01 Jul 11
Originally posted by JS357Yes and I saw the same point, hence my paragraph which you omitted:
I am seeing a difference between iam's "could" and your "would". L thinks, "I could have pointed to either Lt or Wt. I know that is true. So I must lie about that, by not revealing either of the two towns I could have pointed to. So if I point to Tt, I will have fulfilled my duty to lie. It is not my duty to keep him from getting to Ttown."
However maybe your question is designed to mean that the liar could have pointed to one of two roads, both non-true, so a truthful answer this time would be to point at both non-true roads again, and the only way to lie is to point at the remaining road which is true. However I do not think that is the only way to lie. For example he could point to two roads, one of which is true and one false, or point to one false road, which is not identical to two false roads, so again lies about what the earlier answer could have been. Because there are several ways to lie, you cannot infer what you wish from this one answer.
The Liar is not forced to follow the path you want, any more than in my proposed solution (where I only need the fifth question if the liar follows the most difficult path - otherwise I too would solve this quicker by wishful thinking).
This happens in chess all the time - my opponent does not do what I think he has to do.
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01 Jul 11
Originally posted by finneganI've never omitted a single word of anyone's in the quoted post. It may have ben shortened by the RHP bot that handles such things.
Yes and I saw the same point, hence my paragraph which you omitted:
[i] However maybe your question is designed to mean that the liar [b] could have pointed to one of two roads, both non-true, so a truthful answer this time would be to point at both non-true roads again, and the only way to lie is to point at the remaining road which is true. Howev ...[text shortened]... ng).
This happens in chess all the time - my opponent does not do what I think he has to do.[/b]
There was more than one way to lie, but each of them were by that very fact, something the L or the WL *could have done* if he were asked the bald question of which way to go. He was asked what he *could* have done. Each and every untrue indication of which way or ways to go was something he could have done.
So to lie this time, he has to do something he *could not* have done in response to the bald question had it been asked. That fact in itself is enough to force a lie that reveals the truth. He is lying about what his behavior would have been.
I think at this point, all we are going to be able to do is repeat ourselves.
02 Jul 11
Originally posted by JS357Hey I'm really sorry if I seemed aggressive. I just wanted to say you had not taken account of my second argument, which you have of course now picked up. I did not want to impute anything dishonorable.
I've never omitted a single word of anyone's in the quoted post. It may have ben shortened by the RHP bot that handles such things.
There was more than one way to lie, but each of them were by that very fact, something the L or the WL *could have done* if he were asked the bald question of which way to go. He was asked what he *could* have done. Each and e ...[text shortened]... ld have been.
I think at this point, all we are going to be able to do is repeat ourselves.
Otherwise we agree that we can only repeat. I understand your argument but it seems wrong on the ground that there are other ways to lie.
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02 Jul 11
1 edit
Originally posted by finneganIf you think he might point to two roads we can constrain him with a little tweak to the words:
Yes and I saw the same point, hence my paragraph which you omitted:
[i] However maybe your question is designed to mean that the liar [b] could have pointed to one of two roads, both non-true, so a truthful answer this time would be to point at both non-true roads again, and the only way to lie is to point at the remaining road which is true. Howev ...[text shortened]... ng).
This happens in chess all the time - my opponent does not do what I think he has to do.[/b]
Point to a road you could have pointed to if instead of asking this question I had asked you to point to a road that leads to true town.
But I suppose the liar might then say, "I can't point, my arms are glued to my sides" or something. 🙂
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02 Jul 11
Originally posted by iamatigerThere is always going to be a way for the Liar to lie while giving nothing away. In response to the question -- any question, he can say "1+1=3." But usually these kinds of riddles don't go in that direction, because it takes the fun out of doing them. Although I have a brother to whom that would be a fun way to deal with this riddle. So, I figure we can look at it in whatever way we want.
If you think he might point to two roads we can constrain him with a little tweak to the words:
[b] Point to a road you could have pointed to if instead of asking this question I had asked you to point to a road that leads to true town.
But I suppose the liar might then say, "I can't point, my arms are glued to my sides" or something. 🙂[/b]
02 Jul 11
1 edit
Originally posted by iamatigerWhat is this refusal to deal with stuff about? The Liar has other options without descending into silly ones like "my arms are glued to my sides."
If you think he might point to two roads we can constrain him with a little tweak to the words:
[b] Point to a road you could have pointed to if instead of asking this question I had asked you to point to a road that leads to true town.
But I suppose the liar might then say, "I can't point, my arms are glued to my sides" or something. 🙂[/b]
Liar:
If you had asked me to point to Truthtown I could have lied and pointed at WaveringTown. Alternatively I could have lied and pointed to LiarTown.
Now you ask me which road I could have pointed to. Well in point of fact the set of roads I could have pointed to is all three roads.
That is the truthful answer to your question but I want to lie. One possible lie is to say I could have pointed at no road at all from the set (e.g. "None of these roads lead to TruthTown at all at all at all."😉 ). Another lie would be to point to any one road from the three, or any two roads from the three, since in all these cases I would be giving a false answer to your question.
Now I agree that one way to achieve this would be to point at TruthTown, but it is not by any means my only option.
