Arxe Logic

This table illustrates the progression of the fundamental logical concepts of ArXe Theory through a process of successive exentations. Each “Entification” represents a conjunction of previous states, whose corresponding “Exentation” is its negation, resolving into a tautological disjunction or truths that define the next phase of reality.

Exentations: The Logical Links of the Universe in ArXe Theory

In ArXe Theory, exentations are not mere abstract concepts; they are the fundamental logical links that construct reality. They describe how truths “chain together” and develop into progressively more complex logical structures, which, through the axiom relating them to Planck Time (Tp), permeate and shape the universe.

From these emergent structures arises the universe we know: time, space, mass, energy, and all physical phenomena. Exentations establish the minimum logical requirements for the existence of these realities.

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The Analogy of Finitude: Building Reality Step by Step

To better understand exentations, we can use the analogy of finitude, a concept that logically requires a beginning (p) and an end (f), which are inherently opposed to each other.

• • The First Exentation (1 Tp): The Impossibility of Instantaneous Contradiction Since an exentation occurs every 1 Tp (Planck Time), the beginning (p) and the end (f) cannot occur within the same Tp. If they did, a logical contradiction would arise, and by extension, a physical contradiction. The ArXe universe does not allow for this immediate contradiction.

• • The Second Exentation (2 Tp): The Emergence of Basic Finitude It is only from the second exentation (i.e., every 2 Tp) that finitude becomes possible. At this level, a “beginning” and an “end” can exist separated by a minimal temporal interval, avoiding contradiction. However, this initial finitude is unextended; it lacks a “middle” or internal extension. It is like a limit without content.

• • The Third Exentation (3 Tp): The Creation of the “Middle” and Extension For extensive finitude —one that has a beginning, a middle, and an end— a more complex logical structure is required. This requires a third exentation (i.e., every 3 Tp). It is at this point that the “middle” between a beginning and an end becomes possible, allowing for extension and complexity.

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Implications: The Logical Requirement of Physical Phenomena

This pattern illustrates a fundamental principle of ArXe Theory: physical phenomena cannot simply “exist.” They require a minimum logical structure (and therefore, exentations) to manifest. The observed complexity of the universe is a direct result of successive exentations and the “chained truths” they generate. Each exentation adds a new layer of possibility and definition to reality, from simple existence to extension and beyond.