On 20 Aug 2009, at 02:07, David Nyman wrote:
>
> 2009/8/19 Jesse Mazer <lasermazer.domain.name.hidden>:
>
>>>>> I completely agree that **assuming primary matter** computation
>>>>> is "a
>>>>> physical process taking place in brains and computer hardware".
>>>>> The
>>>>> paraphrase argument - the one you said you agreed with - asserts
>>>>> that
>>>>> *any* human concept is *eliminable*
>>>>
>>>> No, reducible, not eliminable. That is an important distinction.
>>>
>>> Not in this instance. The whole thrust of the paraphrase argument is
>>> precisely to show - in principle at least - that the reduced concept
>>> can be *eliminated* from the explanation. You can do this with
>>> 'life', so you should be prepared to do it with 'computation'.
>> Well, not if you believe there are objective truths about
>> computations that
>> are never actually carried out in the physical world, like whether
>> some
>> program with an input string a googolplex digits long ever halts or
>> not.
>
> Yes, but here - in connection with Peter's apparent support for the
> Quinean concept-reduction argument - I was specifically commenting on
> the status of 'computation' **if** you assume primitive matter. In
> that case, I'm not sure what "never actually carried out in the
> physical world" would mean.
On the contrary. If you assume there is a primitive material reality,
a primitive physical universe, then it makes sense to talk about the
computations which are carried out in the physical universe, like the
one done by this or that computer or brains, and the computations
which are not done in that universe, like some possible
counterfactuals (the computations carried out by Julius Caesar meeting
Napoleon), or some extravagant computations like the computation of
the 10^(10^1000) digit of the square root of two. Of course in the
special case of a large multiverse, or in the concrete ever expanding
universe assumed in step seven, the universal dovetailing is
integrally executed so that in such a universe all the computations
are carried out.
> I don't have a problem with step 08 on the basis of the Olympia
> argument, as I've tried to demonstrate - is there some other aspect of
> computational supervenience that you feel I'm missing?
>
>>
>> May be you don't want to do the math? The math for UDA are really
>> basic compared to the math needed for AUDA.
>>
>
> I'm trying to follow the math as you go through it, although I still
> haven't really fathomed where it's leading.
Your second sentence answers the first one. Your paragraph above also.
The current "seventh step series" is leading to the understanding of
what is a computation, and a machine, for a mathematician. With or
without assuming PM (primitive matter) there is an mathematical notion
of computation and of computability. This is amazing, because Cantor
discovered a technic which is capable of demolishing most attempt to
define a real universal thing in math, but as Gödel will eventually
realize, the set of computable functions remains closed for that
technic. Gödel described this as a kind of miracle, and was very
skeptical about it. That "miracle" is Church thesis. Gödel, on its own
saying, missed it, despite he invented one of the candidate for a
definition of what are computations, and what means computable.
The notion of computation does not rely on anything physical.
Computation and computability theory are branch of mathematics, and in
my youth those branches were taught in the "pure mathematics
courses"., not in "applied mathematics course". And in some
universities this remains so. In informatics "applied computer
science", such course on the mathematical computation are not taught:
you have to do pure math to study it, and if you dare to pretend there
could be relations between them, you are consider as a betrayer of
pure math!
I think that what remains unclear in step seven is due to the lack of
knowledge of that "purely mathematical" notion of computation. You
need it to justify why Universal Machine and Universal Dovetailer"
exist and in what sense they are truly universal.
The notion of physical computation *today* is quantum computation, and
this is a priori something else, except it can be shown defining the
same class of computable functions.
A big problem for the comp hyp. consists in explaining why apparently
everything we can touch and smell is described only by quantum
computation. Why in UD* (the infinite execution of the UD, or of any
UD) does the quantum computation wins the "measure battle", at least
from the first person (plural) points of view. Of course the first
person plural indeterminacy explains why, but we have to recover the
detail. The apparent "primitive matter" that we recover from comp is a
priori "too much powerful, and leads to too much "white rabbits". Only
pure mathematical computer science explains why this is not trivial at
all.
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Thu Aug 20 2009 - 11:05:53 PDT