[rookie1ja]

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.

[Tenacioussoul]

Quote

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.

how is the 2nd part true

if he is an swindlecant person than he is not an honest man therefore there is no treasure on the island

Coz the treasure being there is conditioned on the fact that ONLY IF HE IS HONEST MAN THAN THERE IS TREASURE ON THE ISLAND.. RIGHT?

[rookie1ja]

Examined sentence: "On this island is a treasure, only if I am an honest man."
1st part - On this island is a treasure
2nd part - I am an honest man

Swindlecant:
1st part - ?
2nd part - false
So since the whole sentence has to be lie, the 1st part has to be true (see truth table above). So there is a treasure.

Honestant:
1st part - ?
2nd part - true
So since the whole sentence has to be true, the 1st part has to be true (see truth table above). So there is a treasure.

[shiang]

"On this island is a treasure, only if I am an honest man."

-the question is weather you should look for the treasure and since this man could obiously be a honestant, then yes you should look for the treasure.

-however if the man was a swindlecant then the whole statment would be a lie meaning that there could still be treasure even if he was a swindlecant.

[fosley]

"ONLY if I'm an honest man" is a forced Else statement:
If Honestant Then Treasure Else !Treasure

But if the man is really a Swindlecant, he's lying, so it becomes:
If !Honestant Then Treasure Else !Treasure

Regardless of what the man is, there is treasure. Because there is treasure either way, the Else statement is false (there is no condition under which there is no treasure), so the man is lying, making him a Swindlecant (not part of the question, but something extra we can deduce for fun).

[jmull747]

"On this island is a treasure, only if I am an honest man."

If there is no treasure on the island, the entire statement is false, period.

If he said "On this island is a treasure, only if I am wearing a blue shirt." It would make no difference whether he was wearing a blue shirt or not, it would still be a lie.

50/50 chance of treasure.

[larryhl]

you guys need to take a logic (discrete structures) class:

if p, then q. iff = if and only if, basically, the truth of the whole statement.
truth table:
P Q P iff Q
true true true
true false false
false true false
false false true <= most important logical conclusion!!! if both your premises and your conclusion are false, then no matter what, the statement is true. this is a trivial conclusion, meaning that since both are false, you can say anything and what you say will be true. i.e. i can say if the sky is green, then pigs can fly. since the sky isn't green and pigs can't fly, my whole statement is true.

if "i am an honest man" (P), then "there is buried treasure." (Q) if said by an honestant, then it is obvious this is true.

for the swindlecant scenario, things are a little harder. if said by a swindlecant, then the premise is false. the part "there is buried treasure" can be either true or false. to be able to keep the whole statement false, then the part "there is buried treasure" must be true!! if that part was false, then since both parts are false, the whole statement is true so if he was a swindlecant, he wouldn't be able to say this statement.

hence, no matter the speaker, there is buried treasure on the island.

[bonanova]

The answer is - YES - head for the hills and bring your pick and shovel.

But I don't think anyone has given the correct analysis yet.
Here's mine:

First, note the statement that was made:

There is treasure only if I am an honest man.

Some have made the mistake of calling this logical equivalence.
It's not. A only if B is logically the same as if B then A.

Logical equivalence is more restrictive: A if and only if B.
The truth tables differ in the case of a false premise and a true conclusion:
"False implies Truth" is True for if; it's False for if and only if.

Thus, we can restate simply as if B then A:

If I am an honest man then there is treasure.

There are two cases: the speaker is a honestant [H] or a swindlecant [S].

[1] H - the speaker is an honest man

If the speaker is honest, the premise is true [fact] and the logical implication must be true [else he would be lying].

Therefore the conclusion is true: There is treasure.

[2] S - the speaker is lying.

If the speaker is lying, the premise if false [fact] and the logical implication must be false, also, [else he would be telling the truth.]
But, because a false premise validly implies every conclusion, such an implication is always true.
A contradiction.

Thus we must conclude that the speaker could not have been a swindlecant:
one cannot invalidly conclude anything [tell a lie, as a swindlecant must do] starting from a false premise.

Since the speaker must have been a truth-teller, there must be a treasure.

[captainobvious00]

This last analysis is actually the only one that is easy to understand, well done.

[Wordblind]

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