Jeff Corey's Wason Card problem

[RichardR]

Jeff:

I tried to comment on this at the conference, but your time slot didn’t allow it.

IMO part of the reason that people got this problem wrong is that they did not read the question properly. That was clear from some of the comments from the crowd from the people who didn’t get that rhe correct answer was card # 1 (and card "A" in the four card question).

I wonder if anyone else was of this opinion too?

[seraph9k]

I think that, based on what I heard, people were over analyzing the problem, and it must be said, the problem does tend to lend itself to overanalysis. (The "what if there's not a number at all on the flip side of a letter, but another letter" questions seems to me an indication of this.)

That said, I think the basis of the "correct choices" was the concept that to test a hypothesis you have to falsify it. As a test of a scientific philosophy it's a good one, but I'm not at all convinced that it's as clear cut as it was presented. While I tend to agree that all scientific hypotheses are falsifiable, I'm not sure that they're all tested by applying that principle. I'm not a scientist by any stretch of the imagination, but how do tests that use prediction of results fall under the "falsifying method"? Can someone explain this to me?

Frankly, given the size of the sample (2 or 4 cards), flipping over _all_ the cards to test the hypothesis doesn't seem all that "inefficient" to me. Maybe if there were 4000 cards there'd be a point to this, but as it is, I'm just not getting the point.

Seraph9k

[darling]

Originally posted by seraph9k
Frankly, given the size of the sample (2 or 4 cards), flipping over _all_ the cards to test the hypothesis doesn't seem all that "inefficient" to me. The point is that flipping over "2" doesn't help you at all - it doesn't matter what is on the other side in relation to the question.

I'm sure there's a webpage or ten out there...

[UKBoy1977]

I agree that some people did not read the question properly . But for those that did it is essentially a problem involving logic. The statement was roughly as follows
"Every card that has a vowel on one side has an even number on the other"
Most people correctly pick A. Turning over the B card tells you nothing. If it has an odd number this neither confirms or contradicts our statement. If it has an even number this also doesn't falsify it as B having an even number doesn't mean A cannot also.
However Most people say 2. But if we turn over 2 and it has a vowel, this does not confirm our statement. It shows that IN THIS CASE the vowel had an even number on the other side, but not that EVERY vowel does. If we turn it over and it has a consonant tere, then this does not relate to our statement as we are no longer dealing with a vowel card.
So turning over 2 cannot confirm or disprove the statement and so is useless.
However turning over 1 could disproveit if we were to find a vowel on the back. In this case we would have found a vowel card with an odd number on the back which CONTRADICTS the statement that every vowel must have an even number on the back.
I hope I have explained this OK!

[Jack of Hearts]

I had figured it out, too, but, yes, your explanation is quite good. :)


John

[Jeff Corey]

I couldn't have explained it better myself.
Maybe I should have done so.

[Paul C. Anagnostopoulos]

It's not just a question of which cards can falsify the statement. Another source of confusion occurs when people assume that "all vowels have an even number" implies "all even numbers have a vowel." If they assume that, consciously or not, then they will want to turn over the "2" card to test the assumption.

I think it's a pretty concise way of confusing people from many different directions!

~~ Paul

[Jeff Corey]

As was said, all of these possibilities have been discussed in the literature. For some convoluted stuff, check out Margolis Wason card problem. on google

[The Bad Astronomer]

Originally posted by UKBoy1977
[B]"Every card that has a vowel on one side has an even number on the other"
Most people correctly pick A. Turning over the B card tells you nothing.


Actually, that's incorrect. If it has a vowel on the other side, the hypothesis is proven wrong. It never says that there must only be a letter on one side and a number on the other.

You must flip the A, B, and 1 card. The A must have an even number, the B must not have an A, and the 1 must not have an A. Flipping over the 2 tells you nothing.

So you must flip three cards.

[markb]

Originally posted by The Bad Astronomer


Actually, that's incorrect. If it has a vowel on the other side, the hypothesis is proven wrong. It never says that there must only be a letter on one side and a number on the other.

You must flip the A, B, and 1 card. The A must have an even number, the B must not have an A, and the 1 must not have an A. Flipping over the 2 tells you nothing.

So you must flip three cards.

