Deconstructing Superintelligence: Identity, Self-Modification and Différance

2026-04-21

AI Summary

This study investigates the external supplementation mechanisms underpinning self-modification in artificial superintelligence and the resulting collapse of self-referential structures. By constructing a combined algebraic framework that integrates update, discrimination, and self-representation operators, the paper formally characterizes the self-modification process. It introduces, for the first time, Derrida’s concept of “différance” and Priest’s closure schema into superintelligence theory. The work establishes a decomposition theorem for non-commutative propagation, demonstrating that global self-modifying systems inevitably reproduce liar-paradox-like commutative collapse structures. This result furnishes a novel theoretical paradigm for understanding self-reference in artificial intelligence.

Technology Category

• Machine Learning: Unsupervised & Self-Supervised Learning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Self-modification is often taken as constitutive of artificial superintelligence (SI), yet modification is a relative action requiring a supplement outside the operation. When self-modification extends to this supplement, the classical self-referential structure collapses. We formalise this on an associative operator algebra $\mathcal{A}$ with update $\hat{U}$, discrimination $\hat{D}$, and self-representation $\hat{R}$, identifying the supplement with $\mathrm{Comm}(\hat{U})$; an expansion theorem shows that $[\hat{U},\hat{R}]$ decomposes through $[\hat{U},\hat{D}]$, so non-commutation generically propagates. The liar paradox appears as a commutator collapse $[\hat{T},Π_L]=0$, and class $\mathbf{A}$ self-modification realises the same collapse at system scale, yielding a structure coinciding with Priest's inclosure schema and Derrida's diffèrance.

Problem

• superintelligence
• self-modification
• self-reference
• liar paradox
• différance

Innovation

• self-modification
• operator algebra
• commutator collapse
• inclosure schema
• différance