Systems Of Logic/Syllogistic Logic

The Syllogism

A syllogism is an inference, consisting of three statements in which a conclusion follows as a matter of necessity from two given premises. A classic example of a syllogims is:

All humans are mortal (major premise)

All Greeks are human (minor premise)

therefore, All Greeks are mortal (conclusion)

Qualities of Statements

Each of these statements are said to have the quality of being universally affirmative (all humans are mortal), universally negative (no humans are mortal), particularly affirmative (some humans are mortal), or particularly negative (some humans are not mortal). A statement which is universally affirmative may be designated by writing the letter, A. A universal negative statement is designated by the letter, E. A particular affirmative statement is designated by the letter, I, and a particular negative statement, by the letter, O. All of the above statements are universally affirmative.

Exercises 1.1

State whether each of the following statements are universally affirmative, universally negative, particularly affirmative, or particularly negative by designating them with an A, E, I, or O.

The Square Of Opposition and Existential Import