Definition:Figure of Categorical Syllogism
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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