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Honestants and Swindlecants VII.


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34 replies to this topic

#31 bonanova

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Posted 12 March 2009 - 05:25 PM

Spoiler for Recanting my first post as a brain fart....

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#32 Jacca

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Posted 23 March 2009 - 05:24 PM

Honestly ????

An honestant can only tell the truth. IF the statement is made by an honestant then there is treasure. This is obvious by the statement - There is treasure , only if I am an honest man.

If the statement is made by a swindlecant:

Since a swindlecant can only tell a lie - then if a swidlecant says it it MUST be a lie - therefore "There is treasure , only if I am an honest man" is a lie only if there is treasure despite him not being an honest man.

Either case indicates there is treasure.
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#33 SKULLOK

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Posted 21 April 2009 - 06:14 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

That's not quite true. This is an 'if/then' statement. Lemme show you what I mean:

when he says "there is a fantastic treasure on this island, only if I am an honest man," the "only if" says it all. It combines the two statements, making them one "if/then" statement, meaning that if any part of that statement were false, the whole statement would be false. If you were to take OUT the "only if," you would have two separate statements, but it would significantly change the syntax.

Because of this situation, it could be either or, for multiple reasons.

If he were an honestant, then the whole statement must be true, and there must be a fantastic treasure on the island.

If he were a swindlecant, then he might be lying by saying that he would be an honest man if there were treasure, or he might be lying in saying that there would be a treasure. His being an honest man does not affect whether or not there is treasure on the island, and thus that cannot decide whether or not the treasure is there.

Essentially, it's easiest if you think of "if/then" and "either/or" statements as multiplication problems. If there's a negative involved, the answer will be negative, so the only way to get a positive, is to have both positive. If you're not sure which one is negative, in the case that there WERE a negative involved, you would have no way of finding out which part was negative, and thus no way of finding out if the answer was negative, without further inquiry or external intervention.
Basically, unless he is an honestant, you're SOL, and would never know from asking him whether or not there was treasure.

Edited by SKULLOK, 21 April 2009 - 06:16 AM.

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#34 Jad

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Posted 22 April 2009 - 09:34 PM

There is treasure on the island, and here's why in simple terms.

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

Now all we need to do before we start over-analysing is work out the two possibilities.

A) The man is an Honestant
Everything he says has to be true, meaning only (the only actually being irrelevant, but still true) if he is an Honestant is there treasure; he is an Honestant, therefore in this case there is treasure.

Now for the second and final possibility :

B) The man is a Swindlecant
Everything he says is a lie, what he says being There is treasure on this island only if I'm an Honestant.
Another way of phrasing this is If I'm a liar, there isn't treasure on the island
However this statement cannot be taken for truth as he is a Swindlecant, meaning it is false. Therefore we can assume that if:
Him being a liar results in there being no treasure is false, then
Him being a liar results in there being treasure is true.

So either way, there is treasure on the island, regardless of whether the man is a Swindlecant or Honestant (which is left as unknown.)

Hopefully this will clear things up.

Jad
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#35 icemanwky

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Posted 02 September 2009 - 08:52 PM

I am sorry to post on such an old topic, especially when there are good explanations of the problem out there, but there are a couple of issues that I see with some of the posts. cpotting is right on most of the the time, however:

IF-THEN creates a causality relationship.


That's not necessarily true. Example: If the sky is blue then healthy grass is green. That is a true statement but it does not imply causality. It doesn't even imply a correlation. However, your argument still holds up, but i wanted to point that out.



More importantly, I wanted to point out something that I see danced around but not discussed (although admittedly there are some replies that I have only skimmed).

I think some of you are over analyzing the problem. Or rather, the problem was phrased or put together in a way differently than intended.

Because this is the English language, and not pieces of individual logical statements like in computer code, the ENTIRE phrase "If I am a honest man, then there is treasure" need to be evaluated as true or false, not the individual parts within the "if" and "then" statements.

You cannot take "I am an honest man" and "there is treasure" and evaluate them independently.

Example

Honestant:

An Honestant saying that phrase would not be lying, therefore an honest man WOULD indicate treasure.

Swindlecat:

A Swindlecat saying the phrase would mean he is lying, or the entire phrase is false; "If I am an honest man, then there is treasure" is a false statement, so there is NOT treasure.
If you want to get picky, the riddle gets even more vague because you don't know if he is lying about the honest man part, the treasure part, or both, or if he is just completely making things up.


Therefore it is impossible to determine. Also the riddle is poorly constructed.


Cuitarded also needs to take a logic class, but one this he or she is correct on is the fact that we are trying to take English and translate it into Math haphazardly. The original statement was "On this island is a treasure, only if I am an honest man." Some people are translating this to be "On this island is a treasure, IF AND only if I am an honest man." Others translated it "If I am an honest man, then on this island is a treasure." Still others had "If there is a treasure on this island, then I am an honest man." Before you can solve the problem, you have to decide which problem you are solving. I believe the third option is invalid. Look at which phrase has the if in the original and then which phrase has the if in translation 3.

However, either of the other 2 seem valid to me. Mathematically then, you should assume the 2nd one is correct and see if you can arrive at a conclusion since the second one is a subset of the first. That's using the mathematical principle that I try to teach my sophomore Geometry class that you should assume as little as possible in order to solve the problem. When you assume that the 2nd one is the correct translation, then bonanova has a satisfactory solution even though he later recanted.

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.



The following post is what happens when you assume too much.

Let me preface this by saying that I'm going at this from a much less mathematical viewpoint than most of you. I haven't taken a math class since 11th grade Trig, and I don't intend on ever taking one again. I am pretty good at logic, though, so that being said...

Am I the only one who sees some problems with the man's being an Honestant?
The way I see it, the speaker has to be a Swindlecant, but we don't know if there's treasure or not.

The problem with him being an Honestant is the "only if" part. The fact that there is (or is not) treasure on the island has absolutely nothing to do with whether or not the man is telling the truth. There IS (or IS NOT) treasure. The treasure's existence is in no way contingent on the man being honest. Therefore, part of the statement is a lie, and the man is a Swindlecant.

Now that we know he's a Swindlecant, we know he's lying, but about what? Is he lying about the fact that there could ONLY be treasure on the island if he was an honest man (in which case, there is indeed treasure), or is he lying about the existence of treasure in the first place (the idea that if he was an honest man, there would be treasure on the island), which of course would mean that there is no treasure at all?


katemonster is assuming that the Honestant is some kind of perfect angel rather than just a creature that tells the truth 100% of the time. If katemonster were to tell this to an Honestant, they would simply smile and say "well it IS true . . . . TECHNICALLY . . . "

That being said, even if you do assume that "... only if ..." means the same thing as "... if and only if ..." then the original post has a satisfactory solution. I hope in the future however, people take more care with assuming too much and ambiguous English. I enjoyed reading this discussion though. Good work everyone!
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