Transcript reasoning in psych

Logical Reasoning
Deductive reasoning
Inductive reasoning
Deductive Reasoning
Reasoning from the general to the
specific
For example, start with a general
statement: All cars have tires.
You can apply this general statement
to specific instances and deduce that
a Ford Escort, a Toyota Camry, and a
Mercedes Benz must have tires.
Common deductive
reasoning problems
Series problems
Syllogisms
Series problems
review series of statements
arrive at a conclusion not contained in
any single statement
For example:
Robin is funnier than Billy
Billy is funnier than Sinbad
Whoopi is funnier than Billy
Q: Is Whoopi funnier than Sinbad
Syllogisms
Present two general premises
that must be combined to see if a
particular conclusion is true
Syllogism Example
All Intro to Psychology students
love their instructor.
You are all Intro to Psychology
students.
Must you love your instructor?
Syllogism Example
All chefs are violinists.
Mary is a chef.
Is Mary a violinist?
Ways to solve syllogisms
Mental model theories
Pragmatic reasoning
theories
Mental models theories
 To solve a syllogism,
you might visualize
the statements
 All Intro to
Psychology students
love their instructor.
 You are all Intro to
Psychology
students.
 Must you love your
instructor?
Psychology
Biology
Psychology
Biology
Psychology
Biology
Biology
Mental models theories
All Intro to
Psychology
students love
their instructor.
You are all
Biology students.
Must you love
your instructor?
Psychology
Biology
Psychology
Biology
Psychology
Biology
Biology
Mental models theories
Syllogisms that
are easy to
visualize are
more readily
solved than
more abstract
syllogisms
Psychology
Biology
Psychology
Biology
Psychology
Biology
Biology
Mental model theories
To solve a syllogism, you might
visualize the statements
Syllogisms that are easy to
visualize are more readily solved
than more abstract syllogisms
Pragmatic reasoning
theories
Solve syllogisms by applying
information to pre-existing schemas
Problem difficulty related to
importance of problem to our lives
and survival as a species
More relevant = easier to solve
Inductive reasoning
Reasoning from the specific
to the general
Inductive reasoning
18 16 14 12
??
??
10
Rule? Decrease by 2
Q: Why inductive reasoning?
Answer: Take SPECIFIC numbers
(i.e. 18,16,14) and come up with a
GENERAL rule (i.e. decrease by 2)
Inductive Reasoning
Sherlock Holmes is
perhaps a better
example of
INDUCTIVE reasoning
than deductive
reasoning
He takes specific
clues and comes up
with a general theory
Inductive reasoning problems
 7
 4
720
8
8
16 17 25
?? 26
??
5
120
10
24
??
7
??
6
?? 11
??
14
??
2
??
1
Inductive reasoning problems
 5
10 15 20
?? 25
?? 30
?? 35
?? 40
?? 45
?? 50
?? 55
??
 Rule?
 Increase by five
WRONG!!!!!
 What is the correct rule?
 Any increasing number
- the next number could be 87 or 62 or 1,000,006
 Why did everyone guess the wrong rule?
Confirmation bias
Only search for information
confirming one’s hypothesis
Example: reading newspaper
columnists who agree with our
point of view and avoiding those
who don’t
Chris story
Chris is 6’7”, 300 pounds, has 12 tattoos,
was a champion pro wrestler, owns nine
pit bulls and has been arrested for
beating a man with a chain.
Is Chris more likely to be a man or a
woman?
A motorcycle gang member or a priest?
How did you make your decision?
Steve story
Steve is meek and tidy, has a passion
for detail, is helpful to people, but has
little real interest in people or realworld issues.
 Is Steve more likely to be a librarian or
a salesperson?
How did you come to your answer?
Representativeness
Judge probability of an event based
on how it matches a prototype
Can be good
But can also lead to errors
Most will overuse
representativeness
i.e. Steve’s description fits our vision of
a librarian
Most will underuse base rates
Base rate - probability that an event
will occur or fall into a certain
category
Did you stop to consider that there are a
lot more salespeople in the world than
librarians?
By sheer statistics, there is a greatly
likelihood that Steve is a salesperson.
But very few take this into account
Guess the probabilities
How many people die each year
from:
Heart disease?
Floods?
Stop
Plane crashes?
Asthma?
Tornados?
Availability heuristic
Judge probability of an event by how
easy you can recall previous
occurrences of that event.
