In the framework of ArXe theory, reality isn’t founded on static truths, but on a complex dance between logical contradictions and their active resolutions. This inherent dynamic, integral to the unfolding of Time, gives rise to a hierarchy of exentations that progressively construct the properties of the universe as we perceive it. The contradictions themselves—Istencia, Citancia, and Periencia—are not physically existent; they are logical tensions that Time must resolve, leading to their respective exentations, which do manifest as the fabric of reality.
The Principle of Resolution: From Contradiction to Exentation
The fundamental mechanism in ArXe is the negation of a contradiction to generate a truth. This truth, far from being passive, is what gives existence to Time’s properties:
1. Istencia and Ex-istence: The Necessary Truth (e1=T0)
The starting point is Istencia (Is), the fundamental logical contradiction:
\(\text{Is} = (\text{S} \land \neg\text{S})
\)
This proposition is always False. It represents the negation of coherence, “non-being” in its most basic state.
The resolution of this contradiction gives rise to Ex-istence (ExIs), the first exentation, by negating Istencia:
\(\text{ExIs} = \neg(\text{S} \land \neg\text{S}) \equiv (\text{S} \lor \neg\text{S})
\)
Ex-istence is a tautology, always True. This is the necessary truth that grounds the logical coherence of the ArXe universe, associated with the first exentation (e1=T0). It’s the immutable foundation of all possible existence.
2. Citancia and Ex-citancia: Contingent Truth and Motion (e2=T1)
From Ex-istence, a more complex tension emerges: Citancia (Ci). This isn’t a direct contradiction, but a paradox or indirect contradiction, which “cites” Istencia (False) in conjunction with the fundamental Tautology (T, representing Ex-istence):
\(\text{Ci} = (\text{Is} \land \text{T})
\)
Formally, if Is is False and T is True, then Ci is False. Its falsity lies in the attempt to affirm the contradictory alongside the true.
The resolution of Citancia gives rise to Ex-citancia (ExCi), the second exentation, by negating Citancia:
\(\text{ExCi} = \neg(\text{Is} \land \text{T}) \equiv (\neg\text{Is} \lor \neg\text{T})
\)
Since ¬Is is True and ¬T is False, Ex-citancia results in True. However, this is a contingent and dynamic truth. Its truth isn’t static; it’s maintained by a continuous alternation over its components, which conceptually “consumes time.”
Ex-citancia is the logical origin of motion, flow, and P=1/2 probability. It’s directly associated with the second exentation (e2=T1), and its purest physical manifestation is the speed of light (c). “Excitation” is, in essence, this fundamental iteration of Time’s logic upon itself to overcome the paradox of Citancia.
3. Periencia and Ex-periencia: The Truth of Perception and Memory (e3=T−1)
The next level of logical complexity introduces Periencia (Pe). This is a third-order paradox, attempting to reconcile Citancia (False) with Ex-citancia (True and dynamic):
\(\text{Pe} = (\text{Ci} \land \text{ExCi})
\)
Logically, if Ci is False and ExCi is True, their conjunction Pe is False. Periencia represents the tension of trying to conjointly affirm the indirect paradox and its own dynamic resolution.
The resolution of Periencia gives rise to Ex-periencia (ExPe), the third exentation, by negating Periencia:
\(\text{ExPe} = \neg(\text{Ci} \land \text{ExCi}) \equiv (\neg\text{Ci} \lor \neg\text{ExCi})
\)
Since ¬Ci is True (Ex-citancia) and ¬ExCi is False, Ex-periencia is True. This truth enables a higher level of information processing.
Ex-periencia is associated with the third exentation (e3=T−1), which corresponds to frequency. It’s at this level that probabilistic updating (Bayesian calculation) and a form of “memory” are enabled. Frequency, as a measure of iteration, is fundamental for sequencing events and a system’s ability to “keep track” and adjust expectations. This endows time with its perceptible quality, allowing for “temporal experience.” The ability to perceive time flowing and to update information is a direct manifestation of Ex-periencia.
Mappings and Physical Manifestations
It’s crucial to reiterate that contradictions (Istencia, Citancia, Periencia) do not have physical existence. What exists and is observable are their respective exentations, which embody the truths resulting from these logical resolutions.
| Logical Concept | Operation | Exentation in ArXe | Dimensionality | Key Physical Phenomenon | Manifestation of Truth |
|---|---|---|---|---|---|
| Istencia (False Contradiction) | →¬ | Ex-istence | e1=T0 | Fundamental Logical Coherence | Necessary Truth (Logical Being) |
| Citancia (False Paradox) | →¬ | Ex-citancia | e2=T1 | Motion, Speed of Light | Contingent Truth (Dynamism) |
| Periencia (False Paradox) | →¬ | Ex-periencia | e3=T−1 | Frequency, Perceptible Time, Bayesian Probability | Truth of Perception (Memory) |
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