Time for a first report on Adam Elgas Dr Evil paper.
Remember that the guiding principle here is that Adams defending an
indifference principle so hes got to be making a mistake somewhere – the task
is just to find where. I dont have a proof that the rule of inference
used in that last sentence is truth preserving, but I sure hope it is or all
these attacks on indifference principles are a little pointless.
The first thing to say is that, as you might
have guessed given the origin, is that its a very good paper. Adams very
clear at saying what he is and isnt assuming, which makes the life of the
carping critic easier, because were told up front where the attacks should,
and just as importantly should not, be launched. Adam starts by making the
following definitions:
- A
centred world is a possible world with a designated individual and a
designated time. (These centred worlds are sometimes described as the
predicament of the designated individual at that time.) - Two
centred worlds X and Y are similar iff X and Y are associated with the same possible world (in
other words, they differ at most on who is the designated individual or
what is the designated time) and they represent predicaments that are
subjectively indistinguishable. (In other words, the designated
individuals areat the designated timesin subjectively indistinguishable
states. For example, the designated individuals have the same apparent
memories and are undergoing experiences that feel just the same.)
The main aim of the paper is to defend the
following principle:
Similar centred worlds deserve
equal credence.
Elga argues that indifference is true in a
particular case, and then argues that the case is arbitrary, so it holds
generally. The case involves Al. Al knows while hes asleep tonight that a
biased coin (that has a 10% chance of landing heads) will be tossed and then a
duplicate of him will be created. He (or is it the duplicate?!) awakes, and wonders
who he is. Elga thinks he should assign credence 0.5 to being Al, and credence
0.5 to being the duplicate. The argument for that uses the following premises:
(1) P(HEADS) = 0.1
(2) P(HEADS|HeadsAl or TailsAl) = 0.1
(3) P(HEADS|HeadsAl or TailsDup) = 0.1
Here P is Als credence function (or at
least the one he would have were he rational), HEADS is the proposition that
the coin lands heads, HeadsAl is the proposition that the coin landed heads and
he is Al, TailsAl the proposition that the coin landed heads and he is Al, and
TailsDup is (you guessed it!) the proposition that the coin landed tails and he
is Dup. A bit of algebra shows that if (1), (2) and (3) are true then P(HeadsAl
or Tails Al) = 0.5. That is, Als credence that he is Al is 0.5, and that he is
Dup is 0.5, just as INDIFFERENCE requires.
Adam notes the main issue is with (3). Both
(1) and (2) look pretty plausible. To defend (3) he looks at a slightly
different and more disturbing (in an odd way) case. If the coin lands heads
then Al wakes normally, but the duplicate is put into a coma, and presumably
wakes up in a very different kind of situation, if at all. Conversely, if the
coin lands tails then Dup wakes normally, but poor Al is put into a coma, and
presumably he wakes up in a very different kind of situation, if at all. Adam
argues that in this case P(HEADS) should still be 0.1 for whomever wakes up,
and if thats true it would support (3). (Theres a long footnote about why
this implication should hold, but it seems intuitively plausible to me without
any extra argument.) The interesting part is how Adam argues for (3). The core
of the argument seems to be this:
When he wakes up,
his epistemic situation with respect to the coin is just the same as it was
before he went to sleep.
Well return to this point a bit in what
follows, because it is far from obvious. What is true is that he knew he
would awake in a situation that was subjectively indistinguishable from the
one in which he actually awoke. But its a bit of a leap from there to the
claim that his epistemic situation is unchanged. Anyway, I had four concerns,
clearly of varying degrees of importance, about the paper.
First, I wasnt sure why centred worlds were
described as predicaments.
Sure some centred worlds are predicaments, but not all of them. I was
going to list several centred worlds that I wouldnt have described as
predicaments were I the designated agent and it were the designated time, but
for some reason all the ones I could think of involved the twins from the Coors Light commercials. This
isnt a, er, major point I guess. (More careful note: the online dictionaries I
looked at suggested that a predicament is just a state, but calling a state a predicament implicates that its not a state involving the Coors Light twins. I cant
really see how this could be the natural meaning, but perhaps it is
right.)
Secondly, it seems similarity is defined too
liberally for the kind of work Adam wants. The problem is that
indistinguishability is (arguably) intransitive, but it seems Adam needs
similarity to be transitive. This leads to problems in cases like the
following. Jordan is in prison with nothing to do all day but stare at the
clock. In one respect its a good clock, it keeps perfect time, so the
display is continuously changing. In another respect its a pretty bad
clock, the second hand and the minute hand are missing, only the hour hand
crawls around. Its a 60 Hz light source in the room, so Jordan gets to observe
the clock 60 times a second. Between breakfast at 6am and dinner at 6pm one
day, she does nothing but stare at the clock – no reminiscing, no itching,
nothing but the clock. She makes 2,592,000 observations in the day. Each is
subtly different, but adjacent observations are indiscriminable. Jordan is
aware that she makes these observations every day, and that they are pairwise
indiscriminable. Right now its around 4. Let x be Jordans credence
that its exactly 4, i.e. that shes just made the 2,160,000th
observation of the day. By INDIFFERENCE her credence that she just made the
2,159,999th observation should also be x. Since the centred
worlds where she made the 2,159,999th observation of the day and the
2,159,998th observation of the day are similar, her credence that
she just made the 2,159,998th observation should also be x.
