The Facts of the Matter

This chapter concerns the status of the conventionalist theory developed, argued for, and defended throughout the book. It begins by discussing the views that historical conventionalists had about their own conventionalist theories and addresses a recent controversy about whether Carnap was truly a conventionalist. The chapter then argues that conventionalism is the best explanation of the logical and mathematical facts, assessing it according to a number of different theoretical virtues. Then two metaobjections are considered, one based on philosophical progress, and the other based on peer disagreement. Despite the chapter’s defense of conventionalism, it ends by expressing some very personal doubts.