From Unitary to Binary to Ternary: Scoping Logic for the GenAI Age

Leon Como
Sep 4
2 min read

Executive Summary

Across generations, humanity has relied on distinct logics to anchor, solve, and adapt.

Unitary logic grounds us in unchanging fundamentals.
Binary logic powers closed-loop precision.
Ternary logic enables adaptive continuity in open, evolving systems.

This paper argues that while Boolean logic shaped the digital age, the GenAI age requires an heir: a ternary grammar such as the Circles and Triangles Framework (CTF). The task is not replacement but scoping each logic to where it matters most, ensuring continuity without overreach.

The Historical Progression of Logic

Unitary Logic — The Anchor of Fundamentals

Core: “One is.”
Domains: Laws of thermodynamics, precision mathematics, universal moral codes like “do no harm.”
Strength: Provides certainty, coherence, and universality.
Risk when overextended: Absolutism — the “laws of the king” forcing human complexity into rigid unity.

Binary Logic — The Engine of Closed Loops

Core: True/False, 1/0, Yes/No.
Domains: Digital computation, corporate accounting, compliance systems, bounded games like chess.
Strength: Clarity, precision, repeatability.
Risk when overextended: False dichotomies, brittle systems that collapse when nuance is needed.

Ternary Logic — The Compass of Open Loops

Core: Triangles balanced within circles.
Domains: Generative AI, organizational change, ecosystems, governance of evolving societies.
Strength: Adaptability, emergence, balance across tensions.
Risk when overextended: Paralysis from excessive triangulation when simpler logic suffices.

Operational Scoping

Logic	Use Case	Strength	Risks if Misapplied	Example
Unitary	Anchor fundamentals (laws, constants, ethics)	Universality, stability	Absolutism, rigidity	“Do no harm”, Laws of physics
Binary	Solve bounded, closed loops	Clarity, efficiency	False dichotomies, brittle trade-offs	Boolean circuits, accounting
Ternary	Navigate evolving, open loops	Adaptability, emergence	Complexity overload, indecision	Change management, GenAI governance

Decision Flow: When to Use Which

Is the principle unchanging and universal? → Use Unitary.
Is the problem bounded with closed outcomes? → Use Binary.
Is the system open, continuous, evolving? → Use Ternary.

The Need for an Heir to Boolean

Boolean logic gave us the binary skeleton of the digital age. But the GenAI age, with its conditional, probabilistic, and emergent systems, requires a new universal grammar:

Unitary anchors identity and constants.
Binary powers closed-loop execution.
Ternary governs adaptive continuity.

The Circles and Triangles Framework (CTF) offers that ternary grammar. Like Boolean algebra for binary computation, CTF can serve as the Boolean of the Ternary Age.

Conclusion: Conditional Probabilistic Continuity

Technocrats must move beyond digital hyper-optimization. Unitary anchors keep us from drifting, binary engines keep us precise, and ternary cycles ensure resilience. Together, they form a tri-layered logic of continuity: