Is there any logic at all?

In its most general form, logical pluralism is the view that there is more than one correct logic. I call this generic claim "the plurality thesis". Different versions of logical pluralism emerge with different implementations of that thesis and, most notably, of its key components logic and correctness. On some readings of the plurality thesis, logical pluralism is completely uncontroversial, on others it may turn out to be a rather exciting position. In this opening chapter, I identify an interesting, revisionist reading of the plurality thesis that is inconsistent with both logical monism and logical nihilism. Logical pluralism, so understood, claims that there are at least two correct theories of logical consequence. The chapter sketches historical developments of the view and gives an outline of the arguments defended in the book.

In Logical Pluralism and Logical Consequence (Cambridge University Press, 2023), Erik Stei argues for logical monism, the view that there is exactly one correct logic, in opposition to logical pluralism and logical nihilism. The present review aims to challenge two premisses in the main argument of the volume. First, Stei argues that no version of pluralism based on a plurality of senses of the logical connectives succeeds in proving that logical vocabulary is genuinely plural in the required sense. Second, he also argues that pluralism cannot account for the rivalry between logics, which makes the position less charitable than it claims. I will give arguments against the two premisses after presenting the details of the main argument for monism that we find in the book.

Logical pluralism as a thesis that more than one logic is correct seems very plausible for two basic reasons. First, there are so many logical systems on the market today. And it is unclear how we should decide which of them gets the logical rules right. On the other hand, logical monism as the opposite thesis still seems plausible, as well, because of normativity of logic. An approach which would manage to bring a synthesis of both logical pluralism and logical monism is called for. I review the possible forms of logical pluralism and render them more plausible. I thus arrive at logical dynamism, a synthesis of various pluralisms and monism focused on how logic develops.

Some recent work on logical pluralism has suggested that the view might be in danger of collapsing into logical nihilism, the view on which there are no valid arguments. The goal of this chapter is to argue that the prospects for preventing such a collapse vary with one’s account of logical consequence. Section 1 lays out four central approaches to consequence, beginning with the approaches Etchemendy (On the Concept of Logical Consequence. CSLI: Stanford, 1999) called interpretational and representational, and then adding a Quinean substitutional approach as well as the more recent universalist account given in Williamson (Modal Logic as Metaphysics. Oxford: Oxford University Press, 2013; Semantic Paradoxes and Abductive Methodology. In Reflections on the Liar, ed. B. Armour-Garb, 325–346. Oxford: Oxford University Press, 2017). Section 2 recounts how the threat of logical nihilism arises in the debate over logical pluralism. Section 3 then looks at the ways the rival accounts of logical consequence are better or worse placed to resist the threat.

Many authors show how useful logic can be as a tool for building theories that can account for problems in the philosophy of religion, such as paradoxical assertions. As a consequence, one's philosophy of logic is crucial as well, since it determines which logics, from the set of available and constructible logics, one can use to build a theory. In this paper, we present the relatively recent debate between logical pluralism and monism because the positions in this debate determine which logic(s) can, with justification, be applied to build a theory that addresses problems in the philosophy of religion. We begin by presenting the problem of paradoxical assertions and the debate over logical pluralism that bears on the addressing paradoxical assertions. We then canvass strategies for arguing in favor of logical monism, and pluralism; ultimately, we conclude that the Western tradition has reached a stalemate on this issue. We then turn our attention to the potential for Indian religious traditions to contribute to the debate. We present the five‐step‐syllogism from Nyāya‐Hindu philosophy, the four corners of reasoning from Buddhist philosophy, and the seven‐fold theory of predication from Jaina philosophy. The upshot of our presentation is to lay the groundwork for cross‐traditional logical debate by identifying the ways in which Indian discussions of debate and dialogue relate to modern approaches to logic and the philosophy of logic.

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.

Logical pluralism is the view that there is more than one correct logic. This is not necessarily a controversial claim but in its most exciting formulations, pluralism extends to logics that have typically been considered rival accounts of logical consequence – to logics, that is, which adopt seemingly contradictory views about basic logical laws or arguments. The logical pluralist challenges the philosophical orthodoxy that an argument is either deductively valid or invalid by claiming that there is more than one way for an argument to be valid. In this book, Erik Stei defends logical monism, provides a detailed analysis of different possible formulations of logical pluralism, and offers an original account of the plurality of correct logics that incorporates the benefits of both pluralist and monist approaches to logical consequence. His book will be valuable for a range of readers in the philosophy of logic.

