Le 17-juil.-12, à 19:23, Stephen P. King a écrit :
On 7/15/2012 11:14 AM, Bruno Marchal wrote:
On 14 Jul 2012, at 18:48, Stephen P. King wrote:
On 7/14/2012 5:52 AM, Bruno Marchal wrote:
On 14 Jul 2012, at 11:16, Evgenii Rudnyi wrote:
On 14.07.2012 11:00 Bruno Marchal said the following:
On 14 Jul 2012, at 10:42, Evgenii Rudnyi wrote:
...
If to speak about your theorem, it is unclear to me, how the
first
person view accesses numbers and mathematical objects.
Like a digital machine, which can access numbers encoded in their
memory, through logical gates, and so one. More details are given
currently on the FOAR list, but the idea is simple, with comp our
bodies are statistical first person constructs related to
infinities
of number relations, so we access to them a bit like a fish can
access water. The price of this is that we have to abandon
physicalism eventually.
I am not sure if I understand. I would like to have an
explanation for a phenomenon, for example
1) I see a cat;
2) I see a piece of paper with 2 + 2 = 4.
Yet, when you start explaining, the phenomenon seems to disappear.
1) I see a cat. This is explained by the fact that your current
computational state belongs to an infinity of computations making
you singling out some stable patterns that you recognize, by access
to your previous experience as being cat. The qualia itself is
explained by the fact that when you refer to the cat, you are
really referring to yourself (with the implicit hope that it
corresponds to some relatively independent pattern), and the math
shows that such a self-reference involves some true but non
rationally communicable feature. The math explained why, if this
justification is correct, machines/numbers will not be entirely
satisfied by it, for the first person is not a machine from its own
first person view.
Hi Bruno,
No, the reverse is the case. The "belongs to an infinity of
computations making you singling out some stable patterns" requires
the prior existence of the "you" to select it.
With comp, you, the dreamer's bodies, and its soul, already exist (in
different modal sense) in arithmetic. Provably so, even in Robinson
arithmetic, for the 3-view.
Is the selection made on the entities defined by the arithmetic?
Defined? yes.
Decided? No.
How are these entities given such that they are simultaneous for the
selection function?
By the axioms of addition and multiplication. I would not talk of
"selection function", but first person selection, which cannot be
defined in arithmetic, nor in any theory, except at the metalevel
(comp).
Do they form a set of some kind? If so, what kind of set is it?
You can map them on their set of Gödel number description, but that set
is highly complex (not decidable, nor semi-decidable).
The observer (you here) effectively is the measure via a
self-selection rule.
This makes no sense.
Are you familiar with Bostrom's SSA?
We have discuss this a lot, even before Bostrom, on the everything
list.SSA is a case of fist person indeterminacy. We have debated on the
Relative SSA and Absolute SSA dilemma a lot. Comp favors the RSSA
(relative SSA).
I am merely assuming that any observer can experience a universe
compatible with its existence. This would hold even for Boltzmann
brains that might happen to occur in universes with physical laws that
are hostile to life. Such would experience a world that is compatible
with their experience (qualia), even if such is completely a fiction.
But these are almost solipsistic as their is a vanishing probability
that other Bolztman brains would have experiences that would have
events what would be bisimilar to each other.
How do you associate a consciousness with a universe? This is what UDA
shows impossible when assuming comp.
I cannot discount my own existence given the immediate fact that I
am experiencing myself as existing.
You cannot discount the first person experience. But comp does not
discount it. It explains how it arises from the ability of numbers to
observe themselves and extrapolate, etc.
I cannot discount it, it is the one thing that cannot be denied
without contradiction. This was deeply examined by Descartes that
lead to his famous "cogito ergo sum".
Indeed.
Descartes' Cognito ergo Sum is a pointed statement of this
unassailable fact. We cannot put the observer on a level that is
emerging from the computations if the observer is the one that is
selecting the class of computations that are generating said
observer.
? You refute Darwin too?
How would you imagine that I would "refute Darwin"? I see
mutation and selection as a basic principle at work here, e.g. Darwin
rit large.
