On 7/14/2012 4:25 AM, Bruno Marchal wrote:
On 13 Jul 2012, at 21:59, Stephen P. King wrote:
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).
Why do you seem to insist on a global ("on all computations")
This is a consequence of the invariance of consciousness (for delays,
virtual/real shifts, ...). I do not decide this.
Might you see that this is problematic? Because you are using a
particular infinite domain and codomain (N -> NxN) as primitives and
these are ordered, you are stuck. This is one of the many weaknesses of
Plato's program. I admit that the general idea is brilliant and
valuable, it is far to limited and thus constraining on what can be
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
UD* does not bound the measure, and so such requirements can't be applied.
I know this! It is for this reason that I make my claim that your
result is for solipsistic systems only. One cannot hope to define an
explanation of interaction with this method. As Peter Wegner et al point
out here <http://www.cs.brown.edu/people/pw/papers/bcj1.pdf>, it is
defined a priori to only be one thing. Interactions, to be modeled well,
cannot be constrained a priori in this way.
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
This is just an insult in disguise. Please Stephen , just do the math.
I did not intend it as an insult, but that possibility of
interpretation is present. Why are you taking that option? You are
avoiding my point. Why do you dismiss the SAT issue?
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"
In which theory? This cannot work if "we are machine", by the
Right, and that is the problem that I see.
I am not sure what you mean by "explanation" as you are using the
word. Again, AFAIK abstractions cannot refer to specific physical
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!)
Not at all. "I", the first person one, is not a number, and cannot be
associated to any number.
Is it independent of all the numbers? Can it be severed? No! I am
arguing the same thing for computations. Severing computations from
physical implementation is a mistake. You are going to far. I think that
it is like the difference between going to the limit of a function and
jumping the gap to the "at infinity" itself.
How can one ignore the necessity of a (relatively) persistent medium
to communicate? You are still falling into the solipsism trap!
You make a lot of statement without any justification, and ignoring
all previous patient explanations.
Turing Machines operate by a priori definitions, thus they cannot
make good models of interaction. I am just using Peter Wegner's claims
and proofs. See http://www.cs.brown.edu/people/pw/strong-cct.pdf
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.
It seems you come back with primitive (assumed) matter. I have no clue
what that could be, and it cannot work by UDA.
No, I am arguing against primitives entities altogether. I am
claiming that neither matter nor numbers can be truly primitive, both
have to emerge from a common neutral ground. It is the common neutral
ground tht is primitive, not matter nor numbers. Bertrand Russell
already has worked this out in his considerations of neutral monism, you
are simply refusing to consider this possibility.
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").
That is a consequence of arithmetical realism without which Church
thesis and the notion of digital machine cannot be defined.
The fact that they can possibly have hallucinations or dreams must be
It is a theorem of arithmetic. All finite pieces of computations exist
in arithmetic, the first persons cannot not glue them, by what is
explained in the first six step of UDA.
That they are "collective" is an additional matter. You are glossing
over very difficult problems!
I formulate them in a way we can test precise answer.
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.
Here you seem to ignore theoretical computer science.
Theory does not exist independent of minds with the capacity to
discover it. You cannot sever the continuity of the connection between
the two and imagine that they can still connect together. Platonism only
works when its weak dualism is undisturbed. Minds that are completely
severed from the means of interfacing with each other lose their ability
to know anything other than themselves.
You say that computations are totally independent of physical systems,
In the same sense that the content of "17 is prime" is independent of
physics. You have fail to explain the dependence that you suggest.
Independence of a particular physical system is not the same as
independence of physicality. I am arguing for the former and you for the
therefore computations have the same properties and actions if we
eliminate the physical systems altogether. Is this correct?
The "therefore" is too quick. the independence is a consequence of
strong Occam + step seven, or weak occam + step 8.
Step 8 is a monstrosity.
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.
That is Putnam functionalism, and is part of comp. What I say go well
Yes, and I am trying to get you to see that this is a mistake.
To make your claim valid you have to tell me what is not valid in UDA.
You ignore the fact that UDA is required to be communicated and the
means of its communication. It is a castle floating in mid air, after
its scaffolding has been pulled away. It floats for a moment and then
crashes down to the ground.
I am putting computations (the abstract bit strings)
Computations are not bit strings. You confuse a computation with a
description of computation.
at the same ontological level as the physical systems. Neither is
taken as primitive.
So what is your theory? Don't tell me "existence", for that means
nothing at all.
Only the neutral ground of necessary possibility is primitive.
"necessary" and "possibility" are high level notion, and we don't even
have a clue to what you apply it.
You don't, that is obvious.
To rephrase this in more philosophical terms: neither minds nor
bodies can be ontologically primitive.
Like in comp. But numbers (or combinators, ...) can be.
No, because they have particular properties they cannot be taken as
neutral. Neutrality here admits no particularity of property. At best
one can use "all possible properties" or a bare "hanger" like substance
that we can hang properties upon. This is already well known in
philosophy. This article cover this in great detail:
http://plato.stanford.edu/entries/substance/ You might do well to read
all of it.
They co-emerge from the undifferentiated Being-in-itself
simultaneously and equally.
That is the kind of jargon which gives philosophy its bad reputation.
You can't use this to invalidate proof.
Rubbish; it is susceptible to disproof by reduction!
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
That does not make sense. Sorry.
This is discussed in Stephen Wolfram's article:
"...many physical systems are computationally irreducible, so that their
own evolution is effectively the most efficient procedure for
determining their future."
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.
I partially disagree, but that is another debate.
I would very much like to have that debate.
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
<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.
You contradict again yourself.
Where? Are you back to claiming that I am assuming "primitive
matter"? Please, that is stale and already refuted. You simply fail to
want to understand. I have no need to argue what others have already
argued better. It was, among others, Bertrand Russell himself that
argued this case for neutral monism. I can do no better. My problem is
that I cannot cut and paste his text to this media.
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?
Category confusion. Numbers are not located in any space.
Correct, and thus there is no possibility of multiplicity of a
number. There is only one number of each kind. Godel's diagonalization
is a form of "semantic externalization" if you stick to your argument,
therefore your step 8 collapses. This is also explained as the problems
that the "skeptical hypothesis" has:
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.
Space and location emerge from arithmetical relations.
Emerge into what? There is no "there" there! There is no a priori
possibility of anything external to the arithmetic relations, there is
literally no room to put the copies therefore you cannot make copies or
claim properties that only exist in functions on copies.
You reject the arithmetical realism, which makes you coherent, but non
Non-computationalist only because I claim that computations are not
just those that exist on N -> NxN.
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
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
I have answered this many times, and you did not make any specific
Please cite one.
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.
But then do it. What i say has been explained consistent with what
Pratt says. Not Deutsch, who indeed, reify the physical reality, and
makes it primary, as he want keep physicalism intact. He just
contradict elementary computer science, and makes a sort of
revisionism of the Church Turing idea.
You fail to address Deutsch's criticisms directly; they are laid
out explicitly in his new book. I have a copy ( of Beginning of
Infinity) siding on my desk next to me now and have read the passages
regarding this issue many times, Deutsch is not making the physical as
necessarily primary, as you seem to imply here, but he can defend
himself if he chooses to. So far he seems to be explicitly ignoring you.
:_( My point is that you cannot assume all of the properties of matter
and claim that matter is not involved. You are suggesting tacitly that
matter is something separate from its bundle of properties. I disagree!
"Nature, to be commanded, must be obeyed."
~ Francis Bacon
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