Locating Sets: Spatial Semantics of Indefinites and Collective Descriptions

This paper addresses systematic variations in the interpretation of indefinites and plurals when appearing within prepositional phrases and other spatial expressions. We show that these variations are explained when spatial processes in semantics locate the sets associated with properties and other setbased denotations of nominals. Starting with spatial indefinites we consider contrasts like the following. (i) Michael is far from a gas station. (ii) Michael is close to a gas station. In the appropriate context – e.g. a car race in the desert, when Michael’s car is running out of gas – sentence (i) means that Michael is far from all gas stations. By contrast, sentence (ii) only has an existential interpretation, which states that there is at least one gas station near Michael. We show that the existential-universal alternation in (i)-(ii) marks two extremes in a much wider range of (pseudo-)quantificational interpretations of spatial nominals, which cannot be explained by any known theory of quantification over entities. By contrast, this behavior is consistent with property-based theories of indefinites (McNally 2009, “Properties and entity correlates”, in Giannakidou & Rathert, eds., OUP). We propose that properties and other set concepts have a spatial dimension that is operational in locative sentences. Variations as in (i)-(ii) are explained by locating the set extension of the property denoted by the indefinite. Thus, sentences (i)-(ii) make a claim about Michael’s distance from the spatial set concept ‘gas station’. Such properties are located similar to other spatial objects. For example, being far from the property ‘gas station’ means being far from all of its ‘parts’ – individual gas station instances. By contrast, being close to a property means being close to at least one of its instances. Thus, the pseudo-quantificational variation in (i)-(ii) directly follows from meanings of spatial expressions and not from any compositional difference. This account of spatial indefinites naturally extends to spatial sentences with collective descriptions like ‘the lakes’ or ‘the mountain chain’, which show similar interpretative variability. At the same time, we observe some systematic differences between collective descriptions and singular indefinites in spatial constructions. We treat these differences as resulting from the referential cohesion of ‘impure atom’ entities denoted by plurals, as opposed to property denotations of indefinites. Spelling out formally the proposed spatial semantics leads to a general theory of set-based locative expressions.