On 04 Oct 2011, at 22:44, 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
natural
number, natural number remains undefined. If we define 0 as having
no
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
successors,
because just these are the *numbers*. If you define 0 in terms of
natural
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
successors?
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.
But it is technical. I was just saying that we can axiomatize
arithmetic without taking 0 as a primitive. Of course we will need the
additive and multiplicative axiomatic definition, and the technical
definition of 0, will not be an explanation of zero, in the sense you
are using "explanation".
Basically you can define 0 by the formula F(x) = "for all y (x + y =
y)". It is a number such that when add to any other number gives that
other number. Then you might be able to prove that it is unique, and
that it verifies what we usually take as a separate axiom, notably
that such a number cannot be a successor of any number.
If you can't even explain to me what the
fundamental object of your theory is, your whole theory is
meaningless to
me.
You are just supposed to have follow some course in elementary
arithmetic, like in high school.
I'd be very interested in you attempt to explain addition and
multplication
without using numbers, though.
I am not sure this makes any sense. Addition of what?
In scientific theories we don't pretend to explain everything from
nothing. We can only explain complex things from simpler things. The
rest is playing with word.
Comp explains the origin of mind and matter, and their relations, from
any sigma_1 complete theory. but we have still to agree on some axioms
(making that sigma_1 complete theory).
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
truth.
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=&. 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.
If you don't like the numbers, propose me anything else. Combinators
are more cute, and in fact much more easy than numbers, so here is an
alternative theory of everything for the ontic level:
Kxy = x
Sxyz = xz(yz)
Search "combinators" in the archive for the explanation that this is
enough (together with some axioms on equality). I don't need logic.
With the numbers I can also abandon logic, but then the theory of
everything is a bit more complex (see below(*))
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.
Here yo are the one talking like a 19th rationalist who believe that
we can dismiss *intuition*. Since Gödel's rationalist knows that they
can't. In particular we need some undefinable intuition to grasp
anything formalized, be it number, or programs, or machines, etc.
I chose the numbers because people already grasp them sufficiently
well, so that we can proceed.
The sort of explanation of 0 you ask me to give just does not exist at
all. Yet, 0 is used in *all* the sciences.
Bruno Marchal wrote:
Bruno Marchal wrote:
But if the very foundation is undefined, it can mean anything, and
anything
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,
Undefined does not mean that it means 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
specific
meaning. But really, it doesn't. 0 just signifies the absence of
something,
It might be intepreted like that. But that use extra-metaphysical
assumptions.
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
Nobody starts with "nobody knows 0".
We start from "0 ≠ s(x)", or things like that.
and derive something from
that than just start with "nobody knows"-consciousness and just
interpet
what consciousness means to us?
Because 0, as a useful technical object does not put any conceptual
problem. Consciousness is far more complex.
If there is 0€ in a bank account, this is sad, but is not very
mysterious. If someone is in a comatose state, the question of
consciousness is much more conceptually troubling. Humans took time to
grasp zero, but eventually got the point. For consciousness, there are
still many scientist who does not believe in it, lie some people does
not understand the notion of qualia. Is consciousness related to
matter, is it primary, ... all that are question still debated. But
for 0, there is no more problem. Everyone agree on any different
axioms rich enough to handle them in their application. For
consciousness, it is almost like for God: there are too much open
problems.
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.
You have to study mathematical logic. yes I am circling. This is
allowed and encouraged in foundations. There are precise technic to
make such circles senseful.
I have already explain that nobody knows what are the numbers. But
everybody agrees on the main axioms, which appear to be quickly Turing
universal.
In fact it is the key point, Numbers, or combinatirs, or programs are
so terribly complex, that it is preposterous to believe that there is
anything else. They have epistemologies as rich as Plotinus-like
theologies, and those are correct once we assume comp and the
Theaetetus definition of knowledge.
Bruno Marchal wrote:
Bruno Marchal wrote:
because
it's very foundation is undefined. Everything derived from it also
is
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
like
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.
Why?
In which
case 0 does not really mean something else then consciousness or
reality,
because it just represents existence itself.
That sentence does not make sense to me.
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.
Only if you give me your axioms of nothing or for God. Or you are just
coming back to the tradition of playing with words.
Just explains me how you will derive the existence and the mass of the
proton. Comp provides the complete explanation for such kind of
things, like string theory, except that it is far more complex than in
string theory (the advantage of comp is that it explains also the
qulaia), and then, (and this is the UDA point), once you say "yes" to
the doctor, there is no choice in this matter, except question of
taste? If youy don't like numbers and combinators, take java programs,
or Lisp expression, I don't care. Butwhatvere universal system you
chose, give me the axiomatic definitions. (if you want a scientific
theology).
Bruno Marchal wrote:
It gets critical
when COMP is interpreted as an abstract statement about abstract
digital
machines,
I don't do that.
But you do assume that they exist beyond just being mere ideas (with
no
necessary objective relation to reality).
What do you mean by "reality"?
This is what we search, by making some assumption.
What are your assumptions?
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?
If you can derive the mass of the proton from a theory of
consciousness, explain me how.
I have never met any difficulty about any statement I have ever made
on any finite beings constituting universal systems. But on
consciousness, humans have never cease to met difficulties.
The numbers are taught in high school. Consciousness has entered in
*some* university level course, and only with many difficulties.
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.
