On 26 Aug 2015, at 12:47, Peter Sas wrote:
Hi Bruno,
I am not assuming a primary physical universe... precisely not. The
idea is that self-awareness is ontologically primary and that this
self-awareness, through its recursive structure, is awareness of all
natural numbers (and possibly beyond) and thus it computes. We could
then say it computes the physical universe, so that the latter comes
out as a computation done by this absolute self-awareness.
You dismiss the problem of hardware/computing platform, but your own
mathematical platonism serves to explain what the platform is. You
assume the existence of numbers and then say that that existence
facilitates the computations. In your account, the platonic realm of
arithmetic IS the hardware/computing platform.
The physical does not arise from a computation, but from the internal
logic of the space of all computations. The physical arise from a
measure on those computations as expected from the first person
indeterminacy internal to all such computations. Hardware can be
redefined by what win such measure statistics. It is something
emerging. It will be confusing to say that arithmetic is the hardware,
as arithmetic is not physical, and the emerging hardware will be
physical, even if it is not primarily physical.
I, on the other hand, do not want to take the ideal existence of
numbers for granted. I want an explanation why they exist.
We can prove that this is impossible. You need to assume one universal
system (in the Turing sense). Then I take the numbers+add&mult.
because most people are familiar with this. It is not obvious that it
is already Turing universal, though.
From logic, the numbers + addition, you cannot yet derive the
multiplication law. The creative explosion occurs only when you have
the numbers (or equivalent) addition, *and* multiplication. That gives
the universal dovetailing, that is, the (arithmetical) implementation
of all computation.
Here I think the idea of absolute self-awareness, with its infinite
recursivity,
A notion like recursivity assumes the natural numbers.
offers a powerful explanation of what the numbers are and why they
are there,
It is logically equivalent with the numbers + addition + multiplication.
and why they are involved in computational processes. It's a matter
of what is ontologially most basic.
Notion like self, awareness, recursion, are more complex than addition
and multiplication of natural numbers.
Here the idea of self-awareness strikes me as very attractive. Its
circularity allows it explain itself.
I agree with you, but assuming computationalism needs the assumption
of numbers or Turing equivalent. Without them, we don't get any
universal system.
You probably have to talk me again through your idea of obtaining
1st person knowledge by applying Plato's definition of knowledge to
Gödel -- I've forgotten the details I'm ashamed to admit...
I am aware there is a long work to do to get all this right. People
does not really know about mathematical logic. I will think about how
explaining this, but the basic thing is that the logic (provable(p) &
p) is different from the logic of provable(p), despite it is true (but
non provable by the machine) that provable(p) entails p. That
difference is a consequence of incompleteness, and it attach a non
nameable knower to all (correct) machine. It obeys a logic of
knowledge, and verify many principles usually accepted for the "soul".
It is Plotinus' inner God.
I would say: Self-consciousness => Recursivity => Number =>
Computation => Physical appearances => Human consciousness
The problem for me is that I want to explain consciousness, and that I
do think computer science explains it from the numbers (+add&Mult).
I can even explain why the soul cannot believe in comp, and why the
soul does believe that consciousness is more fundamental than the
numbers, but that is a feature coming from our own embedding in
arithmetic or Turing equivalent. What you do is to single out the
first person from the third person, but this is problematical in
science in general, and the reason why it looks like what you say can
be explained by simple third person notions on which everyone agree
like addition and multiplication (which is not the case for more
complex notion like consciousness, self-awareness and even recursion).
Bruno
Op woensdag 26 augustus 2015 12:12:24 UTC+2 schreef Bruno Marchal:
Hi Peter,
I have not much time, but why to assume a (primary) physical
universe. There are no evdience for that. Also if my body is a
machine", the universe cannot be a machine, unless I am the universe
(which I doubt).
"Computation" is a pre -mathematical concept, and actually, an
arithmetical concept. Once you assume the basic laws of the natural
numbers, (mainly the laws of addition and multiplication), then, all
computations exist (in a sense cloase to "prime number exists": NOT
in a speical metaphysical sense), and the apperance of a physical
universe is a consequence of how the numbers perceive the infinitely
many number relations which run their computations. The physical
reality would be, (if my body is a machine) an internal aspect of
arithmetic seen from inside (and taking our relative personal
indeterminacy into account). A priori computationalism entails that
neither Reality, nor the physical reality needs to be computational.
Then I can argue that computationalism explains consciousness, as
another modality of self-presence in arithmetic. Consciousness is
the knowledge of one 1-self, and we get it for free by just applying
the most calssical definition of knowledge to Gödel's (machine's)
provability predicate. And the theory is testable, as physics is
explained in all details by that theory of consciousness, so we can
compare with nature (and its fits pretty well, I would say).
I don't know why people want hardware for computation, as there is
no evidence for hardware, nor can it explain anything (by the UDA
result). Computability is a purely arithmetical notion. It is a
theorem that all machines' "dream" exist in arithmetic. It is an
open problem if that define a universe, a multiverse, or only a
multi-dream.
You have NUMBER => CONSCIOUSNESS => PHYSICAL APPEARANCES => HUMAN
CONSCIOUSNESS
Best,
Bruno
On 26 Aug 2015, at 10:02, Peter Sas wrote:
I thought Tipler's theory is that there will be an actual physical
computer that will be able to do all possible computations as the
Universe collapses - although since he came up with the idea it has
been shown that the Universe won't collapse in the required way.
Yes, it's not Tipler's main theory, which is the one about
'resurrection"... But he also suggested this idea: that the
platonic existence of mathematics might be enough for the
simulation of physical universes with consciousness in them...
Why is the Hard Problem of Consciousness a problem in the
computerless computation scenario?
Yes, this is an unfortunate formulation on my part. The hard
problem is of course a problem for all computational approaches....
Personally I take the hard problem very seriously. I think it shows
that consciousness cannot be fully understood in computational
terms: the what-it's-likeness of consciousness, its involving
qualia, cannnot be accounted for computationally. I think this may
give us a 5th option:
(5) Consciousness, being inexplicable in computational terms, can
be the hardware that ontologically precedes the computations that
ourput the physical universe. How might this work? Here I would
like to invoke an idea from the American idealist philosopher
Josiah Royce, who argued for the infinite complexity of complete
self-awareness. To be self-aware is to be aware that one is self-
aware, and aware that one is aware of one's self-awareness... and
son on. So, as Royce pointed out, there is a recursivity to self-
awareness that mirrors the recursion that generates the natural
number system. Similar ideas were brought forward by the German
philosopher/mathematican Oskar Becker. Anyway, what this suggests
is that if we postulate a primordial self-awareness as the
foundation of all reality, then that self-awareness through its
recursivity could be said to be aware of all natural numbers (the
hierarchy of its reflective levels) and thus also of all relations
between them, i.e. all computable functions. And since it is
basically a self-awareness it singles out those algorithms for
'special attention' that best mirror its self-awareness by forming
universes with conscious beings in them. Of course, the question
remains why one should postulate the existence of such an absolute
self-awareness as the basis of all existence. My guess is that such
a self-awareness can bootstrap itself into existence: if esse est
percipi, then the ultimate observer only exists because it observes
itself. It has often been remarked that there is a circularity in
self-awareness. In my view this circularity is what makes it causa
sui. Royce's story then allows us to conceive of this absolute self-
awareness as a computer... The idea that an absolute self-grounding
self-awareness underlies existence can by the way be found in
Plotinus, the Indian vedanta and German idealism (Fichte,
Schelling, Hegel). Royce allows us to take this idealism into a
computational direction. It is something I am working on...
Peter
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