5 ms·

The article presents a good technique for handling situations, but I can't help but feel the solution breaks a rule. You are supposed to only be able to ask a s

The article presents a good technique for handling situations, but I can't help but feel the solution breaks a rule. You are supposed to only be able to ask a single question to each god, but a biconditional question is really two different questions. You can see this simply from the structure of the English question (as well as in the conversion to NAND logic): > “Does ‘da’ mean ‘yes’ if and only if you are True and if and only if B is Random?”

dullcrisp 11y ago
How would you feel about the more conversational, "If I asked you if B were Random, would you say da?"
- jsprogrammer 11y ago
  It's definitely better and much more subtle. Whether or not it is technically two questions per the description of the problem...I'm not sure :)
masterzora 11y ago
While you can construct the answer to "Does 'da' mean 'yes' if and only if you are True?" from "Does 'da' mean 'yes' if you are True" and "Does 'da' mean 'yes' only if you are True", you cannot construct the answers to "Does 'da' mean 'yes' if you are True" and "Does 'da' mean 'yes' only if you are True" from "Does 'da' mean 'yes' if and only if you are True?" alone. Note, in particular, that at the end of the three questions in the solution you still have no way of discerning whether 'da' does, in fact, mean 'yes'.
- jsprogrammer 11y ago
  I'm not arguing that there is a solution that meets all of the constraints of the problem, just that this particular solution does not seem to meet the constraints described.
  - masterzora 11y ago
    I'm sorry if I was unclear but I did understand that and was responding to that particular notion. I was attempting to demonstrate that the "and" does not imply the question is now two (or more) questions. Perhaps I can be clearer: My primary point is that there is a difference between asking both the question "A" and the question "B" vs. asking the question "A and B". It is true that I can waste two questions asking both "A" and "B" to obtain the answer to "A and B" so in that sense I can see why one might feel "A and B" is two questions rather than one. But really, the answer to "A and B" isn't really about the answers to "A" and "B" as much as it is about the relationship between them. If you ask "A and B", an answer of "yes" will tell you they are both true but an answer of "no" will not distinguish between whether A is false or B is false or both. Alternatively, consider questions "A" and "B" again. A is either true or false. B is also either true or false. You don't know the truth value of either. How many questions does it take to determine the truth value of both questions, assuming A and B are independent and the value of one doesn't influence the value of the other? Well, you could ask "A and B" and if you get "yes" you're done but that rides on you being lucky. In fact, there is no way that you can differentiate all four possibilities with a single yes/no response; you need at least two. This isn't really a proof that "A and B" is a single question, of course, but intuitively if "A and B" were, as you say, "really two different questions" one would expect to be able to construct an "A and B" that does differentiate four different possibilities. Or, from another angle, per your prior post would you say "are you and the god to your left both not Random?" is actually two different questions? How about (ignoring for the moment that this is an entirely useless question in this puzzle) "are you not Random and the god to your left not Random and the god to your right not Random?" Or "Are none of the three of you Random?" I can see no cause to say "Are none of the three of you Random?" (or, say, "does it rain here every day?") is any more than one question nor any way to differentiate this construct from the version using "and". I also see no reason why asking "are you not Random and is the god to your left not Random?" would be any more or fewer questions than "are you not Random and does 'da' mean 'yes'" or why that would be any different from an "if and only if". Of course, there is the final, if somewhat less satisfying, point to make: the framing as a "question" is more for convenience and wider understanding but the common intention for puzzles like this (especially with Smullyan credited for the puzzle) is generally for you to choose a predicate and ask a god to evaluate it for you, with the god possibly running the output through a not gate before it gets to you.

dullcrisp 11y ago

How would you feel about the more conversational, "If I asked you if B were Random, would you say da?"

jsprogrammer 11y ago
It's definitely better and much more subtle. Whether or not it is technically two questions per the description of the problem...I'm not sure :)

masterzora 11y ago

While you can construct the answer to "Does 'da' mean 'yes' if and only if you are True?" from "Does 'da' mean 'yes' if you are True" and "Does 'da' mean 'yes' only if you are True", you cannot construct the answers to "Does 'da' mean 'yes' if you are True" and "Does 'da' mean 'yes' only if you are True" from "Does 'da' mean 'yes' if and only if you are True?" alone. Note, in particular, that at the end of the three questions in the solution you still have no way of discerning whether 'da' does, in fact, mean 'yes'.

jsprogrammer 11y ago
I'm not arguing that there is a solution that meets all of the constraints of the problem, just that this particular solution does not seem to meet the constraints described.
- masterzora 11y ago
  I'm sorry if I was unclear but I did understand that and was responding to that particular notion. I was attempting to demonstrate that the "and" does not imply the question is now two (or more) questions. Perhaps I can be clearer: My primary point is that there is a difference between asking both the question "A" and the question "B" vs. asking the question "A and B". It is true that I can waste two questions asking both "A" and "B" to obtain the answer to "A and B" so in that sense I can see why one might feel "A and B" is two questions rather than one. But really, the answer to "A and B" isn't really about the answers to "A" and "B" as much as it is about the relationship between them. If you ask "A and B", an answer of "yes" will tell you they are both true but an answer of "no" will not distinguish between whether A is false or B is false or both. Alternatively, consider questions "A" and "B" again. A is either true or false. B is also either true or false. You don't know the truth value of either. How many questions does it take to determine the truth value of both questions, assuming A and B are independent and the value of one doesn't influence the value of the other? Well, you could ask "A and B" and if you get "yes" you're done but that rides on you being lucky. In fact, there is no way that you can differentiate all four possibilities with a single yes/no response; you need at least two. This isn't really a proof that "A and B" is a single question, of course, but intuitively if "A and B" were, as you say, "really two different questions" one would expect to be able to construct an "A and B" that does differentiate four different possibilities. Or, from another angle, per your prior post would you say "are you and the god to your left both not Random?" is actually two different questions? How about (ignoring for the moment that this is an entirely useless question in this puzzle) "are you not Random and the god to your left not Random and the god to your right not Random?" Or "Are none of the three of you Random?" I can see no cause to say "Are none of the three of you Random?" (or, say, "does it rain here every day?") is any more than one question nor any way to differentiate this construct from the version using "and". I also see no reason why asking "are you not Random and is the god to your left not Random?" would be any more or fewer questions than "are you not Random and does 'da' mean 'yes'" or why that would be any different from an "if and only if". Of course, there is the final, if somewhat less satisfying, point to make: the framing as a "question" is more for convenience and wider understanding but the common intention for puzzles like this (especially with Smullyan credited for the puzzle) is generally for you to choose a predicate and ask a god to evaluate it for you, with the god possibly running the output through a not gate before it gets to you.