> There is, and on the face of it, it seems almost identical to the one I started with. Instead of asking what would the best essay be? I should have asked how do you write essays well? Though these seem only phrasing apart, their answers diverge. The answer to the first question, as we've seen, isn't really about essay writing. The second question forces it to be.
I'm reminded of a philosophy joke:
An angel came down for a meeting of the American Philosophical Association. Greeting the assembled philosophers, the angel offered to answer any single question for them. Immediately the philosophers set to arguing about what they should ask. So the angel said, “Alright, you figure out what you want to ask. I’ll come back tomorrow.” And he left the philosophers to deliberate.
As the philosophers argued about the best question to ask, one philosopher suggested: “What is the best question to ask?”, in the hope that some day another angel might make a similar offer, at which point they could then ask the best question. But this suggestion was rejected by those who feared that no such opportunity would arise and did not want to waste their only question.
Another philosopher suggested asking "What is the answer to the best question we could ask?" Which was roundly criticized because of the possibility that the answer would give no hint to the question it answered. One philosopher cheekily pointed out that the angel might reply "42 of course."
Finally, the philosophers agreed on the following question: “What is the ordered pair whose first member is the best question to ask, and whose second member is the answer to that question?” Satisfied with their decision, the philosophers went to bed.
The next day, they posed their question, and the angel replied: “Of course: it is the ordered pair whose first member is the question you just asked, and whose second member is the answer I am now giving.” And then he disappeared.
This is like trying to access information buried inside a data structure. You need the right incantations to get the right information content and not just the headers.
...I don't think I get it. Like, if the angel is going to be a jerk, he could be a jerk with any question.
The philosophers could have asked "What is the meaning of life?" and the angel would answer "Of course, it is the meaning of life," without any of this ordered pair nonsense.
I think it is a reference to Gödel's incompleteness theorem.
> What is the ordered pair whose first member is the best question to ask, and whose second member is the answer to that question?
Is isomorphic to:
> What is the highest cardinality set in the set of all sets?
"What is the best question in the set of all questions?" is itself "what is the best question in the set of all questions?"
"What is the highest cardinality set in the set of all sets?" is itself "the set of all sets".
"What is the answer to that question?" is an assumption of bounded size, and therefore isomorphic to saying "the largest set that is not itself."
> What is the answer to the best question we could ask?" Which was roundly criticized because of the possibility that the answer would give no hint to the question it answered. One philosopher cheekily pointed out that the angel might reply "42 of course."
42 is a valid answer because if you assume two contradictory statements are true at the same time, then all statements are true. The cheeky philosopher is pointing out that "What is the answer to the best question we could ask?" implies self reference, which implies a contradiction.
The philosophers asked a self referential question and got a self referential answer.
I'm reminded of a philosophy joke:
An angel came down for a meeting of the American Philosophical Association. Greeting the assembled philosophers, the angel offered to answer any single question for them. Immediately the philosophers set to arguing about what they should ask. So the angel said, “Alright, you figure out what you want to ask. I’ll come back tomorrow.” And he left the philosophers to deliberate.
As the philosophers argued about the best question to ask, one philosopher suggested: “What is the best question to ask?”, in the hope that some day another angel might make a similar offer, at which point they could then ask the best question. But this suggestion was rejected by those who feared that no such opportunity would arise and did not want to waste their only question.
Another philosopher suggested asking "What is the answer to the best question we could ask?" Which was roundly criticized because of the possibility that the answer would give no hint to the question it answered. One philosopher cheekily pointed out that the angel might reply "42 of course."
Finally, the philosophers agreed on the following question: “What is the ordered pair whose first member is the best question to ask, and whose second member is the answer to that question?” Satisfied with their decision, the philosophers went to bed.
The next day, they posed their question, and the angel replied: “Of course: it is the ordered pair whose first member is the question you just asked, and whose second member is the answer I am now giving.” And then he disappeared.