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.

This chapter explores a number of ways to understand the key notions of the plurality thesis. First, I disambiguate three readings of the term logic: (i) purely formal systems, (ii) interpreted logical theories, and (iii) the subject matter of logical theories. I argue that this distinction is relatively lightweight and should be acceptable on all prominent views about the nature of logical consequence. Building on those readings of logic, I then explore different conceptions of what it means for a logic to be correct. In particular, I present a generic view of correctness of logical theories which is broad enough not to exclude pluralists who claim that the plurality thesis should better be put in terms of the legitimacy or the usefulness of a logic. I propose different ways to strengthen the generic view by means of a weak or a strong version of the correspondence view or the logic-as-modeling view. Finally, I introduce different implementations of the plurality thesis resulting from the different readings of logic and of correctness and identify the interesting version of the thesis which will be the subject of the rest of the book.

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.