Hal Finney wrote:
> Many times I've convinced myself that I have a refutation for the DA,
> only to decide on further consideration that it is more difficult than
> it seems.
I know what you mean ;-)
> One possible escape, then, is to suggest that we are special because
> we are living in the time when the DA was just recently discovered.
> We are not a typical member of a long-lived species who learns about a
> DA which was discovered ages ago. If we were then it would be correct
> that the odds are that we are halfway along the species' existence. But
> we are not a random selection, we are special because this is the first
> era when the DA has been discovered. Every species must go through such
> an era, and for those observers who live in exactly that era, it tells
> them nothing about the expected time remaining for their species.
> This argument would be a bit stronger if the DA had been discovered more
> recently. However it has only been popularized within the last couple of
> years and so we really are the first people to be faced with it.
What you are saying here is basically that the appropriate reference class is the set of all observers who know about the doomsday argument. With this reference class, the conclusion would be that there probably won't be a great many observers who know about the doomsday argument in the future. This could either mean that there won't be very many observers, or that there will be lots of observers but they won't know about the DA.
And then there is the question whether that is the right reference class?
> I don't care for formulations of the DA which act as though I might
> have been born at different times. This raises thorny problems about
> the meaning of identity, whether I could be said to be the same person
> if I were born thousands of years in the future.
Do you know which second you were born? If not, and you were asked to guess, you could repond with a probability distribution over a range of seconds. The same with minutes; and it's easy to imagine a situation where you suffer from amnesia and you are not even sure what year you were born. (That is actually quite common among old people in some parts of the world where there were no public records of births. That's why claims for longevity records tend to come from obscure places.) If you can be uncertain what year, then not what decade? Are there any clear limits to how far we can push this reasoning?
> Rather, it is simpler to say that for most observers the DA will be valid.
> However, it will not be valid for those observers who are specially chosen
> as being part of a certain milestone in the history of their race - the
> discovery of fire, or of writing, or of the DA. You can easily imagine
> that the universe is such that most species do not discover fire halfway
> along their history, and the same reasoning applies to the discovery of
> the DA.
I think this can be modeled by saying that some people may have empirical priors that to some extent compensate for the DA.