Formal Operations and
Rationality
Formal Operations
• Using the real vs. the possible
• Inductive vs. deductive reasoning
– Inductive: Specific to general, generalizing
from cases we have seen to infer information
about cases we haven't.
– Deductive: General to specific, involves
deciding what must be true given the rules of
logic and some starting set of facts(premises).
Perry (1968)
• Thinking across Undergraduates:
– Early stage: authorities are the keepers of knowledge
(thinking tightly coupled with logic)
– Later stage: shift toward relativism– equal experts
disagree… often leads to skepticism, if equally right
no point in developing further knowledge
– Last state: Recognize that there is no absolute truth
but viewpoints are supported with evidence that aids
in your assessment of quality. Problem seeking
begins.
Inductive Reasoning Problem
Deductive Reasoning Problem
In a small hospital, there was only 1 room left, which had space for 2 patients.
The nurses were instructed to put patients in the remaining room according
to these rules:
1. A rubella patient cannot be put with a tuberculosis patient, unless they are
both female.
2. If a rubella patient is male, then he can be put with a female emphysema
patient.
3. A cancer patient cannot be put with an emphysema patient if one of them is
male and the other female.
4. A tuberculosis patient cannot be put with an emphysema patient if they are
the same sex.
Which of the following patients could be put in the room if a female emphysema patient
was already accepted into the room?
a) female rubella patient
b) female tuberculosis patient
c) male cancer patient
d) male tuberculosis patient
Reasoning
• Conditional Reasoning: compares the
status of two things, objects, or ideas (e.g.,
if, then statements)
• Syllogistic Reasoning: Specific three
statement logical form (e.g., two premises
and a conclusion)
Conditional Reasoning
• Conditional Reasoning: A reasoning
problem comparing the status of two
things, objects, or ideas. A conclusion is
said to be conditional upon the “truth” of
the relationship of these premises.
• Goal: Determine if the relation between
two events is true
Conditional Reasoning Cont.
Premise:
If this is a glasses case, then this is a
container.
This is a glasses case.
Conclusion:
Therefore, this is a container.
Common Errors in Conditional Reasoning
1. Making only one model of the
antecedent and consequence.
Not every logical possibility is examined.
If she meets her friend, then she will go to the play.
She did not meet her friend.
Therefore, she did not go to the play INVALID
For example: She meets her mom
Common Errors in Conditional Reasoning
2. Trying to confirm a hypothesis, rather than
trying to disprove it.
Looking for positive, but not negative evidence.
Selection task.
RULE: If a card has a vowel on one side, then it
has an even number on the other side.
CARDS: E
J
6
7
Common Errors in Conditional Reasoning
2. Trying to confirm a hypothesis, rather than
trying to disprove it.
Looking for positive, but not negative evidence.
Selection task.
RULE: If a card has a vowel on one side, then it
has an even number on the other side.
CARDS: E
J
6
7
ANSWER: E (affirm the antecedent) and 7
(deny the consequent).
Syllogisms
• Syllogism: A three statement logical form;
the first two parts state the premise, which
are taken to be true, the third part states a
conclusion based on those premises.
• Major premise
• Minor premise
• Conclusion
All M are P
All S are M
All S are P
The Propositional Calculus
• 1. Affirming the antecedent (Valid)
Modus Ponens
If this is an apple, then this is a fruit.
This is an apple.
Therefore, this is a fruit.
• 2. Affirming the consequent (Invalid)
If this is an apple, then this is a fruit.
This is a fruit.
Therefore, this is an apple.
The Propositional Calculus
• 3. Denying the antecedent (Invalid)
If this is an apple, then this is a fruit.
This is not an apple.
Therefore, this is not a fruit.
• 4. Denying the consequent (Valid)
Modus Tollens
If this is an apple, then this is a fruit.
This is not a fruit.
Therefore, this is not an apple.
Example Syllogisms
• All scientists are great thinkers.
• Einstein was a scientist.
• Therefore, Einstein was a great thinker.
• All politicians are great thinkers.
• Bush is a politician.
• Therefore, Bush is a great thinker.
Example Syllogisms
• All polar bear are animals
• Some animals are white
• Therefore, some polar bears are white.
• All A are B
• Some B are C
• Therefore, some A are C
Example Syllogisms
• All polar bears are animals
• Some animals have venomous poison
• Therefore, some polar bears are
poisonous
• Confirmation Bias: The tendency for
people to search for evidence that
confirms their decisions far more than is
logical.