Comprehension Without Competence: Architectural Limits of LLMs in Symbolic Computation and Reasoning

Large Language Models (LLMs) exhibit impressive surface fluency but consistently struggle with tasks that require symbolic reasoning, arithmetic accuracy, and logical consistency. This paper identifies a significant gap between comprehension and competence in LLMs, attributing failures to a computational 'split-brain syndrome' where the pathways for instruction and action are dissociated. The study emphasizes that LLMs articulate correct principles without reliably applying them, highlighting a core limitation in their architectural design.