Ch. 5: Categorical Propositions Flashcards
Deductive argument
An argument whose premises are claimed to provide conclusive grounds for the truth of its conclusion.
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.
Classical or Aristotelian logic
The traditional account of syllogistic reasoning, in which certain interpretations of categorical propositions are presupposed.
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.
Categorical proposition
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.
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.
Venn diagram
Iconic representation of a categorical proposition or of an argument, used to display their logical forms by means of overlapping circles.
Quality
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.
Quantity
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.
Copula
Any form of the verb “to be” that serves to connect the subject term and the predicate term of a categorical proposition.
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.
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.
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.
Contraries
Two propositions so related that they cannot both be true, although both may be false.
Contingent
Being neither tautologous nor self-contradictory. A contingent statement may be true or false.
Subcontraries
Two propositions so related that they cannot both be false, although they may both be true.
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.
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.
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 contraposition.
Mediate inference
Any inference drawn from more than one premise.
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. The original proposition is called the “convertend.
Complement, or complementary class
The collection of all things that do not belong to a given class.
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 nonmammals,” which is called the “obverse” of the original proposition. The original proposition is called the “obvertend.”
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 humans are mammals” is the proposition “All nonmammals are nonhumans.”
