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 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 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.