Hegel’s thesis, antithesis, and synthesis (Solomon) 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”. (quote) 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)

For the Pythagoreans "The triad represents the number three. It is the first born and the eldest number. The equilateral triangle serves as its geometric representation and is the first shape to emerge from the vesica piscis. The triangle contains the smallest area within the greater perimeter. The number three is the only number equal to the sum of the previous numbers. For instance, one plus two equals three. And three is also the only number whose sum also equals their product. Or, one plus two plus three equals one times two times three.” (Hobgood)

It may be inferred that the observation of dimensions is the observation of numerical synthesis. As we observed the natural world through the synthesis of spaces, we observed the world as a synthesis of number. As physical observation begins with height, width, and depth we can come to a conclusion of three as a universal number (when rounded is equivalent to Pi), from which we measure.

From this universality of 3 we observe 1 and 2 as it’s building blocks, and from the universality of 1,2 and 3 as composing both themselves and/or eachother they composed all real non-fractal numbers. As all dimensions reflecting numerical properties as points within themselves, the observation of all dimensions, specifically those in logic, must observe a numerical nature of 1,2 and 3 geometrically approximate to the line, as set of points, and the summation as Pi/circle as universal foundations.

It may simultaneously be inferred that the nature of metrology is the synthesis of dimensions as axioms of spatial elements and that axioms themselves are an innate “metrology” through which we measure the world.

“It is clear they conceived number as the first principle (Greek: Arche), and that the substance of the entire universe is identified with numbers. Philolaos of Tarentum (ca. 475 BCE), in his book on Pythagorean Numbers states: "All things, at least those we know, contain Number; for it is evident that nothing whatever can either be thought or known without Number." (Leonessi)

Rand observed that “measurements exist, but are not specified. That measurements must exist is an essential part of the process. The principle is: the relevant measurements must exist in some quantity, but may exist in any quantity." (Rand, Introduction to Objectivist Epistemology (second ed.))

rom this statement, and the observation of the Pythagorean perspective, it may be inferred that measurement is the observation of quantity, with all quantity being a form of symmetry.

The question occurs that if there is a degree of truth in this, how much more so for the letter, the word, or the sentence? Would numbers even constitute existence without language? “If language is to be a means of communication there must be agreement not only in definitions but also (queer as this may sound) in judgments. This seems to abolish logic, but does not do so.— It is one thing to describe methods of measurement, and another to obtain and state results of measurement. But what we call "measuring" is partly determined by a certain constancy in results of measurement” (philo invest) as a form of medianality of ratios. In this respect we are inevitably lead to "qualitative" measurement.

"According to Aristotle, the Pythagoreans traced the origin of all things back to two principles: the even and the odd. He wrote:

"Evidently then, these thinkers also consider that number is the principle both as matter for things and as forming both their modification and their permanent states, and hold that the elements of number are the even and the odd, and that of these, the latter is limited, and the former unlimited; and that the One proceeds from both of these (for it is both even and odd), and number from the One; and that the whole heaven, as has been said, is numbers." (Leonessi)

For the Pythagoreans, the elements of number are the even and the odd, or the limited and the unlimited; this is because numbers derive from the One, and the One from the even (unlimited) and the odd (limited). Aristotle tells us that the Pythagoreans saw the unlimited as evil, and limited as good. It seems that they also identified the number one (the monad) with the limited, the two (the dyad) with the unlimited. The emergence of the One appears to follow the Law of the Triangle in that it comes from the odd and even and itself produces number or the whole of nature." (Leonessi)

Considering all logistics contain stable and moving elements, odd and even elements, all logistics contain positive and negative elements and therefore do not have to have a nature of “ism” in order to synthesize as an axiom. This synthesis of the axiom results in dimensional limits (or the limits which form a reality) and possible dimensions (un-actualized dimensional limits)

The axiom in this respect is similar to an imaginary number where is manifests a dual nature of “reality [and] imaginary” (Sinha). This same observation can be applied to logistics, where all axioms have a dual structure of "real part as dimension" and a simultaneous "imaginary part as possibility". It is in this respect that:

1) Imaginary numbers are held together by real numbers.

2) Real numbers can be defined by Imaginary numbers.

3) Mathematics/Logic is inevitably axiomatic to a degree, implying all axioms must have a mathematical/logical nature to a degree therefore:

4) Axioms are held together by possible dimensions, as imagination, through the self.

5) Axioms are held together by dimensional limits, as reality, through “evidence”.

6) Axioms are held together by a logic of dimensional limits and possible natures; however logic is composed of axioms.

7) Logic is a synthesis of reality and imaginary dimensions and is synonymous to the axiom.

Logic is the manifestation of dimension, and with dimension is possibility through structure as no possible structure can exist without actual structure. It is in this respect, that to “observe logic” through “logic” simultaneously stabilizes the observed logic in one respect as causal while simultaneously fluxes through propagation of dimensions in a separate respect as acausal.

