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The Nature Of The Axiom As Reflective, Relative And Synthetic Space


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Philosopher's have long sought for a unifying metaphysics from which to establish a balanced understanding of not only the universe but themselves and their immediate surroundings. What we observe today with philosophy, and by extension the sciences and religions, is a continually fracturing quality where a philosophy/science/religion inevitably seem to reproduce various perspectives that mimic or reflect their previous parents.

It is in this effort to establish not only a unity, but an understanding of unity itself, that the nature of these fields of observation seem to follow a very difficult if not impossible course of action. Philosophies establish more philosophies, sciences with more sciences, religions with more religions...and the process of divergence seems to go on into a vortex whose end point, if there is any, lies more at the bottom of an abyss of materialistic flux rather than at the apex of what we deem as deep spiritual truth.

Where is unity to be found? Is their any to begin with? The answer seems to be the point, in a quite literal manner. What we understand of reality fundamentally breaks down to one irreducible axiom breaks down to a form of geometry and nothing more...nothing less.

All philosophy is founded upon the axiom, as point of self evidence whose dual nature of subjectivity and objectivity (under the "self" and "evidence") maintains a dualistic structure of continuous flux. "Truth is strictly subjective" turns itself into a statement of objectivity. "Truth is strictly objective" lends itself to a subjective understanding. Between this subjective and objective nature of the axiom we observe a continual flux between two natures, strictly because of its dualistic structure for a dualism is nothing more than an a form of opposition with that opposition erupting into a continual flux.

The synthesis of this subjective and objective nature of the axiom results in nothing more than geometric space under the guise of the "point". All subjective truth is found in and stems from the "point", along with all objective truth. It is this nature of the axiom as a point, which seems to have eluded philosophers due to its simultaneous simplicity and profundity as evidenced within the nature of its cousins the circle and sphere.

In simpler terms all axioms breakdown to a point. An observation, built upon this point, manifests structure by its reflection, relation, and synthesis of other points. It is this reflection, relation, and synthesis of axioms that in turn not only form other axioms but the very foundations of language and logic (and by extension reality) as we know it.

a) A point as a unified median, fundamentally reflects upon itself to maintain itself as a structure. It is in this self-reflection that a second point is made as an approximate of the first. In this respect that point is a causal element and the second point is an effectual element. This effectual element is fundamentally an approximate of the first point and in this respect shares the same cause nature.

b) However, due to its approximate nature to the first point it in itself is not the first point and not completely a unified. This approximate nature, as a deficiency in unity is akin to "randomness" as a "deficiency". The point as a self-reflective entity in this respect shares a dual role as a causal element and a random element through its nature as reflection. Reflection and the point are synonymous for reflection maintains the points as a unified entity with this unity equivalent in both form and function to stability or "abstraction".

c) It is from this nature of the point as a dimension of Reflection, from which we can observe Reflection as a dimension reflecting upon itself to maintain itself with its approximate as Relativity. The point becomes "deficient" in unity through the nature of gradation with this gradation of the point manifesting itself in both quantity and quality. These gradient points are fractals or particles which in turn are form of further particles. We observe this in material.

d)These particles, as deficient in unity, are subject to flux with this flux being evident in the needed relations of particles in order to exist. A particle relates to another particle other wise it does not exist. As the relation of a particle to another particle produces another particle a flux ensues with the continued relations of particles in many respects manifesting further relations, with further relations manifesting further particles. In this respect the particle has a dual nature of "potential relationships/particles" which define it. Relativity as a dimension of flux within and of itself manifests through a dual nature of actual and potential particles.

e)To step back further, what we understand of logic breaks down to a duality of Reflection (as stability/abstraction) and Relativity (as flux/physicality) which both are points within themselves. With Reflection being caused and Relativity as uncaused (for a deficiency in symmetry as flux is a deficiency in structure as causality) we observe dual dimension whose polarity is at odds and prevents and form of stability. A third dimension or point is introduced as Synthesis.

f) Reflection and Relativity, as points synthesis through a third point as themselves, each other, and the aforementioned point of synthesis that allows all logic and symmetric to maintain a triadic structure. This triadic structure, as the point itself, allows the point to:

1) maintain a dual role of stability and flux through the synthesis of dimensional limits.
2) maintain a dual role of stability and flux through the synthesis of possible dimensions limits.
3) This nature of dimensional limits, or the limit to space, is observed in the curvature of the circle or sphere while its possible dimensional limits are observe as the center point. We can observe this in Pi.

From this nature of Reflection, Relation, and Synthesis we can observe briefly that all logic and observed symmetry is fundamentally 3 dimensional as a point within a point within a point and in this respects allows logic to maintain dual structure of linearism through circularity and circularity through linearism whose apex is in the axiom. It is in these respect that the study of philosophy is fundamentally the study of spatial structure or geometry and what we observe as "reason" best reflects through "rationality" as the "ratio".

From these respects, as observed through the nature of the axiom, philosophy must recommit its course to the understanding of reality through the perspective of the point (as 1 dimension and reflective) the circle (as 2 dimensional and relative) and the sphere (as 3 dimensional and synthetic) as 1 dimension in 3 and 3 in 1.

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