This paper offers a modification of the account in my earlier "Dividing things up" (Natural Language Semantics 2005) of the interaction between or and modals, which accounts for the problematic free-choice reading of modal/or sentences such as "Jane may sing or dance." This paper focusses on a problem not addressed in the earlier one, namely, the fact that under negation (and other downward monotonic operators) the free choice effect disappears.
The new account maintains the view of the earlier paper that or is a set formation operator, with or coordinations taken to denote a set whose members are the (ordinary) denotations of the disjuncts. What is new is the proposal that or coordinations are subject to a Symmetry Constraint, which requires that there be some salient property which holds equally of each disjunct in an or coordination. I demonstrate that the truth conditions compositionally derivable for may/or sentences fail to provide a property which would satisfy this constraint, and argue that free-choice readings are the result of pragmatic strengthening of those truth conditions to satisfy the constraint. The absence of "special" readings in the case of negation is explained by the observation that the compositionally derivable truth conditions of sentences like "Jane may not sing or dance" do in fact satisfy the Symmetry Constraint.