Considering the third sentence "The author of Waverley exists", Russell highlights two issues. First of all, who is the author of Waverley? By naming the person who wrote it, the question can be answered. Secondly, "The propositional function", i.e., x wrote Waverley and the author of Waverley is the same person.

Here, we find two properties. They are:

1. It must be true for at least one x.
2. It must be true for at most one x.

Here 'x' implies an individual to whom this description is made. If one person did not write the Waverley then it does not exist. Hence, it is true for one and only one individual is the author of Waverley. It rewrites as; 'There is an entity c, such that x wrote Waverley is true when x is c'. Similarly it is false when "x is not c". In this regard, Russell said that existence is not a predicate.