One of the results of the illness was that he completely lost confidence in his beliefs. At some point afterwards, he decided to reverse any spontaneous response of his. The moment he feels a desire to say something, he will now say the opposite.

Ok. If that's what really happened, how would we know about it? I don't think that person would go and tell other people what he thinks he's doing, because he wants to lie and he doesn't want other people to know that he is.

Am I right??

But it's just a story, and it's our story at that. I am telling you this story, and you ask me how could I know.

To make my story more palatable, I can add another line. I was the nurse who delivered the boys. As the result, I developed an attachment to the boys, as well as to the mother, who was a single mom too. So we stayed friends after they left the hospital.

The time went by. I continued in my job which paid for my graduate studies and eventually landed a job in a mental clinic. When the liar boy - now a grown up fellow - felt sick, his mother - now my dear friend - sought my advice. So I was in a position to observe the said change in boy's behavior.

In fact, the change was not that sudden. The boy, while in the hospital, began experiencing doubts about his beliefs and shared the doubts with me, his doctor.

> I don't think that person would go
> and tell other people what he thinks
> he's doing

Right, in my story he does no such thing. He only answers questions when asked.

> because he wants to lie and he doesn't
> want other people to know that he is

No, as far as I understand - or rather remember - our conversations, they boy did not care about what other people think, not a little bit. From the birth on and especially after his illness, he was absolutely preoccupied with his own thoughts. He still is.

I don't think the problem said anything about that. But I agree with you.
Still, if both boys were telling the truth then you can't really ask them if they are the truth tellers. What you should ask is if they are crazy or not, and they'll tell you the truth.

Thanks for responding, and sorry for waisting your time.

You are right. I was just trying to come up with a background story for Smullyan's puzzle. That's all.

>But I
>agree with you.

No, no. It's I who agree with you.

>Still, if both boys were telling
>the truth then you can't
>really ask them if they
>are the truth tellers. What
>you should ask is if
>they are crazy or not,
>and they'll tell you the
>truth.

Well, I did ask what I asked.

>Thanks for responding, and sorry for
>waisting your time.

I am sorry you said that. No one can waste my time, but I myself. And no one can force me into correspondence against my will.

You brought up a very valid question, a question that I have overlooked. My first reaction was to just raise my arms and plead guilty. But then the story came up.

The point of the puzzle was not so much to fit the reality as to create a situation in which the same question is not in fact the same. With my bent of mind I never so much as stopped to think as to what made the second fellow a liar when in fact he always was telling truth.

I was very much satisfied with our correspondence, which also served as a nice dinner topic today. Thank you for providing me with an opportunity.

I had no intention of offending you. Please loosen up. The puzzle had a point, and for me this is what was important about it. But different people see the same thing with different eyes. By inventing the story I was trying to refocus your attention to that abstraction that Smullyan had in mind. That's all.

I'm very sorry I made you feel that way, I didn't mean to.

>I had no intention of offending you.

You never did. It would be really hard to offend me even if you tried.

>But different people see the same thing with different eyes.

That's very true. Sometime I don't think about the answer to the puzzle as much as I think about the puzzle itself. I know my points of view will change, because I'm just 14 and I still have lots to learn.

I'm sorry if I sounded mean at some points, I didn't mean to.

Thanks a lot for your time.

Yours is one possible interpretation. But this is definitely not what Smullyan had in mind, as I tried to explain in our previous correspondence.

The fellow has been born with a mental label of which he is aware. It's either this or that. When asked about his identification he simply reports the label.

Smullyan's formulation is clearly ambiguous. I am ready to admit that much. In fact I have. While coming up with other interpretations points to a certain agility of the mind, I am only interested in the one interpretation he has in mind. Otherwise, we shall be treading in circles with no end in sight.

You may be curious to have a look at the discussion on the Monty Hall Dilemma:

www.cut-the-knot.com/hall.shtml

There must be a list of links to other places on the Web. If not, just seaarch the Web. A small problem gave rise to an unending and heated discussion. I'd like to avoid its repetition.