In that case there is confusion; for there are two diverse propositions, namely the proposition for the expositor and the proposition for the recipient.

I put this possibility aside as irrelevant for our discussion, though in practice it may be difficult for two persons to concur in the consideration of exactly the same proposition, or even for one person to have determined exactly the proposition which he is considering.
Again the demonstrative phrase may fail to demonstrate any entity.

In that case there is no proposition for the recipient.

I think that we may assume (perhaps rashly) that the expositor knows what he means.
A demonstrative phrase is a gesture.

It is not itself a constituent of the proposition, but the entity which it demonstrates is such a constituent.