On 13 Jan 2009, at 18:44, Brent Meeker wrote:
>
> Stathis Papaioannou wrote:
>> 2009/1/13 Brent Meeker <meeke...@dslextreme.com>:
>>
>>
>>> In human consciousness, as instantiated by brains, there is a
>>> process in which
>>> signal/information is not local, it is distributed in spacetime
>>> and is connected
>>> causally which means, per relativity, that you cannot make any
>>> unique spacelike
>>> snapshot and label it "the state". I don't go so far as to claim
>>> that
>>> consciousness *must be* instantiated in this way, but I think
>>> there must be
>>> something that makes the "states" part of a process - not just
>>> snapshots. Bruno
>>> gets around the problem of defining states by assuming a digital
>>> Turing like
>>> process, but then he has to provide something besides spacetime to
>>> make the set
>>> of states a sequence; which is he does by invoking the requirement
>>> that they be
>>> a computation. I have some doubts as to whether this is enough,
>>> but at least it
>>> is something.
>>>
>>
>> It comes down to whether the brain is Turing emulable. If it is, then
>> I see no problem describing it in terms of a sequence of discrete
>> states. The question then arises whether the causal links between the
>> states in an intact digital computer are necessary to give rise to
>> consciousness, which is what I thought you were claiming, or whether
>> the same states in disconnected fashion would achieve the same thing.
>> Opponents of computationalism such as John Searle have argued that if
>> a Turing machine can give rise to consciousness then the disconnected
>> states would also have to give rise to consciousness, which is then
>> taken as a reductio against computationalism.
> However a Turing machine is not just a set of states, it also
> requires a
> set of transition rules. So in the same abstract way that the
> integers
> are ordered by "succession" the computational states of a Turing
> machine
> are ordered. Whether just abstract rules, without implementation, are
> sufficient isn't clear to me.
OK, but then the UDA is supposed to explain that.
When we abandon the physical supervenience principle, and still keep
digital mechanism, comp, we have to make clearer the comp
surpevenience thesis. When you say in a previous post, to Stathis:
> Bruno gets around the problem of defining states by assuming a
> digital Turing like
> process, but then he has to provide something besides spacetime to
> make the set
> of states a sequence; which is he does by invoking the requirement
> that they be
> a computation. I have some doubts as to whether this is enough,
I only bet that there is a universal machine with respect to which
that sequence of states is a computation.
UDA makes it *necessarily* enough, once you say "yes" to the
digitalist surgeon. I think.
(then from the first person point of view it will be an infinity of
computations-universal machines)
> but at least it is something.
Thanks. But what a thing! It is no my thing, it is what clearly
"nature" has not stopped to show us with life, brains (amoebas getting
cabled), and computers: apparition and re-apparition of *the* (by
Church thesis) Universal "Machine".
You get a point on Stathis: a sequence of states, or a sequence of
description of states, or a description of a sequence of states, none
of those things can "implement" consciousness ... per se. Sequences of
states ,or description of sequences of states, implement consciousness
only relatively to universal machine, either in the third person way
(get accessed by the UD), or from the first person points of view the
most probable (or credible, or bettable) universal machine(s)
relatively to its indexicaly current state.
I think Stathis can conceive that a stone could implement all
computations. In a sense, this is true (assuming comp), given that a
stone, from *your* point of view should already be described by the
collection of *all* computational history going through the state of
"the stone" (if that exists) or the state of "you + the stone". This
is advanced stuff and could perhaps be resolved by hands, but it is
more funny, deeper, and modest, and then this is what I have done
after all, to directly interview the universal machine itself.
Which leads to AUDA.
Assuming comp, specifying just one universal machine will do,
ontologically. And elementary arithmetic, taught in high school, and
captured by Robinson Arithmetic is enough. It defines implicitly a
universal deployment. If f(x) = z, f computable, then Robinson
Arithmetic will prove that fact (and also that if f(x) = z & f(x) = y
then y = z).
But it is epistemology which counts, in particular Physics is first
person (plural), and to be described, we need a universal machine
which is little bit more introspective. Here there is a theorem (not
mine!): if you had, to Robinson Arithmetic, the infinity of
"induction" formula (Ax means "for all number x ...", )
(F(0) & Ax(F(x) -> F(x+1))) -> AxF(x)
then you get already a sort of unsurpassable, in its introspective
power, universal machine. The one I called Löbian, because it obeys
the modal modesty formula B(Bp->p)->Bp which is Löb's Theorem, "as
said by the machine about itself" (with Bp = Beweisbar('p'), p
arithmetical sentences. I will not coming back to this now, perhaps
later. it is the main axioms of G and G* which provably characterize
such the provable and the true of such systems.
AUDA illustrates the obvious: comp get its main meaning(s) through
theoretical computer science and mathematical logic, which needs some
works.
The hard work has been done by Gödel, Löb and Solovay (and many others).
Note that I would have concluded in the falsity or in the solipsistic
nature of comp, if nature, through Einstein, Everett, Feynman, ...,
didn't give a glimpse of plural, sharable, uncertainties: we share
deep computations, and the bottom seems linear.
It is hard to explain more without being more technical, but the
notion of universal machine is both very easy to define (like a
definition of the Mandelbrot set) and creepily hard to predict (again
like an falling point on the Mandelbrot set).
In a sense, related to abductive power inference, there is already
something uncomputably clever than a universal machine, it is a couple
of universal machines. It is another way to show that reductionism
fails. Universal machines tends to self)accelerate relatively to each
others. In my opinion Babbage, Turing, Post, and many others have made
a major discovery. Now it is Church thesis which makes those universal
machines ... universal.
Comp makes theoretical computer science fundamental. It is used in a
UDA step 7 in a specific way.
Bruno
http://iridia.ulb.ac.be/~marchal/
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