Most will overestimate deaths from
natural disasters because disasters
are frequently on TV
Most will underestimate deaths from
asthma because they don’t make the
local news
Word probabilities
Is the letter “k” most likely to
occur in the first position of a
word or the third position?
Answer: “k” is 2-3 times more
likely to be in the third position
Why does this occur?
Class demonstration
Name words starting with “k”
Name words with the letter “k” in
the third position
Availability heuristic
Because it is easier to recall
words starting with “k” , people
overestimate the number of
words starting with “k”
Finish the sequence problems
 30 24 18 12
?? ??
6 ??
0
Rule?
Decrease by six
 1 3 2 4 ??
3 ??
5 ??
4 ??
6
Rule?
Increase by two, decrease by 1
Finish the sequence problems
 2 3 10 12 13
?? 20
?? 21
?? 22
?? ?? 29
?? 30
??
?? 32
?? ?? 39
?? ??
?? ?? 299
?? 300
?? 301
??
31
200 201
?? ?? ??
??
302
399 2000
Rule?
Increasing numbers starting
with the letter “t”
Chess problem
Two grandmasters played five
games of chess. Each won the
same number of games and lost
the same number of games. There
were no draws in any of the
games. How could this be so?
Solution: They didn’t play against
each other.
Bar problem
A man walked into a bar and asked
for a drink. The man behind the bar
pulled out a gun and shot the man.
Why should that be so?
Solution: The man behind the bar
wasn’t a bartender. He was a
robber.
Bar problem # 2
A man who wanted a drink walked
into a bar. Before he could say a
word he was knocked
unconscious. Why?
Solution: He walked into an iron
bar, not a drinking establishment.
Nine dots problem
Without lifting
your pencil or
re-tracing any
line, draw four
straight lines
that connect all
nine dots
Answer to nine dots problem
Metal Set
Q: Why couldn’t you solve the
previous problems?
A: Mental set - a well-established
habit of perception or thought
Strategies for solving
problems
1. Break mental sets
Number problem mental set
 2 3 10 12 13
?? 20
?? 21
?? 22
?? ?? 29
?? 30
??
?? 32
?? ?? 39
?? 200
?? ??
?? 300
?? 301
??
31
201 ?? 299
?? ?? ??
??
302
399 2000
Most people get stuck in the same
rhythm
Only view problems in terms of math
formulas
Need to break out of this mental set to
solve the problem
Nine dots mental set
 Most people will
not draw lines that
extend from the
square formed by
the nine dots
 To solve the
problem, you have
to break your
mental set
Mounting candle problem
 Using only the
objects present on
the right, attach the
candle to the
bulletin board in
such a way that the
candle can be lit
and will burn
properly
Answer to candle problem
 Most people do not
think of using the box
for anything other
than it’s normal use
(to hold the tacks)
 To solve the problem,
you have to overcome
functional fixedness
Functional fixedness
type of mental set
inability to see an object as
having a function other than
its usual one
Strategies for solving
problems
1. Break mental sets
break functional fixedness
2. Find useful analogy
Find useful analogy
Compare unknown problem to a
situation you are more familiar
with
Strategies for solving
problems
1.
2.
3.
4.
Break mental sets
Find useful analogy
Represent information efficiently
Find shortcuts (use heuristics)
Two general classes of
rules for problem solving
1. Algorithms
2. Heuristics
Two general classes of
rules for problem solving
Algorithms - things the vicepresident might say
Algorithms - rules that, if followed
correctly, will eventually solve the
problem
An algorithm example
 Problem: List all the words in the English
language that start with the letter “q”
 If using an algorithm, would have to go through
every single possible letter combination and
determine if it were a word
i.e. is “qa” a word; is “qb” a word etc.
This would take a very long time
 Instead, what rule could you use to eliminate
these steps?
Rules for “q” problem
Skip ahead and assume the
second letter is a “u”
Assume the third letter has to be
a vowel
These types of rules are called
heuristics
Heuristics
 Any rule that allows one to reduce the
number of operations that are tried in
problem solving
 a.k.a rules of thumb or shortcuts
 Another common heuristic:
Problem: List all the numbers from 1-100,000 that
are evenly divisible by 5
Answer: Rather than divide each and every number,
you would use the rule: Any number ending in 0 or 5
is evenly divisible by 5.
Strategies for solving
problems
1. Break mental sets
2. Find useful analogy
3. Represent information efficiently
4. Find shortcuts
5. Establish subgoals
6. Turn ill-defined problems into welldefined problems