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

A new paper argues that data-driven machine learning systems cannot achieve the rigorous logical reasoning of symbolic methods, identifying fundamental limitations that scaling alone cannot overcome [1]. The preprint, posted to the open-access repository arXiv on June 24, 2026, contends that supervised deep learning faces two methodological barriers to symbolic-level syllogistic reasoning [1][7]. First, training data cannot distinguish all 24 types of valid syllogistic reasoning. Second, the end-to-end mapping from premises to conclusion creates contradictory training targets between the neural components responsible for pattern recognition and those needed for logical deduction [1]. The authors experimentally illustrate this limit using Euler Net, a model they report cannot achieve rigorous syllogistic reasoning [1]. They further tested recent ChatGPT models—GPT-5-nano and GPT-5—on the satisfiability of syllogistic statements presented in four surface forms: words, double words, simple symbols, and long random symbols [1]. The results showed that surface form affects reasoning performance. While ChatGPT GPT-5 reached 100% accuracy on the task, it still provided incorrect explanations for its answers [1]. The researchers note that empirical training processes are typically stopped after achieving 100% accuracy, which can mask underlying failures in logical rigor [1]. The tension between data-driven and symbolic approaches has deep roots in artificial intelligence research. The field was founded at a 1956 Dartmouth workshop where the first AI program, the Logic Theorist, was presented by Allen Newell and Herbert A. Simon [3]. Early researchers predicted machines as intelligent as humans would exist within a generation, but the complexity of replicating cognition proved far greater than anticipated [3]. Classical computationalism in cognitive science posits that mental processes manipulate symbols according to formal rules, similar to how computers execute algorithms, while connectionism models the mind as a complex network of nodes where information flows through communication [5]. Investment in AI has boomed in the 2020s, driven by the transformer architecture introduced in 2017 and the rapid scaling of large language models like ChatGPT [3]. These models exhibit human-like traits of knowledge and creativity and have been integrated into various sectors, fueling exponential investment [3]. The new preprint’s findings suggest that even as these systems achieve perfect accuracy on certain benchmarks, their underlying reasoning may remain brittle in ways that purely empirical training cannot resolve [1].