Definition:Distributed Term of Categorical Syllogism
Definition
A term in a syllogism is distributed if and only if the categorical statement in which it occurs refers to the whole of the class designated by the term.
Distributed Subject
Let $\map {\mathbf \Phi} {S, P}$ be a categorical statement, expressed in abbreviated form.
Let $\mathbf \Phi$ be a universal categorical statement.
Then $S$ is described as being distributed.
Distributed Predicate
Let $\map {\mathbf \Phi} {S, P}$ be a categorical statement, expressed in abbreviated form.
Let $\mathbf \Phi$ be a negative categorical statement.
Then $P$ is described as being distributed.
Examples
Universal Affirmative
Consider the universal affirmative categorical statement $\map {\mathbf A} {S, P}$.
The subject $S$ of $\map {\mathbf A} {S, P}$ is distributed.
The predicate $P$ of $\map {\mathbf A} {S, P}$ is undistributed.
Universal Negative
Consider the universal negative categorical statement $\map {\mathbf E} {S, P}$.
Both the subject $S$ and the predicate $P$ of $\map {\mathbf E} {S, P}$ are distributed.
Particular Affirmative
Consider the particular affirmative categorical statement $\map {\mathbf I} {S, P}$.
Both the subject $S$ and the predicate $P$ of $\map {\mathbf I} {S, P}$ are undistributed.
Particular Negative
Consider the particular negative categorical statement $\map {\mathbf O} {S, P}$.
The subject $S$ of $\map {\mathbf O} {S, P}$ is undistributed.
The predicate $P$ of $\map {\mathbf O} {S, P}$ is distributed.
This can be tabulated as follows:
- $\begin{array}{rcl} \mathbf A & (S, & P) \\ & d & u \end{array} \qquad \begin{array}{rcl} \mathbf E & (S, & P) \\ & d & d \end{array}$
- $\begin{array}{rcl} \mathbf I & (S, & P) \\ & u & u \end{array} \qquad \begin{array}{rcl} \mathbf O & (S, & P) \\ & u & d \end{array}$
where $d$ denotes a distributed term and $u$ denotes an undistributed term.
Also see
- Results about distributed terms of categorical syllogisms can be found here.
Sources
- 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $4$: The Predicate Calculus $2$: $4$ The Syllogism