Ch. 5: Categorical Propositions

Question 1

Deductive argument

Answer 1

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

Question 2

Validity

Answer 2

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.

Question 3

Classical or Aristotelian logic

Answer 3

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

Question 4

Modern or modern symbolic logic

Answer 4

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

Question 5

Class

Answer 5

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

Question 6

Categorical proposition

Answer 6

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

Question 7

Standard-form categorical proposition

Answer 7

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.

Question 8

Venn diagram

Answer 8

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

Question 9

Quality

Answer 9

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

Question 10

Quantity

Answer 10

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

Question 11

Copula

Answer 11

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

Question 12

Distribution

Answer 12

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.

Question 13

Opposition

Answer 13

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.

Question 14

Contradictories

Answer 14

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.

Question 15

Contraries

Answer 15

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

Question 16

Contingent

Answer 16

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

Question 17

Subcontraries

Answer 17

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

Question 18

Subalternation

Answer 18

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.

Question 19

Square of opposition

Answer 19

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.

Question 20

Immediate inference

Answer 20

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 contraposition.

Question 21

Mediate inference

Answer 21

Any inference drawn from more than one premise.

Question 22

Conversion

Answer 22

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. The original proposition is called the “convertend.

Question 23

Complement, or complementary class

Answer 23

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

Question 24

Obversion

Answer 24

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 nonmammals,” which is called the “obverse” of the original proposition. The original proposition is called the “obvertend.”

Question 25

Contraposition

Answer 25

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 humans are mammals” is the proposition “All nonmammals are nonhumans.”