On 7/13/2012 9:04 AM, Bruno Marchal wrote:
On 13 Jul 2012, at 11:55, Stephen P. King wrote:
How exactly does one make a connection between a given set of
resources and an arbitrary computation in your scheme?
From the measure on all computations, which must exist to satisfy
comp, as the UDA explains with all details, and as the translation of
UDA in arithmetic (AUDA) makes precise. We still don't have the
measure, but AUDA extracts the logic of measure one (accepting some
standard definitions). And that measure one verifies what is needed to
get a linear logic à-la Abramski-Girard which makes a notion of
resource quite plausible. Anyway, we have no choice. If the measure
does not exist, comp is false (to be short).
Dear Bruno,
Why do you seem to insist on a global ("on all computations")
measure? I think that this requirement is too strong and is the cause of
many problems. What is wrong with a "on some computations within some
bound" measure? It seems to me that if you would consider the Boolean
SAT problem you would see this... I still do not understand why you are
so resistant to considering the complexity issue. Was not Aaronson's
paper sufficient motivation? A possible solution is a "local" measure
(as opposed to global measures), but this idea disallows for any kind of
global regime or Pre-Hstablished Harmony. (Is this why you are so
dogmatic?) It allow also for the possibility of pathological cases, such
as omega-inconsistent logical algebras, so long as the contradictions do
not occur within some finite bound.
In other words, it may be possible to achieve the goal of the
ultrafinitists without the absolute tyranny that they would impose on
the totality of what exists,. but at the small price of not allowing
abstract entities to be completely separate ontologically from the
physical systems that can possibly implement them. Please notice that I
am only requiring the connection to occur within the "possibility" and
not any arbitrary actual physical system! I distinguish "actual" from
"possible".
I am not sure what you mean by "explanation" as you are using the
word. Again, AFAIK abstractions cannot refer to specific physical
objects
It is better, when working on the mind-body problem, to not take the
notion of physical object as granted, except for assuming that the
physical laws have to be rich enough to support brain and computer
execution, that is, to be at least Turing universal.
This is a bit hypocritical since it is an incarnated number(up to
isomorphism) that is writing this email! (per your result!) How can one
ignore the necessity of a (relatively) persistent medium to communicate?
You are still falling into the solipsism trap! Maybe you are trying to
claim some kind of excuse via "semantic externality"! But that argument
is self-stultifying also... Words cannot exist as mere free-floating
entities.
unless we consider an isomorphism of sorts between physical objects
After UDA, and the usual weak Occam rule, we *know* (modulo comp)
that physical "objects" are collective hallucination by numbers.
You must show why some particular class of numbers (or equivalent)
is the class of primitive entities capable of having "hallucinations"
(or "dreams"). The fact that they can possibly have hallucinations or
dreams must be accounted for! That they are "collective" is an
additional matter. You are glossing over very difficult problems!
You have more than once acknowledge that the physical reality is not
primitive (= cannot be assumed), so I am not sure to see why you come
back with it to challenge the comp consequences.
You are not understanding the definition that I have made here. It
is not a "matter is primitive claim", it is a limit on the way you are
defining computational universality. You say that computations are
totally independent of physical systems, therefore computations have the
same properties and actions if we eliminate the physical systems
altogether. Is this correct?
My claim is that universality entails that any universal
computation is not restricted to a particular physical system, but there
must be at least one physical system that can implement it. I am putting
computations (the abstract bit strings) at the same ontological level as
the physical systems. Neither is taken as primitive. Only the neutral
ground of necessary possibility is primitive. To rephrase this in more
philosophical terms: neither minds nor bodies can be ontologically
primitive. They co-emerge from the undifferentiated Being-in-itself
simultaneously and equally. This is just a restatement of the duality
that I am advocating.
I previously wrote: "[there exists a] isomorphism of sorts between
physical objects and "best possible computational simulations thereof"
". This is the link between mind and body that Descartes was unable to
define in his substance dualism. Descartes' dualism failed because it
could not see process; it saw minds and bodies strictly as "things" that
somehow had to interact on each other and thus it was the substance
assumption is what blew up Rene's beautiful project.
and "best possible computational simulations thereof" as I am
suggesting, but you seem to not consider this idea at all.
Because such an idea has been shown to be inconsistent with comp (UDA).
No! It most certainly has not. You are taking liberties with
definitions, particularly in the MGA and strobe argument, to make claims
that are simply wrong. You cannot communicate nor even refer to any kind
of "action" if there is no means to by-pass the Identity of
indiscernibles
<http://en.wikipedia.org/wiki/Identity_of_indiscernibles>. It is not
permissible to assume multiple or plural cases of identical entities
unless there is some means that allows for an "external" differentiation
between them. For example, we can have multiple electrons in physics
because there is a possible variation in their possible location
relative to each other in some "space". If there is no space (up to
isomorphism) assumed to exist at the same level as numbers, how can
there exist multiple versions of the same numbers? How is the notion of
a plurality of possible versions of the same number represented in your
primitive arithmetic? (+, *, N) does not have enough room unless you are
appending additional structure to it and if you are going to do this
then you must withdraw the claim of primitivity of numbers (or
equivalents) because all of the structure must be at the same level if
only for the sake of access.
Your statement "just study the proof and criticize it" begs the
question that I am asking!
It does not. UDA *is* the explanation why if the brain (or the
generalized brain) works like a digital universal machine, (even a
physical one, like a concrete computer) then the laws of physics HAVE
TO emerge from the laws of the natural numbers (addition and
multiplication) law.
NO! You cannot rest all of the necessity of the physical world on
just one brain and its actions. You are completely neglecting the
important and none negligible role of interactions between many physical
systems.
You might study any textbook in mathematical logic to see that a
computation is a purely arithmetical notion (accepting the
Church-Turing thesis). I am currently explaining this in FOAR, so you
can ask a precise question for anything you would have some problem
with in that list (that you already follow). I can no more explain
this here, as I have done this more than once before.
I am studying the materials that I can access. The problem is that
I have questions that the authors do not consider. The exceptions are
those authors, like Vaughan Pratt and David Deutsch, that you are
discounting. Therefore I have to address you directly.
Bruno
--
Onward!
Stephen
"Nature, to be commanded, must be obeyed."
~ Francis Bacon
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