Re: Objection to the Doomsday Argument?

Nick Bostrom (
Mon, 17 Aug 1998 01:21:38 +0000

Robin Hanson wrote:

> Nick B. writes:
> >> 2) Our concept of "like us" can be biased by where we are in time.
> >It comes down to this: From what class should you regard
> >yourself as being a random sample? ...
> >This, I think, means that you cannot regard yourself as a random
> >sample from the set of all material objects. How far can we push this
> >methodology?
> The reference class of "animal", "conscious mind", "primate" seem
> available without this extreme problem, and seem much less biased
> to me.

"Animal" seems implausible to me. Could you (*you*) forget whether you are a human or a flatworm? If you forgot that, would you still be the same rational entity that you are now, and would what you would think in that condition really say anything about your conditional probabilities? Sounds implausible to me. (We're not just talking about forgetting what the words "flatworm" and "human" mean - that is certainly possible; but forgetting about the facts?) And much the same seem to hold for lower primates, though it's less clear. "Counscious mind" is a rather ambiguous perhaps.

> >Leslie thinks the DA works in the shooting room in the deterministic
> >version. (see p. 254). He doesn't think it works in the radically
> >indeterministic case,
> I couldn't make any sense of Leslie's determinism discussions.

I also have difficulty with that. That is, I am highly unconvinced that he is right, but I now think I know what he means. Basically this: With determinism, the DA is applicable in the straightforward way. With "radical" indeterminism, the probabilities are exactly those given by quantum mechanics, and the DA can't be applied. And in most real world cases, if our world is indeterministic, some kind of compromise between these two extremes would apply; you could sort of apply the DA but it would be weaker. (Don't ask me to explain how this compromise-idea could be coherent!)

> >> Finally, Nick shows how the argument gets weakened as one allows
> >> for alien creatures "like us" who won't get hurt by our local doom.
> >
> >Yes, but the fact that we are not posthumans could be taken to
> >indicate that there will not have been a great many alien
> >posthumans.
> Only if posthumans are taken to be more "like us" than monkeys.

The only thing that is required is that the posthumans would be in the reference class. Whether this means they would have to be more "like us" that monkeys, I don't know.

> >> If one instead assumes that the probability of finding oneself in
> >> a universe is proportional to population of that
> >> universe, the doomsday argument evaporates.
> >
> >Yes, this was the objection that I once thought refuted the DA. But
> >on second thought there turned out to be big problems with it: the
> >no-coincidence objection, and the infinity-objection. I outline these
> >in my Investigations paper. How do you suggest we deal with these
> >difficulties?
> I accept the conclusion that if infinite universes are possible,
> we are most probably in such a universe.

The conclusion of the self-indication axiom is even stronger: if infinite universes are possible, then it is a priori *certain* that the universe is infinite. That's quite a bit to swallow: just by sitting back in your armchair and closing your eyes, you can tell with perfect certainty that the universe is infinite. Try sell that idea to the physicists!

(Incidentally, I think this conclusion is not so absurd as it might seem. For example, David Lewis' idea doesn't seem so implausible to me. He thinks that all logically possible worlds are real.)

> I can't make sense of
> the no-coincidence argument. It seems to me that I can't just
> assume that I would exist, so my existence says something. In fact,
> powerful anthropic arguments come from realizing that our mere
> existence says something about the universe we live in. So how
> can we just assume that we'd be guaranteed to exist?
> (As a formal theorist, I'll say that I really think these discussions
> become much clearer in the context of specific formal models of
> the inferences in question. Can this argument be formalized?)

I doubt that formalism can do much good when trying to decide whether to accept the self-indication axiom. You could easily formalize the SIA itself, I suppose:

	If Nmax is finite, then for n<=Nmax, P(N=n)=alpha*n
					for n>Nmax, P(N=n)=0

where alpha is a normalization constant.

	If Nmax is infinite, then P(N=infinite)=1
				and for all finite n, P(N=n)=0.


I haven't thought it through carefully, but I think this is what you would get if you imagined possible observers existing as disembodied soals waiting to be placed in a real body.

As for the no-coincidence argument (I'm not 100% convinced about it myself), maybe it can be put like this: Is it really reasonable for you to view Robin Hanson as a random sample from all possible observers? Isn't the fact that you choose to focus on this sample, the Robin Hanson sample, correlated with the fact that Robin Hanson is real? Consider all the non-real possible observers: did these have a fair chance of being selected by you as the random sample? (The anmesia chamber experiment certainly cannot be used to argue that you are a random sample from the set of all possible observers. You cannot forget that you exist!)

One possible(?) loophole that you haven't mentioned is that the SIA is false but the universe happens to be infinite anyway. If there are going to be infinitely may observers, then all of them would have turned out to be "infinitely early", so maybe we could draw no conclusion from finding that we are that early too?

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