Wei Dai wrote:

>I have a problem with trying to quantify 1-indetermincy. I'm not sure it's
>a useful exercise, useful in the sense that a decision theory will involve

It depends about what the decision theory is for. If the decision theory
is used by a subject for maximalising some gain, only that subject can
decide what is a gain for him, and this (as Kant realised) can only be
based on first person experiences, lived and expected.

>> To be honest I have not understand your answers to Hal Finney last posts,
>> I agree with Hall's remark though).
>It's probably because I haven't explained my current overall position.
>I'll try to do that now. Do you agree with the following?
>1. All computational facts exist. In other words all statements of the
>form "the output of GTM x converges to y" or "the output of GTM x doesn't
>converge" have objective truth values.

I agree. (This is entailed by any form of arithmetical platonism).

>2. Any statement that has a truth value is equivalent to a computational

Mmh...In general this is false. Most arithmetical truth are beyond
computational accessibility, unless you count those truth proved by
machine betting theories (the dreaming machines!).
But with some formalised and explicit version of computationalism
(like in AUDA) you can restrict arithmetical truth to the computationnaly
accessible arithmetical truth. This is what I do with my restriction
to Sigma_1 sentences (which are equivalent to sentences with the form:
"it exists n such that P(n)", P being an algorithmically verifiable
statement. So OK (but with comp).

>For example "1+1=2" is equivalent to "The output of x is '2'" 
>where x is a GTM for computing 1+1.


>"I will win the lottery tomorrow with
>m-measure at least 1/2 of my current m-measure, where m is defines as ..." 
>is equivalent to "The output of x converges to 'true'" where x is a GTM
>that simulates all universes in parallel, while keeping track of an upper
>bound on m(me-now) and a lower bound on m(me winning the lottery
>tomorrow), and outputing 'true' when the ratio between the two drops below

I'm not sure what you mean by the GTM (Great Turing Machine?). 
I partially agree with you in the sense that I know there is a Universal
Dovetailer capable of simulating all "universes" in parallel (+ all
dream of universes, etc...) and capable of generating all version of
"me-now", but I stop here, because no Turing machine can keep track
of the "me-now", and besides, even if such machine could exist (and
it cannot by a theorem of RICE) then for any UD you can build another
UD which will, on any finite portion of its execution, give
different ratio between the me-now and their continuations (only in the
infinite will the "ratio" be the same).
(RICE theorem say that no machine can decide in finite time if two
presented machine have or not the same behaviour). 

>3. Caring about anything is equivalent to caring about computational

OK but not necessarily recognised as such.

> That is, your goals are equivalent to goals in the form "I want the
>output of GTM x to converge to y".

Not necessarily because I cannot associate or name x even I know
I want y. Comp entails non computationalist facts in the neighborhood.

>This goal makes sense if you are part
>of the computation of x and can influence its history. The problem of
>consciousness, or the mind-body problem, then becomes how do I tell which
>computations I am a part of?

I agree.
I believe (both from QM and comp) that it is very plausible that
we belong to an infinity (even a continuum) of computations at once.
This entails the first person indeterminacy which takes the
form of a wave (apparently). Well that is what remains to be
explained for those who bet on comp.
I don't believe we belong to a unique computation or a unique universe
and that we should quantify on all universes, I believe we belongs
to a sheaf of "universe-computations" and that the indeterminacy is 
relative to what we know and don't know.

>There is no objective standard about what goals one should have, or how
>much weight one should put on each goal.


>From this position it appears that there is no need or room for an
>objective measure.

??? This is exactly what I don't understand (and where I agree with
Finney's reply). 

Once such or such person has some (subjective and personal) goals,
and has decided to put much weight on that goal, it seems to me that
it is better for him/her to take into account the most objective 
measure she/he can calculate or bet on his/her continuations.
Exemple: 1) my goal is to drink a hot coffee. I put a recipient of
water onto the stove (or cooker?). I use some implicite high measure
on the probable boiling water phenomenon.
2) I use teletransport everyday because I got a job on Mars.
Now the channel has been made secure (thanks to some quantum
protocol). My goal here is to make as little as possible the
probability of being duplicate without my consent by some sadical
channel-pirate in need of flesh (not chair!). So I decide to pay
the bill for the quantum protocol.

I don't pretend we can know for sure any objective measure, but
from classical mechanics to quantum mechanics we do have made some
And all what I say is that with comp we have an a priori explosion of 
continuations, and if comp is true that explosion should not
be greater that the "natural" Everett MWI one, and should behave
in that same strange wavy way. After all QM *does* quantify on our 
(first person plural) ignorance, like comp say any ultimate "physics"
should do.


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