The Model is the relationship between Nonexistence and Existence. Without the two, the Model would seem like a bunch of words scrambled together that have no relations or connections. Nonexistence (the “time” fragment of absolute nothing) is an implicit concept along with Existence (the ultimate superset, or absolute everything). Here is a way to conceptualize it in three operative steps.
The first operation: the concept of Nonexistence
Follow the formula: Y ≡ X & X, where Y is Nonexistence and X is Existence. Y ≡ X & X becomes:
Nonexistence is Existence and Existence
Nonexistence is Existence and itself
Since there is no second Existence, the Conceptual Common Denominator is the relationship of Existence to itself, so we take Existence to mean the causal action directed at itself, and we get:
Nonexistence is Existence exists
How can we interpret this? I interpret it that the fact that “Existence exists” outside of time is itself enough proof that it is also Nonexistence (the time aspect of it). Here is how you can visualize it:
Imagine standing at a spot and cannot move anywhere else since there is no other place. Sure, you can stretch and extend yourself somewhat, but you still can’t move no matter how hard you try. But imagine that you did move. If you were to virtually move away from the spot where you are standing, you will find nothing there–nothing at the spot where you “just stood”! Of course, you would not be there, if you weren’t there. So, where you are standing is the spacetime that is inseparable from you while you are in it or it is in you. And if you are everything, then the only remainder that constrains you is nothing. You move in time and yet you are timeless. Time is within you, and you can reach it by overcoming yourself and yet becoming your greater new self, the inner self that has always been you. The boundaries of Nonexistence and Existence now are known to match. You are one and the same, always have been and always will be.
I mentioned earlier that the context in this case will become the content (and vice versa), since there is nothing beyond Existence (literally). This means that Nonexistence can only be within Existence or wholly be itself Nonexistence, since we cannot differentiate when exactly this Nonexistence is (i.e., everywhen). Existence is everywhere, and Nonexistence is everywhen. With the help of the formula and the illustrative scenario, we have to conclude that they are the same. However, what we have forgotten is that we have just formed a new concept, which is not mere Existence or Existence exists. I call this concept APEIRON.
The second operation: relating the concept of Nonexistence
To comprehend APEIRON, we have to first really comprehend Nonexistence (since you already comprehend Existence by itself sufficiently, I think). In order to understand how Nonexistence is a true concept (even though it’s cyclic and somewhat meaningless), we need to look at the right, contextual side of the Model (notice that these are also all spacetimes, but they are specific and relative to specific existents). The concepts I am referring to are, in sequence and with some additional information in parentheses: (vacuum) Energy, (atomic) Field, (crystal) Lattice, Cytoplasm, (cellular) Matrix, (bio) Pulse, (bio-field) Aura, Environment, Nature, World, (solar) System, Nebula, Cluster, Cosmos, (universal) Plenum, Ratium, Limits, and (metaphysical) Nonexistence.
I suppose that the two concepts to help you at least visually comprehend the conceptual nature of Nonexistence are: Energy and Plenum. I want to stress that these are neither Nonexistence nor are they the most related concepts to it. In fact, these are merely two out of 17 contextual concepts that relate Nonexistence to Existence through the internal dynamic. I picked them for an illustration in hopes that they will suffice.
The third operation: epistemological integration
For simplicity, I will drop the concept of time from spacetime and will only concentrate on space. I want you to see how Energy and Plenum are differentiated. Energy is the context of Particle. Virtual particles and bosons, such as photons, interact with or through Energy. The context of Energy is limited to Particle(s). It is a part of Plenum on the subatomic scale. Now, expand the space in your mind and see how Plenum is the space of Cosmos, which had a source in Plenum. Although both of the concepts–Energy and Plenum–are analogous in basic terms of content, they are vastly different in terms of space. That’s because they are relational concepts. Energy relates particles, and Plenum relates universes (imagine that there are many). Now think of all universes that existed, exist, or will ever exist. In such an expansive context, we analogously have absolute everything around and outside of Nonexistence.
To summarize the three operations
The concepts of the Model on the left side refer to existents that exist in contextual spacetime, which is formulated by the concepts on the right side of the Model. The left and the right sides are both summed in Existence, but overall they are related by coming from Nonexistence. The right side concepts help in integrating with the left side concepts to end up, with the ultimate integration, in APEIRON. Now you see how spacetime is also a “part” of absolute everything even though spacetime is not a “thing.”
Going on to APEIRON
I have shown the conceptual nature of APEIRON along with the nonlinear formulas, but I have not shown how it could be viewed logically. An issue happens when you linearize the formulas incorrectly. We know the two-valued logic, but here we are dealing with the infinity-valued logic. In other words, it is a logic that has infinitely many logical values (and what I mean by infinite is not merely unbounded but a true mathematical infinity). Either all of them are true and it’s the absolute truth and objectivity, or all of them are false and it’s the absolute relativity and subjectivity. Since you have already seen the conceptual grounds of my Model and how all concepts relate contextually, I would rather keep you in the first than have you fall off at the second. Before we go on, let me have a purview of Objectivist logic.
Ayn Rand wrote in ITOE (1990, p. 120): “whether it is concepts of outside existents or of one’s own consciousness, the concepts always refer to some facts which one is conceptualizing, and never to one’s method or process.” The “method or process” is the two-valued logic with its main law – “A is A.” Reaching the fact of Existence or, more so, “Existence exists” with this logic shows how potent this method is. Although there are many black holes and other various singularities that may be ignored (or even created) along the way, you indeed reach this end, and the means justify it. Kudos to the genius and perseverance of Ayn Rand in creating such a beautiful integrative whole, the trinity of Existence, Identity, and Consciousness! Yet, I have also shown that you can go beyond Existence and without merely repeating it an infinite amount of times (Existence exists, exists, exists, etc.). However, for the new feat, you need another, more complex logic.
Let us return to the formula then. In the infinity-valued logic, it can be viewed in the following two ways:
- Existence is infinitely and eternally the same as Nonexistence. To linearize this properly into the two-valued logic, we will have: A is A. Remember that this is APEIRON, and that you cannot see the two sides (as boundaries) around it. They are absolutely the same when you are looking at APEIRON from outside of APEIRON. APEIRON never changes and is ever perfect.
- Existence is infinitely and eternally distinct from Nonexistence. To linearize this properly into the two-valued logic, we will have: A is not non-A. This is when you look inside APEIRON, that is, when you look specifically in the Model. All you see then are various absolute differences that can be changed or corrected if needed.
To summarize fully at last
What we have done is linearize the nonlinear, infinity-valued formula of APEIRON to show how concepts are related “of” the Model and in the Model. Then, APEIRON can be defined in any one of three ways.
- “Definition through integration”: absolute everything and absolute nothing, as metaphysical Existence and Nonexistence, integrated in the center of the Model;
- “Definition through wholeness”: integration of the last level of the Model (all the concepts in it);
- “Definition through epistemology”: the final formula in Theory of Nested Concepts that describes the Model.