In this paper, the meanings of sentences containing the word or and a modal
verb are used to arrive at a novel account of the meaning of or coordinations.
It is proposed that or coordinations denote sets whose members are the denotations
of the disjuncts; and that the truth conditions of sentences containing or
coordinations require the existence of some set made available by the semantic
environment which can be ‘divided up’ in accordance with the
disjuncts. The relevant notion of ‘dividing things up’ is made
explicit in the paper. Detailed attention is given to the question of how
the proposed truth conditions are derived from the syntactic input. The account
offered allows for the derivation of both the disjunctive and the non-disjunctive
readings of modal/or sentences, including the much-discussed free choice
readings of may/or sentences.