Definition:Figure of Categorical Syllogism/II
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Definition
The second figure of a categorical syllogism, traditionally denoted figure $\text {II}$, is the pattern where:
- In the major premise, the middle term is placed second
- In the minor premise, the middle term is placed second.
Let $P$ denote the primary term, $S$ denote the secondary term and $M$ denote the middle term of a categorical syllogism.
Then figure $\text {II}$ can be tabulated as:
Major Premise: | $\map {\mathbf \Phi_1} {P, M}$ |
Minor Premise: | $\map {\mathbf \Phi_2 } {S, M}$ |
Conclusion: | $\map {\mathbf \Phi_3} {S, P}$ |
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 $\mathbf O$.
Also known as
This figure is classically known as the figure of exclusions, from the fact that in order to be valid, its conclusion needs to be negative.
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): syllogism