The axiom manifests as a measurement system which in turn forms further possible axioms.

From this respect that nature of the axiom can be synthesized with the perspective of Lewis's Modal Realism where:

1) Possible axioms exist - they are just as real as our axioms ;

2) Possible axioms are the same sort of things as our axioms - they differ in content, but not as the synthesis of a person(s);

3) Possible axioms cannot be reduced to something more basic – possible axioms are the manifestation of dimensions in their own right (however of a negative nature).

4) Actuality is gradation. When we distinguish our axiom quantums from other possible axiom quantums by claiming that it alone is actual, we mean only that it is our axiom which is the unified universal causal field or unifying median of all axioms and in this respect, is universal .

5) Possible axioms as logistic structures are unified as reflections of a universal causal logistics field;

6) Possible axioms as logistic particles are acausally isolated from each other through their need to relate as a particulate dimension.

7) In this respect all axioms maintain a dual nature of "extension" of a universal "whole" (positive value) and a "particulate" composed

of further particulatue (negative value).

Studies within physics argues that extra dimensions may be “curled up” at unobservable scales (CMS Collaboration ), and some dimensions are observed only as fractal dimensions (Song, Havlin and Makse). It is in these respects, as a mirror of reality, that logic must follow a similar form and function in regards to the axiom.

In this respect all Measurement Systems contain further Measurement Systems.

## Synthesis of Axiomatic Measurement as Modal Realism

### Re: Synthesis of Axiomatic Measurement as Modal Realism

In a quick summary of the above, what we understand of reality as both subjective and objective, through the axiom is a product of synthesis resulting in further axioms.

This synthesis of axioms in turn formulates and determines the nature of the measurement systems we use to observe reality. It is within this observation of reality through the axiom, that a form of Modal Realism manifests itself fundamentally as the "synthesis" of realities.

This synthesis of realities, through the synthesis of axioms, in turn formulates a multidimensional understanding of reality where a multitude of dimensions co-exists at the same time both reflecting and relating to one another. These axioms as limits which form reality through a process of measurement in turn exist through the synthesis of further possible axioms.

Measurement, as a dimensional limit which forms reality, synthesizes further possible measurement systems which in turn are extensions of the original. These measurement systems have a dual role of both being stable and constantly moving and provide the boundaries which enable the nature of "definition" as a system of "realization".

The act of measuring forms limits which in themselves both maintain certain realities, through dimensioality, and simultaneously allow them to move, by providing a form of individuation.

In these respects that axiom manifests a dual role of unity and multiplicity whose median point is the symbol. This nature of the "symbol" acts as an extension of the unified "whole" in one respect while allowing multiplicity through individuation in another.

A symbol is merely a curvature of reality through a summation of points and the gradation of the circle. In these respects, all symbolism is inherently linked and tied into a universal geometry and acts as a median between dimensions in one respect while being a dimension in and of itself.

The nature of the axiom, through the symbol, in these respects acts as "a whole world" in and of itself while being an extension of the subjective individual. This in turn ties the empirical observation of the world in with the inherent anthropormative spiritual qualities of ancient cultures as symbolism is the means between the subjective and objective.

This dualism of subjective and objective space manifests through a third median of neutrality which is observable in and of itself as neither space nor not space but rather strictly "curvature".

This synthesis of axioms in turn formulates and determines the nature of the measurement systems we use to observe reality. It is within this observation of reality through the axiom, that a form of Modal Realism manifests itself fundamentally as the "synthesis" of realities.

This synthesis of realities, through the synthesis of axioms, in turn formulates a multidimensional understanding of reality where a multitude of dimensions co-exists at the same time both reflecting and relating to one another. These axioms as limits which form reality through a process of measurement in turn exist through the synthesis of further possible axioms.

Measurement, as a dimensional limit which forms reality, synthesizes further possible measurement systems which in turn are extensions of the original. These measurement systems have a dual role of both being stable and constantly moving and provide the boundaries which enable the nature of "definition" as a system of "realization".

The act of measuring forms limits which in themselves both maintain certain realities, through dimensioality, and simultaneously allow them to move, by providing a form of individuation.

In these respects that axiom manifests a dual role of unity and multiplicity whose median point is the symbol. This nature of the "symbol" acts as an extension of the unified "whole" in one respect while allowing multiplicity through individuation in another.

A symbol is merely a curvature of reality through a summation of points and the gradation of the circle. In these respects, all symbolism is inherently linked and tied into a universal geometry and acts as a median between dimensions in one respect while being a dimension in and of itself.

The nature of the axiom, through the symbol, in these respects acts as "a whole world" in and of itself while being an extension of the subjective individual. This in turn ties the empirical observation of the world in with the inherent anthropormative spiritual qualities of ancient cultures as symbolism is the means between the subjective and objective.

This dualism of subjective and objective space manifests through a third median of neutrality which is observable in and of itself as neither space nor not space but rather strictly "curvature".

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