Re: on formally describable universes and measures

From: Marchal <>
Date: Sat Feb 10 09:23:04 2001

Jesse Mazer wrote:

>Marchal wrote:
>> What does your theory predict with respect to
>>the following experience: You are scanned read and annihilate
>>at Amsterdam. I reconstitute you in Washington tomorrow, and at
>>Moscow in one billion years. Are your expectations different
>>from the situation where the two reconstitutions are simultaneous.
>I tend to agree that in this case the delay shouldn't matter in terms of
>your first-person expectations.

I'm glad earing that!

>Earlier I asked you a question about the
>thought-experiment where you would only be duplicated if the coin landed
>> >Are you saying that you support the 2/3 view, meaning that the
>> >of my "next moment" depends on a kind of integral over all possible
>> >histories?
>>Yes. I am less sure than George Levy for the precise computation of the
>>probability, but I am sure (with the comp hyp.) that my "next moment"
>>depends on a kind of integral over all possible histories.
>I think so too--*given* the assumption that continuity of consciousness is
>real, it seems very likely that our theory of consciousness should make use
>of this sort of integral.

I'm glad earing that too!

>The question is, though, is this integral going
>to be incomputable?

There is no a priori reason to expect it not to be computable.
If the domain of undeterminacy is "continuous", it could even make the
measure theory more simple.

>Even if it is, I suspect it is the sort of thing that
>could be approximated by a series of larger and larger computations.

It is certainly computable in the limit + random oracle.
It *has* a random oracle. We have no choice (IMO).
That is the price of dovetailing on *all* computations.

>In any case, I think it's pretty plausible that a theory of consciousness
>will involve only a countable number of distinct possible observer-moments,
>whether these moments correspond to distinct computations or to some other
>mathematical structure (a question that would depend on the form taken by
>the theory itself).

I think that at some point we are forced to take into account the
sheaf of possible computations going through that "observer-moments".
That is
the motivation for "histories". The Turing emulability put constraints
on the mathematical structures.

>However, if the integral is over all possible "histories" it may have to be
>taken over all possible *series* of observer-moments, which may indeed be

Yes, indeed. But it is still open if we can just reason
on a countable equivalence partition on that set. I don't know.

>I'd like to know a bit more about what you think a theory of consciousness
>would say about these questions, so I can understand better what you mean
>when you say that I am splitting uncountably many times in each instant.

Suppose a cat is hunting a mouse. Suddenly the mouse disappear under a
wardrobe. Then, the cat is waiting near the wardrobe.
The cat, instinctively, anticipates the possibility of
"the being still there of the mouse", "the ability of its own acting for
capturing the mouse", and even some backround like "the absence of the
neighbor's dog", etc. I'm not supposing the cat verbalised all this, nor
am I supposing it will reflect about that. But the cat has some "image"
of what's going on including its near possible futures. It capitalised
what it feels being important or pleasurable for him/her/it ...

In logical/computer-science term (sorry for the gap) we can consider a
machine emulating, automatically, a collection (perhaps vaguely unified)
of consistent extensions of itself.
(The qualia aspect will be linked with true but not communicable
self-referential truth, including observable intensity, etc.)

I will stop here before being long and boring. Of course I could propose
you the Godelian modal logics shortcuts. Have you read my post where I
summarize the second part of my thesis:

(I study what sound machines can tell about their consistent extensions.
Thanks to Godel Lob Solovay Boolos Goldblatt Visser result
a lot can be said).

I take seriously the idea that Godel's theorems are the first theorems
in the "exact" psychology of the (ideally ?) sound machine.

I link consciousness with betting (partially instinctively)

(I link self-consciousness with consciousness + reflexive ability.
I agree with Hal Finney's distinction).

Received on Sat Feb 10 2001 - 09:23:04 PST

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