A Concise Introduction to Logic | Chapter 4: Categorical Syllogisms

Categorical Proposition

A proposition that relates two classes (or categories) (pg. 200).

Subject Term

In a standard-form categorical proposition, the term that comes immediately after the quantifier (pg. 200).

Predicate Term

In a standard-form categorical proposition, the term that comes immediately after the copula (pg. 200).

Standard-Form Categorical Proposition

A proposition that has one of the following forms: "All S are P" "No S are P" "Some S are P" "Some S are not P" (pg. 201).

Quantifiers

In standard-form categorical propositions, the words "all," "no," and "some" (pg. 201).

Copula

In standard-form categorical propositions, the words "are" and "are not" (pg. 201).

Quality

The attribute of a categorical proposition by which it is either affirmative or negative (pg. 204).

Affirmative Propositions (statements)

A proposition/statement that asserts class membership (pg. 204).

Negative Propositions (statements)

A proposition/statement that denies class membership (pg. 204).

Quantity

The attribute of a categorical proposition by which it is either universal or particular (pg. 204).

Universal Propositions (statements)

A proposition/statement that makes an assertion about every member of its subject class (pg. 204).

Particular Propositions (statement)

A proposition/statement that makes a claim about one or more (but not all) members of a class (pg. 204).

A Proposition

A categorical proposition having the form "All S are P" (pg. 204).

E Proposition

A categorical proposition having the form "No S are P" (pg. 204).

I Proposition

A categorical proposition having the form "Some S are P" (pg. 204).

O Proposition

A categorical proposition having the form "Some S are not P" (pg. 204).

Distribution

An attribute possessed by a term in a categorical proposition if and only if the proposition makes a claim about all the members of the class denoted by the term (pg. 205).

Existential Import

An attribute of a categorical proposition by which it implies that one or more things denoted by the subject term actually exist (pg. 209).

Venn Diagrams

A diagram consisting of two or more circles used to represent the information content of categorical propositions (pg. 212).

Modern Square of Opposition

A diagram that illustrates the necessary relations that prevail between the four kinds of standard-form categorical propositions as interpreted from the Boolean standpoint (pg. 214).

Contradictory Relation

The relation that exists between statements that necessarily have opposite truth values (pg. 215).

Logically Undetermined Truth Value

A condition that exists when a certain statement is not necessarily either true or false, given the truth value of some related statement (pg. 215).

Vacuously True

Truth that results merely from the fact that the subject class is empty (pg. 215).

Immediate Inferences

An argument having a single premise (pg. 215).

Unconditionally Valid

Valid from the Boolean standpoint (pg. 215).

Existential Fallacy

A fallacy that occurs whenever an argument is invalid merely because the premises lack existential import (pg. 218).

Conversion

An operation that consists in switching the subject and predicate terms in a standard form categorical proposition (pg. 221).

Logically Equivalent Statements

Statements that necessarily have the same truth values (pg. 222).

Illicit Conversion

A formal fallacy that occurs when the conclusion of an argument depends on the conversion of an A or O statement (pg. 223).

Obversion

An operation that consists of changing the quality of a standard-form categorical proposition and replacing the predicate term with its term complement (pg. 223).

Term Complement

The word or group of words that denotes the class complement (pg. 223).

Contraposition

An operation that consists in switching the subject and predicate terms in a standard-form categorical proposition and replacing each with its term complement (pg. 226).

Illicit Contraposition

A formal fallacy that occurs when the conclusion of an argument depends on the contraposition of an E or I statement (pg. 227).

Traditional Square of Opposition

A diagram that illustrates the necessary relations that prevail between the four kinds of standard-form categorical propositions as interpreted from the Aristotelian standpoint (pg. 232).

Contrary Relation

The relation that exists between two statements that are necessarily not both true (pg. 232).

Subcontrary Relation

The relation that exists between two statements that are necessarily not both false (pg. 233).

Subalternation Relation

The relation by which a true A or E statement necessarily implies a true I or O statement, respectively, and by which a false I or O statement necessarily implies a false A or E statement, respectively (pg. 233).

Illicit Subcontrary

A formal fallacy that occurs when the conclusion of an argument depends on an incorrect application of the subcontrary relation (pg. 234).

Illicit Contrary

A formal fallacy that occurs when the conclusion of an argument depends on an incorrect application of the contrary relation (pg. 234).

Illicit Subalternation

A formal fallacy that occurs when the conclusion of an argument depends on an incorrect application of the sub alternation relation (pg. 234).

Conditionally Valid

Valid from the Aristotelian standpoint on condition that the subject term of the premise(s) denotes actually existing things; conditionally valid inferences (pg. 236).

Singular Proposition (statement)

A proposition/statement that makes an assertion about a specifically named person, place, thing, or time (pg. 252).

Parameter

A phrase that, when introduced into a statement, affects the form but not the meaning (pg. 252).