At 20:06 -0700 12/07/2002, Wei Dai wrote:
> > The mind-body problem I am talking about is the one formulated by Descartes
>> (but also by Hindu philosophers before J.C). It is really the problem
>> of linking private (first person) sensations and third person communicable
>> phenomena. How a grey brain produces sensation of color, as someone put it.
>
>Could you state the problem more formally?
The mind-body problem is hard to formulate purely formally because it
search a link between the somehow formal body and the non formal mind.
My whole work, i.e UDA and AUDA(*), can be considered as an attempt to
*state* the problem, in the frame of the computationalist hypothesis.
The UDA still uses an "intuitive/informal" notion of "you" because it is
asked to "you" if you accept an digital body transplant. Nobody can
known for sure that you will survive such a transplant, but this is true
for any operation, and I am just looking for consequences in the case you
do survive (comp). The AUDA is more subtle with respect to that
informal/formal relation.
It happens that, in a quite precise sense, the S4Grz logic (and the X and X*
logics) capture formally the lack of formal description of the subject.
This is really difficult to explain shortly and I propose we postpone this
after the more easy UDA is made completely transparent.
>Also, you asked me whether I
>was aware of the mind-body problem. What did my answer tell you?
?
> > Those I have encapsulated in the label "comp". Precisely it consists in
>> 1)accepting a minimal amount of arithmetical realism, i.e. the truth of
>> elementary statements of arithmetic does not depend of me or us ...
>
>I agree with (1).
Thank you for telling me. Note that among those who understands the
uda proof, because they rarely like to endorse the conclusion, they often
choose to reject Arithmetical Realism.
(Church thesis has never been rejected, nor, curiously enough
the existence of a the substitution level).
Note that I don't really care: my point is only that AR+TC+BJ entails
the psycho/physico reversal.
A referee told me he is convinced that my reasoning still goes through
along with a weakening of the three part of comp. I think he is right but
this would make the UDA reasoning much longer and more difficult.
(AR = Arithmetical Realism, TC = Church Thesis, BJ = Big Jump (saying yes to
the brain/body surgeon).
> > 2) the Church Thesis (also called the Church Turing Thesis, or the
>> Post Law, etc.)
>> i.e. all universal machine are equivalent with respect to their simulation
>> abilities (making abstraction of the duration of those simulation).
>
>I don't think that is settled yet. We may be able to build machines that
>are more powerful than Turing machines. I don't think we should rule it
>out at this point.
I do also believe that we may be able to build machines that are more
powerful than Turing machines. But this has nothing to do with Church
Thesis (look at the Copeland paper you mentionned yourself). Church
thesis is just the thesis that all *digital* universal machine are
equivalent. But of course not all machine are digital machine. In particular
I have argued more than once that if comp is true (i.e. CT + ... are true),
then we should find in "nature" non computable processes. The first person
white rabbits appears for similar reasons and they are a priori non
computational. I know there are a lot of confusions in the literature.
Now I insist that my work uses comp as a working hypothesis. I am not
to much interested in discussing alternative hypothesis at this stage.
> > 3) The existence of a level of description of my body (whatever it
>> is) such that
>> my first person experience remains invariant through a functional
>>substitution
>> made at that level.
>
>Can you state this more formally? Specificly how do you define "functional
>substitution"?
Come on, I'm sure you see what I mean. (Of course "functional substitution"
is an interesting concept by itself. It would be just a slight exaggeration
to say that the lambda calculus and even category theory has been invented
for making that concept precise). In the uda frame, once the level of
digital substitution has been chosen, a substitution is functional if it
preserves the counterfactuals input/output relations of the thing which
is substituted.
> > (Note that the Arithmetical uda makes it possible to eliminate
>the "3)" above).
>
>I guess I'll have to wait for your English paper to understand how.
I have written more in this list than I will ever be able to write in
a paper. I have begin at least four papers; I don't know if I will
finish them. "Our field" overlaps too much disciplines. Either the
papers grow too much, or the paper became relatively incomprehensible.
Perhaps I should write a book instead. I don't know.
I must think about that. Advices are welcome.
At least some logicians begin to realize I give challenging
new mathematical problems. But then most usual technics doesn't apply,
and, because they lack the physical/bio/psycho-logical motivations,
they prefer to concentrate on their usual tasks.
Also, I think it is preferable to have a thorough understanding of
the UDA before tackling the AUDA. (except for the mathematicians, or those
who like logics and math).
> > But the UD, because he is shallow, will generate an infinite number of
>> computations in which you will experience drinking a cup of tea (if
>> not a white rabbit), and this although you have the same experience
>> of the past which include
>> your preparing that cup of coffee).
>
>You can just ignore those universes because their algorithmic
>complexities are very high (and therefore their measures are very low).
>
>> The "invariance lemma" prevents "easy" use of (Kolmogorov or
>> Chaitin) complexity
>> notion for dismissing those abnormal stories.
>
>Why? I just did it. Are you saying each copy of you in any universe counts
>equally regardless of how small the measure of the universe is? If that is
>what you mean by "invariance lemma" then I certainly don't agree with you.
>
>> The comp indeterminacy hints to transform that problem into a search
>> of a measure,
>> and into showing that relatively abnormal consistent
>> extension/stories are rare.
>> This is not unlike the Feynman integration on path in quantum mechanics.
>
>I do not see the necessity of it.
It is the whole purpose of the uda to show that necessity character, *once*
we accept comp (i.e AR + TC + BJ), if only for the sake of the argument.
Bruno
--------------
(*) for newcomers: uda =, the universal dovetailer argument, auda =
the arithmetical universal dovetailer argument. Roughly speaking it is
a translation of the uda in the language of a universal digital machine.
--
http://iridia.ulb.ac.be/~marchal/
Received on Wed Jul 17 2002 - 07:12:03 PDT