Re: practical reasoning and strong SSA

From: Wei Dai <weidai.domain.name.hidden>
Date: Mon, 7 Jun 1999 00:25:50 -0700

On Fri, Jun 04, 1999 at 12:30:52PM -0700, hal.domain.name.hidden wrote:
> I don't see that the SSSA would play a role, because you are explicity
> excluding the possibility that you are someone else in the specific
> conditional probability under consideration. The strong SSA says that
> you should consider yourself a random selection from among all observers.
> But we are stipulating in the conditional probability that you are,
> in fact, yourself, here and now. Whether you might have been someone
> else is therefore irrelevant to the calculation and to the definition.
>
> The way I have seen this calculation justified is to consider that you
> are randomly chosen from among all possible observers who are consistent
> with what you are experiencing here/now. This is more limited than
> the SSA because the reference set is just those observers who share
> identical mental states. Each person does his probability calculations
> with regard to that reference set. From his perspective, he is in one
> of many possible universes, constrained by what he observes and knows.
> But there is no chance that he is a tentacled alien on alpha centauri.

This is what I meant by forgetting the old way of thinking. The above
paragraph probably would have made sense before I learned about the SSA,
but now it doesn't. If the reference set is just those observers who share
identical mental states, then everyone in the reference set must be having
identical observations, right? Or are you saying the reference set is just
those observers who are in a similar mental state as my own (e.g. everyone
who have the same memories as me and are reading a Mathematica output but
not necessarily "N[Pi]=3.14159")? This has many problems, but let me make
sure I understand you first.

> Consider the "extra strong" SSA where the reference set is all subsystems
> of all universes, not just conscious ones, so that you consider the
> possibility that you might have been a rock in your calculations.
> You will get the same answer for the probability above under this
> assumption as well as the conventional SSSA, because in both cases we
> exclude from consideration any other possibility than that you are you.
> So this extra strong SSA should be just as good as the strong SSA in
> terms of defining the conditional probability, so therefore the strong
> SSA must not be a necessary philosophical underpinning.

Actually you have just set up my next argument for me. The strong SSA does
not apply to unconscious reasoning machines, so it can't be used as a
universal principal of reasoning. The extra strong SSA works for conscious
beings, but also applies to unconscious beings. Furthermore, it eliminates
the need to define "conscious", something that we have not shown is even
possible.

The strong SSA (without the SIA) and the extra strong SSA do not have
identical implications for conscious beings, however. The extra strong SSA
allows one to draw conclusions from the fact that one is conscious,
whereas the strong SSA does not. For example, if we can show that the
truth of a certain mathematical statement implies that the universe
contains more conscious beings (for whatever definition of "conscious"
that includes me), then under the extra strong SSA the fact that I am
conscious is evidence for that statement being true.

Interestingly, the extra strong SSA and the strong SSA with the SIA do
produce identical conclusions for conscious beings. The DA (Doomsday
Argument), for example, is neutralized by the extra strong SSA as well as
by the SIA. I think the SIA should really be seen as an implication of the
extra strong SSA rather than as a fundamental axiom of reasoning.

(SIA, the Self-Indication Axiom, is defined by Nick Bostrom as: The fact
that one is an observer gives one some reason to believe that the world
contains many observers.)
Received on Mon Jun 07 1999 - 00:27:17 PDT