A Reconfiguration of Ontological Foundations
Introduction
ArXe theory proposes an ontological reconfiguration that directly addresses two central issues in philosophy of science: circularity and Platonism. The key to this reformulation lies in a strict distinction between essence, existence, and truth. By separating these domains, contradiction can possess formal status without constituting an existing entity or a true proposition. Within this framework, circularity is not a logical defect but a structural mechanism of stabilization, and no ultimate positive ontological foundation is required. ArXe does not replace Platonism with a negative absolute; rather, it replaces transcendent foundations with temporal structural stabilization without prior ideal entities.
1. Breaking the Classical Co-Implication
Much of classical metaphysics—and the ontological background presupposed by modern science—operates under a structural co-implication between:
- Being
- Existence
- Truth
- Non-contradiction
What is, in some relevant sense, exists and is susceptible to truth. Contradiction, accordingly, lacks ontological status: if something is contradictory, it is false; if false, it cannot ground anything.
ArXe breaks this co-implication.
The theory formally distinguishes:
- Essence (being)
- Existence
- Truth
Thus, something may have formal status without existing or being true. This separation is the necessary condition for redefining both contradiction and circularity.
2. The Formal Status of Contradiction
In ArXe, contradiction (S ∧ ¬S):
- Does not exist
- Is not true
- Is not a physical fact
- Has no temporality or localization
It is not an ontological principle nor a universal foundation. It is merely a formal configuration of indeterminacy.
Its “being” is neither existence nor truth, but formal status. Consequently, contradiction cannot stabilize as a determinate fact.
This is decisive: contradiction does not ground, explain, or necessitate anything. It simply cannot constitute a stable determination.
3. Circularity as Structural Closure
In classical logic, circularity is an argumentative defect. In ArXe, by contrast, circularity is structural.
Formal indeterminacy is not eliminated through falsity; it is integrated through closure. The theory refers to the stratification of closure levels as n-arity, whereby indeterminacy is absorbed without collapsing into triviality.
Circularity here does not imply self-justification or logical presupposition. It indicates that certain regimes of determination stabilize through structural return.
Thus:
- There is no petitio principii.
- There is no tautological self-grounding.
- There is no transcendent external foundation.
There is structural stabilization.
4. Exentation and the Fundamental Act
The negation of contradiction, ¬(S ∧ ¬S), is formally valid. However, logical validity does not entail ontological necessity.
Exentation designates the first regime of stabilization. With it, temporality emerges. The fundamental act:
- Is temporal
- Is non-spatial
- Is not an ideal entity
- Is not an eternal truth
- Is not a positive ontological affirmation
There is no prior domain in which forms or principles reside. Space emerges later as a structural effect.
If one speaks of a foundation at all, it is not an entity or truth but a minimal temporal act of stabilization.
5. Structural Anti-Platonism
Ontological Platonism posits an ultimate positive foundation: eternal truth, ideal form, or structure independent of process.
ArXe posits none of the following:
- A transcendent domain
- An original eternal truth
- An ungenerated ideal entity
- An absolute ontological principle
Contradiction cannot fulfill this role, as it lacks existence and truth. The fundamental act cannot fulfill it either, as it is temporal and non-spatial rather than eternal and ideal.
ArXe therefore does not replace Platonism with a negative absolute. It removes the necessity of any transcendent ontological foundation.
Conclusion
ArXe redefines circularity and the problem of foundations by distinguishing essence, existence, and truth. Contradiction acquires formal status without becoming an entity; circularity becomes a mechanism of structural stabilization; foundation ceases to be transcendent and becomes a minimal temporal act.
Accordingly, ArXe is not Platonist in any strong ontological sense. It proposes an ontology of stabilization without a positive metaphysical absolute.