Some writers object to logical pluralism on the grounds that logic is normative. The rough idea is that the relation of logical consequence has consequences for what we ought to think and h...

We develop and defend a new approach to counterlogicals. Non-vacuous counterlogicals, we argue, fall within a broader class of counterfactuals known as counterconventionals. Existing semantics for counterconventionals, 459–482 ) and, 1–27 ) allow counterfactuals to shift the interpretation of predicates and relations. We extend these theories to counterlogicals by allowing counterfactuals to shift the interpretation of logical vocabulary. This yields an elegant semantics for counterlogicals that avoids problems with the usual impossible worlds semantics. We conclude by showing how this approach (...) can be extended to counterpossibles more generally. (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)

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)

According to the logical pluralism of Beall and Restall, there are several distinct relations of logical consequence. Some critics argue that logical pluralism suffers from what I call the collapse problem: that despite its intention to articulate a radically pluralistic doctrine about logic, the view unintentionally collapses into logical monism. In this paper, I propose a contextualist resolution of the collapse problem. This clarifies the mechanism responsible for a plurality of logics and handles the motivating data better than the original (...) view. It is a major improvement that should be embraced by all logical pluralists. (shrink)

In this paper we discuss the extent to which the very existence of substructural logics puts the Tarskian conception of logical systems in jeopardy. In order to do this, we highlight the importance of the presence of different levels of entailment in a given logic, looking not only at inferences between collections of formulae but also at inferences between collections of inferences—and more. We discuss appropriate refinements or modifications of the usual Tarskian identity criterion for logical systems, and propose an (...) alternative of our own. After that, we consider a number of objections to our account and evaluate a substantially different approach to the same problem. (shrink)

Logical pluralism is the view that there is more than one correct logic. Most logical pluralists think that logic is normative in the sense that you make a mistake if you accept the premisses of a valid argument but reject its conclusion. Some authors have argued that this combination is self-undermining: Suppose that L1 and L2 are correct logics that coincide except for the argument from Γ to φ, which is valid in L1 but invalid in L2. If you accept (...) all sentences in Γ, then, by normativity, you make a mistake if you reject φ. In order to avoid mistakes, you should accept φ or suspend judgment about φ. Both options are problematic for pluralism. Can pluralists avoid this worry by rejecting the normativity of logic? I argue that they cannot. All else being equal, the argument goes through even if logic is not normative. (shrink)

When discussing Logical Pluralism several critics argue that such an open-minded position is untenable. The key to this conclusion is that, given a number of widely accepted assumptions, the pluralist view collapses into Logical Monism. In this paper we show that the arguments usually employed to arrive at this conclusion do not work. The main reason for this is the existence of certain substructural logics which have the same set of valid inferences as Classical Logic—although they are, in a clear (...) sense, non-identical to it. We argue that this phenomenon can be generalized, given the existence of logics which coincide with Classical Logic regarding a number of metainferential levels—although they are, again, clearly different systems. We claim this highlights the need to arrive at a more refined version of the Collapse Argument, which we discuss at the end of the paper. (shrink)

Logical pluralism is the view that there is more than one correct logic. A key objection to logical pluralism is that it collapses into monism. The core of the Collapse Objection is that only the pluralist’s strongest logic does any genuine normative work; since a logic must do genuine normative work, this means that the pluralist is really a monist, who is committed to her strongest logic being the one true logic. This paper considers a neglected question in the collapse (...) debate: what is it for a logic to do genuine normative work? As well as having wider upshot for the connection between logic and normativity, grappling with this question provides a new response to the Collapse Objection on behalf of the pluralist. I suggest that we should allow logics to generate pro tanto reasons in a way that bears not just on combinations of attitudes but on how an agent’s attitudes are based on one another. This motivates adopting normative principles that allow the pluralist’s weaker logics to earn their normative keep. Rather than being ad hoc, these principles capture a sense in which good reasoning goes beyond the consistency of an agent’s attitudes. Good reasoning is also concerned with how an agent’s attitudes are based on one another. (shrink)

