Deconstructing Superintelligence: Identity, Self-Modification and Diff’erance

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 $mathcalA$ with update $hatU$, discrimination $hatD$, and self-representation $hatR$, identifying the supplement with $mathrmComm(hatU)$; an expansion theorem shows that $[hatU,hatR]$ decomposes through $[hatU,hatD]$, so non-commutation generically propagates. The liar paradox appears as a commutator collapse $[hatT,Pi_L]=0$, and class $mathbfA$ self-modification realises the same collapse at system scale, yielding a structure coinciding with Priest’s inclosure schema and Derrida’s diff`erance.