Suppose we want to claim that some class of sentences that are grammatically like those of straightforwardly fact-stating, representational, belief-expressing discourse actually have a quite different semantic function (and remember, this is going to be Weir’s line about mathematical sentences: where a fictionalist error-theorist sees a failed representation, or a kinder fictionalist sees a pseudo-representation made in a fictional mode, Weir is going to argue that mathematics isn’t in the business of representation at all). How then might we further explicate this idea of superficially representational claims which in fact have a different role?
One context in which such an idea has been developed and put to work is in the neo-Humean “projectivist” account of morals, modals, and the like, as nowadays particularly associated with Simon Blackburn. The root idea is that a judgement like ‘X is good’ doesn’t express a belief about how the world is with respect to some special property of goodness, but rather a sincere such judgement is keyed to the utterer’s attitude of approval of X. NB, it isn’t that the judgement is about the attitude; rather that it is semantically appropriate, other things being equal, to assertorically utter the judgment when you have the right attitude. Likewise, ‘E is highly probable’ doesn’t express a belief about the occurrence in the world of a special property of objective chance, but rather a sincere judgement is keyed to the utterer’s having a high degree of belief in the occurrence of event E. And so it goes.
But of course, the devil is in the details! The root idea here is equally available to the crudest expressivist: the hard work for the Blackburnian projectivist comes in explaining (a) why, despite the anchoring of the judgements in non-cognitive attitudes, it is still appropriate that they have the logical “look and feel” of cognitive judgements — i.e. can be negated, embedded in conditionals, and the like — and there’s related work to be done in explaining (b) why it makes sense to reflect “In my view, X is good, but I could be wrong” and the like. What distinguishes the projectivist from the crude expressivist is the sophisticated way in which he tries to explain (a) and (b).
Weir’s §2.I touches on the projectivist’s treatment of these matters — but in a way that I expect is going to be far too quick for those philosophers of mathematics (surely most of them!) who aren’t already familiar with a particular strand of contemporary debate that’s mostly conducted remote from home, in meta-ethics. In particular, Weir’s constrast between earlier and later Blackburn, and the role of the idea of non-correspondence truth in his later work, will probably mystify (well, I can’t say I found it at all clear or helpful, and I start probably knowing a bit more than many logicians about these things, having Blackburn as a colleague!).
And as well as the discussion going too quickly, Weir’s discussion of projectivism is oddly framed. The full title of the section is “Projectivism in the SCW framework”, and you’ll recall that in his §1.III, the so-called sense/circumstances/world picture is exemplified in the treatment of demonstratives and the story about how the situation represented by an utterance involving “that” is co-determined by the literal meaning (or sense) of the utterance and the relevant circumstances of utterance which make a particular thing appropriately salient. But that was a story about context sensitivity in fixing what state of affairs was being represented (it is still good old-fashioned representation that is going on). The new issues raised by projectivist stories about non-representational content seem, then, to be quite orthogonal to the issues about how we need to tweak Fregean semantics to cope with demonstratives.
OK: we have a story about what is happening in the use of sentences with demonstratives and another story about sentences with “good” or “probable” (or whatever else invites projectivist treatment), and in each case the story deploys concepts (salience, pro-attitudes, degrees of belief) which are not part of the thought expressed in the circumstances. But there the similarity surely ends. Needing circumstances to help fix what is being represented is one thing; going in for non-representational thinking is surely something else, about which we need a quite different sort of story than is provided within the confines of the SCW framework as introduced in §1.III.
Still, let’s agree that Weir’s (over?) brisk remarks serve to point up that there is possibly space for, though also problems attending, treatments of areas of statement-making discourse as non-representational. And that’s perhaps all we really need for now, given that Weir has already announced in his Introduction, p. 7, that he doesn’t want to offer a projectivist account of mathematical discourse. So let’s not get unnecessarily bogged down in worries about how best to develop projectivisms.
Though let me end this instalment with a very small protest about calling projectivism a species of reductionism (rarely a helpful label, of course). Projectivism “populates the world … with certain naturalistically unproblematic attitudes or relations between humans and objects”, and in so doing does away with the need to postulate problematic properties of goodness, chance or whatever. So, to be sure, projectivism reduces ontology — but, if we want one word to describe what is happening, we are eliminating the need for the supposedly troublesome non-natural properties.