Definition:Singular Statement/Designatory Function
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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.
- $2 x + 1$
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.
- 1946: Alfred Tarski: Introduction to Logic and to the Methodology of Deductive Sciences (2nd ed.) ... (previous) ... (next): $\S 1.2$: Expressions containing variables