The projectivist’s root idea is that a judgement that “X is G”, for a predicate G apt for projectivist treatment, is keyed not to a belief that represents X as having a special property but to an appropriate non-cognitive attitude to X. But what does being “keyed” to an attitude amount to? Well, for a start, there should be a basic preparedness to affirm X is G when one has the right attitude. But, as we noted, the projectivist wants to put clear water between his position and that of the crude (strawman?) expressivist for whom the judgement is no more than a “snapshot” evocation of the speaker’s current attitudes. So the projectivist will want to complicate the story to allow what Weir calls “correctional practices”, where snap judgments are allowed to be corrected in the light of thoughts about the judgements of others and oneself at other times, thoughts about how attitudes might be improved, etc.
Weir is pretty unspecific about how the story about correctional practices is to work out in detail, even in the case of “tasty”, which is rather oddly his favourite replacement for “G”. Maybe his reticence about the details is not so surprising given his choice of example: for I rather doubt that there are enough by way of correctional practices canonically associated talking about what’s “tasty” to makes ideas of “correct judgement” robustly applicable here. But still, I’m willing to go along with Weir’s general hope that there are might be other cases where projectivism works, and so (i) can illustrate how anchorage in “snapshot-plus-correctional” practices can be meaning-constituting for “X is G”, (ii) without giving the judgement realist truth-conditions, while (iii) imposing enough discipline to make it appropriate to talk of such a judgement being correct/true (at least in a thin enough, non-correspondence sense).
As I said before, I doubt that Weir’s discussions will do enough to really help out those philosophers of maths to whom the idea of projectivism is (relatively) new. But in this section he goes on to offer another purported illustration of how we might get a (i)/(ii)/(iii) story to fly, this time in a context which will probably be a lot more familiar to logicians, i.e. the treatment of discourse about fiction.
Thus consider Weir’s example ‘Dimitry Karamazov has at least two half-brothers’ in the context of discussion of Dostoyevsky’s book. He suggests (as a first shot at describing the relevant “snapshot dispositions”)
It is constitutive of grasp of ‘Dimitry Karamazov has at least two half-brothers’, in the context of discussion of a given English translation of The Brothers Karamazov, that one sincerely assent (if only ‘privately’) to the sentence iff one believes that the sentence ‘flows from’ the translated text.
Here ‘flows from’ is to be elucidated in turn roughly (again, as a first shot) along the lines of “what experienced readers would, on reflective consideration, judge must form part of the story if it is to make overall sense”, and this gives us a role for “correctional practices”.
I’m not sure why Weir relativizes to a particular translation, which seems unnecessary; but let that pass. And “must form part [sic] of the story” must mean something like “must belong to any sensible/natural filling out of the story text”, which raises more problems which we’ll let pass too. But the root idea, at any rate, is that (i) the sketched “snapshot-plus-correctional” story means that that (ii) when we say ‘Dimitry Karamazov has at least two half-brothers’ we are not representing D.K. or expressing truths about the real world (not even truths about what is written in a certain book), nor indeed expressing truths about some other world (whatever that quite means) but are going in for a different kind of speech-performance, as it were a going-along-with a bit of story-telling. But the framework in which we do this is not subject merely to our creative whim (after all we are not Dostoevsky, who is more entitled to carry on just as he wants!) but is constrained enough for us to be able to talk of (iii) correct and incorrect ways of going along with the story-telling.
I don’t myself have decided views about discourse about fiction, and don’t know whether this line is a “best buy” (indeed Weir himself raises some issues). But it does serve, I think, to give us a case where it seems that the (i)/(ii)/(iii) schema can be filled out in a prima facie plausible way, without tangling with the special problems of projectivisms. So that’s a plus point. The attending minus point, I suppose, is that the more you like this account of the semantics of discourse about fiction, the more tempted you might be to recycle it to serve the ends of a fictionalist account of mathematics. So why does Weir after all prefer “neo-formalism” to a brand of fictionalism? We’ll have to see …!