You may argue with me that, being a liar, I could not have pointed to TruthTown. Well I wonder how you identify that I am a liar, without asking any other questions at all. If you asked me I would tell you I am not a liar and how would you know that was a lie without another question?
But leaving that important problem aside, if you had asked me to point to TruthTown, then I might indeed have pointed to TruthTown depending on the way in which you worded the question and I interpreted it. It is a possible scenario which you cannot discount without asking more questions.
And leaving that aside, if I understand by your question that you want me to point to TruthTown this time, so that was the deep meaning beneath your confusing use of langauge, then I would deceive you by pointing to another town or towns.
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02 Jul 11
4 edits
First of all, the new question says "Point to a town", not "point to some towns". So if he obeys the instruction he has to point to one and only one town.
Secondly, if he points to wavering, he is telling the truth, because if I had asked him to point to truth town he could have pointed to wavering; since telling the truth is against his nature, he can't point there. Similarly he can't point to lie town, so his only option is to point to truth town.
Thirly, if I ask him "Point to a road that leads to truth town", he can't point at truth town, his nature forbids it. So the set of roads he could have pointed to is not all three roads.
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02 Jul 11
Originally posted by iamatigerYes, I will point out the OP said "You know he will answer only the minimum number of questions that are necessary to reveal the correct way to go..." which does not mean he has an aversion to revealing the correct way to go. He only has an aversion to going against the rules of his village. It would be an added stipulation to say he has an interest in deceiving you as to which way to go.
First of all, the new question says "Point to [b]a town", not "point to some towns". So if he obeys the instruction he has to point to one and only one town.
Secondly, if he points to wavering, he is telling the truth, because if I had asked him to point to truth town he could have pointed to wavering; since telling the truth is against his nature, ...[text shortened]... nature forbids it. So the set of roads he could have pointed to is not all three roads.[/b]
03 Jul 11
Originally posted by iamatigerYes the reformulated question does prevent pairs of roads in any answer. Fair enough. That leaves enough options for my argument to stand.
First of all, the new question says "Point to [b]a town", not "point to some towns". So if he obeys the instruction he has to point to one and only one town.
Secondly, if he points to wavering, he is telling the truth, because if I had asked him to point to truth town he could have pointed to wavering; since telling the truth is against his nature, ...[text shortened]... nature forbids it. So the set of roads he could have pointed to is not all three roads.[/b]
The Liar COULD , however, have pointed to TruthTown - it is in the set of roads available for pointing.
Because he always lies, he never WOULD, but he always COULD.
Think chess positions. Many more moves could be made than would be made. It is a form of blindness to imagine they never could, because you may evaluate the position differently to your opponent - and I usually do.
Similarly, depending on context and interpretation, a Liar could point at TruthTown, so it must always remain one of the set of possibilities. What discounts it is not that he cannot point there, but that doing so would, on some occasions, be truthful and therefore inappropriate for purposes of telling lies. Would and could are different.
By the way the problem remains that these liars always lie, not that they are constitutionally incapable of telling the truth. One scenario - a woman from WaveringTown goes to live with a man in LiarTown and, having changed her residence changes her habits accordingly, much to the disapproval of her former associates.
03 Jul 11
Originally posted by JS357That is fair too, but my point is really that we have to consider the worst possible outcomes, not the best. In my solution, many responses would permit a solution in less than five questions; the Liar presents my worst case scenario that I have faced and you seem to me to be evading.
Yes, I will point out the OP said "You know he will answer only the minimum number of questions that are necessary to reveal the correct way to go..." which does not mean he has an aversion to revealing the correct way to go. He only has an aversion to going against the rules of his village. It would be an added stipulation to say he has an interest in deceiving you as to which way to go.
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03 Jul 11
5 edits
Originally posted by finneganI disagree with that, if I asked the liar to point to truth town, pointing to truth town would be just about the only thing he COULDN'T do, his nature would forbid it.
The Liar COULD , however, have pointed to TruthTown - it is in the set of roads available for pointing.
Because he always lies, he never WOULD, but he always COULD.
You may as well say, if you asked him "what is 1 + 1" he could answer 2. Surely that is wrong, he is a liar!
If you think "could" is ambiguous for some reason we can replace it with "might" or some other wording that pins him down to the set of roads that we might actually see him point to if we asked the way to truth town; but I think it is pretty obvious that "could" is good enough.
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03 Jul 11
1 edit
Originally posted by finneganI agree it is certainly not in his nature to never point at truth town, especially if I ask him to point to lying town! However, if I ask him "point to truth town", it is definitely against his nature to point there then.
His nature may be to lie, but it is not his nature to never point at TruthTown.
04 Jul 11
Originally posted by iamatigerIt is not in our "nature" to do many things that we could do. They remain options - part of the set of things that could happen.
I agree it is certainly not in his nature to never point at truth town, especially if I ask him to point to lying town! However, if I ask him "point to truth town", it is definitely against his nature to point there then.
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04 Jul 11
2 edits
Originally posted by finneganSigh:
It is not in our "nature" to do many things that we could do. They remain options - part of the set of things that could happen.
"Point to a road that I might have seen you point to (comfortably, within your natural inclination to lie or tell the truth or current waver preference) if instead of asking this question I had asked you to point to a road that leads to true town.