A unifying theory of natural language connectives treats or as semantically asymmetric. In many such theories, the intuitive symmetry of or (illustrated by the intuitive equivalence of, e.g., John is unmarried or his spouse is away and John’s spouse is away or he is unmarried) is accounted for as a result of local presupposition accommodation. I argue against this approach, based on conditional sentences with presuppositional disjunctive antecedents.