Generalising, she should assign the same credence to the hypothesis that she
just made the nth observation of the day for any n.
But this is crazy. She is looking at the clock, so she knows it is not, say, 9
in the morning.
I think what Adam should do here is adopt a
stronger version of indistinguishability. Say two observations are alike iff
they are indistinguishable from the same observations. Although Jordans
sequential decisions are (arguably) indistinguishable, they cant be alike, for
alikeness implies indistinguishability, but is transitive. Then define similar
situations in the way Adam does. It looks like a cheap way out, but it probably
looked like a cheap objection to start with.
Thirdly, Adam is using a very particular,
and not very popular, conception of evidence here. The argument for (3)
crucially involves the premise that Al gets no new evidence when he
wakes up. In particular, he gets no evidence that he didnt already have. But
this seems clearly mistaken in one direction, and possibly (probably?) mistaken
in another. When Al wakes up, presumably something or other is the first
thing to cross his mind. Unless he knew what that was going to be, hes got some
evidence he didnt have before, so his credences in (3) could change.
(Perhaps he did know what he was going to first think about. Perhaps he always
thinks of the same thing every morning. Maybe Al is Milton Friedman, so the first thing he
thinks about is the money supply. But perhaps not.) Now Adam could argue
that the new evidence Al gets should be probabilistically independent of the
coin toss, and I guess thered be some reason to think thats true.
Though as I point out at the end of the sims
paper, its a very bad thing to infer from the lack of a reason for a probabilistic
connection to the existence of probabilistic independence. Im pretty sure that
isnt the kind of mistake Adam is likely to make, so Im sure this can
be dealt with without serious problems.
The more serious point is that when Al wakes
up and looks around he sees Al. Adam needs it to be that that isnt
epistemically relevant, that all thats relevant is that he has an experience
as of seeing Al. For if the fact that Al sees Al is part of Als evidence, then
Al has different evidence to Dup, who plainly does not see Al. (Unless they are
sleeping together I suppose.) In short, Adam needs here an internalist
conception of evidence, and my impression is that theyre not altogether
popular in epistemology nowadays. Its also my impression that the reasons that
they arent very popular are not exactly compelling reasons, so perhaps Adam
can handle this difficulty. But the underlying issue about the nature of evidence
needs to be handled somehow.
Finally, it looks like INDIFFERENCE
leads to violations of the Principal Principle in some Shooting Room like
cases. Dr. Evil wakes up one morning and decides he wants to torture some
people who are epistemic duplicates of Sam. Sam (or at least the duplicate of
Sam currently talking to Dr. Evil) is not particularly happy about this, but Dr. Evil
reassures her that hes going to give her a fair chance. Hes going to play an
iterated game with the following rules.
At stage 1 hell create 9 duplicates of Sam
and tell them about his plan. Hell roll two fair dice. If they come up double
six, then hell torture those ten people. Otherwise theyll be free to go.
At stage 2 hell use the blueprint for Sam
he took when he first kidnapped Sam, make 90 duplicates and tell each of them
about his plan. Hell then roll two fair dice. If they come up double six, then
hell torture those ninety people. Otherwise theyll be free to go.
At stage 3 hell use the blueprint again to make
900 duplicates of Sam and tell each of them about his plan. Hell then roll two
fair dice. If they come up double six, then hell torture those ninety people.
Otherwise theyll be free to go.
And so on until he gets to torture someone.
Sam doesnt know whether anyone will be
tortured, for she knows Dr. Evils game could continue infinitely, or until Dr.
Evil dies, or perhaps Austin Powers comes to the rescue. But sadly, Austin was
killed in a tragic accident involving the Coors Light twins last week, Dr. Evil
recently discovered the secret of immortality, and he doesnt get bored with
games very easily. Still, the dice might continue coming up something
other than double six indefinitely. But that has probability 0. And if the dice
every come up double six, 90% of Sams epistemic twins will be tortured.
So after been told the plan Sams credence
that 90% of her epistemic duplicates will be tortured should be 1. As far as I
can tell, by INDIFFERENCE that implies that Sams credence at the time shes
told the plan that she will be tortured should be 0.9. But thats a
mistake. Her credence at that time should be 1/36, because thats the chance of
the dice coming up double six. If that isnt her credence, then she violates
the Principal Principle. I think in this case Sam has no choice but to violate
either the Principal Principle or INDIFFERENCE. And I say it should be
INDIFFERENCE that goes.
This isnt just a judgement call about which
of two principles is to be preferred. Adams argument for INDIFFERENCE uses the
Principal Principle, so if INDIFFERENCE undermines the Principal Principle, it
undermines its own support. So we can hardly use INDIFFERENCE to get rid of the
Principal Principle.
Disclaimer: The Shooting Room case is hard.
Im not sure I fully grasp the importance of the results of Paul Barthas and
Chris Hitchcocks impressive paper on one of the paradoxes associated with it.
I think that because in my case the duplicates of Sam are being created ex
nihilo at every stage the case Ive discussed is importantly different to
the one they discuss. But Im not sure about this, so Im not sure how
technically sound this objection is. Still, its kinda fun, and that should be
enough!
Hopefully I can say more about the
pro-difference case in the future. (That sounds better than anti-indifference,
no?) If you havent read Adams paper, you should go read it, and if you come
up with the killer objection that keeps another version of the indifference
principle held down, circulate it as widely as possible!