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.

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 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.

In previous chapters, I construed logical pluralism as the view that there are multiple correct theories of extra-systematic logical consequence. Against this background, it may be tempting to think that logical pluralists are committed to the postulation of a plurality of extra-systematic logical consequence relations. In this chapter I argue that further options are available. I first show that, depending on the underlying notion of correctness, logical pluralism is compatible with any account of the cardinality of extra-systematic logical consequence. I then identify readings of the plurality thesis that give rise to the revisionist reading of logical pluralism that is the target of this book. The most obvious one is genuine plurality—the view that there is more than one extra-systematic consequence relation. A less obvious one acknowledges monism about extra-systematic consequence but argues that there cannot be a single precise theory that captures this relation. I propose a monist approach to logic in both the theory sense and the subject of investigation sense that rejects revisionist logical pluralism.