This document discusses the structure and rules of categorical syllogisms. It explains that a categorical syllogism has three terms - the major term, minor term, and middle term. The major term is the predicate of the conclusion, the minor term is the subject of the conclusion, and the middle term occurs in both premises but not the conclusion. It then lists 10 rules that categorical syllogisms must follow regarding the terms, propositions, quantity, and existential import. Examples are provided to illustrate valid and invalid syllogisms.

1. Kate S. Magpoc
BSTM- 3A
THE SIMPLE CATEGORICAL SYLLOGISM
THE BASIC STRUCTURE
A Simple Categorical Syllogism is composed of three (3) categorical or attributive propositions so put
together that the subject (t) and predicate (T) of the conclusion are united or separated through the
intermediacy of a middle term (M) Every animal is mortal; but every dog is an animal; therefore every
dog is mortal.
THE SIMPLE CATEGORICAL SYLLOGISM
The first proposition is the major premise; the second proposition is the minor premise; and the third is
the conclusion. “Mortal” the predicate of the conclusion, is the major term; “dog,” the subject of the
conclusion, is the minor term; and “animal,” which occurs in both premises but not in the conclusion, is
the middle term.
A. Major Term The major term is the predicate of the conclusion. It must occur in the conclusion and in
the premise, generally the first, which is therefore called the major premise . The major term shall be
symbolized by T , or, to display the structure of a syllogism more graphically, by a rectangle .
B. Minor Term The minor term is the subject of the conclusion. It must occur in the conclusion and in the
premise in which the term does not occur. It is often introduced by the adversative conjunction “but”
(because in controversy it introduces a turn of thought to the expectations of an opponent). Minor term
shall be designated by t , or, to display the structure of a syllogism more graphically, by an ellipse .
C. Middle Term The middle term occurs in each of the premises but not in the conclusion. In the major
premise, it occurs in conjunction with the major term; and in minor premise, in conjunction with the
minor term. It is the medium through which the major and minor term are united in the affirmative
syllogism and separated in the negative syllogism. As opposed to the middle term , the minor and major
terms are called extremes.
Example of a graphically marked simple categorical syllogism: Every animal is mortal; But every dog is
an animal; Therefore every dog is mortal.
GENERAL RULES OF THE CATEGORICAL SYLLOGISM
THE RULES OF THE TERMS
1. Their Number and Arrangement
Their Number…
2. Their Quantity, or Extension 3. The Quantity of the Minor and Major Terms: …
Their Arrangement…
4. The Quantity of the Middle Term: …
GENERAL RULES OF THE CATEGORICAL SYLLOGISM
The Rules of the Terms
1. THEIR NUMBER AND ARRANGEMENT
Rule 1. There must be three terms and only three- the major term, the minor term and the middle
term. The necessity of having only three terms follows from the very nature of a categorical

