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# Categorical Syllogisms

“Great Logic Branch,” 1875, woodcut by Alfred James Swinbourne [1]

Syllogisms are two premise arguments. Most arguments, other than those that are relational, statistical, and multi-term, can be reduced into syllogistic form.

Today, syllogistic logic has assimilated into sentential and predicate logic; however, syllogistic reasoning is still often used in legal and everyday reasoning.

Several different techniques of evaluating syllogistic arguments are discussed whereby the reasoning can be conclusively evaluated to be either valid or invalid.

1. Alfred James Swinbourne, “Image: Woodcut: The Great Logic Branch,” Picture Logic; or, The Grave Made Gay,” (London: Longmans, Green: 1875), 73.

• ### Syllogistic Terms, Part I

Rewriting an argument in standard form and standard order enables the identification of major and minor premises and conclusion; the major, minor, and middle terms; and the mood and figure of a syllogism. Subsequently, a syllogism is easily evaluated.

• ### Syllogistic Terms, Part II

A review of the terms used in syllogistic reasoning is employed in the evaluation of an ordinary language syllogism.

• ### Refutation by Logical Analogy

The technique of refuting an invalid syllogism by inventing an argument with the same form but with better understood terms is explained.

• ### Venn Diagrams

The Venn Diagram technique is shown for a number of typical as well as unusual syllogisms.

• ### Syllogistic Fallacies

The rules for valid syllogisms and their corresponding fallacies are described and illustrated with examples.

• ### Testing Standard Form Syllogisms

Practice exercises with answers are given for testing syllogisms.

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