Go back to school. There are good teachers there. In science we don't
need to know what things are, unless we approach scientifically the
ontologies (which is not well seen by continental philosophers for the
same reason the church was angry when science begin to tackle question
on the shape of the cosmos). But even there, we will admit axioms and
define ontologies from there.
Bruno Marchal wrote:
So can "material" or "consciousness". What's the
difference?
It is hard for me to follow you.
What does it matter what we call the mystery? Isn't it ultimately one
mystery anyway?
Sure. But the goal of science is terrestrial.
We want to understand the how and why of the quanta and the qualia.
And my point is that we assume mechanism (like 99,999% of scientist
and laymans) we have to derive the quanta from the qualia. Then I show
that universal number already provide the explanation, and this in a
way which makes the theology testable (and thus academical).
Are you defending the pope or what?
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,
seperate
experiences, this attempt is bound to fail.
On the contrary, comp maps the experience with the internal
brain(s)
processes.
But how can we map the experience, if it is indivisible? There is no
useful
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.
Inseparable, perhaps. That is not a reason to confuse them, if they
are not the same.
But in which theory? Are you suggesting an axiom on consciousness?
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,
Not at all. I submit it to the judgment of others. And of course I
have problem with those who want continue to manipulate the others
through fuzzy arbitrary pseudo-theories (which unfortunately can be
influent members of academies which betrays the very idea of what is
an academy).
and rational reasoning in general.
That is implicit in my defense of coming back to a scientific approach
to theology.
If you defend irrationality in the public argument, you make the money
stealer happy.
Innumeracy makes easy to convince people that cheap plant are bad, and
expensive pharmaceutical BS is good.
it is the same, in more complex and more "taboo" with theology.
I know how to well how and why machines and numbers can and use
irrationality to short term ego centered purpose.
Bruno Marchal wrote:
I have no theory. It just seems natural to me that the ultimately we
can
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
clearly,
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
rationality.´
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.
That would lead to complete arbitrariness. That leads to suffering.
That leads to the defense of the special interest against the common
interest.
But rationality seems inherently pretty
limited to me.
You might have a limited view of rationality. Here Gödel's
incompleteness result illustrates that rationality can justifies the
existence of irrationality, but this does not mean we have to defend
its public use).
Bruno Marchal wrote:
Science is like describing the parts of the
mandelbrot, far enough from the border, that can be easily described
without
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,
Which is already true for the "real epistemology" of the numbers.
and it only
happens to be possible to represent it with numbers, which makes it
possible
for mathematics to point beyond itself.
OK.
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.
The ontology does not matter, OR you are saying that comp is false,
and you are the one acting again freedom.
(OR you believe there is a flaw in the reasoning).
I just see no evidence at all that numbers are the basic
ontology, or that this is even meaningful.
Comp (by UDA).
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
because
it is beyond space, and at small scales space breaks down.
I negate all current theories, because I don't believe theories can
describe
reality, ultimately. They just describe a tiny fragment of it.
Even in
current physical theories infinities (whose meaning is pretty much
undefined
in physics) appear at very crucial points. If there is an infinity
already
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.
Yes. The (generalized) brain.
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.
It reveals that arithmetic, or the science of the java programs, or
any Sigma_1 complete set, or Post's creative set, seen from inside, by
java programs (or, ...) is bigger than anything ever conceived by
physicists (but not by logicians and theologians).
Now, if you believe that you are different from all java programs,
then just say no to the doctor.
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...
It is not a dogma. (but it is used to make sense on expression like
"programs", "machines", numbers", "finite", which we already used.
Comp is not a dogma. It is a testable theory, which really means only
a refutable theory, as understood by Popper.
Bruno
(*) Here is a theory of everything based on numbers, but without
assuming logic, only equality. It constitutes a universal system of
diophantine equations (easily transformable in a unique giant degree
four polynomial). Most mathematicians, did bet that such diophantine
turing universal system would not exist, and it took about a century
for Putnam, Davis, Robinson and eventuall Matiyasevitch to isolate it.
The following one comes from Jones. Again search in the archive on
"Matiyasevitch" to find more explanation of this 'miracle'.
Nu = ((ZUY)^2 + U)^2 + Y
ELG^2 + Al = (B - XY)Q^2
Qu = B^(5^60)
La + Qu^4 = 1 + LaB^5
Th + 2Z = B^5
L = U + TTh
E = Y + MTh
N = Q^16
R = [G + EQ^3 + LQ^5 + (2(E - ZLa)(1 + XB^5 + G)^4 + LaB^5 + +
LaB^5Q^4)Q^4](N^2 -N)
+ [Q^3 -BL + L + ThLaQ^3 + (B^5 - 2)Q^5] (N^2 - 1)
P = 2W(S^2)(R^2)N^2
(P^2)K^2 - K^2 + 1 = Ta^2
4(c - KSN^2)^2 + Et = K^2
K = R + 1 + HP - H
A = (WN^2 + 1)RSN^2
C = 2R + 1 Ph
D = BW + CA -2C + 4AGa -5Ga
D^2 = (A^2 - 1)C^2 + 1
F^2 = (A^2 - 1)(I^2)C^4 + 1
(D + OF)^2 = ((A + F^2(D^2 - A^2))^2 - 1)(2R + 1 + JC)^2 + 1
http://iridia.ulb.ac.be/~marchal/
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