Categorical Syllogism

Standard form of Syllogism: A syllogism is a deductive argument in which a conclusion is inferred from two premisses. A categorical syllogism consists of three categorical propositions that contain exactly three terms. A categorical syllogism is in standard form when its premisses and conclusion are all standard-form categorical propositions (A, E, I, or O) and arranged in a specified standard order. The conclusion of a standard-form categorical syllogism is the key to defining its elements:

The predicate term of the conclusion is called the major term.
The subject term of the conclusion is called the minor term.
The third term, the term that occurs in the two premisses but not in the conclusion, is called the middle term.The premiss that contains the major term is called the major premiss.The premiss that contains the minor term is called the minor premiss.

· In a standard-form categorical syllogism, the categorical propositions are in the following order: the major premiss is stated first, the minor premiss second, and the conclusion last.

Figure of categorical syllogism:

Mood and figure determine the particuar logical form of a categorical proposition: the figure of a categorical proposition determines the particular logical form of a categorical syllogism; the figure is determined by the position of the middle term in the two premisses. Because the middle term can occupy one of two positions-subject or predicate-in each premiss, there are four possible figures. These are conventionally labeled one through four.

In the first figure, the middle term is the subject of the major premiss and the predicate of the minor premiss.
In the second figure, the middle term is the predicate of both premisses.
In the third figure, the middle term is the subject of both premisses.
In the fourth figure, the middle term is the predicate of the major premiss and the subject of the minor premiss.

Categorical Syllogism (Robinson's power-point presentation)