Two Diamonds Are More Than One
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 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.
KeywordsAccessibility Relation Restriction Strategy Restricted Version Epistemic Possibility Factivity Constraint
Earlier versions of the material in this paper were given in 2005 at the Arché Modality Seminar (University of St Andrews); in 2006, at the International Colloquium on (Anti-)Realisms, Logic and Metaphysics (University of Nancy 2); in 2007, at the Arché Epistemology Seminar (University of St Andrews). I would like to thank all these audiences for very stimulating comments and discussions. Special thanks go to Ross Cameron, Roy Cook, Bob Hale, Jonathan Lowe, Agustín Rayo, Sven Rosenkranz, Crispin Wright and an anonymous referee. In writing this paper, I have benefitted, at different stages, from an AHRC Doctoral Award and from a RIP Jacobsen Fellowship.
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