This document defines and explains syllogisms, which are deductive arguments with two premises and a conclusion. It covers the key components of syllogisms including terms, figures, moods, and validity rules. The four figures refer to the position of the middle term in the premises, and the mood depends on whether the terms are universal or particular in each proposition. Only certain combinations of moods under each figure result in valid deductive arguments. Examples are provided to illustrate each type of valid syllogism.

1. SYLLOGISM
Terms, Premises, Figures
and Moods

2. SYLLOGISM (…meaning)
• 6.1. Syllogism -- a
deductive argument in
which a conclusion is
inferred from two
premises

3. Categorical S…
• Categorical Syllogism is a
deductive argument
consisting of three
categorical propositions that
together contain exactly
three terms, each of which
occurs in exactly two of the
constituent propositions

4. Conclusion…
• Conclusion of a standard-form
syllogism is a standard-form
categorical proposition that
contains two of the syllogism’s
three terms. The conclusion is
always used to identify the
terms of the syllogism

5. The Three Terms…
• 6.2. The Three Terms: (1) Major
Term -- predicate of the
conclusion; symbolized by P; (2)
Minor Term -- the subject term of
the conclusion; symbolized by S;
(3) Middle Term -- third term of
the syllogism, which does not
occur in the conclusion,
appearing instead in both
premises; symbolized by M

6. Premises…
• 6.3. Premises: Major premise contains
the major term while Minor premise
contains the minor term
• 6.4. The Law of All and the Law of None:
• 6.4.1. The Law of All states: “What is
affirmed of a logical whole may be
affirmed of a logical part of that whole.”
• Example: Insects are worth-watching;
Butterflies are insects; Therefore,
butterflies are worth watching.

7. Law of None
• 6.4.2. The Law of None states:
“What is denied of a logical
whole may be denied of a
logical part of that whole.”
• Example: All Africans are not
Caucasians; St. Augustine is
an African; Therefore, St.
Augustine is not Caucasian

8. General Rules…
• 6.5. General rules for valid syllogisms
• 6.5.1. Only three terms may appear in the syllogism, each of
which is used in the same sense throughout the argument.
• 6.5.2. Neither the major nor minor term may be a universal in
the conclusion, if it was only a particular term in the premises.
If the minor term or major term in the premises is not the
same in quantity in the conclusion, the fallacies committed are
either fallacy of illicit minor or the fallacy of illicit major.
• Example of a Syllogism with Illicit Major:
• Every teacher is professional
• Mr. John Foster is not a teacher
• Therefore, Mr. John Foster is not professional.
• Example of a Syllogism with Illicit Minor:
• All Varsity players are scholars
• All Varsity players are not medical students
• Therefore, all medical students are scholars.

9. Cont’n…
• 6.5.3.The middle term may not appear in the
conclusion.
• 6.5.4. The middle term must be distributed at least
once in the premises, that is, used as a universal.
Violation of this rule is called Fallacy of the
Undistributed Middle Term.
• 6.5.5. If both premises are affirmative, the
conclusion must also be affirmative.
• 6.5.6. Both premises may not be negative; one at
least must be affirmative. Failure to abide by this
rule is called Fallacy of Two Negative premises.
• Example:
• All villages are not safe;
• All commercial districts are not villages;
• Therefore, all commercial districts are not safe.

10. Cont’n…
• 6.5.7. If either premise is negative,
the conclusion must be negative
otherwise you draw an affirmative
conclusion which is invalid. Fallacy of
Drawing an Affirmative Conclusion
from a Negative Premise is
committed when the above rule is
violated.
• Example:
• Traditions are not modern;
Observance of Lent is a tradition;
Therefore, observance of Lent is
modern.

11. Cont’n…
• 6.5.8. No conclusion can be drawn
from two particular premises; one at
least must be a universal
proposition.
• Example: Some beaches are clean
and fresh;
• Some beaches are located far away;
• Therefore, some located far away
places are clean and fresh.
• Existential Fallacy is committed when
the rule is not observed.

12. Figures and Moods…
• Figures and Moods of
Categorical Syllogism. The
figure of a syllogism indicates
the position of the middle term
in the premises.
• The mood of a standard-form
syllogism is determined by the
types (identified by letter: A, E,
I or O) of the standard-form
categorical propositions

13. Cont’n…
• The following are the valid figures and their
corresponding moods of syllogisms:
• Figure 1 Figure 2 Figure 3 Figure 4
• M P P M M P P M
• S M S M M S M S
• S P S P S P S P

14. Cont’n…
• Figure 1: AAA, EAE, AII, EIO
• Examples:
•
• Figure 1 – AAA: All drivers are licensed; All
messengers are drivers;Therefore, all messengers are
licensed
• Figure 1 – EAE: No animals are worthless; All cats are
animals; Therefore, No cats are worthless.
• Figure 1 – AII: All Christians are baptized; Some
Chinese are Christians; Therefore, some Chinese are
baptized.
• Figure 1 – EIO: All employees are not discriminated;
Some accountants are employees; Therefore, some
accountants are not discriminated.

15. Cont’n…
• Figure 2: EAE, AEE, EIO, AOO
• Figure 2 – EAE: No squatters are rich; All
executives are rich;Therefore, all executives
are not squatters.
• Figure 2 – AEE: All terrorists are bad people;
No seminarians are bad people; Therefore, no
seminarians are terrorists.
• Figure 2 – EIO: No children are burdensome;
Some lawless elements are burdensome;
Therefore, some lawless elements are not
children.
• Figure 2 – AOO: Every school administrator is
a responsible person; Some workers are not
responsible persons; Therefore, some workers
are not school administrators.

16. Cont’n…
• Figure 3: IAI, AII, EIO Examples:
• Figure 3 – IAI: Some nursing students
are scholars; All nursing students are
law-abiding citizens; Therefore, some
law-abiding citizens are scholars.
• Figure 3 – AII: All passengers are safe;
Some passengers are children;
Therefore, some children are safe.
• Figure 3 – EIO: No activists are
violent; Some activists are students;
Therefore, some students are not
violent
2nd TO THE LAST SLIDE

17. Cont’n…
• Figure 4: AEE, IAI, EIO
Examples:
• Figure 4 – AEE: All boxers are brave individuals; All
brave individuals are homosexuals; Therefore, all
homosexuals are not boxers.
• Figure 4 – IAI
• Some chefs are internationally known people
• All internationally known people are respected
ones
• Therefore, some respected ones are chefs.
• Figure 4 – EIO
• All utensils are not imported items
• Some imported items are costly goods
• Therefore, some costly goods are not utensils.
•
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