A description of a (putative) object as the single, unique, bearer of a property: ‘the smallest positive number’; ‘the first dog born at sea’; ‘the richest person in the world’. In the theory of definite descriptions, unveiled in the paper ‘On Denoting’ (Mind, 1905), Russell analysed sentences of the form ‘the F is G’ as asserting that there is an F, that there are no two distinct Fs, and that if anything is F then it is G. A legitimate definition of something as the F will therefore depend on there being one and not more than one F. To say that the F does not exist is not to say, paradoxically, of something that exists that it does not, but to say that either nothing is F, or more than one thing is. Russell found the theory of enormous importance, since it shows how we can understand propositions involving the use of empty terms (terms that do not refer to anything or describe anything) without supposing that there is a mysterious or surrogate object that they have as their reference (see subsistence). So, for example, it becomes no argument for the existence of God that we understand claims in which the term occurs. Analysing the term as a description, we may interpret the claim that God exists as something like ‘there is a unique omnipotent, personal creator of the universe’, and this is intelligible whether or not it is true.

Formally the theory of descriptions can be couched in the two definitions:

The F is G=(∃x)(Fx & (∀y)(Fy → y=x) & Gx)

The F exists=(∃x)(Fx & (∀y)(Fy → y=x)

See also acquaintance and description.