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Chapter Summary

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 diagram—three 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.

Categorical Equivalence

  • Understand the three types of categorical equivalence—conversion, obversion, and contraposition—and know when different categorical claims are equivalent.


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