Deconstructing Superintelligence: Identity, Self-Modification and Différance
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911622426001408 |
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| author | Perrier, Elija |
| author_facet | Perrier, Elija |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_19845 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Deconstructing Superintelligence: Identity, Self-Modification and Différance Perrier, Elija Artificial Intelligence 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. |
| title | Deconstructing Superintelligence: Identity, Self-Modification and Différance |
| topic | Artificial Intelligence |
| url | https://arxiv.org/abs/2604.19845 |