Ok, I'll try to summarize my position too.
The doomsday argument is a one application among many others of the anthropic principle. The DA, as I understand it, does not show that doom is likely to strike soon. What the DA does is place interesting constraints on what views of the future and of the universe at large are tenable. To assume an impending doomsday is one way of taking account of the DA, but at least at our present level of understanding there seem to be alternative interpretations, some of which may (hopefully) fit with the transhumanist vision of the future. Further analysis is required before we can say anything more specific than that.
I think Robins' position can be characterized as follows: He accepts what I call the self-indication axiom (SIA) and he thinks that also non-observers should be included in the reference class.
As for the SIA, I think it is consistent to accept it. There are problems - the problem with infinities and the no coincidence argument - that I think seriously detract from the plausibility of the SIA. But these counterarguments are inconclusive, and I do not rule out the possibility that the SIA should be accepted. The difference between Robin and me here seem to be one of degree of belief or disbelief in the SIA.
Robin's view that we should include non-observers in the reference class, on the other hand, seems incoherent to me. I have raised several objections against this, including the who's-the-apple-and-who's-the-pear problem. Two additional difficulties with this view also occured to me yesterday:
(1) Using a meta-level argument: If there are all these other
inanimate objects in the reference class, how comes you are not one of them? If you were equally likely to turn out to be a grain of sand as an observer, then you finding yourself to be an observer would have been extremely unlikely.
(2) What exactly are the members in the reference class supposed to
be? Are the bacteria in your body separate members or are they only there as a part of you? If only fundamental particles are members, then you couldn't have been a human since a human is not a particle. Which chunks or entities count as individuals?
So I definitely do not think you can solve the reference class problem by including non-observers. It is still unclear, however, exactly what (e.g. posthumans?) should be included, and that is perhaps the biggest remaining philosophical problem in anthropic reasoning.
http://www.hedweb.com/nickb email@example.com Department of Philosophy, Logic and Scientific Method London School of Economics