On 3/20/2012 12:01 PM, Bruno Marchal wrote:
On 19 Mar 2012, at 06:20, Stephen P. King wrote:
COMP is just a formal model of the a form of the relationships
between numbers and the content of observer moments, but it assumes
that some particular set of numbers are ontological primitives and
some idealization of actions that we only know to occur when we run
actual calculations on our computers of work out in long form stuff
on chalkboards of by the actions of the neurons in our brains.
I don't think you can say that COMP is just a formal model. COMP is a
crucial act of faith about your survival after an annihilation and a
reconstitution. You don't ask the doctor for a model of a working
brain in your skull, you are asking for the "real thing", which is not
a formal thing (indeed it will be provably not formalizable, yet
meta-formalisable by the "Bp & p", which *cannot* be translated in the
language of the machine, and cannot be duplicated in any provable way
by the machine or any machine that the initial machine can understand.
That is one reason I insist saying that comp is a (quite strong)
Good Day Professor Marchal!
I distinguish between an arbitrary physical implementation of the
idea that we denote as "COMP", as for example in my print out of your
paper SANE04, and a human being's idea of COMP. The former I consider to
be the identity of an equivalence class and the latter is a particular
member of said equivalence class. A "doctor" is a class of physical
systems implementing a category of behaviors that may be represented by
a finite list of enumerable recursive algorithms, but which one exactly
gets matched up with the needs of a particular patient is not specified
in advance nor should be considered to be specified in advance.
The concept of Bp&p ("Belief that P and P is true") is a brilliant
concept and should be part of every logician's lexicon, but I am trying
to think of it in a wider context. For example, how does the "p" of Bp&p
obtain its significance and how is it different from all other possible
Comp does not even assume that numbers are ontologically primitive. It
just assumes that you agree with what has been taught to you in
highschool (and the "yes doctor" act of faith).
Oh OK, then what is assumed to be ontologically primitive in your
thinking? Your ontology theory seems to be a continuously mutating
target... Is it ontologically neutral, ala Russell's neutral monism or
not? I am trying to examine many possible ontological theories to see
which works best with my metric being "explains the most with the least
number of assumptions".
All scientific theories assume the numbers in this weak sense.
As they must to be said to be quantitatively predictive. But in
philosophy we must consider more than just quantities, we need to
examine qualitative relations and other organizational principles, just
to start a very long list.
Numbers (or equivalent) become ontologically primitive only when we
realize that the physical reality can no more be ontologically
primitive. Indeed we have to assume at least one (Turing) universal
entity. Which one is not relevant, except that we cannot use a
"physical one" without taking the risk to loose the quanta/qualia
I agree, with your claim here. You have shown a sound argument as
to how material monism is untenable as a ontological theory and have
introduced a brilliant and sophisticated version of ideal monism. I
critique it in the same way and for the same reason that I critique
Berkeley's idealism. All forms of monistic ontologies suffer from
incompleteness problems, in that there are always objects and processes
that cannot be included for consistency reasons and must be hand waved
away as "epiphenomena". It is for that reason that I argue for some form
of rehabilitated dualism that does not have the epiphenomena problem.
Leibniz proposed such an ontology but his idea had a problem of its own,
which is, surprisingly, equivalent to a "many bodies problem": how it
that the content of monads is coordinated and synchronized such that
they appear internally to interact with each other without any actual
"substance exchange" between them - "monads have no windows".
COMP is an idealism, a beautiful fiction.
No, it is not. It can be false, and indeed my point is that we can
experimentally refute it.
Could you write up an example of such an experiment?
But it might be true. Joseph Knight is right, you can say that comp is
true or false. The excluded middle can be applied in this highly
classical theological theory. Comp just does not make sense in pure
intuitionist philosophy, making such a philosopher forces to say "no"
to the doctor, or to abandon momentarily intuitionist philosophy when
in the hospital. We cannot construct provably our "3-I", we can only
bet on them. "saying yes" to the doctor asks for a minimal amount of
realism/platonism, but it is weaker than any physical realism, which,
as you know, appears to be incompatible with the comp hypothesis.
I am distinguishing between theories as immaterial concepts of
minds and the physical implementation of their objects and relations.
