A Rational Cosmology: The Ubiquitous Qualities of Volume, Length, Width, and Height

Having previously discussed the ubiquitous quality of matter, which all entities must possess, we now proceed to consider other qualities which are universal to all entities: volume, length, width, and height.

Volume- Volume is an entity's expanse. Anything possessing the quality, matter, must have an expanse that corresponds in some proportion (though it could correspond in a variety of proportions) to the amount of the quality "matter" that the entity has.

That is, if the quality " matter" exists in an entity, it must have a real manifestation; this manifestation is volume. If the quality "matter" and the quality "volume" did not coexist and were not inextricably connected, we would encounter absurdities.

Volume without matter does not describe anything whatsoever. It would be just an arbitrarily picked region of space-as-absence, the latter being nothing whatsoever. Matter without volume, too, describes what cannot exist.

This would be tantamount to the quality, matter, existing nowhere, i.e., not existing, and the consequences would be the same: space-as-absence. It is self-evident that both qualities must be present, in some magnitude and combination, in every entity.

Linear Measurements:Length, Width, and Height- A line, in Euclidean geometry, denotes the shortest conceivable path which an entity would need to travel in order to reach any location from any other location.

The linear measurements of an entity are the measurements of those qualities which express the separation of various parts and boundaries of that entity with respect to the shortest conceivable path between them.

There are three independent linear measurements, which are mutually perpendicular. Any other linear measurement is in fact some combination (a vector sum) of any or all of these three mutually perpendicular linear qualities, which are known as length, width, and height (or, in the three-dimensional Cartesian coordinate system, as the x, y, and z-axes). Length, width, and height, as qualities, can also be termed dimensions.

It is important to note that these dimensions do not exist independently, but rather pertain to the entities that exhibit them. Each entity must have a certain maximum length, width, and height, though these measurements may vary in some relation to each other, i.e., depending on the particular region of the entity one examines.

For example, an entity may have a certain height somewhere along its length, and have its height increase or decrease farther along its length. In relation to one of the three dimensions, an entity can conceivably have any measurements in the other two dimensions, but must have some measurements.

As a primary, it is not space-as-relationship that is three-dimensional (as relationships cannot exhibit qualities qua relationships), but rather every single entity that exists or can conceivably exist. It has already been demonstrated that different entities can be separate in their boundaries, and the degree of this separation is precisely what space-as-relationship denotes.

Because, moreover, all entities exhibit the three dimensions as qualities, their separation can only be expressed as a combination of three measurement parameters. After all, one entity can be separated from another by a distance A in the X direction, as well as in either the Y or the Z direction. In each of these three cases, the relationships are not the same, and were there four entities thus positioned (including the original entity and the three entities separate from it), each would occupy a distinct position and would be separated from every other.

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