On 10/4/2011 1:44 PM, benjayk wrote:

Bruno Marchal wrote:

Bruno Marchal wrote:
But then one 3-thing remains uncomputable, and undefined,
namely the very foundation of computations. We can define
computations in
terms of numbers relations, and we can define number relations in
terms of
+,*,N. But what is N? It is 0 and all it's successors. But what is
0? What
are successors? They have to remain undefined. If we define 0 as a
number, natural number remains undefined. If we define 0 as having
successor, successor remains undefined.
All theories are build on unprovable axioms. Just all theories.
Most scientific theories assumes the numbers, also.
But this makes not them undefinable. 0 can be defined as the least
natural numbers, and in all models this defines it precisely.
But natural *numbers* just make sense relative to 0 and it's
because just these are the *numbers*. If you define 0 in terms of
numbers, and "least" (which just makes sense relative to numbers), you
defined them from something undefined.
So I ask you: What are natural numbers without presupposing 0 and its
This is a bit a technical question, which involves logic. With enough
logic, 0 and s can be defined from the laws of addition and
multiplication. It is not really easy.
It is not technical at all. If you can't even explain to me what the
fundamental object of your theory is, your whole theory is meaningless to
I'd be very interested in you attempt to explain addition and multplication
without using numbers, though.

It's easy. It's the way you explain it to children: Take those red blocks over there and ad them to the green blocks in this box. That's addition. Now make all possible different pairs of one green block and one red block. That's multiplication.

Bruno Marchal wrote:
But to get the comp point, you don't need to decide what numbers are,
you need only to agree with or just assume some principle, like 0 is
not a successor of any natural numbers, if x ≠ y then s(x) ≠ s(y),
things like that.
I agree that it is sometimes useful to assume this principle, just as it
sometimes useful to assume that Harry Potter uses a wand. Just because we
can usefully assume some things in some contexts, do not make them universal
So if you want it this way, 1+1=2 is not always true, because there might be
other definition of natural numbers, were 1+1=&.

It's always "true" in Platonia, where "true" just means satisfying the axioms. In real life it's not always true because of things like: This business is so small we just have one owner and one employee and 1+1=1.


So you might say that you
mean the usual natural numbers. But usual is relative. Maybe for me 1+1=&  is
more usual. Usual is just another word anyway. You fix the definition of
natural numbers and use this to defend the absolute truths of the statements
about natural numbers. This is just dogmatism. Of course you are going to
get this result if you cling to your definition of natural numbers.

Anyway, even if I completely agree on these principles, and you derive
something interesting from it, if you ultimately are unable to define what
numbers are, you effectively just use your imagination to interpret
something into the undefinedness of numbers, which you could as well
interpret into the undefinedess of consciousness.

Bruno Marchal wrote:

Bruno Marchal wrote:
But if the very foundation is undefined, it can mean anything, and
derived from it can mean anything.
Then all the scientific endeavor is ruined, including the one done by
the brains. This would mean that nothing can have any sense. This is
an argument against all science, not just mechanism.
No. It is an argument against science based on rationality. We can
use it
based on our intuition.
That is something else. Science is build from intuition, always.
Rationality is shared intuition. Choice of axioms are done by
intuition. And comp explains the key role of intuition and first
person in the very fabric of reality. I don't see the link with what
you are saying above. It seems on the contrary that you are the one
asking for precise foundation, where rationality says that there are
none, and which is something intuition can grasp.
OK. I don't see how from the foundation being undefined, and possibly
meaning anything, ruins the scientific endavour. If anything, it makes it
more inclusive.

Bruno Marchal wrote:

Bruno Marchal wrote:
One might argue that even though 0 and
successor can not be defined it is a specific thing that has a
meaning. But really, it doesn't. 0 just signifies the absence of
It might be intepreted like that. But that use extra-metaphysical
OK. But what else is 0?
Nobody knows. But everybody agrees on some axioms, like above, and we
start from that.
So why is it better to start with "nobody knows"-0 and derive something from
that than just start with "nobody knows"-consciousness and just interpet
what consciousness means to us?

Bruno Marchal wrote:

Bruno Marchal wrote:
which makes sense if we count things, but as a foundation for a TOE,
it is
just meaningless (absence of anything at all?), or could mean
anything (the
absence of anything in particular). Successor signifies that there
is "one
more" of something, which makes sense with concrete object, but what
is one
more of the "absence of something" (which could mean anything).
1 is the successor of 0. You are confusing the number 0 and its
cardinal denotation.
OK. But what else is 1?
The successor of zero. The predecessor of 2. The only number which
divides all other numbers, ...
(I don't see your point).
But what does successor mean? You are just circling within your own
definitions, which doesn't explain anything.

Bruno Marchal wrote:

Bruno Marchal wrote:
it's very foundation is undefined. Everything derived from it also
undefined, that is, it is totally open to interpretation. We can
just name
the "undefinedness" of 0 as "matter" or "consciousness",
No, we can't. or prove it.
I don't have to prove that we can tack a name onto something. It is
asking you to prove that the name of 1 is "one".
It is a common rule to not use a word which has some meaning for
another concept. It can only confuse people.
You might remember what "glory" means, for Humpty-Dumpty.

May be we cannot defined 0 (in some broad sense), and we cannot define
"consciousness", but even in that case, we are not allow to equate them.
In fact we have a pretty clear intuition of what is 0, and what is
consciousness. There are many things which we cannot defined, and
still can have a lot of precise idea about.
OK. The point is that the intuition of what 0 is breaks down if we regard
something that is immeasurable and uncountable, as reality itself. In which
case 0 does not really mean something else then consciousness or reality,
because it just represents existence itself.

