On 28 Sep 2011, at 15:53, Pierz wrote:
At what point does mathematical truth stop? It seems to be the
existence of
some would imply the existence of all.
Like I said, I need to let this marinate in my consciousness a while.
I agree that all mathematical constructs must have the same kind of
existence, the same ontological status. But I see a distinction
between the type of existence pi has, and the type of existence that
time, space and matter have. Well, obviously. The question is, are
they prior to such instantiated entities, or emergent from them?
Similar to the question, are physical laws objectively extant, or mere
descriptions of 'habits'?
Do you agree that at least something has to be primitively real?
Well I can't really escape that, can I? :) I favour consciousness as a
prior reality, a spiritual position I suppose, though I also believe
these categories may well just be prejudices in our mental make-up.
For physicists, it's the quantum field, for mathematicians it's
number, for saints it is love. All perhaps faces of an unnameable
prior something. I've read Bruno arguing for number's capacity to
explain qualia, and I find it unconvincing.
Do you mean by this that you think that we are not machine?
Are you rejecting Theaetetus theory of knowledge (true opinion)?
What is not convincing?
Mathematics is pure
structure and qualia are non structural, non quantifiable, not that
they are 'uncomputable', but just don't fall into the computable/
uncomputable opposition at all.
Modal logic is both mathematics, and it handle the non-computable, and
the qualitative.
In particular some of the variant of self-reference modal logic handle
explicitly and in a formal way the knowledge that the machine itself
is unable to formalise. It is (meta) formal logic of the non
formalisable.
If a person had no right brain at all,
he might argue the way Bruno does on this point. (I'm worried about
insulting him again now. I don't mean it's half brained. I mean it is
blind to all but the quantifiable, and therefore will never satisfy an
artist, for instance).
Those who have the less problem with mechanism and its consequences
are the artists and the engineers.
So qualia make me prefer to seek my ontological
roots in the notion of consciousness rather than number.
This is frequent with mystically inclined people, but I think it is
just due to a reductionist conception of numbers and machines, which
is provably untenable since Gödel's discovery of incompleteness. You
are the one dismissing qulaia for a vast type of entity, in case you
use this to refute mechanism.
We also are aware of every possible goodness or blessing. At a
minimum,
this realization should compel us to treat each other better. In
the end,
the conclusion is little different from the golden rule or the
concept of
karma. All the good things we do are experienced by others
(ourselves),
same with all the bad things.
Yes, yes and double yes. I made the exact same point in that blog post
I mentioned on the subject. If we knew this, truly believed in this
unity of the observer, we would move quick smart to a society
optimized for the benefit of all. We can never gain at another's
expense. Not "There but for the grace of God go I" but simply "There
go I."
OK. But this is non communicable by (sound) machines. In fact in the
ethics of the ideally correct machine, asserting moral principle is
immoral. We can only encourage people to understand or discover this
by themselves.
Bruno
On Sep 28, 3:09 pm, Jason Resch <[email protected]> wrote:
On Tue, Sep 27, 2011 at 10:44 PM, Pierz <[email protected]> wrote:
OK, well I think this and the other responses (notably Jason's) have
brought me a lot closer to grasping the essence of this argument. I
can see that the set of integers is also the set of all possible
information states, and that the difference between that and the
UD is
the element of sequential computation. I can also see that my
objection to infinite computational resources and state memory comes
from the 1-p perspective. For me, in the "physical" universe, any
computation is restricted by the laws of matter and must be embedded
in that matter. Now one of the fascinating revelations of the
computational approach to physics is the fact that a quantity such
as
position can only be defined to a certain level of precision by the
universe itself because the universe has finite informational
resources at its disposal. This was my objection to the UD. But I
can
see that this restriction need not necessarily apply at the
'higher' 3-
p level of the UD's computations. What interests me is the question:
does UDA predict that the 1-p observer will see a universe with such
restrictions? If it explains why the 1-p observer seems to exist
in a
world where there is only a finite number of bits available, despite
existing in a machine with an infinite level of bit resolution, then
that would be a most interesting result. Otherwise, it seems to me
to
remain a problem for the theory, or at least a question in need of
an
answer, like dark matter in cosmology.
I am going to have to meditate further on arithmetical realism.
Nice.
I
don't believe in objective matter either (it seems refuted by Bell's
Theorem anyway),
Do you agree that at least something has to be primitively real?
but a chasm seems to lie between the statement "17
is prime" and "the UDA (Robinson arithmetic) executes all possible
programs". The problem is one of instantiation. I can conceive of a
universe - a singularity perhaps, with only one bit of information -
in which the statement "17 is prime" can never be made. To
formulate,
ie instantiate, 17, requires a certain amount of information.
True, a certain amount of information is required to realize or
represent
certain mathematical truths. Our universe may be large, but there
are
numbers so big we cannot represent them either. My opinion is that
this
practical restriction placed on us does not mean such mathematical
truth is
non-existent, only inaccessible. In the same sense that before
there were
high-powered computers, finding large Mersenne primes was beyond our
capacity, but that did not mean they were not already there waiting
to be
found.
To say
that a program executes, as opposed to saying it merely is implied
by
a set of theoretical axioms, requires the instantiation of that
algorithm. I suppose this is a restatement of the problem above.
Arithemetical realism then would be the postulate that everything
implied in arithmetic is actually instantiated. It seems to me I can
grant 17 is prime, without granting this instantiation of
everything.
At what point does mathematical truth stop? It seems to be the
existence of
some would imply the existence of all. If you think Pi has an
objective
value, then you should also accept that Chaitin's constant (http://mathworld.wolfram.com/ChaitinsConstant.html
) has a certain value.
If it does, it requires the platonic execution of all programs.
Sadly when you start to talk about the difficulty of proving that
our
histories in the UD are more random than the actual histories we
observe, I can't follow you any more - too much theory I'm
unfamiliar
with. I can see however that many (nearly all) of the infinite
computations passing through our aware states will destroy us, as it
were, so we can never exist in those computations (sort of anthropic
principle). This also suggests a kind of immortality, the same
kind as
I propose in a blog post I wrote called the 'cryogenic paradox' in
which I argue that there can only be a single observer, a single
locus
of consciousness underlying all apparently separate consciousnesses,
which would really be just different perspectives of this one
observer. It seems irresistible as a conclusion (from philosophical
arguments quite different to the UDA), and yet also kind of
horrific.
Only a sort of state-bound recall barrier prevents us from being
aware
that we suffer every fate possible.
We also are aware of every possible goodness or blessing. At a
minimum,
this realization should compel us to treat each other better. In
the end,
the conclusion is little different from the golden rule or the
concept of
karma. All the good things we do are experienced by others
(ourselves),
same with all the bad things. In a sense this thought is scary,
but it is
also can be unifying and fill us with awe at the infinite
possibility and
experience that awaits us.
Jason
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