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Proto-Identity as Emergence
Here is a symbolic argument:
There is a point, it is indistinct as there is only a point: ●
The point repeats and becomes distinct by the act of repetition creating contrast: ●●
The contrasting points are effective one point as many as the set is now a unified entity as a relation: (●●)●
The one point as many, is still one point thus repeats again creating scale: (●●)●●
This process repeats and as it repeats so does scale repeat: (((●●)●●)●●)
One scale exists relative to another thus contrast occurs by difference (●●●)(●●);
however one scale (●●●) contains the other scale (●●) as condensed where the difference is (●);
Further, one scale (●●) generates another (●●●) as expanded where the difference is (●);
The difference of ●, across expansion and condensation, reveals ● as the limit of the distinction itself as both that appears in accords to angle of another scale: ((●●●)(●●))(●●●●●)
● exists across scale as the limit of the scale by its own repetition;
the repetition of ● is the distinction of the point as the scale as the self reference results in self contrast and the self contrast results in structure as scale.
the repetition of ●● is the distinction of scales as the point as self-reference results in self-containment and the self containment results emergence of scale.
Scale is identity as context or condition as the boundaries by which identity is derived reflexively: the contained identified by what it is contained by, the container identified by what it contains.
The distinction of a thing is its repetition, its repetition is self contrast, its self contrast is self containment, its self containment is its emergence as identity.
Identity is purely emergence, the foundational identity is a single point as all limits, intuitively or observationally, are both reduced to (a) point(s), converge to (a) point(s), or build to (a) point(s). In these respects a single point becomes transcendental symbolism of ontological realities, as the progressive emergence of ● results in corresponding limits that are moved beyond without negation of origin (evidenced by the symbolic formalism).
Distinction is repetition by self contrast that inversely results in the whole of the relation as self-contained, as the self-contrast is a self repetition unto condition, thus identity is derivative of itself as process as identity becomes a scale of process(es) with the scale being a relative meta-scale for another scale.
The identity of ●● is derivative of both the identity of ● and the identity of ●●● as:
●● contains ●●● as both ● (the foundation of ●●●) and (●●●)(●●●) {as ●●● is reducible to ● from another scale}.
●● contrasts to ●●● as both ● is the difference and ●●● is reducible to the contrast of (●●)(●●)(●●) {as ●● is reducible to ● from another scale}
Identity is the limit of process in accord to the scale(s) external and internal of said process thus effectively is emergence by degree.
Emergence is process, process is scale, scale is identity; the identity of this assertion is the ratio of the applied meanings in natural language by means of symbols, the proto-logical symbol of language is ● as ● is the most primitive symbol of beginning, conclusion, unification and divergence, summarized fully as transitional, in accords to context of use.
The next degree of this emergence is the basic protological symbol of the line segment which emerges from ●●
There is a line segment.
The line segment is composed of infinite line segments, which in turn are composed of infinite line segments;
The line segment composes infinite line segments, with each line segment composed infinite line segments.
The level of division of the line segment retains the division as the line segment itself across scale as the line segment being the degree by which the line segments are divided as line segments.
Division requires that which divides, the limit of division is that which divides thus resulting in division as self-scaling of what is dividing within the context of that which is divided.
Division as self scaling inversely result in magnification of what is dividing for a line segment X which contains line segments Y is effectively Y repeated multiplicatively as the whole line segment X as scale.
Division and multiplication are inverses, these inverses are fractal states unfolding by degree of compression (division) and expansion (multiplication).
What remains is scale invariance as the fixed point of division or multiplication resulting in scales; a line segment as two line segments is the one as a ratio of itself, two line segments as one line segment is the two as the ratio itself.
This scale invariance results in compounding of dimensions as the line segment is 1 dimensional by nature. The inversion of one line segment results in a horizon and vertice, the inversion of horizon and vertice results in depth, so on an so forth as dimensions occur holographically as each dimension is but the scale invariance of one that occurs recursively, the inversion of dimensions is but the inherent contrast induced by recursion as argued prior.
The nature of material phenomena becomes that of recursive scales that correspondingly results in a particle/wave duality as relative scales of the other, recursive by degree of structure (a particle repeating across space, a wave as repetition through alternation) with the field be holographic dimension of the two.
Number occurs as the distinction of space, in use obviously, but as structure as well where the recursion of points is the recursion of number, the recursion of number resulting in the dualisms of addition and subtraction (where positive and negative are but embedded addition and substraction, the recursion of addition/subtraction as multiplication/ division, the recursion of multiplication/ division as exponents/roots.
Unifying the results is in that act of awareness itself as awareness is observed as nothing, and indistinct point, when observed, and the objects of awareness are the scales by which awareness is imprinted and contain through said scales in a manner that further loops the dynamic between subject and object.
