Indicative Conditionals and Graded Information

I propose an account of indicative conditionals that combines features of minimal change semantics and information semantics. As in information semantics, conditionals are interpreted relative to an information state in accordance with the Ramsey test idea: "if p then q" is supported at a state s iff q is supported at the hypothetical state s[p] obtained by restricting s to the p-worlds. However, information states are not modeled as simple sets of worlds, but by means of a Lewisian system of spheres. Worlds in the inner sphere are considered possible; worlds outside of it are ruled out, but to different degrees. In this way, even when a state supports "not p", it is still possible to suppose p consistently. I argue that this account does better than its predecessors with respect to a set of desiderata concerning inferences with conditionals. In particular, it captures three important facts: (i) that a conditional is logically independent from its antecedent; (ii) that a sequence of antecedents behaves like a single conjunctive antecedent (the import-export equivalence); and (iii) that conditionals restrict the quantification domain of epistemic modals. I also discuss two ways to construe the role of a premise, and propose a generalized notion of entailment that keeps the two apart.