Theory of Nested Concepts and the Model

Let us start with the Theory of Concepts (TC) of Objectivism. It is basically the following: sensations make up perceptions make up conceptions make up sensations, etc.

The whole undifferentiated concept of the theory consists of three differentiations:

1. concept of sensation (S),
2. concept of perception (P),
3. concept of conception (C).

We have the following formula:

concept of (TC) = concept of (S + P + C)

This is a crucial step in order to differentiate sense data like colors from concepts of colors.

C (TC) = C (S + P + C)

TC = S + P + C

The simplified formula of the theory does not change. The general tendency in practicing the formula (as Objectivists use it) is going more toward conception, but the unnecessary imbalance of the differentiations has already been removed. So, this invariance can be displayed by our TC formula base, where each element is taking exactly 1/3 of the whole.

Our TC formula base:

1 = S + P + C

This unity does not change, but if we make the “1” a variable, we can allow expansion into a dynamic model of everything, such as the seventeen levels of the following Model (see the illustration for the logic involved):

***IMPORTANT: elements of this Model may change, may be corrected and updated, and new ones may be added[1]***

Holographic circles of contracting part and expanding whole of contrasting concentrations converge in the middle, in the critical points of the dialectical continua of the Model.

Call a critical point on the Model (M) an undifferentiated concept Csub(n). Then we have:

Csub(n) = x sub(Csub(an) + Csub(bn)) = x sub(Csub(n(a+b))),

where x is “a concentration,”

a – “a left ‘part’ of M,”

b – “a right ‘whole’ of M,”

n – level, n >= 1.

The index summation does not follow mathematical laws since it is a summation of concept-empty entities. The undifferentiated concept of level n is Csub(n), and it is equal to the conceptual level of Msub(n) when no concepts are differentiated. Thus, we have:

Msub(n) = Ssub(n(a+b)) + Psub(n(a+b)) + Csub(n(a+b)) = (S + P + C)sub(n(a+b))

The formula for Csub(n) is substituted for Msub(n), and we get what is equivalent with the base formula of Objectivism except transferred to Msub(n):

x sub(C(n(a+b))) = (S+P+C)sub(n(a+b))

If n > 1 > |x|, then n = n – 1;

If |x| > 1 and n < 17, then n = n + 1;

If |x| > 1 and n = 17, then Msub(n) = M.

Levels decrease if the modal value of x, ignoring the qualitative signs, is less than the complete concentration of 100%. This is called fragmentation. Levels increase if the concentration is greater than 100%. This is called integration. Going beyond the last level produces the entire Model (M) which will be:

M = sum(n=1, 17, Msub(n)) = sum(n=1, 17, x sub(Csub(n(a+b)))) =

= sum(n=1, 17, (S+P+C)sub(n(a+b)))

This means that various unequal quantities of sensations, perceptions, and conceptions can be found on every level of the Model, but in the Model as a whole, also known as APEIRON, they are present equally. The new absolute unity becomes APEIRON where individual proportions can still be found (incompletely) in varying quantities. Epistemologically, one cannot go outside APEIRON, but can only be somewhere inside.

Thus metaepistemologically formalized, levels 1, 9, and 17 closely correlate with (the now metacategories) Sensation, Perception, and Conception, respectively, the center of the Model being our immediate reality as well as the product of the unchanging APEIRON.[2] Although the Model consists of epistemological entities, it refers to actual (ontological) entities that can be found by the means of the Model.[3]

In summary, from the Theory of Concepts (TC) to Theory of Nested Concepts (TNC), the new formula base replaces ‘1’ with the variable ‘x’ without losing completeness.

The TNC formula base:

x = S + P + C

With the epistemological formula providing the approach to crucial integrations, following discussions will explain the elements of the Model in greater detail.

[1] All corrections and additions to the Model are based on arguments passed by consensus that depend on magnifications and extensions of knowledge.

[2] As we will see later, the center ought to be our immediate reality, but at the time it isn’t. This divergence shall be known as the problem of our immediate reality.

[3] The use of the word “epistemology” in any context on this site implies onto-epistemology, since the physical and mental aspects are hereby inseparable while distinct.