On 14 Jul 2014, at 02:04, meekerdb wrote:
Yet that seems to be what Quentin requires in order to say to
instances of the MG compute the same function. Knowing the
universal number or knowing the function is like the problem of
knowing all the correct counterfactuals.
The MG is supposed to have been made at some right substitution
level, by us, by chance (whatever), then (and here I am not sure of
Quentin's wording, but each computation at some level is emulated
"in parallel" at infinitely many coarse grained level in
arithmetic, that looks like more primitive computations.
To give an example, imagine a Lisp program computing a factorial
function. You have a well defined computation in term of the
stepping (tracing) function associated to an interpreter Lisp and
the input (factorial 5), say.
As Lisp is a universal number, that *counts* as a computation.
But then imagine the computation of the Lisp program emulating a
boolean Graph (Nor gates and their link and delays) emulating a Z80
processor, emulating itself a Lisp interpreter computing (factorial
5) with the same algorithm as above.
Does that comp for a computation of (factorial 5). It does. Is it
the same computation? Not really. It is a different path in the
UD*. If that process incarnate the conscious flux, then both does,
but one if (by construction) at the simplest right level (program
in Lisp computing fact 5), and the other is, notably, emulating a
lower level, that is the Boolean graph of the Z80 processor.
Are they the same because they both compute 5!; even if they used
different algorithms?
No. If they use different algorithm, the function computed is the
same, but the computation differs. But in the above case, I suppose it
is the same algorithm, but we look at the implementation at a lower
level. Again the computation differ at that lower level, and does not
differ at the higher level. In the UD*, this will correspond to
different phi_i(j)^n, and thus different computations, but equivalent
from the "point of view of the factorial" (say).
Bruno
And, yes, knowing the universal number and its data, you know, or
can derive, the counterfactuals.
Comp says that there is a level of description of myself such
that those computation *at the correct level" "carries my
consciousness".
There's where I agree with JKC. You keep fudging what "comp"
means. The above is *not* the same as betting that the doctor
can give you a physical brain prosthesis that maintains your
consciousness.
I don't see this. Please explain.
I think the level description would have to include not only you
but your "world".
Well, I agree, that is why we need to distinguish []p and []p &
<>p, and []p & p.
Universal numbers can justify their own incompleteness and they can
bet, and intuit, the thing with respect to which it is incomplete.
The []p is just a believer. The " & <>p" nuance is equivalent with
giving him a world satisfying p. The " & p" nuance consists in
keeping intact the relation between belief and truth (or "God", or
"Real world", etc.).
The math shows that such nuances obeys different, but related, laws.
So I could say "yes" to the doctor even though I don't think the
computational brain he installs in me is sufficient, by itself, to
instantiate my consciousness.
Sure, me too.
But Brent, and Peter Jones, adds that the computation have to
be done by a "real thing".
This is a bit like either choosing some particular universal
number pr, and called it "physical reality", and add the axioms
that only the phi_pr computations counts: the phi_pr (j)^n.
I think Peter, like me, questions the existence of numbers as
any more than elements fo language.
This is conventionalism. I consider that this view is refuted by
number theory implicitly, and by mathematical logic explicitly.
The existence of not of infinitely many prime number twins is
everythi,g but conventional. With comp, the existence of your
dreams in arithmetic, and their relative proportions, are not
conventional.
So it is not like choosing a universal number, it's saying that
some things exist and some don't.
Define "exist". If you say "exists physically" then you beg the
question, and I will ask you to define "physics".
Define "exists".
See the preceding post. The TOE derived from the mechanist
reincarnation belief, needs only to agree with the first order
standard definition, mainly that a theory proves that something
exists having some property P when the theory verifies (proves) P
for some object. It is the rule A(x) -> B / ExA(x) -> B, (useful
in more general setting), or more simply
the classical A(n) / ExA(x).
But that begs the question of whether the axioms are true. It is
just "existence" relative to some axioms and rules of inference.
Isn't that why you include &<>p...to assume the truth of the axioms
in some world?
Then the points of view are definable, either directly in
arithmetic, or indirectly, in term of precise , yet non definable
in arithmetic, collection of numbers). Comp makes the use of
computer science handy to make all this precise.
One can give a precise description of a unicorn, but that doesn't
make it exist.
Then, each points of view defines its own notion of existence, and
they are captured formally (at the meta-level) by the modal
existence, like []Ex[]P(x), etc.
Well, this would just select (without argument)
It's based on observation not axiomatic inference.
That is explain in the comp theory. Observation is an internal
modality of the arithmetical truth.
That I would like to learn more about.
You are using some "real existence" fuzzy notion to make a
reasoning invalid, in the same way that a creationist can say
that "Evolution Theory" needs a God-of-the-gap.
I don't see the parallel. We can presumably agree on whether or not
something physically exists, whether we can interact with it by
perception.
a special sub-universal dovetailing among (any) universal
dovetailing. The only "force" here is that somehow the quantum
Everet wave, seen as such a phi_pr do solve the measure problem
(accepting Gleason theorem does its job).
But just choosing that phi_pr does not solve the mind-body
problem, only the body problem in a superficial way (losing the
non justifiable parts notably).
Or they make that physical reality non computable (as comp
needs, but they conjecture that it differs from the non
(entirely) computable physics that we can extract from
arithmetic (with comp). But then it is just a statement like
"your plane will not fly". Let us make the test, and up to now
it works.
Yes, I'm willing to accept your argument as an hypothesis.
Comp is the hypothesis. the argument is not.
But it seems to me that it proves that consciousness and physics
necessarily complement one another.
It is more than that. It makes physics the analog of a surface of
what is real independent of me (the mind of the universal
machine) which is more like a volume having that physical surface
as a border.
Sounds like a good metaphor, but what exactly does it mean and how
do you show it?
Starting from arithmetic you must solve both the mind problem
and the body problem at the same time. I don't see that you've
made psychology more fundamental than physics. You've made
arithmetic more fundamental.
ARITHMETIC ==> NUMBER's PSYCHOLOGY ==> CONSCIOUSNESS ==> MATTER
APPEARANCE ===> PHYSICS.
I agree with Brent, and I think everybody agree, when he says
that reducing does not eliminate. But we can't use that to
compare consciousness/neurons to temperature/molecules-kinetic.
In that later case we reduce a 3p high level to a 3p lower
level. And indeed, this does not eliminate temperature. But in
the case of consciousness, we have consciousness which is 1p,
and neurons which are 3p. Here, the whole 3p, be it the
arithmetical or physical reality fails (when taken as a
complete explanation). The higher level 1p notions are not just
higher 3p description, it is the intimate non justifiable (and
infinite) part of a person, which wonderfully enough provably
becomes a non-machine, and a non nameable entity, when we apply
the definition of Theaetetus definition to the machine.
But what does it mean to "apply a definition to a machine". And
why should we apply *that* definition, which is far from
axiomatic.
The accepted axiomatic is T or S4, that is []p -> p (with or
without []p -> [][]p).
machine's have their "[]" well defined, and to apply the
Theatetus' definition consist in define knowledge of p by []p & p.
But you equivocate on []. Sometimes is means "provable (from some
axioms...Peano?)" and sometimes it means "believes".
It means provable by any "rich enough" machine. I limit myself to
machine having correct arithmetical beliefs, and their
arithmetically sounds extensions.
But you assume it "knows" *all* provable theorems - which cannot be
true of any human being.
Brent
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