Indifference
I've been assigned some boring administrative work, but that's finished now, I hope. Here are some rough thoughts on indifference and Adam Elga's Dr. Evil paper (PDF).
There are many possible individuals whose mental state is subjectively indistinguishable from my current mental state insofar as they all share my current phenomenal experiences and my (real or quasi-) memories. Some of them inhabit worlds that are exactly as I believe the actual world is, and are located in that world exactly where I believe I am located in the actual world. Others occupy very different places in very different worlds: they are brains in vats or inhabitants of gruesome counterinductive worlds. How should I distribute my credence among all these possibilities?
One suggestion, the general indifference principle, is that I should assign equal credence to all possibilities compatible with my current evidence. Let's ignore technical difficulties arising in cases where there are infinitely many of the relevant possibilities. I will also set aside the allegation that the principle confuses risk and uncertainty, because I'm not convinced that this is true.
Besides these possible problems, what's wrong with the principle is that it leads to skepticism. For it presumably entails that I should assign rather high credence to various counterinductive and vat possibilities. And that's not something I want a principle of rationality to entail.
Another remaining problem, I think, is that the principle is incompatible with the Principal Principle relating chance and credence: if my evidence settles all questions except the outcome of a certain random process, and I know that the odds for outcome A are 0.9, I should not assign equal credence to all possible outcomes.
So the principle should be restricted. Adam Elga argues for a version that is restricted to possibilities located at the same world: if two open possibilities differ only in where they locate me in a given world, I ought to assign them equal credence. For example, if O'Leary knows that he'll wake up twice during the night, and that the two awakenings will be subjectively indistinguishable (because by the time of the second he will have completely forgotten the first), he should be uncertain whether it's the first or the second when he wakes up for the first time.
This restricted principle says nothing about how I should distribute my credence concerning the time when I wake up in the middle of the night unless I'm sure that at least two indistinguishable awakenings of that kind actually take place. So the principle can hardly replace the general principle as a general rule for distributing credence among open possibilities.
It also seems to me that the restriction it imposes is somewhat ad hoc and in need of justification: why should it matter whether two of my epistemic counterparts are located in the same world, any more than it matters whether they are located in the same city?
But most importantly, the restricted principle does not really escape the skeptical consequences of the unrestricted principle. It's only that, due to its limited applicability, it affects fewer actual beliefs. Yet it still implies that if I know that there actually is a brain in a vat with experiences indistinguishable from mine, I should assign rather high credence to the assumption that I am that brain. Thus by creating vat counterparts -- which only requires skill and money --, the skeptic can win any argument.
Moreover, it seems plausible that if I'm sufficiently uncertain about whether P obtains, and if I know that if P does obtain then I should be very uncertain about Q, then I should not be very certain about Q. But I'm not very certain that I have no brain in a vat counterpart somewhere in spacetime; and assuming that I have such a counterpart, e.g. somewhere in the future, Elga's restricted principle says I should be very uncertain whether I have hands. It follows that I shouldn't be very certain that I have hands.
Just as the general principle conflicts with the Principle Principle, Elga's restricted principle conflicts with the 'intensity rule' relating 'branch intensity' and credence in the branching interpretation of Quantum Mechanics (see Lewis, "How many lives has Schrödinger's cat?" (PDF)). This isn't quite as bad though, as it is controversial whether the intensity rule makes any sense as a primitive rule of rationality. (The branching interpretation of Quantum Mechanics is of course even more controversial, but if the intensity rule were acceptable, the restricted indifference principle would still rule out a live physical theory on a priori grounds, which isn't nice.)
So we should also reject Elga's restricted principle.
However, the O'Leary case seemed plausible. We might try to restrict the principle even further, perhaps to intra-individual alternatives: if two open possibilities agree in who I am and what world I inhabit, but disagree about which of my stages is present, they ought to be assigned equal credence.
But that seems just as ad hoc as Elga's principle, and it also raises skeptical doubts, for I can't be sure about my future (and to some degree, past) predicaments. It also rules out the following application of indifference: if I know that my world is a world of two-way eternal recurrence, either spatially or temporally, I ought to be uncertain about the section I inhabit.
The recurrence case supports a different very restricted indifference principle: if two open possibilities agree about all qualitative facts concerning both the world and my location in it, they ought to get equal credence.
This principle, modulo technical refinements dealing with infinite possibilities, sounds quite plausible to me. It seems to create no skeptical worries nor does it conflict with any chance principles. It also doesn't impose arbitrary restrictions on the co-locality of the considered possibilities.
But of course its applicability is very limited indeed. It doesn't even apply to the O'Leary case. So here is another version that also sounds attractive to me: if two possibilities are equally compatible with both my current evidence and my (prior) beliefs, they ought to get equal credence.
Consider all the possible individuals that have the same experiences and memories that you currently have. Suppose two of them live at a place in a world that is exactly as you believe your place in the world is (or rather, as you believed your place is before you got the evidence). Then the principle says you should assign equal credence to the possibilitiy that you are the one and the possibility that you are the other. Or suppose two of those possible individuals live at places equally different from how you believed your place to be. Again, you should assign them equal credence.
Like all the other restricted principles, this principle can't do all the work one might have wanted the unrestricted indifference principle to do. In fact, it only restricts belief update: it says that posterior credence should be a function of prior credence and evidence.
But that's fine. Look at it in terms of confirmation theory: the unrestricted principle says that all theories compatible with the available evidence should be assigned equal credence: creationism is just as good as evolution theory and as Russell's 'theory' according to which the world came into existence 5 minutes ago. That's silly. Further restrictions are needed. The last restriction I proposed corresponds to subjective Bayesianism.
Subjective Bayesianism doesn't tell us directly how to distribute our credence among the available theories. It only tells us how to redistribute our credence in the light of further evidence. If, before looking at the evidence, you started out uncertain about whether creationism or evolution theory is true, Bayesianism entails that you should firmly believe in evolution theory after considering the evidence. But if you started out being dead certain of creationism or (worse) Russell's theory or (even worse) social constructivism, according to which the world was recently created not by God but by our social practices, the evidence will leave you quite untouched. (But notice that then you can't say, like we believers in evolution can, that your belief is supported by such and such evidence.) It would be nice, perhaps, if we had some further principles restricting the distribution of initial beliefs. Of course we do have such principles, but it is hard to see how they could be justified as principles of rationality: skepticism about the external world isn't irrational in the way that, say, accepting contradictions is.
So Dr. Evil, unless he is a skeptic, should be unimpressed.