The Meta-Mathematical Root of AI Hallucination--- A Diagnosis Based on the Zhu--Liang Holism Theorems

Abstract

The ``hallucination'' problem of current large language models---generating content that contradicts facts and ruptures logic---is widely regarded as a target for engineering optimization. Based on the core theorems of the Zhu--Liang Holism Axiomatic System (Whole--Part Correspondence Theorem, Truth Function Theorem, Terminal Coalgebra Theorem), this paper provides, for the first time, a rigorous meta-mathematical diagnosis of AI hallucination: \textbf{AI hallucination is the recurrence of Russell's paradox in the domain of cognitive engineering; both stem from the absence of the compatibility constitution $f_Q|_P = f_P$}. We prove that current AI architectures (token-level autoregression, embedding space vectorization, ``emergence'' narrative) fully reproduce the threefold murder perpetrated by reductionist generalization upon the foundation of set theory---dissolving the compatibility condition, reversing logical priority, and forgetting the functoriality of the whole function. Every hallucinatory output of an AI is the engineering equivalent of the inevitable ``illegitimate set'' $R = \{x \mid x \notin x\}$ produced in the absence of compatibility constraints. This paper further provides a therapeutic path: only by explicitly constructing a global semantic function $F$ and constraining every local generation with the compatibility condition can AI ascend from a formal symbol game to a legitimate substructure of the Truth Space $\Omega$. Conclusion: AI hallucination is not an engineering limitation, but the inevitable manifestation of an erroneous meta-mathematical foundation.

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