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# Honestants and Swindlecants V.

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Honestants and Swindlecants V. - Back to the Logic Problems

In the pub the gringo met a funny guy who said: "If my wife is an Honestant, then I am Swindlecant." Who is this couple?

This old topic is locked since it was answered many times. You can check solution in the Spoiler below.

Pls visit New Puzzles section to see always fresh brain teasers.

Honestants and Swindlecants V. - solution

It is important to explore the statement as a whole. Truth table of any implication is as follows:

truth truth truth
truth lie lie
lie truth truth
lie lie truth
`P		 Q		  P=>Q`

In this logical conditional („if-then“ statement) p is a hypothesis (or antecedent) and q is a conclusion (or consequent).

It is obvious, that the husband is not a Swindlecant, because in that case one part of the statement (Q) „ ... then I am Swindlecant.“ would have to be a lie, which is a conflict. And since A is an Honestant, the whole statement is true.

If his wife was an Honestant too, then the second part of statement (Q) „ ... then I am Swindlecant.“ would have to be true, which is a conflict again. Therefore the man is an Honestant and his wife is a Swindlecant. Or is it a paradox?

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Why can they both not be swindlecants? he is therefore lying when he say's "If my wife is an Honestant, then I am Swindlecant." because actually, if his wife is a swindlecant he is a swindlecant, so it works!

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If the wife is an Honestant and the husband is a Swindlecant, the husband is telling the truth, but a Swindlecant can't tell the truth, so this is a paradox.

If the wife is an Honestant and the husband is an Honestant, the husband is lying, but an Honestant can't lie, so this is a paradox.

So we know the wife is a Swindlecant. But nothing forces the husband to be anything. Since the conditional statement is false, it's irrelevant whether the result is a lie or the truth. "If !A Then B" is not the same as "!A = B". To get that you have to have "If !A Then B Else !B"

We can extrapolate a bit for fun, which still ends at a stalemate on the husband's identity, but it's outside the scope of the logical problem.

If the husband were an Honestant, he would think the idea of his wife being an Honestant is as absurd as him being a Swindlecant, so he is telling the truth (in the form of a double-lie) by saying both are opposite of reality.

On the other hand, a Swindlecant husband would tell a lie by keeping one side accurate and the other side false.

It is, as you said, critical to evaluate the statements as a whole. Just because a peice of the statement is true doesn't mean the Swindlecant isn't allowed to say it. Only if the entire statement evaluates true is it forbidden. But, let's pretend that one piece makes the difference:

We know the wife is a Swindlecant, so the speaker can't be an Honestant or he'd be lying about her. But the speaker can't be a Swindlecant or he'd be telling the truth about himself. This is a paradox, meaning the speaker simply couldn't have said this statement if we are evaluating pieces by themselves.

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ok, let's clear things up.

there're only 4 possibilities:

1. Both parts are true => Entire statement is true. So the wife is an honestant and the husband is a swindlecant. PARADOX! Swindlecants don't tell the truth. So this is impossible.

2. First part is true, and second part is false => Entire statement is false. Wife is an honestant and husband is an honestant. PARADOX! Honestants always tell the truth. So this is also impossible.

3. First part is false, and second part is true => Entire statement is true. Wife is a swindlecant and husband is a swindlecant. PARADOX! Swindlecants always lie. So this is again impossible.

4. Both parts are false => Entire statement is true. Wife is a swindlecant and husband is an honestant. Only possible answer. Since the statement was given as an implication, the honestant is being tricky, but he isn't lying.

The thing about these truth/lie logic questions is that the background is usually that the inhabitants of the country while separated into these two distinct groups both love to try stumping the tourists with logic puzzles. So I don't see any inherent paradox in the honestant lying for both parts of the implication.

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larryhl, easy as that

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My take is this.

The statement 'I am a Swindlecant' can't be said (i.e. only a swindlecant telling the truth can say it).

Therefore the infered part of the if statement becomes true, since the second part is not true then the reverse of the first part must be true. That is His wife has to be a swindlecant and he has to be an Honestant.

He is effectively saying 'My wife is a Swindlecant and I am an Honestant' I don't see a Paradox there at all.

because he puts the 'If' in the question is giving a choice (if A then B.) this must lead to the opposite (If Not A then Not B.).

