A categorical statement in categorical logic is a statement or proposition that asserts or denies something without qualification. It is a statement or proposition that is not hypothetical. Aristotle divided the categorical statement into two, namely, the subject class and the predicate class.
There are four interpretations in which these two classes can be related to one another. Only four types of propositions must be translated into one of these types, namely:
- Every member of one class is also a member of the other class;
- No member of one class is a member of another class;
- Some members of one class are also members of another class; and
- Some members of one class are not members of another class.
A standard way of writing these four types of propositions to illustrate their relationship is as follows:
- All men are mortal.
- No men are mortal.
- Some men are mortal.
- Some men are not mortal.
The four categorical statements or propositions above suggest the inclusion or exclusion of one class (subject class) in the other class (predicate class). If it affirms the inclusion of the subject class in the predicate class, it is called an affirmative statement. If it denies the inclusion of the subject class in the predicate class, it is called a negative statement. Furthermore, it the suggestion is total inclusion, it is a universal affirmative statement; if total exclusion, then it is a universal negative statement. If it means only partial inclusion, then it is called a particular affirmative statement; if partial exclusion, it is called a particular negative statement.
Thus, going back to the examples above, we can say that the first categorical statement is universal affirmative because it suggests the total inclusion of the subject class “men” in the predicate class “mortal”. The second example is universal negative because it suggests a total exclusion of the subject class “men” in the predicate class “mortal”. The third example is particular affirmative because it suggests partial inclusion of the subject class “men” in the predicate class “mortal”. And the last example is particular negative because it suggests a partial exclusion of the subject class “men” in the predicate class “mortal”.
Where letter S and P are used to represent the subject and the predicate terms respectively, the examples above can be schematically represented as follow:
It is customary to use the letters A and I to represent the universal and particular statements respectively, taken from the first two vowels of the Latin word Affirmo, which means “I affirm”. The letters E and O are used to represent the universal and particular negative statements respectively, presumed to come from the Latin word Nego, which means “I deny”.