Rotating Rotator I (Detail) by Eric J. Heller. "The simplest rotator consists of two rigid bars pivoted together end to end. The bars are free to rotate around the pivot like the segments of an old-fashioned carpenter's ruler, only without the friction. If you throw such a rotator into the air, the segments will pivot around each other in interesting ways, while the object as a whole flies smoothly through the air. If there are three or more segments, the pivoting is chaotic. First one segment may spin wildly, then all three segments may rotate as a unit, then perhaps the two end segments spin in opposite directions, etc."

According to the CCP, the multiplicity of things at any one time rests on surfaces. This means that spatial extension exists in advance of the multiplicity, for only what has spatial extent can be cut up by the 3-dimensional equivalents of cookie cutters. This is how we come to think of physical space as a self-existent expanse.

If the parts of material objects are defined by the parts of space, the parts of space exist in advance of the parts of material objects. This is how we come to think of physical space as an intrinsically divided expanse.

There are physiological limits to the acuity of visual perception. This implies that the spatial differentiation of the visual world — the world as we perceive it — is incomplete. It doesn't go "all the way down." Visual space isn't divided into arbitrarily small regions. But if one thinks of physical space as an intrinsically divided expanse, then it is hard to see why it is not divided at all conceivable scales. This is how we come to think of physical space as an infinitely or completely divided expanse.

Exceptions are found in the literature on quantum gravity, where it is occasionally observed that a fuzzy metric conflicts with the postulation of a manifold of points that are sharply localized relative to each other.

But if this is how we think, fuzzy positions are inconceivable. If parts are defined by geometrical boundaries, the relative positions of parts are as sharply defined as their boundaries, and there isn't anything fuzzy about the way geometrical boundaries are defined. In an intrinsically and completely differentiated spatial expanse, all conceivable parts of space exist "by themselves," in an absolute sense, and are therefore real for all material objects. For every material object O, and for every conceivable region R, the proposition "O is in R" possesses a truth value all times.

In other words, if this is how we think, the ontological implications of the quantum-mechanical probability assignments — such as the fuzziness of all relative positions and the incomplete spatiotemporal differentiation of the physical world — are inconceivable. Small wonder, then, that some of the best known physicists have decided that quantum mechanics cannot be understood or makes no sense.