TWO DIAMONDS ARE MORE THAN ONE∗ Transitivity and the Factivity of Feasible Knowability

After introducing semantic anti-realism and the paradox of knowability, the paper considers a new threat posed to a restricted version of semantic anti-realism by a group of recent arguments. These arguments purport to achieve with respect to a restricted version of anti-realism what the paradox of knowability achieves with respect to an unrestricted version. Building on features of the informal notion of feasible knowability which occurs in the formulation of the anti-realist’s thesis—in particular, on its factivity—the paper shows how the accessibility relation for the relevant modality must be relativized to particular facts, and how this relativization can lead to peculiar failures of transitivity. The paper also argues—again, on the basis of the factivity of feasible knowability—that the relevant modality cannot be identified with (non-transitive) epistemic possibility. Together, these results suffice to show the unsoundness of the arguments considered, and contribute to an appreciation of the distinctive semantics and logic underlying the anti-realist’s notion of feasible knowability.