Statements and Classes
- Every categorical statement has a subject term and a predicate
term. There are four standard forms of categorical statements: (1)
universal affirmative (All dogs are mammals), (2) universal negative (No
dogs are mammals), (3) particular affirmative (Some dogs are mammals), and
(4) particular negative (Some dogs are not mammals).
Translations and Standard Form
- Categorical statements must be translated into standard form
before you can work with them.
- Translating involves identifying terms and ensuring that they
designate classes and determining the quantifiers.
Diagramming Categorical Statements
- Drawing Venn diagrams is a good way to visualize categorical
statements and to tell whether one statement is equivalent to another.
Sizing Up Categorical Syllogisms
- A categorical syllogism is an argument consisting of three
categorical statements (two premises and a conclusion) that are
interlinked in a structured way.
- The syllogism consists of a major term, minor term, and middle
term. The middle term appears once in each premise. The major term appears
in one premise and the conclusion, and the minor term appears in the other
premise and the conclusion.
- The easiest way to check the validity of a categorical
syllogism is to draw a three-circle Venn diagramthree overlapping circles
with the relationship between terms graphically indicated. If, after
diagramming each premise, the diagram reflects what’s asserted in the
conclusion, the argument is valid. If not, the argument is invalid.
The Square of Opposition
Understand how standard-form statements are
related to one another, as illustrated in the square of opposition.
Know how to use the square of opposition to
deduce the truth values of standard-form categorical claims.
Understand the three types of categorical
equivalenceconversion, obversion, and contrapositionand know when different
categorical claims are equivalent.