explain standard form of categorical proposition
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Chapter Summary
Chapter 5
A categorical proposition is a proposition that relates two classes of objects. Categorical propositions contain a subject and a predicate term. The subject term comes first in a standard-form categorical proposition. The predicate term comes second in a standard-form categorical proposition.
A standard-form categorical proposition has a quantity and quality, and a specific distribution method for the subject or predicate term (or both). “Universal” and “particular” refer to the quantity of a categorical proposition. “Affirmative” and “negative” refer to the quality of a categorical proposition. The words “all,” “no,” and “some” are called “quantifiers.” They tell us the extent of the class inclusion or exclusion. The words “are” and “are not” are referred to as “copula.” They are simply forms of “to be” and serve to link (to “couple”) the subject class with the predicate class. If a categorical proposition asserts something definite about every member of a class, then the term designating that class is said to be distributed. On the other hand, if the proposition does not assert something definite about every member of a class, then the term designating that class is said to be undistributed.
There are four types of categorical proposition:
A-proposition: Asserts that the entire subject class is included in the predicate class (“All S are P”).
I-proposition: Asserts that part of the subject class is included in the predicate class (“Some S are P”).
E-proposition: Asserts that the entire subject class is excluded from the predicate class (“No S are P”).
O-proposition: Asserts that part of the subject class is excluded from the predicate class (“Some S are not P”).
It is important to be conversant with the following concepts:
Opposition: Occurs when two standard-form categorical propositions refer to the same subject and predicate classes, but differ in quality, quantity, or both.
Contradictories: Pairs of propositions in which one is the negation of the other. A- and O-propositions are contradictories, as are E- and I-propositions.
Contraries: Pairs of propositions that cannot both be true at the same time, but can both be false at the same time. A- and E-propositions are contraries.
Subcontraries: Pairs of propositions that cannot both be false at the same time, but can both be true; also, if one is false, then the other must be true. I- and O-propositions are subcontraries.
Subalternation: The relationship between a universal proposition (the superaltern) and its corresponding particular proposition (the subaltern).
Immediate argument: An argument that has only one premise.
Mediate argument: An argument that has more than one premise.
Conversion: An immediate argument created by interchanging the subject and predicate terms of a given categorical proposition.
Conversion by limitation: When we first change a universal A-proposition into its corresponding particular I-proposition, and then we use the process of conversion on the I-proposition.
Obversion: An immediate argument formed by changing the quality of the given proposition, and then replacing the predicate term with its complement.
Complement: The set of objects that do not belong to a given class.
Contraposition: Formed by replacing the subject term of a given proposition with the complement of its predicate term and then replacing the predicate term of the given proposition with the complement of its subject term.
Contraposition by limitation: When subalternation is used to change the universal E-proposition into its corresponding particular O-proposition. We then apply the regular process of forming a contrapositive to this O-proposition.
Existential import: When a proposition presupposes the existence of certain kinds of objects.
The modern square of opposition offers a new interpretation of the various relationships between the four standard-form categorical propositions.
Venn diagrams use circles to represent categorical proposition forms.
Singular proposition: Asserts something about a specific person, place, or thing.
Exceptive propositions: Statements that need to be translated into compound statements containing the word “and.” (For example, propositions that take the form “All except S are P” and “All but S are P.”)