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CATEGORICAL
SYLLOGISM
TOPIC OUTLINE:
I. Definition of terms
II. Categorical Syllogism in Standard Form
III. Structure of a Categorical Syllogism
IV. Moods and Figures of C.S.
V. Rules of a Categorical Syllogism
VI. Fallacies of Categorical Syllogism
SYLLOGISM
a deductive argument composed of exactly two premises and
one conclusion
CATEGORICAL TERM
- designates a class of things
- basic unit of meaning or content in the deductive system
- usually expressed grammatically as a noun or noun phrase
CATEGORICAL PROPOSITION
a statement about the relationship between categories. It states
whether one category or categorical term is fully contained with
another, is partially contained within another, or is completely separate.
Contains the following elements:
a. Quantity - may refer to all, some, or no members of a category
Universal prepositions: refers to "all", "none"
Particular prepositions: refers to "some"
b. Quality - affirmative ( represented by A and I; Affirmo) or negative
(represented by E and O; nEgO)
c. noun or noun phrase - the class or category is expressed by a noun
or noun phrase
Noun: genera, species, time, fruits, date, etc.
Noun phrase: involves modifier and noun (ex. a vicious lion, a
friendly dog)
d. Copula - conjugation of the verb "to be" ( "is" or "are" )
- can be negated or not
Example: Some politicians are not corrupt
Some politicians are corrupt
A categorical proposition affirms or denies that at least one,
or all members of the subject category are members of the
predicate category.
CATEGORICAL SYLLOGISM
a kind of mediate deductive argument which is composed of
three categorical propositions (2 premises + a conclusion)
with exactly three categorical terms, each of which appears in
exactly two of the three propositions
Examples of Categorical Syllogism:
All toads are reptiles
No cows are toads
No cows are reptiles
All parrots are birds
All birds are animals
All parrots are animals
STRUCTURE OF A CATEGORICAL SYLLOGISM:
1.MAJOR PREMISE
2.MINOR PREMISE
3.CONCLUSION
The premise that
contains the major term
The premise that
contains the minor term
The agreement or
disagreement b/w P and S
is expressed or
enunciated.
Major Premise
Conclusion
All mammals are animals
All cats are mammals
All cats are animals
Minor Premise
STRUCTURE OF A CATEGORICAL SYLLOGISM:
4.MAJOR TERM
(P)
5. MINOR TERM
(S)
6. MIDDLE TERM
(M)
The predicate term of
the conclusion
The subject term of
the conclusion
The term repeated in
the premises but not in
the conclusion
All mammals are animals
All cats are mammals
All cats are animals
minor term
(S)
major term (P)
middle term (M)
CATEGORICAL SYLLOGISM IN
STANDARD FORM
MAJOR PREMISES
+
MINOR PREMISES
+
CONCLUSION
Examples:
All fish can swim.
A guppy is a fish.
Therefore, a guppy
can swim.
No geese are felines.
Some birds are geese.
Therefore, some birds
are not felines.
Activity 1:
Identify the terms and premises in the syllogism.
All fish can swim.
A guppy is a fish.
A guppy can swim.
All fish can swim.
Major Premise
A guppy is a fish.
Minor Premise
A guppy can swim.
Major term: swim
Minor term: guppy
Middle term: fish
Activity 2:
WHICH CATEGORICAL SYLLOGISM IS IN STANDARD FORM?
All birds are animals
All parrots are birds
All parrots are animals
No cows are toads
All toads are reptiles
No cows are reptiles
All birds are animals
All parrots are birds
All parrots are animals
No cows are toads
All toads are reptiles
No cows are reptiles
The argument is in standard form
categorical syllogism.
The argument is NOT in a
standard-form categorical
syllogism.
