Re: Doomsday Example

Nick Bostrom (
Mon, 24 Aug 1998 18:19:50 +0000

Robin Hanson writes:

> I accept that given your postulated prior, learning you are human
> strongly suggests you are in the universe made only of humans, rather
> than made mostly of stones.

I think that's a bit counterintuitive. What do you say about the following:

Suppose we change the example slightly. Now, an A universe contains 10 humans and nothing else. A B universe contains 10 humans and one trillion trillion stones. There is a small C universe (of negligible size), and it spawns one thousand baby-univeses through a random process (like rolling fair dice) that has a 10% chance of yielding an A and 90% of a B.

It seems clear that there will probably be about 100 A univeses and 900 B universes. But that means about 90% of all humans will find themselves in an B universe. So if all you knew was the set-up and that you were a human, then you should believe that there was a 90% chance that you were in an B universe.

And yet, if you include stones in the reference class, then it seems you should believe you are in an A universe. For if you are in a B universe, then there exists in total at least one trillion trillion stones and then you would probably have been one of these stones rather than a human.

So we should exclude stones from the reference class, because otherwise we will have to make a recommendation that will probably lead to 90% of all who follows it to be wrong; whereas if we don't include stones in the reference class, then 90% will be right.

> >Are there then ten physically identical possible worlds
> >in each of which you are really a different rock? Sounds very
> >metaphysical to me.
> Consider the analogy of death. Imagine in one universe I live for
> 100 years and another where I life for 50. The difference between
> the two universes is that, after 50 years are up, in one universe "I"
> would be alive and in the other universe, "I" would be dead. The
> atoms that would make up a living body are instead, for example, in
> a charred material preserved in the lava flow that enveloped me. That
> material is the material that would have been "me" had I been alive.

Presumably not, since the atoms making up your body would have been replaced anyway through natural metabolic processes.

Suppose these discarded atoms had been used as fertilizer and re-entered the food chain and become part of someone else's body. Would you then have been this other person?

But even granting for the sake of argument that the material "would have been you" if you had been alive, it *isn't* you since you are in fact dead. Your spacetime tube has come to an end...

> There *is* an "I" associated with that dead rock.

... so this argument couldn't show that there is an "I" associated (in any interesting sense) with the rock.

> Similarly, if some small event had never triggered life on Earth, the
> matter that would have me alive would instead be rock near Earth's
> surface. There is a sense it which it makes sense to ask which rock
> it would have been.

I agree that maybe you can meaningfully ask: Where would the atoms currently making up my body have been if such and such an event would not have happened on Earth 4 billion years ago. (Though I suspect that quantum-statistical phenomena means that the answer could even in principle only be in terms of something that would be smeared out enough that it might coincide with where the atoms making up Hal Finney's body would have been.) But I don't think this is relevant.

Even if you could in principle trace where your current body's atoms would have been if such and such events had happened, and this allowed you to say that you would then have been this aggregate of atoms (which I don't agree with!), this proceedure still does not indicate what "I" should be associated with rocks that consist of atoms that have never and will never make up any person's body. Could "you" "have been" these rocks? Are they in the reference class?

Is there one (otherwise empty) possible world in which you are an apple and I am a pear, and another (otherwise empty) possible world in which I am an apple and you a pear. What is the difference? It doesn't make any sense to me to distinguish between these worlds, unless you believe in a metaphysical soul.

> Yes, it would be a real pain to track down which atoms those would be.
> But I don't see any other way to make sense of the hypothesis that "I"
> might not have existed, other that to describe what would otherwise
> have become of the material and space-time I now occupy.

Maybe it's simple: "You would not have existed." means "There would have been no RobinHansonian information processing system. :-(".

> >Similarly, I would say that finding that you are an observer does not
> >give you reason for thinking that a large fraction of all slots in
> >the universe is occupied by observers.
> Your error is to say "large fraction." The fact that life exists
> on Earth *does* make it more likely that our universe has other planets
> where life has evolved in a similar time. It just isn't enough to
> conclude the fraction of Earth-like planets with life is "large."

Above you said:

> I accept that given your postulated prior, learning you are human
> strongly suggests you are in the universe made only of humans,
> rather than made mostly of stones.

There it seems you were saying that the finding that you are a human has an effect on what you should believe about the fraction of humans to stones.

And now you say that finding that life exists on Earth should not affect your beliefs about about the fraction of Earth-like planets with life.

You did say "given you postulated prior", which was fifty-fifty for the two universes. But we can , for the sake of argument, assume a similar fifty-fifty prior in the second case: a fifty-fifty prior chance that a large fraction of Earth-like planets have life.

Why the difference in treatment between these two cases?

Nick Bostrom
Department of Philosophy, Logic and Scientific Method London School of Economics