Categorical propositions

Validity

A characteristic of any deductive argument whose premises, if they were all true, would provide conclusive grounds for the truth of its conclusion. Such an argument is said to be valid.

Square of opposition

A diagram in the form of a square in which the four types of categorical propositions (A, E,I.and O) are situated at the corners, exhibiting the logical relations ( called "oppositions") among these propositions.

Obversion

A valid form of immediate inference for every standard-form categorical proposition. To obvert a proposition we change its quality (from affirmative to negative, or from negative to affirmative) and replace the predicate term with its complement. Thus, applied to the proposition "All dogs are mammals," obversion yields "No dogs are non mammals ," which is called the "obverse" of the original proposition. The original proposition is called the "obvertend."

Conversion

A valid form of immediate inference for some but not all types of propositions. To form the converse of a proposition the subject and predicate terms are simply interchanged. Thus, applied to the proposition "No circles are squares," conversion yields "No squares are circles," which is called the "converse" of the original proposition is called the "convertend ."

Contraposition

A valid form of immediate inference for some, but not for all types of propositions. To form the contrapositive of a given proposition, its subject term is replaced by the complement of its predicate term, and its predicate term is replaced by the complement of its subject term. Thus the contrapositive of the proposition "All non mammals are non humans."

Deductive argument

An argument whose premises are claimed to provide conclusive grounds for the truth of its conclusion.

Quality

An attribute of every categorical proposition, determined by whether the proposition affirms or denies class inclusion. Thus every categorical proposition is either universal in quality or particular in quality.

Quantity

An attribute of every categorical proposition, determined by whether the proposition refers to all members or only some members of the class designated by its subject term. Thus every categorical proposition is either universal in quantity or particular in quantity.

Existential import

An attribute of those propositions that normally asserts the existence of objects of some specified kind. Particular propositions (I and O propositions) always have existential import; thus the proposition "Some dogs are obedient" asserts that there are dogs. Whether universal propositions (A and E propositions) have existential import is an issue on which the Aristotelian and Boolean interpretations of propositions differ.

Distribution

An attribute that describes the relationship between a categorical proposition and each one of its terms, indicating whether or not the proposition makes a statement about every member of the class represented by a given term.

Immediate inference

An inference that is drawn directly from one premise without the mediation of any other premise. Various kinds of immediate inferences may be distinguished , traditionally including conversion, obversion, and contra position.

Standard-form categorical proposition.

Any categorical proposition of the form "All S is P" (universal affirmative), "No S is P" (universal negative), "Some S is P" (particular affirmative), or "Some S is not P" (particular negative). Respectively, these four types are known as A, E, I, and O propositions.

Copula

Any form of the verb "to be" that serves to connect the subject term and the predicate term of a categorical proposition.

Existential fallacy

Any mistake in reasoning that arises from assuming illegitimately that some class has members.

Contingent

Being neither tautologous nor self-contradictory. A contingent statement may be true or false.

Vent diagramm

Iconic representation of a categorical proposition or of an argument, used to display their logical forms by overlapping circles.

Modern or modern symbolic logic

The account of syllogistic reasoning accepted today. It differs in important ways from the traditional account.

Class

The collection of all objects that have some specified characteristic in common.

Opposition

The logical relation that exists between two contradictories, between two contraries, or in general between any two categorical propositions that differ in quantity, quality, or other respects. These relations are displayed on the square of opposition.

Boolean interpretation

The modern interpretation of categorical propositions, named after English logician George Boole. In the Boolean interpretation, often contrasted with Aristotelian interpretation, universal propositions (A and E propositions) do not have existential import.

Contradictories

Two propositions so related that one is the denial or negation of the other. On the traditional square of opposition, the two pairs of contradictories are indicated by the diagonals of the square: A and E propositions are the contradictories of O and I, respectively.

Subcocontraries

Two propositions so related that they cannot both be false, although they may both be true.

Contraries

Two propositions so related that they cannot both be tru, although both may be false.

Complement, or complementary class

the collection of all things that do not belong to a given class

Categorical proposition

A proposition that can be analyzed as being about classes, or affirming or denying that one class, S, is included in some other class, P, in whole or in part.

Subalternation

The relation on the square of opposition between a universal proposition (an A or an E proposition) and its corresponding particular proposition (an I or an O proposition, respectively). In this relation, the particular proposition (I or O) is called the "subaltern" and the universal proposition (A or E) is called the "superaltern."

Classical or Aristotelian logic

The traditional account of syllogistic reasoning, in which certain interpretations of categorical propositions are presupposed.