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:	$\map {\mathbf \Phi_3} {S, P}$

Sources

• 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $4$: The Predicate Calculus $2$: $4$ The Syllogism
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): syllogism
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): figure: 4.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): syllogism