The document outlines the eight rules of syllogism. It explains that there are three terms in a syllogism, with two premises relating the minor and major terms through a common middle term. The rules prohibit having more than three terms, the conclusion extending a term beyond its use in the premises, the middle term appearing in the conclusion, the middle term being particular in both premises, inconsistent conclusions based on the premises' qualities, and conclusions from two particular premises. Examples demonstrate violations of each rule.

1. RULES OF SYLLOGISM

2. THE EIGHT RULES
These eight rules are grouped into Rules on Terms (1-4) and Rules on Proposition (5-8).
RULE ONE: There must be three and only three terms.
◦ * A syllogism establishes the identity or non-identity of the minor and the major term on the
basis of their respective relation to a common third term or middle term. A syllogism with
four terms does not establish a sequence.
◦ EXAMPLE:
Every man is rational,
but Peter is a man,
Therefore, Peter is rational.

3. • A syllogism having four terms is called a “logical quadruped” (four feet).
1. Arithmetical Addition is adding a fourth term
Example:
Every Dog is an animal,
But every cactus is a plant,
Therefore, (no possible conclusion because the premises are not related to each other)
2. Equivocation is giving a term two or more meanings resulting in having a fourth term which
destroys the sequence
Example:
A pitcher is a water container,
But Mr. Sanders is a pitcher.
Therefore, Mr. Sanders is a water container.
3. Changing supposition consists changing the point of view or usage of a term
Example:
A mother is a woman giving birth, (real supposition)
but a nun is a mother, (metaphorical)
therefore, a nun is a woman giving birth.

4. RULE TWO: No term must have greater extension in the conclusion than
it has in the premises.
This applies to the minor and major terms. Any of them may not be a universal term in the
conclusion if it is a particular term in the premise.
*illicit minor – when the over-extended term is the minor term
*illicit major – when the over-extended term is the major term
a.) ILLICIT MINOR
Example:
Every girl is a female,
But every girl is a young person, (particular)
Therefore, every young person is a female. (universal)

5. b.) ILLICIT MAJOR
Example:
Some candies are chocolate, (particular)
But no fruit is a chocolate,
Therefore, no fruit is a candy. (universal)
RULE THREE: The middle term must not appear in the conclusion.
The middle term serves as the common third term which relates the minor and the
major terms. Therefore, it has no place in the conclusion. It is easy to see if the middle
term is in the conclusion because it comes out three times in the syllogism.
Example:
Every student is a learner,
But every learner is an achiever,
Therefore, every learner is a student. (misplaced middle)

6. RULE FOUR: The middle term must be universal at least once.
Because a particular term signifies an indeterminate portion of a whole, what it says
does not necessarily apply to the whole totality. An error of this rule is called
“undistributed middle”
Example:
Every man is human being, (particular)
But every scientist is a human being, (particular)
Therefore, every scientist is a man.
The middle term “human being” is a particular term since it is a predicate of both
affirmative propositions.

7. RULE FIVE: Two affirmative premises yield an affirmative conclusion.
The conclusion will always be an affirmative when the premises are affirmative.
Violation of this rule is called “negative affirmation” since it denies what should be
affirmed in the conclusion.
Example:
Some women are writers,
But all writers are educated,
Therefore, some educated are women.

8. RULE SIX: Two negative premises will produce no conclusion.
When both premises are negatives, nothing is stated so that nothing could be
concluded. Call this error – ‘double negation”
Example:
No stone is an organism,
But no stone is edible,
Therefore, ( no conclusion possible).

9. RULE SEVEN: If one premise is negative, the conclusion must be
negative; if one premise is particular, the conclusion must be
particular.
Since the conclusion comes from the premises, it cannot declare more than what is
implied in the premises. Error of this rule is “affirmed negation”
Example;
No tree is able to walk, (negative)
But an acacia is a tree,
Therefore, an acacia is able to walk. (affirmative)

10. RULE EIGHT: When both premises are particular, there is
no conclusion.
Two particular premises will not establish a sequence. It leads to the error of “undistributed
middle” or ‘‘illicit major”
Example:
Some trees are tall,
But some men are tall, (undistributed middle)
Therefore, some men are trees.
Some trees are tall,
But some tall (things) are not buildings,
Therefore, some buildings are not trees. (illicit major)