Testing the Characterisation

We’ll conclude this chapter by seeing how well the characterisation that I’ve given deals with the test cases that have come up over the course of this chapter. Before we start, it’s useful to notice that, since we only have a necessary condition for vague-ness so far, the most our characterisation can be asked to do is to correctly predict as many precise expressions as possible to be precise, and to correctly identify any vague expression as satisfying a necessary condition for vagueness — we don’t have the resources to outright judge any expression to be vague given this characterisation alone.

The characterisation I’ve offered won’t predict that ‘early thirties’ is precise: al-though it will say that we could expect stable lines to be drawn by speakers between those to whom it does apply and those to whom it doesn’t (when looking at people just over thirty and just under), the fact that there are no such stable lines when looking at older people still means that ‘early thirties’ satisfies the necessary condition given.

This isn’t enough to predict that it’s vague, but that isn’t the aim of the characterisation as it stands.

In contrast, it will predict that ‘child*’ is precise, since there’s a stable way of di-viding up all cases into children*, non-children* and any others. There could well be a diversity of answers among speakers about the status of people who are between

17 and 18, but this is accounted for by how broadly ‘other’ is interpreted. It therefore seems that this characterisation makes the correct prediction.

What about borderline categories? When we have a vague term like ‘steep’, is ‘nth-order b‘nth-orderline case of ‘steep’’ vague for any (or indeed all) n? It’s difficult to answer these questions directly because the notion of a ‘borderline case’ is ambiguous, and, as I pointed out earlier, ambiguity can interfere with speakers’ judgements in a mislead-ing way. So let’s try to refine the question. Is ‘nth-order epistemic borderline case of

‘steep’’ vague for any n? In our terms, this amounts to the following question: would competent users of ‘can be known to be steep’ (and/or ‘can be known to be knowable to be steep’ and/or ‘can be known to be knowable to be knowable to be steep’, and so on) make stable sets of judgements about successively steeper objects, which divided them into those ones which could be known to be steep (or known to be knowable to be steep, and so on), those which cannot, and any others? It seems unlikely for any of the terms in question: each of them seem clearly applicable to some cases (Blake Street, for one) and clearly not to others (West Street, say), yet it’s hard to see where speakers could identify a point at which they all felt too uncomfortable to outright judge cases to be knowable (or knowable to be knowable, or. . . ). So ‘nth-order epistemic border-line case of ‘steep’’ looks like it satisfies our necessary condition for vagueness for any n we like. We get the same result for semantic interpretations of ‘borderline case’, too

— consider what happens when you replace ‘can be known to be’ and ‘knowable to be’ with ‘can truly be said to be’ and ‘truly described by’, for example.

An interesting observation we can make on this theme is that, for any vague term, speakers will never identify a stable ‘other’ category in the ordering that’s relevant to a vague term. This is trivial in the case where no speakers identify any objects as

‘others’. When some speakers would identify some objects as ‘others’, if they were to stably identify some particular set of objects as ‘others’, this would also amount to them stably picking out all the objects to which that term applied, and all of those to

which it didn’t, and so the term wouldn’t be vague after all. This seems to explain why vague terms exhibit the appearance of ‘higher-order vagueness’ described in the previous paragraph: for the apparent higher-order vagueness in this sense to be ‘cut off’ at some order, there would need to be a stable ‘other’ category drawn by users of vague terms.

It’s worth noting that we haven’t just demonstrated that vague terms also all satisfy a necessary condition for exhibiting higher-order borderline vagueness. In chapter 1 I distinguished between this sense of higher-order vagueness and higher-order vague-ness in the sense of the apparatus we use to describe vague terms (and so the term

‘borderline case of’ and its iterations) itself being vague. Since we’re not endorsing the assumption that all vague terms have borderline cases, even if ‘nth-order borderline case of ‘steep’’ is vague for all n, this doesn’t allow us to infer that ‘steep’ has nth-order borderline cases for all n, and so we need only have the necessary conditions satisfied for the second, weaker, sort of higher-order vagueness.

Let’s finish with a word about theory neutrality. The shift in focus that we’ve been making use of (from ‘meaning’ to ‘use’) allows us to keep things theory neutral. From an epistemicist perspective, the ‘meaning’ counterpart that we might construct from the ‘use’ characterisation that we’ve arrived at, (presumably) that there’s no correct way to sort objects into those to which a vague expression applies, doesn’t apply, or has some other relation, is a non-starter. But the characterisation we’ve arrived at does better than this in that it’s consistent with epistemicist, as well as non-epistemicist, views, while not entailing either.

3 Conclusion

This chapter has extracted some key elements from some promising characterisations of vagueness (focusing on Eklund and Horgan’s in particular), and has improved on

some of the flaws of each, culminating in a new necesary condition for vagueness. I’ve shown why I don’t take this to be a sufficient condition (while gesturing towards a way to get one), but have shown how the necessary condition itself deals with the problem cases presented in this chapter. In the next chapter, we’ll see that this characterisation, while theory neutral, can lead to surprising results.

Chapter 5