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)
theological assumption.
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).
All scientific theories assume the numbers in this weak sense.
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
distinction.
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. 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.
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.
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.
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.
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).
2) That it is (in principle) possible *is* the comp assumption.
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.
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.
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
space.
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.
Bruno
http://iridia.ulb.ac.be/~marchal/
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