Definition:Singular Statement/Designatory Function

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.