Caring about the Vague

One might take exception to the Indifference principle on the grounds that there are phenomena that on the face of it seem closely related to vagueness, yet where it seems as though there’s absolutely nothing wrong with caring in these cases.

I think in this case it’s tempting to turn the argument on its head. To my mind, this makes for a fairly compelling argument that truths about the future are not indeterminate, they are just epistemically inaccessible. Certainly, either there will be a sea battle tomorrow or there won’t, and we do not know which, but that surely does not mean that there is no fact of the matter. The fact that it’s perfectly rational to care about which outcome will obtain seems a reason to think that there is a fact of the matter for us to care about. Also, unlike in the case of vagueness, we do know some truths about the future—I know what I’m having for dinner tonight, and lots of

³ Once we assume that each cell is uncountable, the preceding argument would need to be formulated more carefully, in terms of integration.

other mundane facts about the near future. If we combine this observation with the fact that we can care about the future, the analogy between the future and borderline cases quickly dissipates.

Other objections in a similar vein I think represent a misunderstanding of the Indifference principle.

Let us consider a (highly idealized) sorites for happiness: suppose that you are going to give me a portion of a cake, measured in grams. If you give me a 1g crumb of cake, I will not be happy, whereas if you give me a large 200g slice, I will be happy. Keeping other variables relevant to my happiness fixed, there will be some amount of cake in the middle such that it is borderline whether I'd be happy if you gave me that much cake. Since it is borderline whether I'm happy in these scenarios, I don't know whether I'm happy when I get that much cake. Now consider two epistemic possibilities in which I receive that borderline amount of cake and which differ only in that in one I'm counted as happy and in the other I'm not. It seems to me that since I am receiving exactly the same amount of cake in both scenarios, and ex hypothesi the other factors relevant to my happiness are fixed, it would be bizarre to think that I should countenance a difference in value between the two cases. Happiness is not something you can directly pursue; it is a side effect of pursuing more specific things, and it is those things that you should care intrinsically about.

It is worth stressing that Indifference is for this reason a substantive postulate.

It is also worth emphasizing that the putative counterexamples to Indifference do not rest solely on judgements about what it is permissible to care about. They rest, rather, on the conjunction of those judgements with judgements about which propositions are precise. But we have seen that the naive, pretheoretic notion of precision should not be the target of our theorizing (an issue we will return to, especially in section 12.2), and we have also suggested that precise propositions are rarely expressible by sentences of a natural language. One might wonder how we can properly theorize about precision without mooring it to those pretheoretic judgements, or to the sorts of things we can express in language. This is exactly where Indifference helps—it pins precision down by its role in thought. Once you have figured out which things it is permissible to care about, it is possible to figure out which propositions are the precise ones. We will give a precise recipe for doing this in chapter 13, but for the purposes of this discussion it suffices to note that theses concerning what it's permissible to care about may lead to interesting theses about which propositions are precise.

Some predictions of the Indifference principle apparently conflict with other aspects of the role of precision in thought, and these cases require further discussion.

Now, Williams argues convincingly that in such cases Alpha should care, at least to some degree, about what happens to Omega. For example, if Alpha had the chance to pay a small amount of money to prevent Omega undergoing a large amount of pain, she should probably pay that money. We could explain this, as Williams does, by supposing that the person before the episode cares intrinsically about what happens to her, and since she does not know whether she is the person after the episode or not, she should derivatively care about what happens to the person after the episode. This style of explanation would be disastrous for the Indifference principle, for it supposes that Alpha cares intrinsically about whether Alpha is in pain, and as we have seen, it is borderline whether Alpha undergoes the painful experience in the scenarios where Alpha doesn’t pay the money. Thus Alpha cares intrinsically about the vague and seems rational in doing so.

However, I think there are a few complications with this argument that make it unclear whether it really conflicts with the Indifference principle.

The ‘standard' story locates the vagueness in the names Alpha' and ‘Omega'— according to that story Alpha' is referentially indeterminate between referring to A and to C, and ‘Omega' is referentially indeterminate between referring to B and to C; thus the sentence ‘Alpha=Omega' is linguistically borderline. Of course, for a non-linguistic theorist a different story would be told about the source of the vagueness. However, they will nonetheless also accept the above thesis about the referential indeterminacy of ‘Alpha' and ‘Omega' and the linguistic borderlineness of Alpha=Omega' (recall that a sentence is linguistically borderline if it expresses a borderline proposition). Note also that what I am calling the ‘standard story' hasn't taken sides on the mereological situation involved here: we could think of C as the fusion of A and B, or we could think of it as mereologically disjoint but coincident with both, or in some other way—it will not matter for our purposes.

Now, since, by hypothesis, Alpha is a self-interested person, and either Alpha is identical to A or Alpha is identical to C, it follows by logic that either A or C, or maybe even both, are self-interested people. On the assumption that Alpha is identical to A, A is a self-interested person and therefore cares only about what happens to A.

This is, I think, enough to deflate Williams' argument. Nonetheless, one might still be left with a feeling of puzzlement—why is it that it seems as though A ought to act as though she were uncertain about what will happen to her? Why does A seem to act as though she cares about what happens to the person after the disruption? Fortunately, we can explain this without invoking vagueness-related uncertainty or desire. At time t before the episode, A and C have exactly the same subjective experiences (or at least, things that are not determinately not subjective experiences), so it is natural to think that both A and C have self-locating uncertainty: for all A knows, she's C and is going to survive, and for all C knows, she is A and is not going to survive. So neither A nor C know whether they’re the entity that survives, and thus will do things that benefit the entity that survives to the extent that they think that they are the entity that survives.

Thus, in the scenario described above, the only thing A cares intrinsically about is what happens to A. The problem is that A doesn't know whether she occupies the qualitative role A actually occupies or the qualitative role that C occupies, and, therefore, doesn't know whether she will survive. However, it is a perfectly precise matter what happens to A on either hypothesis so she does not care intrinsically about the vague; similarly for C.

10.3