- the premises are not in the
right order
MOODS AND
FIGURES OF
SYLLOGISM
To know if the syllogisms are valid or invalid, we must determine
the following:
MOOD
a series of three letters corresponding to the type of proposition the
premises (major and minor), and the conclusion are (A,E,I or O)
FIGURE
a number that corresponds to the placement of the two middle terms
MOODS
In logic, it is the
classification of categorical
syllogisms according to the
quantity (universal or
particular) and quality
(affirmative or negative) of
their constituent
propositions.
Forms of Propositions
A (Universal Affirmative)
All S are P
E (Universal Negative)
No S are P
I (Particular Affirmative)
Some S are P
O (Particular Negative)
Some S are not P
EXAMPLE:
All soldiers are patriots. (A)
No traitors are patriots. (E)
Therefore no traitors are soldiers (E).
The syllogical form based on the mood is AEE.
Activity 3:
Identify the mood of this syllogism.
All ducks are birds.
All griffins are ducks.
Some griffins are
birds.
All ducks are birds
-A
All griffins are ducks - A
Some griffins are birds - I
The syllogical form based on the mood is AAI.
FIGURES
In logic, it is the classification of categorical syllogisms
according to the arrangement of the middle term,
namely, the term (subject or predicate of a
proposition) that occurs in both premises but not in
the conclusion.
FORMS OF FIGURES:
FORMS OF FIGURES:
EXAMPLE:
All soldiers are patriots.
No traitors are patriots.
Therefore no traitors are soldiers
The syllogical form shown is 2nd figure.
(AEE-2)
Activity 4:
Identify the figure of this syllogism.
All cats are felines
No dogs are cats
No dogs are felines
All cats are felines
No dogs are cats
No dogs are felines
-A
-E
-E
The syllogical form shown is 1st figure
(AEE-1)
RULES OF
CATEGORICAL
SYLLOGISM
RULE 1
A valid categorical syllogism only has three terms:
major, minor and middle term.
RULE 2
Each term must occur in two prepositions of the
argument.
RULE 3
A major or minor term may not be universal in the
conclusion, unless they are universal in the
premises.
P1: All politicians are sociable
people
P2: All councilors are politicians
C: All councilors are sociable
people
Major term: sociable people
Minor term: councilors
Middle term: politicians
RULE 4
The middle term must be distributed in at least one
premise.
RULE 5
If both the premises are affirmative, then the
conclusion must also be affirmative.
RULE 6
If one premise is affirmative and the other is
negative, the conclusion must be negative.
Example:
All politicians are sociable people
All councilors are politicians
All councilors are sociable people
Example:
All risk-takers are gamblers. (A)
Some Filipinos are gamblers. (I)
Some Filipinos are risk-takers. (I)
Example:
No computer is useless. (E)
All ATM are computers. (A)
No ATM is useless. (E)
RULE 7
A categorical syllogism cannot have two negative
premises.
RULE 8
At least one premise must be universal.
Example:
No country is leaderless. (E)
No ocean is a country. (E)
No ocean is leaderless. (E)
Example:
Some kids are athletic. (I)
Some Filipinos are kids. (I)
Some Filipinos are athletic.(I)
RULE 9
If a premise is particular, the conclusion must also
be particular.
RULE 10
The actual existence of a subject may not be
asserted in the conclusion, unless it has been
asserted in the premises.
Example:
All eagles are winged-beings. (A)
Some creatures are eagles. (I)
Some creatures are winged-beings. (I)
Example:
This wood floats
That wood floats
All wood floats
FALLACIES IN STANDARD
-FORM CATEGORICAL
SYLLOGISM
SYLLOGISTIC FALLACY
A "fallacy" is the name for a mistake in logic. Syllogistic
fallacies happen when logical fallacies occur in the syllogisms
of deductive reasoning. This occurs with a reference to
something general, and then makes a conclusion about
something more specific.
Examples of Categorical Syllogism:
All sharks are fish
All salmon are fish
Therefore all salmon are sharks.
The two generalities in the first two
statements are true, but they do not
validate the conclusion being drawn.
