By a “denoting phrase” I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the centre of mass of the Solar system at the first instant of the twentieth century, the revolution of the earth around the sun, the revolution of sun around the earth. Thus a phrase is denoting solely in virtue of its form. We may distinguish three cases: 1) A phrase may be denoting, and yet not denote anything; e.g. “the present King of France”. 2) A phrase may denote one definite object; e.g. “the present King of England”. 3) A phrase may denote ambiguously; e.g. “a man” denotes not many man but an ambiguous man. Russell, On Denoting, p.479

My theory, briefly, is as follows: I take the notion of the variable as fundamental; I use “C(x)” to mean a proposition in which x is a constituent, where x, the variable, is essentially and wholly undetermined. Then we can consider two notions: - “C(x) is always true” - “C(x) is sometimes true” (which can be defined by means of the first as: “It is not true that ‘C(x) is false’ is always true”) Then, everything and nothing and something (which are the most primitive of denoting phrases) are to be interpreted as follows: - C(everything) means “C(x) is always true”; - C(nothing) means “ ‘C(x) is false’ is always true”; - C(something) means “It is false that ‘C(x) is false’ is always true” (or “C(x) is not always false” or “C(x) is sometimes true”). Here the notion of “C(x) is always true” is taken as ultimate and indefinable and the others are defined by means of it. Everything, nothing and something are not assumed to have any meaning in isolation, but a meaning is assigned to every proposition in which they occur. This is the principle of the theory of denoting I want to advocate: that denoting phrases never have any meaning in themselves, but that every proposition in whose verbal expression they occur has a meaning. Russell, On Denoting, p.480

The difficulties concerning denoting are, I believe, all the result of a wrong analysis of propositions whose verbal expressions contain denoting phrases. Russell, On Denoting, p.480