[rookie1ja]

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?

Spoiler for Solution:

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?

[carnagecox]

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!

[fosley]

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.

[larryhl]

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.

[rookie1ja]

larryhl, easy as that

[normdeplume]

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.).

[Ploper]

I see three possible answers here.
one is the admins answer.
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.

[Ploper]

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

[Wordblind]

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.

[cpotting]

Quote

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.