GXEX1406
Thinking and Communication Skills
Categorical
Reasoning
INTRODUCTION
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Arguments generally are divided into two
types: deductive and inductive.
Deductive arguments? Valid or invalid?
Inductive arguments? Strong or weak?
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
Valid or invalid DR?
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If Flipper is a dolphin, then Flipper is a mammal.
Flipper is a dolphin. So Flipper is a mammal.
If Bigfoot is human, then Bigfoot has a heart.
Bigfoot is not human. So Bigfoot doesn’t have a
heart
Bill: I guess some of the seniors were late to
practice this morning. Diane: how do u know? Bill:
Because the coach said that anyone late to
practice this morning would’ve to do sprints and I
just saw some of the seniors doing sprints. That’ll
teach them.
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
Categorical
Reasoning
Getting deeper into logic
CATEGORICAL REASONING
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A form of deductive argument.
Also called syllogism.
Consists of two or more premises that
precede the conclusion.
Reasoning conclusions about the properties
of individuals from more general premises
that concern all the members of the relevant
categories.
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
CATEGORICAL REASONING
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Example:
All whales live in water (Premise)
All fish live in water, too (Premise)
All fish must be whales. (Conclusion)
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
CATEGORICAL REASONING
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If the conclusion of an argument is not
guaranteed by the truth of the premises then
the syllogism is not valid.
An invalid argument involving categories is
called a categorical fallacy.
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
CATEGORICAL REASONING
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Example:
All German cars are reliable
All BMW are German cars
All BMW will be reliable
In this case, the conclusion is valid
because the premises are true and the
conclusion follows necessarily from the
premises.
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
CATEGORICAL REASONING
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Generally, the paradigms for a valid
universal syllogism are as follows:
All X are Y.
Z is X.
Therefore, Z is Y.
Or
All X are Y.
No Z is Y.
Therefore, no Z is X.
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
CATEGORICAL REASONING
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From the general form of categorical reasoning in the
previous slide, notice that:
 Each argument has 3 terms which are X, Y and Z.
 Each term occurs exactly twice in exactly two
different claims. Example:
All X are Y.
Z is X.
Z is Y.
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
CATEGORICAL REASONING
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A syllogism is a two premise deductive argument
which are:
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Major premise
Minor premise
The parts of a categorical syllogisms are labeled
as follows:
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Major term – the term that occurs as a predicate term
of the syllogism’s conclusion
(cont)
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
CATEGORICAL REASONING
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Minor term – the term that occurs as the subject term of
the syllogism’s conclusion
Middle term – the term that occurs in both of the premises
but not at all in the conclusion.
The most frequently used symbols for these three
terms are:
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P –> major term
S –> minor term
M –> middle term
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
CATEGORICAL REASONING
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In a categorical syllogism, each of the
premises states a relationship between the
middle term and one of the others.
M
premise
premise
P
S
conclusion
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
CATEGORICAL REASONING
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Categorical syllogism features:
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Every proposition is in standard categorical form
There are three terms.
The major premise is listed first, the minor is
listed second.
Each term is used in the same sense throughout
the argument.
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
CATEGORICAL REASONING
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Example:
All German cars are reliable (major premise)
All BMW are German cars (minor premise)
All BMW will be reliable (conclusion – derived from
relationship between minor premise and major
premise)
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
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CATEGORICAL REASONING
Explanation:
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Reliable is the major term since it is the predicate of the
conclusion
BMW is the minor term since it is the subject of the
conclusion
German cars is the middle term since it is the term
which occurs in both of the premises but not in the
conclusion
All German cars are reliable (major premise)
All BMW are German cars (minor premise)
All BMW will be reliable (conclusion – derived
from relationship between minor premise and major
premise)
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
CATEGORICAL REASONING
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When is a categorical arguments said to be sound
and valid?
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When the conclusion follows necessarily from the
premises
When the form of the argument guarantees that the
conclusion will follow, the argument is considered valid.
When the premises can be assumed to be telling the truth,
the argument is said to be true.
If an argument is both true and valid, that argument is said
to be sound.
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
Let’s think…
1.
What can you conclude from the following premises:
“All Communication and Thinking Skill classes are full. Marina
found a class that wasn’t full.”
A. Not all Communication and Thinking Skill classes are full.
B. Marina didn’t find all the classes.
C. Marina found a class that wasn’t Communication & Thinking
Skill..
D. All Communication and Thinking Skill classes were not
found.
(cont)
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
Exercises
2. Which of the following major premises forms a valid argument
with the minor premise, “Malaysians invented the first written
language," and the conclusion, “Malaysians created the modern
world.“
A. The inventors of written language created the modern world.
B. The Malaysian created the modern writing.
C. Written language is the foundation of the modern world.
D. The argument is invalid.
(cont)
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
Exercises
3. Consider the following chain argument: "All libraries
are quiet. Only quiet places are restful. The places
where I like to study are restful."
