Not necessarily do logic, but mimic it, like it can mimic coherent writing and basic conversation despite only being a statistical token muncher. The hope is that there’s sufficient information in the syntax to model the semantics, in which case a sufficiently complex and well-trained model of the syntax is also an effective model of the semantics. This apparently holds up well for general language tasks, meaning “what we mean” is well-modeled by “how we say it.” It’s plausible, at face value, that rigorous argumentation is also a good candidate, which would give language models some way of mimicking logic by talking through a problem. It’s just not very good in practice right now. Maybe a better language model could do better, maybe not for a reasonable cost.