This paper scrutinizes the debate over logical pluralism. I hope to make this debate more tractable by addressing the question of motivating data: what would count as strong evidence in favor of logical pluralism? Any research program should be able to answer this question, but when faced with this task, many logical pluralists fall back on brute intuitions. This sets logical pluralism on a weak foundation and makes it seem as if nothing pressing is at stake in the debate. The (...) present paper aims to improve this situation by looking at a promising case study and drawing general lessons about the kind of evidence that would support logical pluralism. I argue that the best motivation for logical pluralism will ultimately be rooted in certain kinds of performative data. (shrink)

We are logical pluralists who hold that the right logic is dependent on the domain of investigation; different logics for different mathematical theories. The purpose of this article is to explore the ramifications for our pluralism concerning normativity. Is there any normative role for logic, once we give up its universality? We discuss Florian Steingerger’s “Frege and Carnap on the Normativity of Logic” as a source for possible types of normativity, and then turn to our own proposal, which postulates that (...) various logics are constitutive for thought within particular practices, but none are constitutive for thought as such. (shrink)

Logical pluralism is the view that there is more than one right logic. A particular version of the view, what is sometimes called domain-specific logical pluralism, has it that the right logic and connectives depend somehow on the domain of use, or context of use, or the linguistic framework. This type of view has a problem with cross-framework communication, though: it seems that all such communication turns into merely verbal disputes. If two people approach the same domain with different logics (...) as their guide, then they may be using different connectives, and hence talking past each other. In this situation, if we think we are having a conversation about “¬A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lnot A$$\end{document}”, but are using different “¬\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lnot $$\end{document}”s, then we are not really talking about the same thing. The communication problem prevents legitimate disagreements about logic, which is a bad result. In this paper I articulate a possible solution to this problem, without giving up pluralism, which requires adopting a notion of metalinguistic negotiation, and allows people to communicate and disagree across domains/contexts/frameworks. (shrink)

We are logical pluralists who hold that the right logic is dependent on the domain of investigation; different logics for different mathematical theories. The purpose of this article is to explore the ramifications for our pluralism concerning normativity. Is there any normative role for logic, once we give up its universality? We discuss Florian Steingerger’s “Frege and Carnap on the Normativity of Logic” as a source for possible types of normativity, and then turn to our own proposal, which postulates that (...) various logics are constitutive for thought within particular practices, but none are constitutive for thought as such. (shrink)

The most serious objection to Beall and Restall’s case-based logical pluralism is the so-called collapse argument. According to the collapse argument, logical pluralism is not genuinely pluralistic and collapses into a single privileged relation of logical consequence. In response, Caret offered an account of logical contextualism that supposedly maintains the merits of Beall and Restall’s case-based logical pluralism while circumventing the collapse argument. In this paper, I first point out a gap in the collapse argument in that it does not (...) affect pluralists who assume that there is no uniquely strongest admissible consequence relation. This gap, then, is closed by an improved version of the collapse argument, which makes use of Eklund’s classification of types of pluralism. Finally, I discuss how Caret’s logical contextualism cannot hold up against this new formulation of the collapse argument unless implausible assumptions about the contents of normative operators are made. Moreover, by reformulating the collapse argument, I determine the extent to which logical monism and pluralism oppose each other, paving the way for fruitful future discussion. (shrink)

Logical pluralism is commonly described as the view that there is more than one correct logic. It has been claimed that, in order for that view to be interesting, there has to be at least a potential for rivalry between the correct logics. This paper offers a detailed assessment of this suggestion. I argue that an interesting version of logical pluralism is hard, if not impossible, to achieve. I first outline an intuitive understanding of the notions of rivalry and correctness. (...) I then discuss a natural account of rivalry in terms of disagreement about validity claims and the argument from meaning variance that has been raised against it. I explore a more refined picture of the meaning of validity claims that makes use of the character-content distinction of classical two dimensional semantics. There are three ways in which pluralists can use that framework to argue for the view that different logics may be rivals but could nevertheless be equally correct. I argue that none of them is convincing. (shrink)

