There is no really adequate definition of singular term. Here are some definitions proposed by different writers:
A term that tells us which individual is being talked about (Mill, Prior[?], Strawson)
A term that is grammatically singular, i.e. a proper name (proprium nomen), a demonstrative pronoun (pronomen demonstrativum) or a demonstrative pronoun with a common name (cum termino communi) (Ockham).
A term that is inherently about the object to which it applies or refers. (Frege)
A term that is true "in the same sense" of only one object (Peter of Spain[?]).
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