2. syllogism, in which a minor (t) and a major (T) term are united or separated through the intermediacy
of a third term, the middle term (M).
The terms must have exactly the same meaning and (except for certain legitimate changes in supposition)
must be used in exactly the same way in each occurrence. A term that has a different meaning in each
occurrence is equivalently two terms. We must be especially on our guard against ambiguous middle
terms. Example: Every animal is mortal; but every dog is an animal; therefore every dog is mortal.
Violation: Men must eat; but the picture on the wall is a man; therefore the picture on the wall must eat.
Rule 2. Each term must occur in two propositions. The major term must occur in the conclusion, as
predicate, and in one of the premises, which is therefore called the major premise. The minor term must
occur in the conclusion, as subject, and in the other premise, which is therefore called the minor premise.
The middle term must occur in both premises but not in the conclusion. Hence, there must be three
propositions. The necessity of having three terms arranged in this way in three propositions also follows
from the very nature of a categorical syllogism. Two propositions (the premises) are required for the
middle term to fulfill its function of uniting or separating the minor and major terms and a third
proposition (the conclusion) is required to express the union or separation of the minor and major terms.
1. THE QUANTITY, OR EXTENTION, OF THE TERMS The reason for this rule is that we may not
conclude about all the inferiors of a term if the premises have given us information about only some of
them. The conclusion is an effect of the premises and must therefore be contained in them implicitly; but
all are not necessarily contained in some —at least not by virtue of the form of argumentation alone.
Violation: All dogs are mammals; but no men are dogs; therefore no men are mammals. Rule 3. The
major and minor terms may not be universal (or distributed) in the conclusion unless they are universal
(or distributed) in the premises.
Violation of this rule is called either extending a term or an illicit process of a term. There is an illicit
process of the major term if the major term is particular in the premise but universal in the conclusion;
and an illicit process of the minor term, if the minor term is particular in the premise but universal in the
conclusion. Take note that there is no illicit process if the major or minor term is universal in the premises
and particular in the conclusion. To go from a particular to a universal is forbidden, but to go from a
universal to a particular is not permissible.
Rule 4. The middle term must be universal, or distributed, at least once. The reason for this rule is that
when the middle term is particular in both premises it might stand for a different portion of its extension
in each occurrence and thus be equivalent to two terms, and therefore fail to fulfill its function of uniting
or separating the minor and major terms. Violation: A dog is an animal; but a cat is an animal; therefore
a cat is a dog. Violation of this rule is often called the fallacy of the undistributed middle.
GENERAL RULES OF THE CATEGORICAL SYLLOGISM
The Rules of the Propositions
1. THE QUALITY OF THE PROPOSITIONS Rule 5. If both premises are affirmative, the conclusion
must be affirmative. The reason for this rule is that affirmative premises either unite the minor and major
terms, or else do not bring them into relationship with one another at all—as when there is an
undistributed middle. In neither case may the major term be denied of the minor term. Hence, to get a
negative conclusion you must have one—and only one—negative premise. Violation: All sin is
detestable; but some pretense is sin; therefore some pretense is not detestable.
As soon as you see that both premises are affirmative but the conclusion negative, you can be sure that
your syllogism is invalid. Be on your guard, however, against apparent affirmative or negative

3. propositions. Example: Animals differ from angels; but man is an animal; therefore man is not an angel.
The syllogism is valid because ‘differ from’ is equivalent to ‘are not’.
Rule 6. If one premise is affirmative and the other negative, the conclusion must be negative. The reason
for this rule is that the affirmative premise unites the middle term with one of the extremes (that is, with
either the minor or the major term) and the negative premise separates the middle term from the other
extreme. Two things, of which the one is identical with a third thing and the other is different from that
same third thing, cannot be identical with one another. Hence, if a syllogism with a negative premise
concludes at all, it must conclude negatively. Violation: Every B is a C; but some A is not a B; therefore
some A is a C.
However, there are apparent exceptions to this rule. Keep in mind that many negative propositions are
equivalent to affirmative propositions and can be changed into them by one or other kinds of immediate
inference. Example: Dogs are not centipedes; but hounds are dogs; therefore hounds differ from
centipedes. This is a valid syllogism since the conclusion is equivalently negative, since “differ from” is
equivalent to “are not”.
Rule 7. If both premises are negative—and not equivalently affirmative—there is no conclusion at all. To
fulfill its function of uniting or separating the minor and the major term, the middle term must itself be
united with at least one of them. But if both premises are negative, the middle term is denied of each of
the extremes and we learn nothing about the relationship of the extremes towards one another. Violation:
A stone is not an animal; but a dog is not a stone; therefore a dog is not an animal.
2. THE QUANTITY OF THE PROPOSITIONS Example: Every animal is mortal; but every dog is
an animal; therefore every dog is mortal. Rule 8. At least one premise must be universal. Rule 9.
If a premise is particular, the conclusion must be particular.
3. THE EXISTENTIAL IMPORT OF THE PROPOSITIONS The reason for this rule is the general
principle that nothing may ever be asserted in the conclusion that has not been asserted implicitly in the
premises. This rule takes us out of the domain of formal logic, which does not consider existence except
incidentally. We mention it only as a practical aid to argumentation. Rule 10. The actual real existence of
a subject may not be asserted in the conclusion unless it has been asserted in the premises.
4. Contradictories are opposites; but black and white are opposites; therefore black and white are
contrdictories. 5. All mammals have lungs; but most fish do not have lungs; therefore most fish are not
mammals. 6. No dog is a man; but Fido is not a man; therefore Fido is a dog. 7. All mammals are
viviparous; but whales are viviparous; therefore whales are mammals.
8. Those who are not sick may go; but Johnny is not sick; therefore Johnny may go. 9. No dog is not an
animal; but no hound is not a dog; therefore all hounds are animals. 10. Democracies are free; but some of
the governments of the Middle Ages were not democracies; therefore some of the governments of the
Middles Ages were not free.