Definition:Standard Instance of Categorical Syllogism

Definition
For each categorical syllogism, there are four figures:


 * $\begin{array}{r|rl}

\mathbf I & & \\ \hline \\ \text{Major Premise}: & \mathbf \Phi_1 & \left({M, P}\right) \\ \text{Minor Premise}: & \mathbf \Phi_2 & \left({S, M}\right) \\ \hline \\ \text{Conclusion}: & \mathbf \Phi_3 & \left({S, P}\right) \\ \end{array} \qquad \begin{array}{r|rl} \mathbf {II} & & \\ \hline \\ \text{Major Premise}: & \mathbf \Phi_1 & \left({P, M}\right) \\ \text{Minor Premise}: & \mathbf \Phi_2 & \left({S, M}\right) \\ \hline \\ \text{Conclusion}: & \mathbf \Phi_3 & \left({S, P}\right) \\ \end{array} \qquad \begin{array}{r|rl} \mathbf {III} & & \\ \hline \\ \text{Major Premise}: & \mathbf \Phi_1 & \left({M, P}\right) \\ \text{Minor Premise}: & \mathbf \Phi_2 & \left({M, S}\right) \\ \hline \\ \text{Conclusion}: & \mathbf \Phi_3 & \left({S, P}\right) \\ \end{array} \qquad \begin{array}{r|rl} \mathbf {IV} & & \\ \hline \\ \text{Major Premise}: & \mathbf \Phi_1 & \left({P, M}\right) \\ \text{Minor Premise}: & \mathbf \Phi_2 & \left({M, S}\right) \\ \hline \\ \text{Conclusion}: & \mathbf \Phi_3 & \left({S, P}\right) \\ \end{array}$

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 $\mathbf O$.

A standard instance of a categorical syllogism is obtained by substituting $\mathbf A$, $\mathbf E$, $\mathbf I$ or $\mathbf O$ for each of $\mathbf \Phi_1$, $\mathbf \Phi_2$ and $\mathbf \Phi_3$ in one of the above figures.

Not all of these standard instances are valid.