Cognitive Processes
PSY 334
Chapter 10 – Reasoning
Logic vs Human Reasoning
 Logic – a subdiscipline of philosophy and
mathematics that formally specifies what
it means for an argument to be correct.

Human deviations from logic were thought
to be malfunctions of the mind.
 AI systems guided by logic are also
deficient, lacking common sense.
 Prescriptive or normative models do not
predict human behavior very well.
Demos of Human Irrationality
 Four main areas of research have
studied how humans deviate from
prescriptive models:


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Reasoning about conditionals
Reasoning about quantifiers
Reasoning about probabilities
Decision making
Two Kinds of Reasoning
 Reasoning – the process of inferring new
knowledge from what we already know.
 Deductive reasoning – conclusions
follow with certainty from their premises.

Reasoning from the general to the specific.
 Inductive reasoning – conclusions are
probable (likely) rather than certain.


Reasoning from the specific to the general.
Probabilistic – based on likelihoods.
Syllogisms
 Syllogism – a series of premises
followed by a logical conclusion.
 All poodles are pets Congruent 84%
All pets have names
.: All poodles have names – T or F?
All pets are poodles Incongruent 74%
All poodles are vicious
.: All pets are vicious -- T or F?
Content-Free (Abstract)
 Subjects did better judging syllogisms
that were consistent with reality
(congruent).
 Content-free syllogisms use symbols
instead of meaningful sentences:
All P are B
Abstract 77%
All B are C
.: All P are C – T or F?
Different Brain Regions Active
 Logic problems can be approached in
two different ways:


Ventral prefrontal & parietal-temporal
areas active when reasoning about
meaningful content
Posterior parietal active when reasoning
about content-free material.
Different Brain Regions Active
Conditionals
 If-then statements.


Antecedent – the “if” part.
Consequent – the “then” part.
 Rules of inferences using conditionals:


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Modus ponens -- If A then B, observe A,
conclude B
Modus tollens – If A then B, observe not-B,
conclude not-A
Notation: negation, implication, therefore.
Table 10.1
Anderson: Cognitive Psychology and Its Implications, Seventh Edition
Copyright © 2010 by Worth Publishers
Modus Ponens and Tollens
 If Joan understood this book, then she
would get a good grade. If P then Q


Joan understood .: she got a good grade.
This uses modus ponens. P .: Q
 If Joan understood this book, then she
would get a good grade. If P then Q


She did not get a good grade .: she did not
understand this book.
~Q .: ~P
This uses modus tollens.
Logical Fallacies
 Denial of the antecedent:


If P then Q, not-P, conclude not-Q
If P then Q, not-P, conclude Q
 Affirmation of the consequent:
 If P then Q, Q, conclude P
 If P then Q, Q, conclude not-P
 Subjects seem to interpret the
conditional as a biconditional – “if”
means “if and only if”
Denial of the Antecedent
 If Joan understood this book, then she
would get a good grade. If P then Q


Joan did not understand .: she got a bad
grade. – This is not necessarily true.
This is a fallacy. ~P .: ~Q
 If it rains, then I will carry an umbrella.


It is not raining .: I will not carry an
umbrella.
But I may carry an umbrella for shade!
Affirmation of the Consequent
 If Joan understood this book, then she
would get a good grade. If P then Q


Joan got a good grade .: she understood
the book. This is not necessarily true.
This is a fallacy. Q .: P
 If someone is abused as a child, then
they will show certain symptoms.

They show symptoms .: They were abused
as a child. Symptoms may not be of abuse!
Frequency of Acceptance
How People Reason
 People may be reasoning in terms of
conditional probabilities.

Conditional probabilities can be found that
correspond to acceptance rates for
fallacies.
 Wason selection task – if there is a
vowel on one side, then there must be
an even number on the other side.


Can be explained in terms of probabilities.
Also explained by a permission schema
Sample Wason Task
E
K
4
7
E
87%
K
16%
4
62%
Affirming the consequent
7
25%
Failure to apply modus tollens
Only 10% make all of the right choices
A Contextualized Version
 In order to drink beer, someone must be
21 years of age:
DRINKING
A BEER
DRINKING
A COKE
22 YEARS
OF AGE
Which ones would you check?
16 YEARS
OF AGE
Explanations
 Three proposed theories:



Logic – people routinely fail to apply
modus tollens.
Probabilistic – this task produces failures
only with certain underlying probabilities.
Permission schema – the logical
connective is interpreted in terms of social
contract.
 A cheating context improves the results.
Conditional “If”
 A strict logical construction means “If
and only if”
 People tend to adopt the more
probabilistic condition if that means
“under certain circumstances”


In this case, the conditional statement is
interpreted in light of the probabilities and
circumstances.
If a car has a broken headlight…
Which would you check?
Car with a broken headlight – check the
taillight.
2. Car without a broken headlight – don’t check
taillight.
3. Car with a broken taillight – check to make
sure it has no broken headlight even though
unnecessary.
4. Car without a broken taillight – reluctant to
check every car in the lot although logically
correct to check every car.
1.
Quantifiers
 Categorical syllogism – analyzes
propositions with quantifiers “all,” “no,”
and “some.”
 Fallacies:
Some A’s are B’s
Some B’s are C’s
Conclude: Some A’s are C’s
 Some women are lawyers, some lawyers are
men, conclude some women are men.
Atmosphere Hypothesis
 People commit fallacies because they
tend to accept conclusions with the
same quantifiers as the premises.



Some A’s are B’s
Some B’s are C’s
Conclude Some A’s are C’s, not No A’s are
C’s
 Universal premises go with universal
conclusions, particular with particular.
Two Forms of Atmosphere
 People tend to accept a positive
conclusion to positive premises, negative
conclusion to negative premises.

Mixed premises lead to negative
conclusions.
 People tend to accept universal
conclusions from universal premises (all,
no), particular conclusions from
particular premises (some, some not).
Limitations
 Atmosphere hypothesis describes what
people do, but doesn’t explain why.
 People sometimes violate predictions of
the atmosphere hypothesis.


They are more likely to accept a syllogism
if it contains a chain leading from A to C.
People should accept a syllogism with two
negative premises, but correctly reject it.
Process Explanations
 People construct a mental model to think
concretely about the situation and ask if
it is possible, not if it is inevitable.

Correct conclusions depend upon choosing
the correct mental model.
 Errors occur because people overlook
possible explanations of the premises:

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All the squares are shaded
Some shaded objects have bold borders.
.: Some of the squares have bold borders.
Possible Interpretations
Is it this way?
Or this?
Possible Meanings
All A are B
A
Some A are B
A B
Some A are B
A B
No A are B
A
AB
B
B
A
B
A
B
AB
A
A
B
B
Hypothesis Testing
 Hypotheses are formed inductively from
premises:



Given this series: 1, 2, 4, ?
What number comes next? 8th is a guess
It exemplifies the rule: each number is
double the previous number.
 There is not usually a single conclusion
consistent with the premises.
Hypothesis Formation
 Bruner, et al. (1956) presented series
of boxes containing objects varying on
four dimensions:


Number of objects, number of borders,
shape, color.
+ identified a positive instance, negative (not an instance).
 Subjects had to identify the concept
exemplified by the stimuli.
Sample Sequences
+
+
Confirmation Bias
 Focusing on instances that are
consistent with a hypothesis instead
of those that disconfirm it can lead to
mistaken conclusions.


This may not be a mistaken strategy if
selecting instances consistent with a
hypothesis led to disconfirming it.
Drinking orange juice before an exam, if
tested further, would quickly show itself
to be wrong.