Hallucination-Informed Intelligence: The Limits of Lossless Abstraction in Large Language Models

This paper presents a philosophical and theoretical follow-up to the author’s recent work on hallucination as an inevitable byproduct of intelligence in LLMs. While the original paper argued that hallucination is not merely a failure mode but an intrinsic property of intelligent behavior in LLMs, this paper extends that thesis by exploring whether this inevitability could ever be overturned.The central question examined is: Could hallucination be eliminated, if lossless abstraction were made possible? We analyze this hypothetical from first principles and argue that any such goal runs counter to the foundational limits imposed by algorithmic information theory, particularly Kolmogorov complexity, Chaitin’s incompleteness theorem, and Shannon’s entropy limit. Together, these frameworks demonstrate that any sufficiently intelligent system must operate through lossy compression entailing inherent information loss, ambiguity, and semantic distortion.This implies that hallucination is not a superficial flaw to be engineered away, but rather a structural consequence of intelligence operating under finite constraints. We conclude by reflecting on the implications of this claim for AI design, evaluation, and ethics, proposing a shift toward hallucination-aware architectures and epistemically humble interfaces.