Categorical Proposition

• A categorical proposition gives a direct assertion of agreement between the subject and predicate terms; it is also known as a simple proposition.

Elements of a Proposition

• Subject.
• Predicate.
• Copula.

Standard Form of Categorical Proposition

• Standard categorical propositions are divided into three parts: quantifier, predicate term, and subject term.

Quantifier

• A quantifier indicates the degree of universality (quantity) of the subject.
• It is divided into two categories: universal and particular.

Universal Quantifier

• Universal quantifier takes the subject in its entirety, using terms like "all," "every," and "any," as well as "no," "none," and similar terms for negative propositions.
• Example: All laptops are expensive, or none of them are good.

Particular Quantifier

• Particular quantification uses terms like "some," "at least one," "most," "almost all," and "the majority."
• These quantifiers assert that at least one member of the subject class is (or is not) a member of the predicate class.
• Example: Some students are scholars, or at least one student is a scholar.

Subject and Predicate Terms

• The subject term is what is being affirmed or denied about, and the predicate term is what is affirmed or denied of the subject term.
• Both terms constitute the matter of the proposition.
• In "Some preachers are lay people," the subject term is 'some preachers' and the predicate term is 'lay people'.

Copula

• The copula is the linking verb, such as "is" (am, are, was, were) and "is not" (am not, are not, was not, were not), indicating agreement or disagreement between the subject and predicate.
• The quantifier determines the degree of disagreement or agreement.
• It is the copula that gives the form of the proposition.
• The standard form follows the subject-copula-predicate arrangement.
• Example: All soldiers are disciplined.

Quality and Quantity of Categorical Propositions

• Quality refers to the relation between the two terms: if there is agreement, the proposition is affirmative, and if there is disagreement, it is negative.
• Examples: "All deep-thinkers are philosophers" is affirmative, while "An angel is not a devil" is negative.
• Quantity refers to the number of individuals to whom the subject term applies.
• If the proposition uses a universal quantifier, then it is universal, and if it uses a particular quantifier, then it is a particular proposition.

Quality and Quantity Combined & Square of Opposition

• A proposition
• E proposition
• I proposition
• O proposition

Types of Logical Opposition

• Contradiction exists between propositions that differ in both quantity and quality (A and O, E and I).
• Contrariety exists between universal propositions that differ in quality only (A and E).
• Subcontrariety exists between particular propositions that differ in quality only (I and O).
• Subalternation exists between two propositions with the same quality but differing in quantity (A and I, E and O); this is the only relation where the starting proposition matters.