On 08 Oct 2011, at 20:51, benjayk wrote:
Bruno Marchal wrote:
On 08 Oct 2011, at 13:14, benjayk wrote:
Bruno Marchal wrote:
On 04 Oct 2011, at 21:59, benjayk wrote:
Bruno Marchal wrote:
On 03 Oct 2011, at 21:00, benjayk wrote:
I don't see why.
Concrete objects can be helpful to grasp elementary ideas about
numbers for *some* people, but they might be embarrassing for
others.
Well, we don't need concrete *physical* objects, necessarily, but
concrete
"mental" objects, for example measurement. What do numbers mean
without any
concrete object, or measurement? What does 1+1=2 mean if there
nothing to
measure or count about the object in question?
It means that when you add the successor of zero with itself you
get
the successor of one, or the successor of the successor of zero.
But that does this *mean*? These are just a bunch of words. You
could as
well write
"It means that when you colmüd the pööl of ämpod with itself you
get
the pööl of trübda, or the pööl of the pööl of ämpod.".
Exactly! That is the point of axiomatization.
Hilbert said this to explain what his axiomatic geometry means: "you
can replace the terms 'points', 'lines', and 'planes', by the term
'elephant', 'table' and 'glass of bear'.
Now, doing this would not be pedagogical, and we use the most
commonly
used symbols. That is "+" for colmüd, "s" for pööl, and the symbol
"0" for your ämpod. We already have some axioms for logic and
equality, and all you need consists in agreeing or not with the
following principles:
0 ≠ s(x)
s(x) = s(y) -> x = y
x+0 = x
x+s(y) = s(x+y)
x*0=0
x*s(y)=(x*y)+x
The intended meaning being 0 is not a successor of any number, etc.
You can say "the ämpod is different from all pööls". No problem,
but
it is obviously quite unpedagogical, I think.
You don't get the point. Of course I can agree with these principles
concerning countable and measureable things.
But then, unless you see a flaw in the reasoning, you should know that
at the obtic level, we don't need more, nor can we use more than the
countable collection of finite things, once we assume mechanism.
The point is that successor and 0 become meaningless, or just mere
symbols,
when removed from that context.
What context are you talking about. The theory is interpretation
independent. The interpretations themselves are part of model theory.
For using the axiom you need only the inference rules.
I don't agree with these axioms removed from any context, as without
it,
they are meaningless. I don't necessarily disagree with them,
either, I just
treat them as mere symbols then.
They are much more than that. There are symbols + finitist rule of
manipulation. The difference is as big as the difference between what
you can feel looking at the string "z_n+1 = (z_n)^2 + c" and what you
can feel looking at a rendering of what it describes, like this:
http://www.youtube.com/watch?v=n7JLHxBm0eY
Of course we can still use them in a meta-sense by using .. = "2" as a
representation for, say a nose, and ... = "3" as a representation
for a rose
and succesor= "+1" as a representation for smelling, and then 2+1=3
means
that a nose smells a rose. But then we could just as well use any
other
symbol, like ß or more meaningfully ":o) o-".
I am not sure that you are serious. There are intented meaning, and
logics is a science which study the departure between intended meaning
and a mathematical study of meaning. Logic studied both the
syntactical transformation (a bit like neurophysiologist study the
neuronal firings) and the space of the possible interpretations.
Interesting things happen for the machine doing that on themselves.
Bruno Marchal wrote:
Personally, I might prefer to use the combinators. But we have to
agree on some principle about some initial universal system to see
how
they reflect UDA, in such a way that we can explain the quanta and
the
qualia, with the comp assumption in the background, and in the theory
itself.
Yes, you can use any universal system, which is going to be just as
meaningless as numbers.
That is like saying that a brain, which only manipulate finite
meaningless information pattern (assuming comp) is useless.
Are you just telling me that, like Craig, you assume non-comp?
Let's take a programming language. When the code says "while(i<5)
then i++;
print "Nose smells rose" end" then this make sense for the user as
he can
read "nose smells rose". But in an abstract context, "nose smells
rose" has
no particular meaning and the while loop is just a loop, which also
has no
particular meaning (though it has a particular function).
This is false, it has a meaning (mainly that if the condition occur it
has to print some string). What you do with that information is more
complex, as it needs to study your brain, body, context (indeed). But
you illustrate that you agree that "xhile (i<5) ..." has a meaning.
Obviously, it has nothing to do with rose and smell. But both
mechanist cogniticians and reseracher in AI are not *that* naive.
Smell and rose require deeper loops, like the LUMs can manage (but not
a two line program).
No matter what the
programming code says, it only makes sense through a user, or an
intelligent
programmer.
Comp entails that self-referential machines (UMs and LUMs) can do that.
Are you telling me that a human having got an artificial digital brain
is a zombie?
But you remove it from that context also, leaving no meaning
left, except empty symbol manipulation which could mean anything
So a brain in a vat would be unable to make a person feeling like
living a dream?
I get more and more the feeling that you are assuming non-comp.
(which
rescues the meaning by making it possible to interpret everything in
it, but
this defeats the purpose of using numbers or other formal systems).
