The View that Vagueness is Merelya Kind of Ignorance

Why does decision theory look different on a purely epistemic understanding of vagueness? The thought, to put it in very broad terms, is that according to an interpretation in which vagueness is just a special kind of ignorance, there’s really nothing to distinguish decisions made under uncertainty about factual things, and decisions made under uncertainty about borderline things: borderlineness just is a kind of uncertainty about factual things according to that view.

In this chapter I shall focus on a precisification of the practical irrelevance thesis that, I think, does capture an important truth about the difference between our beliefs and desires about vague outcomes and about precise outcomes: while we can care intrinsically about the latter, it seems as though there's something incoherent about caring intrinsically about the vague.

To demonstrate what this might amount to, let us consider an example. Suppose Bob has the telic desire to be bald, and, for simplicity, let us suppose this is the only thing he cares about. He could have this desire in a number of ways—for example, he might have the desire derivatively in virtue of his having the desire to have no hairs at all. Let us suppose that this desire is not had derivatively, and is the strongest proposition about his head that he desires: Bob wants to be bald and any other epistemic possibility about the state of his head that he finds desirable is already entailed by his being bald.

Compare this with another case. Alice cares intrinsically about whether there is intelligent life elsewhere in the universe right at this second. Although Alice expects never to be able to know the answer to this question, I think that this kind of desire is still perfectly coherent. Perhaps Alice is a science fiction enthusiast, or assigns high value to worlds with more diversity and culture than worlds with less. Or perhaps she is a fundamentalist Christian, and disvalues possible worlds where humans do not occupy the role of being the sole bearers of intelligent life in the universe. Whatever the story, it seems like something it could be perfectly rational to care about (even if eccentric).

For simplicity, again, we may assume this is the only thing she cares about. Like Bob, she doesn't really care about other features of the universe. Let's also suppose that she's certain that if there is intelligent life, it's well outside the region spanned by her light-cone at any point in her life. Whether or not there is intelligent life out there is completely causally independent of her and is something she could never hope to verify. Nonetheless, she thinks that if there is intelligent life out there, that would be a pretty cool thing.

I think there are two kinds of reactions you could potentially have to these two examples.

Reaction 1.

It is not unnatural to associate the first kind of reaction with an epistemicist who thinks that vagueness is merely a matter of ignorance, albeit a special kind of ignor­ance. For the epistemicist, facts about baldness in borderline cases are not especially different in kind from facts about life in the far reaches of the galaxy. Since it is perfectly fine to care about things you are ignorant about—even when that ignorance is impossible to remove—there is no distinctive reason why we could not care about whether a borderline case of baldness is bald or not.

The second kind of response is naturally associated with supervaluationists and other theorists who think that in borderline cases, there simply is no fact out there to be known, and no fact worth caring about. Propositions about life in the galaxy are different, since, while they are like borderline cases in the sense that they are unknowable, there is still a fact of the matter out there which one could reasonably care about. For this latter kind of theorist, Alice's desire is perhaps a little eccentric, perhaps even irrational in a loose sense, but it is not incoherent.

This observation is intended to help us with the problem we raised in chapter 8. If epistemicists and other ‘factualists' think that vagueness is just a matter of uncer­tainty, then what is this extra thing, beyond uncertainty, that those who deny the factual nature of borderline cases think these cases involve? According to the theory I'm advancing, that difference is articulated by two further theses: (i) there cannot be rational differences of opinion that are solely differences of opinion about the vague and (ii) you shouldn't care intrinsically about the vague. The thought, in both cases, is that if vagueness amounts to nothing more than uncertainty, then there would be no reason to think there couldn't be rational disagreements about purely vague matters, or to think that one couldn't care intrinsically about vague matters. There is no general reason to think that one cannot disagree or care intrinsically about things we are uncertain about, so these two principles give us two ways in which vagueness amounts to more than the presence of uncertainty.

The first principle was formulated precisely in terms of the supervenience of vague on precise beliefs in chapter 8, and was defended there. We shall spend the rest of this section sharpening and defending the second claim.

Before I do that, it will be worth noting that the conjunction of (i) and (ii) have fairly drastic decision-theoretic consequences. For a view in which vagueness is merely the presence of uncertainty—i.e. an account in which neither constraint (i) nor (ii) are accepted—vague beliefs and desires, far from being epiphenomenal, can play a fairly concrete, even surprising, role in informing our actions. The cases that most starkly demonstrate this are cases which have the following structure. Suppose there are two rational agents, Alice and Bob, such that:

1.        Alice and Bob have exactly the same evidence and assign the same credences to every precise proposition.

2.        Alice and Bob have exactly the same desires (their utility functions are identical).^[CXLIV]

3.        Alice and Bob are in a position to make exactly the same propositions true.

If we accept both (i) and (ii), then it is pretty straightforward to show that Alice and Bob must assign the same V -values to all propositions, and thus make the same proposition true if they are rational (assuming, for simplicity, that there are no ties).

Alice and Bob are in an auction house and they are both bidding on a relatively inexpensive vase which is a shade of turquoise that is borderline between being blue and green.

Now suppose we know the following things about Alice and Bob. Firstly, they have exactly the same telic desires and have the same credences in the precise propositions. We also know the following facts. (1) As it happens they are both very peculiar people and they care intrinsically about owning green things. (2) Although they both know exactly what precise shade the vase is, Alice is more confident than Bob is that the vase is green.

The scenario described violates both (i) and (ii): it requires that Alice and Bob care intrinsically about the vague and that they disagree to some degree about whether the vase is green, even though they know the relevant precise facts such as its exact shade.

In the above scenario it is clear that Alice should bid more than Bob for the vase. Since they care about the same things, its value is the same for both Bob and Alice. However, since they know that it is borderline whether the vase is green, they are uncertain whether it is green and, therefore, the purchase is a gamble on its being green. However, according to Alice's subjective credences the odds that it is green are better than they would be according to Bob's. Therefore, Alice ought to outbid Bob.

On the proposed view the kind of scenario described above requires Alice and Bob to have deeply irrational preferences, and at least one of Alice and Bob to have incorrect credences. On the other hand, the scenario would be permitted on the ‘mere uncertainty' account of vagueness. According to that kind of factualism about vagueness, one can reasonably disagree about a proposition, even given all the relevant precise evidence, and, moreover, one can care intrinsically about the vague.

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