Data-driven Machine Learning Cannot Reach Symbolic-level Logical Reasoning – The Limit of the Scaling Law

Recent advancements in neural networks, particularly Large Language Models (LLMs), have led to impressive performance across many tasks. However, a fundamental question remains: can these data-driven systems achieve the rigor of symbolic logical reasoning simply by scaling up training data and computation? This paper argues that they cannot, identifying inherent methodological barriers that prevent supervised learning from reaching the level of formal syllogistic reasoning.

The authors identify two primary reasons why supervised learning fails to achieve symbolic-level rigor. First, training data is fundamentally insufficient to distinguish all 24 valid types of Aristotelian syllogisms. Because logical correctness is determined by structural rules rather than statistical regularities, the models struggle to differentiate between valid conclusions and those that are merely statistically probable.

Second, the end-to-end mapping process creates a conflict between two neural components: pattern recognition and logical reasoning. Pattern recognition systems are designed to infer the whole from parts, a feature that often leads to the injection of extraneous information or "hallucinated" objects into the reasoning process. In contrast, logical deduction requires strict adherence to the information provided in the premises. The model cannot simultaneously optimize for both pattern recognition and logical constraint, leading to failures in reasoning even when the model achieves high accuracy on benchmark datasets.

The authors tested these claims using Euler Net—a convolutional neural network designed for syllogistic reasoning—and the latest iterations of ChatGPT (GPT-5). While these models can achieve high accuracy on standard benchmarks, they remain sensitive to surface-level variations (such as the use of words versus random symbols) and often provide incorrect or inconsistent explanations for their answers. Because training typically stops once a model achieves high accuracy, there is no mechanism to force the model to correct these underlying logical defects. Consequently, the authors conclude that scaling laws do not guarantee the emergence of rigorous logical reasoning.