Here's an example of a self-referential statement:
"The set of all sets that do not contain themselves."
In this statement, "contain themselves" is a property that is being considered for defining the set. However, the property itself involves the set that is being defined. Therefore, the statement is self-referential.
Self-reference can also occur in paradoxical situations, such as:
"The statement 'I am lying' is true."
If the statement is true, then it means that the statement is lying, which contradicts the statement being true. Therefore, the statement is paradoxical and self-referential.