That is not correct though. With the question phrased this way the second and third logicians don’t know if the previous ones want a drink or not.
The question is if any of them want a drink. Ie if at least one of them wants a drink.
If the first person wants a drink then they know at least one person wants a drink and so could answer "yes". If they don't personally want a drink they don't know if either of the other 2 might want a drink so they would reply "I don't know"
On the upside, this makes for a good way to test the logical abilities of a LLM. On the downside, whatever part was considered a "joke" before has been completely obliterated.
> The second logician hears the first one's answer and concludes that the first logician must want a drink, because if he didn't, he would have said "no"
> The third logician hears both answers and realizes that since neither of the first two said "no," they both must want a drink.
IOW, when asked the puzzle with "anyone", it repeated the explanation for "all", which seems to support the hypothesis that even GPT-4 is still just a "stochastic parrot" repeating what it sees and unable to reason about slight variations.