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

Large Language Models (LLMs) display striking surface fluency yet systematically fail at tasks requiring symbolic reasoning, arithmetic accuracy, and logical consistency. This paper offers a structural diagnosis of such failures, revealing a persistent gap between comprehension and competence. Through controlled experiments and architectural analysis, we demonstrate that LLMs often articulate correct principles without reliably applying them—a failure rooted not in knowledge access, but in computational execution. We term this phenomenon the computational split-brain syndrome, where instruction and action pathways are geometrically and functionally dissociated. This core limitation recurs across domains, from mathematical operations to relational inferences, and explains why model behavior remains brittle even under idealized prompting. We argue that LLMs function as powerful pattern completion engines, but lack the architectural scaffolding for principled, compositional reasoning. Our findings delineate the boundary of current LLM capabilities and motivate future models with metacognitive control, principle lifting, and structurally grounded execution.

Introduction. When asked whether 9.9 is greater than 9.11, Claude Sonnet 4 confidently states that 9.11 is larger, explaining that “since 90 is greater than 11 in the hundredths place, 9.11 is the larger number”—while simultaneously calculating that 9.11 - 9.9 = 0.21 (incorrect). GPT-4o claims that “9.11 is greater than 9.9” in mathematical contexts, invoking software versioning to justify the confusion. Yet when asked to explain how to compare decimal numbers, both models provide flawless algorithmic descriptions: “Write the numbers one above the other, aligning the decimal points... Compare digit by digit from left to right.” Claude Sonnet 4 even works through the exact same comparison correctly as an instructional example, concluding that “9.90 > 9.11.” Both models articulate decimal comparison procedures with textbook precision while failing to execute them reliably. This disconnect reveals a fundamental limitation in Large Language Models: they exhibit comprehension without competence—a systematic dissociation where models can perfectly explain principles they cannot reliably execute.

Discussion / Conclusion. The apparent intelligence of LLMs belies a deeper fragility. Despite their success in pattern-rich tasks, these models consistently fail to generalize principles, execute symbolic computations, or reason reliably—even under idealized conditions. Our analysis reveals that these failures are not incidental but structural: LLMs dissociate instruction interpretation from execution, leading to a computational split-brain syndrome that prevents the formation of robust, composable operations. This diagnosis clarifies why interpretability tools often uncover expressive artifacts rather than reliable algorithms, and why model self-explanations may diverge from the actual pathways used in computation. It also explains how training order can influence which internal patterns are embedded and where—even when outward behavior remains stable—causing interpretability efforts to surface path-dependent artifacts rather than consistent mechanisms.