Then you argument above cannot work. For in Darwin the observer emerges
from computations too, even is physical.
A possible escape from this is to allow for non-well founded sets
and such things as non-principle ultrafilters, but I don't know your
stand on their existence.
Good tools.
Our observation of the cat is a symmetric (within bounds)
relationship, otherwise we fall into solipsism.
?
If I observe a cat, for example, and the cat cannot observe me,
then it follows that for the cat, I do not exist.
The cat does not need to believe that you don't exist, which need to be
the case for making it solipsist. He is just agnostic by lacking
information. You confuse ~Bp and B~p.
My claim is that the same thing follows for mathematical entities.
We cannot claim that mathematical (or any other "abstract" entity!)
is such that we (the observers and understanders thereof) are
emerging from them.
Prove that claim. Then by UDA, you refute comp.
The fact that the only efficient simulation of a physical system
of sufficient complexity is the evolution of that system itself is my
proof.
As I said, this is already true in arithmetic. With your definition of
physical here, physics is already in arithmetic.
This was explained well by Stephen Wolfram in this article:
http://www.stephenwolfram.com/publications/articles/physics/85-
undecidability/2/text.html
The proof already exists for you to inspect.
This is very well know by logicians, and is not original in Wolfram,
and has absolutely nothing to do with physics.
This would require that the "independence" is not and cannot be an
unbridgeable gap at all, but a analytic continuum connecting the
particular instance of a physical system with the knowledge and
meaning of the abstraction. Maths do not refer explicitly to the
physical media that they are represented upon by patterns, but this
does not allow us to imagine them as completely independent and thus
severable from the physical instances.
So many implicit assumption. You seem again to assume the physical.
For the sake of this interaction between you and I via email (or
by any other means!) one must assume the physical.
Like Quentin told you a lot, we do assume the physical in comp. We do
not assume the primitively physical. Neither primitive matter, nor
physicalism.
That is exactly the point that I have been trying to get you to
understand. Without the physical, there is no way for interaction to
occur between computations. Computations, ala Church-Turing machine
are strictly closed system. This is well known, except to you, it
seems.
Even Plato's idea of the Forms as "casting shadows on the wall
of the cave" tacitly assumes continuity between the Forms and what
we the ideas in our individual minds. If I am not mistaken the idea
of conic sections where used to argue the idea. Shadow or
projections cannot be severed from the object casting them!
Which can be N, +, *.
How? Where in {N, +, *} is there a action potential? You have by
definition eliminated all forms of action in step 8, therefore any
appeal to actions is a gross contradiction.
But this is false. "IN" arithmetic, as seen from inside, computations
can interact. Indeed the UD dovetails on all possible interaction. For
you to be correct, you need non Turing emulable interaction, and that
would make comp false.
You cannot expect the results of physical behavior to occur when the
physical has been eliminated.
The physical is not eliminated. On the contrary the mind-body problem
is reduced to the problem of justifying the physical from the
arithmetical.
2) The same with "2+2=4 written on some paper". It is also a
stable pattern in the computations going through your state. Here
you might just refer to what you have learned in school, and you
might considered that the truth referred by that sentence on a
paper is more stable than a cat, but the conscious perception of
cat or ink on paper admits the same explanation: some universal
number reflect a pattern belonging to almost all computations going
through your state. You have to take the first person indeterminacy
into account, and keep in mind that your immediate future is
determined by an infinity of computations/universal number, going
through your actual state. For example, all the Heisenberg matrices
computing the state of the galaxy at some description level for
some amount of steps. They all provably exist independently of us
in a tiny part of elementary arithmetic, and admit at least as many
variants as there are possible electron location in their energy
level orbitals.
This paragraph 2) gets dangerously close to my criticism of
your scheme and so it might help us come to some mutual
understanding. For me, the "truth of the sentence 2+2=4" (i will
denote this as X) is not the same thing as the "piece of paper with
the symbols '2+2=4' on it" (I will denote this as Y).
That's part of my point.
OK, what is it that is making the distinction between them?
I was explaining that. See below.
What is the "pattern belonging to almost all computations going
through [one observers] state" generating in your thinking? Both X
and Y?
