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Full Idea
Russell's analysis of 'the baby is crying' seems to imply that this can only be true if there is just one baby in the world; ..to dispose of the objection, it seems necessary to appeal implicitly or explicitly to a 'domain of discourse'.
Gist of Idea
Russell implies that 'the baby is crying' is only true if the baby is unique
Source
comment on Bertrand Russell (On Denoting [1905]) by A.C. Grayling - Russell Ch.2
Book Ref
Grayling,A.C.: 'Russell' [OUP 1996], p.37
A Reaction
This objection leads to ordinary language philosophy, and the 'pragmatics' of language. It is standard in modern predicate logic to specify the domain over which an expression is quantified.