Geometrical Semantics for Spatial Prepositions

A mong the most frequently used words in English are simple prepositions like in or on whose basic meaning is spatial in character. What we propose in this article is a classification of the kinds of geometry that underlie the basic meaning of various spatial prepositions. The distinctions among geometries underlying these prepositions has not, as far as we can tell, been previously noted in the literature of linguistics and philosophy. In fact, in spite of the spate of articles in the last decade or so on locative expressions, spatial prepositions, and the like, detailed attention to the kinds of geometry needed to give a semantic analysis of the various locative expressions does not seem to have been previously attempted. For example, consider the work of Cresswell (1978) which gives an interesting analysis of points of view, meaning spatial points of view, that are implicit in understanding the meaning of such words as come, go, left, right, and behind, to use his initial list. Cresswell goes far beyond what we attempt here in that he gives a formal semantics in terms of the categorical semantics he has written about extensively. But while we do not formalize the semantics we outline, in contrast with Cresswell we distinguish between spatial prepositions requiring a point of view and those that do not and we place this distinction, along with others, in a geometrical framework. For example, if someone says The book you want is to the left of the dictionary we all immediately understand that a point of view is involved. On the other hand, we are just as firmly convinced, without argument, that in many uses of language we describe the world in terms of the relations between objects and possibly other phenomena, without any attention to an implicit point of view on the part of the speaker or writer. It would seem absurd in most contexts to say that the pencil is on the table from my point of view but not from yours. Thus the ordinary primitive or basic meaning of on is in terms of' a geometry that does not assume a point of view. However, the preposition on assumes a physical ori-