Definition:Categorical Syllogism/Shorthand

Definition

In order to specify the pattern of a categorical syllogism completely, it is necessary and sufficient to specify:

$(1) \quad$ The figure ($\text I$ to $\text {IV}$) of the syllogism

and

$(2) \quad$ The types of the three categorical statements that compose the syllogism.

Hence, for example, the following categorical syllogism, which is of the first figure:

$\begin{array}{r|rl}

\text I & & \\ \hline \text{Major Premise}: & \mathbf E & \tuple {M, P} \\ \text{Minor Premise}: & \mathbf I & \tuple {S, M} \\ \hline \text{Conclusion}: & \mathbf O & \tuple {S, P} \\ \end{array}$

is specified completely by:

$\text I: EIO$

Sources

• 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $4$: The Predicate Calculus $2$: $4$ The Syllogism: $150$