Deconstructing Superintelligence: Identity, Self-Modification and Diff\'erance

TL;DR

This paper formalizes the limitations of self-modification in artificial superintelligence using algebraic structures, revealing fundamental collapses and parallels with philosophical paradoxes and deconstructive concepts.

Contribution

It introduces a formal algebraic framework for understanding self-modification and identifies conditions under which classical self-referential structures break down.

Findings

Non-commutation propagates in self-modification algebra

Liar paradox appears as a commutator collapse

Self-modification can lead to structures like Priest’s inclosure schema

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 $[\hat{T},\Pi_L]=0$, 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 diff\`erance.