Alice in Wonderland

[wblipp]

Originally Posted by Mr. P-1

"If my colour isn't the same as my shirt, then the problem is insolvable, therefore the colour must be same as my shirt".

I don't understand how this could be a true statement. I understand how "If my colour is different from every colour I see, then the problem is unsolvable" is true - it's because there are at least two colours that are different from every colour I see, and there is nothing in the problem to further narrow the possibilities. Please elucidate.

[Mr. P-1]

Originally Posted by Mr. P-1

"If my colour isn't the same as my shirt, then the problem is insolvable, therefore the colour must be same as my shirt"

Originally Posted by wblipp

I don't understand how this could be a true statement.

You don't understand how the entire statement "<premise> therefore <conclusion>" could be true? Or you don't understand how the premise which is itself an if ... then statement is true.

I understand how "If my colour is different from every colour I see, then the problem is unsolvable" is true - it's because there are at least two colours that are different from every colour I see, and there is nothing in the problem to further narrow the possibilities. Please elucidate.

This statement is true. Any statement of form "if <foo> then the problem is unsolvable" is true. This is because the problem isn't solvable. Saying that it is doesn't make it so.

[Mr. P-1]

Consider the "problem" defined by the following:

1. Johnny's shirt is green.
2. This problem is solvable.
3. What colour is Sarah's skirt?

Would any one seriously argue that the correct answer is "green" because "there are at least two colours that are different from green, and there is nothing in the problem to further narrow the possibilities"?

[chalsall]

Originally Posted by Mr. P-1

3. What colour is Sarah's skirt?

Given enough bullets and bombs, RED.

[wblipp]

Originally Posted by Mr. P-1

You don't understand how the entire statement "<premise> therefore <conclusion>" could be true? Or you don't understand how the premise which is itself an if ... then statement is true.



This statement is true. Any statement of form "if <foo> then the problem is unsolvable" is true. This is because the problem isn't solvable. Saying that it is doesn't make it so.

I have provided a reasoning for the particular premise I stated. Your reasoning is circular. Your generic <foo> statement is true only if the problem is unsolvable - but you haven't proven that the problem is unsolvable, you have postulated that. At least I don't understand how you have proven it is unsolvable, and I think I have solved it.

[ZFR]

Originally Posted by Mr. P-1

Consider the "problem" defined by the following:

1. Johnny's shirt is green.
2. This problem is solvable.
3. What colour is Sarah's skirt?

Would any one seriously argue that the correct answer is "green" because "there are at least two colours that are different from green, and there is nothing in the problem to further narrow the possibilities"?

In fact, if there are only 2 people at the table and not 31, then the solution to the problem is no longer looks so natural. The professor draws a dot on both heads, asks them to guess the colour and tells them it is solvable. Would you expect them to guess that it has to be same as the other person? It could just as naturally be the colour of their car.

Mr. P-1, would you say the problem (our problem) would be solvable if the following was added:

[...]
At this moment, Little Johnny, the youngest of the group, interrupted him and asked: "But professor, are you sure that we'll be able to solve this task?"
"Do not worry, young man," the Professor replied calmly. "It is possible to solve this task because I..." Unfortunately Alice could not hear the rest of his sentence.
[...]

[wblipp]

Originally Posted by ZFR

In fact, if there are only 2 people at the table and not 31, then the solution to the problem is no longer looks so natural. The professor draws a dot on both heads, asks them to guess the colour and tells them it is solvable. Would you expect them to guess that it has to be same as the other person? It could just as naturally be the colour of their car.

I guess we don't agree on what "it is solvable" means. Yes, I would expect the two logicians to know their colours are the same because any other coloring is unsolvable.

[Mr. P-1]

Originally Posted by wblipp

I have provided a reasoning for the particular premise I stated. Your reasoning is circular. Your generic <foo> statement is true only if the problem is unsolvable - but you haven't proven that the problem is unsolvable, you have postulated that. At least I don't understand how you have proven it is unsolvable, and I think I have solved it.

I have proven it unsolvable:

Originally Posted by Mr. P-1

I cannot see how any choice of dot colours would enable any of the participants to deduce anything with the information provided: Suppose there is. Let C be such a configuration and let Fred be the name of one of the four who moves to the tree at the first bell. Then C can be replaced by a different configuration C' identical to C except that Fred's colour is different. The information available to Fred is identical in the two cases, so Fred cannot distinguish between them. Therefore Fred cannot move to the tree at the first bell. Contradiction.

Originally Posted by wblipp

I guess we don't agree on what "it is solvable" means. Yes, I would expect the two logicians to know their colours are the same because any other coloring is unsolvable.

It is you with the circular argument. The problem as stated is unsolvable because there are multiple (in fact infinite) possibilities consistent with the information given. You've conjured up an additional criterion not stated in the problem which restricts the solution space, and justified this additional criterion on the grounds that it renders the problem solvable. But there is nothing unique about this additional criterion. The problem is rendered solvable with the additional criterion that each logician was given his favourite colour, etc.

[Mr. P-1]

Originally Posted by ZFR

"Do not worry, young man," the Professor replied calmly. "It is possible to solve this task because [B]I..."

"... told four of you the colour I was going to give them in a private conversation this morning, and sewed clues for the rest of you on the seat of their pants."

[Mr. P-1]

Originally Posted by ZFR

In fact, if there are only 2 people at the table and not 31, then the solution to the problem is no longer looks so natural. The professor draws a dot on both heads, asks them to guess the colour and tells them it is solvable. Would you expect them to guess that it has to be same as the other person? It could just as naturally be the colour of their car.

To take this to it's logical conclusion: The professor draws a dot on both heads, and asks them to determine whether the two dots are the same colour or a different colour, and says that this problem is solvable. Are we and the logicians to deduce that the colours must be the same?

[ZFR]

Originally Posted by Mr. P-1

"... told four of you the colour I was going to give them in a private conversation this morning, and sewed clues for the rest of you on the seat of their pants."

But in this case there is no reason for all of them not to go on the first bell.

Unless they take different amount of time to get the clues from the seat of their pants...

------------------------------
So what if the problem has the following:
[...]
The bell doesn't sound every minute. You have all the time in the world to think about it and look around. Only when each of you says whether he knows the colour or not will the bell sound. Restrictions on communicating and reflective surfaces still apply.
[...]
"It is possible to solve this task because I put the following restriction on the colours..." Unfortunately Alice could not hear the rest of his sentence[...]

------------------------------

Now the restriction that the professor put, could be "they are the same as the colour of your socks" or something similar, but in such case they would all go at the first bell.