A number of inference patterns involving epistemic modalities, including Modus Ponens, display a split behavior. They seem valid by the lights of all-or-nothing judgments: whenever the premises are accepted as true, the conclusion must be accepted as true as well. But they seem invalid by the lights of probabilistic judgments: we can specify intuitive credal assignments where the drop in probability between premises and conclusions is incompatible with validity. I suggest that we explain this asymmetry by endorsing two bridge principles between logical notions and rational constraints on attitudes. The first links a notion of classical consequence to rational constraints on probabilistic states. The second links a broadly dynamic notion of consequence (so-called informational consequence) to rational constraints on acceptance. In existing literature, classical and informational consequence are seen as alternatives; I argue instead that we can and should have both.
Dan Lassiter (Stanford)
Recent years have seen successful new applications of probabilistic semantics to epistemic modality, and there are signs of a revival of a classic probabilistic approach to conditionals. These models have a simple implementation using tools from intensional and degree semantics, and they have considerable appeal in terms of capturing inferences that are problematic for classical models in some cases. However, they generally fare worse than classical models in two key respects – they have trouble explaining the update/learning potential of epistemics and conditionals as well as their interpretations when embedded. Focusing on epistemic language, I’ll describe some of the reasons for the probabilistic turn, explain why embeddings and learning present a problem, and suggest a way to deal with the problems by adopting an enriched probabilistic semantics based on Bayesian networks. Time permitting, I’ll venture some speculations about attractions of, and challenges to, an extension to conditionals in the style of Kratzer 1986.