Interested in presupposition projection? Check for Grice's earliest reference

Are you interested in the Projection of presuppositions? You should.

A presupposition of a part of an utterance is sometimes also a presupposition of the whole utterance, and sometimes not.

It's the intelligent crowd who can discriminate there.

The phrase "my wife" triggers the presupposition

"I have a wife".

The first sentence below carries that presupposition, even though the phrase occurs inside an embedded clause.

In the second sentence, however, it does not. John might be mistaken about his belief that I have a wife, or he might be deliberately trying to misinform his audience, and this has an effect on the meaning of the second sentence, but, perhaps surprisingly, not on the first one.

(1) John thinks that my wife is beautiful.
(2) John said that my wife is beautiful.

Thus, this seems to be a property of the main verbs of the sentences, think and say, respectively.

A HOLE.

After work by Lauri Karttunen,[1] verbs that allow presuppositions to "pass up" to the whole sentence ("project") are called holes.

A PLUG.

Verbs that block such passing up, or projection of presuppositions are called plugs.

A FILTER:

Some linguistic environments are intermediate between plugs and holes: They block some presuppositions and allow others to project. These are called filters.

An example of such an environment are indicative conditionals ("If-then" clauses). A conditional sentence contains an antecedent and a consequent. The antecedent is the part preceded by the word "if," and the consequent is the part that is (or could be) preceded by "then." If the consequent contains a presupposition trigger, and the triggered presupposition is explicitly stated in the antecedent of the conditional, then the presupposition is blocked. Otherwise, it is allowed to project up to the entire conditional. Here is an example:

If I have a wife, then my wife is blonde.

Here, the presupposition triggered by the expression my wife (that I have a wife) is blocked, because it is stated in the antecedent of the conditional: That sentence doesn't imply that I have a wife. In the following example, it is not stated in the antecedent, so it is allowed to project, i.e. the sentence does imply that I have a wife.

If it's already 4am, then my wife is probably angry.
Hence, conditional sentences act as filters for presuppositions that are triggered by expressions in their consequent.

A significant amount of current work in semantics and pragmatics is devoted to a proper understanding of when and how presuppositions project.

REFERENCES:

Grice, H. P. (1970). Presupposition and conversational implicature. Note that Grice (WoW:vii) dates that as '1970'.
Wilson, Deirdre Susan Moir. (1974) "Presuppositions and non-truth-conditional semantics". PhD dissertation. Department of Foreign Literatures and Linguistics
--- Presupposition, Assertion, and. Lexical Items, Linguistic Inquiry, vol. 6 (Citing "Projection problem of presupposition")