Definition:Reduction to First Figure

Definition
Reduction to the first figure is a method for determining the validity of a categorical syllogism, as follows:


 * $(1): \quad$ Certain "self-evident" patterns are identified in the first figure of the categorical syllogism.


 * $(2): \quad$ Using various rules of categorical statements, the valid patterns of other figures of the categorical syllogism are deduced.

There are two forms this procedure takes:

Historical Note
This technique for analysis of categorical syllogisms was devised by Aristotle.


 * Reduction is of great historical interest, as being perhaps the earliest known attempt to derive conclusions systematically from given assumptions. Though Aristotle's presentation is crude and informal by modern standards of rigour, it is possible to follow the outlines of his programme and derive the valid syllogisms as conclusions, by purely propositional calculus reasoning, from a very small set of syllogistic assumptions.
 * &mdash; : $\S 4.4$: The Syllogism