Bruno Marchal wrote:

Bruno Marchal wrote:
What you say here is meaningless.
What is meaningless about saying we can call something that remains
undefined, and unspecified pretty much every term that is so broad
as to be
undefined, and unspecified.
What is your question? What I mean is that if we talk about everything we
could as well just use the nothing, or God.

Bruno Marchal wrote:
It gets critical
when COMP is interpreted as an abstract statement about abstract
I don't do that.
But you do assume that they exist beyond just being mere ideas (with no
necessary objective relation to reality).

Bruno Marchal wrote:

Bruno Marchal wrote:
and there we have
the very same mystery we wanted to explain.
No. It follows from comp that we have to derive physics from Number
theory. This is a theorem, and not an assumption.
Yes, but what are numbers? This is the mystery.
Er, well yes.
Yes. So you want to explain mysterious consciousness and substitute the
equally mysterious numbers. Where exactly lies the explanation in that?

Bruno Marchal wrote:
Numbers can represent
everything, or nothing.
That's not true. Actually numbers, in arithmetic, are the object we
talk about. They do not represent anything than themselves, but they
can partcipate in computational relations, and sometimes they can play
the role of addresses (like in 17 is the number street of my friend).
But they are not arbitrary beings.
If they do not represent anything, then please explain what numbers are in
the first place.

Bruno Marchal wrote:
So can "material" or "consciousness". What's the
It is hard for me to follow you.
What does it matter what we call the mystery? Isn't it ultimately one
mystery anyway?

Bruno Marchal wrote:
Bruno Marchal wrote:
That's even worse, so we have an
infinity of undefined computations. Every computation (or infinite
computations) can correspond to every (or none) experience, that is,
ultimately COMP says nothing about experience. If it would, it had
to give a
mapping of computation (/infinite computations) to experiences...
But since
experience is ultimately not divisible in chunks of concrete,
experiences, this attempt is bound to fail.
On the contrary, comp maps the experience with the internal brain(s)
But how can we map the experience, if it is indivisible? There is no
mapping if the domain of the mapping consists of only one thing.
You confuse consciousness and content of consciousness. Universal
person and particular moment of particular person.
I think that we have to confuse consciousness and content of consciousness.
They are inseperable, even though they are not the same. Consciousness is
all of its content, and content is all there is to consciousness (even if is
just the feeling of self-existent being).

Bruno Marchal wrote:
Anyway, I defend no ideas. I shows just that f the brain is a machine,
then the theology of aristotle does not work, and we have to come back
to Plato's one.
To be frank, I think you are dishonest here. You defend a lot of ideas, like
the validity of your reasoning, and rational reasoning in general.

Bruno Marchal wrote:
I have no theory. It just seems natural to me that the ultimately we
just rely on our direct observation, which cannot be predicted by
any laws.
Science is just a tool of consciousness for it to learn to observe
and see that there is an order in things. But just a tiny part of it
can be
made sense of by science.
I think you restrict science too much. Like I think you restrict
It all depends on what we mean with science, and rationality. The words have
no predefined meaning, we have to give them meaning itself. Personally, I am
willing to extend the meaning of science to the very act of observing
itself, making everything science. But rationality seems inherently pretty
limited to me.

Bruno Marchal wrote:
Science is like describing the parts of the
mandelbrot, far enough from the border, that can be easily described
using any fractal (recursive) math.
I see your point. But actually you are confusing science and
scientists. The "Gödel's discovery" is the discovery that what we
understand in the mathematical reality is about just a little scratch
on the "real thing".
I would say the real thing is just not mathematical at all, and it only
happens to be possible to represent it with numbers, which makes it possible
for mathematics to point beyond itself.

Bruno Marchal wrote:
The universe is just kind enough to make
a part of nature understandable through relatively easy rules, but
the vast
majority is beyond it.
I can't hardly agree more. Today we know that this is the case even in
just arithmetic. We have understood why it has to be like that.
Don't confuse the poor reductionist scientific approach of today, with
the theology of numbers of tomorrow.
Sadly I think it is just another kind of reductionism, reducing the ontology
to numbers. I just see no evidence at all that numbers are the basic
ontology, or that this is even meaningful.

Bruno Marchal wrote:
It could be built
in a way that apparently small quantum entaglements between brains
"transmit" (I know transmission is a litte inaccurate in that
context) large
amount of information. The only reason it may appear small to us is
it is beyond space, and at small scales space breaks down.
I negate all current theories, because I don't believe theories can
reality, ultimately. They just describe a tiny fragment of it. Even in
current physical theories infinities (whose meaning is pretty much
in physics) appear at very crucial points. If there is an infinity
at the big bang, why should it ever dissappear? And if doesn't,
there is
infinity everywhere, making everything ultimately, non-emulable.

OK. Most things entailed by comp *are* non Turing emulable.

Yes, but itself rests on the assumption that a critical aspect is turing
emulable. It isn't difficult to sense the incoherence of that. If there is
so much uncomputable stuff even assuming COMP, maybe this just points to the
fact that the uncomputable is real and fundamental, and COMP just reveals
it, even though its assumption are ultimately wrong.

Bruno Marchal wrote:
Sure, it is not stuffy, but hardly any intelligent materialst
thinks of material as "stuffy".
OK, subconsciously it appears they do (which
is my main point of disagreement with them, they regard matter as
"unintelligent", which seems to stem from the belief in "solid"
matter), but
intellectually they don't.
But they think it as primitive. They take as dogma that it is outside
there, and obeys laws, and then extrapolate from their seeings (like
all animals does, because it works very well locally).
Yes, I don't agree with this either. But I also don't believe the dogma that
numbers is outside there, and obeys laws, etc...


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