aiqbench analysis
This research formalizes the tension between self-modification and persistent identity in artificial superintelligence using associative operator algebra. By demonstrating that non-commutation propagates to self-representation, the study suggests that strong self-modification capabilities may inherently undermine the stable identity required for such systems. The findings bridge formal logic with philosophical concepts like Derrida's *différance*, offering a rigorous mathematical framework for analyzing the limits of autonomous AI evolution.
Deconstructing Superintelligence: Identity, Self-Modification and Diff\'erance
arXiv:2604.19845v4 Announce Type: replace 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.
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{différance}. Our results show that the strong self-modification taken to define superintelligence may undermine the persistent identity upon which such systems are premised.
Artificial Intelligence (cs.AI)
arXiv:2604.19845 [cs.AI]
(or arXiv:2604.19845v4 [cs.AI] for this version)
Full text under the publisher's open licence · 138 words
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