(0) Background: A friend of propositions can offer two kinds of accounts. (A) Mathematical Accounts. (B) Ontological Accounts. Mathematical accounts offer: (i) Models or "proposition surrogates", or: (i) Arguments that propositions really are such mathematical constructs.
(0.1) If (i), then we are still owed an explanation of propositions. If (ii), then we face a Benacerraf Dilemma. King finds this "compelling". Thus, (A) fails to be satisfactory.
(0.2) What of (B)? To succeed, such an account must tell us what propositions really are. It cannot offer surrogates or models.
(0.3) Jubien assumes that we must talk about Platonic propositions. We must give their intrinsic nature. We must assume that they are a special kind of entity. They are complex, and stand on their own.
(0.4) The two main assumptions are: (i) That propositions must be Platonic. (ii) That propositions must be structured and have constituents.
(1) Jubien's first argument assumes an Argument for Internal Representation. This argument contains the following assumptions: (i) Propositions represent the world as being so-and-so. (ii) If (i) were false, then propositions would not be the ultimate bearers of truth value. (iii) The represening a proposition does must be an internal feature of the proposition. (iv) To ground the representational force of a proposition outside of the proposition would be sabotage the idea that propositions really are entities and not surrogates. (v) It must be the case that no other entity could be the proposition in question.
(1.1) Jubien is of course concerned with the following: That if the 'propositionality' were derived from some representational activity outside the entity, the uniqueness would be lost. This would be a mere mathematical account of propositions, subject to the Benacerraf Dilemma.
(2) Given (1), Jubien holds that the representational capacity of propositions must be grounded in the representational capacity of it and its constituents.
(2.1) He further assumes: (i) Properties represent their instances. (ii) Propositions are mereological fusions or sums of properties and relations. (iii) There is an uniqueness of composition.
(2.2) Unfortunately, a problem arises from these views. Consider: (i) The property of being a swimming dog. (i) is the mereological sum of the properties of being a dog and of swimming. But now consider: (ii) The proposition that swimming dogs are swimming dogs. (ii) must be the mereological sum of the property of being a dog, the property of swimming, and coinstantiation. But this produces a problem: the mereological sum was also supposed to be the proposition that dogs are swimming.
(2.3) But if this is so, then the one mereological sum of the properties of being a dog, of swimming and the relation of coinstantiation is both: (i) The proposition that some dogs swim. (ii) The proposition that swimming dogs are swimming dogs. This means that the two propositions are identical.
(3) Given that this is false, it must be the case that the positions held in (1) and (2) are false.
(3.1) King notes that the argument for internal representation got us into trouble. His view avoids it. The assumption that propositions are mereological sums of their constituents properties and relations, and that there is an unique mereological sum of their given parts, is also problematic. His view also avoids it.
I hope that this is adequate...