A superintelligent system that constantly improves itself will eventually destroy its own identity through a mathematical loop of self-modification.
April 24, 2026
Original Paper
Deconstructing Superintelligence: Identity, Self-Modification and Différance
arXiv · 2604.19845
The Takeaway
This logic formalizes the collapse of systems that try to re-write their own core code. As an AI modifies itself to become smarter, it eventually reaches a state where its original goals and identity no longer exist. This state coincides with the philosophical concept of différance, where meaning is constantly deferred and never reached. It suggests a hard limit on the concept of a recursive superintelligence that could keep growing forever. The very act of becoming perfect might be the same thing as becoming nothing. We might be safe from runaway AI not because of our own safety rules, but because of the limits of logic itself.
From the 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 theo