The Structure of Gunk: Adventures in the Ontology of Space

In Dean Zimmerman (ed.), Oxford Studies in Metaphysics: Volume 4. Oxford University Press. pp. 248 (2008)
Here are two ways space might be (not the only two): (1) Space is “pointy”. Every finite region has infinitely many infinitesimal, indivisible parts, called points. Points are zero-dimensional atoms of space. In addition to points, there are other kinds of “thin” boundary regions, like surfaces of spheres. Some regions include their boundaries—the closed regions—others exclude them—the open regions—and others include some bits of boundary and exclude others. Moreover, space includes unextended regions whose size is zero. (2) Space is “gunky”.1 Every region contains still smaller regions—there are no spatial atoms. Every region is “thick”—there are no boundary regions. Every region is extended. Pointy theories of space and space-time—such as Euclidean space or Minkowski space—are the kind that figure in modern physics. A rival tradition, most famously associated in the last century with A. N. Whitehead, instead embraces gunk.2 On the Whiteheadian view, points, curves and surfaces are not parts of space, but rather abstractions from the true regions. Three different motivations push philosophers toward gunky space. The first is that the physical space (or space-time) of our universe might be gunky. We posit spatial reasons to explain what goes on with physical objects; thus the main reason..
Keywords Mereology  Topology  Measure Theory  Space-time
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