# Definition:Singular Statement/Designatory Function

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## Definition

A **designatory function** is a propositional function which, on replacement of the operand with a constant, becomes an individuating description.

## Also known as

A **designatory function** is also known as a **descriptive function**.

## Example

The expression:

- $2 x + 1$

is a **designatory function**.

Substituting the constant $2$ for the variable $x$ turns $2 x + 1$ into the individuating description $2 \times 2 + 1$.

Returning to a previous example:

**The King of Siam in the year $x$**

is arguably **not** a **designatory function**, because not every value of $x$ returns a valid [Definition:Individuating Description|individuating description]].

For example, setting $x$ to the value $2014$ returns a predicate which uniquely describes **no** particular object.

## Sources

- 1946: Alfred Tarski:
*Introduction to Logic and to the Methodology of Deductive Sciences*(2nd ed.) ... (previous) ... (next): $\S 1.2$: Expressions containing variables