Summary Franz Brentano, 1838–1917, introduced the intriguing concept of “plerosis” in order to account for aspects of the continuum that were “explained” by formal mathematics in ways that he considered absurd from the perspective of intuition, especially visual awareness and imagery. In doing this, he pointed in directions later developed by the Dutch mathematician Luitzen Brouwer. Brentano’s notion of plerosis involves distinct though coincident points, which one might call “atomic entities with parts”. This notion fits the modern concepts (...) of “receptive field” in neurophysiology, “perceptive field” in psychology and “differential operator” in the formal theory of scale space. We identify Brentano’s boundary points as the primordial atomic Gestalts of visual imagery. The concept deserves to play a key role in Gestalt theory. (shrink)

This article presents an edited excerpt from a hitherto unknown fragmentary treatise by Rush Rhees. In the treatise, Rhees gives his account of the problem of continuity that he had started elaborating before he became acquainted with Wittgenstein. The excerpt, which contains Rhees' original distinction between outer and inner surfaces of bodies, builds on Brentano's theory of the continuum and his doctrine of plerosis. This treatment of continuity sheds light on Rhees' early philosophical development and confirms that even though (...) he and Wittgenstein discussed the problem of continuity, Rhees' own approach remained distinct from that of Wittgenstein. (shrink)

This article presents an edited excerpt from a hitherto unknown fragmentary treatise by Rush Rhees. In the treatise, Rhees gives his account of the problem of continuity that he had started elaborating before he became acquainted with Wittgenstein. The excerpt, which contains Rhees' original distinction between outer and inner surfaces of bodies, builds on Brentano's theory of the continuum and his doctrine of plerosis. This treatment of continuity sheds light on Rhees' early philosophical development and confirms that even though (...) he and Wittgenstein discussed the problem of continuity, Rhees' own approach remained distinct from that of Wittgenstein. (shrink)

According to Brentano's theory of boundaries, no boundary can exist without being connected with a continuum. But there is no specifiable part of the continuum, and no point, which is such that we may say that it is the existence of that part or of that point which conditions the boundary. - An adequate theory of the continuum must now recognize that boundaries be boundaries only in certain directions and not in others. This leads to consequences in other areas, too.

We outline Brentano’s theory of boundaries, for instance between two neighboring subregions within a larger region of space. Does every such pair of regions contain points in common where they meet? Or is the boundary at which they meet somehow pointless? On Brentano’s view, two such subregions do not overlap; rather, along the line where they meet there are two sets of points which are not identical but rather spatially coincident. We outline Brentano’s theory of coincidence, and show how he (...) uses it to resolve a number of Zeno-like paradoxes. (shrink)