Arxe Logic

The quest for a theory of everything has propelled theoretical physics to explore frameworks that transcend traditional descriptions of matter and energy. In this context, the ArXe Theory emerges as a bold proposal that postulates a fundamental equivalence between the logical coherence of existence and a physical constant, potentially opening a path toward the unification of logic and physics at the deepest scales of reality.

---

The Central Axiom: Exentation and Planck Time

The core of the ArXe Theory lies in a single, powerful axiom, anchored in the concept of exentation. We define exentation (E) as the negation of a logical contradiction. If S represents any entity or proposition and ¬S its contradictor, a contradiction (C), or Istence (I), is expressed as:

\( C \equiv I \equiv (S \land \neg S) \)

Exentation is then:

\( E \equiv \neg C \equiv \neg (S \land \neg S) \)

Applying De Morgan’s Laws and double negation, exentation simplifies to a tautology (T):

\( E \equiv (\neg S \lor \neg (\neg S)) \equiv (\neg S \lor S) \equiv T \)

The fundamental axiom of the ArXe Theory establishes a direct identity between this exentation (the negation of a contradiction, which is always a tautology) and Planck Time (Tp​):

\( E \equiv T_p \) or, more directly:

\( \neg C \equiv T_p \)

Planck Time (Tp​≈5.39×10−44 s), derived from the fundamental constants c (speed of light), G (gravitational constant), and ℏ (reduced Planck constant), is universally recognized as the temporal scale where quantum gravity effects become dominant. It’s commonly interpreted as the “minimum physically meaningful time,” the threshold below which our current physical laws cease to be applicable and spacetime itself might have a granular structure.

The audacity of this axiom lies in equating the process of guaranteeing the logical coherence of existence (exentation) with the universe’s fundamental temporal unit. It’s no longer just any elementary logical operation, like a simple negation, that’s equated to Tp​. Instead, it’s the intrinsic act of resolving a contradiction to affirm the existence of a logical truth. This posits that the most basic “pulse” of reality is the very validation of its non-contradiction.