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To clarify, by "Grice's theory of meaning" I am referring to the view that the informational content or meaning of an utterance is made up of three components:

  1. what is said - the actual proposition expressed.
  2. what is implied - everything that follows logically from what is said.
  3. what is implicated - everything that follows from the assumption that the speaker is adhering to the Conversational Maxims.

I'm learning about definite descriptions and have just been introduced to two of the main logical accounts of the phenomenon:

  • Russell's account, which treats definite descriptions as quantificational expressions, and
  • Frege's account, which treats them as referential expressions.

From what I understand, the difference between the two accounts essentially stems from their treatment of the uniqueness assumption that underlies a definite description. On my first reading, it seemed to me that Russell treats the uniqueness assumption as being part of what is said (and therefore, part of what is implied), whereas Frege takes it be an implicature, i.e. part of what is implicated. But most sources I have come across (e.g. 1 and 2) mention that Frege's theory takes the uniqueness assumption to be a presupposition (not an implicature, as I had initially guessed).

I'm not familiar with presuppositions, but it seems that they are different from implicatures in the sense that while a (conversational) implicature can be cancelled, a presupposition cannot. But If presuppositions are not implicatures, then where do they fit into Grice's theory of meaning as outlined above?

EDIT: As per user Conifold's comment below, Grice regarded the existence and uniqueness of F to be an entailment in "the F is G", and an implicature in "the F is not G." But I don't really have a clear understanding of what entailment is and how "to entail" differs from "to imply". Does that mean that I am incorrect in thinking that uniqueness is implied in the Russellian approach?

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    They do not fit into Grice's theory. Presuppositions come instead from Strawson's rival theory. For example, Grice followed Russell in interpreting existence and uniqueness of definite descriptions as implications, rather than presuppositions, and in negative sentences, which do not imply them, as implicatures, see Bezuidenhout, Grice on Presupposition.
    – Conifold
    Commented Nov 24, 2023 at 12:53
  • Thank you @Conifold, but aren't implications the same as implicatures? Do you mean he takes existence and uniqueness to be entailments in the unnegated case ("the F is G"), and implicatures in the negated case ("the F is not G")?
    – user51462
    Commented Nov 24, 2023 at 22:59
  • Yes, btw the link has an abstract that goes over this, which should be accessible.
    – Conifold
    Commented Nov 24, 2023 at 23:01
  • There is a technical difference between implication (first-order material conditional) and entailment (meta-relation of inferring) in mathematical logic, but it does not matter here due to the deduction meta-theorem. In particular, Bezuidenhout uses "implication" and "entailment" interchangeably.
    – Conifold
    Commented Nov 25, 2023 at 7:36
  • I see, thanks @Conifold.
    – user51462
    Commented Nov 25, 2023 at 23:43

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