Transformer models are universal, which isn't very surprising given they're made of things which are also universal when configured right, so they absolutely can learn the rules of logic.

Some say that reason requires consciousness, which I'm… frustrated by given the 50 common meanings of the word "consciousness"; but to merely use logic as your standard here?

Why, of all the things people could object to in an LLM, why is logic what people want to pick on? It's the weakest possible objection IMO.