Of Chisholm’s many signal contributions to analytic metaphysics, perhaps the most important is his treatment of boundaries, a category of entity that has been neglected, to say the least, in the history of ontology. We can gain some preliminary idea of the sorts of problems which the Chisholmian ontology of boundaries is designed to solve, if we consider the following Zeno-inspired thought-experiment.

There are conflicting intuitions concerning the status of a boundary separating two adjacent entities (or two parts of the same entity). The boundary cannot belong to both things, for adjacency excludes overlap; and it cannot belong to neither, for nothing lies between two adjacent things. Yet how can the dilemma be avoided without assigning the boundary to one thing or the other at random? Some philosophers regard this as a reductio of the very notion of a boundary, which should accordingly (...) be treated a mere façon de parler. In this paper I resist this temptation and examine some ways of taking the puzzle at face value within a realist perspective—treating boundaries as ontologically on a par with (albeit parasitic upon) extended parts. (shrink)

In the process of arguing against all theories of extended material objects made up of simples, Dean Zimmerman has recently argued against the compossibility of continuous closed and continuous open material objects. But it is surely undeniable that point-like material objects are possible; plausible principles of recombination and the principle of unrestricted composition then lead to the possibility Zimmerman rejects. Fortunately, Zimmerman’s arguments can be resisted: what appear to be implausible modal consequences of the compossibility of open and closed continuous (...) material objects turn out to be merely the results of a decision to use ‘material object’ in a certain way. (shrink)

Absolutely no one still believes that every physical interactionconsists of material bodies bumping into each other. Those who have tried to work out a completely mechanistic physics have been unable to explain common phenomena like liquidity, gravitation and magnetism. In fact, there is great reason to doubt that such a physics could ever account for attractive forces in general.

This book combines physics, history, and philosophy in a radical new approach to introducing the philosophy of physics.

Körner has made an important distinction between dependent and independent particulars, noting that any adequate theory of categories will divide particulars into those that are independent and those that are not. In the present paper, the concept of a spatial boundary is used to illustrate the concept of a dependent particular. It is suggested that, if we follow Brentano and think of such boundaries as ontologically dependent upon the things of which they may be said to be boundaries, then we (...) will be able to throw light upon a number of philosophical questions about the spatial continuum. These questions pertain to such topics as: the distinction between parts and boundaries; the definition of dimensionality; and the nature of contact and physical continuity. (shrink)

Given Lewis’s views about recombination and spatial relations, there are possible worlds in which space is discrete and yet the Pythagorean theorem is true – contrary to the so-called Weyl-Tile argument that concluded that the Pythagorean theorem must fail if space is discrete.

Physical boundaries and the earliest topologists. Topology has a relatively short history; but its 19th century roots are embedded in philosophical problems about the nature of extended substances and their boundaries which go back to Zeno and Aristotle. Although it seems that there have always been philosophers interested in these matters, questions about the boundaries of three-dimensional objects were closest to center stage during the later medieval and modern periods. Are the boundaries of an object actually existing, less-than-three-dimensional parts of (...) the object—that is, are solids bounded by two-dimensional surfaces, surfaces by one-dimensional “edges” or “physical lines”, edges by dimensionless “simples”? If not, how does a perfectly spherical object manage to touch a perfectly flat object—what part of the sphere is in immediate contact with the plane, if the sphere has no unextended parts? But if such parts be admitted, are we not then saddled with “actual infinities” of simples, lines, and surfaces spread throughout each continuous object—the boundaries of all the object’s internal parts? Does it help to say that these internal boundaries exist only “potentially”? (shrink)

This is a book that no one but Weyl could have written--and, indeed, no one has written anything quite like it since.

Absolutely no one still believes that every physical interactionconsists of material bodies bumping into each other. Those who have tried to work out a completely mechanistic physics have been unable to explain common phenomena like liquidity, gravitation and magnetism. In fact, there is great reason to doubt that such a physics could ever account for attractive forces in general.