Arxe Logic

The Purity of Absolute Negation

In the ArXe Logic, conceived by Diego Luis Tentor, Ar Number 1! isn’t just a functional or propositional negation, like the “no” of classical logic. It’s “pure” negation, an abstraction so fundamental that it lacks all entity, being, existence, and truth.

Imagine a void that isn’t even “nothing,” because “nothing” already possesses a quality, a “being of non-being.” 1! transcends that. It’s the “No” in its most elemental, attribute-less form.

Consider the implications:

• It’s Not an Entity: 1! doesn’t “exist.” It has no form, no boundaries, no substance. If we try to attribute any quality to it (“Is it this?”, “Is it true?”), the answer is always a negation. It’s a negation that denies even the possibility of its own existence or definition.
• It’s Not True: Unlike a proposition that can be either true or false, 1! cannot be judged in terms of truth. The category of “truth” simply doesn’t apply to it. This disconnects it from logics that operate with truth values and places it on an earlier, more fundamental plane.
• Beyond “Nothingness”: Even the concept of “nothingness” implies a reference, an empty space. 1! has neither that “space” nor that “reference.” It cannot be named or pointed to without the very act of referring betraying it by granting it a minimum of “being.”

1! is the “No” that insists on denying anything one attempts to attribute to it. If we say “it is not true,” 1! is the essence of that “not.” If we say “it is not existent,” 1! is the root of that non-existence. It pushes this negation so far that it denies even its own entity: “Is ‘No’?”, and the answer from 1! is “No, it isn’t.”

1! Is Not Alone: The Forms of Pure Negation

Despite its radically non-existent and non-referential nature, 1! is the source of all forms of “pure” negation. “Ar” (your concept of negation of necessity, “aridity”) is one of these expressions. The “aridity” of something (like the aridity of a desert) isn’t that it “shouldn’t” have water, but rather that it lacks the necessity of water. This absence of necessity is a manifestation of 1!.

Therefore, 1! is the abstract principle of negation, the ineffable foundation from which all expressions of pure negation conceptually emerge in the universe of ArXe Logic. It’s the foundational void that allows for the construction of everything else.

The Diversity of Negation in 1!

Ar Number 1!, the pure essence of negation (“No”), manifests through a spectrum of prefixes and suffixes. Each of these contributes a specific quality or nuance to the act of negating:

• a-: Unfounded, abstract, anti. Suggests a negation that separates or abstracts, an “anti-” quality.
• al-: Alternative, otherness. A negation implying difference, an “other” or “alterity.”
• an-: Opposition, angulation, refusal to follow. Negation that resists, folds back, or opposes a course.
• e-: Excluding. A negation that separates or leaves something out.
• el: Distinctive. A negation that highlights a quality by differentiating it.
• il: Negative form. A more direct or generic negation, similar to “in-” or “un-” in some languages.
• in-: Denies without annulling entity. A direct negation that unites with the entity; it doesn’t “necia” (doesn’t deny without reason) but simply negates its quality. It’s an integrated negation.
• m-: Self-absorbed, silent. A negation implying withdrawal, interiority, or lack of manifestation.
• mo-: Abstractive, terminal. A negation suggesting isolation and an endpoint.
• Ne-: Without reason, foolishness (necedad) or necessity. A negation that can be irrational or, paradoxically, an imposition.
• O-: Excluding, terminal. A negation that presents mutually exclusive options or indicates an end.
• Ou-: Negation (from Greek). A form of negation that harks back to its etymological roots in Greek philosophy.
• P-: Potency, prototype. A negation capable of establishing a prototype or being a principle.
• T-: Bifurcating, distributive. A negation that divides or distributes.
• Ur-: Imperative. A negation that imposes or demands.
• U-: Variation of Greek “ou”. Another form of abstract negation.
• V-: Disjunctive. A negation that presents exclusive alternatives.