# TTP, 11. Disentangling neo-formalism

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 …

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### 2 Responses to TTP, 11. Disentangling neo-formalism

1. Alan Weir says:

As with TTP10, this nicely sets out something pretty close to my position. I’d make just a couple of qualifications or expansions.

Minor elaborations: i) where you say ‘in such a case, correctness is plain truth’ and talk of ‘truth in fiction’, I, as a fully-fledged deflationist would prefer to say truth is always plain, as it were. But I explicitly argued (pp. 42-3) neo-formalism is not wedded to full-blown deflationism, mild deflationism would be enough, perhaps indeed a correspondence theorist could adopt the view by holding her nose when ‘truth’ rather than correctness is used. So though I wouldn’t phrase things that way, I take it be a way of thinking compatible with neoformalism.

ii) Similarly I don’t use morality as an example in the discussion of projectivism because I’m not a projectivist about morality but am about taste, (p. 39 fn 1); but I think the particular examples one uses doesn’t matter.

Indeed I probably shouldn’t have let my partisan support or rejection of particular metaphysical views intrude here because, as you say, my strategy is to ‘soften’ you all up for the idea that there is a distinction between transparent sense- ‘informational content’- and something less transparent, metaphysical content, which determines truth conditions. The strategy was to try to find a varied menu of plausible examples where as many philosophers as possible will find some subset plausible. So for that reason I probably should have included anti-realism about colour and secondary ‘qualities’, and not excluded it because, as it happens, I’m rather ardently realist about them and ‘secondary’ qualities, or better concepts, in general.

Finally two more substantive points, firstly on ‘non-transparently representational’. I agree that ‘that animal is a mammal’ though having non-transparent metaphysical content, ‘explanatory correctness-conditions’ in your terminology, is (at the least) ‘partially representational’ whereas ‘Schoenberg’s 12-tone music is execrable’ is, on my version of projectivism, not. Degrees of representationality perhaps make sense but for me the more important issue is that of ontological reduction (Chapter Two esp. Section III pp. 56-64).

The account I sketch of fiction is reductionist because a metatheory which explicates our understanding of fictional discourse does not entail Sherlock Holmes exists, indeed is, I claim, compatible with its denial. There is nothing comparable with regard to demonstratives and the divergence between informational and metaphysical content there. Similarly projectivism about aesthetics is reductionist because in the metatheory which explains how the sentence about Schoenberg’s music is true we are not committed to there being a property of being execrable applicable to the music, indeed it is compatible with denying the existence of such a property whilst affirming the existence of entities such as acoustic properties.

In like fashion, then, an anti-realist reductionist about colour, for me, puts forward a theory which explains how ‘the tomato is red’ is understood, what its ‘makes-true conditions’ are, how they can be satisfied, without commitment in the metatheory to redness as something instantiated by tomatoes; indeed in the truly anti-realist case whilst denying in the metatheories that tomatoes are red though affirming the existence of reflectance properties vis a vis various wavelengths of light etc.

But I don’t understand how such a view attributes a confused idea to those who understand ‘red’, even realists (but then I’m not a Leibnizian). If John and Iain both say ‘Schoenberg’s music is execrable’ and ‘that tomato is red’, and John is an anti-realist (of my reductionist sort) about aesthetics and colour, Iain a realist about both then, if John’s theory is right, Iain will be wrong, confused if you like, philosophically. But the ‘linguistic phenenomology’ of utterances of the two sentences, the phenomenology of the judgements thought by using those sentences, will be the same for both.

So I don’t see ‘colour’ for the antirealist being a ‘confused idea’. Not in the way, e.g. if I have some idea of what a recursive function is, but am unable to see the distinction between such functions and recursively enumerable ones, despite your attempts to enlighten me; that’s a case of having a confused idea, at least in a fairly straightforward sense of the term, surely.

• Peter Smith says:

Re your (i), I meant — and have now corrected to — “in this case, correctness is plain truth in almost anybody’s book”. For myself, I’m with you on deflationism. I’ve been talking hereabouts of “correctness conditions” rather than “truth conditions” not because I’d want to draw a distinction (at least where assertions in some pretty minimal sense are in question) but because others might. And as you say, we needn’t get too entangled with that potential dispute with others. Agreement!

(ii) But now disagreement begins. I suggested, as another example where there is a gap between sense (informational content) and explanatory correctness conditions the case of colour talk, on a certain view. It is perhaps instructive that you call this “anti-realist reductionist”. In fact I had in mind the thumpingly realist view of colours as roughly dispositions to engender certain neural responses in typical humans under typical conditions (which I defended in PASSV 1987, when the world was young). Redness, on this view, is a perfectly real physical dispositional property, and is well instantiated by ripe tomatoes. But of course, speakers don’t conceptualize it like that, but deploy a merely recognitional concept; in your terms, there are dispositions to make snapshot judgments in certain perceptial circumstances and to allow some minimal correcting procedures. But that’s all the speaker needs to grasp.

Leibniz would have said our ideas of colour are “clear” (we know one when we see one!) but “confused” (its analysis isn’t transparent). Our concept of a thing

is confused when I cannot enumerate one by one the marks which are sufficient to distinguish the thing from others, even though the thing may in truth have such marks and constituents into which its concept can be resolved. Thus we know colours … and other particular objects of the senses clearly enough and discern them from each other but only by the simple evidence of the senses and not by marks that can be expressed. [Loemker, p. 291.]

But I guess it was/is unhelpful to casually allude to Leibniz’s way of talking as I did: sorry to have put you on the wrong track! Let’s be clear then: the issue isn’t one of confusion in an ordinary sense, but an issue of ignorance. To put it at its very crudest, someone who understands ‘triangle’ (or ‘mammal’) will ipso facto be in a position to have something to say about what triangles (or mammals) are; someone who understands ‘red’ will struggle to do better than ‘something is red if it is like that‘. But this doesn’t mean that claims about redness aren’t in the business of representing the world: just that the representation ‘red’ isn’t very richly informative, and so(?) won’t appear in a decently explanatory story about what’s going on.

(Or something like that. It’s not that I have a really worked out story about this sort of thing. But I do think that it is pretty evident — if we are going in for the game of giving explanatory correctness conditions at all, as you want to — that we will want to allow for cases where the explanatory correctness conditions for a claim that is in the business of representation go beyond what is grasped in grasping the representation. And not because there is, as it were, a “gap” that needs to be filled by context (as with the demonstrative), but because the representation is too thin to feature in explanatory theory. The colour case was just an example of this sort of case that appeals to me. But I don’t want to rest too much on the example, as opposed to the thought that there are such cases. Anyway …)

In your example of the pair of claims ‘Schoenberg’s music is execrable’ and ‘that tomato is red’ I’d agree that the ‘linguistic phenenomology’ of utterances is much the same. But that, I’d say, is quite consistent with giving a projectivist story about the first and the sort of story I was alluding to about colour for the second. The first is in the non-representational business of expressing an attitude, the second (on the story in question) is representing how things are, representing a dispositional property there in the physical world, but in a not-very-rich way. (Part of the projectivist’s non-trivial task is to explain, of course, how the linguistic phenomenology in the expressive and the representational cases can be much the same, despite the big metaphysical difference.)