Position, Motion, and Acceleration

Ayn Rand thought philosophy was not dependent on other knowledge, that philosophy proceeded mostly by means of reason. Obviously, reason alone cannot discover anything, all by itself. That is the philosophical dead end of Rationalism and Idealism. It is as daVinci said, “saper vedere” (to see is to know), and Ayn Rand was a staunch empiricist. What Ayn Rand meant is someone who’s observation of the world is objective and not distorted by subjectivism or mysticism ought to be able to reason from that observation to any correct philosophical principle. She would have disagreed that the sciences, for example, were necessary before any particular philosophical concepts could be fully developed.

I have a great deal of sympathy with this view, so a little explanation is required here. The first three levels of the hierarchy of differentiation could not have been discovered before the advents of Galileo and Newton. If I take Ayn Rand’s view on this, they cannot technically be called philosophy, and I think that is probably correct. However, they are necessary to the explanation of the remainder of the hierarchy and I question whether the concepts I am about to describe would be possible otherwise.

What I am about to describe will seem quite incredible, because I intend to show that every attribute and quality of every existent in the universe, can ultimately be described in terms of the six “qualities” or attributes in this hierarchy. I do not mean that is how we do describe them or are ever even aware that they can be described in that way, only that they can be. Furthermore, I will show that because this is true, the ultimate nature of all existents and the relationships between them is also explained by this hierarchy.

Finally, I will explain how all of these attributes are derived empirically to demonstrate there are no a priori concepts, which will establish the objective nature of our knowledge.

Six Primary Differentiating Qualities

The full explanation of the hierarchy is quite lengthy because each level is important to many different philosophical issues and because each raises many important questions that need to be answered. In this section, a brief overview of each level and the overall hierarchy will be presented. The detailed explanation of each level will be provided as subsections to this one.

The first three qualities I call, “relative qualities,” for reasons which will become apparent.

Position

The first characteristic I listed under “The Existence We Actually Live In.” was plurality, meaning reality consists of many existents. This of course contradicts all those philosophical mistakes that attempt to make existence some kind of, “single thing,” or, “unity.” We know the real world consists of an indefinite number of existents.

We know for anything to exist it must be different in some way from everything else that exists. The second Corollary of Identity as restated, says, “every existent has some quality or combination of qualities which is different from some quality or combination of qualities of all other existents.”

In our experience, there a many things that seem identical, even if there are minuscule differences we cannot detect, like precision ball bearings. If there are differences in them, it is difficult to detect them, and some things, like molecules of water, are conceived as having identical characteristics. But bearings and molecules must have some difference if there is more than one of them. There is an attribute of all things that differentiates them, and could differentiate them even if all their intrinsic qualities were identical. That attribute is a relative quality, that is, a quality arising from the relationship between existents. Every existent is different from every other existent, and even if there were no other difference, there is always the difference of position. It is what is meant by the expression, “two things cannot occupy the same space at the same time.”

I prefer to express the principle this way: no two things may have the same position. By positions, I mean the geographic or geometric relationship of existents to one another.

Position is the primary differentiating quality, because it differentiates existents even if all their other qualities are identical. It is a relative quality, because it only has meaning (and can only be identified) in relationship to other existents.

This does not imply that the quality, position, is sufficient, in itself, to identify an entity, only that, if there are entities, the only quality that is necessary to differentiate them is position. It also means every material existent has a positional quality, and that it is different from the positional quality of all other existents.

Measurements of Position

Position, like all relationships is identifiable by means of measurable qualities. Positions have two measurable qualities: direction and distance.

These two measurable qualities are sufficient to indicate the position of any entity relative to any other entity. However, for there to be a unit with which to make such measurements, there must be at least three entities (that is, three different positions).

If we label any three physical entities as A, B, and C, there are the following distance relationships, AB, BC, and AC. There are six direction relationships, however, AB, BA, BC, CB, AC, and CA.

Position is also a quality of the relationship between parts of an existent, and also essential a thing’s size and shape.

The important point for this overview is that every existent has a positional quality which defines its relationship to all other existents and differentiates it from all other existents. In our hierarchy, therefore, position is the first level of differentiation.

Motion

The second characteristic I listed under “The Existence We Actually Live In.” was dynamism, meaning reality consists of events and processes.

Since existence is dynamic and therefore must be capable of change, and since the minimum relative quality that differentiates existents is position, it is that quality, position, to which change must pertain. That, in fact, is exactly what motion is, change in position.

Measurements of Motion

Just as every existent has a positional quality relative to all other existents which is unique, every existent has motion relative to all other existents, and is differentiated from all other existents by that motion, but motion is not possible without position.

Motion is change of position A change in position means that the measurements by which a position is identified must change. Either the direction an entity is from other entities, or the distance an entity is from other entities, or both, must change for there to be motion.

Motion, like position, is identifiable by means of measurable qualities. Motion also has two measurable qualities: velocity and time.

Both velocity and time compare the change in distance or direction of entities, using some motion as a standard. In the case of velocity, it is the difference in the change of distance of the measured motion compared to the standard motion moving a fixed distance. In the case of time, it is the difference in the change of distance of the standard motion compared to the measured motion moving a fixed distance.

Since motion is “position-changing”, it has all the qualities of position, (distance and direction), and also the additional qualities of motion itself, (velocity and time). This is an important principle of ontology. Each level of differentiation adds or augments all previous levels, and includes all qualities of all previous levels.

Obviously it is motion that makes the dynamic world possible. In our hierarchy, motion is the second level of differentiation.

Acceleration

The third and fourth characteristics I listed under “The Existence We Actually Live In.” were duration and interaction.

Thus far, the qualities of position and motion, with their measurable qualities, distance, direction, velocity, and time, have accounted for the plural and dynamic characteristics of material existence. If this were all there were, however, we would have to picture existence as myriad positions, like geometric points, in constant, random, and unrelated motion. If there are to be real entities something more is needed because real entities have two characteristics that motion alone cannot account for, continuity and interaction.

Real entities have duration or continuity, they exist for some amount of time, and while aspects of them may continuously change, some aspects must remain unchanged. The aspects that must remain unchanged are those attributes or qualities which are the entities identity.

Real entities interact. If real entities had motion and continuity but did not interact, it would be as though they did not exist relative to each other. To interact, the behavior of entities must be related in some way to the behavior of other entities.

Since continuity and interaction are not possible if there is only position and motion, another level of differentiation is required to account for them. Since motion is the highest level of differentiation so far, motion must be differentiable, just as position is differentiable.

That differentiation of motion, like the differentiation of position, is again, change. A change in motion is called acceleration. A change in motion may be a change in any of its parameters, time, velocity, direction, or distance.

Both duration (continuity) and interaction are phenomena of acceleration. While the plural and dynamic nature of material existence is explained by the position and motion, acceleration explains not only duration and interaction, but virtually all other characteristics of “physical” material existents. This is not obvious or intuitive, however.

All of physics can be reduced to these three attributes, position, motion, and acceleration, including the attributes of force, mass, and energy. This is a very large subject, however, and cannot be fully addressed here.

Measurements of Acceleration

Acceleration, like position and motion, is identifiable by means of measurable qualities. Acceleration also has two measurements, one of which is rate-of-acceleration. This measurement is analogous to velocity as a measurement of motion. The other measurable quality of acceleration is mass. Mass is not usually considered a measurement of acceleration, but there can be no acceleration without mass (both because there must be a mass to be accelerated and because mass is, itself, an agent of acceleration).

Acceleration might be measured by taking a standard acceleration and comparing other accelerations to it, but the usual way of measuring acceleration is the change in the velocity for a given amount of time (which is actually a fixed distance covered by some standard motion).

Just as the measurements of position are included as measurements of motion, so the measurements of both position and motion, (direction, distance, velocity, and time), are included in measurements of acceleration. All the measurements associated with acceleration are direction, distance, velocity, time, rate-of-acceleration, and mass.

Acceleration is the third level of differentiation in the hierarchy.

Halfway There

I said that technically, the first three levels or first three primary qualities of existence were not really philosophical in nature. The description of them might very well have been done by a physicist, though it is unlikely a physicist who was not also a philosopher would understand the significance.

For this overview, there are four significant concepts to be derived from the first three levels of the hierarchy.

First, each level requires the previous level, and is possible only as a differentiation of the previous level. Second, each level includes all its own specific characteristics as well as all the characteristics of each of the previous levels. Third, no arrangement or configuration of any attributes of any level is capable of producing the characteristics of any level above it. Fourth, no characteristic or property of any level violates or changes any characteristic or property of any level below it. The significance of these four concepts will become apparent in my discussion of the next level in the hierarchy, Life.

—Reginald Firehammer (02/08/05)

Summary

1. Position is the primary differentiating quality, because it differentiates existents even if all their other qualities are identical. It is a relative quality, because it only has meaning (and can only be identified) in relationship to other existents.
2. Positions have two measurable qualities: direction and distance.
3. Since existence is dynamic and therefore must be capable of change, and since the minimum relative quality that differentiates existents is position, it is that quality, position, to which change must pertain. That, in fact, is exactly what motion is, change in position.
4. Motion also has two measurable qualities: velocity and time.
5. Acceleratin is differentiation of motion. The differentiation of motion, like the differentiation of position, is again, change. A change in motion may be a change in any of its parameters, time, velocity, direction, or distance.
6. Acceleration also has two measurable qualities: rate-of-acceleration and mass.