Deconstructing Superintelligence: Identity, Self-Modification and Différance

Abstract

Self-modification is routinely treated as constitutive of artificial superintelligence (\textbf{SI}), yet modification is a relative action requiring a \emph{supplement} outside the operation. We formalise this on an associative operator algebra $\mathcal{A}$ with update operator $\hat{U}$, difference operator $\hat{D}$, and self-representation operator $\hat{R}$, identifying the supplement with $\mathrm{Comm}(\hat{U})$. A propagation theorem shows $[\hat{U},\hat{R}]$ decomposes through $[\hat{U},\hat{D}]$, so non-commutation propagates to self-representation. The liar paradox is the rank-one case $[\hat{T},{\hat{I}}_L]=0$, and \emph{class $\mathbf{A}$} systems, in which $\hat{U}$ acts on $\hat{D}$, reproduce it at system scale, yielding a structure coinciding with Priest's inclosure schema and Derrida's \emph{différance}. Our results show that the strong self-modification taken to define superintelligence may undermine the persistent identity upon which such systems are premised.

Camera-ready version, AGI-2026