Plural logic has become a well-established subject, especially in philosophical logic. This book explores its broader significance for philosophy, logic, and linguistics. What can plural logic do for us? Are the bold claims made on its behalf correct? After introducing plural logic and its main applications, the book provides a systematic analysis of the relation between this logic and other theoretical frameworks such as set theory, mereology, higher-order logic, and modal logic. The applications of plural logic rely on two assumptions, namely that this logic is ontologically innocent and has great expressive power. These assumptions are shown to be problematic. The result is a more nuanced picture of plural logic’s applications than has been given so far. Questions about the correct logic of plurals play a central role in the last part of the book, where traditional plural logic is rejected in favor of a “critical” alternative. The most striking feature of this alternative is that there is no universal plurality. This leads to a novel approach to the relation between the many and the one. In particular, critical plural logic paves the way for an account of sets capable of solving the set-theoretic paradoxes.

This final chapter summarizes the main arguments given in the book. The central aim has been to defend logical monism–the view that there is only one correct answer to the question of whether or not a given argument is valid–against the challenges raised by the logical pluralist. The first task was to get clear on what, exactly, those challenges amount to. It turned out that pluralism, understood as the thesis that there is more than one correct logic, is not necessarily a controversial view. In some readings, it is obviously true. Crucially, logical monism, properly understood, needs no defense against those readings. But there are other versions of logical pluralism that do conflict with logical monism. Those are the readings I call revisionist. The account offered in this book allows for the obviously true readings of logical pluralism while resisting the revisionist approaches pursued by some pluralists. The basic tenets of this account are (i) that there is exactly one notion of extra-systematic logical consequence and (ii) that there is exactly one logical theory that provides the best account of this notion.

Logical pluralism is the view that there is more than one correct logic. This view emerged in a dialectical context in which certain laws of logic were hotly debated by philosophers. For example, philosophers have spilled a great deal of ink over the logical principle of explosion ('from a contradiction, everything follows'). One side in the debate accepts this principle, the other side rejects it. It is exceedingly natural to assume that these rival points of view are incompatible, hence one side of the debate is correct while the other is incorrect. This is logical monism: the view that there is exactly one correct logic. Pluralists argue that the monistic assumption is subtly and surprisingly wrong. According to the pluralist, some logics that appear to be irreconcilable rivals are, in fact, both correct in their own ways. This Element will explain the debate over logical pluralism in an accessible manner.

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.

In this paper we are going to characterize the idea of logical pluralism according to Beall and Restall. In order to do that, this paper is divided into three sections. In the first section, we shall define briefly what Beall and Restall’s theory is about. In the second, we shall deal with some problems with the theory and some possible answers. Finally, three objections will be raised. Keywords: logical pluralism, logical monism, Beall, Restall, Priest.

Philosophy of logic is a fundamental part of philosophical study, and one which is increasingly recognized as being immensely important in relation to many issues in metaphysics, metametaphysics, epistemology, philosophy of mathematics, and philosophy of language. This textbook provides a comprehensive and accessible introduction to topics including the objectivity of logical inference rules and its relevance in discussions of epistemological relativism, the revived interest in logical pluralism, the question of logic's metaphysical neutrality, and the demarcation between logic and mathematics. Chapters in the book cover the state of the art in contemporary philosophy of logic, and allow students to understand the philosophical relevance of these debates without having to contend with complex technical arguments. This will be a major new resource for students working on logic, as well as for readers seeking a better understanding of philosophy of logic in its wider context.

Philosophy of logic is a fundamental part of philosophical study, and one which is increasingly recognized as being immensely important in relation to many issues in metaphysics, metametaphysics, epistemology, philosophy of mathematics, and philosophy of language. This textbook provides a comprehensive and accessible introduction to topics including the objectivity of logical inference rules and its relevance in discussions of epistemological relativism, the revived interest in logical pluralism, the question of logic's metaphysical neutrality, and the demarcation between logic and mathematics. Chapters in the book cover the state of the art in contemporary philosophy of logic, and allow students to understand the philosophical relevance of these debates without having to contend with complex technical arguments. This will be a major new resource for students working on logic, as well as for readers seeking a better understanding of philosophy of logic in its wider context.

Logic is loosely regarded as a key factor that drives our decisions. However, logic is actually separated into different systems, such as intuitionistic logic and classical logic. These systems can be explained by different theories, such as logical monism and logical pluralism. This paper aims to challenge logical monism, which posits that only a single logical system adheres to the principles of validity. It explains this on the basis of different systems held as equally strong in terms of their ability to establish definitive conclusions, and adhere to systems of validity relative to each system.