Definition:Figure of Categorical Syllogism/III

Definition
The third figure of a categorical syllogism, traditionally denoted figure $\text {III}$, is the pattern where:


 * In the major premise, the middle term is placed first
 * In the minor premise, the middle term is placed first.

Let $P$ denote the primary term, $S$ denote the secondary term and $M$ denote the middle term of a categorical syllogism.

Then figure $\text {III}$ can be tabulated as: where $\mathbf \Phi_1$, $\mathbf \Phi_2$ and $\mathbf \Phi_3$ each denote one of the categorical statements $\mathbf A$, $\mathbf E$, $\mathbf I$ or $\mathbf O$.

Also known as
This figure is classically known as the figure of examples, from the fact that in order to be valid, its conclusion needs to be particular.