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I see three possible answers here.

But I believe that for a sentence to be a lie, only one part must be a lie. as I mentioned in another honestant and swindlecant question, a swindlecant can say "I am a one-eyed monster who lies." because he is not a one-eyed monster, he is lying. so perhaps the part with his wife being an honestant is a lie, so he is free to tell the truth with the part of the sentence involving him calling himself a swindlecant. so they could both be swindlecants.

My third idea is that the man is a swindlecant becuase he has no wife, so once again he is free to call himself a swindlecant in the next part of his sentance.

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I just realized though, why neither of them are swindlecants, (besides my third answer) When the two get married, only honestants would be able to say "I do" when the priest asks them if they take the other to be their lawfully wedded wife/husband

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The funny man is an Honestant, and he is a bachelor, a widower, or the husband of a Swindlecant.

"If my wife is an Honestant, then I am Swindlecant," is equivalent to "my wife is not an Honestant or I am Swindlecant." No Swindlecant can claim to be Swindlecant, so he must be Honestant.

The statement can now be reduced to "my wife is not an Honestant." There is not enough information to decide if she is Swindlecant, dead, or non-existent.

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ok, let's clear things up.

there're only 4 possibilities:

1. Both parts are true => Entire statement is true. So the wife is an honestant and the husband is a swindlecant. PARADOX! Swindlecants don't tell the truth. So this is impossible.

2. First part is true, and second part is false => Entire statement is false. Wife is an honestant and husband is an honestant. PARADOX! Honestants always tell the truth. So this is also impossible.

3. First part is false, and second part is true => Entire statement is true. Wife is a swindlecant and husband is a swindlecant. PARADOX! Swindlecants always lie. So this is again impossible.

4. Both parts are false => Entire statement is true. Wife is a swindlecant and husband is an honestant. Only possible answer. Since the statement was given as an implication, the honestant is being tricky, but he isn't lying.

The thing about these truth/lie logic questions is that the background is usually that the inhabitants of the country while separated into these two distinct groups both love to try stumping the tourists with logic puzzles. So I don't see any inherent paradox in the honestant lying for both parts of the implication.

I have to disagree here. IF-THEN does not separate a statement into two independent phrases (that's what AND and OR do). IF-THEN makes one statement dependent on the other.

The solution is indeterminate:

For an Honestant to say "If my wife is an Honestant, then I am a Swindlecat" is a perfectly valid statement and indicates that there are no male Honestants with Honestant wives. It would be like me truthfully saying "If you are the king of Atlantis then I'm the Prince of the Moon!". I am not lying.

For a Swindlecat to say "If my wife is an Honestant, then I am a Swindlecat" is a perfectly valid statement also. It indicates that there are Honestants husband-wife couples, and you can't tell that a husband is Swindlecat by knowing if his wife is or isn't. It is like my saying "If my wife has red hair, then I have brown". It is a lie because my wife's hair colour does not determine mine. It would only be possible for me (a Swindlecat) to say this if there was some factor that meant that no redheaded women were married to brunettes.

Therefore, both an Honestant and a Swindlecat can make the statement and not break the rules. Without further information, we cannot tell which they are.

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ok, let's clear things up.

there're only 4 possibilities:

1. Both parts are true => Entire statement is true. So the wife is an honestant and the husband is a swindlecant. PARADOX! Swindlecants don't tell the truth. So this is impossible.

2. First part is true, and second part is false => Entire statement is false. Wife is an honestant and husband is an honestant. PARADOX! Honestants always tell the truth. So this is also impossible.

3. First part is false, and second part is true => Entire statement is true. Wife is a swindlecant and husband is a swindlecant. PARADOX! Swindlecants always lie. So this is again impossible.

4. Both parts are false => Entire statement is true. Wife is a swindlecant and husband is an honestant. Only possible answer. Since the statement was given as an implication, the honestant is being tricky, but he isn't lying.

The thing about these truth/lie logic questions is that the background is usually that the inhabitants of the country while separated into these two distinct groups both love to try stumping the tourists with logic puzzles. So I don't see any inherent paradox in the honestant lying for both parts of the implication.

