Sentence Tokens and Truth Conditions

I'm still reading Smith's book (Language and Time), and I've noticed that Smith, along with everyone he's critiqued thus far, makes an assumption about the truth conditions of sentence tokens that, frankly, seems false to me.

First, let me explain what a sentence token is. Consider the sentence "It is raining" uttered on two separate occasions. In the first instance, Bob utters "it is raining" at 2pm EST in Peoria, Illinois; in the second, Sally utters "it is raining" at 8am in Lihue on the island of Kauai. Each is an utterance of the same sentence type because it consist of the same string of words; nevertheless, each is an utterance of a distinct sentence token. So in these two instances we have two sentence tokens of one sentence type, namely, "it is raining."

Now, if you were able to follow that, then you should also be able to see that the two sentence tokens, uttered under the specified circumstances, would normally differ in meaning. The first would seem to say

(1) It is raining at 2pm EST in Peoria, Illinois.

whereas the second would seem to say

(2) It is raining at 8am EST in Lihue, Kauai.

Now, the assumption that Smith and nearly everyone else working in the philosophy of time make is this:

(3) A sentence token uttered at time T and place P is true if and only if what the sentence asserts is true at that time and place.

What (3) implies is that Bob's utterance of "it is raining" is true only if (1) is true and Sally's utterance of "it is raining" is true only if (2) is true. Thus (1) and (2) give the truth conditions for Bob's and Sally's utterances, respectively.

This seems mistaken to me. Here's why. When we consider what a particular sentence token means, we not only take into account the spatiotemporal context of the utterance, but we also factor in what we make of the doxastic (i.e., belief) state of the speaker. And if we don't think the speaker is accurately cognizant of the spatiotemporal context of the utterance, then we shouldn't pack information about that spatiotemporal context into our interpretation of the utterance.

For example, if a two-year old child utters "it is raining" at 2pm EST in Peoria, Illinois, it seems to me quite implausible to assume that the child means (1), for the child may have only the vaguest of ideas (or even wildly wrong ideas) of the time and place. But if the child doesn't mean (1), then (1) does not give the truth conditions of that sentence token.

Here's a starker example. Suppose that Bob, while uttering "it is raining" at 2pm EST in Peoria, Illinois, is under the spell of a powerful hallucination that has him utterly convinced that he is in Lihue, Kauai and that the time is 8am. On those assumptions, when Bob says "it is raining" what he means is (2), not (1). Hence (2), not (1) captures the truth conditions of Bob's utterance.

Summing up, (3) is false because it assumes that information about the speaker's doxastic state is irrelevant for fixing truth conditions. But such information is not irrelevant. What is meant by a given sentence token is controlled more by the speaker's beliefs than it is by the de facto context of utterance.