6 FALLACIES OF CATEGORICAL
SYLLOGISM
Fallacy of Four Terms
Fallacy of Undistributed
Middle Term
Fallacy of Illicit
Major and Minor
Fallacy of Exclusive
Premises
Fallacy of Drawing an
Affirmative Conclusion
from a Negative Premise
Existential Fallacy
Fallacy of Four Terms
The fallacy of four terms is the formal fallacy
that occurs when a syllogism has four (or
more) terms rather than the requisite three.
This form of argument is thus invalid.
Fallacy of Undistributed
Middle Term
The fallacy of the undistributed middle is a
formal fallacy that is committed when the middle
term in a categorical syllogism is not distributed
in either the minor premise or the major
premise. It is thus a syllogistic fallacy.
Distribution:
If a categorical proposition asserts
something definite about every member
of a class, then the term designating
that class is said to be distributed.
Categorical Propositions
A - All S are P
E - No S are P
Categorical Propositions:
A: S is distributed to P
E: Both terms are distributed
I: Both terms are not distributed
O: P is distributed to S
I - Some S are P
O - Some S are not P
EXAMPLES
ALL S ARE M
ALL M ARE P
ALL S ARE P
SOME S ARE M
SOME M ARE P
SOME S ARE P
Fallacy of Illicit Major and
Minor
Illicit major is a formal fallacy committed in a categorical
syllogism that is invalid because its major term is
undistributed in the major premise but distributed in the
conclusion.
Illicit minor is a formal fallacy committed in a categorical
syllogism that is invalid because its minor term is
undistributed in the minor premise but distributed in the
conclusion.
EXAMPLES
Illicit Major
Illicit Minor
ALL HOTDOGS ARE FAST FOOD.
ALL CATHOLICS ARE CHRISTIAN.
NO HAMBURGERS ARE HOTDOGS.
ALL CHRISTIANS ARE JESUS LOVERS.
THEREFORE, NO HAMBURGERS ARE
FAST FOOD.
THEREFORE, ALL JESUS LOVERS ARE
CATHOLIC.
Fallacy of Exclusive
Premises
The fallacy of exclusive premises is a syllogistic fallacy
committed in a categorical syllogism that is invalid because
both of its premises are negative
EXAMPLES
No kangaroos are MMA fighters.
Some MMA fighters are not
Mormons.
Therefore, some Mormons are
not kangaroos.
No animals are insects.
No insects are dogs.
Therefore, no dogs are animals.
No animals are insects.
Some insects are not dogs.
Therefore, some dogs are
not animals.
Fallacy of Drawing an
Affirmative Conclusion from a
Negative Premise
Affirmative conclusion from a negative premise is a formal
fallacy that is committed when a categorical syllogism has
a positive conclusion and one or two negative premises.
EXAMPLES
No people under the age of 66
are senior citizens.
No senior citizens are children.
Therefore, all people under the
age of 66 are children.
No donkeys are fish.
Some asses are donkeys.
Therefore, some asses are fish.
Existential Fallacy
A formal logical fallacy, which is committed when a
categorical syllogism employs two universal premises (“all”)
to arrive at a particular (“some”) conclusion.
EXAMPLES
All babysitters have pimples.
All babysitter club members are
babysitters.
Therefore, some babysitter club
members have pimples.
All forest creatures live in the
woods.
All leprechauns are forest
creatures.
Therefore, some leprechauns live
in the woods.
ACTIVITY:
Determine if the following categorical syllogisms are valid or not.
Some parrots are not
pests.
All parrots are pets.
Therefore, no pets are
pests.
AAA - 2
Some parrots are not pests.
All parrots are pets.
Therefore, no pets are pests.
ANSWER: INVALID
All S are M
All P are M
All S are P
ANSWER: INVALID
THANK YOU FOR LISTENING!
Prepared by:
Keth Arvin B. Burac
Sophia Loren V. Dagñalan
Precious M. Mella