Deconstructing Superintelligence: Identity, Self-Modification and Différance
This addresses foundational issues in AI safety and philosophy for researchers in superintelligence, but it is incremental as it builds on existing formal and philosophical frameworks.
The paper tackles the problem of self-modification in artificial superintelligence by formalizing it on an associative operator algebra, showing that non-commutation generically propagates and leads to a structure coinciding with known paradoxes and philosophical concepts.
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.