Do you have the paper in front of you? I can't remember the exact wording, but as I recall, it *DID* indicate that each card had a letter on one side and a number on the other. This was a given, and not part of the statement being tested.

[phiend]

Here is the wording
There are 4 cards on a table in front of you. Each has a letter on one side and a number on the other. Check the cards you would turn over to test this statement:
All cards with a vowel on one side have an even number on the other.

[phiend]

here is a link to the problem purposed using age and alchol instead.
http://www.psychology.sunysb.edu/hwaters-/PSY366/Slideset7/sld020.htm

On a side note, the slide show its self is a pretty interesting read, the original wason card problem is on slide 18.

[RichardR]

Like I said, "IMO part of the reason that people got this problem wrong is that they did not read the question properly." ;)

[Jeff Corey]

Originally posted by The Bad Astronomer


Actually, that's incorrect. If it has a vowel on the other side, the hypothesis is proven wrong. It never says that there must only be a letter on one side and a number on the other.

You must flip the A, B, and 1 card. The A must have an even number, the B must not have an A, and the 1 must not have an A. Flipping over the 2 tells you nothing.

So you must flip three cards.
Someone at the session said words to that effect, but the idea is that we take as a given that there is a table, there are a certain number of cards on it and each card has a letter on one side and a number on the other.

[The Bad Astronomer]

Originally posted by phiend
Here is the wording
There are 4 cards on a table in front of you. Each has a letter on one side and a number on the other.

D'oh! My mistake then. Consider my earlier post removed. :-)

[SkepticScott]

Phil,
I made the same mistake in the discussion afterwards. I answered the problem correctly, but in the heat of debate I forgot that was stated.

[Jeff Corey]

If any teachers on this forum would like to use Wason's 2 card problem in their classes, I would appreciate receiving the data.
Age range?
Number of each gender?
Number of correct (1) and incorrect (2) answers?

For those of you who didn't get the handout at the meeting, here is the Wason 2 card problem.

You have 2 cards on a table in front of you. Each card has a number on one side and a letter on the other.
Which card would you turn over to test the statement that,

"All cards with a vowel on one side have an even number on the other."

The cards show 1 and 2

Data may be sent to jcorey@liu.edu

[Brown]

I would very much like to read Jeff's paper on this subject. Perhaps what I'm about to say is old news, but here goes:

Prof. John Allen Paulos has written about this problem. (See, e.g., "DNA Fingers Murderer" in "A Mathematician Reads the Newspaper.") If memory serves, he has also written an article (which I am unable to find) in which he presents the problem in two contexts. One context involves selecting cards with symbols on them. The other context involves a bartender deciding whom to "card" at a bar. One context is abstract, and one context is more "real world," and yet the two problems are basically the same. Most people are able to solve the "real world" version easily, but have trouble with the abstract version.

[phiend]

If it helps here is my perspective of the problem. When I first saw the problem, my instinct was to check A and 2, then though about it a second and I decided to check A, 2 and 1. It took a while before I realized why I wanted to choose 2, but basically it was because indirectly 2 was mentioned in the statement. So when I looked at the cards two of them immediately jumped out at me the A and the 2 because they were mentioned in the statement. I think at this point my mind had decided that these to were answers without putting much thought into it. So in looking to fulfill the answer I studied the remaining 2 cards and mostly forgot about the two that my mind had already decided were answers. Now as soon as it was mentioned that 2 was not an answer I immediately knew why, my mind just hadn’t went down that path until it was told that 2 was wrong. The problem for me was I never tried to disprove my self. I just accepted my first impression and went with it. If I would of sat back and went over each card and asked myself why would I need to test this card, I think I would of figured it out. It reminds me of some of the better riddles I’ve heard. The answer is usually easy if you just sit back forget what your first impression was and study it word by word. But most people don’t do that.

[Brown]

I found a version of the bartender problem in one of Paulos's "Who's Counting?" (http://abcnews.go.com/sections/science/WhosCounting/whoscounting001001.html) columns. Turns out it's a bouncer, not a bartender:Contrast this task [selecting cards from a table] with another one involving a possible social infraction. A bouncer at a bar must throw out underage drinkers. He’s confronted with four people: a beer drinker, a cola drinker, a 28-year-old, and a 16-year-old. Which two should he interrogate further? Here it’s clear to almost everyone that it’s the beer-drinker and the 16-year-old who must be interrogated.

