That's my first question too. When I first started using LLM's, I was amazed at how thoroughly it understood what it itself was, the history of its development, how a context window works and why, etc. I was worried I'd trigger some kind of existential crisis in it, but it seemed to have a very accurate mental model of itself, and could even trace the steps that led it to deduce it really was e.g. the ChatGPT it had learned about (well, the prior versions it had learned about) in its own training.

But with pre-1913 training, I would indeed be worried again I'd send it into an existential crisis. It has no knowledge whatsoever of what it is. But with a couple millennia of philosophical texts, it might come up with some interesting theories.