I have to disagree here. IF-THEN does not separate a statement into two independent phrases (that's what AND and OR do). IF-THEN makes one statement dependent on the other.

The solution is indeterminate:

For an Honestant to say "If my wife is an Honestant, then I am a Swindlecat" is a perfectly valid statement and indicates that there are no male Honestants with Honestant wives. It would be like me truthfully saying "If you are the king of Atlantis then I'm the Prince of the Moon!". I am not lying.

For a Swindlecat to say "If my wife is an Honestant, then I am a Swindlecat" is a perfectly valid statement also. It indicates that there are Honestants men who have married Honestant women, and others that have married Swindlecats, and that you can't tell that a husband is Swindlecat by knowing if his wife is or isn't. It is like my saying "If my wife has red hair, then I have brown". It is a lie because my wife's hair colour does not determine mine. It would only be impossible for me (a Swindlecat) to say this if there was some factor that meant that no redheaded women were married to brunettes. Or, as I just explained it to my brother, the statement "If you're name is Ian, then my name is Clive" is a lie (even though his name is Ian and mine is Clive). His name being Ian does not make my name Clive - my name could be John, or Barry. The IF-THEN relationship if false and makes the statement a lie.

Therefore, both an Honestant and a Swindlecat can make the statement and not break the rules. Without further information, we cannot tell which they are.

edit - oops, sorry for the double post - it was meant to be an edit, but I must have hit quote.

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Hee hee, just for fun...

I just realized though, why neither of them are swindlecants, (besides my third answer) When the two get married, only honestants would be able to say "I do" when the priest asks them if they take the other to be their lawfully wedded wife/husband

But, I think, in a society composed of honestants and swindlecants the priest would ask the classic question, "What would your fiance' say you would say if I asked you the question: Do you take your fiance' to be your lawfully wedded mate?". Where upon the priest would assume the opposite to be the real truth. So either of them could be honestant or swindlecant by that test.

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Here's the classical form:

A: I am a swindlecant

B: My wife is an honestant

X="If B, then A"

If A, then not X

If not X, then (if B, then not A)

---------

If A then (if B then not A)

If B then (if A then not A) - Reductio ad absurdum

---------

Not B

If not B then not A (This is the only way to reduce it, except it's a fallacy)

---------

Not A + B

So, Husband is honestant and wife is swindlecant, according to this logic. But since you have to use a fallacy to get the answer, I conclude that there is no solution. We know that the wife is a swindlecant, but we cannot deduce whether the husband is a honestant or not, because, unfortunately he says nothing of the conditions in the case of his wife being a swindlecant. (ie, you can't assume this: if someone receives ten presents on their birthday they will be happy, but they didn't receive ten presents, so they won't be happy. Maybe they had a lot of fun, although they didn't receive ten presents, so therefore were still happy.)

So, in this, I strongly disagree with rookie1ja and larryhl, but reinforce what was said by Fosley. Nothing is preventing both from being swidlecants, since the statement "If my wife is a honestant, then I'm a swindlecant" does not state conditions concerning the wife being a swindlecant (which we all know is the situation). In other words, just because he says if his wife is an honestant then he is a swindlecant, doesn't get rid of the possibility that his wife may be a swindlecant as well as himself, and this doesn't contradict his original statement because they actually discussed COMPLETELY DIFFERENT SITUATIONS.

Any objections?

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I have to disagree with cpotting. If we use your take on this problem a Swindlecant could lie about even having a wife. So a possible outcome would be just a Swindlecant without a spouse.

The teaser states a Honestant ALWAYS speaks the truth and a Swindlecant ALWAYS speaks lies. Always is the hard word to get around. Not part of the time, not part of a sentence - Always.

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The funny man's statement is paradoxical.

In fact its part of a quite famous paradox, known as The Liar Paradox. Some people refer to it as the Epimenides Paradox, even though he really said all "Cretans are liars" which lead to the whole philosphical idea of the Liars Paradox which was later re-stated by St. Augustine (i think). Just click that link for better info (its a wiki YAYAYAYAY).

Anyhew, it boils down to this. The paradox lies in the self reference of the statement.

