Hi Bruno Marchal
I'm way out of touch here. What is comp ?
I don't think you can have a symbolic theory of subjectivity, for theories are
in symbols, and subjectivity is awareness of the symbols and hopefully what
CS Peirce differentiates the triadic connections between symbol and object and
in his theory of categories:
FIRSTNESS (perceiving an object privately) -- raw experience of an apple
SECONDNESS (comparing inner and outer worlds) - looking up the proper word
symbol for the image in your memory
[Comparing is the basis of thinking.]
THIRDNESS: (doing or expressing publicly in words) - saying "That's an apple."
Roger , rclo...@verizon.net
----- Receiving the following content -----
From: Bruno Marchal
Time: 2012-08-13, 11:53:51
Subject: Re: Why AI is impossible
On 13 Aug 2012, at 17:04, Jason Resch wrote:
On Mon, Aug 13, 2012 at 8:08 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:
On 12 Aug 2012, at 18:01, William R. Buckley wrote:
The physical universe is purely subjective.
That follows from comp in a constructive way, that is, by giving the means to
derive physics from a theory of subejectivity. With comp any first order
logical theory of a universal system will do, and the laws of physics and the
laws of mind are not dependent of the choice of the initial universal system.
Does the universal system change the measure of different programs and
observers, or do programs that implement programs (such as the UDA) end up
making the initial choice of system of no consequence?
The choice of the initial universal system does not matter. Of course it does
matter epistemologically. If you choose a quantum computing system as initial
system, the derivation of the physical laws will be confusing, and you will
have an hard time to convince people that you have derived the quantum from
comp, as you will have seemed to introduce it at the start. So it is better to
start with the less "looking physical" initial system, and it is preferable to
start from one very well know, like number + addition and multiplication.
So, let us take it to fix the thing. The theory of everything is then given by
the minimal number of axioms we need to recover Turing universality.
Amazingly enough the two following axioms are already enough, where the
variable are quantified universally. I assume also some equality rules, but not
x + 0 = x
x + s(y) = s(x + y)
x * 0 = 0
x*s(y) = (x *y) + x
This define already a realm in which all universal number exists, and all their
behavior is accessible from that simple theory: it is sigma_1 complete, that is
the arithmetical version of Turing-complete. Note that such a theory is very
weak, it has no negation, and cannot prove that 0 ? 1, for example. Of course,
it is consistent and can't prove that 0 = 1 either. yet it emulates a UD
through the fact that all the numbers representing proofs can be proved to
exist in that theory.
Now, in that realm, due to the first person indeterminacy, you are multiplied
into infinity. More precisely, your actual relative computational state appears
to be proved to exist relatively to basically all universal numbers (and some
non universal numbers too), and this infinitely often.
So when you decide to do an experience of physics, dropping an apple, for
example, the first person indeterminacy dictates that what you will feel to be
experienced is given by a statistic on all computations (provably existing in
the theory above) defined with respect to all universal numbers.
So if comp is correct, and if some physical law is correct (like 'dropped
apples fall'), it can only mean that the vast majority of computation going in
your actual comp state compute a state of affair where you see the apple
falling. If you want, the reason why apple fall is that it happens in the
majority of your computational extensions, and this has to be verified in the
space of all computations. Everett confirms this very weird self-multiplication
(weird with respect to the idea that we are unique and are living in a unique
reality). This translated the problem of "why physical laws" into a problem of
statistics in computer science, or in number theory.
Now, instead of using the four axioms above, I could have started with the
combinators, and use the two combinator axioms:
((K x) y) = x
(((S x) y) z) = ((x z) (y z))
This define exactly the same set of "all computations", and the same
statistical measure problem, and that is what I mean by saying that the initial
axioms choice is indifferent as long as you start from something which define a
UD, or all computations (that is: is Turing or sigma_1 complete).
Now, clearly, from the first person points of view, it does look like many
universal system get relatively more important role. Some can be geographical,
like the local chemical situation on earth (a very special universal system),
or your parents, but the point is that their stability must be justified by the
"winning universal system" emerging from the competition of all universal
numbers going through your actual state. The apparent winner seems to be the
quantum one, and it has already the shape of a universal system which manage to
eliminate abnormal computations by a process of destructive interferences. But
to solve the mind body problem we have to justify this destructive interference
processes through the solution of the arithmetical or combinatorial measure
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