(( This ended up very long -- apologies. ))
Having pressed that distinction I'm going to muddy the waters a bit. Quite a bit.
There's a certain way of speaking about sentences I find quite natural but have been agonizing over in my contributions to this thread. (I also find it a little surprising that no one has called me on it -- if tgw were still here, I think he would have.)
I have described the Liar as purporting to predicate falsity of itself but failing to. I posted comments along those lines several times, and each time I had to decide whether to bother about the little pedant on my shoulder chastising me: 'Sentences do not attempt, do not purport, and so on; a speaker uttering the sentence with assertoric force would be attempting or purporting, and so on.' This is not a minor quibble: Austin, for instance, claimed that it is the historical stating of a sentence -- the speech act which ordinary usage might pick out with words like "He asserts that ..." or "She is claiming that ..." -- which is true or false, not the sentence itself, and certainly not the meaning of the sentence.
Even if Austin's view strikes you, as I think it does most, as wrong, there is some appeal to the idea that a sentence can only be true or false relative to a particular occasion of (perhaps hypothetical) utterance, since what a sentence means, if it is not a tautology, is in quite obvious ways dependent to some degree or other upon those circumstances (of time, place, environment, and of course language), and for sentences involving indexicals or anaphora, as the Liar does, that degree might be considerable. But situation semantics is not my interest in this little post.
A natural thought is that, while it is the sentence itself that is the truth-bearer, we take asserting that sentence as a sort of prerequisite for the assertibility of judgments of truth and falsity. Thus, in telling a story, or reading aloud, or going over a witness's statement, we are not taken to have made an assertion, to have ourselves made any claim to truth, and so in turn the audience is not asked or expected to endorse what we say or not. Insofar as the speaker makes no claim, the audience is not asked or expected to either. Except when they are: you might repeat another's claim, neither explicitly giving nor withholding your endorsement, but to submit it to your audience's judgment. But then we have the original speaker's claim on the table, if not yours. Inverted commas may remove the assumption that the speaker is making an assertion, but leave intact the assumption that the original speaker was. -- But that's all on the side of assertibility, and it still seems clear that whether invited to or not, the hearer of an indicative sentence is always at liberty to judge it true or false; it's just that their judgment may be inappropriate or inconsequential.
And I'm finally getting to the point I actually want to raise: there is a way of talking about sentences that takes the sentence itself as its own speaker. 'What does this sentence here say?' 'What is question no. 3 asking for?' 'This paragraph claims just the opposite.' 'The sign says you have to wait here.' 'The instructions tell you what to do if it doesn't work.' There's even pleonastic speech:
As I went walking I saw a sign there
And on the sign it said "No Trespassing."
But on the other side it didn't say nothing,
That side was made for you and me. — Woody Guthrie
We can take all of this as just a casual way of talking to be analysed away: that to describe a sentence as "saying" something is just to say that it means what a speaker would mean if they spoke that sentence -- a kind of metonymy, in which we attribute to the sentence an intentionality that properly only belongs to the (perhaps hypothetical) speaker, as if the sentence "borrows" its apparent capacity to mean something from its (perhaps hypothetical) speaker, when in truth it's just a sound or a mark, an inert object.
But if we're also going to distinguish, as it seems we very often need to, between sentence-meaning and speaker-meaning -- between "what the words say" and what the speaker "meant by saying those words" -- we might begin to see the point of imagining the "borrowing" going the other way: when we mean something by saying some words, perhaps it is we as speakers who are borrowing the capacity of words to mean something, a capacity which we lack not being signs or symbols but persons. (We certainly produce signs and symbols, but if they have meaning, is it because we imbue them with what
we mean, or do we produce them because they already have meaning? Is what
we mean the same kind of thing?) There would be some sense, then, to the widespread persistence of idioms which treat sentences as their own speakers, despite everything else which tells us that this is plainly false.
Which brings us back around to the problem of semantic content and assertion. There is a sense in which we naturally read indicative sentences as asserting themselves. (Frege's original version of the
Begriffsschrift, if I recall correctly, had a "judgment-stroke", a symbol to indicate that an expression was being asserted, but later versions of the predicate calculus dropped it as unnecessary -- assertion is taken as built-in.) There is a natural reading of the Liar as saying that it's false, "saying" in some "full blooded" sense, asserting its falsity just as much as we would be if we sentient speakers were to assert, 'The sentence 'This sentence is false' is false.'
Bare unspoken sentences that implicitly assert themselves are quite handy for doing logic, of course. It's practically the whole point, to divorce what is said from the person who happens to be saying it; except when you can't, because of indexicals and anaphora, for instance, and then you need quite a bit more machinery than you get from Frege to start making sense again. But there is another point to looking at indicative sentences this way: an assertion is a
claim to truth. Who is to sit in judgment of that claim? The speaker is supposed, or assumed, to have already judged a sentence true, so if anyone is to judge the claim, it will have to be someone else; as the speaker, you have already cast your vote. What would be the point of you voting again, by endorsing your own claim? If you tried to pass off your vote in favor of the claim as separate from it, as an additional independent vote, you would be doing something illegitimate. Like everyone else, you get one vote, not two. Thus it is when a sentence makes semantic claims about itself. Sentences like 'This sentence is meaningful/meaningless' or 'This sentence is true/false' appear to be doing something which may be impossible -- cf. that a picture is (or isn't) an accurate representation of something cannot be part of that picture -- but I for one have a strong sense that it is at least illegitimate. The Liar has already cast the vote that all indicative sentences cast for their own truth; it does not get an extra vote to declare itself false as well.