The Ontology of Space
by Adam Reed
The concept of space is fundamental to physics, and therefore to all physical science. But does this concept correspond to a real existent? The naïve answer would be "no:" to the non-scientist, space denotes emptiness, the absence of existents. And of course absence is not an existent. Fortunately, this naïve view is wrong. To demonstrate exactly how it is wrong, one must track the concept of space back to the very identity of existence qua existence. And existence is identity.
What, then, is Identity?
The identity of an existent consists of the measurable values ("measurements") of its attributes. Thus for space to exist, its attributes would have to have measurements. But in what sense can space have measurements? What is a measurement—or more precisely, a measurable value of an attribute—anyway? For identity to refer to existence, the components of identity must be existentially extrinsic to consciousness. So the relevant referent is not the result of the conscious action of measurement. It is rather the existential fact that the action of measurement measures. Indeed, the primacy of existence implies that while one's ability to measure that existential value—and arrive at a result of measurement—is contextual and depends on the state of one's knowledge, the existential value remains the same—even while one's ability to measure it, and the nature of the result of the measurement, undergoes transformations commensurate with the knowledge in which one's measurement procedures are grounded.
To illustrate the relation of an extrinsic measurable value to increasingly sophisticated methods of objective measurement, I will use the example of measuring color.
The simplest method of measurement, and the first one learned by children, is nominal measurement. The child first learns by ostensive definition the names of some exemplary colors—red, blue, yellow, green, orange, purple and so on. The sensation of color from the newly perceived object is then compared to the known exemplars, and the name of the closest match is attached to that color as a result. For example, if the closest match was previously identified by the name "blue," the result of nominal measurement will be "blue." This result depends on the context of what colors the child already knows. Once the child learns the color "turquoise," the same extrinsic value may yield a new name.
Once the child begins to learn about the qualities of light, it becomes possible to measure a color on a linear instead of a nominal scale. Instead of a best match to one of previously learned named colors, the given color is compared to the whole rainbow laid out by wavelength of light, and the wavelength at which the contrast is at a minimum is noted. Now the measurement of color is a wavelength, a number on a continuous scale—a scalar.
Studying light further, one will notice that colors of the same scalar wavelength may still look different from each other. That is because the retina of the human eye has three kinds of color-sensitive receptors, and light in which the same wavelength seems dominant may in fact contain different proportions of light that stimulates red, green and blue cells. One can measure the amount of red, green, and blue in the given color, and the result of this measurement is a vector—an ordered array—of three numbers.
Suppose, finally, one is measuring the same color in order to duplicate it in a camouflage paint for ships of war. Potential enemies may use detectors at any possible wavelengths, not just the wavelengths seen by the retinal cells of the human eye. In that case, one must measure and duplicate not just the proportion of red, green and blue, but the distribution of light intensities in the whole spectrum of wavelengths. The result of this last measurement is a continuous distribution of light intensity as a function of wavelength. And all these measurements—nominal, scalar, vector, and continuous function—are measurements of the same existential value of the color attribute of some existent. We see that in its existential sense as a component of identity, the concept of measurement is quite general; it may refer to something a great deal more complicated than the simple scalar numbers one ordinarily thinks of as "measurements."
What, then, are the measurable attributes of space? That would be an appropriate question if "space" were a unit of some concept. But space is not a unit—it is the collective name of all the locations in the universe, or perhaps of all the locations not otherwise occupied by specific material existents—particles and so on. So the question becomes: is a point, a specific location in some inertial frame of reference, an existent?
If one took the standard materialist tack, and confined the notion of an existent to entities of matter and energy only, then the answer would have been "no." However, once existence is understood as coextensive with identity, then the only requirement of an existent is that it have attributes with measurements. In the transcript of the discussion session on the topic of axiomatic concepts (p. 241 in the 1990 Meridian paperback edition of Introduction to Objectivist Epistemology), in answer to "Prof. B" during discussion of axiomatic concepts, Ayn Rand says that an existent is "anything which you can isolate, whether it is an entity, a relationship, an action, or an attribute." Therefore, if a point has an identity—attributes with measurements—then a point, in the sense of a location in space, is also a kind of existent.
Such attributes are not difficult to find. For example, the gravitational field of every mass extends throughout space. The electric field of a charge also extends through all points, and so on. Therefore the strength and direction of physical fields (such as the electric and magnetic fields) are attributes that have specific values at each specific location in every inertial frame of reference. Therefore every point in space is an existent in its own right. "Space" refers to a collection of real existents—and therefore space exists.
Note that space exists without necessarily having to be filled with a substance, such as the "ether" commonly postulated in late-nineteenth century physics. Whether a substantial "ether" exists is a question for physics, not philosophy. As long as there is no physical evidence of a substantial "ether," the sensible presumption remains that there is no such thing.
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