A categorical proposition is a proposition which relates two classes to each other (through a direct assertion of agreement or disagreement between them), both of which are delineated with a categorical term. There are only four forms of a categorical proposition:
All S are P.
No S are P.
Some S are P.
Some S are not P.
The first, All S are P, is a universal affirmative. The second, No S are P, is a universal negative. The third, Some S are P, is a particular affirmative. The fourth, Some S are not P, is a particular negative.
The classes are represented by the letters, S and P. The categorical terms are the quantifiers: All, No, Some.
Categorical propositions are usually divided up into four groups: A, E, I and O:
A: All S are P (One category is a subset of another)
E: No S are P (The two categories do not intersect)
I: Some S is/are P (The two categories intersect)
O: Some S is/are not P (One category is not a subset of another)
A key issue is the nature of distribution. A category is said to be distributed if the proposition refers to every member of the category. The first term is distributed in A propositions; the second is distributed in O propositions; both are distributed in E propositions; and none are distributed in I propositions.
One distinguishing feature of categorical propositions is quantity:
- Universal propositions (A, E) refer to all members of the class designated by its subject term.
- Particular propositions (I, O) refer just to some members of the class designated by its subject term.
Another distinguishing feature of categorical propositions is quality:
- Affirmative propositions (A, I) express a relationship of inclusion between members of the classes designated by its terms.
- Negative propositions (E, O) express a relationship of exclusion between members of the classes designated by its terms.
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