The Relativity of AGI: Distributional Axioms, Fragility, and Undecidability

TL;DR

This paper explores the theoretical limits of defining and certifying Artificial General Intelligence (AGI), revealing its inherent relationality, fragility, and undecidability, which challenge the notion of universal, self-verifiable AGI.

Contribution

It formalizes AGI as a distributional, resource-bounded semantic predicate and derives fundamental limitations on its invariance, robustness, transferability, and certifiability.

Findings

AGI is inherently relational and cannot be distribution-independent.

Small changes in task distribution can invalidate AGI properties.

AGI cannot be fully certified or self-verified by any computable procedure.

Abstract

We study whether Artificial General Intelligence (AGI) admits a coherent theoretical definition that supports absolute claims of existence, robustness, or self-verification. We formalize AGI axiomatically as a distributional, resource-bounded semantic predicate, indexed by a task family, a task distribution, a performance functional, and explicit resource budgets. Under this framework, we derive four classes of results. First, we show that generality is inherently relational: there is no distribution-independent notion of AGI. Second, we prove non-invariance results demonstrating that arbitrarily small perturbations of the task distribution can invalidate AGI properties via cliff sets, precluding universal robustness. Third, we establish bounded transfer guarantees, ruling out unbounded generalization across task families under finite resources. Fourth, invoking Rice-style and G\"odel--Tarski arguments, we prove that AGI is a nontrivial semantic property and therefore cannot be soundly and completely certified by any computable procedure, including procedures implemented by the agent itself. Consequently, recursive self-improvement schemes that rely on internal self-certification of AGI are ill-posed. Taken together, our results show that strong, distribution-independent claims of AGI are not false but undefined without explicit formal indexing, and that empirical progress in AI does not imply the attainability of self-certifying general intelligence.