| | Hey Adam,
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.
First, points are traditionally viewed as infinitesmal, which could mean there're an infinite number of them. Do you accept that there can be an infinite number of something?
Second, the examples of attributes you gave look more like the attributes of other things, not of space. Like an attribute of a mass' gravitional field or of the charge of an electric field is its extension through space. Extension through space isn't an attribute of space. And "space" here could really just be synonymous with "dimension." Does dimension exist? Sure. Does it exist independent from material existents? Not so sure.
Third, there is some evidence that space is materially filled, that each point is filled with material. Discussing vacuum fluctuations as the stuff space is made of, Timothy Ferris, in his The Whole Shebang: A Statement of the Universe Report (1998, pg 236), writes:
The plenum held sway in the nineteenth century, when most physicists assumed that space was full of the so-called aether. Then the Michelson-Morley experiment proved that the aether does not exist, and Einstein demonstrated that it was theoretically superfluous as well.
But no sooner had the vacuum been emptied than quantum physics filled it up again The quantum vacuum is a frothing sea of activity... Owing to what is called wave-particle duality, quantum physics sees nature as if through two eyes, one of which beholds particles and the other waves. Look through the particle eye and we find that for every "real" (meaning long-lived) electron there are countless "virtual" electrons and positrons. Look through the wave eye and we find the quantum field roiling the vacuum like winds across water. We tend to think of fields mostly in terms of energey ("force fields"), but matter, too, may with equal accuracy be depicted, via wave mechanics, as composed of quantum fields. (Asking which is "really" nature - particles or fields - is like asking with which eye you are really seeing when you have both eyes open.)
So the vacuum today is a kind of mix. As the nuclear physicists Hand Chrisian von Baeyer writes, "The modern vacuum represents a compromise between the opinions of Democritus and those of Aristotle: The former was right to insist that the world consists of atoms and the void, and the latter when he claimed that there is no such thing as true and absolute emptiness...The dynamic vacuum is like a quite lake on a summer night, its surface rippled in gentle fluctuations, while all around, electron positron pairs twinkle on and off like fireflies. It is a busier and friendlier place than the forbidding emptiness of Democritus or the glacial aether of Aristotle."
All for now. Interesting topic.
Jordan
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