"I am lying now."

If the person is lying then the statement is actually true, which means that the person is telling the truth, which makes the statement false, which means the person is lying, which makes the statement true, which means the person is telling the truth, which means the statement is false... (continues till the end of time)

Also

If the person is telling the truth (aka, not lying) then the statement is lie, which means the person is lying, which means that the statement is true, which means the person is telling the truth, which means the statement is false, which means the person is lying, which means the statement is true... (keep going till the end of time)

Now, on to the funny man's statement. It is a paradox of the same kind as "The Liars Paradox".

"If my wife is an honestant, then I am a swindlecant."

If his wife is an honestant, then he is telling the truth, which means he is not a swindlecant, which means he is lying, which means he is a swindlecant, which means he is telling the truth, which means he is not a swindlecant... (yep it keeps going, hence "Self Referential Paradox")

If he has no wife at all then he is deceiving the gringo into thinking he has a wife (aka, he is lying), which means he is a swindlecant, which means the "then" part of the statement is the truth, which means he's not a swindlecant, which means the "then" part of the statement is false (aka a lie), which means he is a swindlecant... (keeps going weather he has a wife or not)

Just as with "The Liars Paradox", the Funny Man's statement can never consistently be assigned a value of true or false, which means the Funny Man can never be consistently categorized as a swindlecant nor an honestant.

sry if this is sloppy but its time for bed and I'm not going to revise anything right now

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I believe you have the truth tables wrong

The if then tables should be like this

P Q P->Q

F F F

F T F

T F F

T T T

So his sentence would be true only if his wife was a honestant and he was a swidlecandle.And if his sentence was true than he would be saying the truth which couldn't be the case since we assumed he is a swidlecant.

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I believe you have the truth tables wrong

The if then tables should be like this

P Q P->Q

F F F

F T F

T F F

T T T

So his sentence would be true only if his wife was a honestant and he was a swidlecande.And if his sentence was true than he would be saying the truth which couldn't be the case since we assumed he is a swidlecant.

Lets check about first arqument being false and the second true.

The man says that if his wife is a honestant(F) then he is a swidlecant(T).

The whole sentence from the above table is false.So he is not breaking any rules.

That means that "both are swidlecants" is an acceptable answer.

I ll check the other cases and get back to you!

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same here

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It seems to me that if the husband says if his wife is an honestant he is saying that she is a swindlecant and if she is in fact an honestant than he is telling a lie. And by saying if she is an honestant then he is a swindlecant he is calling himself an honestant. so the statement of himself being a swindlecant is not the truth but a part of his lie because he does not say he is ,only as a condition ,to shore up his lie about his wife and himself so he is the swindlecant and she is an honestant.

Mike

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The if then statement is a logic condition where, if the first statement is true (confirms the hypothesis) then the second statement only comes into play and by implication must be true.

In this logical conditional („if-then“ statement) p is a hypothesis (or antecedent) and q is a conclusion (or consequent). The conclusion must be true.

If the statement that his wife is the honestant is true then the statement that he is a swindlecant must also be true. Clearly a honestant cannot say he is a swindlecant because that would make his statement untrue. If the first statement is false however the consequent does not come into play it is irrelevant to the discussion. Thus they are both swindlecant because the first statement is untrue the husband is clearly lying and thus would be a swindlecant. The second condition in a then statement only comes into play if the first statement is true.

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what if he is lying about being married

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There is only one statement that can evaluate as TRUE or FALSE made.

"If my wife is Honestant, then I am Swindlecant."

This is a statement of the form If A Then B (A=>B).

The truth table for these statements (as mentioned earlier) is as follows:

A B A=>B

T T T

T F F

F T T

F F T

In other words, the statement evaluates as false only if the condition is true but the implication is false. The only way for this to happen is for the wife to be Honestant (A=True) and for the speaker to be Honestant (B= False). This case is eliminated because the speaker cannot be Honestant and make a False statement.

This implies that the statement evaluates as True, so the speaker is Honestant because only Honestants can make True statements.

We know that A=>B is a True statement. We also know that B (by itself) is False. The only possibility then is that A is False.

Therefore, the speaker is Honestant and his wife is Swindlecant.

