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Naturally, singular terms (including proper names used as singular terms) are always distributed, for they refer only to one object and cannot refer to fewer.
Most semantic theories of the simple demonstratives 'this' and 'that' treat them as singular terms.
Terms for natural kinds like 'gold' and 'water' are widely supposed to function as singular terms some of the time.
The distinction between the surface appearance of definite descriptions, as singular terms, and the fully analyzed sentences from which they seem to disappear was seen as a model for making problematic notions disappear upon analysis.
Just as some common terms, such as 'sun' and 'moon', in fact have only one referent, so there are referring phrases which in fact have only one referent, but do not count as singular terms because by the mode of their signification they could supposit for more than one thing.
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It seems then implausible to categorize these subject-expressions as abstract singular terms, on a par with 'justice'mercyrcy' and 'refinement'; they are most naturally described as generic expressions, and are happily so-called by linguists.
Assume that this analysis is correct and that each plural term thus has some objects as its semantic value, just as each singular term has one object as its semantic value.
For one thing, just as Frege took singular terms to be a vehicle for commitment to objects, he took incomplete expressions to be a vehicle of commitment to concepts and (more generally) functions.
So far as syllogistic was concerned, some logicians, such as Lambert of Auxerre (or Lagny) gave a standard account of the Aristotelian syllogism which is centered on the universal and particular quantification of general terms at the same time as they gave examples with singular terms, such as "Every man is an animal, Socrates is a man, therefore Socrates is an animal".
But it is possible to accommodate the opposite intuition by adopting a negative free logic, i.e., a semantics that treats atomic sentences with non-referring singular terms as false, and their negations as true.
Advocates of psychologism agree with platonists that in the sentence '3 is prime', '3' functions as a singular term (i.e., as a denoting expression).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com