I thought I had a “Eureka!” moment on the weekend – suitably enough in a bathtub – but it probably wasn’t that big a deal.

Where we left off last time was trying to find a way to define vaugeness using theories whose only distinctive resources operated at the level of sentences rather than words. For instance, the epistemicist only has the distinctive operator “Is knowable (in the right kind of way)” and, at this stage, all I’ve got is the “Is as true as 0=0” and “Is less true than 0=0” operators, and they only apply to sentences. But we really want to know what _words_ are vague.

I was trying one or two fancy tricks when something very simple hit me. Let’s say that the meta-language (and ideally the object language) are partially Lagadonian, so they include entities, truth values, worlds and times (and functions built recursively from these) as names for themselves. And let’s assume (because it’s true) that these objects are not themselves vague. And remember from last time we’re still assuming, as good Montagovians, that every term denotes something. (Either an entity, or a truth value, or a world, or a time, or a function composed of the above.) Now consider the metalanguage sentences:

bq. (V) _t_ denotes L

where _t_ is a term and L is a self-naming object.

I make the following bold conjecture. For any _t_ if there exists an L such that (V) is indeterminate (however you interpret indeterminate on your preferred theory of vagueness) then _t_ is vague.

It looks all so simple, and it probably is, but I think it’s a nice move forward. Here are the things we might still worry about.

1. Is the determinacy operator defined in the extended language that includes self-naming objects?
I guess it is. Why wouldn’t it be? It would be nice to have an argument that it is though.

2. What will you do if the Montagovian assumptions turn out to be wrong and ‘very’ or ‘and’ don’t denote anything?
Panic. Hopefully at ground level because panicking at the top of St Rule’s tower could have bad consequences. Seriously, if ‘very’ and ‘and’ don’t denote something like a function, I suspect it will be very hard to give a reductive account of what it is for them to be vague.

3. Are you still thinking Fieldian/Quinean indeterminacy is just a variety of vagueness?
Yes. It would be hard work to qualify the bold conjecture in order to not have that as a consequence. And because of the ‘lumpy’ cases I don’t think it would be worthwhile.

4. Is ‘very’ vague?
Don’t know, though Daniel suggested a nice argument for it being vague. One’s prior probability that it is vague must be high, for the general metaphysical reasons that we think terms are normally vague. So conditionalising on evidence, like “There’s the North Sea” produces a high posterior probability that ‘very’ is vague. And we should believe things with high posterior probabilities. Daniel may have meant this argument somewhat flippantly.

The main thing that worries me about this move is that it is too simple. I was hoping to write a long paper on what it is to be vague, something that made me look deep and profound, but now I look like someone who believes in simplistic technical answers to substantive philosophical questions. C’est la vie.

Having said that, there is a lot to be written about a) why previous definitions are no good, b) whether this use of Lagadonian languages is permissible, c) whether I need an indeterminacy/vagueness distinction, d) whether this definition yields support for one or other substantive theories of vagueness, e) whether we can use the definition to tell whether ‘very’ really is vague or not, and f) whether this means that Trenton Merricks was right back when he said that semantic theories of vagueness turn out to be metaphysical theories of vagueness when you push them hard on their preferred metaphysics of representation, and hence whether I was wrong to criticise him over that argument. So that looks a bit like a possible paper plan, and not necessarily a superficial one, I hope.