The Socratic Society Forum Logic Problems

One of my favorite parts of Philosophy class is exercising logic. One of the ways you can gauge your logic is to have some fun with Logic Problems. They're an interesting way to see how you think. I have a particular favorite kind, however, and that's what I'll share here. Feel free to link or create your own.


There are two kinds of people on a mysterious island. There are so-called Honestants who speak always the truth, and the others are Swindlecants who always lie.

Three fellows (A, B and C) are having a quarrel at the market.

A gringo goes by and asks the A fellow: "Are you an Honestant or a Swindlecant?"

The answer is incomprehensible so the gringo asks B: "What did A say?"

B answers: "A said that he is a Swindlecant."

And to that says the fellow C: "Do not believe B, he is lying!"

Who are B and C?








[answer]

A is unknown, B is a swindlecant, and C is an honestant.

How:

First suppose what A must have said ~~~> if A said "I am a Swindlecant", then he can neither be lying nor telling the truth. A Swindlecant can't say he's a Swindlecant because that'd be telling the truth, so to be a Swindlecant they would have to say "I'm an Honestant." Alternatively, an Honestant can't say "I'm a Swindlecant" because that would be lying. So it is a truth that A must have said "I'm an Honestant". Now, moving on, it's irrelevant what A actually is (we can't actually figure that out with the given information).

The next step then is to consider that if A must have said "I'm an Honestant", then B is lying by saying that A said he is a Swindlecant. Therefore, B is a Swindlecant and C must be telling the truth when he says "B is lying", therefore making C an Honestant.