Four Kinds of Categorical Proposition
Taking into account both the quality and quantity of the proposition at the
same time results to four kinds of categorical proposition. These are the (1)
universal/singular affirmative; (2) universal/singular negative; (3)
particular affirmative; and (4) particular negative. Since the early Middle
Ages these four kinds of categorical proposition have commonly been
designated by letter symbols corresponding to the first four vowels of the
Roman alphabet: A, E, I, O. Symbol A stands for the universal/singular
affirmative proposition, E for the universal/singular negative proposition, I for
the particular affirmative proposition, and O for the particular negative
proposition. The four letters were said to have been derived from the first two
vowels in the Latin word affirmo (“I affirm”) and nego (“I deny), thus:
Universal
Particular
n
E
A
f
f
I
r
m
o
g
O
Using the letter symbols, four types of the categorical proposition can be
diagrammed as follows:
QUANTITY
Universal/Singular
QUALITY
Affirmative
Negative
A
E
Particular
I
O
The following are examples of categorical proposition with certain quality
and quantity represented by symbols A, E, I, O.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Proposition
All men are mortal beings.
Some men are God-fearing.
Jesus Christ is the son of God.
Cows are not horses.
Some houses are not strong.
That dog is not mine.
Every person is rational.
Some horses are black.
No X are Y.
Some roses are not white.
Symbol
A
I
A
E
O
E
A
I
E
O
Quantity
Universal
Particular
Singular
Universal
Particular
Singular
Universal
Particular
Universal
Particular
Quality
Affirmative
Affirmative
Affirmative
Negative
Negative
Negative
Affirmative
Affirmative
Negative
Negative
Note:
A: All X are Y./ All men are rational beings.
E: No X are Y.
I: Some X are Y.
O: Some X are not Y.