Axiomatic Restrictive Principles of Reality and Illogical Functionality

This chapter will demonstrate that the physical reality of the universe that we perceive, and of which we are a part, is nothing more than an Apparent Reality, generated solely by absolutely immaterial geometric elements called Alpha Components or Compalphas. Here, through the Axiomatic Restrictive Principles of Reality and Functionality, it is argued that it is simply impossible to distinguish nothingness—termed Absolute Empty Space—from what we suppose to be matter or energy. It further asserts that the supposed corpuscular materiality of conventional physics cannot interact in the manner we currently understand it to occur. It demonstrates that the universe cannot be dimensionally finite, and that purely geometric mechanisms, devoid of substance, can generate only an Apparent Reality.

The Nature and Methodology of TUGIA

TUGIA is a reductionist ontological theoretical model of the structure and functional mechanisms of universal being. It is a qualitative model with an analytical methodology, presented in a conceptual and descriptive form, where quantifications are virtually non-existent, given that traditional physics—especially classical physics—already establishes them with great precision through what physicists consider to be the fundamental laws of nature. What this theory proposes, through logical reasoning derived from the analysis of the structural elements constituting what we suppose to be material reality, is to demonstrate the true forms of these structural elements and their true fundamental functional mechanisms, thus revealing what the generators of this supposed substantial reality truly are.

TUGIA asserts that this absolute understanding cannot, under any circumstances, be achieved through experimentation—via a process of direct or indirect observation—since the object and the observer are essentially constituted by elements of the same nature, and are therefore reciprocally indistinguishable. Thus, TUGIA guarantees that we can only know the absolute truth about the structures of the universe through inferences regarding indubitable elements, such as geometric and mathematical ones, and that these indubitable aspects can only be deduced through the full use of reason, by means of its Four Axiomatic Restrictive Principles of Reality and Logical Interactivity: the Indistinction of Void and Matter, Necessarily Indefinite Fragmentation, Logical-Constructive Interactive Incapability, and Necessarily Indefinite Containment—all presented as clear and self-evident axiomatic principles.

The problem concerning the existence of supposed "solid" elements and their impossible functionalities, as proposed by physicists, arises when we accept that substance exists as something absolutely different from non-existence; this is a problem intrinsic to conventional models. For it is certain that if substantiality truly existed, there would be absolutely nothing to restrict its structure and functional mechanisms from being merely corpuscular. However, we would never achieve a fundamental structural formation that is subsequently functional and logical, such as the one we observe. From an absolutely logical point of view, the existence of substantial structural elements would be restricted by these four principles, which would necessarily exist and be intrinsic and inseparable from those same elements. Thus, the order of the Axiomatic Restrictive Principles of Reality and Logical Interactivity applied to these elements would be as follows:

If substantiality existed, then the Axiomatic Principle of Necessarily Indefinite Fragmentation would exist, making the search for the fundamental structural element of this substantiality infinite; and the Axiomatic Principle of Logical-Constructive Interactive Incapability would exist, making the direct and necessary connection between these same supposed fundamental structural elements impossible. Both principles exist only if these same supposed fundamental structural elements exist, forming a finite universe or infinite finite universes, but always as a function of them and within the Absolute and dimensionless Empty Space that would necessarily contain them—a space guaranteed by the Axiomatic Principle of Necessarily Indefinite Containment, which would cause any supposed quantified universal volume to be contained by a dimensionless volume. However, as the Axiomatic Principle of the Indistinction of Void and Matter simply renders these three principles impossible, what remains, consequently, is only that same Absolute and dimensionless Empty Space.

The Corpuscular Being and the Geometric Non-Being

When we look at the elements and mechanisms of the world surrounding us—at the microcosm, the macrocosm, and ourselves—it is light that reveals, through diverse means, that absolutely everything is made of the same elements, whatever their fundamental nature may be. Thus, we give the name "reality" or "existence" to the set of elements and mechanisms observed in this way. Consequently, "to exist" means "to be," and "to be," then, is something absolutely opposed to "non-being," to "not-existing," to what we might call "absolute nothingness"—yet here referred to as Absolute Empty Space. In physical terms, "to exist" means to be constituted by "fundamental particles" of matter (or energy), by "one-dimensional strings" of energy, or even by a type of "magical information," whereas "not to exist" means not to be constituted by any of these supposed "real elements."

We may consider, then, that the great problem with the atomic and universal models of conventional physicists—such as those of "fundamental particles," "one-dimensional energy strings," and the "holographic" model, which are currently in vogue—is the unconditional acceptance of their real substantiality, of their finite spatial and temporal existence, and of their supposed spontaneous emergence from nothingness by means of a Big Bang. However, according to TUGIA, since there is no verb that can express that what "exists" is what does not "exist," or that what is not, is what is, we may make use of the term Immaterial Geometry. This represents those elements that are non-material, non-energetic, non-informational, and non-substantial; it is precisely the term utilized by this theory to assert that being is the very non-being. Therefore, according to TUGIA's propositions, the universe does not exist substantially, as a "non-being sprinkled with being everywhere," but only "exists" geometrically, as a "non-being sprinkled with non-being everywhere"—as something constituted by an Immaterial Geometry, a geometry that does not alter the state of "non-being," of the Absolute and dimensionless Empty Space that is the universe.

