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.

The previous chapter highlighted the difficulties of combining logical pluralism with a semantic account of rivalry between correct logics. This chapter discusses the weaker conception of applicational rivalry and its relation to the idea that logical consequence has a certain kind of normative force. I argue that all variants of logical pluralism that meet the following three conditions are susceptible to what has been called the collapse problem for logical pluralism: (i) that there are at least two correct logical systems characterized in terms of different consequence relations, (ii) that there is applicational rivalry among the correct logics, and (iii) that logical consequence is normative. I argue that if a position satisfies all these conditions, then that position is unstable in the sense that it collapses into competing positions. In a final step, I show how the collapse problem persists even without an explicitly logical normativity constraint, leaving only conditions (i) and (ii). The problem can therefore be viewed as a result of two core assumptions: plurality and a very weak sense of rivalry that is endorsed by virtually all logical pluralists.

The chapter is concerned with a commitment of the logical pluralist: if there are at least two correct logics, then these logics will either involve different logical vocabulary or they will assign different meanings to the shared vocabulary. A central question is how this plurality in meaning can be implemented within a pluralist framework. Pluralists typically endorse claims to the effect that (i) the connectives of the logics have different meanings or (ii) that the notion of validity employed by one logic may be relevantly different from the one employed by the other. A further important question is whether the plurality of meanings is confined to the theoretical level only or whether a corresponding plurality is postulated regarding the extra-systematic counterparts of the logical vocabulary of correct logics. I argue that both connectives pluralism and consequence pluralism are implausible when construed as pluralistic theories. Meta-contextualism–the view that the question of whether the meaning of the logical terminology is the same or different in different contexts is itself subject to semantic variability–is shown to have exceedingly radical implications.

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.

This chapter offers a detailed discussion of domain-based pluralism. In line with observations of previous chapters, the main focus is on the claim that logic in its canonical application to logical consequence is domain-dependent. I first review arguments brought forward in support of the domain-dependence of logic understood in that sense. I argue that none of them is conclusive. I then discuss two indirect arguments for domain-dependence in the form of arguments against universal applicability and argue that both can be resisted. I then highlight some open problems for domain-based logical pluralism. Combining the insights of these discussions, I argue that, as things stand, there is no good reason to assume that logical theories are domain-dependent.

Logical pluralism is sometimes motivated by the claim that it affords a more charitable interpretation of important debates in philosophical logic than monism does. This chapter argues that this claim is false. Pluralists are unable to account for important parts of logical and mathematical practice since they are in no position to account for potential rivalry between different logics. This is a problem for the charity-based project because most non-classical logicians formulate their theories of logical consequence as rivals to classical logic. I introduce three approaches to rivalry that focus on semantics, metasemantics, and applications, respectively. I argue in this chapter that neither the semantic nor the metasemantic approach offer a sense of rivalry that is plausible from a pluralist perspective, leaving the applicational approach for the following chapter. I further argue that this supports the conclusion that, at least as far as issues concerning the meanings of logical vocabulary are concerned, the correct logics are ultimately compatible. If we are interested in potential rivalry between the logics, we will have to look elsewhere.

The central concepts of the book are introduced: formalism freeness and logical entanglement.The stability of the syntax/semantics distinction is discussed, as is J. Burgess’s distinction between formal and linguistic semantics. A special kind of logical pluralism is introduced, and likened to the theme of multi-scalarityas defined in Mark Wilson’s work.

This chapter presents a dialogical rationale based on the Prover–Skeptic model for the three main features of deduction identified in Chapter 1: necessary truth-preservation, perspicuity, and belief-bracketing. Moreover, it addresses four important ongoing debates in the philosophy of logic: the normativity of logic, logical pluralism, logical paradoxes, and logical consequence. It is shown that the Prover–Skeptic model provides a promising vantage point to address the questions raised in these debates.