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First, an apology for how fucking long this ended up being, in part thanks to how long winded AI responses are. David wanted me to post it here so I'm posting.

When you ask GPT4 a question about a common paradox or a puzzle, it almost always provides a correct answer. Does it "understand" the answer, or is it merely regurgitating? What would be the difference?

Without delving too deep into the philosophical aspects of whether next word prediction can possibly be said to reason or "understand" anything, what puts "under" in understanding is that concepts are built on top of simpler, more basic concepts.

You could test if a human understands something by modifying the problem enough that memorization no longer helps.

A couple simple probes:

Prompt:

The village barber shaves himself and every other man in the village who don't shave himself. Does he shave himself?

Note that the above is not a paradox. This is how you would expect an ordinary barber to work in a small village.