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?
How are these entities given such that they are simultaneous for the
selection function? Do they form a set of some kind? If so, what kind of
set is it?
The observer (you here) effectively is the measure via a
self-selection rule.
This makes no sense.
Are you familiar with Bostrom's SSA
<http://meteuphoric.wordpress.com/anthropic-principles/>? 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.
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".
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.
A possible escape from this is to allow for non-well founded sets and
such things as non-principle ultrafilters
<http://mathoverflow.net/questions/15872/non-principal-ultrafilters-on>,
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.
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. 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 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. 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. You cannot expect the
results of physical behavior to occur when the physical has been
eliminated.
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?
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. 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 implies that for X to be
true there must exist a condition that could make X false, otherwise
truth is a meaningless concept
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!
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).
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
As I see it, 1p indeterminacy is strictly an a posteriori condition.
?
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".
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) and is not primitive (as it
is not neutral).
--
Onward!
Stephen
"Nature, to be commanded, must be obeyed."
~ Francis Bacon
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