On 5/17/2012 9:50 AM, Bruno Marchal wrote:

On 17 May 2012, at 14:21, Craig Weinberg wrote:

On May 17, 5:49 am, Bruno Marchal <marc...@ulb.ac.be> wrote:
On 16 May 2012, at 17:37, Craig Weinberg wrote:


On May 16, 10:41 am, Bruno Marchal <marc...@ulb.ac.be> wrote:
On 15 May 2012, at 19:44, Craig Weinberg wrote:

On May 15, 1:03 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:

But a deterministic world, if rich enough to add and multiply,
and
thus to contain universal internal observers,  leads already to
indeterminist first person realities (even without comp, although
it
is simpler to use comp to justify this).

If a wave washes one pile of sand onto another, thereby 'adding'
them
together, why does that generate universal internal observers?

Adding is not enough. You need multiplication, and iteration.

Then universal digital creatures appear, by logical consequences,
and,
as always, reflect themselves and all universal creatures, digital,
and non digital, which leads them to harder and harder problems and
questions.

Even if that's true, from where do they appear? To say they appear
is
to admit that they are not themselves contained within addition or
multiplication.

They are. Anything Turing emulable appears, and reappears in
arithmetic, related to bigger and bigger natural numbers.

The appearance is contingent though, upon something being able to
recognize the pattern which is appearing to them.

That's correct. It is contingent of the universal number, and the
universal numbers making the first one more relatively probable. But
all that exist in arithmetic.

What are the properties of arithmetic contingent on?

The idea is that such properties are not contingent.

You could take any universal system, instead of arithmetic. From the computability perspective, they are equivalent.

Hi Bruno,

I would like to add comments in defense of what I think Craig is trying to communicate.

Universality is relative independence to a particular means of expression. It is not Independence in the sense of mutual isolation or complete absence of relations.





That pattern
recognition is not automatically guaranteed by any arithmetic logic.

In your non-comp theory.

We need a physical machine that remembers that it can remember,

That's "Bp -> BBp". Universal machine are like that.

Those are just letters and symbols. What or who makes them mean
something and why?

Bp means that some universal machine utters p. Absolutely. Independently of you and me.
BBp means that the same universal machine now utters Bp.
For any arithmetic (or equivalent) proposition, Bp > BBp, means that if that machine utters p, it will soon or later utters Bp. And that is a theorem of arithmetic, making it true independently of you and me.

And these statements have a definite meaning only because there is a relatively unambiguous structure of relations within our collective minds that gives meaning to them. Apart from that structure they are meaningless. Statements, like objects, cannot have inherent and definite properties other than just some spectrum of possible properties. Why? Because properties are the result of actual observations/interactions by physical systems. Absent the actual means to count the quantity of fruit in a basket, it is incoherent to say that a certain quantity of fruit in the basket. We have goten away with talking in ambiguous terms for far too long.





and
can experience that memory as an event. It needs to know what kinds of
strings of remembered digits constitute a meaningful pattern, or that
there could even be such a thing as a pattern. To say that patterns
appear and reappear in arithmetic takes the appearance of pattern
itself for granted, then usurps the primacy of the sense experience
which provides it.

Not really, for it appears and reappears only in the mind of universal
numbers. It makes sense for them, and indeed they will be astonished
that apparent material can lead to that sense. But although locally
true, this is globally wrong. Sense is necessarily a first person
notion, and relies on the abstract but real configuration involving
infinities of arithmetical relations.

I don't think sense is a first person notion, it is the very capacity
to define first person and third person as separate (opposite) on one
level, and united on another. Sense creates the arithmetical
relations, but not infinitely. Arithmetical relations are derived a
posteriori of sense embodiments.

You confuse arithmetic and the human's apprehension of arithmetic.

No, you do. You are assuming that differences exist in the absence of the means to define differences.



Sense generates the capacities,
intentions, symmetries, and rhythms that underlie recursive
enumeration, as well as frames the context of all sequence and
consequence. It all has to make sense.

We need only the idea that a reality can exists beyond human sensing. This is what I assume by making explicit the arithmetical realism, and that can be shown enough when we assume that we work locally as machine, at some description level.

Of course, but this idea requires that there is an entity that can have those ideas in the first place. We can only reason backwards from where we are and what we know now.

As I already told you, to make this false, you need to build an explicit non computable and non Turing recoverable function having a genuine role for the mind. This unfortunately only makes more complex both mind and matter, making your non-comp hypothesis looking like a construct for making impossible to reason in that field.


Goedel, Turing and others already did this when they proved the existence of non-computable numbers, relations, etc. The existence of a non-halting Turing machine is a proof of such. Why is it so difficult for you to understand this? Recursively enumerable functions are exactly those functions that can be represented in some formal system. Formal systems are structures that are known within the minds of conscious entities that can communicate with each other about these formal systems. Absent the existence of those conscious entities there are neither formal systems nor recursively enumerable functions.




Not everything has to make
numbers. Dizzy doesn't make numbers, but it makes sense.

But numbers does not make only numbers. They make and develop sense for many things far more complex than numbers, that is the point. Arithmetical truth itself is far beyond of numbers, yet numbers can relatively develop some intuition about those kind of things.

You are projecting your ability to know the meaning of a set of symbols onto the symbols themselves.

