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The term "no farmer" is not a referential expression, so "his" cannot be coreferential with it.
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Directly referential expressions contribute their referents (in a context) to the propositions expressed (in that context) by the sentences containing them.
This volume brings together contributions by prominent researchers in the fields of language processing and language acquisition on topics of common interest: how people refer to objects in the world, how people comprehend such referential expressions, and how children acquire the ability to refer and to understand reference.
Rigid directly referential expressions would evidently be rigid de jure.
Adopting this structured proposition account makes it simple to distinguish between directly referential expressions and other expressions, rigid or not.
Non-directly referential expressions contribute some complex that may or may not determine the same individual in all possible circumstances.
Thus Kaplan wrote that directly referential expressions "refer directly without the mediation of Fregean Sinn as meaning".
But it is plausible that all directly referential expressions, assuming there are any, are rigid and rigid de jure.
Even though there are rigid designators that are not directly referential, it is plausible to suppose that all directly referential expressions are rigid designators (as Kaplan suggests: 1989b, p. 571).
Despite the apparent simplicity of definite and indefinite descriptions, the past 100+ years have seen heated debates about their proper analysis ranging from treating them as referential expressions to treating them as quantificational expressions to treating them as predicational expressions.
Kaplan intended to contrast directly referential expressions with expressions such as definite descriptions, which, though designating particular individuals, do so by means of descriptive conditions being expressed by the description and satisfied by the designated individual.
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CEO of Professional Science Editing for Scientists @ prosciediting.com