Matteo Plebani

A counterpossible is a counterfactual with an impossible antecedent. Matthias Jenny has argued that relative computability theory provides examples of false counterpossibles. If Jenny were right, it would be highly significant, since it would follow that the standard analysis of counterfactuals, according to which counterpossibles are all vacuously true, is incorrect. In this paper, we argue against the claim that computability theory provides examples of false counterpossibles. We distinguish two ways of reading the alleged false counterpossibles. Under the first reading, they are indeed false, but, as we will argue, they are not genuine counterpossibles. Under the second reading, they are genuine counterpossibles, but they are true. There is a way to interpret the alleged false counterpossibles as false, and there is a way to interpret them as counterpossibles, but under none of these two interpretations they are false counterpossibles.

The platonism/nominalism debate in the philosophy of mathematics concerns the question whether numbers and other mathematical objects exist. Platonists believe the answer to be in the positive, nominalists in the negative. According to non‐factualists (about mathematical objects), the question is ‘moot’, in the sense that it lacks a correct answer. Elaborating on ideas from Stephen Yablo, this article articulates a non‐factualist position in the philosophy of mathematics and shows how the case for non‐factualism entails that standard arguments for rival positions fail. In particular, showing how and why non‐factualists reject nominalism illuminates the originality and interest of their position.