A categorical proposition is a proposition that affirms or denies a predicate of a subject. In mathematics, a predicate is a relation. ...

Examples:

Midshipman Davis serves on the H.M.S. Invincible. (subject: Midshipman Davis; predicate: serves on the H.M.S. Invincible)

Some politicians are corrupt. (subject: politicians; predicate: corruptness)

Nobody ever got fired for buying IBM. (subject: people; predicate: getting fired for buying IBM)

The subject and predicate are called the terms of the proposition. The subject is what the proposition is about. The predicate is what the proposition affirms or denies about the subject. A categorical proposition thus claims something about things or ways of being: it affirms or denies something about something else. International Business Machines Corporation (IBM, or colloquially, Big Blue) (NYSE: IBM) (incorporated June 15, 1911, in operation since 1888) is headquartered in Armonk, NY, USA. The company manufactures and sells computer hardware, software, and services. ...

Categorical propositions are distinguished from hypothetical propositions (if-then statements that connect propositions rather than terms) and disjunctive propositions (either-or statements, claiming exclusivity between propositions).

Quality, quantity and distribution

Categorical propositions can be categorized on the basis of their quality, quantity, and distribution qualities. Quality refers to whether the proposition affirms or denies the inclusion of a subject to the class of the predicate. The two qualities are affirmative and negative. On the other hand, quantity refers to the amount of subjects in one class which are included in the other class. The first quantifier is the universal, "all". This means that every subject of one class has membership in the predicated class. The other quantifier is called a particular. It is an indefinite number, which could mean five, twenty or, perhaps, all, but always at least one. From quality and quantity are four types of categorical propositions designated alphabetically:

• A proposition is a universal affirmative: All S is P
• E proposition is a universal negative: No S is P
• I proposition is a particular affirmative: Some S is P
• O proposition is a particular negative: Some S is not P

All four types have different distribution properties. Distribution refers to what can be inferred from the proposition. An A proposition distributes the subject to the predicate, but not the reverse. Consider the following categorical proposition: all dogs are mammals. All dogs are indeed mammals but it would be false to say all mammals are dogs. E propositions do distribute bidirectionally between the subject and predicate. From the categorical proposition, no beetles are mammals, we can infer that no mammals are beetles. Both terms in an I proposition are undistributed. For example, some Americans are conservatives. Neither term in the proposition can be entirely distributed to the other term. From this proposition it is not possible to say that all Americans are conservatives or that all conservatives are Americans. In an O proposition only the predicate term is distributed. Consider the following: some hardware are not nails. Knowing that screws are considered hardware, it can be stated that there exist some members outside the class of nails that are members of the class of hardware. However, it can be inferred that all nails are hardware. Thus, only the predicate term is distributed in an O proposition.