Chapter 8 - Normativity and Collapse

Summary

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.