Category:Figures of Categorical Syllogisms
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This category contains results about Figures of Categorical Syllogisms.
Definitions specific to this category can be found in Definitions/Figures of Categorical Syllogisms.
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: | $\map {\mathbf \Phi_3} {S, P}$ |
Subcategories
This category has the following 4 subcategories, out of 4 total.