Week 5- Chapter 12: Categorical Syllogisms: Standard Form, Mood, Figure, and Validity

Vocabulary practice flashcards covering key definitions, components, figures, validity conditions, and diagramming methods for categorical syllogisms.

Major Term

The predicate term of the conclusion in a standard form categorical syllogism.

Minor Term

The subject term of the conclusion in a standard form categorical syllogism.

Middle Term

The term in a standard form categorical syllogism that appears once in each premise and does not appear in the conclusion.

Major Premise

The first premise in a standard form categorical syllogism, which contains the major term and the middle term.

Minor Premise

The second premise in a standard form categorical syllogism, which contains the minor term and the middle term.

Standard Form Categorical Syllogism

An argument composed of three standard-form categorical statements containing exactly three terms, where the major premise is listed first, the minor premise second, and the conclusion third.

Mood

A series of three letters that represent the letter type ($A$, $E$, $I$, or $O$) of the three statements in a standard form categorical syllogism in sequential order.

Figure

A number between $1$ and $4$ that signifies the placement and arrangement of the middle terms in the premises of a standard form categorical syllogism.

Figure 1

The syllogistic arrangement where the middle term is in the subject position of the major premise and the predicate position of the minor premise.

Figure 2

The syllogistic arrangement where the middle term occurs in the predicate position of both premises.

Figure 3

The syllogistic arrangement where the middle term occurs in the subject position of both premises.

Figure 4

The syllogistic arrangement where the middle term is in the predicate position of the major premise and the subject position of the minor premise.

Barbara Syllogism

A classic standard form categorical syllogism with the mood and figure $AAA\text{-}1$, consisting of two universal affirmative premises and a universal affirmative conclusion.

Unconditionally Valid Syllogism

A syllogistic mood and figure that is valid from the Boolean standpoint without requiring any existential assumption that its terms exist.

Conditionally Valid Syllogism

A syllogistic form that is valid only under the added assumption that a specific term (the subject, predicate, or middle term) exists.

Circled "x"

A notation on a Venn diagram placed in the final open region of a term circle to indicate that an entity is assumed to exist rather than explicitly asserted by the premises.

Obversion

A valid statement operation that replaces the predicate term with its term complement and changes the statement's quality while preserving its truth value.

Contraposition

A statement operation that swaps the subject and predicate terms and replaces both with their respective term complements.

Circle of Syllogisms

A multi-ring circular color diagram used to evaluate the validity and existential assumptions of any categorical syllogism without requiring the reduction of terms.