Originally posted by AThousandYoung No, the signs are not necessarily true or false. You said the signs have "merit" because they are either true or false, but this is not the case.
Here. Let's examine the possibilities for the first pair of doors.
[b]The first choice:
door A. "Only one of these signs is false"
door B. "This is the door you should go through"
...[text shortened]... n, I could set up the signs such that B is the correct door. This is not physically impossible.[/b]
No. Door B cannot be the one to go through. Because then sign B is true, and sign A is a contradiction: it cannot be true because of what it says, and if it is false, then B had to be false too.
The key is that these puzzles are based around a 'consistent' set of premises. If you cannot accept that, then this is not your cup of tea, which is totally acceptable.
Originally posted by Mephisto2 No. Door B cannot be the one to go through. Because then sign B is true, and sign A is a contradiction: it cannot be true because of what it says, and if it is false, then B had to be false too.
The key is that these puzzles are based around a 'consistent' set of premises. If you cannot accept that, then this is not your cup of tea, which is totally acceptable.
So what if sign A is a contradiction?
I understand what you're saying, I think. However I feel the error is on the part of bobbob for not wording the problem correctly, not on me for not assuming certain things that were never stated.
Originally posted by AThousandYoung So what if sign A is a contradiction?
I understand what you're saying, I think. However I feel the error is on the part of bobbob for not wording the problem correctly, not on me for not assuming certain things that were never stated.
With a 'consistent set of premises' I meant that there are no contradictions in a statement or between statements when the correct logical value is used (true or false). So, there must not be contradictory statements.
Another thing is that it is not necessary to allways find out the true/false condition of each statement, because several combinations may lead to the same conclusion (in this case about which door to chose).
Originally posted by Palynka You are right, of course. Interesting, nevertheless, the number of assumptions we make everyday without even thinking about them...
Logic can be a tough thing to get one's mental arms around at times. We so badly want to hold on to our preconceived notions that we can't open our eyes and see the truth.
If you're familiar with the old "Let's make a deal" problem, which I think has surfaced a few times in this forum, you know what I'm talking about. I've tried to explain that one to folks for 30 minutes and they still couldn't grasp the concept....
Originally posted by Mephisto2 With a 'consistent set of premises' I meant that there are no contradictions in a statement or between statements when the correct logical value is used (true or false). So, there must not be contradictory statements.
And my point is that you need to state your premises if you want the problem to make sense. Apparently you and Bobbo have a psychic connection that allowed you to understand his unstated premises - apparently, I missed out....🙂😕
Originally posted by The Plumber Logic can be a tough thing to get one's mental arms around at times. We so badly want to hold on to our preconceived notions that we can't open our eyes and see the truth.
If you're familiar with the old "Let's make a deal" problem, which I think has surfaced a few times in this forum, you know what I'm talking about. I've tried to explain that one to folks for 30 minutes and they still couldn't grasp the concept....
Can you provide a link to that problem or re-post it?
I think, that with your first statement you are stretching it. The assumptions are to be taken in the spirit of the problem, because otherwise you would need to define everything from scratch. Even language is a set of premises...
Pedantism is the epitomy of boredom to everyone else but the pedant. It doesn't mean the pedant is wrong, which he usually isn't.
Originally posted by Palynka Can you provide a link to that problem or re-post it?
I think, that with your first statement you are stretching it. The assumptions are to be taken in the spirit of the problem, because otherwise you would need to define everything from scratch. Even language is a set of premises...
Pedantism is the epitomy of boredom to everyone else but the pedant. It doesn't mean the pedant is wrong, which he usually isn't.
Originally posted by The Plumber And my point is that you need to state your premises if you want the problem to make sense. Apparently you and Bobbo have a psychic connection that allowed you to understand his unstated premises - apparently, I missed out....🙂😕
It has already been stated that each sign is either true or false. You say we have a psychic connection only because we both understand the problem and why it does make sense.
Originally posted by The Plumber Logic can be a tough thing to get one's mental arms around at times. We so badly want to hold on to our preconceived notions that we can't open our eyes and see the truth.
If you're familiar with the old "Let's make a deal" problem, which I think has surfaced a few times in this forum, you know what I'm talking about. I've tried to explain that one to folks for 30 minutes and they still couldn't grasp the concept....
Are you suggesting we are holding (incorrect) preconceived notions? Please state them. And the "Let's make a deal" problem has nothing to do with this.
Originally posted by bobbob1056th I found this at http://www.wordsmith.demon.co.uk/paradoxes/:
The unexpected hanging
1st paragraph
[A man condemned to be hanged] was sentenced on Saturday. "The hanging will take place at noon," said the judge to the prisoner, "on one of the seven days of next week. But you will not know which day it is until you are so informed on the morning o ...[text shortened]... is is merely an exercise to see if you can completely understand the above story/paradox thingy.
Because no one seems to be interested, I will state the obvious "solution". There are, however, ways to greatly complicate the issue by changing the puzzle, but I won't go into that. Basically when the judge says he will execute the prisoner in the next seven days, the prisoner doesn't even know if this is true. So it is obviously true that the prisoner doesn't know when he will be executed. In fact, the judge can even have him executed on Saturday and the prisoner would still not know it would happen until they start the execution process. The judge could even say: You will be executed tomorrow and don't/won't know which day you will be executed until we start the procedure. He is basically saying
1. Such and such will happen
2. You don't know if I am telling you the truth
Originally posted by bobbob1056th Are you suggesting we are holding (incorrect) preconceived notions? Please state them. And the "Let's make a deal" problem has nothing to do with this.
(sigh)
Refer back to my post in the middle of Page 2 (number 24 in the thread). I explained what the unstated assumption was and what the problem with the problem as stated is.
Palynka thinks I'm being pedantic, and he may be right, but the pedant never thinks his observations are pedantic. 🙂
Refer back to my post in the middle of Page 2 (number 24 in the thread). I explained what the unstated assumption was and what the problem with the problem as stated is.
Palynka thinks I'm being pedantic, and he may be right, but the pedant never thinks his observations are pedantic. 🙂
I really do not understand what you want to achieve with this debate. The 'assumptions' as you call them are the common and obvious ones for this type of logical puzzle. Many IQ-tests contain puzzles like these, without any more 'assumption' statements.
Some puzzles
28 Jun '05 11:12
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