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Full Idea
Being a 'singular term' is not a category in contemporary syntactic theory and it doesn't correspond to any of the notions employed there like that of a singular noun phrase or the like.
Gist of Idea
'Singular terms' are not found in modern linguistics, and are not the same as noun phrases
Source
Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 02.3)
Book Ref
Hofweber,Thomas: 'Ontology and the Ambitions of Metaphysics' [OUP 2018], p.25
A Reaction
Hofweber has researched such things. This is an important objection to the reliance of modern Fregeans on the ontological commitments of singular terms (as proof that there are 'mathematical objects').