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

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 $\operatorname{Comm}(\hat U)$. 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 $[\hat T,\Pi_L]=0$, 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{diff\'erance}. Our results show that the strong self-modification taken to define superintelligence may undermine the persistent identity upon which such systems are premised.