Many have accepted that ordinary counterfactuals and might counterfactuals are duals. In this paper, I show that this thesis leads to paradoxical results when combined with a few different unorthodox yet increasingly popular theses, including the thesis that counterfactuals are strict conditionals. Given Duality and several other theses, we can quickly infer the validity of another paradoxical principle, ‘The Counterfactual Direct Argument’, which says that ‘A> ’ entails ‘A> ’. First, I provide a collapse theorem for the ‘counterfactual direct argument’. (...) The counterfactual direct argument entails the logical equivalence of the subjunctive and material conditional, given a variety of assumptions. Second, I provide a semantics that validates the counterfactual direct argument without collapse. This theory further develops extant dynamic accounts of conditionals. I give a new semantics for disjunction, on which A or B is only true in a context when A and B are both unsettled. The resulting framework validates CDA while invalidating other commonly accepted principles concerning the conditional and disjunction. (shrink)

According to one tradition, uttering an indicative conditional involves performing a special sort of speech act: a conditional assertion. We introduce a formal framework that models this speech act. Using this framework, we show that any theory of conditional assertion validates several inferences in the logic of conditionals, including the False Antecedent inference. Next, we determine the space of truth-conditional semantics for conditionals consistent with conditional assertion. The truth value of any such conditional is settled whenever the antecedent is false, (...) and whenever the antecedent is true and the consequent is false. Then, we consider the space of dynamic meanings consistent with the theory of conditional assertion. We develop a new family of dynamic conditional-assertion operators that combine a traditional test operator with an update operation. (shrink)