Space

John Drummond

pp. 162-175

in: Michael Huemer, Approaching infinity, Basingstoke, Palgrave Macmillan, 2016

Abstract

In standard geometry, space is said to be composed of indivisible parts called "points". There are continuum many of these in any region with a nonzero size. All geometric objects — lines, planes, triangles, circles, and so on — are said to be built out of points. It is usually said that these geometric objects are sets of points; however, it makes more sense to regard them as fusions of points, so that is how I shall henceforth speak. The fusion of a and b is understood as an object that has a and b as parts and has no other parts that don't overlap with a or b. (The generalization to cover fusions of any number of objects should be obvious.) Fusions differ importantly from sets: for example, the fusion of two physical objects is itself a physical object, whereas a set of physical objects would be an abstract, mathematical object. Similarly, the fusion of some spatial regions would plausibly be a spatial region, whereas the set containing some spatial regions would not itself be a region but would instead be some abstract object.