Scaling Law Limits: Data-Driven ML Fails Symbolic Logical Reasoning.

This research posits that data-driven machine learning systems, despite advancements in scaling laws, are fundamentally limited in their ability to achieve rigorous symbolic-level logical reasoning. The authors identify two primary methodological constraints preventing this: first, training data often lacks the granularity to differentiate all valid syllogistic reasoning types; second, end-to-end mapping from premises to conclusions can introduce conflicting training signals for neural components responsible for pattern recognition versus logical inference. To support their theoretical analysis, the paper presents experimental evidence. It demonstrates that Euler Net, a neural network designed for logical reasoning, fails to achieve rigorous syllogistic reasoning. Furthermore, tests on recent ChatGPT models (GPT-5-nano and GPT-5) reveal that the surface form of syllogistic statements—whether presented as words, double words, simple symbols, or long random symbols—significantly impacts reasoning performance. While GPT-5 might achieve 100% accuracy on certain tasks, the study highlights that its explanations can still be incorrect, indicating a lack of true symbolic understanding. The conclusion is that supervised machine learning, even when achieving high accuracy, does not attain the same level of rigor as symbolic logical reasoning, suggesting a ceiling to the scaling law's effectiveness in this domain.