Wolfgang Schwarz :: Stealing Ideas (and a very difficult logic puzzle)

Stealing Ideas (and a very difficult logic puzzle)

Posted on Friday, 21 Mar 2003.

First, the puzzle:

In a certain country there are two Gods, called A and B. One of them (A or B, you don't know which) only tells the truth, the other one only falsehoods. One day you meet a God in this country and want to find out whether it's A or B. You're only allowed to ask a single yes/no question. Unfortunately, you don't understand the language of the Gods (even though they understand yours). All you know is that their words for "yes" and "no" are "qwer" and "poiu", but you don't know which of these means "yes", and which "no". With what question will you be able to find out whether it's A or B you're talking to?

I can't really say that I have made up this puzzle. Well, I have made it up, but I took all the main ingredients from puzzles by George Boolos, who himself owes them mainly to Raymond Smullyan and a computer scientist whose name I forgot.

Now what if I decide to use this puzzle as an exercise in the logic book? I'm not sure if I will, as it is probably far too difficult. (In fact, nobody I've told it so far was able to solve it. If you find a solution without having read Boolos' article "The hardest logical puzzle ever", send me an email!) But if I use it, should I credit Boolos for the main ingredients? Or Boolos and Smullyan and that other person whose name I forgot? Should I credit Smullyan whenever I mention people that only say true or false sentences?

The same question arises in cases where I would like to steal an example from another textbook. E.g. Tomassi's Logic contains the nice inference

Nothing is better than eternal happiness.
A cheese sandwich is better than nothing.
Therefore a cheese sandwich is better than eternal happiness.

If I use an example like this (that is, an alleged inference that has the same grammatical form), should I credit Tomassi for the idea?

I'm not only interested in the legal facts, but also in what you intuitively think would be appropriate.

Comments

# Mike on 12 March 2008, 20:49

I know this is not exactly what you're looking for, but the cheese sandwich problem is actually a case of grammatical ambiguity. Basicaly if you use math symbols and a straight translation, you get the result you have, but if you use actual predicate logic (which is what is used in serious academic logic) it translates in a way that makes it impossible to have the strange outcome of the paragraph's argument.

basically it's like so:
yours:
N>E
S>N
therefore S>E (transitive property)

however, using predicate logic you get
there does not exist anything that is better than E
all things that are sandwiches are better than nothing
and finally from that you would get that E is better than S which is better than nothing

hope this helps

# M. on 15 March 2008, 14:36

maybe this helps: when I read the puzzle I immediately thought "That is a Smullyan", it is kind of generic (at least for anybody who has read one of his books).

Even if this puzzle is ours in the sense that you put together the pieces, I would think it would be good to add a note that says, "used with "Motive" from B. and S."

M.
NB: the name you forgot was McCarthy by the way :)

# Tom on 20 March 2008, 21:04

I think I've solved the puzzle. There probably are other solutions--I mean, there may be alternative questions to ask which might be simpler and equally effective. The question to ask, in order to tell whether I'm talking to A or B, is this:

Is it true that if 'qwer' means yes, then A will say 'qwer' in reply to the following question: 'Does 'qwer' mean yes in your language?'?

If the person I'm talking to says 'qwer', then he is A; if he says 'poiu', then he is B.
But the answer can't reveal whether the person I'm talking to is the truth-teller or the liar.

The puzzle is very interesting to think about. Thanks for making it up!

# wo on 21 March 2008, 06:32

Hey everybody!

Tom: your solution works well in cases where 'qwer' actually means yes. But what if it means no and, say, you're talking to God A who always tells the truth? Is it then true that *if* 'qwer' means yes, then A will say 'qwer' in reply to 'does 'qwer' mean yes?'? That depends on how we understand the conditional. On the truth-functional (material) understanding, the conditional comes out true, so A will reply affirmatively, saying 'poiu'. That would break your solution. On the other hand, I guess there is a different, perhaps more natural understanding of the conditional on which your solution works.

I've posted another (somewhat simpler) solution in the follow-up entry: http://www.umsu.de/wo/archive/2003/03/24/Exercises_and_Puzzles.

In general, since this entry is (exactly) 5 years old now, those issues aren't really urgent any more. The logic textbook I was working on at the time has long been published.

# Tom on 22 March 2008, 23:17

Thanks for your comment, Wo!

I didn't realize that my 'solution' has such a problem. But you are right. I should have put more thought into it. What if I make a little revision:

If 'qwer' means yes, will it be true that A will say 'qwer' in reply to the following question: 'Does 'qwer' mean yes in your language?'?

# Dave on 04 May 2008, 01:26

If I were to encounter such a God, I would ask:

"If 1) I were to stipulate that 's' denotes a "poiu/qwer" question so hard that answering with either a 'poiu' OR 'qwer' would be a false answer and 2) I were to ask you, "s?" what, if anything, would you say in response: 'poiu' or 'qwer'?"

If the God says anything it's B; if the God says nothing, it's A.

5 years too late? ah well. I suspect I'm a big fat cheater anyway.

# carlllord on 16 December 2008, 14:44

If the riddles of Raymond Smullyan likes you, then this web ( http://4chests.blogspot.com) too. Sure.

Wolfgang Schwarz

Stealing Ideas (and a very difficult logic puzzle)

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