Definition:Existential Import

Definition

Let $S$ be a statement.

Let $S$ have a term $T$ such that $S$ is false if and only if $T$ has no instances.

Then $S$ has existential import.

Examples

Reducible Fraction

The statement:

Some fractions are reducible

is assumed to have existential import.

Also see

• Results about existential import can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): existential import
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): existential import