In chapter 2 (around page 34), King claims that the syntax, or syntactic concatenation, provides instructions as to how to evaluate the truth of a sentence. He kind of takes this for granted and as far as I can tell his argument for this goes something like:
1) The sentence "Rebecca swims" is true iff Rebecca instantiates the property of swimming.
2) The way we know if Rebecca instantiates the property of swimming is by looking at the syntactical make-up/organization/concatenation of the sentence (Syntactically concatenating a name with a one-place predicate in English in the manner of "Rebecca swims" has the result that we evaluate the sentence as true if the semantic value of the name instantiates the semantic value of the predicate).
3) So, this syntactic concatenation in (3) provides instructions as to how to evaluate the sentence.
Summed up: The way that a sentence is built syntactically (it's syntactic make-up) is the instructions on how to evaluate whether the sentence is true or false. Put another way, when we look at a sentence, the syntactic concatenation tells us what to look for in the world to know if the sentence is true or false.
King says that even if you do not want to grant existence to propositions, you would still have to admit this "instructional quality" of a sentence's syntax. He kind if leaves it at that from what I can see.
I have two objections to this claim.
The first is an objection to the argument as a whole. I want to point out the leap King makes from the premises to the conclusion. King goes from saying that the syntax of a sentence in a way "sets the parameters for" or in some way "determines" the truth value for the proposition in question, to saying that the syntax "provides instructions on how to go about figuring this out". This is just plain false. An example that I think illustrates this is that of a map. If you give someone a map of a city and point out to them the spot on the map where they are right now, and point out where you want them to end up, the map does not 'give instruction' on how to get there even though it does contain all the information they need in order to make the trip.
The line I am drawing here is very thin and precise and I could understand how some people might think the difference in negligible. I am not sure how to press this point further. There must be some procedure or cognitive process pre-existing and functioning correctly in order for the person to utilize the map for the purpose of direction. Otherwise it is just a bunch of names and lines on paper. The same goes for the syntax of a proposition. Even though the syntax might give you the information you need in order to evaluate the truth of a proposition, it does not direct you how to do so.
Without the ability to instruct people how to find truth or falsity, I think King still has to account for how we come to know the truth of a sentence based on its syntax (I think he would probably have to add some cognitive process of "deriving instruction from...").
My second objection is against premise 2 of the above argument.
It seems to me that the syntactical structure of a sentence is independent of it's context or intent, and therefore cannot be used to evaluate truth value. For example, when I say "Oxygen is good for us" in the context of right now it is true. Over time, however, "Oxygen is good for us" is false (over the course of a lifetime is causes cellular decay, tissue oxidation, cellular reproductive defects, etc...), even though it has the exact same syntactical make-up and truth conditions (I picked this example because it can illustrate two different contexts without changing the speakers location in space or time, thus eliminating possible responses from King).
I think that this objection shows an obvious problem with premise 2 and is more difficult for King to respond to that simply saying "evaluation changes relative to the context the syntax is in". I have clearly shown that the same syntax can have 2 different evaluations at the same location, time, but different contexts. Basically what I am saying is that if syntax can be the same (independent) in 2 different contexts, how can you know which evaluation to use when looking for truth value? Therefore the syntax must not instruct us in regards to evaluation.