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