Definition:Figure of Categorical Syllogism/III

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Definition

The third figure of a categorical syllogism, traditionally denoted figure $\text {III}$, is the pattern where:

In the major premise, the middle term is placed first
In the minor premise, the middle term is placed first.


Let $P$ denote the primary term, $S$ denote the secondary term and $M$ denote the middle term of a categorical syllogism.


Then figure $\text {III}$ can be tabulated as:

  Major Premise:   $\map {\mathbf \Phi_1} {M, P}$
  Minor Premise:   $\map {\mathbf \Phi_2} {M, S}$
  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 examples, from the fact that in order to be valid, its conclusion needs to be particular.


Sources