Definite Descriptions are phrases of the form “the X” where X is a noun phrase. The description is said to be proper when the phrase applies to exactly one object, and conversely, it is said to be improper when either more than one potential referents exists, as in “the senator from Ohio”, or none at all, as in “the king of France”.
In conventional speech, definite descriptions are implicitly assumed to be proper, hence such phrases trigger the presupposition that the referent is unique and existent.
- John saw the man with one leg.
Definite Description: there exists a man with one leg.