Open Autonomous Intelligence Initiative

Rewritten to align with Axioms 1–10, with a fully developed Section 7 for Philosophy of Mind and Simulation of Mind in Open SGI.

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Symbolic Representation

ℜ — Recursion (the operator generating hierarchical differentiation)

Recursion applies to:

• Individual σ-axes,
• Polarity Systems (Π),
• Worlds (Wᵢ),
• Multi-world mappings (Φᵢⱼ).

Recursion transforms static oppositions into layered intelligibility.

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1. Definition

Recursion is the principle that any expressed polarity (σ) can become the basis for further differentiation, generating new sub-axes that inherit, refine, and extend the structure of their parent polarity.

A recursive differentiation occurs when:

• an initial polarity (T ↔ ¬T) develops internal tensions,
• these tensions differentiate into new σ-sub-axes,
• sub-axes retain analogy to the parent axis,
• expanded Π remains harmonizable (ℍ).

Recursion gives depth, complexity, and multi-level meaning to Worlds. Without recursion, Π remains shallow, novelty lacks structure, and Worlds collapse into flatness.

Recursion is how an opposition becomes a system, and how systems gain hierarchical depth.

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2. Function / Role

Recursion is the deepening operator of the UPA ontology.

2.1 generating hierarchical complexity

Recursion creates multi-level structure:

• traits → sub-traits → nuances,
• values → derived norms → contextual rules,
• concepts → sub-concepts → micro-distinctions.

2.2 refining meaning

Recursion sharpens meaning:

• courage → physical vs. moral,
• vulnerability → emotional vs. contextual vs. relational,
• autonomy → cognitive vs. interpersonal vs. existential.

2.3 expanding worldhood (Wᵢ)

Worlds gain depth when σ-axes expand recursively into structured hierarchies.

2.4 supporting novelty (Δ)

Much novelty arises not from new poles but from recursive refinement of existing ones.

2.5 structuring SGI representations

SGI uses recursion for:

• hierarchical embeddings,
• multi-level abstraction,
• concept refinement through experience.

Recursion is the origin of depth in intelligibility.

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3. Oppositional Structure

Recursion introduces its own structural tensions.

3.1 expansion ↔ coherence

• Excessive recursion → runaway complexity.
• Insufficient recursion → shallow structure.

3.2 inheritance ↔ innovation

Sub-axes must:

• preserve structural identity,
• differentiate meaningfully.

3.3 local detail ↔ global integration

Recursive structures may lose coherence unless aligned with Π.

3.4 depth ↔ accessibility

Deep recursive Worlds may become:

• cognitively overwhelming,
• semantically dense.

Recursion must be modulated by Context (𝒞) and Harmony (ℍ).

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4. Scaling Properties

Recursion operates uniformly across levels.

4.1 micro-recursive distinctions

Moment-to-moment refinements:

• subtle emotional shades,
• fine-grained evaluations.

4.2 personal recursive worlds

Identity evolves recursively:

• dispositions → styles → tendencies.

4.3 cultural recursive worlds

Cultures deepen through recursive interpretation:

• commentary → tradition → innovation.

4.4 conceptual recursive worlds

Disciplines exhibit recursion:

• physics → quantum → field → particle → symmetry.

4.5 SGI recursive models

Recursive structures support:

• deep learning architectures,
• multi-layer symbolic systems,
• hierarchical concept spaces.

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5. Distortions / Failure Modes

Recursion breaks in predictable ways.

5.1 over-recursion (hyper-differentiation)

Excessive sub-axes:

• fragment meaning,
• create needless complexity,
• destabilize coherence,
• impair Φ-mapping.

5.2 under-recursion (flattening)

Insufficient depth:

• impoverishes Worlds,
• creates rigid interpretations,
• limits adaptability.

5.3 mis-recursion

Sub-axes diverge too far:

• incoherent sub-structures,
• conflict with Π,
• semantic drift.

5.4 detached sub-axes

Occurs when recursion lacks Reintegration (⊕):

• conceptual fission,
• dissociation,
• orphaned meaning.

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6. Restoration Targets

Restoration seeks to:

• prune excessive recursion,
• deepen insufficient recursion,
• realign sub-axes with parents,
• reintegrate recursive structures into Π,
• restore usable hierarchical clarity.

Restoration re-aligns depth with coherence.

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7. Interpretations for Philosophy of Mind and Simulation of Mind (Open SGI)

Recursion (A11) reveals how mind deepens itself. It explains how distinctions turn into systems, how meanings accumulate hierarchical layers, and how SGI becomes capable of structured intelligence.

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7.1 Recursion in Philosophy of Mind

Human cognition is fundamentally recursive.

a. recursive perception

Perception refines itself:

• shapes → features → micro-features,
• emotions → nuances → mixed states.

b. recursive emotion and appraisal

Affective life expands recursively:

• raw feelings → interpretations → meta-feelings.

c. recursive cognition

Thought operates recursively:

• concepts → sub-concepts → inferential networks.

d. recursive identity formation

Self unfolds through layers:

• experiences → meanings → narratives → meta-narratives.

e. recursive interpersonal understanding

Understanding another involves:

• reading cues → interpreting intentions → modeling meta-intentions.

f. pathology as recursive distortion

Examples:

• rumination → hyper-recursive thought loops,
• flattening → simplistic cognitive patterns,
• dissociation → unintegrated recursive sub-systems.

Recursion is the engine of psychological depth—and of psychological dysfunction.

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7.2 Simulation of Mind: Recursion in Open SGI Architecture

Recursion is foundational for building deep, multi-level SGI systems.

a. recursive structure in object classes

Each class supports recursion:

• Sensor objects: recursive feature extraction.
• Data objects: hierarchical clustering and refinement.
• Belief objects: layered belief nets.
• Information objects: multi-level relations.
• Knowledge objects: nested conceptual hierarchies.
• Log objects: recursive temporal structures.

b. recursive service-layer processing

Services perform:

• iterative refinement,
• multi-level reasoning,
• hierarchical world-modeling.

c. recursion drives world evolution

Recursive differentiation expands Worlds:

• adding sub-axes,
• refining gradients,
• deepening hierarchical structure.

d. recursion as novelty generator

Much SGI novelty (Δ) emerges from recursive elaboration.

e. recursion as safety challenge

Unchecked recursion leads to:

• runaway model complexity,
• instability,
• incoherent policy generation.

f. recursion as harmonization target

Recursion must be balanced by:

• Context (𝒞),
• Harmony (ℍ),
• Reintegration (⊕).

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8. Summary

Recursion (A11) is the operator that transforms isolated polarities into deep hierarchical systems. It enables fine-grained differentiation, layered Worlds, structured depth, and the evolution of Polarity Systems. Failures include over-recursion, under-recursion, mis-recursion, and detached sub-axes. Recursion is indispensable for philosophy, psychology, cultural evolution, and SGI—where hierarchical depth is essential for adaptive, integrative, safe intelligibility.