Thinking

Thinking is the attempt to resolve doubt about: Thinking is one determinant of actions. Others are learning, reflexes, and emotions.

Thinking = search + inference

Search for:

Diagram of the search-inference framework

Types of models

Normative
Standard for evaluation
What is the right answer for this task? Why?
Descriptive
Psychological explanation of departure from normative
Heuristics, strategies, mathematical models, perceptual principles, mental models
"Bias" = systematic and non-normative
Prescriptive
Advice or prescription: heuristics, decision analysis
Designed to increase evaluation by normative standard
"Irrational" = departure from prescriptive?

Normative models of inference:

An example of a bias: Outcome bias

A fault condemned but seldom avoided is the evaluation of the intention of an act in terms of the act's outcome. An agent who acted as wisely as the foreseeable circumstances permitted is censured for the ill-effects which come to pass through chance or through malicious opposition or through unforeseeable circumstances. Men desire to be fortunate as much as they desire to be wise, but yet they fail to discriminate between fortune and wisdom or between misfortune and guilt (Arnauld, 1662/1964, p. 285)

Item used by Baron and Hershey (1988)

A 55 year old man had a heart condition. He had to stop working because of chest pain. He enjoyed his work and did not want to stop. His pain also interfered with other things, such as travel and recreation.

A type of bypass operation would relieve his pain and increase his life expectancy from age 65 to age 70. However, 8% of the people who have this operation die from the operation itself.

His physician decided to go ahead with the operation. The operation succeeded.

Evaluate the physician's decision to go ahead with the operation.

Another item

A 25-year-old man is unmarried and has a steady job. He receives a letter inviting him to visit Quiet Pond Cottages, where he has been considering buying some property. As a prize for visiting the property, he is given a choice between:

Option 1. $200.

Option 2. An 80% chance of winning $300 and a 20% chance of winning nothing.

He must mail in his decision in advance, and he will be told the outcome of Option 2 whether he chooses it or not.`

Design issues

Normative model: what subjects think vs. independence of outcome

Within-S transparent vs. within-S hidden vs. between-S

Summary

Normative models are standards:

Descriptive models take several approaches:

Prescriptive models are addressed to different audiences:

Basic descriptive principles

Big table

Creative Thinking

Definition: NOVEL and USEFUL at the time it is created

Examples:

Stages of creative thinking:

Example: Finding a creative solution to global warming

Your assignment: A creative solution to healthcare

Assignment 1

Logic: normative model

Alice is to the left of Betty.
Betty is to the left of Carol.
So, Alice is to the left of Carol.

An X can be a Y.
A Y can be a Z.
Therefore, an X can be a Z.

Are these valid?

Descriptive model: Johnson-Laird's theory

all a are b     some a are b
all b are c     all b are c

 a = b = c       a = b = c
    (b)= c      (a) (b)= c
        (c)             (c)

Conclusion:
all a are c     some a are c

More mental models

  no a are b       some a are not b
  all b are c        all b are c

   a                  a
  -----------        -----------
       b = c         (a)  b = c
          (c)                (c)

   a
   a      (c)         a      (c)
  -----------        -----------
       b = c         (a)  b = c

   a      (c)
  -----------
       b = c

some c are not a     no conclusion

A hard one (from Johnson-Laird)

Suppose that only one of the following assertions is true about a specific hand of cards:

1. There is a king in the hand or there is an ace in the hand, or both.

2. There is a queen in the hand or there is an ace in the hand, or both.

Which is more likely to be in the hand, the king or the ace?

The solution

There is a king in the hand or there is an ace in the hand, or both.
k
a
k a

There is a queen in the hand or there is an ace in the hand, or both.
q
a
q a

~k and ~a
OR
~q and ~a

Logical attitudes

An engineer, a physicist and a mathematician were driving in the country when they came upon pasture after pasture with only black cows in them. The engineer said, "There seem to be only cows colored black in this area." The physicist said, "That doesn't quite follow. The only cows we have seen are black." Then the mathematician said, "I don't think you are right there. The only cows we have seen are black on one side."
(Submitted by Ed Howland, ehowland@cyber.net)

Theorem:
A cat has nine tails.

Proof:
No cat has eight tails.
A cat has one tail more than no cat.
Therefore, a cat has nine tails.

Wason's four-card problem (modified)

K
L
2
4

Rule to test:
If K, then 2.
Which cards must you turn over?

Multi-card task (Beattie and Baron)

A1A2A3
B1B2B3
C1C2C3

Test: If A, then 2.
Which cards would you ask about to find out whether this rules holds for all the cards?

A response to the multi-card task.

(S is asked to imagine an A on the back of the 3 in the unnegated 4 card task.)
S: I would just think that there happened to be an A on the other side.
(S is asked whether an A I and an A3 would be informative in the unnegated multi-card task.)
S: No. Because... I was looking for A2 only.
E: But your goal is to find out ii the rule is true or false. If there was A I or A3 in there, would that be informative...?
S: No.
E: If the agent came back and said there was an A 1 and an A3 in the pouch, do you think that the rule would be true?
S: Yes.
E: You think it would?
S: Yes.
E: Even though there are As that don't have 2s on them.
S: Yes. Because.. the rule says if there is an A then there is also a 2. It doesn't say there couldn't be an Al or an A3.

Example of Polya's heuristic methods

x4 - 13x2 + 36 = 0

Could you imagine a more accessible related problem?

Naive theories (Roncato & Rumiati, 1986)

Wertheimer on understanding

Transfer problems

Kye's method (Ginsberg, "Children's arithmetic")

 64
-28
---

Teacher: "You can't take 8 from 4, so ..."

Kye: "Oh, yes you can. 4 minus 8 is negative 4. And 40 and negative 4 give you 36." 

 64
-28
---
 -4
 40
---
 36

Another example from Ginsberg

  16      16+9=25 (counting out)
 + 9 
 --- 
  15
I: So when we count we get 25 and when we do it this way we get 15. Is that okay to get two answers or do you think there should be only one?
S: (Shrugs his shoulders.)
I: Which one do you think is the best answer?
S: 25
I: Why?
S: I don't know.
I: If we had 16 cookies and 9 more, would we have 15 altogether?
S: No.
I: Why not?
S: Because if you counted them together you would get 25.
I: But is this (points to the answer of 15) right sometimes? or is it always wrong?
S: It's always right.

Perkins and Baron compared

PerkinsBaron
structurepossibility
purposesgoals
argumentsevidence

Summary: Approaches to thinking errors

Insufficient search for alternative models

Heuristics

Naive theories

Failure to understand