Relationalism and Holism can be observed as duals similar to the principle: "That which is Below corresponds to that which is Above, and that which is Above corresponds to that which is Below, to accomplish the miracle of the One Thing" (Scully). The “one” being Compositism as a median of the Macrocosm/Holism and the microcosm/Relationalism as the “axiom”.

All logistic duals can be implied as having a "rotary" element, with this "rotation" enabling a degree of further symmetry and stability. The axis of this duality, in turn manifests as the "density of information" inherent within the logistic. This implication of "rotation" within all logistics duals, further implies a necessary degree of flux within logistics with a simultaneously stable axis that grounds them.

Generally, duality is a set of 2 systems, abstract or physical which share a non-trivial degree of equality or are a dual observation of the same phenomenon (Zwiebach) However, it may be argued that regardless of the degree of equality between duals, the observation of a duality observes a minute degree of difference within these natures, where the equivalency may hold true in the same way that 1 = .9999999....∞.

Hegel’s thesis, antithesis, and synthesis (Solomon)[2] was termed by Johann Fichte (Breazeale) and is summarized as such: (1) a beginning proposition called a thesis, (2) a negation of that thesis called the antithesis, and (3) a synthesis whereby the two conflicting ideas are reconciled to form a new proposition. (Hx) The origin of thesis and antithesis originated with Kant, according to Thomas McFarland, however the question allowing for this triad was originally posed by Fichte (Coleridge): “Are synthetic judgments a priori possible?

No synthesis is possible without a preceding antithesis. As little as antithesis without synthesis, or synthesis without antithesis, is possible; just as little possible are both without thesis”. From this question Fichte observed "thesis–antithesis–synthesis" (Ritter) for the first time (Williams) as "The action here described is simultaneously thetic, antithetic, and synthetic." (Fichte and Breazeale)

Consider all logistics contain Holistic and Relative elements, all logistics contain positive and negative elements and therefore do not have to have a nature of “ism” in order to synthesize.

Hegelian synthesis can further be extended to Thesis, Antithesis, Synthesis, Probable Thesis and Antithesis, Potential Thesis and Antithesis, Thesis dimensional form, and Possible Thesis dimensional form. It is in this respect that Logisitical "isms" may have 7 or 9 dimensions, dependent upon interpretation. Synthesis, Holism, and Relationalism can be observed dimensionally as 3 in 1 and 1 in 3.

Further similarities may be implied between Holism, Relationalism, and Compositism through Plato. The surviving works of Plato do not contain any set of form logics (Kneale) however they offer three important questions fundamental in all fields of logic.

What is it that can properly be called true or false (Theaetetus)? Holism as existence and non-existence of structure.

What is the nature of the connection between the assumptions of a valid argument and its conclusion (Kneale)? Relationalism as relations of logistic particles and quantums.

What is the nature of definition (Kneale)? Compositism as the synthesis of logistic axioms as boundaries akin to symbols.

While there may be infinite number of axioms, implying infinite degrees of truth, it does not necessarily mean all axioms are equal in “truth”, they are equal in existence as a degree of truth. Implied false axioms, or contradictions in logic, still contain degrees of truth however the construction of these logistic determines their validity by their stability. Axioms maintain this same structure as degrees of truth regardless of whether they are “real” or “possible”.

In a simultaneous respect, a subjective logic is possible, as a synthesis of Nietzsche’s Perspectivism, which claims "that no evaluation of objectivity can transcend cultural formations or subjective designations (Mautner)". A paradox occurs as what is perceived objectively determines cultural formations and subjective designations in a simultaneous and different respect. The subjectivity of the axioms, through the "self", reflects and relates to the "objectivity" of axioms as "evidence". It is in this respect that the "axiom" as "self-evidence" is a synthesis of "the subjective self" and "objective proportions of space" as an irreducible "synthesis as cause".

It can be further argued that "rules (i.e., those of philosophy, the scientific method, etc.) are constantly reassessed according to the circumstances of individual perspectives (Schacht)" as subjectivity is a continual flux through "Relationalism". In a separate respect these “rules” simultaneously manifest a stability through the "limits of belief" as a logistics dimension. It is this flux and stability of the axiom through “rules” that is imaged fully through the “symbol”. The formulation of logistic and mathematical symbols can simultaneously be argued as an inherent subjective nature of Logic and mathematics, however the derivation of Wittgenstein’s “meaning as usefulness" (Rayner)

It can comfortably be assumed that Axioms are the synthesis of symbols and in this respect, all logic has an informal element of art. However, art as an expression of truth is art as objectivity. The axiom as the symbol can be observed across many branches and disciplines of “observation” and can be observed as the median point between representation and reality. As a median point, the symbol and the axiom manifest a form of abstract/physical equilibrium. This importance of the symbol and the axiom can be further observed in mathematics. Haskell Curry argued that mathematics is at its core a disciplined system of symbols whose forms and function manifest further formula as "the science of formal systems". (Curry) Much can be inferred from this observation as these symbols were developed by Leonhard Euler in the 16th century (Mx) where before mathematics was simply an extension of common language (Kline).

As a “the science that draws necessary conclusions” (Peirce) a continuation on the importance of axiomatic symbolism was observed through Russell’s definition of “All Mathematics is Symbolic Logic” (The Principles of Mathematics). It can be inferred that the importance of axiomatic symbols stems back to the Pythagorean emphasis on the importance of form over matter (Stumpf)and that this emphasis on form may connect the mathematical Logicist’s position to the symmetrical, but not agreeable, perspective of the Mathematical Intuitionist whose view is that" Mathematics is the mental activity which consists in carrying out constructs one after the other" (Snapper) or the formalist perspective of a "the science of formal systems [symbols]". (Curry, Outlines of a Formalist Philosophy of Mathematics.)