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, the knowledge norm and the truth 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 the view that there is more than one correct logic. Stei assumes that the correctness of a logic is a matter of the relation between the formal validity of a logical theory and extra-theoretic validity. I reject the assumption, on the grounds that it’s not clear that extratheoretic validity can be determined independently of formal validity. I formulate instead quietist logical pluralism, which is quietist with respect to the nature of extra-theoretic validity and its relation to formal (...) validity. Because of this, quietist logic pluralism needs a different correctness criterion for logic: correctness is a matter of a logic’s having normative upshot for deductive reasoning. I argue that this approach has the advantage of resisting the collapse of logical pluralism into monism. In particular, I suggest that deductive reasoning has two distinct roles, one with respect to the coherence of our attitudes and another with respect to how our attitudes are based on one another. I give two different normative principles that correspond to these roles; doing so requires abandoning the idea that normative bridge principles are universally quantified over all logics. That idea has been inherited from MacFarlane, but it’s not clear why the pluralist should accept it, as long as she can avoid giving principles that are ad hoc. By tying the principles to crucial roles of deductive reasoning, I aim to avoid both ad hockery and collapse. (shrink)

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. (shrink)

It is commonly thought that logic, whatever it may be, is normative. While accounting for the normativity of logic is a challenge for any view of logic, in this paper I argue that it is particularly problematic for certain types of logical pluralists, due to what I call the normative problem for logical pluralism. I introduce the NPLP, distinguish it from other problems that logical pluralists may face, and show that it is unsolvable for one prominent type of logical pluralism.

In philosophy, as in any other theoretical endeavor, it is not rare to find conflicting but equally well grounded positions. Besides defending one of the positions and criticizing the other, philosophers can opt for pursuing other, more sophisticated, approaches aimed at incorporating the insights, intuitions, and arguments from both sides of the debate into a unified theory: Dialetheism, Analetheism, Gradualism, Pluralism and Relativism. The purpose of this article is to present each strategy's basic argumentative structure, relative strengths, and challenges, trying (...) to determine in which situations one is more appropriate than the others. Despite substantial differences between them, all four options have deep structural similarities; and which option is better for which dilemma or paradox will depend ultimately on a combination of epistemological, linguistic, and metaphysical factors. (shrink)

There was a time when both Rudolf Carnap and Jc Beall were thought to be arch logical pluralists. Beall has since renounced his pluralistic views, but Carnap is still largely regarded as a pluralist. In this paper, I will show that there is good reason to think that Carnap is not a logical pluralist, at least in the way he is presented in the literature. Instead, I argue, he can be seen as a Beall-style logical monist at the meta-level, in (...) line with the views expressed in Beall (APHI 14:1–29, 2017 and NOUS 28:30–54, 2018). (shrink)

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 res...

Logical realism is the metaphysical view asserting that the facts of logic exist and are mind-and-language independent. McSweeney argues that if logical realism is true, we encounter a dilemma. Either we cannot determine which of the two logically equivalent theories holds a fundamental status, or neither theory can be considered fundamental. These two conclusions together constitute what is known as the _Unfamiliarity Dilemma_, which poses significant challenges to our understanding of the epistemological and metaphysical features of logic. In this article, (...) I present two strategies to address McSweeney’s dilemma. If these arguments prove effective, they would demonstrate that our knowledge of logic is not susceptible to the skeptical concerns raised by McSweeney’s hypothesis. (shrink)

How many correct logics are there? Monists endorse that there is one, pluralists argue for many, and nihilists claim that there are none. Reasoning about these views requires a logic. That is the meta-logic. It turns out that there are some meta-logical challenges specifically for the pluralists. I will argue that these depend on an implicitly assumed absoluteness of correct logic. Pluralists can solve the challenges by giving up on this absoluteness and instead adopt contextualism about correct logic. This contextualism (...) is naturalistically appealing. (shrink)

