A puzzling logic puzzle.

[Jim__]

4th Quarter 2010 issue of TPM has an article (not available online), Against the Logicians, by Don S Levi, emeritus professor of philosophy at the University of Oregon. The article largely argues that logic should not be a separate field of study because most people are able to think logically and they have problems in logic class because the problems they are given have no real world context. As part of the article, he gives an example. It's a good example for making his point about lack of context and the frustration of dealing with these puzzles - especially if he is giving us the correct answer. I believe that the answer the professor gives to the puzzle is wrong. I think it's a typo rather than an error on his part. A small excerpt that contains the complete description of the puzzle:

Whether logic is anything more than a field onto itself is an issue unintentionally raised by the Wason Selection Task. If you are like most people. you will do badly when given the task. So, you may want to consider the possibility that the experimenters are wrong about what answers are right and wrong in thinking that getting the right answers requires being logical, rather than relying on the knowledge of how things are supposed to work within the field of logic.

The Selection Task involves cards, which have a letter on one side and a number on the other. Subjects are given a "rule" about these cards, such as: "If a card has a vowel on one side, then it has an odd number on the other." Then they are told about 4 cards, where the visible sides are, for example, 5, E, 12, G, and asked which cards have to be turned over to determine whether the rule is being followed.

The right answer is: 5 and 12. They need to be turned over because it is possible for a vowel to be paired with an even number with each card, and this is the very possibility that is ruled out. The other cards do not need to be turned over because what is ruled out is not possible with either card.

This explanation makes clear that experimental subjects would have done much better if the rule had been worded: " A vowel is not paired with an even number."

I believe the right answer is E and 12. What do you think?

I am more confident of my answer having found the Wason Selection Task on wikipedia. The puzzle is slightly different there, but I agree with their logic and I believe it agrees with my selection of E and 12.

The answer 5 and 12 highlights the frustration I have taking certain tests where I feel the question if easy, but different interpretations of the question leads to different possibilities.

[trackfan]

1. I also say E and 12.

You don't need to turn 5 because it can have either a vowel or consonant, since the rule implies all vowels must back odd numbers, but not all odd number must back vowels. So 5 can back a consonant or vowel without violating the rule.

E has to be turned becuase it would violate the rule if backed by an even number.

12 has to be turned because it would violate the rule if backed by a vowel.

G needn't be turned as there is no rule for what backs consonants.

[ZombieHorde]

2. I would guess cards E and 12.

"If a card has a vowel on one side, then it has an odd number on the other."

This rule does not seem to forbid odd numbers to paired with consonants. The rule only seems to forbid vowels to be paired with even numbers.

[Ready4Change]

7. I agree. E and 12.

.

[SouthernLiberal]

3. Here's my take...

The rule is that a vowel must be paired with an odd number. I do not see anything in that rule that prohibits the pairing of a consonant with an odd number.

So, which cards will tell me if a vowel is paired with an even number, which would invalidate the rule.

5 - no, because it is an odd number, which the rule allows to be paired with any letter.
E- yes, because it is a vowel, so it the other side has an even number, the rule in invalid
12 - yes, because it is an even number, and if the other side is a vowel, the rule is invalid
G - no, because it is not a vowel, and the rule says nothing about what kind of number may be on the other side.

So I agree with you, the correct answer is E and 12.

My field is information processing. I have learned the the most important thing in my field is making sure you have the right question, and that you are interpreting it correctly. No one cares if you give the right answer to the wrong question.

[drm604]

4. You're right about the answer.

The answer is E and 12. I don't know what "real world context" could give anyone a different answer.

I'm not sure what is meant by "logic should not be a separate field of study". Not separate from what? I think it's usually considered part of mathematics. What should it be combined with? Geometry? Algebra? Calculus? I don't see how it makes sense to say that it shouldn't be a separate field of study. Admittedly I haven't read the article so I could be missing the point.

[Fumesucker]

5. Clearly Prof Levi has never done any online argumentation..

If he had there is no way he would claim that most people are capable of thinking logically.

[Jim__]

6. Thanks for all the answers.

I was really curious because the article stated: Whether logic is anything more than a field onto itself is an issue unintentionally raised by the Wason Selection Task. If you are like most people. you will do badly when given the task. I certainly did badly considering the answer given in the article. It'll be interesting to see if the magazine has anything to say about it in its next issue - at least in the letters section.

[dimbear]

8. In real life, turn all the cards over.

Don't trust anybody.