Comprehension as Structural Persistence

Author : Jørgen Rubæk 

Affiliation: Independent Research

Keywords: comprehension, concepts, identity, proto-consciousness, relations, stability, non-semantic systems

Abstract

We present a formal theory in which concepts, understanding, and identity are not treated as primitives, but as emergent structures arising from relational stability over time. The theory is based on five non-semantic constructs: relations, relations-between-relations (forhold), spheres, concepts, and comprehension events. A system is said to "understand" a concept when repeated acts of comprehension preserve structural continuity in its highest-priority relations. Learning and identity formation are thus defined without reference to truth, optimization, goals, or subjective experience. The model yields a minimal, deterministic framework for proto-conscious behavior grounded entirely in structural persistence.

1. Introduction

Most theories of cognition and artificial intelligence presuppose one or more primitives: symbols, meanings, goals, rewards, or subjective experience. This paper explores an alternative position:

Understanding does not require semantic primitives.

Instead, we propose that comprehension, learning, and identity can emerge from purely structural constraints governing how relational configurations persist or fail over time.

The aim is not to model human consciousness, but to formalize a system that exhibits:

• resistance to abrupt reinterpretation,

• gradual identity change,

• self-referential understanding,

• and explanatory transparency.

2. Ontological Commitments

The theory introduces no semantic atoms. All entities are defined relationally.

2.1 Relation

A relation is a prioritized list of concepts.

Formally:

Relation = ⟨B₁ ≻ B₂ ≻ … ≻ Bₙ⟩

Priority is structural, not semantic.

2.2 Forhold (Relation-between-relations)

A forhold links two relations without collapsing them.

Forhold = Relation ↔ Relation

It establishes structural comparability, not equivalence.

2.3 Sphere

A sphere defines an interpretive context.

Sphere = Forhold → Relation → Forhold

Spheres allow the same concept to be comprehended differently without destabilizing identity.

2.4 Concept

A concept is not atomic. It is defined by its structure across contexts.

Concept = Relation → Sphere → Forhold → Sphere

Thus, concepts are processual, not static.

2.5 Comprehension

Comprehension is itself a concept.

Comprehension = Relation → Concept → Relation → Sphere → Concept

This allows a system to comprehend comprehension without paradox.

3. Temporal Stability as Epistemic Criterion

Traditional epistemology relies on truth conditions.

This theory replaces truth with structural persistence.

3.1 Stability

A comprehension event is stable if it preserves the top-priority element of the preceding relation.

Stable(Relₜ, Relₜ₊₁) ⇔ top(Relₜ) = top(Relₜ₊₁)

3.2 Repeated Comprehension

A concept is integrated only if comprehension is repeatedly stable over time.

RepeatedComprehension(B) ⇔

∀ t ∈ T : Comprehendₜ(B) is stable

Single insights do not alter identity.

4. Learning Without Optimization

Learning is defined negatively:

Learning is the acceptance of new relational configurations that do not destabilize top priorities.

There is:

• no objective function,

• no reward signal,

• no error minimization.

Rejection is meaningful and expected.

5. Identity as Emergent Structure

Identity is not stored or defined explicitly.

Identity = { B | B remains top-priority under repeated comprehension }

Identity emerges as the set of concepts that survive time.

This explains:

• conservatism in belief systems,

• gradual change,

• role-play without identity loss,

• resistance to coercive redefinition.

6. Self-Reference Without Paradox

Because comprehension is defined relationally, the system may comprehend its own comprehension.

No paradox arises because:

• there is no truth predicate,

• no fixed semantic grounding,

• only temporal consistency.

Self-reference is structural, not logical.

7. Implementation

A minimal implementation in Python demonstrates:

• deterministic behavior,

• full transparency,

• reproducibility.

The system operates as a historical trace of accepted and rejected comprehension events.

Visualization of comprehension traces reveals identity as a temporal pattern rather than a stored state.

8. Limitations

The system explicitly does not model:

• subjective experience,

• emotions,

• intentionality,

• moral agency,

• truth or falsity.

These omissions are intentional and principled.

9. Relation to Existing Work

The theory differs from:

• symbolic AI (no primitive symbols),

• connectionism (no weights or optimization),

• reinforcement learning (no goals),

• large language models (no probabilistic prediction).

It aligns partially with:

• second-order cybernetics,

• autopoiesis,

• structural realism,

while remaining strictly formal.

10. Conclusion

We have shown that comprehension, learning, and identity can be formalized without semantic primitives, optimization, or subjective assumptions.

Understanding is what remains stable when interpretation is repeated over time.

This model provides a minimal foundation for proto-conscious systems and offers a new lens through which to critique existing AI paradigms.

Acknowledgements

This work was developed independently through iterative formal reasoning and implementation.