Bertrand Russell

“ 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 present King of France, the center of mass of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. ”

“ For suppose that C is our complex; then we are to say that C is the meaning of the complex. Nevertheless, whenever C occurs without inverted commas, what is said is not true of the meaning, but only of the denotation, as when we say: The center of mass of the solar system is a point. Thus to speak of C itself, i.e. to make a proposition about the meaning, our subject must not be C, but something which denotes C. Thus 'C', which is what we use when we want to speak of the meaning, must not be the meaning, but must be something which denotes the meaning. ”

“ What we know is 'So-and-so has a mind which has such and such properties' but we do not know 'A has such and such properties', where A is the mind in question. In such a case, we know the properties of a thing without having acquaintance with the thing itself, and without, consequently, knowing any single proposition of which the thing itself is a constituent. ”

“ Thus according to the meaning of denotation lately explained, 'the difference between A and B' has a denotation when A and B differ, but not otherwise. This difference applies to true and false propositions generally. If 'a R b' stands for 'a has the relation R to b', then when a R b is true, there is such an entity as the relation R between a and b; when a R b is false, there is no such entity. Thus out of any proposition we can make a denoting phrase, which denotes an entity if the proposition is true, but does not denote an entity if the proposition is false. ”

“ A proposition about Apollo means what we get by substituting what the classical dictionary tells us is meant by Apollo, say 'the sun-god'. All propositions in which Apollo occurs are to be interpreted by the above rules for denoting phrases. ”

“ If 'Apollo' has a primary occurrence, the proposition containing the occurrence is false; if the occurrence is secondary, the proposition may be true. So again 'the round square is round' means 'there is one and only one entity x which is round and square, and that entity is round', which is a false proposition, not, as Meinong maintains, a true one. 'The most perfect Being has all perfections; existence is a perfection; therefore the most perfect Being exists' becomes:
'There is one and only one entity x which is most perfect; that one has all perfections; existence is a perfection ”

“ This assumes that such phrases as 'the present King of France', which do not denote a real individual, do, nevertheless, denote an individual, but an unreal one. This is essentially Meinong's theory, which we have seen reason to reject because it conflicts with the law of contradiction. With our theory of denoting, we are able to hold that there are no unreal individuals; so that the null-class is the class containing no members, not the class containing as members all unreal individuals. ”

“ Now the, when it is strictly used, involves uniqueness; we do, it is true, speak of 'the son of So-and-so' even when So-and-so has several sons, but it would be more correct to say 'a son of So-and-so'. Thus for our purposes we take the as involving uniqueness. Thus when we say 'x was the father of Charles II' we not only assert that x had a certain relation to Charles II, but also that nothing else had this relation. The relation in question, without the assumption of uniqueness, and without any denoting phrases, is expressed by 'x begat Charles II'. ”

“ And C must not be a constituent of this complex (as it is of 'the meaning of C') ; for if C occurs in the complex, it will be its denotation, not its meaning, that will occur, and there is no backward road from denotations to meaning, because every object can be denoted by an infinite number of different denoting phrases. ”