[4] For Russell, a denoting phrase is a semantically complex expression that can serve as the grammatical subject of a sentence.
According to Russell's theory, denoting phrases do not contribute objects as the constituents of the singular propositions in which they occur.
In any case, after clarifying the sense of the term "denoting phrase" and providing several examples to illustrate the idea, Russell explains the epistemological motivations for his theory.
In this way, Russell points out, it will turn out that all statements containing non-referring descriptions (e.g. "The present king of France is a great writer") are false.
[5] One of the fundamental puzzles that Russell hopes to resolve with the theory of descriptions is the problem of non-referring expressions or, as they are now called, negative existentials.
He finally explains how his theory resolves this problem after invoking a distinction between what he calls primary and secondary occurrences of denoting phrases.
Since definite descriptions are just quantificational devices on Russell's view, they can enter into scope relations with other logical operators.
Contemporarily, it is customary to discuss Russell's primary/secondary distinction in the more logically exact terms of wide and narrow scope.
He refers to an example similar to Frege's puzzle about identity: "George IV wondered whether Scott is the author of Waverley."
In the de re case, the above sentence can be interpreted as follows instead: Finally, Russell suggests that fictional names such as "Apollo" can be treated as abbreviated definite descriptions that refer to nothing.
In his essay, "On Referring", P. F. Strawson criticised Russell's characterisation of statements where the object does not exist, such as "the present King of France", as being wrong.
[7] Strawson also argued that we often need to know the use of a word to understand its meaning, such as in statements of the form, "The table is covered with books."