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[Russell]

[SOLVED] #123 Green - Illogical

[Sasuntsi Davit]

2 and A?

[Russell]

But that would not prove that the other cards dont have an A on the reverse, I think the answer is K and 7

[Sasuntsi Davit]

lol, read the question wrong...

yeah it would probably be K and 7.

[Zogger]

Maybe I'm missing something, but if you turn over K and 7, you don't know that A has a 2 on the back.

It does only say "a card," though, not every card - might not mean anything, though.

[Sasuntsi Davit]

I go back to my original answer....A and 2.

The question asks you to find out if the statement is true. Not if the other cards have A on the back or 2.

So by turning over the two cards mentioned, you will find out if what she said was true.

[Zogger]

Ah

no

it's A and 7

K can't have an A on the back, as there's always a letter on one side and a number on the other

whether or not there's an A on the other side of 2, it doesn't matter, because it's a 2.

You just need to know that 7 doesn't have an A and that A doesn't have a 7

[smile]

Surely it has to be A and 2 - because if you turn those over, you'll know whether that rule is correct, it states that it must have an A on one side and a 2 on the reverse - it works both ways.

... this would also mean theres another rule that K have a 7 on the reverse... this seems right - but its fishy

[Zogger]

[smile]

its 'a' card - not 'the' cards... if you shuffled them and relaid them, I imagine the rule would have to apply? but I see your point - hmmm

[nap1er]

work on the basis that the statement is true, and consider what each card must have on the reverse if A has 2:

A -> 2
K -> 2 OR 7
2 -> A OR K
7 -> K


i'm rubbish at explaining aren't i?!

[Sorites]

This experiment is called a Watson Selection Task created by Peter Watson in the 1960's. More recently it's been used in the work of Leda Cosmides and John Tooby to try and show that people reason differently about conditionals in different contexts.

The correct answers are A and 7. The reasoning, is that the original rule is a conditional, that is to say it has the logical form, if P then Q. (if the card has and A on one side then it has a 2 on the other) Conditionals are only false when the antecedent (the first part - the P) is true and the consequent (the second part - Q) is false.

That means that all counterexamples to the rule have to be one's in which the P is true and the Q is false, in this particular case, then, the rule is only proved false if there exists a card which shows has and A on one side, but does not have a 2 on the other.

The card with the K is irrelevant, that's an example of P being false.
The card with the 2 is also irrelevant it's an example of Q being true. If this is confusing, take a rule that says if you are drinking beer, you must be 21. If you know that the people in questions are over 25, there is no need to check to see whether they are drinking beer or apple juice. Regardless of what they are drinking they cannot counterfeit the rule.

So that leaves A and 7 as the only cards that could possibly show the rule to be false.

Lastly, the most interesting thing about this test is that something like 80% of people get it wrong, regardless of education (even in formal logic) however, when we change the context (from cards with numbers and letters to questions about following social rules) people virtually always get it right, despite the fact that the reasoning is logically identical in both cases.

[Sasuntsi Davit]

slaps self for not getting it right, (I was on to the solution though, just didn't think for long enough).

I think trying to figure out how proof by natural deduction has frazzled my brain. (I read computer science at uni by the way and have a module on formal logic, even more reason to slap self)

[vibration13]

Thanks for the excellent explaination. I was thinking that it was some kind of flip-flopping infinity loop puzzle, that kept changing it's answer mischeiviously whichever way you looked at it. Which goes to show where my head's at today.

[Guest1]

Do you guys really consider this card solved? Surely one small puzzle a 10 year old could solve is not the ONLY puzzle on the card?



FWIW, I find the choice of numbers and letters interesting...

AK is the BEST non-paired starting hand in Texas Hold'Em Poker (obviously for this quiz they couldnt use AA) and 27 is considered the WORST starting hand.