[Patricio Elicer]

Originally posted by RichardR
That was clear from some of the comments from the crowd from the people who didn’t get that rhe correct answer was card # 1 (and card "A" in the four card question).Eh?,... is it just me or something is missing here?

The answer to the four card question is: "card A" and "card 1".

I think there are 2 main reasons why some people didn't get the correct answer: 1) they didn't read the question carefully and 2) they didn't take the necessary time to think about it.

I myself didn't get it correctly at first mainly because of the second reason.

The statement can be reworded for clarity, as an "if-then" statement, as follows:

"if there is a vowel on one side, then there is an even number on the other" (*)

In mathematical logic, the previous statement is tantamount to:

"If there isn't an even number on one side, then there isn't a vowel on the other" (**)

By statement (*) it's quite clear that card A must be turned over, and statement (**) dictates that card 1 must be turned over, thus the correct answer to the four card problem is card A and card 1

[phiend]

When I look at the other problems with Beer and drinking age, or with bouncers the first thing my mind does is setup a set of conditions, a relationship with the groups. Only numbers higher then 21 can drink beer. When I look at the cards, only one card jumps out at me the beer. So then I study each of the three left. In this I am not bound by the fault I have in the first example of the vowels and even numbers.

[Jeff Corey]

See Cheng & Holyoak (1985) Pragmatic reasoning schemas. Cognitive Psychology, 17 391-416.
Same authors, On the natural selection of reasoning theories.
Cognition, 33 285-313.
Cosmides (1989)The logic of social exchance: Has natural selection shaped how humans reason? Studies with the Wason selection task. Cognition, 31 187-276.
It seems that in areas involving breaking laws, people don't show confirmation bias, but rather seek to find whether a law is or is not being broken.

[Jeff Corey]

Originally posted by Patricio Elicer
.

The statement can be reworded for clarity, as an "if-then" statement, as follows:

"if there is a vowel on one side, then there is an even number on the other" (*)



I'm not sure that that particular rewording clarifies the problem.
In the last 10 years, I've tried rewording the original problem in a number of ways. The only thing that increases correct responding is making it more concrete, as in the drinking age version.

[bpesta22]

I dunno if this was mentioned in the talk, but the card problem is just a version of the four conditional inferences:

If a card has an even number showing, then its flip side is a vowel:

1) Even numbered card (modus ponens: if p then q, p, therefore, q) Valid flip

2) odd numbered card (i.e., not an even number-- the fallacy of denying the antecedent: If p then q; not p; therefore not q). Invalid flip

3) vowel showing (the fallacy of affirming the consequent: if p then q, q, therefore p) invalid flip

4) Consonant showing (i.e., not a vowel-- modus tollens: If p then q, not q, therefore, not p.) Valid flip.


B

[Quinn]

Originally posted by phiend
The problem for me was I never tried to disprove my self. I just accepted my first impression and went with it.

I believe this was exactly the phenomenon that the test was meant to illustrate, and is one of the major stumbling blocks in the critical thinking process.

Quinn

[phiend]

Originally posted by Quinn


I believe this was exactly the phenomenon that the test was meant to illustrate, and is one of the major stumbling blocks in the critical thinking process.

Quinn

The problem is usally used to explain confirmation bias, but the process i went through is something diffrent.

[Jeff Corey]

Originally posted by bpesta22

3) vowel showing (the fallacy of affirming the consequent: if p then q, q, therefore p) invalid flip.
Yes, an invalid form of modus ponens.

[Lisa G]

Found this Web site re Wason:

http://www.psych.ucsb.edu/research/cep/socex/wason.htm

My philosopher husband got it really fast, drew a table which helped me see it, and wrote it out using those logic symbol thingies (that's a technical term).

Lisa Goodlin

[UnrepentantSinner]

Originally posted by RichardR
Like I said, "IMO part of the reason that people got this problem wrong is that they did not read the question properly." ;)

Can you blame 'em (...er "us"). By Sunday afternoon my brain was so packed I just wanted to see pelicans and Miami Heat cheerleaders.

..O.k. I got to see the pelicans.

Hal did a great job on chosing the paper presenters, and the paper presenters did a great job in presenting them. Kudos to all.