There are more ways in which our psychological and/or neurobiological makeup leads us down the garden path. Whereas we readily agree that red, round, or a smile cannot exist without a red or round object or a smiling face, we just as readily believe that positions can exist without being possessed: they are there, regardless of whether they are "occupied" or "empty". We are prepared to think of material objects as substances (things that can exist without being the properties of other things), and we are not prepared to think of the properties of material objects as substances — except for one: we think of positions as if they existed by themselves, rather than by virtue of being properties of material objects.

If there is any "justification" for thinking of positions as entities rather than as properties, it is psychological and/or neurobiological. The visual cortex is teeming with feature maps. A feature map is a layer of the cerebral cortex in which cells map a particular phenomenal variable (such as hue, brightness, shape, motion, or texture) in such a way that adjacent cells generally correspond to adjacent locations in the visual field. Every phenomenal variable has a separate map (and usually not just one but several maps at different levels within the neuro-anatomical hierarchy) except location, which is present in all maps.

If there is a green box here and a red ball there, "green here" and "red there" are signaled by neurons from one feature map, and "boxy here" and "round there" are signaled by neurons from another feature map. "Here" and "there" are present in both maps, and this is how we know that green goes with boxy and red goes with round. Position is the integrating factor. In the brain, and consequently in the visual world, positions pre-exist — in the brain at the scale of neurons, in the visual world at visually accessible scales. They exist in advance of visual objects, and this is another reason why we tend to take for granted that they also exist in advance of physical objects, not only at the scale of neurons or at visually accessible scales, but also at the scales of atoms and subatomic particles. The transition from visually accessible scales to subatomic scales is an unwarranted extrapolation, but (as said) if one postulates a pre-existent spatial expanse that is intrinsically differentiated at some scales, then it is hard to see why it is not intrinsically differentiated at all scales.

There is yet another reason why we tend to think of positions as substances (that is, as if they existed "by themselves," without being possessed): the role that position plays in perception is analogous to the role that substance plays in conception. Among the various ideas that philosophers have associated with the word "substance," the following is relevant here: while a property is that in the world which corresponds to the predicate in a sentence composed of a subject and a predicate, a substance is that in the world which corresponds to the subject. It objectifies the manner in which a conjunction of predicative sentences with the same subject term bundles predicates. While substance serves as the "conceptual glue" that binds a material object's properties, position serves as the "perceptual glue" that binds a visual object's features.

And there are still more reasons why the existence of an intrinsically and completely differentiated spacetime manifold is all but universally accepted by the community of physicists. Theoretical physicists are first of all mathematicians. It goes without saying that they need to be good with the math. So at home they are in the world of mathematical ideas that this has for them a reality almost equal to (if not greater than) the physical world. At any rate, such is the state of mind in which they write their papers. But the single most basic mathematical concept is that of a set, defined by Georg Cantor, the inventor of set theory, as

The physical world, on the other hand, is rather

as we have seen.