Definition of a "fair split" varies across cultures

[The Brain]

Many cultures are stupid.

[Jacob]

For a more contrived example: One of Mike's friends is wearing a hat. Is it true that if Mike has no friends, then you are wearing a hat? By the rules of formal logic, this is a perfectly good question, with the answer "yes". But by the usual (Western?) rules of human interaction, it would have the answer "no", with a strange look at the person asking. The assumptions are unnatural enough that the person being questioned applies the rules of "this guy is being a dick" rather than the rules of logic.

That's a good illustration

[Admiral Yi]

How is the logical answer to that "yes?" 

[mongers]

For a more contrived example: One of Mike's friends is wearing a hat. Is it true that if Mike has no friends, then you are wearing a hat? By the rules of formal logic, this is a perfectly good question, with the answer "yes". But by the usual (Western?) rules of human interaction, it would have the answer "no", with a strange look at the person asking. The assumptions are unnatural enough that the person being questioned applies the rules of "this guy is being a dick" rather than the rules of logic.

That's a good illustration

Yes.

What needs to be factored is how seriously different cultures take these contrived question/thought experiments ?

My gut reaction is people from our western culture and specifically 'us' who spend many hours arguing the toss about ideas/constructs/issues on the interwebs, might take it far more seriously than someone from a poorer country, who's used to hard physically work and a less comfortable lifestyle.

Many of those people might culturally react as if it was a pie in sky style question, not taking it seriously and being bemused/amused ?

[Razgovory]

How is the logical answer to that "yes?" 

It's one of those material implication thingies.  The first two parts contradict each other so it doesn't matter what the third part is, it will be true.  At least I think.  It's all very confusing.

[mongers]

How is the logical answer to that "yes?" 

It's one of those material implication thingies.  The first two parts contradict each other so it doesn't matter what the third part is, it will be true.  At least I think.  It's all very confusing.

I thinks it's a joke based on the notion that "no friend of Mike wears a hat" ?   

[Razgovory]

If you say so.  I'm weak on logic and British culture.  I just gave it my best shot.

[mongers]

If you say so.  I'm weak on logic and British culture.  I just gave it my best shot.

I'm strong on British logic and weak on culture, therefore I could be entirely wrong.   

[Eddie Teach]

How is the logical answer to that "yes?" 

The statement is "If Mike has no friends, you are wearing a hat." Since Mike has a hat-wearing friend, the first part of the conditional is false, so the second part is immaterial.

[Admiral Yi]

The statement is "If Mike has no friends, you are wearing a hat." Since Mike has a hat-wearing friend, the first part of the conditional is false, so the second part is immaterial.

I got that.  But I still don't see how that makes yes a correct answer.

[Eddie Teach]

Because he's asking you to evaluate the truth of a proposition "x -> y " when x is false. That proposition will be true so the answer will be yes, it's true.

[Admiral Yi]

Because he's asking you to evaluate the truth of a proposition "x -> y " when x is false. That proposition will be true so the answer will be yes, it's true.

You're given two contradictory predicates that have no relaationship to the outcome variable.  I could be missing something basic, but it seems to me the correct answer is "there's no way of knowing given the information you've provided."  Or i suppose i could feel the top of my head.

[Eddie Teach]

You don't know if I'm wearing a hat. However, you do know that Mike has a friend. So Mike not having friends can imply anything you want. For x -> y to be true doesn't require that y is true.

[Razgovory]

I suppose we'll need to wait for Fish Taco or Jake to explain it to us then.  JR may know.  He's talked about that kind of stuff before and may be literate in the weird world of formal logic.  I remember some of this from college but to me it seemed like a magical language of symbols created for the purpose of making elves disappear or some other unholy sorcery.

[The Brain]

For the people who don't understand logic there's always cooking and embroidery.