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

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arXiv:2604.19845v1 Announce Type: new 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

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Computer Science > Artificial Intelligence [Submitted on 21 Apr 2026] Deconstructing Superintelligence: Identity, Self-Modification and Différance Elija Perrier 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 diffèrance. Comments: Under review Subjects: Artificial Intelligence (cs.AI) Cite as: arXiv:2604.19845 [cs.AI] (or arXiv:2604.19845v1 [cs.AI] for this version) https://doi.org/10.48550/arXiv.2604.19845 Focus to learn more Submission history From: Elija Perrier [view email] [v1] Tue, 21 Apr 2026 11:39:50 UTC (677 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev | next > new | recent | 2026-04 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)

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