" As should by now be clear, the existence of sentences such as 'Rebecca swims' brings into existence facts such as 4b'' where, let us suppose, the propositional relation doesn't yet encode the instantiation function, but the sentenctial relation of 'Rebecca swims' does. Since we now claim that the propositional relation encoding the instantiation function is part of the fact that is the proposition that Rebecca swims, 4b'' is not yet that proposition. Indeed, neither the proposition that Rebecca swims, nor, we may suppose, any other proposition exists yet... However sentences have truth conditions, in part in virtue of the sentential relations encoding functions"
So, on this view we can have a totally functional language with truth conditions for sentences without ever having propositions. The only time we need propositions is when we start having propositional attitude verbs, modal operators and that-clauses.
I think this is a bad route for King to take. Consider a world in which there is a language as rich as english, but there are still no propositional attitude verbs, modal operators and that-clauses. Most of the arguments in favor of propositions still apply, though in a different way. Recall that King has to make rampant use of the true-in true-at distinction. Since I get these confused, let's say a proposition is true-in a world iff that proposition exists at that world and is true of that world. Let's say a proposition is true-at a world iff the proposition exists in the actual world and is true of the significant counterfactual world.
Ok, suppose we have this counterfactual world and we have ben and marry. They have a little discussion:
Ben: I love you
Marry: You love me
It is true-at this world that Ben and Marry share a belief. But for this to be so, they must bare a common attitude to something. It's not any sentence, since they express their beliefs using different sentences. It must be a proposition. But that means that propositions must not only be true-at that world, there must be propositions true-in that world. Otherwise it would be false-at that world that Ben and Marry share a belief.
Thankfully for King, I don't think he has to be committed to this strange view. He can hold that when we have truth-conditions for a sentence, we have a proposition that sentence expresses that has the same truth conditions. But if he says this then much of the motivation for thinking that we in fact use this propositional relations to represent propositions falls away. I'll give the crux of his support found on page 61:
"As speakers began to attempt to talk about structured contents by means of that-clauses, they implicitly took these contents to have the same truth conditions as the sentences with those contents."
If speakers were already using propositions in a representational way, then the further occurrence of the use of that-clauses described here is irrellevant for arguing what they were using to represent. If King were to digress and say that speakers implicitly took the propositions to have the contents he described back when the language was created, he is at pains to motivate us to think they were using propositions in this representational way. It's clearer to see how representation is bestowed upon propositions when propositions are the things being talked about, it is less clear when they are not.
Furthermore, he supposes that those who speak of propositions speak of structured propositions implicitly. I think it would be hard to walk up to... say... Robert Stalnaker and tell him "you Robert Stalnaker are talking about structured propositions" and have that be compelling. Since he takes everyone to be talking about propositions as described in his view, the same would apply to anyone with a view contrary to his.
This dilemma is by no means a knock-down argument against his view. However I think it shows that his view does not have a virtue that he thinks it has.