The focus of my paper is a puzzle raised by disjunctive antecedent conditionals (DACs):
(1) If Amy or Beth comes to the party, it will be fun.
So if Amy comes to the party, it will be fun, and if Beth comes to the party, it will be fun.
The puzzle is whether and in what sense the inference from a DAC to its simplifications holds. Conditionals like (1) seem to endorse the inference as an entailment, but conditionals like (2) suggest it cannot be an entailment (since (2) seems like it could be true, but one of its simplifications seems necessarily false).
(2) If the US spends more than half its budget on defense or education, it will spend more than half its budget on defense.
#So, if the US spends more than half its budget on education, it will spend more than half its budget on defense.
I argue that the correct resolution of this puzzle is that DACs are ambiguous. I offer several independent arguments for this conclusion, drawing on intuitions about a range of simple and complex DACs, as well as the interaction between disjunction and focus, which reveal a new pattern of data. I then argue that existing theories cannot account for this data, and none satisfactorily explain away it either (this includes existing ambiguity theories). I then sketch an improved theory of DACs that accounts for the new data.