2001. Nick Bostrom
Greenberg's article actually consists of several independent objections.
I'll respond to just a few of them here.
- First, it is crucial to note that SSA does not speak about objective chances but about rational subjective credence. Greenberg fails to distinguish between these two notions throughout his article. It is certainly true that my chance of being born with birth rank r is not the same for all values of r (up to some maximum) - indeed, it's very doubtful that there is a well-defined chance of "me having rank r" at all. (At a minimum, one would expect such a chance to vary over time, as events develop, and eventually become 1 for one particular value of r at the moment when I am born.) Instead, SSA specifies what value I should give to the conditional credence P("My rank is r" | "The total number of observers is n"). SSA does not assert the existence of any objective chances. Thus, when Greenberg writes:
"But it is a consequence of elementary statistics - and a notorious source of confusion - that the overall proportions in a population may not reflect the relevant probabilities for any individual, even an average one. The overall distribution of outcomes can be skewed by factors irrelevant to each individual's chances. As a result, the overall rates of different outcomes can actually be inverse to the probabilities for every individual. It can be true that a higher proportion of Floridians die each year than Georgians, yet that any individual's chances of dying are lower in Florida than in Georgia."
he is pointing out a truth which is irrelevant. [Now, one
might think that we know so much more about ourselves than our birth rank so
that even if though it is correct to view oneself as if one were a random
sample if all one knew was what rank one has, it is incorrect to view oneself
as if one were random in the actual case. But this would be a misunderstanding.
Just as a randomly sampled ball from an urn remains a random sample even after
we have looked at it and found that it's #10, so too are you a random sample
(in the sense of SSA) even after you have plenty of additional information.
This information is information ABOUT the random sample, which of course you
need to take into account. And you do that by conditionalizing this
information, but not by adopting a new prior probability function which has a
different value for P("My rank is r" | "The total number of
observers is n"). So for example, although SSA entails a higher prior
probability of you being an American than you being Swede (given the difference
in population), it does not entail (absurdly) that you should think that you
are probably an American after you've discovered that you were born in
Stockholm. But, if you were uncertain about the relative population between the
two countries, then finding that you were a Swede would indeed be some evidence
in favor of the hypothesis that Sweden is the large country.]
- Greenberg goes on to assert:
"We are necessarily alive at the time we consider our position in human history, so the Doomsday Argument excludes from the selection pool everyone who is not alive now."
This objection rests of an ambiguity. Yes, it is necessary
that if I am at time t considering my position in the human history, then I am
alive at time t. But no, it is not necessary that if I think "I am alive
at time t", then I am alive at time t. You may well be wrong about when
you are alive, and hence you may be ignorant about it. Imagine that you
suffered from amnesia and forgot your birth rank. A reliable person then informs
you that there will have been either 200 billion or 200 trillion people in
total. In this situation, I claim that it is perfectly rational for you to set
your conditional credences P('My rank is 60 billion" | "The total is
200B") = 1/ 200B, and P('My rank is 60 billion" | "The total is
200T") = 1/ 200T. Given that there are a total of 200B people, you have no
reason to think it more probable that you are any particular one of these, and
hence the probability of you being, e.g. #60B is one in 200B; and similarly
1/200T given that there are 200T. If you then later discover that your birth
rank is in fact #60B, you update your credence in the hypothesis "The
total is 200B" according to Bayes's theorem. It is necessary that this
credence is larger than before learning about your rank, for otherwise you
would have known that finding out about your rank could only decrease your
credence in "The total is 200B" (namely if you found your rank to be
>200B) and could never decrease it - and that would be incoherent.
Now, the credence you end up assigning to "The total is 200B" after first forgetting about you rank and then relearning it is the same the credence that you should assign to that hypothesis in the actual case where you always knew what your rank is; for the information you end up having is the same in both cases. Thus, if you thought that the probability "The total is 200B" was 50% before conditionalizing on your rank, and the probability of "The total is 200T" was also 50% (maybe because you knew that which of these hypotheses were to be true was determined by an quantum event with an objective chance of 50% of yielding either outcome) then after conditionalizing on your rank=60B, you should become highly confident that "The total is 200T" is false.
- Greenberg proceeds:
"Even if someone who merely happens to live at a particular time could legitimately be treated as random with respect to birth rank, the Doomsday Argument would still fail, since, regardless of when that someone's position in human history is observed, he will always be in the same position relative to Doom Soon and Doom Delayed."
This difficulty is easily avoided by substituting specific
hypotheses for "Doom Soon" and "Doom Delayed" - e.g.
