1. Overview
Unity–Polarity provides the generative foundation for modeling reality as an ontologically unified field whose expression manifests through structured oppositions. These oppositions are not merely contrasts but mutually implicating aspects whose coherence constitutes being itself. Part I introduces the formal and narrative scaffolding for the UPA framework that supports semantic-world modeling and SGI architectures.
Reality is modeled as unity-first (A1) and polarity-expressive (A2). Rather than beginning from isolated substances or purely relational voids, UPA asserts that unity is ontologically prior and polarity is structurally necessary for intelligible differentiation. Axes of polarity are generative, and σ‑pairs define relations between opposite but mutually defining aspects. Semantic worlds (Wᵢ) emerge as structured instantiations under interpretive conditions.
This section establishes why polarity is not derivative of unity nor merely a metaphor, but an essential organizing principle across physical, cognitive, and moral domains. By grounding opposites in generative structure rather than simply conceptual contrast, we provide a coherent mathematical, philosophical, and computational substrate on which SGI can be built.
2. Motivation
Classical metaphysics divides reality into substance and properties; modern information systems often assume independent entities communicating across fixed channels. Both approaches fail to capture the generative dynamism by which world, mind, and meaning arise together. Without polarity as a structural primitive, models are either inertly monistic or fragmented pluralities without unifying explanation.
Unity–Polarity resolves this by introducing a minimal ontology: unity expresses itself through polar differentiation governed by contextual conditions. This minimal generative structure explains how novelty arises (A3), how opposites co‑define (A5), and how semantic transfer is possible (A13–A14). It also allows worlds (Wᵢ) to be modeled in a way that supports inter‑world mapping—a core SGI requirement.
Computationally, polarity provides a structured basis for distributed representation, enabling relational generalization and analogy through σ‑pairs. This avoids the brittleness of symbolic representation and the opacity of uninterpretable embeddings by providing interpretable axes that scaffold semantic inference.
3. Key Concepts
Mini‑Definitions: Each concept below includes (a) a minimal formal description; (b) example signatures; and (c) an illustrative micro‑world (Wᵢ) instantiation where relevant.
3.1 Ontological Unity (A1)
Mini‑definition: The primordial, undivided Whole from which all structured differentiation proceeds. Unity does not exclude multiplicity; rather, multiplicity is its mode of expression.
- Formal hint: Unity ⇒ {possible σ‑axes}
- Example: In World W₀, all potential axes exist in latent form; no differentiation is yet active.
3.2 Structured Polarity (σ‑pairs) (A2)
Mini‑definition: A σ‑axis is a direction of differentiation; a σ‑pair is the opposed aspects that co‑instantiate that direction.
- Formal hint: σᵢ = (+ᵢ, −ᵢ) where +ᵢ↔−ᵢ by co‑definition.
- Example: In World W₁, an Activity–Receptivity axis defines interaction potentials among all entities.
3.3 Novelty (A3)
Mini‑definition: The lawful emergence of new semantic configuration via contextual interaction of σ‑pairs.
- Formal hint: Novelty = f(σ, context)
- Example: In World W₂, new composite roles arise when Activity couples with Self–Other.
3.4 Correlated Similarity (A4)
Mini‑definition: Opposed aspects are correlated in their variation so that their expressions preserve recognizable relational structure.
- Example: In World W₃, Self–Other similarity underlies kinship groupings.
3.5 Co‑Definition (A5)
Mini‑definition: Neither pole of a σ‑pair can be defined without the other; they are mutually intelligible.
- Example: In World W₁, Self has meaning only via Other; change in one modulates the other.
3.6 Transformation (A6)
Mini‑definition: Lawful change along σ‑axes that preserves contextual intelligibility.
- Example: In World W₂, Activity transforms into Receptivity under resource scarcity.
3.7 Contextuality (A7)
Mini‑definition: Activation of σ‑pairs is modulated by local/relational conditions.
- Example: In World W₄, Self–Other balance shifts situationally (e.g., caregiving).
3.8 Harmony / Viability (A15)
Mini‑definition: Polar expression is viable when σ‑pairs remain dynamically balanced relative to context; imbalance triggers loss of coherence.
- Example: In World W₅, excessive Self vs. diminished Other yields social collapse.
4. Part‑Specific Appendix Notes (Preview). Part‑Specific Appendix Notes (Preview)
This part draws on Appendix I to situate Unity–Polarity within broader intellectual traditions. Key influences include:
- Smuts: Holism as integrative but lacking polarity structure.
- Hegel: Dialectic anticipates co‑definition but assumes contradiction + synthesis.
- Laozi: Complementarity emphasizes balance yet lacks generative minimal structure.
- Whitehead: Process ontology aligns with continual becoming but lacks axis formalism.
- Rosen & Varela: Relational + enactive models support contextual viability but need cross‑world formalism.
- Gärdenfors & Spivak: Geometric + categorical tools support structured mapping but lack σ‑pairs.
These sources are integrated and renovated by UPA to form a minimal foundation for world modeling that supports SGI.
5. Forward Linkage
Part II develops the formal axioms and demonstrates how structured polarity generates worlds through semantic instantiation. Part III applies these structures to model cognition, ethics, and simulation—showing how SGI emerges from Unity–Polarity through recursive composition, contextual modulation, and functorial correspondence.
The architecture developed here enables:
- Translating between worlds (A13–A14)
- Modeling identity + difference (A4–A5)
- Handling novelty (A3)
- Ensuring viability (A15)
By grounding SGI in minimal generative principles, we ensure interpretability, extensibility, and ethical coherence.
Open Autonomous Intelligence Initiative 