34 replies to this topic

[Jules McWyrm]

... the truth table presented in the solution is the truth table for logical implication...

On further reflection, I see that this is not the case. The solution provided by rookie1ja is correct, although I still don't see the need to bring biconditionals into it. The same conclustions are reached regardless if one reads this statment as if-then' or if-and-only-if.

[flowstoneknight]

On further reflection, I see that this is not the case. The solution provided by rookie1ja is correct, although I still don't see the need to bring biconditionals into it. The same conclustions are reached regardless if one reads this statment as if-then' or if-and-only-if.

Actually, the only people who have posted correct answers are cpotting and m_mylin. They correctly interpreted the statement in terms of logic. Here's why:

"On this island is a treasure, only if I am an honest man."
means
"For there to be treasure on this island, I must be an honest man."
means
"If there is treasure on this island, I am an honest man."
means
IF "there is treasure on this island" THEN "I am an honest man"

Most people made the mistakes of either interpreting "only if" as "if and only if" or as just "if". Now if we take P to be "there is treasure on this island" and Q to be "I am an honest man", we can use a simple truth table for P->Q to solve this.

P   Q   P->Q
T   T	T
T   F	F
F   T	T
F   F	T

It is important to note that in the two cases (#3 and #4) where P is false, the implication of P->Q is still true. For example, "if you meet me by 10AM, I'll buy you lunch" is still true even if you meet me later, say 11AM, and I decide to buy you lunch anyway. The statement does not preclude the possibility of your being late and my buying you lunch regardless. In the same vein, if you're late and I don't buy you lunch, my statement would still be true, because I would have bought you lunch if you had been on time. Either way, the implication as a whole is still true.

So let's get back to the treasure.

If the speaker were a swindlecant, P->Q must be false (a lie) and Q must be false, because the speaker is not an honest man. The only case where P->Q is false is if P is true and Q is false. Therefore, there is treasure on the island and the speaker is not an honest man.

If the speaker were an honestant, P->Q must be true and Q must be true. Looking back at the truth table, we can see that there are two cases. In case #1, P->Q is true, Q is true and P is also true. In case #3, P->Q is true, Q is true but P is false. Both of these cases are possible if the speaker were an honestant. One shows that there is treasure and one shows that there is no treasure. We can't be sure.

So if the speaker were a swindlecant, there is treasure. If the speaker were an honestant, there may be treasure, but we're not sure. So all in all, we can't be sure of the existence of the treasure with the information we're given.

On a side note: first post, yay!

[Jules McWyrm]

Most people made the mistakes of either interpreting "only if" as "if and only if" or as just "if". Now if we take P to be "there is treasure on this island" and Q to be "I am an honest man", we can use a simple truth table for P->Q to solve this.

Huh - you're right. What a horribly obnoxious contruction.

[gandi]

Honestants and Swindlecants VII. - Back to the Logic Problems
Going out of the pub, the gringo heard about a fantastic buried treasure. He wanted to be sure so he asked another man who replied:
"On this island is a treasure, only if I am an honest man."
So shall he go and find the treasure?

Spoiler for Solution

Honestants and Swindlecants VII. - solution
It is important to explore the statement as a whole. Truth table of any logical equivalence is as follows:

P		Q		P<=>Q
truth	truth	truth
truth	lie	  lie
lie	  truth	lie
lie	  lie	  truth

If the man is an Honestant, then the whole statement must be true. One part of it, where he said that he is an honest man is true then and so the other part (about the treasure) must be true, too. However, if he is a Swindlecant, the whole statement is a lie. The part mentioning that he is an honest man is in that case of course a lie. Thus the other part must be truth. So there must be a treasure on the island, no matter what kind of man said the sentence.

Swindlecant's can only tell the false, the extent of their lies however is not defined. lying about a lie is still infact, a lie, regardless of the outcome. my lie on lie may be the truth or be a lie, BUT it STILL is a lie regardless. because Lying is the act of misleading, misleading the misled is the best situation a liar would want anyone to be in. because they do not know if the liar has led them to the truth or to a deadend lie. therefore the Swindlecant can say there is a treasure ONLY if he was an honestant, because he has to lie, lying about a lie is still a lie. It is ILLOGICAL to assume liars are so simple. By classifying them as liars is to classify ALL their information as nulled because u do not know the extent they can lie to.

