This, as many others, is probably misquoted, as it is a total logical falacy.
It could be any day of the week, as the only thing that is told about how many liars there are is that they won't tell how many there are! As there are obviously not enough of them to cover every day of the week, there is no way of telling if any are telling the truth. Two people are capable of lying and saying that it is one certain day of the week in different ways. Percentages of people who would be lying in the case that one particular day was the truth is not the way to solve a logic problem.
If you had 99 swindlecants and 1 honestant, the only honest answer you would get would be 1% of the whole, and thus it would have to be false? NO!! You would have to use logical bridges in order to retrieve through double negativity or complete positive answers. If you were to rephrase this question to:
If someone here were telling the truth- or had one person covering each day of the week- and had at least two of them comment on whether or not another was telling the truth, you could find the answer. Under these conditions, however, there is no concrete answer.
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.
A paradox is neither a truth, nor a lie. It is simply an impossibility. If one is only capable of telling the truth, then they cannot speak a paradox. Only one capable of lying could speak a paradox.
Look at it like this. If you're telling the truth, saying something that is impossible would not be telling the truth.
The simple fact is, that this particular one has two answers:
Either A: they are both swindlecants (as it is one sentance, and as such, one statement, meaning that if part of it is false, the whole statement is false)
Or B: His wife is a swindlecant, and he is an honestant, because he is stating that if he were to say that his wife were an honestant, that he would have to be a swindlecant as he would be lying.
I realize this is a long time after this post was made, but yes, it is you. Ok, look at it this way, there's been no thorough explanation of this as of yet, at least as far as Lehman's terms go, so I'll have a whack at it.
Case 1: The honestant IS standing at the door to freedom-
Ok, if you ask if an honestant stands at the door to freedom, the honestant, if he were standing at the door to freedom, would say yes, because he has to tell the truth. The swindlecant, if the honestant WERE standing at the door to freedom, would have to say NO, so as to mislead you to walk into HIS door, which in this case was NOT the door to freedom.
Case 2: The swindlecant is standing at the door to freedom-
Arite, if you asked the swindlecant if the honestant was standing at the door to freedom, and the honestant was NOT standing at the door to freedom, the false boolean response ( a lie as a "yes" or "no" answer) would have to be yes, as the honestant, again, is NOT standing in front of the door to freedom. However, if you asked the honestant, and the swindlecant was standing in front of the door to freedom, being honest, the honestant would have to tell you NO.
So, if the honestant only says yes when the door to freedom is the door that THEY are standing by, and the swindlecant only says yes when it is the door that THEY are standing by, and the opposite for no (meaning that it is always the OTHER door when they say no), the question works.