Arxe Logic

A conceptual framework developed by Diego Tentor

What is the Logic of ArXe?

The Logic of ArXe is a system of reflection and reasoning centered around the ArXe, a foundational structure that encompasses the Numbers of Ar, their hierarchical ordering, their associated terms, and their underlying justifications.

This framework was developed by Diego Tentor as an attempt to organize and reason through all possible terms, including—and especially—those involved in reasoning itself. It seeks to systematize thought from its most elementary origins to its most complex forms, organizing concepts according to their logical necessity.

---

Logical Ordering of Terms

Imagine we could take all concepts and words and arrange them according to the necessity of their meaning. For example:

• One cannot define “cow” without first defining “animal,” since every cow is an animal, but not every animal is a cow.
• Likewise, “animal” presupposes “living being,” which we may refer to more precisely as “biota.”
• And “biota” in turn presupposes the concept of “being,” since every living thing is a being, but not every being is alive.

This reveals a fundamental ordering principle: necessity. A concept must appear earlier in the hierarchy if it is required to define another.

---

Reflexivity: Reasoning About Reason

The Logic of ArXe goes further. It aims to order not only known terms, but also those that emerge during the act of reasoning itself. Thus, terms such as “order,” “necessity,” “relation,” “foundation,” or “reason” must also be included in the system and properly placed.

For example, if we define “biota” as “a being that is alive, real, and existent,” then terms like being, alive, real, and existent must also be accounted for and ordered hierarchically.

---

The Logic of ArXe as a Conceptual Game

Beyond its philosophical and analytical depth, the Logic of ArXe can also be approached as a game of conceptual construction, governed by three simple rules:

1. Assigning Terms
   Each Number of Ar may be assigned as many terms as desired, provided that each term belongs to one and only one Number of Ar.
2. Justifying the Assignment
   Each term must be founded on one or more terms or Numbers of Ar lower in the hierarchy.
   • Higher-order terms cannot be used as foundations.
   • All justifications are valid—some may be stronger, others more tentative.
   • Multiple foundations are allowed.
3. Interpretation
   The player or theorist may freely interpret the foundations provided, comparing constructions by their coherence and strength.

---

Objective of the Logic of ArXe

The ultimate goal is to assign the greatest possible number of meaningful terms to the Numbers of Ar, achieving maximum solidity in their foundations. This creates a hierarchical logical system—a universal language of structure and meaning, where each concept has a proper place and rationale.

---

This theory was developed by Diego Tentor as part of the broader ArXe framework, exploring the deep interplay between logic, language, and physics.