[Vanity Elric]

What I see here isnt a riddle asking anything about who the islander is or if there really IS treasure, but if the guy should go find the treasure.

OK so its a LOGIC question, so yes he should go search for the treasure regardless of who the person is. Even if there isnt treasure its human nature to explore these kinds of things right? plus then you wouldnt have so much on your mind that if you dont go "Could there really be treasure? What is someone already took it? How much or what kind of treasure?" ect. I mean something like taht can really bug a person.

[MUSICKAL]

I think bonanova was close, but he made one mistake; "A if only B" should be A->B, not B->A. For Example, "the sky is blue, only if 1+1=3" is false.

Therefore, "On this island is a treasure, only if I am an honest man," becomes "If treasure, then I'm honest," becomes "no treasure, or I'm honest."

It's one of those fun situations where you hope the guy is lying to you. Honestants<->50/50 , Swindlecants<->treasure

LETS MAKE IT SIMPLE. I JUST FINISHED HIS SENTANCE FOR HIM. ON THIS ISLAND IS A TREASURE, ONLY IF I AM AN HONEST MAN, BUT IF I WERE A LIAR THEN THERE IS NO TREASURE. HE IS THE HOENEST MAN. <_<

[heterophonic]

The entire puzzle is moot.

on this island there are only Honestants and Swindlecants. The presence of a Gringo negates this immediately, since a gringo is neither a honestant or a swindlecant but an anomaly. There are, then 3 types of people on this island: those who tell the truth, those who tell lies, and those who can do either. And all you Mexicanos out there know : if there is one gringo, there's sure to be another. He may have been talking to another Gringo therefore.

This Entire puzzle is thereby rendered unsolvable and thereby useless.

Thanks :-D

[Michael C. Herrera]

There are a lot of uncertain assumptions being made with this problem. Everyone can agree that if the man is an honestant, then there is treasure. Here is where some people are going wrong. You are assuming that if it is a swindlecant, that the swindlecant is making to factual statements, that must both be false. In reality he is making only one statement, and it is of course false.

incorrect assumption: There is treasure (fact), only if I am an honest man (fact).
See, he doesn't actually say that he is an honest man, nor does he say that there is in fact treasure.

what he does say: There is treasure, ONLY IF (fact) I am an honest man.
and the only that can be 100% deduced from his statement is that the "ONLY IF" (which is the only part of his statement that is a definite) is in fact false. Hence, there could in fact still be treasure, even if he isn't an honest man.

You cannot assume he is lying about statements that he didn't actually make (i.e. there is treasure, or that he is an honest man)

[Michael C. Herrera]

actually..for that matter, you cannot assume there is treasure, even if the a honestant makes the satement, because he is still saying "only if". Another way to interpret the definite part of the statement (only if), is "there IS NOT treasure if I'm NOT honest." If an honestant says this, then all you can 100% deduce from that is, there might be treasure, because he is in fact an honest man.

[the-genius]

The question is, ---> "there is treasue, only if I'm Honestant" then
case 1: There is infact treasure.
a) Consider that the statement is a true statement. So only honestant can say that statement
b) Consider that the statement is false. So only swindlecant can tell the statement. But meaning of false for the statement is "There is a treasue, only if I'm Swindlecant". So, if Swindlecant speak that sentence it would be true speaking since there is treasure and he is a swindlecan't too. So it becomes paradoxical for the swindlecant to speak such sentence.
case 2: There is no treasure
A swindlecant can't tell "There is a treasue, only if I'm Honestant" ==>"there is no treasure if I'm Swindlecant" because He is a swindlecant and there is no treasure. So, the statement is true and can't be told by him
also, An honestant can't tell that statement


So, there must be treasure.

Edited by the-genius, 10 March 2009 - 11:04 AM.