King kind of confuses me right at the start of chapter 6 when he talks about how propositions "must and must not change truth value across time and location". He makes this claim before he even starts laying out his position, but I am still trying to see the problem that he is so adamant about.
My understanding of where King starts from:
1) If the truth value of propositions is determined by the semantic value (relative to context) of sentences, then (2) & (3).
2) Propositions, according to his 'in Carnelian Bay' example, change truth value over different worlds, locations, and times.
3) Propositions, according to his 'Santa Monica based belief' example, do not change truth value over time or location.
4) ~ [(1) & (2)]
5) Therefore, further inquiry into the relation between propositional truth value and the semantic value of sentences is required.
I am having trouble with the examples that King is using in (2) and (3). In (2), he says (referring to the sentence "In Carnelian Bay there is a boat launching ramp") that "If 'there is a boat launching ramp' expressed a proposition (relative to that context) that didn't vary its truth value over locations, the locational operator 'In Carnelian Bay' would be vacuous, and the sentence would "feel" like 'In Carnelian Bay arithmetic is incomplete.' But it doesn't!" (pg 166).
I have no idea what King means when he says that the two sentences would "feel" the same. Furthermore, from what I understand, I think King has the example backwards. If propositions did not change their truth value over location, then wouldn't changing "In Carnelian Bay" with any other location (operator) result in "the same feeling" as the original sentence (instead of changing the proposition and keeping the location the same)?
For example, what King should have said is that if propositions do not change their truth value over location, then "In Carnelian Bay there is a boat launching ramp" (where the truth determining context lies in 'there is a boat launching ramp') would "feel" the same as "In the Sahara Desert there is a boat launching ramp". This poses much more of a problem because here the vacuous operator should not affect the truth of the proposition (being that the context of 'there is a boat launching ramp' stays with 'there is a boat launching ramp') but the truth value has obviously changed. I don't think, however, that in King's example the two sentences necessarily "feel" different.
If this line of thought is true, then it is an objection to (2) and the argument is no longer valid.
Now to address (3).
Again, King confuses me with the example that he uses. He says that he is in Santa Monica right now and when he says "I believe the sun is shining" it is about Santa Monica right now. From this he claims that if he were to change location or time, the proposition would still be about "Santa Monica at this time" and so would not change in truth value. I think King is either confusing two different propositions or is being lazy in his speaking. Technically speaking, when King asserts "The sun is shining", he is not asserting anything about Santa Monica; or at the very least that he is implying that the context he is in at the time he says that sentence is to be taken as part of the proposition itself (some kind of non-spoken magically attaching part). Basically, I think King is just trying to get away with being lazy when it comes to saying when you really meant when you expressed a proposition.
The proposition King actually said was: "The sun is shining".
The proposition King intended the listener to understand was: "The sun is shining where I am right now", or "The sun is shining in Santa Monica right now", or "The sun is shining in Santa Monica at 3:05pm", etc. etc. etc.
When you blur this distinction, but then claim that people are wrong to say that your belief is not about Santa Monica when you say "The sun is shining", you are just confused by your own vagueness (and laziness - which is not a bad thing because speaking would become lengthy, tedious, and robotic if we were to speak as precisely as is needed in order to avoid these shortcuts in meaning).
If this line of argument is true, then it is an objection to (3) and King's starting argument is invalid.