X is far more general than Y. Y is not even well defined, only "the
truth that some numbers observe something like Y". Y belongs only to
the extension of human-like numbers belonging to stable extension in
front of piece of paper-like objects. X belongs to all consistent
extensions.
I really don't understand this remark. I can only speculate about
it. At some point you need to deal with how "truth" is defined. You
seem to be using something like Kant's "a priori synthetic" idea. I
would like to better understand how "truth" is defined in the
Platonist picture.
I use the common truth theory by Tarski, which is, for arithmetic, the
same as used in high school and by laymen.
My understanding of "truth" follows a Kripkean definition; something
like: X is true if there is at least one accessible (by the
evaluator) world that has a model of X.
This defined consistency, not truth. As you know I used Kripke for the
epistemologies, not the ontology.
This implies that for X to be true there must exist a condition that
could make X false, otherwise truth is a meaningless concept
Of course. No problem with that.
For me, X and Y are duals that are related by the fact that there
exists at least one physical instance (experienced by multiple
observers in a incontrovertible way) that implements a
representation of "2+2=4". Similarly by the duality relation as I am
using it, the particular abstract statement, "2+2=4" is true because
there exists multiple observers that agree on its truth.
That is idealism.
Please elaborate!
To believe that "2+2=4" needs observers is an idealist conception of
arithmetic. It makes comp wrong at the start. Church thesis is
meaningless with such a conception of arithmetic. You can't defined the
meaning of a "a program which does not stop without anyone being able
to prove that it does not stop".
Truths are conditional in my accounting. They are only absolute
if they are incontrovertible over *all possible* observers. Truths
do not exist independent of observers, they are not severable from
the possibility of observation of instances of their physical
implementation.
That is shown the case, in some sense, for physical truth. But we
need some theory to start. You have not presented one, and this makes
many of your statement philosophically or metaphysically, or
theologically ambiguous. This is troubling when you present them as
making invalid a derivation, which should be theory independent. Comp
-> non physicalism is valid independently of comp.
Physical truths are instances of physical systems that are exact
models of themselves in the sense of Wolfram (explained above).
Give a precise quote please. In any case, nothing can model itself per
se, in the comp sense of modeling, and Wolfram point has noting to do
with physics. Complex process needing to be computed to get an
emulation abounds in arithmetic.
I cannot be sure if this helps you as it relies to some
familiarity with the first person indeterminacy and the fact that
our comp states are distributed in an infinity of distinct, from a
third person pov, computations (existing in arithmetic).
Bruno
?
1p indeterminancy requires the evaluation of the diary entries
for a 3p definition of the differences between, say "Being in Moscow"
contra "Being in Helsinki".
This is fuzzy. I can agree, but see no problem there.
One's theory must postulate the prior possibility of multiplicity of
locations or instances that are distinguishable and that is not
possible if there is not an observer (up to functional
equivalence!). Does this help you understand my claim?
The theory is arithmetic. You can prove in arithmetic the existence
of the multiple instances and their relative situations. And this
leads to a problem, indeed. An interesting problem in math and
physics capable of testing the comp idea, or of challenging the
classical theory of knowledge.
Arithmetic is not a single unique entity (there exist many
self-non-contradictory models of arithmetic)
Yes, but all what you can prove in arithmetic theory like PA will be
true in all those models, by Gödel's completeness result.
and is not primitive (as it is not neutral).
It is primitive, as choice of an easy starting theory.
It is primitive, as being not definable in any theory assuming less or
equivalent.
And it is neutral, in the philosophy of mind sense of being neutral
with respect to mind and matter.
This post was entitled "contra-step 8", and does not address at all the
step 8. You did not answer my question on the 323 principle, as I have
restate it for you. You continue to avoid the reasoning to just explain
that somehow you want to keep comp and physicalism from philosophical
conviction, instead of using that conviction to find a flaw in the
proof.
Bruno
PS I have a connection problem, and I might take some time to reply. It
is an opportunity to search the MGA posts (Movie Graph Argument) and
try to find the flaw.
http://iridia.ulb.ac.be/~marchal/
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