"On Denoting" is an essay by Bertrand Russell. It was published in the philosophy journal Mind in 1905. In it, Russell introduces and advocates his theory of denoting phrases, according to which definite descriptions and other "denoting phrases ... never have any meaning in themselves, but every proposition in whose verbal expression they occur has a meaning." This theory later became the basis for Russell's descriptivism with regard to proper names, and his view that proper names are "disguised" or "abbreviated" definite descriptions.

In the 1920s, Frank P. Ramsey referred to the essay as "that paradigm of philosophy". In the Stanford Encyclopedia of Philosophy entry Descriptions, Peter Ludlow singled the essay out as "the paradigm of philosophy", and called it a work of "tremendous insight"; provoking discussion and debate among philosophers of language and linguists for over a century.

For Russell, a denoting phrase is a semantically complex expression that can serve as the grammatical subject of a sentence. Paradigmatic examples include both definite descriptions ("the shortest spy") and indefinite descriptions ("some sophomore"). A phrase does not need to have a denotation to be a denoting phrase: "the greatest prime number" is a denoting phrase in Russell's sense even though there is no such thing as the greatest prime number. According to Russell's theory, denoting phrases do not contribute objects as the constituents of the singular propositions in which they occur. Denotation, in other words, is a semantically inert property, in this view. Whereas Frege held that there were two distinct parts (or aspects) of the meaning of every term, phrase, or sentence (its sense and reference: Sinn and Bedeutung), Russell explicitly rejects the notion of sense (Sinn), and gives several arguments against it.

However, at the very beginning of the article, Russell distinguishes between cases where "a phrase may be denoting and yet not denote anything (e.g. 'the present King of France')" (there was no king of France at the time of Russell's article) and cases where they may denote "one definite object (such as 'the present King of England')" (Edward VII was the king of England at the time of Russell's article). If this passage is interpreted as saying that descriptions may "refer" to one definite object, then it could be that Russell actually recognised the two distinct uses of definite descriptions (attributive and referential) that Keith Donnellan later proposed.

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. Russell believes at this point that there are essentially two modes of knowing: knowledge by description and knowledge by (direct) acquaintance. Knowledge by acquaintance is limited to the sense data of the phenomenal world and to one's own private inner experiences, while knowledge of everything else (other minds, physical objects, and so on) can be known only by way of general descriptions.

Russell starts out by defining the "fundamental" notion of a propositional function. This is basically a modified version of Frege's idea of unsaturated concepts. Hence, "C(x) stands for a proposition in which x is a constituent and where x, the variable, is essentially and wholly undetermined." Then everything, nothing and something ("the most primitive of denoting phrases") are to be interpreted as follows:

where E stands for everything, N stands for nothing and S stands for something. All is taken as primitive and indefinable and the others are defined in terms of it. Russell emphasises that denoting phrases can have no meaning apart from that which is assigned to them within the propositions in which they occur, all of which are meaningful. This is the foundation of Russell's theory of descriptions as he proceeds to illustrate.

The phrase "the father of Charles II (F) was executed (E)" is interpreted as the following quantificational assertion: