Nick B. writes:
>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.
Er, don't you have to assume a non-zero probability for infinite universes, and then don't you only get a probability one for infinite? Things can be possible and have zero prob, and can be prob one without being certain.
>From what class should you regard yourself as being a random sample? ...
>"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? ... much the same seem to hold for lower primates, ...
>[Leslie] ... means ... With determinism, the DA is applicable in
>the straightforward way. With "radical" indeterminism, the probabilities
>are exactly those given by quantum mechanics, ...
>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?
I think I'm having the same problem with all these arguments:
>> (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 ....
No, no, let me explain what I mean by formalize.
Let us stipulate for now that there are only a finite set of possible universes that we can imagine, and that each such universe is finite in all important respects. In this case, we have very well developed analytical tools for formalizing arguments such as the doomsday argument.
The standard "information partition" approach is to first specify a set of possible states, including all possible universes and all states a universe could be in. For each state, one identifies all the agents of interest existing there (including those at different points in space-time).
For each agent, one can describe what they know by referring to the cognitive tools they have for excluding states. That is, given that they are in some state, how can they indentify other states that they are *not* in? If one then applies all their state-excluding tools and combine all their implications, then for each state s there is a set of remaining possible states P(s) (containing s) that that agent could never exclude. And since for every e in P(s), P(e) = P(s), what each agent knows can be described by a partition of the set of all states.
Every valid informational inference of interest can be rationalized using such partitions. So my problem with all your DA points is that I have trouble imagining the set of states implied, and the relevant agent information parititions which rationalize them. When I ask for formalism, this is what I want.
While one can certainly make valid arguments without formalizing them, it is hard to formalize invalid arguments. So failed attempts at formalization suggest sloppy invalid thinking. My current best guess is that the DA is at root incoherent, and so attempts to formalize it will better reveal this.
I found the formal examples in the papers I cites (including yours) informative, but they all drive me away from the DA. You seem to acknowledge these pressures, but end up supporting the DA based on informal arguments I just don't get yet.
For example, I don't get how determinism vs. indeterminism can be formalized in terms of partitions, nor can I see how my inability to forget that I am not a chimp would help me exclude states where my descendants are numerous. And I just can't make any sense out of your coincidence argument.
Robin Hanson
hanson@econ.berkeley.edu http://hanson.berkeley.edu/
RWJF Health Policy Scholar, Sch. of Public Health 510-643-1884
140 Warren Hall, UC Berkeley, CA 94720-7360 FAX: 510-643-2627