This observation of axioms as the synthesis of symbols can be further extended to metaphors. Metaphors can be observed as logistic equations, equivalent to complex calculations where natural objects, and their implied universal forms may be equivalent to "logistic symbols" as inherent logistic equations of their own. For example: "It is easier for a camel to pass through the eye of a needle, than for a rich man to go to heaven." equates to an equation of spatial reflection, relativity, and synthesis through the "angles" of "camel" "eye of needle" "rich man" "heaven". Metaphors, much like the objects that they contain, manifest geometric dimension. A question could be made from the angle of the Pythagoreans: If all is number, then why not metaphors also?

While this nature of untestable axiomatic symbolism in mathematics may not permit it to be considered as science according to some, such as Karl Popper (Shasha and Lazere) the objective uses for it (economic, scientific, philosophical, etc.) argue for its objective nature as truth. Disciplines, such as physics and it’s corresponding String Theory, further propagate mathematical discovery as a necessity for advancement (Johnson and Lapidus) as these disciplines, including the aforementioned physics, require at its core a study of symmetry (Anderson) as a synthesis of axiomatic symbols. Logic can be further argued as the universal study of symmetry as a sort of transcendentalism. However, this symmetry does not have to be limited to any practical or objective purposes as certain disciplines, such as algebraic operations (Essai de dialectique rationelle), do not have to be completely understood to be observed. The axiomatic nature of symbols allows for the approximation of knowledge.

Arguments and perspectives are fundamentally the manifestation of axioms as ratios. It is the axiom as a ratio and the dual ratio as the axiom, which further manifests at the macro level as the argument or perspective of which they become complex axioms in themselves as self-reflective structures. These axiom/ratios further manifests at the micro level as individual words, letters, syllables etc which in turn become complex axioms as the relation between logistic particles. It is this duality with the axiom as a flux between “the macro” and “the micro” which in many respects gives it many similarities to the particle-wave of physics. It is this similarity of natures that’s simultaneously points to the axiom as a “paradox” of logic. Yet this “paradox” observes the values of “truth” and “falsity” so to rush to judgement and make the statement that the paradox is a “problem” would be equivalent to arguing the “point” is a problem in geometry. Yet the truths of geometry and the axioms, regardless of the perceived “depth” maintain themselves through their continual reflections, relations, and synthesis.

As ratios within mathematics observe how many times the second number fits in the first, multiplication and division are the fundamental operations that manifest ratios. It is in this respect that the propagation of axioms, as multiplication, is a form of operational stability while the divergence of axiom, as division is a form of operational flux.. Arguably the simplicity of the axiom is observing it for what it is: an axiom a point of creation, destruction, and neutrality.

In these respects the axiom, through the symbol, takes on a similar nature to an "uncaused cause". It can be argued as similar to the Greek Logos, where the symbol begins fundamentally as the point.

Logistic calculus must observe necessary geometric proportions as intuitive, through the collective consciousness of man or the individual, as we refer to logistics and perspectives as linear or circular, through "points" and "angles, and the ability to "curve" them. The intersection of new and/or old perspectives manifests from intersections from which further perspectives and arguments are formed.

Russel argued that “you can get down in theory, if not in practice, to ultimate simples, out of which the world is built, and that those simples have a kind of reality not belonging to anything else” (Russell, Excursus into Metaphysics: What There Is)

The continual synthesis of axioms, points to a necessary element of continuity within simplicity. In simpler terms, simplicity is continuity. With the enumerable synthesis of axioms, there may in fact may be no solution to certain problems as evidenced by this very possibility of enumerable axioms. Furthermore Godel’s incompleteness theorems observe that not all things, most specifically arithmetic, can be both consistent and complete (Hamilton) and can be further observed in the Mathematic Subject Classification containing hundreds of specializations within mathematics. (Mathematics Subject Classification 2010) This “lack of completeness” through the axiom, extending throughout logic and mathematics can be inferred as a reverse problem of practicality where completeness is only practical if it is axiomatic that it is. Where pure mathematics [and logic], have been found by Eugene Wigner to have practical applications (Wigner), Wittgenstein’s “meaning as use” (Rayner) implies practicality as synonymous to the synthesis of axioms. It is in this respect that the “incompleteness” of mathematics/logic is practical as an axiom if an only if it moves mathematics towards a symmetry as propagation. It may be inferred from this the number of mathematics/logic may be infinite and if so implies an infinite degree of “meaning” through “use”. In simpler terms, the propagation of mathematics is the propagation of stability as an infinity synthesis of symmetry.

Contradiction as a deficiency in structure, implies a movement towards order, so a logistic system which ends in contradiction does not necessary mean the system is false but rather that it is in a state of flux and this relates, but is not equal to, Graham Priests observation that there are true contradictions (Priest). Inconsistency also implies a necessary degree of "fuzzy" logic as approximation and a degree of relativity as what is "inconsistent" or "asymmetrical" at one point may not be at another point.

The axiom can be observed as the height of paradox, and in this respect, points to the necessity of paradox within all logistic forms and functions. It may be implied that no geometric structure can be composed without the line or the circle (or a degree of it) at the macro level, and as points and angles at the quantum level, so no logistic structure can exist without the paradox.

It can be accurately argued that paradoxes are logistic singularities of positive or negative values corresponding to logistic progression or regression. With the nature of the paradox being inevitable within philosophy, the job of the logician is to address any known paradox and deduce further knowledge from it until the paradox is either eliminated or a separate paradox or set of paradoxes is derived from it allowing the paradoxes to manifest a symmetry between each other which in this case allows a certain logistic geometry to be formed. In this respect paradoxes can be observed as “points” or observations, equivalent in both form and function to the axiom.

## Relationalism and Holism as Syntheticism

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