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 …!
3 thoughts on “<em>TTP</em>, 7. §2.II Snapshot dispositions, correction, fiction”
“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 …!”
Indeed! I probably don’t say enough in the book. The most obvious mathematical analogue of the view sketched on fiction (which isn’t Field’s ‘fictionalism’ at any rate) would be to say that a mathematical sentence is true if it appears in the mathematical corpus (textbooks, journal articles etc.) or can be deduced from such a sentence. But then lots of falsehoods will come out as true, since there is a rich and abundant history of incorrect proofs many of them of falsehoods. If the mathematical domain in question is sufficiently well axiomatised, these pseudo-theorems may will be inconsistent with the axioms, but then on this view the whole domain fails to generate a body of truths, at least on a non-paraconsistent view of derivability.
One might revise the theory to say something like: only what is deducible from those items in the canonical texts marked as axioms is true. But now we can ask, what do mathematical sentences mean then? Are they elliptical for [if AX then S] for some axiom set AX? Then we have deductivism, and I say a few standard things against that in chapter four §II.1. If the appeal to provability from axioms is not part of the sense or literal content, then what relation does this content have to what we understand when we grasp the sentence?
If you answer this by moving to something like my informational content/metaphysical content distinction, then this is neo-formalism I’d say (though of course the precise title doesn’t matter much). And you have a whole bunch of question to answer: what counts as proof? What about formally incomplete theories? Are proofs abstract objects- whence the advantage over platonism then? If not what are they? How do you specify their structure, prove general facts about them? What about sentences in complete theories where most of the proofs are far too long for any human to grasp or write down?
The book attempts to answer these sorts of questions; if it left them to one side with an appeal simply to a generalisation of the above idea about fiction it would be a lot shorter! But wholly inadequate to the task surely.
As you say, I’m not sure about this view about fiction myself, but I like it, I think it would be good if it worked- being averse to some at least of the alternatives such as Meinongianism. And I wanted to try to provide a few examples of non-representational modes of assertion outside maths which seemed workable because it seems to me the position in maths is more plausible if it is part of a general approach which seems to be of value elsewhere.
On translations of books and Aidan’s point- the Cockney translation of TBK isn’t the one I have or I probably wouldn’t understand it! But I agree something could be true of one translation and not another. There’s a more basic point too: the ‘snapshot dispositions’ of (most) English readers with respect to the original Russian text (actually that is not a clear-cut entity either, as with lots of literary works) won’t settle on any judgements since they won’t understand the text.
The relativization to a particular translation does seem right to me, though perhaps it’s not needed for the particular example given in the quote from Alan. Apparently the most widely read translation of TBK has certain characters speak in Cockney English. Any sentences capturing their dialogue presumably won’t ‘flow from’ the text of any other translation. Generalizing, it seems that if acceptable translations can differ dramatically and we don’t relativize, then it becomes too demanding a requirement on sincere assenting to a sentence that one believe that the sentence flow from the text.
Ps. I’m very much enjoying following along this discussion, even though I haven’t yet had a chance to read Alan’s book, so many thanks.
That seems right: it will vary with the sort of judgement we are making what the implicit context is (any version of TBK, this translation by Pevear and Volokhonsky …).