Presuppositions for Proportional Quanti ers

Most studies of the so-called Proportion Problem seek to understand how lexical and structural properties of sentences containing adverbial quanti ers give rise to various proportional readings. This paper explores a related but distinct problem: given a use of a particular sentence in context, why do only some of the expected proportional readings seem to be available? That is, why do some sentences allow an asymmetric reading when other structurally similar sentences seem to require a symmetric reading? Potential factors suggested in the literature include the distribution of donkey pronouns, certain uniqueness implications, and focus structures. I argue here that a use of an adverbial quantier presupposes HOMOGENEITY: all individual situations that get lumped into a single case for the purposes of evaluating the quanti cation must agree on whether they satisfy the nuclear scope. For instance, in order for a token of Usually, if a farmer owns a donkey, he beats it to be felicitous when construed under a farmer-dominant asymmetric reading, the context must be consistent with the proposition that each farmer either beats all or none of his donkeys. Thus proportional sentences are indeed systematically ambiguous, but only some readings will be felicitous in a given context. 1. Truth conditions for proportional adverbial quanti ers It has been well known at least since Partee (1984) that sentences involving adverbial quanti ers can be ambiguous across a number of distinct sets of truth