Le 19-sept.-07, à 09:59, Youness Ayaita wrote (in two posts):
> You mentioned the ASSA. Yesterday, motivdated by your hint, I have
> read about the ASSA/RSSA debate that is said to have divided the list
> into two camps. Since I have trouble with the reasoning I read, I will
> probably send a new message hoping for leaving the misunderstanding
> behind.
> Searching for the Universal Dovetailer Argument, I found a quite
> formal demonstration that you wrote in the list, and an even more
> formal demonstration that you published in the original work. I do see
> the advantage to have such a formal demonstration when it comes to
> detailed discussions, but sometimes I'd prefer a simplified outline to
> get the basic idea and the main conclusions before going into detail.
> If you have written such an outline (in English or in French as well)
> I would be thankful to get the link. Otherwise I'll read one of the
> formal versions in the future.
Actually I like to say that the UDA is informal, yet rigorous. The
*formal* counterpart of the UDA is given by the "interview" of a lobian
machine (or a couple of lobian machines). Thios part is called
sometimes AUDA for Arithmetical UDA because it gives a translation of
the thought experiment and its consequence into arithmetic. It leads
also to a theory of everything: intensional number theory (which is
equivalent to informal extensional number theory + computer
science/mathematical logic, in a large sense).
Now the main consequence of the UDA is so startling (relatively to our
current Aristotelian (naturalistic, materialist, physicalist
prejudices) that I prefer that people got them by themselves. By
knowing just the result, you could aswell decide I should go in some
asylum! But I can give you a short (but risky, thus) outline:
I use the computationalist thesis as a working hypothesis. The idea is
to take seriously that hypothesis and to derive consequences from it.
If the consequences are too much absurd, then this can be seen as an
argument against comp. But up to now comp does not lead to
contradiction; it leads just too some weirdness.
BY comp I mean CT + "Yes doctor". CT is for CHURCH THESIS (sometimes
called Church Turing Thesis; Post Law, etc.). CT asserts the existence
of a *universal* language (or of a universal machine, which is the one
"understanding" that language). The universality concerns computability
abilities (not the provability one, for which there is no equivalent
theses). CT has many forms, like: the language LAMBDA is universal,
FORTRAN is universal, JAVA is universal, etc. Those are provably
equivalent. "Yes doctor" is the assumption that there is a level of
description of myself such that I survive (or see nothing changed) when
a functional substitution is made at that level. It is almost an
operational definition: you are a comp practitioners when you accept
that your doctor substitutes *any* part of what you think to be your
body.
Amateurs of MATRIX and novels like SIMULACRON III can appreciate this
... (like amateurs of Plato ...).
The UDA then consists in a many steps thought experiment showing that
IF comp is correct THEN physicalism is false, and to solve the mind
body problem you have to, not only get a theory of mind, but you have
to justify the belief in natural law entirely through a relative
measure on Sigma_1 sentences (corresponds to the state accessible by
the UD).
>
> On 18 Sep., 16:23, Bruno Marchal <marc....domain.name.hidden> wrote:
>> So without putting any
>> extra-stcruture on the set of infinite strings, you could as well have
>> taken as basic in your ontology the set of subset of N, written P(N).
>> Now, such a set is not even nameable in any first order theory. In a
>> first order theory of those strings you will get something equivalent
>> to Tarski theory of Real: very nice but below the turing world: the
>> theory is complete and decidable and cannot be used for a theory of
>> everything (there is no natural numbers definable in such theories).
>> From this I can deduce that your intuition relies on second order
>> arithmetic or analysis (and this is confirmed by the way you introduce
>> time).
>
> Bruno and Russell, I don't want to interfere with your discussion. But
> I want to say something concerning the mathematics applied to study
> the ensemble of infinite bitstrings (which is, as you, Bruno,
> mentioned correctly, equivalent to the power set of the natural
> numbers). For me, the Everything ensemble is something given.
I have no problem with that.
> I'm not
> forced to restrict myself to the use of mathematical structures
> definable by the structure of the Everything ensemble. I can use the
> whole of mathematics developed until today in order to study the
> Everything ensemble.
Yes, you are right; at least concerning the way you prove propositions
about the "Everything Ensemble". But obviously, if your "everything
ensemble" is supposed to be the ontiic part of the "theory of
everything" you have to relate that ontic base with what we observe and
think. For doing that, you are free to use any "meta-theory" you want,
as far as we can agree on it. Actually, by incompleteness, we have ot a
lot of choice in the matter. In my appoach this difficulty can be
circumvented by interviewing a couple of lobian machine, once being
richer (in provability power) than the other.
>
> Let's consider our universe that is studied by physics.
The problem is that after UDA an expression like "universe" has to be
use with much caution, especially if you mean "ohysical universe".
> Probably, we
> won't find the set of natural numbers within this universe, the number
> of identical particles (as far as we can talk about that) of any kind
> is finite.
Not in all "models" (cf type 1 multi-realty of Tegmark).
> Nonetheless, it is useful to define the natural numbers and
> to construct rational, real and even complex numbers in order to study
> the universe.
>
> A vivid though quite ridiculous example might be: When we study the
> unaffected tropics, we go there with cameras despite of the fact that
> cameras don't come from the tropics.
>
> As Everything ensemble, we use the set of infinite bitstrings. But the
> Theory of Everything, which doesn't really exist so far, may use every
> mathematical structure that proves to be useful.
... at the metalevel. Sure. I agree 100%.
> This of course
> differs seriously from arithmetical realism.
Ah? Why? Here I disagree 100%. First arithmetical realism is just the
"humility statement" saying that whatever happens to me, with me =
bruno marchal, that will not change the truth status of the
arithmetical propositions. I have never met someone who does not accept
arithmetical realism. It is NOT the statement that ONLY arithmetical
reality (AR) is independent of myself. It is the statement that
arithmetical truth is independent. That statement is accepted by both
classical and intuitionist thinkers. I have stopped to put explicitly
AR in COMP, because Church thesis already subsumes AR. Comp, under the
form "yes doctor" + Church thesis + AR is redundant. No need to accept
"actual infinite" to accept comp.
> Youness
>
>
> >
>
http://iridia.ulb.ac.be/~marchal/
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Received on Wed Sep 19 2007 - 09:19:37 PDT