5. THE FOUR KINDS OF CATEGORICAL PROPOSITIONS.

Categorical propositions are divided according to their quantity into Universal and Particular and according to their quality into Affirmative and Negative.

A universal proposition is one in which the predicate refers to the whole of the logical subject.

ILLUSTRATIONS:

(1) All men are mortal.

(2) All civilized men cook their food.

(3) No dogs are immortal.

(4) Every man was once a boy.

Considering the first proposition, “mortal,” the logical predicate, refers to the whole of the logical subject “men.” Similarly “cook their food” refers to the whole of the term “civilized men”; “immortal” to the whole of the term “dogs,” and “once a boy” to the whole of the term “man.”

In considering the definition of a universal proposition it is necessary to keep in mind the distinction between a logical and a grammatical subject, as in the second proposition the logical predicate, “cook their food,” refers to only a part of the grammatical subject, men, and, therefore, the proposition might fallaciously be termed a particular proposition rather than a universal.

A particular proposition is one in which the predicate refers to only a part of the logical subject.

ILLUSTRATIONS:

(1) Some men are wise.

(2) Some animals are not quadrupeds.

(3) Most elements are metals.

(4) Many children are mischievous.

In the foregoing propositions some, most and many are quantity signs and, therefore, must not be considered as a part of the logical subjects. Considering the logical subjects and predicates in order, the term wise refers to only a part of the men in the world, quadrupeds to only a part of the animals, metals to only a part of the elements and mischievous to only a part of the children.

An affirmative proposition is one which expresses an agreement between subject and predicate.

A negative proposition is one which expresses a disagreement between subject and predicate.

Affirmative propositions conjoin terms, negative propositions disjoin terms. In the first the agreement is affirmed; in the second the agreement is denied.

ILLUSTRATIONS:

None of the captives escaped. Negative.

Some teachers are just. Affirmative.

All trees grow towards heaven. Affirmative.

Some people are not companionable. Negative.

No person is above criticism. Negative.

Dividing both universal and particular propositions as to quality, gives four kinds; namely, universal affirmative, universal negative, particular affirmative and particular negative. No topic in logic demands greater familiarity thanthese four types, as every proposition must be reduced to one of the four before it can be used as a basis of reasoning.

For the sake of brevity the symbols A, E, I and O are used to designate respectively the universal affirmative, the universal negative, the particular affirmative and the particular negative. A and I, symbolizing the affirmative propositions, are the first and second vowels in Affirmo, while E and O, symbolizing the negatives, are the vowels in Nego. The common sign of the universal affirmative, or the A proposition is all; of the universal negative, or E proposition no; of the particular affirmative, or I proposition some; of the particular negative, or O proposition some with not as a part of the copula. The accompanying classification summarizes these facts, S and P being used to symbolize the terms “subject” and “predicate.”

Illustrations
Categorical PropositionsUniversalAffirmative-AAll S is P
Negative-ENo S is P
ParticularAffirmative-ISome S is P
Negative-OSome S is not P

Henceforth the symbols A, E, I, O will be used to designate the four kinds of categorical propositions. The propositions have other quantity signs aside from the ones used above. These may be summarized:

Quantity signs ofA—all, every, each, any, whole.
E—no, none, all-not.
I—some, certain, most, a few, many, the greatest part, any number.
O—some - - not, few.