# Definition:Distributed Term of Categorical Syllogism/Predicate

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## Definition

Let $\mathbf{\Phi} \left({S, P}\right)$ be a categorical statement, expressed in abbreviated form.

Let $\mathbf{\Phi}$ be a negative categorical statement.

Then $S$ is described as being **distributed**.

## Examples

### Universal Affirmative

Consider the Universal Affirmative categorical statement $\mathbf A \left({S, P}\right)$.

The subject $S$ of $\mathbf A \left({S, P}\right)$ is distributed.

The predicate $P$ of $\mathbf A \left({S, P}\right)$ is undistributed.

### Universal Negative

Consider the Universal Negative categorical statement $\mathbf E \left({S, P}\right)$.

Both the subject $S$ and the predicate $P$ of $\mathbf E \left({S, P}\right)$ are distributed.

### Particular Affirmative

Consider the Particular Affirmative categorical statement $\mathbf I \left({S, P}\right)$.

Both the subject $S$ and the predicate $P$ of $\mathbf I \left({S, P}\right)$ are undistributed.

### Particular Negative

Consider the Particular Negative categorical statement $\mathbf O \left({S, P}\right)$.

The subject $S$ of $\mathbf O \left({S, P}\right)$ is undistributed.

The predicate $P$ of $\mathbf O \left({S, P}\right)$ 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.

## Sources

- 1965: E.J. Lemmon:
*Beginning Logic*... (previous) ... (next): $\S 4.4$: The Syllogism