Coordinating Ifs

Accounting for the behavior of conjoined and disjoined if-clauses is not easy for standard theories of conditionals that treat if as either an operator or restrictor. In this paper, I discuss four observations about coordinated if-clauses, and motivate a semantics for conditionals that reorients the compositional structure of the restrictor theory. On my proposal, if-clauses provide restrictions on modal domains, but they do so by way of a higher type intermediary—a set of propositions—that is collapsed by the modal. I argue that combining this view with an independently plausible type-shifting operation applied to or and and predicts the range of data we find for conditionals with coordinated if-clauses.