The first axiom of the argument is a simple one: what we understand of all phenomena, at minimum, is strictly an observation of space. It is the one universal axiom which exists as the limits that give structural boundaries to reality. In a separate and simultaneous respect, it is absent of the very same definition as no-limit. Space observes a dualistic nature of limit and no-limit.
Observing the definition of space, within any given dictionary source, one is placed into a paradox. A whole host of definitions are given, which include but are not limited to: “area” “volume”, “dimension”, and “limit” (Space, 2018) (Space, 2018) These definitions, summated under the last definition as “limit”, reflect back upon the process of definition as a form of limit in itself by which a phenomena exists through the inherent limits which form it. Space as limit is limit through space, with the observation of any dictionary definition resulting in a dualistic circular and linear form of reasoning where one definition leads to another while simultaneously circling back to the original. Under these terms circular rational is justified through inherent linear elements and vice versa while observing, under certain degrees, Mirimanoff’s concept of “wellfoundedness” in which the definition as a set of information contains no infinite descension (Levy, (2002)(1986),(1988)) further implying an original source. This dualism of progressive linear and circular definition provides a limit in itself through a process of mirroring in which the further corresponding definitions in turn follow this same process.
The axiom of space follows this definition process in which a limit reflects itself through a further limit, rationally in both form and function as circular, and reflects further limits, rationally in both form and function as linear, in which an observation of no-limit occurs. This observation of “no-limit” is founded inherent within the dictionary definitions of space in an immediate respect within the aforementioned definition itself (Space, 2018). In a separate respect, function follows form where these definitions reflect through further definition ad-infinitum in a dual circular and linear regressive/progressive manner. Limit and No-Limit are dependent on a dual form of circular and linear reasoning that simultaneously manifests further definition while maintaining there own under spatial terms.
This dualistic understanding of space can further be observed in many of the works of the pre-socratic including but not limited to the Pythagoreans and Anaximander. The Pythagorean Philolaus observed “that all things in the universe result from a combination of the unlimited and the limiting; for if all things had been unlimited, nothing could have been the object of cognizance.” (Smith, 1870) Aristotle observed “[the Pythagoreans] plainly say that when the one had been constructed, whether out of planes or of surface or of seed or of elements which they cannot express, immediately the nearest part of the unlimited began to be drawn in and limited by the limit.” (Smith, 1870) He further implied that the Pythagorean teaching of the limit and no-limit were direct results of the philosopher Anaximander who argued “(that which is) unlimited”, “boundless”, “infinite”, or “indefinite” as “Apeiron” (Liddell & Scott) and “peras” as “end, limit, boundary”. (Liddell & Scott)
Modern philosophical instinct and training implies the definition of space as limit and no-limit in dual linear and circular terms questionable considering one is presented with two perspectives: They are an empirical contradiction (Horn, 1989) (Smiley, (1993)) or a transcendental paradox (Smith W. K., 2011) (Zhang, 2015) (Bowen, 2016) in the respect that logic either nullifies itself or transcends pasts its origins. (quote) Neither school of thought gives any real justification as they manifest a dualism in which one perspective attempts to wrestle over the other, resulting in a Neitschian view of force embodied as “perspectivism” (Neitzche), Pythagorean definition where duality is conduce to change (Kahn), or the problem of Wittgenstein where “[a]ll the propositions of logic are generalizations of tautologies and all generalizations of tautologies are generalizations of logic. There are no other logical propositions.” (McGuinness, 2008)
Paradoxically, the western empirical linearism and eastern transcendental circular forms of logic, both need eachother as one exists as the “limit” which defines the other. The western laws of logic observe the “fallacy of circularity” (Dowden, 27 March 2003) as a justification for linearism. The eastern views observe the deficiencies of individuative linearism promote holistic circularity. (Biao, (JULY - AUGUST 2002)) (I Ching) In a separate respect both observe a nature of “no-limit” through western regressive and progressive rationality dependent to a degree on infinitism (Klein & Turri) (Klein, "Human Knowledge and the Infinite Regress of Reasons", 1999) and eastern circularity dependent on holisitic centering and rotation as absent of limit. (Biao, (JULY - AUGUST 2002)) (Ma, June 5, 2009)
The problem occurs in the respect that we are constantly limited to dualisms, and the problems of logic and definition are reduced to ones of dimension. These dualisms create a problem of definition dependent upon polarity, observed in the hermetic philosophy as the “Principle of Polarity” (Atikinson, 1912). One polarity defines the other while simultaneously causing a perpetual sense of definition between the two. Polarity can be viewed as a contradiction of force under the Nietzschean metaphors of Apollo and Dionysus (Neitzche F. , 1872), an absence of structure as the Pythagorean Dyad (Kahn), and an alternation of definition through the hermetic “Principle of Frequency” (Atikinson, 1912). Or it may simply just be observed as a problem in the same manner of Cartesian Dualism (Robinson) and Platonic Dualism (Robinson) leading to the competing substance, property, and predicate dualistic perspectives (Robinson) that provides for the universal means of division in philosophy between materialism and idealism (Priest, 1991) (Novack, 1979).
A third more rational approach must be taken in order to deal with the multiple dualisms inherent through the limit and no-limit definitive nature of space in both form and function, quantity and quality, circularity and linearism, and western empirical and eastern transcendental logic. Without a solution to these reoccurring duals a process of fracturing takes place in which each definition is dependent on an infinite linear regression, circular justification or simply an acceptance of the axioms without any observable definition, all of which are observed in the Munchausen Trilemma (Albert, 1968).
This fracturing can be implied as a form of logistic Atomism, observed by the more modern philosophers Russel, Wittgenstein and Carnap (Carnap, (1934)) and stemming from the pre-Socratic philosophers Leucippus and Democritus of Abdera (Seyffert, (1894)), in which the linear regressive separation, circular definition, and axioms can be observed as individual units in themselves that must relate through a process of continual change. Hence it may be implied that dualisms are dependent on relativistic logistic unit-particles that exist through continual individuation as a form of definition.
The problem occurs in the respect that the very problem of definition we seek to avoid, change, appears to be one of the very foundations for this very act of definition. We can simply observe this as relativity merely being individuative limits and no-limits that exist as spatial dimensions of change as unit-particulate. This provides the foundation for not only materialistic change as a refutation of idealism observed by Kant (Kant, Archived 6 February 2007) (Kant, Critique of Pure Reason (NKS translation)) , further evidenced by physics dependence on Principle of Locality in the Principle of Relativity (Salençon & Lyle, 2001), but further change in abstract logistic structures such as moral relativism (Swoyer, 2003), truth and cultural relativism (Baghramian), methodological relativism (Collins, 1998), relationalism (Baghramian M. , 2004) and dialectic materialism (Thomas, 2008). However, the observation of change as a constant, through logisitic unit-particulate, observes a consistency. This can be summated into a paradox or contradiction, however considering these dimensions exist in themselves as foundations of the argument from which both side gains definition, this further results in another dualism. In this instance it is an observation of change and no-change. The problem is further exacerbated by the number of aforementioned dualities premised in spatial limit and no-limit.
The solution to the dualism lies within the axiom of the problem: our understanding of phenomena is often times one of quantitative and qualitative spatial dimension, in this case a dualism. In turn this Dualism results in a third dimension, as one dimension in itself, which maintains the dualism while simultaneously justifying it and providing logical grounds through a medial center point conducive to origin.