What can you conclude from the minor premise, "My
bedroom is a place where I like to study"?
A. My bedroom is restful, quiet and a library.
B. My bedroom is restful and quiet.
C. Libraries are restful and my bedroom is quiet.
D. Libraries and my bedroom are places I like to
study.
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
Categorical reasoning
Argument that makes a claim about the
relationship between two or more classes or
categories of things. The argument has one
of the following standard forms:
 All S are P
STANDARD FORM
 No S are P
CATEGORICAL
 Some S are P
STATEMENTS
 Some S are not P
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
Examples
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All fruits are apples
No fruits are apples
Some fruits are apples
Some fruits are not apples
You may test the validity of these simple categorical
arguments by the use of Venn diagrams.
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
Our everyday statements lack
explicit categorical reasoning
Koalas are marsupials.
All koalas are marsupials
Men are IT savvy
Some men are IT savvy
Politicians are liars
Some politicians are liars
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
Variant of “All S are P”
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Every S is a P
Whoever is an S is a P
Whatever is an S is a P
If anything is an S, then it is a P
If something is not a P, then it is not an S
Any S is a P
Each S is a P
S are all P
S are always P
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
Variant of “No S are P”
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No P are S
S are not P
Nothing that is an S is a P
Not a single S is P
All S are non-P
If anything is an S, then it is not a P
None of the S are P
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
Variant of “Some S are P”
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Some P are S
A few S are P
There are S that are P
Several S are P
Many S are P
Most S are P
Nearly all S are P
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
Variant of “Some S are not P”
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Not all S are P
S are not always P
Some S are non-P
Most S are not P
Nearly all S are not P
Several S are not P
A few S are not P
There are S that are not P
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
Is this argument valid?
No sharks are pets, since no barracuda are
pets, and no sharks are barracuda.
No one who is a Nobel Prize winner is a rock
star. A number of astrophysicists are Nobel
Prize winner. Therefore a number of
astrophysicists are not rock stars
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
Is this argument valid?
Anyone who eats pizza every night is at risk for
heart disease. Some people who are at risk
for heart disease are cab drivers. So, some
cab drivers are people who eat pizza.
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
General advice:
Always try to restate the speaker’s or writer’s intended
meaning as accurately as possible.
E.g. There are e-mail messages that are not spellchecked. There are inter-office memos that are email messages. Therefore there are interoffice
memos that are not spell-checked.
Some e-mail messages are not spell-checked. Some email messages are inter-office memos. Therefore
some interoffice memos are not spell-checked.
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
Exercise 1: Translate the following into
standard categorical form
1.
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6.
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9.
10.
Maples are trees
Roses are red
Each insect is an animal
All that glitters is not gold
If anything is an igloo, then it is made of ice
Success has ruined many a man
Only the educated are free
The questions that can be answered is not worth
asking
There are birds that cannot fly
Cheaters never prosper
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
Answers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
All maples are trees
Some roses are red
All insects are animals
Some that glitters are gold
All igloo is made of ice
Some men have been ruined by success
All free persons are educated persons
No questions that have answers are questions
that worth asking
Some birds cannot fly
No cheaters are persons who prosper
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
Categorical Syllogisms
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Syllogism – a three-line deductive argument
(A deductive argument that has 2 premises & a
conclusion)
Categorical syllogism – a syllogism in which all
statements in the argument are categorical
reasoning
E.g. No doctors are professional wrestlers
All cardiologists are doctors
So, no cardiologists are professional wrestlers
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
More example
All painters are artists
Some magicians are artists
So, some magicians are painters
Is this argument valid?
Invalid
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
The Venn diagram technique
to check validity
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Translate arguments into standard-form categorical
statements
Draw & label three overlapping circles, one for each
term
Use shading to represent the information in “all” or
“no” statement. Use Xs to represent the information
in “some statements”
Diagram the two premises. Place X appropriately
Look to see if the completed diagram contains all
information in the conclusion. If it does, argument is
valid. If it does not, argument is not valid.
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
So….are these arguments
valid?
No sharks are pets, since no barracuda are
pets, and no sharks are barracuda.
Invalid
No one who is a Nobel Prize winner is a rock
star. A number of astrophysicists are Nobel
Prize winner. Therefore a number of
astrophysicists are not rock stars
Valid
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
Is this argument valid?
Anyone who eats pizza every night is at risk for
heart disease. Some people who are at risk
for heart disease are cab drivers. So, some
cab drivers are people who eat pizza.
Invalid
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning
Discuss with friends:
At least one lawyer is not a golfer. Only persons who
have attended law school are lawyers. So, at least
one person who has attended law school is not a
golfer.
Every person who drinks and drives is an irresponsible
person. Not every person who talks on a car phone
is an irresponsible person. Hence not every person
who talks on a car phone is a person who drinks
and drive.
GXEX1406 Thinking and Communication Skills – Week 9 Categorical Reasoning