By attributing an unquestionable material reality to the structures of the universe, physicists fail to take into account a Principle of Void-Matter Indistinction and a Principle of Necessarily Indefinite Fragmentation that would exist if "fundamental particles" or "energy strings" actually existed, which would simply render the existence of any such supposed substantial elements impossible. They also fail to consider that if substantial elements did exist, a Principle of Logical-Constructive Interactive Incapability would prevent them from interacting in a logical manner across space, since they would need to be continuously connected to do so. Furthermore, they do not account for the fact that the universe itself could not have emerged; if it had, it would have to have come from something necessarily prior, and its quantified totality would be insignificant before a Principle of Necessarily Indefinite Containment, which establishes that any given volume must always be contained by a larger volume. These four principles are, therefore, intrinsic to any potential elements.

The problem of substance, according to TUGIA, is that "particles" or "strings" cannot exist, for there can be absolutely no difference between being and non-being; this is the Principle of Void-Matter Indistinction. However, if, incomprehensibly, differentiation were to exist, there would still remain the Restrictive Principles of Necessarily Indefinite Fragmentation and of Logical-Constructive Interactive Incapability. The Principle of Necessarily Indefinite Fragmentation establishes that any supposed particle or string would be constituted by internal parts of the same nature, yet even smaller than itself and possessing the same property of indefinite fragmentation. The Principle of Logical-Constructive Interactive Incapability establishes that these supposed particles or strings could not interact in any logical way across the empty space between them, regardless of the distance separating them, unless there were a third element of the same nature absolutely connected to these elements.

Synthesis of the Axiomatic Restrictive Principles of Reality and Functionality

Synthesis of the Axiomatic Principle of Void-Matter Indistinction (PIVM) The Axiomatic Principle of Void-Matter Indistinction, proposed by TUGIA, is intrinsic to supposed substantial structural elements, establishing that it is impossible to distinguish between such a supposed substantial structural element and the Absolute Empty Space that would necessarily surround it. This logical, axiomatic principle demonstrates that the truly fundamental problem of the existence of substantiality is related solely to the logical impossibility of differentiation between Absolute Empty Space and these then-supposed substantial structural elements. For that which "is" and that which "is not" can only be identical to themselves; as they cannot be different from themselves, an absolute non-being cannot become an absolute being, or vice versa—for from nothingness, something real cannot arise, just as something real cannot disappear. Based on these fundamental premises, we can extract only two—and only two—fundamental hypotheses regarding what we understand to be the substantiality of the universe, though we shall see that only one is absolutely logical: the first is that this supposed substantiality has an eternal existence, and the second is that such substantiality is eternally non-existent.

Synthesis of the Axiomatic Principle of Necessarily Indefinite Fragmentation (PFNI) The Axiomatic Principle of Necessarily Indefinite Fragmentation, proposed by TUGIA, is intrinsic to supposed substantial structural elements, as it establishes that it is impossible to have any type of substantial structural element with a quantified dimension that cannot be divided. This logical, axiomatic principle runs counter to the very existence of the supposed substance of being, since an elementary and indivisible unit of anything is impossible, except for the unit of the geometric point. It thus establishes that for any supposedly substantial structural element of matter or energy, of any dimension, its half or any other proportion must necessarily exist.

Synthesis of the Axiomatic Principle of Logical-Constructive Interactive Incapability (PIILC) The Axiomatic Principle of Logical-Constructive Interactive Incapability, proposed by TUGIA, is intrinsic to supposed substantial structural elements with quantified dimensions, establishing the impossibility of any two elements interacting logically without a third element of the same nature directly connecting them. This logical, axiomatic principle establishes that the interaction between a structural element A and a structural element B, separated by the Absolute Empty Space that necessarily surrounds them, must be mediated by a structural element C, directly connected to both A and B. Thus, this principle leads us to the understanding that interaction—with the necessary attractive, repulsive, or oscillatory/vibrational action—only occurs if there is some type of contact between structural elements of whatever exists, whether they are substantial or immaterial, for it is these interactions that form all existing universal structures.

Synthesis of the Axiomatic Principle of Necessarily Indefinite Containment The Axiomatic Principle of Necessarily Indefinite Containment, proposed by TUGIA, is intrinsic to a supposed structural element with a quantified dimension, establishing that its supposed quantified structural dimension must be contained by a dimensionless structural element. This logical, axiomatic principle makes it evident that there cannot be an uncontained structural element, implying that if there were a dimensionally finite universe, or even infinite dimensionally finite universes, something external would be necessary to contain them which, consequently, would have to be dimensionally infinite. This dimensionally infinite "something" is, obviously, a common infinite space—a common infinite place that could contain the eventual infinite universes—but which, according to TUGIA's propositions, is the one and only infinite universe, being solely an Absolute Empty Space called the Omega Dimension.

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