Definition:Categorical Syllogism

Definition
A categorical syllogism is a logical argument which is structured as follows:

$(1): \quad$ It has exactly two premises and one conclusion.
 * The first premise is usually referred to as the major premise.
 * The second premise is usually referred to as the minor premise.

$(2): \quad$ It concerns exactly three terms, which are usually denoted:

$(3): \quad$ Each of the premises and conclusion is a categorical statement.

Also known as
Some sources refer to this as the syllogism, narrowing down its field of definition to the precise structure as defined here.

Historical Note

 * The predicate calculus was undiscovered 100 years ago... For well over 2,000 years before that, some of the same logical material was handled by the theory of the syllogism, which we owe to ; virtually nothing was added to it in that period. There can today be no doubt that predicate calculus has replaced the syllogism as an instrument for serious logical work; predicate calculus is to syllogism what a precision tool is to a blunt knife... There are no reasons other than historical ones for studying the syllogism; but this theory has been of importance in the history of both logic and philosophy, and perhaps therefore deserves a place in a modern logic course.
 * &mdash; : $\S 4.4$: The Syllogism