Abstract

In the mid twentieth century, logical positivists and many other philosophers endorsed a simple equation: something was necessary just in case it was analytic just in case it was a priori. Kripke’s examples of a posteriori necessary truths showed that the simple equation is false. But while positivist-style inferentialist approaches to logic and mathematics remain popular, there is no inferentialist account of necessity a posteriori. I give such an account. This sounds like an anti-Kripkean project, but it is not. Some of Kripke’s remarks even suggest this kind of approach. This inferentialist approach reinstates neither the simple equation nor pure conventionalism about necessity a posteriori. But it does lead to something near enough, a type of impure conventionalism. In recent years, metaphysically heavyweight approaches to modality have been popular, while other approaches have lagged behind. The inferentialist, impure conventionalist theory of necessity I describe aims to provide a metaphysically lightweight option in modal metaphysics.