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

Self-modification is routinely treated as constitutive of artificial superintelligence (SI), yet modification is a relative action requiring a supplement outside the operation. We formalise this on an associative operator algebra A with update operator hat U, difference operator hat D, and self-representation operator hat R, identifying the supplement with operatornameComm(hat U). A propagation theorem shows [hat U,hat R] decomposes through [hat U,hat D], so non-commutation propagates to self-representation. The liar paradox is the rank-one case [hat T,PiL]=0, and emphclass A systems, in which hat U acts on hat D, reproduce it at system scale, yielding a structure coinciding with Priest's inclosure schema and Derrida's diff'erance. Our results show that the strong self-modification taken to define superintelligence may undermine the persistent identity upon which such systems are premised.