Monotonicity, Substitution Sources, and the Robustness of Disjunct Alternatives

Disjunctive sentences hace their disjuncts as formal alternatives. I present evidence that these alternatives are resistant to contextual pruning: the pragmatics treats them as necessarily relevant.I take some preliminary steps in making sense of this observation but stipulations remain. I also present evidence that the scalar implicatures/ignorance inferences disjunct alternatives give rise to are mandatory. If ignorance inferences are computed by the Maxim of Quantity free from syntactic stipulations (Fox, 2007), this means that, contrary to common assumptions, quantity inferences are not cancellable. I suggest a way to think about the maxims that would make this natural. I end with evidence from numerals suggesting that there may be a limited role for structure-building in the generation of alternatives (using Internal Merge), with potential consequences for Condition B effects and scope ambiguities