Your example here, is of what actually happens in a physical and mental
interaction between a patient seeking a brain hardware repalacement and
a doctor with the skills and means to perform such a replacement. The
patient must have a reasonable belief that the doctor is capable to
performing such a procedure, which is a 3-p assumption as we are
considering it, but what actually goes on "in the patient's head" is a
1-p. While the patient can be considered by us voyeuristic bystanders as
making an informed decision that we can model as 3-p, as we can discuss
among ourselves and within that particular discussion it is indeed a
binary logical decision subject to "true or false" rules (excluded
middle and bi-valence) but more generally, as we are discussing
ontological theories here, there are more considerations involved that
do not allow such a quick rule.
Comp is not proposed as a formal explanation of mind and matter. It is
proposed as an hypothesis in cognitive science, which is really a
theological belief akin to a form of reincarnation. The protocol
assumes the doctor is choosing the right level of substitution, and
that you will survive integrally. If we were allowing amnesia, we
might accept other even stronger form of comp for which the excluded
middle might no more be applicable, but this is not what we do to
prove the reversal.
I understand that and am very interested in COMP for those (and
other reasons). Please remember that I am a student (and thus not some
expert) and I am asking questions because I am trying to understand the
larger ramifications of COMP.
This is cheating since we have learned that one thing that Nature is
not is biased about any framing, basis or mereology. Why Integers and
not a large but finite field? Why not the P-adics? Why not the surreals?
Because comp is based on Church thesis which makes computation
equivalent with (sigma_1) arithmetical proposition, roughly speaking.
If the doctor uses a p-adic number system, by Church thesis, this will
be equivalent to a standard arithmetical set-up. Nature *is* biased
toward natural numbers (or equivalent) once you assume Church thesis.
So if you assume comp, the good old natural numbers that everyone
knows are quite good enough.
So would you agree that COMP is not specific to a particular
Category of representational quantities? If it is biased toward some
particular representation then it is not "truth", by definition.
Why not some form of non-standard numbers? Each of these sets have
different properties and computational features, we should never be
so anthropocentric to think that "Man is the measure of all things!",
But comp and computer science makes the Universal Turing Machine the
measure of all things. We have no choice in that matter.
But this is just "not even wrong!"; UTMs do not define any kind of
measure beyond that which is inherent in recursively enumerable
functions (modulo isomorphisms). The many body problem requires
considerations beyond that Category to find a solution as it is
necessary, I claim, to model interactions that might not be faithfully
represented in terms of recursively enumerable functions. Peter Wegner
has written extensively <http://www.cs.brown.edu/%7Epw/>on this. You
yourself have shown that there are problems that are not computable
within COMP's implications and I need nothing more than your own result
to show the proof of my claim. My personal problem is my disability to
write up symbolic representations because of my dyslexia, but I try to
work around this as best I can.
If your complaint against me is that I am a pitiful agent to
discuss these Ideas, then I plead guilty as charged, but does this
prevent your consideration of the problems and Ideas themselves?
which is exactly what we are claiming when we say that "... our
generalized brains ..." are this and that, such as what is implied
by "...the latter is just a restatement of the former." The point is
that we first need to dig a bit deeper and establish by natural
mathematical means that 1) digital substitution is a sound
mathematical concept and 2) that it is possible.
1) Yes, thanks to the notion of level, digital substitution is well
defined, and sound (if the level is correctly chosen).
Yes, and this makes it "local" not "global" and thus is not
consistent with a representation in Platonic terms.
2) That it is (in principle) possible *is* the comp assumption.
OK, but you are assuming more. You are assuming that computations
have particular and definite properties merely because they are true,
you are claiming implicitly that properties supervene on the soundness
of the object having such properties. This is, I claim, equivalent to
postulating the existence of a Universal Observer that can somehow
percieve all UTM strings and define by fiat which are equivalent to
which without having to actually implement all of them and doing the
calculation of an infinite NP-Complete problem. Basically, I accuse you
of claiming that not only P= NP but also that we do not even need to
actually expend the physical resources to perform the computation of the
Polynomial complete problem. This is simply a violation of the rule
that "there is not such thing as a free lunch" as it allows for
knowledge to occur without any work to gain it. Even God itself cannot
perform a computation without actually implementing the computation in a
physical form. It is because of this simple fact, I claim, that the
physical world is both "real" and ontologically necessary, but it is not
ontologically primitive. There is a difference here, it is the same kind
of difference as between situations where "no implementation exists" and
"no particular implementation is necessary".
