Deconstructing Superintelligence: Identity, Self-Modification and Différance

• URL: http://arxiv.org/abs/2604.19845v3
• Date: Sat, 25 Apr 2026 00:44:20 GMT
• Title: Deconstructing Superintelligence: Identity, Self-Modification and Différance
• Abstract summary: Self-modification is often taken as of artificial superintelligence (SI), yet modification is a relative action requiring a supplement outside the operation.<n>We formalise this on an associative operator $mathcalA$ with update $hatU$, discrimination $hatD$, and self-representation $hatR$, identifying the supplement with $mathrmComm(hatU)$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $[\hat{T},Π_L]=0$, 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.

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