An Ar Number is a positive, ordinal, whole number, represented with an inverted exclamation mark (¡), for example: 1¡, 2¡, 3¡, and so on. Each Ar Number is associated with one or more conceptual terms, indicating its position in the hierarchical list of the ArXe Logic.
We establish the following fundamental rule:
- Each term corresponds to one and only one Ar Number.
- A single Ar Number, however, can correspond to multiple terms.
This defines a non-injective relationship between Ar Numbers and terms.
Examples:
Incorrect (a single term linked to multiple numbers is not allowed):
1¡ => "Being"5¡ => "Being"
Correct (multiple terms linked to the same number):
1¡ => "Being"1¡ => "Entity"
or more compactly:1¡ => "Being", "Entity"
Conceptual dynamics
An important observation: the terms assigned to Ar Numbers can change over time. At any point, we may revise or reorder the assignments based on new interpretations or developments in the system.
For instance:
- Initially:
1¡ => "Being", "Entity" - Later, we decide to distinguish them:
1¡ => "Being",2¡ => "Entity" - Still later, we might reverse the order:
1¡ => "Entity",2¡ => "Being"
This reveals a key property of the system:
Terms may shift or disappear, but Ar Numbers remain fixed.
The structure of the ArXe does not rely on the words themselves, but on the logical order they aim to express.
Interpretive foundation
The Logic of ArXe can therefore be understood as an interpreted set of Ar Numbers. What gives meaning to the system is the way we assign and interpret the terms linked to each number.
This assignment is inherently subjective and arbitrary, though it may be more or less solid depending on criteria such as necessity, coherence, or conceptual depth.
Leave a Reply