Arxe Logic

The ArXe Logic, developed by Diego Luis Tentor, introduces an innovative perspective on organizing logical thought. Unlike traditional logics that focus on the truth value of propositions, ArXe is a terminological ordering system. Its primary purpose is to pinpoint, distinguish, and precisely classify logical relationships, centering on the inherent role of Ar numbers as fundamental logical entities.

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Core Concepts of the ArXe System

At the heart of this system, we find:

• Ar Number 1! (Unit of Pure Negation): This number represents “pure” negation in its most abstract essence. It’s not a specific negation like “no” or “¬,” but rather the fundamental basis of negation itself. “Aridity” (Ar), defined as a negation of necessity (an absence or lack that doesn’t imply an obligation to exist), is one of the expressions or forms through which 1! manifests. For instance, “arid” illustrates the lack of moisture not as a prohibition, but as an inherent characteristic, not necessary for its definition.
• Ar Number 2! (Unit of Pure Affirmation): Similarly, 2! encapsulates the abstract essence of affirmation. “Xe” is the chosen conceptual expression to represent this affirmation, serving as the counterpart to aridity.
• Ar Number 3! (Unit of Contradiction/Conjunction): This number arises from the combination of the preceding ones, such as in 1! + 2!. It represents the conjunction of negation and affirmation, which conceptually translates into contradiction or the coexistence of opposing elements.

The key insight is that Ar numbers (1!, 2!, 3!, etc.) are the primary logical entities. Negation is a form of 1!, and affirmation is a form of 2!. The terms we assign to them (the “logisms”) are merely labels or conceptual representations that help us understand and communicate the logical relationships inherent to these numbers.

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Rules for Assigning “Logisms”

“Logisms” are the precise terms assigned to each Ar number to represent a specific logical relationship. Diego Luis Tentor has established rigorous rules for their creation and assignment:

1. Lexical Formation:
   • Pseudoetymology: Logisms can be created by concatenating base elements within brackets, such as in [ar][xe]. The resulting Ar number is obtained by summing the Ar numbers of each component. For example, Arxe = [ar][xe] = 1! + 2! = 3!.
   • Term Uniqueness: Each logism must be a single word, without spaces (e.g., “incosa” instead of “no thing”).
   • Integrated Negation: Explicit negations like “non-” are avoided. When a logism implies negation, it must be intrinsically embedded in its structure, reflecting the subtle nature of the negation of necessity.
2. Conceptual Identification:
   • Philosophical/Conceptual Justification: Assigning a logism to an Ar number must be supported by a clear philosophical or conceptual correspondence with the logical relationship that number represents.
   • Belonging to a Set of Meanings: Logisms can be grouped under an Ar number if they share a coherent semantic field or set of meanings.
3. Logism-Ar Number Relationship:
   • Multiple Logisms per Number: A single Ar number can have several associated logisms, each capturing different nuances or aspects of the logical relationship it symbolizes.
   • Unique Logism per Number: However, each individual logism can only designate a single Ar number, ensuring univocity.
4. Reflection on the Number’s Logical Aptitudes:
   • This rule adds an extra layer of abstraction, allowing logisms to be assigned based on the inherent logical properties of cardinal numbers. For example, the logism “One” is associated with 1! because it’s the intrinsic property of a single element. The logism “Even” is associated with 2! as it’s an inherent quality of a set of two. If there are two ideal and indistinguishable elements, “Both” is an appropriate logism for 2! because it refers to their totality without individual distinction.

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The Purpose of ArXe Logic

The ArXe Logic stands as a conceptual tool for logical taxonomy. By focusing on Ar numbers as the roots of logical relationships and by providing a rigorous system for assigning logisms, Diego Luis Tentor’s system offers a unique way to categorize and comprehend the vast complexity of logical interactions, using the negation of necessity as its starting point and central axis.