>I read the puzzle of identical
>twins and I don't think
>I understand all parts of
>it.

I believe you understood the puzzle well enough to pose a very valid question about it.

>Now, calling him a liar wouldn't
>be true, because even though
>he thinks wrong and says
>the opposite, he's still telling
>the truth.

Right. People are not judged by their thoughts, but by their actions. In so far as two people outwardly behave the same, they should be given an equal treatment in any court of law.

>If they both are telling the
>truth, then why would you
>want to find the liar??

In truth, there seldom exists a good reason for us to do what we are doing, not to mention mathematicians who get paid mostly for doing unreasonable things.

>I would appreciate if someone tell
>me if I'm thinking right.

Seriously, you are absolutely right. We can't call a fellow a liar who only tells truth.

But forget for a moment about the reality and try to think about the abstraction that Smullyan might have had in mind.

Or, think of the following scenario. Two boys were born - one a truth teller and the other a liar. They played and grew together and for a long while they were what they were destined to be, an honest man and a liar. The honest brother was loved and esteemed, the liar was despised and unhappy. He suffered terribly, especially mentally. Not yet 30, he suffered a stroke, from which he recovered fully physically, but not mentally. 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.

It rains. Does it rain now?
Thinks yes, has an impulse to say no, says yes.

Is this tomato blue?
Thinks no, has an impulse to say yes, says no.

Are you a truth teller?
Thinks no, has an impulse to say yes, says no.

How does it sound to you?