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.
The observer (you here) effectively is the measure via a self-
selection rule.
This makes no sense.
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.
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?
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.
?
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.
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.
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, +, *.
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.
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.
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.
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.
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.
?
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.
Bruno
http://iridia.ulb.ac.be/~marchal/
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