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

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# Honestants and Swindlecants VII.

### #21

Posted 26 March 2008 - 05:58 PM

### #22

Posted 21 May 2008 - 06:53 PM

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!

### #23

Posted 22 May 2008 - 06:39 PM

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.

### #24

Posted 20 June 2008 - 09:50 AM

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

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.

### #25

Posted 21 July 2008 - 12:28 PM

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.

### #26

Posted 05 September 2008 - 06:43 PM

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. <_<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 thosefunsituations where you hope the guy is lying to you. Honestants<->50/50 , Swindlecants<->treasure

### #27

Posted 13 January 2009 - 09:08 PM

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

### #28

Posted 02 February 2009 - 04:49 AM

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)

### #29

Posted 02 February 2009 - 05:01 AM

### #30

Posted 10 March 2009 - 11:02 AM

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.**

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