics, namely generality, necessity, and time. But I am not satisfied with its treatment of normativity, so my comments are exclusively on that topic. (shrink)

Logical monism is the view that there is ‘One True Logic’. This is the default position, against which pluralists react. If there were not ‘One True Logic’, it is hard to see how there could be one true theory of anything. A theory is closed under a logic! But what is logical monism? In this article, I consider semantic, logical, modal, scientific, and metaphysical proposals. I argue that, on no ‘factualist’ analysis (according to which ‘there is One True Logic’ expresses (...) a factual claim, rather than an attitude like approval), does the doctrine have both metaphysical and methodological import. Metaphysically, logics abound. Methodologically, what to infer from what is not settled by the facts, even the normative ones. I conclude that the only interesting sense in which there could be One True Logic is noncognitive. The same may be true of monism about normative areas, like moral, epistemic, and prudential ones, generally. (shrink)