"The total is 200B" vs. "The total is 200T" (strictly
speaking there are of course many more hypotheses we need to consider, but for
simplicity we can focus on these two). It is true that some proponents of the
DA speak of "Doom Soon" vs. "Doom Delayed", but I have
noticed that this causes a lot of confusion since under an non-rigid construal,
what hypotheses are expressed by these phrases depend on who is uttering them.
It's therefore better to talk in terms of specific numbers.
- Greenberg's final objection is somewhat more substantial:
"As the in-the-pool condition specifies, you can infer that you would more probably have been alive now if Doom Soon were true only if you know that you would definitely exist if Doom Soon were true. ... That your chance of being born would have been smaller if there were not to be so many humans - and correspondingly greater if there were to be more - follows from his assumption that your position in human history is random. The intuition that your chance of being born would not have been affected by the total number of humans may well be correct. If it is, your position in human history cannot be random."
The idea here (which has been developed in more
detail by Dennis Dieks) is that those who are convinced of the SSA are committed
to also accepting the SIA (the self-indication assumption, which says, roughly,
that finding yourself alive gives you reason that favors hypotheses on which
there are many people, since there would then be more "slots for you
to be born into"). It can be shown that if one accepts the SIA then it
precisely cancels the probability shift introduced by the SSA in DA-like situations,
and we get back our ordinary intuitive probabilities that we started from.
Some people have argued (e.g. Olum, Bartha, Hitchcock, Eckhardt etc.) that
SIA ought to be accepted. This would not refute SSA but rather, when used
in combination with SSA, would remove the most counterintuitive consequences
of SSA. However, SIA has some highly counterintuitive consequences of its
own, which is why I do not accept it (see e.g. the Presumptuous Philosopher
gedanken in the paper I sent you). So I, for one, certainly think one can
accept SSA without accepting SIA. So how do I reply to the apparent inconsistency
that Dieks and Greenberg point to?
In outline, as follows. What we are interested in assessing are the conditional credences of the type P(h | "I have evidence e"). Writing the right-hand side of this expression as "I have evidence e" rather than the less informative "e" is important in some contexts where observational selection effects are involved. The conditions under which e were obtained must be taken into account when we are evaluating the bearing of our total evidence on some hypothesis. (I enclose a paper where I argue in detail for why this is necessary when evaluating certain sorts of cosmological theories in particular.) Now, saying that you should reason as if you were a random sample from all observers in your reference class is a useful principle that specifies a way of determining such conditional credences, and I have provided arguments for why this principle is plausible in a wide range of cases. But notice that it says "AS IF you were a random sample". It does not assert that you actually are a random sample, in the sense that there were an objective chance that you should turn out to be any person. As already noted, I don't believe there is such a chance. But there is a methodological principle (the SSA) that specifies a certain set of subjective conditional credences. According to this principle, you should reason as if you were a random sample from all (actually existing) observers in your reference class, not from some set that includes merely possible observers. In order to effectively criticize this principle, one would in my opinion have to do three things (1) Show that it yields unacceptable results in some cases; (2) Show why the arguments given in favor of the principle fail; and (3) (ideally) propose a better methodological principle for how to reason in cases where observational selection effects have filtered the evidence we get (there are many such cases apart from the Doomsday argument, and they occur in real scientific contexts as well, as I've showed in my PhD). Greenberg does neither of these things.
A full justification of SSA is of course more than I can undertake in an email, but I have done so elsewhere (briefly in the first part of the paper I attach, and in more detail in my dissertation, which is available at http://www.anthropic.principle.com/phd). Let me make two very brief remarks:
First (and this is admittedly a somewhat obscure point), it is not an accident that the person that is your "random sample" - i.e. you - is an actual human rather than a merely possible one. For the reason why this became selected as a sample is that there were an actual person there to select it, i.e. yourself. The merely possible persons never become such random samples for anybody. There is, thus, a kind of observational selection effect at work here: Out of all the possible humans, the only ones that can become selected as a "random sample" are those that actually exist - for being selected in this way depends on there actually being a suitable observer there to select them. "me" should be regarded as if it were a random sample from the set of actual observers, rather than from a set which includes merely possible ones.
Second, notice that one of the arguments one can give for SSA (the amnesia story told above) does not work for SIA. For it is impossible to imagine a situation in which you are ignorant about whether you exist and in which you should therefore assign a uniform probability distribution over some set including merely possible beings. So at least this reason for accepting SSA is no reason whatever for accepting SIA. And I think the same holds for all other reasons for accepting SSA.