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# Categorical Propositions

“Rules of Science [of Logic] 2,” 1875, woodcut by Alfred James Swinbourne [1]

The study of categorical propositions reveals how inferences can be made conclusively. If the form of an argument is valid and the premises are true, the conclusion follows with absolute certainty.

Take some care with the logical relations called contrariety and subcontraiety. For some persons, these inferences are initially counterintuitive.

Understanding the topics for ordinary language inferences and Venn Diagrams for Proposition will prove essential for working with the logic of syllogistic arguments later in the course.

#### Notes

1. Alfred James Swinbourne, “Image: Rules of Science [of Logic] 2,” Picture Logic; or, The Grave Made Gay,” London: Longmans, Green: 1875), 18.

• ### Quantity, Quality, and Distribution

The properties of standard form categorical propositions are illustrated and explained with examples.

• ### The Square of Opposition

The logical relations of contradictory, contrariety, subcontrariety, and subalternation are illustrated and explained with examples.

• ### Further Immediate Inferences

The Square of Opposition is reviewed, and three additional inferences are explained and illustrated: conversion, obversion, and contraposition.

• ### Successive Immediate Inferences

Example problems using the square of opposition and successive immediate inferences are posed with answer key. Problems are taken from I.M. Copi and Carl Cohen's Introduction to Logic 13th ed. (Upper Saddle River, NJ: Pearson, 2009), 205-206.

• ### Strategies for Successive Inferences

The technique of successive applications of logical relations drawn from the square of opposition and further immediate inferences is discussed and illustrated.

• ### Ordinary Language Inferences

Ordinary language examples of using immediate inferences demonstrate the uses of standard form categorical propositions and their logical relations.

• ### Venn Diagrams for Propositions

The technique of representing the logic of statements by means of pictures is illustrated and explained with examples.

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