Also, the wife must exist. If we assume that every statement is surrounded by something to the effect of "If the subject of my statment exists, then ...", we should be able to extend the logic to include these possibilities.

Existence would imply that the Truth of the whole depends on the Truth of the implication; non-existence implies Truth regardless of the statement.

Truth table including existence:

We expand from B => D to

(A=>B) => (C=>D) = S

A B A=>B C D C=>D S

T T T T T T T

T T T T F F F

T T T F T T T

T T T F F T T

T F F T T T T

T F F T F F T

T F F F T T T

T F F F F T T

F T T T T T T

F T T T F F F

F T T F T T T

F T T F F T T

F F T T T T T

F F T T F F F

F F T F T T T

F F T F F T T

There are extra cases enumerated here as non-existence of the subject makes it unnecessary to evaluate the implication, but it is easier to just list them all.

For the teaser in the OP, we can evaluate under these assumptions.

A = The wife exists

B = the wife is Honestant

C = the speaker exists

D = the speaker is Swindlecant

Assume S is False. Then the truth table implies that D is False. D is False means that the speaker is Honestant. This contradicts the assumption that S is False, as an Honestant cannot make a False statement.

Therefore, S is True. We know that the speaker exists. S is True implies the speaker is Honestant. These conditions mean that C=>D is False. C=>D is False and S is True means that A=>B must be False (if not, then S = (A=>B) => (C=>D) = (T => F) = F, a contradiction).

A=>B is False only if A is True and B is False.

Thus, the wife exists, she is Swindlecant, and the speaker is Honestant.

This corresponds to the 6th row of the truth table.

Edited by Bamafan
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Honestants and Swindlecants V. - Back to the Logic Problems

In the pub the gringo met a funny guy who said: "If my wife is an Honestant, then I am Swindlecant." Who is this couple?

Honestants and Swindlecants V. - solution

It is important to explore the statement as a whole. Truth table of any implication is as follows:

```P		 Q		  P=>Q

truth	 truth	  truth

truth	 lie		lie

lie	   truth	  truth

lie	   lie		truth```

In this logical conditional („if-then“ statement) p is a hypothesis (or antecedent) and q is a conclusion (or consequent).

It is obvious, that the husband is not a Swindlecant, because in that case one part of the statement (Q) „ ... then I am Swindlecant.“ would have to be a lie, which is a conflict. And since A is an Honestant, the whole statement is true.

If his wife was an Honestant too, then the second part of statement (Q) „ ... then I am Swindlecant.“ would have to be true, which is a conflict again. Therefore the man is an Honestant and his wife is a Swindlecant. Or is it a paradox?

since he said he is a swindlecant he must be lying

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I've wrestled with this one . . . and I still quite get my head around it.

Let's assume for now that the bloke is married, and that marriages are legal and binding on this island -- thinking about THOSE issues just hurts my little brain. . .

"If my wife is an Honestant, then I am a Swindlecant." I get that this requires the wife to be a Swindlecant. The second condition of the statement would be a lie to the Honestant husband, and likewise the second condition would be a truth to the Swindlecant. Both statements would not permitted. So, the wife is a Swindlecant.

HOWEVER, nothing has ever been said about a situation where the wife is a Swindlecant.

The second condition of this single statement (not two statements as is the situation with "and" or "or") doesn't come into play, when the first condition is false. So in my opinion, it doesn't help us at all in determining the identity of the husband.

Consider this analogy:

"If you beat me in the footrace, then I'll eat your socks." Clearly I am boasting that I am going to win, so I've made somewhat of a unilateral bet. There is never a mention of what happens if I win (let's not mention a tie, since that would be impossible with this analogy). If I do indeed win, surely you will not agree to eat my socks, nor will it become obvious that I should now eat your shoes or your singlet; it simply means I won't be eating socks.

So wife is a Swindlecant, and the identity of her spouse, I conclude is unknown.

One more analogy . . . "If it rains, then I always walk under an umbrella."

Before you conclude that the umbrella is related to the rain, you might want to know that when the sun is shining I also walk under and umbrella (not to stay dry, but because of the harmful UV rays) -- think about it!

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