Evidence for non-existential readings of locative indefinites

While (1) only requires that there exists a gas station nearby, the prominent interpretation of (2) is that all gas stations are far away. We examine two accounts of this kind of contrast. Under one possible explanation, far from decomposes into its negated antonym (henceforth Implicit Negation, or IN, cf. in another context Heim [1]). 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 (Property Eigenspace Hypothesis, or PEH, see [3,4]). We present new evidence, with experimental support, for the PEH and against IN: sentences containing indefinites with projective locatives like left of, south of have a salient false interpretation also in situations where the existential reading is true. IN cannot explain these interpretations, whereas they are directly predicted by the PEH. Our results imply that indefinites uniformly denote properties, and only indirectly, through derivational ambiguity, existential quantifiers. Contrasts as in (1)-(2) show that locative indefinites may give rise to a salient non-existential and a less salient existential interpretation. However, this is so only for far from in (2) but not for close to in (1). Another example [3,4] is the contrast between (3) and (4), where (3) only requires that Fido be inside of some doghouse, but (4)’s prominent interpretation is that Fido is outside of all doghouses: