https://arxiv.org/abs/2402.09733
https://arxiv.org/abs/2305.18248
https://www.ox.ac.uk/news/2024-06-20-major-research-hallucin...
So I don't think it's that they have no concept of correctness, they do, but it's not strong enough. We're probably just not training them in ways that optimize for that over other desirable qualities, at least aggressively enough.
It's also clear to anyone who has used many different models over the years that the amount of hallucination goes down as the models get better, even without any special attention being (apparently) paid to that problem. GPT 3.5 was REALLY bad about this stuff, but 4o and o1 are at least mediocre. So it may be that it's just one of the tougher things for a model to figure out, even if it's possible with massive capacity and compute. But I'd say it's very clear that we're not in the world Gary Marcus wishes we were in, where there's some hard and fundamental limitation that keeps a transformer network from having the capability to be more truthful as a it gets better; rather, like all aspects, we just aren't as far along as we'd prefer.