Evidence for non-existential readings of locative indefinites

We report on experimental results which show that sentences involving locative indefinites can give rise to non-existential readings. We are far from a gas station, for example, was judged as false by about two thirds of our subjects in situations where we are close to the nearest gas station, yet there also is a more
distant gas station such that we are far from it. We examine two accounts of his kind of reading. Under one possible explanation, far from decomposes into its negated antonym. Under an alternative account, indefinites denote properties which are associated with eigenspaces —the spatial regions inhabited by the entities in the extension of the property. We present new evidence, with experimental support, for the latter account: sentences containing indefinites with projective locatives have a salient false interpretation also in situations where the existential reading is true—and decomposition into negated antonyms fails to explain this. Our results imply that indefinites denote properties first and, through derivational ambiguity, existential quantifiers second.