The introductory sketch in the last post reveals at least this much about Weir’s neo-formalism: it is the marriage of two independent lines of thought.
One idea — call it “formalism about arithmetical correctness” — is that, at a first approximation, what makes an arithmetical claim correct (and we’ll stick for the moment to the example of arithmetic) is something about what can be done in a some formal game(s) played with uninterpreted tokens.
To introduce the other idea, let’s first say that the content of a claim C is transparently representational when what we grasp in grasping C is just its correctness condition according to our best explanatory metaphysical-cum-semantic theory. Thus, plausibly, in grasping “cats are mammals” we grasp what best theory surely will say is its correctness condition, i.e. just that cats are mammals. But it isn’t like this, according to Weir, for arithmetical claims. Here, the suggestion goes, the content of a claim, as grasped by an ordinarily competent speaker, falls short of the thought that its correctness conditions are satisfied (which the formalist takes to mean: falls short of a thought about what can be done in the relevant formal game). Here, then, the content is not transparently representational; so call this the idea that arithmetic has “NTR content” for short
Both ideas need to be embroidered in various ways to give us a decently worked through position, and Weir offers his versions, about which more anon. But the first point to make is that these plainly are two quite different basic ideas and their further developments will be very largely independently of each other. You could buy Weir’s line on one without buying his story about the other.
For example, if you are a modal structuralist, who gives a quite different account of the correctness conditions for arithmetical assertions, you might — very reasonably — also want to say that the content of the ordinary arithmetician’s claims doesn’t involve concepts of possible worlds or whatever. In other words, although no formalist, you might very tempted to embrace some story about how arithmetic content is not transparently representational (again holding that what is grasped in our ordinary understanding of an arithmetical claim falls short of grasping what makes the claim correct, according to your preferred story). So you might be interested to see whether you could borrow themes from Weir’s story about NTR content. Alternatively, of course, you could embrace something like Weir’s formalism about correctness while not liking the way he spins his account of NTR content.
So we’d better clearly disentangle the two themes. We’ll turn to “formalism about arithmetical correctness” in later posts. Here let’s begin to consider how Weir handles the idea of NTR content.
Weir’s first two chapters are supposed to have softened us up for the viability of this idea. For recall, he has given three examples of cases where, it seems, the idea of NTR content looks appealing. First, and least controversially, there is the case of assertions involving demonstratives: “that animal is a mammal”. Here the story about correctness (in such a case, correctness is plain truth in almost anybody’s book) will talk about the most salient animal given contextual indications (pointings etc.) But what the ordinary conversationalist grasps surely isn’t a thought involving the concept of salience, etc. Second, and much more controversially, there’s the case of assertions supposedly inviting a Blackburnian projectivist treatment, e.g. moral claims. Here the story about correctness (and perhaps correctness can be thought of a matter of truth again, if we are sufficiently minimalist about truth) will talk about appropriateness of attitudes: but the content of a moral claim is not a thought about human attitudes. Third, Weir considered claims made in elaborating a fiction: “Holmes lived less than five miles from the Houses of Parliament”. Here correctness (‘truth in the fiction’, perhaps) is keyed to what experienced readers would, on reflective consideration, judge must belong to an elaboration of the Holmes stories if everything is to make good enough overall sense. Again the content of the claim about Holmes, on the lips of a casual conversationalist, is not plausibly to be said to involve ideas about the coherence of a fictional corpus.
OK. But let’s note again, as I’ve noted before, that these are three very different stories about instances of NTR content. We might say that, in the demonstrative case, the content — though not fully transparently representational — is still partially representational: the claim “that animal is a mammal”, in context, aims to represent the world as it is. But a projectivist will say that moral judgements, by contrast, are in a different game from representation, they get their content from the practical business of encouraging and coordinating attitudes. As for fictional claims, they aren’t representational either, but are articulating a make-belief.
So: a claim can fail to be (fully) transparently representational because it is representational but part of the representation has to be supplied by context; it can fail because it actually isn’t primarily in the game of representation at all; or it can be fail because it is only pretending to represent. But that’s not the end of it. Here’s another sort of case which Weir doesn’t mention. On a plausible metaphysical view, it is correct to say of something that it is green just if it is disposed, in normal viewing conditions for things of the relevant kind, to produce a certain characteristic response in normal viewers. But again, it seems wrong to say that the ordinary speaker, in grasping the content of “grass is green” is grasping a thought about dispositions or normal viewers. (To use a favourite style of argument of Weir’s, Alan can believe that grass is green without believing that grass is disposed, in normal viewing conditions, etc. etc.). So, “grass is green” also has NTR content. But it isn’t that “grass is green” is non-representational or is only pretending to represent: rather, it represents, but in a foggy way (that doesn’t transparently yield correctness conditions). It seems apt to echo here Leibniz’s talk of “confused ideas”.
The question, then, for Weir is this. Let’s grant him the idea that (in our terminology) some claims are not transparently representational: their sense peels apart from their explanatory correctness conditions. But the divorce can arise in various ways. Weir himself distinguishes three model cases; we’ve just added a fourth. So which of these models, if any, is the appropriate one when it comes to elucidating the idea that arithmetical claims have NTR content?
To be continued …