It is customarily assumed that paracomplete and paraconsistent solutions to liar paradoxes require a logical system weaker than classical logic. That is, if a logic is not fragile to liar paradoxes, it must be logically weaker than classical logic. Defenders of classical logic argue that the losses of weakening it outweigh the gains. Advocates of paracomplete and paraconsistent solutions disagree. We articulate the notion of fragility with respect to the liar paradox and show that it can be disentangled from logical (...) strength. Strength and resilience to paradox do not force a trade-off with respect to liars: there can be logics which are not weaker than classical logic and are solid to the liar. (shrink)

In this paper, I critically examine the monist interpretation of the logic-as-model view that Erik Stei puts forth in Logical Pluralism and Logical Consequence. I will argue that, in addition to the three dimensions presented in the book, there is a fourth dimension on which pluralism in logic could arise, namely epistemological pluralism. An example of such a form of pluralism is model pluralism, being the idea that we need multiple models to fully account for the subject matter of logic. (...) Such a form of pluralism is well-recognized and widely acknowledged in (model-based) science. I argue that if we endorse the logic-as-model view, then we should also recognize such a form of model pluralism in logic. While model pluralism is consistent with metaphysical monism — the idea that there is ultimately only one extra-systemic logical consequence relation — it does put pressure on the idea that there is one uniquely best model that fully captures that phenomenon. (shrink)

We investigate a hitherto under-considered avenue of response for the logical pluralist to collapse worries. In particular, we note that standard forms of the collapse arguments seem to require significant order-theoretic assumptions, namely that the collection of admissible logics for the pluralist should be closed under meets and joins. We consider some reasons for rejecting this assumption, noting some prima facie plausible constraints on the class of admissible logics which would lead a pluralist admitting those logics to resist such closure (...) conditions. (shrink)

What is the relation or connection between formalizations of induction and the actual inductive inferences of scientists? Building from recent works in the philosophy of logic, this paper argues that these formalizations of induction are best viewed as models and not literal descriptions of inductive inferences in science. Three arguments are put forward to support this claim. First, I argue that inductive support is the kind of phenomenon that can be justifiably modeled. Second, I argue that these formalizations have the (...) features that define models—that they have representors, artefacts, and idealizations. Third, I argue that these formalizations being models explains their plurality and revisability. (shrink)

Most of the most prominent discussions within metaphysics assume without argument that our metaphysical theorizing should be constrained by classical logic. I examine why this is the case and then argue that it should not be. That is, I argue that we should not take our metaphysical theorizing to be constrained by classical logic.

There is an apparent conflict in Quine’s work between, on the one hand, his clear commitment to the rational revisability of logic and, on the other, his principle of charitable translation and ‘change of logic, change of subject’ argument. I argue that the apparent conflict is mostly resolved under close exegesis, but that the translation argument normatively rules out collaborative revision and allows only revision by individuals. However, I articulate a Neo-Quinean view that preserves the rational acceptability of collaborative revision. (...) On that view, everything is rationally revisable in some manner or other — it’s just that the logical principles that laypersons find (actually or potentially) obvious and tacitly use to govern their everyday inferences can’t be rationally revised quickly and all at once. Since, in Quine’s view, what most people find obvious resists change, rational changes to laymen’s logic must be gradual. (shrink)

This paper argues that adopting a particular dialogical account of logical consequence quite directly gives rise to an interesting form of logical pluralism, the form of pluralism in question arising out of the requirement that deductive proofs be explanatory.

An agnostic pluralist approaches inquiry with the assumption that it is possible for more than one account of the phenomenon in question to be correct. A monist approaches inquiry with the assumption that only one account of the phenomenon in question is correct. The purpose of my paper is to support the claim that agnostic pluralists are less susceptible to a sort of bias that I call dialectical bias than monists.

11We thank Rohan French for a detailed discussion of this review. We also wish to reciprocally thank Shawn Standefer for detailed discussions about the book.Logical pluralism is the view according...