Don't confuse Arithmetic (which is a meaning) with Peano Arithmetic
(which is a machine or a theory, or a number) handling part of
arithmetic.
All the (formal) universal systems you can name have the exact same
flaw as
numbers.
They only make sense in a context, otherwise they just function as
symbols making them as useful as saying
"ÜGFDÖÜGÖGÜÖFGÜFGÄFÄFÄFGÄFG--#-äsd#-ds#-d##" and then
explaining that this
means "earth".
If that is a flaw, do you agree that you can say the same thing about
brains? (even without comp, actually).
This is what COMP&C (this means comp and conlusion) does. It makes a
lot of
complicated assumption and long-winded explantions and
interpretation of
symbols, just to conclude that the 1-p (which is practically the only
perspective there is) cannot be captured by any rational means anyway.
But it get good formal approximation at the metalevel. Indeed, it can
even explain why it has to jump from a level to another to understand
its non formal nature.
Then
it claims to be a refutable theory, but without making any particular
prediction that is not obvious already.
This is a gratuitous false assumption showing you don't take the time
to study the work, as you have already confess. You seem to just have
a prejudice against machine. You believe that you are different. It is
your right, but you might try an argument.
Bruno Marchal wrote:
If you just have a bunch of words without being able to make sense
of them,
everything you "derive" from it will just be whatever you happen to
interpret in a bunch of non-sensical words.
The axioms above are used by all scientists everyday, implicitly or
explicitly.
Of course they are! I say nothing to the contrary. The axioms are
used as
*tools* because they reflect some aspect of reality.
This contradicts what you said above.
Then the point is that by assuming comp ("yes doctor"), the observable
feature of reality are explainable from that aspect of reality, and we
don't need to make anything else explicit. We get also the
communicable and non communicable part of that (epistemological)
reality.
But they can only be
used where this is the case, namely comparable measurements and
countable
things.
On the contrary. It explains why machines, even if they desire to
grasp their countable bahaviors only, HAVE to believe in the
uncountable, big infinities, etc.
COMP claims to explain quanta and qualia, which as such are not
measurable and countable (of course particular quanta can be
measured, but
not quanta as such), therefore it uses a tool that is useless in this
endavour (and useless here means meaningless).
Hmm... What can I say. from this I can only encourage you to study the
theory.
The result is the same as
just using the axioms p and ~p. You get whatever you manage to
interpret
into the axioms, which doesn't mainly depend on the axiom, but
rather your
compassity to be creative with your ability of interpretation.
I just assume we can survive with digital brain, and then I explain
that Aristotle naturalism must be replaced by Platonian form of
reality view.
Bruno Marchal wrote:
What you say does not make sense.
Then just explain what numbers mean.
The numbers are the object of discussion. They *are* the meaning, when
I talk about them. If you have forget what they mean, just buy a book
on arithmetic. Then computer science explain how numbers can develop
themselves and becomes conscious (together with the whole context of
arithmetic), etc.
You could have asked me what is the meaning of "brain", or of "neural
firing".
And no, repeating the axioms does not
constitute an explantion. They just make (obvious) sense with
regards to
countable things. Please explain the sense beyond that.
Once you are willing to suppose that your physical brain is a finite
machine, then many things I am saying are rather easy to figure out.
If not, then you are obliged to study computer science to get the
point that numbers can at least behave (relatively to other numbers)
in an intelligent way.
Bruno Marchal wrote:
What axioms are you disagreeing with?
All. They make little to no sense in the context you use them.
You could say: Einstein theory of gravitation makes no sense at all.
The guy does not explain why 1+1=2, but is using all the time that idea.
If for you something like " different natural numbers have different
successors" makes no sense, I can hardly help you.
Bruno Marchal wrote:
Bruno Marchal wrote:
Bruno Marchal wrote:
The diophantine equation x^2 = 2y^2 has no solution. That fact
does
not seem to me to depend on any concreteness, and I would say
that
concreteness is something relative. You seem to admit that naive
materialism might be false, so why would little "concrete" pieces
on
stuff, or time, helps in understanding that no matter what: there
are
no natural numbers, different from 0, capable to satisfy the
simple
equation x^2 = 2y^2.
This is just a consequence of using our definitions consistently.
Not really. In this case, we can indeed derived this from our
definitions and axioms, but this is contingent to us. The very idea
of
being realist about the additive and multiplicative structure of
numbers, is that such a fact might be true independently of our
cognitive abilities.
Yeah, so I ask what is the meaning of being realist about it? I
can't see
any. The only meaning is when we work with countable objects, or
measurements, which indeed follow some rules that mathematics
describe.
Mathematics is born from the fact that abstract things can have
meaning.
Obviously. So what? I am not denying that.
OK. Then it is just a question of patience and technic to grasp that I
am not using anything more than that.
Having meaning does not mean
"being realist about".
The idea is that the meaning is independent of the machine which
handle that meaning.
They are real as epistemological constructs, and what
they describe is a part of reality. But real in an ultimate sense is
only
reality itself (awareness).
