# Definition:Figure of Categorical Syllogism

## Definition

There are four patterns of categorical syllogism depending on the order of the terms in the major premise and minor premise.

Let $\mathbf \Phi_1, \mathbf \Phi_2, \mathbf \Phi_3$ each be one of the categorical statements $\mathbf A$, $\mathbf E$, $\mathbf I$ or $\mathbf O$.

Let $P$ denote the primary term, $S$ denote the secondary term and $M$ denote the middle term.

The four possible figures are as follows:

### $\text I$

 Major Premise: $\map {\mathbf \Phi_1} {M, P}$ Minor Premise: $\map {\mathbf \Phi_2} {S, M}$ Conclusion: $\map {\mathbf \Phi_3} {S, P}$

### $\text {II}$

 Major Premise: $\map {\mathbf \Phi_1} {P, M}$ Minor Premise: $\map {\mathbf \Phi_2 } {S, M}$ Conclusion: $\map {\mathbf \Phi_3} {S, P}$

### $\text {III}$

 Major Premise: $\map {\mathbf \Phi_1} {M, P}$ Minor Premise: $\map {\mathbf \Phi_2} {M, S}$ Conclusion: $\map {\mathbf \Phi_3} {S, P}$

### $\text {IV}$

 Major Premise: $\map {\mathbf \Phi_1} {P, M}$ Minor Premise: $\map {\mathbf \Phi_2} {M, S}$ Conclusion: $\map {\mathbf \Phi_3} {S, P}$