Structural Models for Williamson's Modal Epistemology

In this paper, I examine Williamson's [15] counterfactual-based account of modal epistemology. I argue that such an account faces two serious problems-the cotenability problem and the gap problem. As I diagnose it, these problems somehow indicate that our standard way of understanding counterfactuals under the received possible-worlds semantics may have insufficient 'structures' to distinguish various different kinds of constraints on our counterfactual thinking. The remedy, I suggest, is to invoke the 'structural semantics' as developed by Pearl [10] and Halpern [4]. Based on this semantics, I offer some philosophical elucidation for various kinds of modality, and thereby provide a more satisfactory account of how our modal knowledge can be grounded in our knowledge of counterfactuals.