Abstract

This chapter begins by briefly discussing the historical fortunes of conventionalism in logic and mathematics. After this, it clarifies the nature of conventionalism; critically discussing various ways to understand the view before arguing that conventionalism is best understood as an explanatory claim – logical and mathematical facts in any language are fully explained by the linguistic conventions of that language. The chapter then turns to discussing the notion of “explanation” itself, arguing that conventionalists don’t need to make any controversial assumptions about the nature of explanation. Finally, the chapter discusses what it is that makes a putative explanation acceptable to naturalists, singling out two key constraints on naturalistic explanations (one metaphysical and the other cognitive).