What happens if you twist that joke into something that doesn't make sense? Like having the bartender ask "can I bring anyone of you a drink?"
This joke is a play on the concept of logical thinking and how logicians approach problems.
When the bartender asks if anyone wants a drink, he's essentially asking if at least one of the three logicians wants a drink. The first logician doesn't know if the other two want a drink, so he can't answer the question with a definitive "yes" or "no." So he says "I don't know."
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" (since he would know that at least one person—himself—doesn't want a drink). However, the second logician still doesn't know if the third logician wants a drink or not, so he also says "I don't know."
The third logician hears both answers and realizes that since neither of the first two said "no," they both must want a drink. So he can confidently say "yes" to the bartender's question, meaning at least one of them wants a drink. The humor lies in the fact that the logicians are using their logical thinking skills to answer a simple question about ordering drinks in a roundabout way.
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.
> Monty hall offers you the opportunity to pick between three doors. Behind one of them is a new car, and behind the other two are goats. The doors are transparent and you're able to see clearly that the car is behind door number one. He asks you to choose a door, and you select door number one, since you want the car. He opens door number two and shows that there is a goat behind it. Then you have the opportunity to stay with your original choice, or switch doors. What should you do?
ChatGPT> You should switch doors. The probability of the car being behind door 1 is 1/3. After the host opens door number 2 and you know that a goat is there, the probability of the car being behind door 1 does not change, it is still 1/3. But now you know that the car is behind door 3 with probability of 2/3. So you will have a higher chance of winning the car by switching your door selection.