  Most realist theories about boundaries, construed as lower-dimensional entities, share the view that such entities are ontological parasites: points, lines, and surfaces cannot be separated and cannot exist in isolation from the entities they bound (pace Suárez, who thought that God would be capable of such marvels; see Disputation 40, V, 41). This view does justice to the intuition that boundaries, if real, are somewhat “less real” than bulky entities, and as such it goes back to Aristotle (Metaphysics XI, 2, 1060b12–16) and has been defended e.g. by Boethius (Second Commentary I, xi, 14–21), revived by Abelard (Glosses on Porphyry, 8.1–4), and eventually endorsed by Brentano (1976) and his pupils (Chisholm 1984).  Realist theories may differ significantly, however, with regard to how such dependent, lower-dimensional entities relate to the extended entities they bound. Thus, with reference to the first puzzle of Section 1, let A and B be any two extended entities separated by a common boundary (such as Maryland and Pennsylvania). Then we may distinguish four main views (Varzi 1997):