So I ask again: Why are we putting our selves through such convoluted
abstractions to talk about the simple idea of moving though space-time?
Because we are interested in the comp mind body problem. Not in
physics, per se. But with comp, to solve the mind-body problem we are
OBLIGED to explain all the space-time feature from the
"block-mindscape", which is itself entirely structured by the +/*
number structure. That is the result: a reduction of the mind-body
problem to a well defined body problem in arithmetic/machine-theology.
AUDA gives already the propositional solution. To extend it to the
whole physics of qualia and quanta, you need to extend AUDA at the
first order logical level, which is not simple.
If you read Pratt's paper carefully you would see that he points
out that there is no mind-body problem, there is only the problem of
minds (or bodies) interact with each other. There is no dichotomy or gap
between mind and body as they are just dual aspects (via Stone duality)
of the same basic and neutral monad. We can model interactions via
residuation or quantum games and gossiping graph models but only in a
finite and local sense. There is no global pre-established harmony.
At least try to understand my point here. I am trying to explain
that there are things that numbers alone cannot do, they cannot count
themselves. They cannot perform any form of activity, they are purely
and perpetually static and fixed. Therefore any talk that involves
any kind of activity or change is nonsense in COMP. Everything is
assumed to occur simultaneously as if the speed of light where
infinite, the laws of thermodynamics do not apply to information
processing and there is no such thing as a space or time.
But this critics works for any theory which does not assume a
primitive "real time" (and what would that mean?). Any physics with a
notion of block universe is criticized by your argument. If you
believe that there is a primitive time, then UDA should convince you
not only that COMP is false, but quantum mechanics (without collapse)
too, and general relativity too.
The "block universe" idea does not work. I am not the first to
point this out. John Longley's paper
<http://homepages.inf.ed.ac.uk/jrl/Research/laplace1.pdf> here is a good
example of a deep examination of the problems it has and David Albert's
papers on non-narratability
is another. This paper <http://arxiv.org/abs/quant-ph/0105013> is
another discussion of what I am refering to. I could point out more if
necessary. That idea is a stinky red herring. I have argued against any
thing like "primitive time" as such requires a measure to exist and such
a measure is of the same kind as the one that you are looking for. As
Hitoshi Kitada has pointed out <http://arxiv.org/abs/quant-ph/0410061>,
the non-existence of global measures does not preclude the existence of
local measures of changing quantities, so we can in fact have "local"
times and can discuss notions of time, but again, I claim that there is
no such thing as primitive time. Your ontology denies the existence of
change itself and therefor precludes any possibility of time. (I
apologize for the links to papers, ut those are for you and others
should they seek to visit the discussion of others on the subject.)
Personally I find that assuming notion like space and time answer
nothing, and that is what motivated me in showing that comp implies
that such notion cannot be used to explain our perception of time and
The fact that you have no answer to questions as to the emergence
of local time and notions of spaces is my complaint. You refuse to look
at how this is a problem in your thinking because you will never address
the concurrency issue.
If we are going to invoke concepts of continuity and differential
mapping into continuities then we had better know what we are talking
about! Which infinity are you assuming? Are you assuming the
continuum hypothesis of Cantor to be true of false? So many
unanswered questions just being glossed over.
But those questions have not yet appear. They are premature, and more
complex than the technical question we can already formulated. You
seem to continue to think that comp is a theory/model that we can used
to explain things. But comp is a (scientific, modest) theology, in
which we can "believe", hope, or fear, and which makes just many
fundamental question technically formulable. In particular it does
answer the question "where does the universe come from?". The answer
is, by the truth about addition and multiplication, and the technical
details are accessible to any universal machines.
You will ask: "where does addition and multiplication comes from".
This, in the comp theory can be answered: we will never know, at least
in any publicly communicable way. We already need the numbers to give
sense to the question, and we can show that without assuming them (or
equivalent) we cannot recover them.
We can only examine an ontology theory by its long range
implications. This is why philosophers are so repudiated by most
scientists as the ideas of philosophers are almost always empty of
physical implications and can and should be ignored as "mental
masturbation". Again I ask you, exactly how do we test for the truth of
COMP? One simple test would be to do an actual Yes Doctor and replace a
portion of living human's brain with "functionally" equivalent hardware
and test for changes in qualia.
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