On Drawing Lines on a Map Barry Smith Department of Philosophy and Center for Cognitive Science, State University of New York at Buffalo, NY 14260-1010 phismith@ubvms.cc.buffalo.edu Abstract The paper is an exercise in descriptive ontology, with specific applications to problems in the geographical sphere. It presents a general typology of spatial boundaries, based in particular on an opposition between bona fide or physical boundaries on the one hand, and fiat or human-demarcation-induced boundaries on the other. Cross-cutting this opposition are further oppositions in the realm of boundaries, for example between: crisp and indeterminate, complete and incomplete, enduring and transient, symmetrical and asymmetrical. The resulting typology generates a corresponding categorization of the different sorts of objects which (complete) boundaries determine or demarcate. The theory is applied first of all in the areas of geography and of administrative and property law. Indications are then given as to how the typology may be applied also in other fields where physical and fiat boundaries are at work, including the field of cognitive linguistics and the related field of the ontology of truth. Dividing Reality Thomas Jefferson famously called into being the states of the so-called Northwest Ordinance by drawing lines on a map.! A number of issues are involved in understanding the peculiar creative magic at work in such a performance. These have to do with the nature of Jefferson's politico-geographical authority and with the practical and legal problems of translating ink-lines of a certain thickness on paper into working territorial borders on the ground. To deal in coherent fashion with these issues, however, it will be necessary first of all to consider certain more fundamental ontological questions relating to such creative actions and their products. What sorts of entities are these, which can be brought into being simply by drawing lines on a map? What are the forms and limits of such creativity, and how do the created entities relate to entities of the more humdrum sort? The remarks which follow, offered in answer to these questions, relate to a body of axiomatic work on what has come to be called 'mereotopology', an alliance of topological methods with the ontological theory of part and whole. 2 I shall here confine myself to informal consideration of the 1 When Jefferson first draw his map in 17841drawing off 14 neat checkerboard squares between the boundaries of the Atlanticcolonies and the Mississippi River, his map was sufficiently inaccurate that it did not even have the Great Lakes in the right place. In the end, 10 states were nonetheless created in this area, having boundaries which follow Jefferson's lines in large degree. 2 This work is summarized in Smith 1993, in Eschenbach, et at. 1994 and in Casati and Varzi (forthcoming). For a useful overview of related formal work by geographers on these issues, which however does not include a treatment of mereological ideas, see Herring 1991.