Definition:Figure of Categorical Syllogism/I
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Definition
The first figure of a categorical syllogism, traditionally denoted figure $\text I$, is the pattern where:
- In the major premise, the middle term is placed first
- 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 $\text I$ can be tabulated as:
Major Premise: | $\map {\mathbf \Phi_1} {M, P}$ |
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 $\mathbf O$.
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