Web Exclusives: PawPlus

January 29, 2003:

More logic problems

All the Frenchmen in the restaurant are gourmets.

Some of the gourmets are wine drinkers.

Does it follow that some of the Frenchmen are wine drinkers?

Seventy-eight percent of students given this problem at Sussex University by Stuart Professor of Psychology Philip Johnson-Laird, and colleagues drew that conclusion. It is plausible, but it certainly doesn't follow.

When the researchers replaced "wine drinkers" with "Italian," so that it read:

All the Frenchmen in the restaurant are gourmets.

Some of the gourmets are Italian.

What follows?

Only 8% say "Some of the Frenchmen are Italian." Same form, but background knowledge shows it's not plausible.


Philip Johnson-Laird says: Individuals search harder for counterexamples to preposterous conclusions.When the following two questions are asked one at a time of students,

How happy are you?

How many dates did you have last week?

The correlation between answers = .12

(Correlation runs between -1 and 1. A correlation of 0 means there is no relationship between two variables. A correlation of 1 would be a perfect positive correlation, such as, for example, between the number of hours a person who is paid hourly works and that person's paycheck. So, a correlation of 0.12 says there is very little relationship between these two variables when asked this way.)

If the order of the questions is reversed:

How many dates did you have last week?

How happy are you?

The correlation jumps to = .66

Reason: emotional reaction to the number of dates; when asked how happy, the mind is full of emotional reaction.Professor Psychology and Public Affairs Eldar Shafir studies decision-making. He has found that context is critical. "Instead of making decisions about outcomes in the world," he says, "people make decisions about outcomes as they are presented."


A guiding theme in a lot of the work he has been doing is that one needs to consider how a choice or decision is presented to someone, because that often leads to different preferences.Shafir says that a tendency for people to search for additional information can lead to inconsistent decisions. This is perhaps a lesson in humility ... we can be swayed by nuances.

For example: The following scenario was presented to experienced nurses affiliated with kidney dialysis centers:

A 68-year-old relative needs a kidney transplant. You are a suitable match. Would you donate?

56% Yes

4% No

Another group of nurses presented with the same scenario, but instead told:

It is not known if you are a suitable match. Would you be tested?

69% Yes

31% No [therefore, would not donate]

If you indicated a willingness to be tested and the test indicated you were a suitable match, would you donate?

93% Yes

7% No

So, overall, of this group, 55 of 85 or 65% say Yes to donation, 35% say No


The following two problems were devised by Peter Wason, who was Phil Johnson-Laird's thesis adviser. Wason Selection Task

You are presented with four cards on a table, each has a number on one side and a letter on the other. You see only one side. Which cards should you turn over to determine whether the following rule is valid?

RULE: If a card has an even number on one side, then it will have a vowel on the other.

Here are the cards as you see them:

2 5 E S

Answer: The logically correct answer is to choose the 2 (to see if there is a vowel on the other side) and the S (to see if there is an even number on the other side). It doesn't matter, for the validity of the rule, what is on the other side of the 5 card or the E card.


THOG Problem

Suppose that there are four possible kinds of objects:

an unhappy dodecahedron

a happy dodecahedron

an unhappy cube

a happy cube

Suppose as well that I have written down on a hidden piece of paper one of the attitudes (unhappy or happy) and one of the shapes (dodecahedron or cube). Now read the following rule carefully:

An object is a GOKE if and only if it has either the attitude I have written down, or the shape I have written down, but not both.

I will tell you that the unhappy dodecahedron is a GOKE. Which of the other objects, if any, is a GOKE? Answer: Happy cube. If unhappy dodecahedron is a GOKE, it means that the questioner has written down one of the two attributes "unhappy" or "dodecahedron" and the opposite of the other. The possibilities:

Unhappy cube implies that unhappy dodecahedron is a GOKE or happy cube is a GOKE

Happy dodecahedron implies that happy cube is a GOKE or unhappy dodecahedron is a GOKE