Reasoning
Reasoning
Normative: How should we reason?
Descriptive: How do we reason?
Deductive (analytic) Reasoning
– Closed system of axioms (givens) and theorems
(conclusion) derivable from axioms by rules.
– Evaluate validity of argument
Inductive (synthetic) Reasoning
– Basis for drawing conclusions based on evidence
– Evaluate truth of argument
Deductive (analytic) Reasoning
– Closed system of axioms (givens) and theorems
(conclusion) derivable from axioms by rules.
– Evaluate validity of argument
- Symbolic logic
Inductive (synthetic) Reasoning
– Basis for drawing conclusions based on evidence
– Evaluate truth of argument
- Bayes’ Theorem
Psychological work compares:
- People’s behavior
- Normative theories
Psychological work compares:
- People’s behavior
- Normative theories
People differ systematically from normative theories,
showing biases
This research strategy contrasts with:
- Research on components of cognition, e. g.,
attention, memory
- Research on problem solving, driven by
- problems themselves
- models of problem solving
Confirmation Bias:
– Tendency to produce and use positive but not
negative information in reasoning
– Tendency to search for confirming evidence,
not disconfirming evidence
Confirmation Bias
- Examine first in deductive, then inductive reasoning
- Some argue that distinction is not a sharp one
Rule: If a card has a vowel (p) on one side, it has an
even number (q) on the other side.
A
D
4
7
Which card(s) do you need to turn over to verify if
rule is true or false?
p & q
A&4
59
p
A
42
p, q & q
A, 4, & 7
9
p & q
A&7
5
other
13
128
( W a s o n & J o h n s o n- L a i r d )
How could rule be false?
If vowel (p) then even number (q)
Odd number on A
Vowel on 7
not even number implies not vowel
Card
Correct
Flip Side
Incorrect
A
even number
odd number
D
either
---
4
either
---
7
consonant
vowel
Why do people fail?
Don’t automatically look for disconfirming evidence
Look at other formulations of problem
-Structurally identical
- Differ in content
Rule: Every time I go to SF, I go by train.
SF
LA
TRAIN
10 / 17 succeed
2 / 16 succeed at vowel / number
CAR
If a letter is sealed, it has a 5d stamp on it.
Imagine you’re a postal worker looking for violations
– 92%
postal problem
– 29%
vowel / consonant problem
5
ΛΣϑΥΜΒ
69 Γαλϖεζ Στρεετ
Στανφορδ, ΧΑ 94305
4
ΛΣϑΥΜΒ
69 Γαλϖεζ Στρεετ
Στανφορδ, ΧΑ 94305
If a receipt is more than $50, the department head must
countersign.
Φαλσταφφ Λιγητ
Βαχαρδι Βλαχκ
Ιχε
Μιξερ
Βλενδερ
Φρεση Φρυιτ
Μυνχηιεσ
4
10
4
10
20
3
9
$60
ΦΚΨ
Τρυµπετσ
Τροµβονεσ
Μελλοπηονεσ
Τενρζ
Τοοβζ
15
3
6
8
15
2
$49
Emma M. Beaux
Supervisor
Emma M. Beaux
Supervisor
If you’re drinking alcohol, you must be over 21.
Pabst
Beer
Coke
Old
Young
Implications so far:
- We don’t do well with bare-boned logic
- We do succeed at certain specific problems
Implications so far:
- We don’t do well with bare-boned logic
Seems to contradict Piagetian notion of
formal operations
- We do succeed at certain specific problems
Contradicts notion that we have logical rules
in our minds
Familiarity, however, is not sufficient
- Some familiar problems aren’t easily solved
- “If I eat haddock, I drink gin”
People’s reasoning cannot be
characterized as either:
- syntactic content-free rules of inference
- memory of specific experiences
People’s reasoning cannot be
characterized as either:
- syntactic content-free rules of inference
- memory of specific experiences
Something in between:
Pragmatic Reasoning Schemas
Pragmatic Reasoning Schema
• Generalized set of context-sensitive rules
• Defined in relation to classes of goals
e.g., permissions, obligations, causations
(Cheng & Holyoak, 1985)
Permission Schema
1. If the action is to be taken, the precondition must
be satisfied.
2. If the action is not to be taken, then the
precondition need not be satisfied.
3. If the precondition is satisfied, then the action
may be taken.
4. If the precondition is not satisfied, then the action
must not be taken.
Permission Schema
1. If the action is to be taken, the precondition must
be satisfied (drink beer).
2. If the action is not to be taken, then the
precondition need not be satisfied (drink coke).
3. If the precondition is satisfied, then the action
may be taken (old man).
4. If the precondition is not satisfied, then the action
must not be taken (young man).
Other schemas should work, such as
causal reasoning schema
-- If there’s smoke, there’s fire
- If you’ve had a measles vaccine, you’re immune to
measles
- If you study, you pass exam
Other schemas should work, such as
causal reasoning schema
-- If there’s smoke, there’s fire
no fire implies no smoke
- If you’ve had a measles vaccine, you’re immune to
measles
no immunity implies no vaccine
- If you study, you pass exam
no pass implies no study
Now turn to inductive reasoning....
What is task of scientist?
- Develop hypothesis about the way things are
- Collect data from world to verify hypothesis
Hypothesis testing
Hypothesis: All ravens are black
- We do: Here’s a raven, it’s black. Another raven,
it’s black
- We don’t do: Here’s something not black, it’s not a
raven....
Hypothesis: All ravens are black
- We do: Here’s a raven, it’s black. Another raven,
it’s black (seeking confirmation)
- We don’t do: Here’s something not black, it’s not a
raven.... (seeking disconfirmation).
Karl Popper:
“It is easy to obtain confirmations or
verifications for nearly every theory--if we
look for confirmation.”
Number sequence: What’s rule?
2, 4, 6
Wason & Johnson-Laird
• 6 participants announced correct rule
– No incorrect rules
– Varied their hypotheses
• 22 participants gave at least one incorrect
– Even after being told hypothesis incorrect, still produced
sequences that corresponded to incorrect
Confirmation Bias is strong
• Financial incentives had no effect
• Thinking of set of possible rules had no effect
• Telling participants a sequence that disconfirmed
facilitated slightly
Another example:
• Siamese cat
• What’s the rule?
Confirmation bias in real life:
- Medical example: People with back pain
- Get MRI
- MRI shows abnormalities
- Get surgery
Confirmation bias in real life:
- Medical example: People with back pain
- Get MRI
- MRI shows abnormalities
- Get surgery
- Dr. Brant-Zewadski gave MRIs to 98 people
without back pain
-2/3 had abnormalities, 1/3 more than one disk
Confirmation bias in real life:
- Challenger Disaster Retrospective: Engineers
brought cases of O-ring failure and low
temperatures
Confirmation bias in real life:
- Challenger Disaster Retrospective: Engineers
brought cases of O-ring failure and low
temperatures
- Didn’t bring cases of O-ring successes and low
temperatures
Confirmation bias in real life:
- Entire scientific enterprise
Confirmation bias in real life:
- Entire scientific enterprise
- Scientific processes is dialectic
Confirmation Bias is Pervasive
- Deductive reasoning
- Inductive reasoning
- Practice
- Science
Confirmation Bias is Pervasive
- Deductive reasoning
- Inductive reasoning
- Practice
- Science
Corrective: Free market place of ideas
But: not always present, especially in individual
Confirmation bias in real life:
- experienced clinicians a battery of diagnostic test
scores and asked for ratings on 8 diagnostic
categories: paranoid, borderline personality,
hysteria, bipolar, etc.
- sketch of person suggestive of paranoid or
borderline personality