I am not again the idea that reality is awareness, and I show comp go
in that direction. But comp makes it possible to explain this from
simpler third person communicable proposition (like "the prime numbers
behave randomly", etc.).
This means that persons (including myself!),
objects, physical reality also don't exist as fundamentally real.
OK.
Just
awareness does, and these things are expressions of it (the more
concrete
things just temporary expressions, like my body).
OK, but if you say "yes" to the doctor (and agree that you survived)
then you can understand where awareness come from (as amazing as it
might seem: I agree it is not obvious at all).
Got the feeling that you want awareness to be more primitive than the
numbers. You might try a theory going in that direction, and then we
will see if your theory forces you to say "no" to the doctor. That
would be interesting.
Bruno Marchal wrote:
Bruno Marchal wrote:
We don't know if there is an infinity of twin primes, but we can
still
believe that "God" has a definite idea on that question.
We could as well say that our definitions make the answer to that
question
well-defined, even if we haven't yet figured out what the answer is.
So the answer does no more depend on us. That is what I mean by being
realist.
The answer depends on us as we invented the numbers (we = rationally
intelligent beings., including all forms of aliens that might
exists, I
guess that they are probably humanoid as well). There is no
requirement that
we know all the consequences of everything we invent.
Numbers have been discovered by humans, not invented. You put too
much, or not enough, credits in the humans.
Bruno Marchal wrote:
This
doesn't mean that the answer describes an independently existent
entity.
It implies that the truth of existential arithmetical proposition
does
not depend on us.
It doesn't in the way that when the humans on this earth die there
will most
probably still be other intelligent beings left that can assert the
proposition.
But even if they do not depend on us as humans, they may not be true
independently of the context, that is, they only make sense with
respect to
some aspects of reality, not all of it (which would be required for a
meaningful TOE).
That's the case for all theories.
Bruno Marchal wrote:
but this doesn't mean they have any
independent aspect.
You said yourself that the question is well defined.
So? Why does that entail that they are independent?
It means that once we agree *enough* on what are the natural numbers,
the truth on the twin prime numbers is independent of us. It is the
same with the electron or any stable patterns we can approximate.
Then with comp even a proposition like "Mister X suffer from headache
during a major part of its life" will be independent of you (and of
the big bang, electron, etc.).
Bruno Marchal wrote:
That is, I don't think our mathematical formulation of
numbers describe numbers as a thing of itself, but rather are a
particular
expression of regularity in awareness.
Most probably. But assuming comp, they give a very good coordinate
system to study the computations. The laws of mind and matter does
not
a priori depends on the initial choice. Numbers (with + and *) are
just the simplest and the most well known, even if very few people
got
the impact of Gödel's discovery, which makes two times more sense
with
the mechanist assumption.
Bingo, "The laws of mind and matter does not a priori depends on the
initial choice." (though I don't think that they are any absolute
laws, just
local ones,
With comp, this was an open problem, but now we know that there are
universal physical laws (as a highly non trivial consequence of that
comp assumption. It took 30 years of research to get that result).
but let's just call the regularities laws, even if they can't be
written down). This choice can be an abitrary thing whatsoever. If I
decide
to explain everything with the word "Kartoffelbrei" the universe
will still
be the same.
Not exactly. If the commandant of a plane you are in asks an
explanation on the climate, an justification like "Kartoffelbrei"
might just end your terrestrial life, making in change in that
universe. Explantion have to be as much as possible referentially
correct for species to develop (instead of disappearing).
Of course you can use numbers (or other computations), the point is
rather
that this is pointless, even if "theoretically possible". Using some
convoluted way of reprenting things beyond numbers with numbers is
just
useless, as we can more easily represent these things with concepts in
language (you have to resort to that anyway, as examplified by your
heavy
use of words in critical points).
The question is not can we think. The question is can a machine think?
Can we continue to think when we got a digital body? is there a
physical primary universe or are we in a video game, etc.
Bruno Marchal wrote:
Some universal system can play some more important role to figure out
some aspect of reality, but that has to be deduced from a theory
independent approach to computation if we want to extract and
distinguish the quanta and the qualia (like trough the logics of
self-
reference).
Why make it so complicated?
We have no choice, when we tackle a complex question.
Ulitamtely, logic can't capture self-reference
anyway,
That is what logic handles the better. That's "Cantor Post Gödel
Turing revolution".
so why not skip that stage and just go to the source of
self-reference, the self itself (yourself).
I agree the main point relies there. But then it is fun to see that
the numbers can go there too. It is deep also, and it makes us more
modest, and it changes the world around us. Without arithmetic and
some human knowledge of it, we would not been unable to have this
conversation, notably.
My deepest goal is humanitarian. I sincerely believe that the more we
will be rigorous (and thus modest to begin with) in theology (as
opposed to centuries of dogma), the most we will be happy and
peaceful. Possible truth might be a bit frightening, for the
unprepared, but hiding them is worst in the mid run, and fatal in the
long run.
Bruno
http://iridia.ulb.ac.be/~marchal/
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