Week 4- Chapt 8 & 9 Categorical Statements, Venn Diagrams, and Immediate Inferences

Vocabulary practice flashcards covering categorical statements, standard forms, Venn diagrams, immediate inferences, and the traditional square of opposition from Chapters 8 and 9.

Categorical Logic

The logic which deals with group membership, inclusion and exclusion, using particular or universal statements.

Venn Diagrams

A kind of visual depiction of the relationship between two or more groups using interlocking circles.

Categorical Statement

A statement that asserts that members of one group either are or are not members of another group.

"Some" (in Categorical Logic)

A quantifier used in a restricted, technical sense meaning "at least one."

Term

A word or phrase which identifies a group or collection of individuals.

Subject Term

The name of the group which is mentioned in the subject of a categorical statement.

Predicate Term

The name of the group mentioned in the predicate of a categorical statement.

Universal Statement

A categorical statement that refers to all members of the subject term.

Particular Statement

A categorical statement that refers to some members of the subject term.

Affirmative Statement

A categorical statement that refers to group inclusion.

Negative Statement

A categorical statement that refers to group exclusion.

A-Statement

A universal affirmative standard form categorical statement of the form "All $S$ are $P$," asserting that all members of $S$ are included in $P$.

E-Statement

A universal negative standard form categorical statement of the form "No $S$ are $P$," asserting that all members of $S$ are excluded from $P$.

I-Statement

A particular affirmative standard form categorical statement of the form "Some $S$ are $P$," asserting that some members of $S$ are included in $P$.

O-Statement

A particular negative standard form categorical statement of the form "Some $S$ are not $P$," asserting that some members of $S$ are excluded from $P$.

Copula

A connecting verb in a categorical statement, limited in standard form to "are" or "are not."

Corresponding Statements

Categorical statements which have the same subject and predicate terms as each other.

Predicate Adjective

An adjective used in the predicate of a sentence that modifies the subject; it must be supplemented with a more general plural noun to be rendered into standard categorical form.

Quantificational Ambiguity

A condition occurring when a categorical statement is unclear and can be understood as having different quantifiers.

Euler Circles

A visual system representing categorical relationships that only shows spaces that are logically possible, moving the circles as needed so that ruled-out spaces have no place on the diagram.

Shading (in Categorical Venn Diagrams)

The convention in logic of darkening an area of a Venn diagram to assert that the region is empty and has nothing in it.

"X" Mark (in Categorical Venn Diagrams)

A mark placed in an area of a Venn diagram in logic to assert that the area is non-empty and definitely contains at least one individual.

Circled-"X" (in Categorical Venn Diagrams)

A symbol drawn in an open area of a Venn diagram to represent a member of a term that is presumed or assumed to exist, rather than asserted to exist by the given statement.

Immediate Inference

An argument with one premise which leads directly to its conclusion.

Term Complement

A term which includes everything not included in a given term, often formed by adding the prefix "non-".

Existential Import

A property of statements when the fact that they are true implies the existence of their subjects.

Enthymeme

An argument with a missing premise, conclusion, or both.

Begging the Question

Relying on circular reasoning, or depending on an unstated, faulty premise.

Existential Fallacy

A fallacy committed in an argument when it relies on the existence of a non-existent term.

Square of Opposition

A visual diagram displaying all the logical relationships (contradictories, contraries, sub-contraries, and sub-alternation) between corresponding standard form categorical statements.

Contradictories

Statements which by necessity have opposite truth values, such that it is impossible for both to be true and impossible for both to be false (holds between A and O statements, and between E and I statements).

Contraries

Corresponding universal categorical statements (A and E) that cannot both be true, but can both be false, given that their subjects exist.

Sub-Contraries

Corresponding particular categorical statements (I and O) that cannot both be false, but can both be true, given that their subjects exist.

Sub-Alternation

The relationship between a universal categorical statement and the corresponding particular statement of the same quality (A and I; E and O), where truth flows downward and falsity flows upward.

Illicit Subalternation

A fallacy committed in an argument when the conclusion is obtained from the premise through subalternation in an improper fashion (such as inferring the falsity of a particular statement from the falsity of a universal statement).

Illicit Contraries

A fallacy committed in an argument when the conclusion is the contrary of the premise, but is drawn in an improper fashion.

Illicit Subcontraries

A fallacy committed in an argument when the conclusion is the subcontrary of the premise, but is drawn in an improper fashion.

Vacuously True

A status describing a universal categorical statement regarding a non-existent subject being true simply because the subject region outside the predicate is empty.