You just seems stuck in a reductionist conception of numbers and machines. We know such conception are wrong.

    Yes we do, so why persist in error?




It is a
sensation that makes sense to an embodied animal, but not to a
computer.

How could we know that? Why should we believe that?

Because we can demonstrate the ability by physically doing some action that is meaningful as a computation. It is not difficult to grasp.







To say they are creatures implies a creation.

Why not. You could say that they are created by the addition and
multiplication laws. You need only to bet that 1+1=2 and alike does
not depend on us.

Because there's no mathematical logic to how or why that creation
could occur.

But there is.

What is it?

That the existence of universal numbers, and their many dreams, is a consequence of logic and arithmetic.

    Not just the existence of universal numbers.






If we posit a universe of arithmetic realism, how can we
accept that it falls off a cliff when it comes to the arithmetic of
it's own origins? What makes 1+1=2? Sense.

Truth.

Truth requires sense.

Why?

Because truth is a valuation that is not assigned or even meaningful in the absence of the ability to distinguish one value as different from another.




Not everything that makes sense is true (fiction
for example), but everything that is true makes sense.

For who?

    You, me, Donald Duck...





Why do you want someone to assess the truth for something being
true. That is anthropomorphic.

It's ontologically necessary. What is a truth without it being
detectable in some way to something?

It is an unknown truth. A billion digit numbers can be prime without us being able to know it. Some universal machine does not stop on some argument without anyone being able to prove or know it. Some pebble on some far away planet can be eroded without anyone knowing it.

Only a possible content of a mind can be true, not something independent of it.





Th greek get well that point, and
originate the whole scientific enterprise from there, as in the
conclusion of this video:

http://www.youtube.com/watch?v=69F7GhASOdM

This assumes a set of objects that have specific properties independent of the observers in the cave. It assumes a pre-existing world. It assumes many things that are not necessarily real.


Great video, but now you are the one anthropomorphizing. Just because
the released man doesn't create the outside world by seeing it doesn't
mean that the outside world can exist without being held together by
experienced sense relations on every level. My computer doesn't create
the internet, but that doesn't mean that the internet isn't created on
computers.

But where the first observer come from?

Why do you assume that there is a "first"? What if the notion of "A is first" is just a valuation in the mind of some observer. You might consider that observers always exist and that it is only within their field of observations that such concepts as universes and numbers are meaningful entities.





If not, it is the whole idea of a reality which makes no more sense,
and we get solipsist or anthropomorphic.

That's where sense comes in. Sense divides the totality into
solipsistic/anthropomorphic and objective/mechanemorphic on one level,
but bleeds through that division on another level, thus creating a
diffracted continuum that oscillates through time but remains
continuous across space (and vice versa).

Time and space, looks concrete, thanks to millions years of evolution, but are much more sophisticated notion than elementary addition and multiplication to me.

You might try to write up a mathematical model of space and time, or study the tensor based model of General Relativity. It helps to actually learn what is necessary to model spatial and temporal relations for multiple objects to have an intuitive grasp on this question that you are asking.



Numbers are a synthetic
analysis of that process, distilled to a nearly meaningless but nearly
omnipotent extreme of universality (qualitative flatness). Numbers are
the opposite of the solipsistic personal experience (qualitative depth
asymptotic to 'Selfness' itself). They are the least appropriate tools
to describe feeling.

Atoms, fields, space, time seems as much.

Are they, or are these words just place-holders for the hope of meaningfulness?





Not primitive sense either,
but high order cognitive abstraction. There is no '1' or '2'
literally, they are ideas about our common sense - what we have in
common with everything. Numbers are literally 'figures', symbols which
can be applied mentally to represent many things,

No. That's number description. Not numbers.

I'm not talking about the characters "1" or "2", I'm talking about
what they represent. The concept of numbers defines them as figurative
entities, but you make them literal. That's ok with me if you are
doing that for mathematical purposes since it is a powerful way to
approach it, through the negative symmetry, but just as you might
trace a picture better if it's upside down, eventually you should turn
it right side up when you finish. To say that numbers literally exist
but matter does not is the logo-morphic position, orthogonal to both
anthropomorphic and mechanemorphic, but it is still as pathologically
unreal if taken literally. Again, thats ok with me, we need
surrealists too, I'm just saying, when the rubber hits the road, it's
not sanity.

Hmm...

Do the symbols 1, 2, 3, ... actually refer to objects or do they refer to some pattern of connections in a physical system? If they are objects, what other properties do they have? How is is that we can come to know of these properties?





and to deploy
orderly control of some physical systems - but not everything can be
reduced to or controlled by numbers.

But that's what number can discover by themselves.

In your logopomorphic theory of comp.

Be polite!

:)

    He is being polite! Me, maybe not so much.



Once you are at the
treshold of numbers, the complexity of the relations (even just
between numbers) get higher than what you can describe with numbers.
the numbers already know that, with reasonable account of what is
knowledge.

If the complexity exceeds the capacity of numbers, then you need to
invoke even more complexity in the form of additional forms of
expression of that complexity...out of thin air?

It develops from intuition. Numbers, relatively to universal numbers, can develop intuition, due to the true relation existing between numbers, including the truth that they cannot rationally justified. So it comes from truth.

    So numbers have minds of their own?




With sense,
complexity is generated recursively from bottom up entropy, while
simplicity pulls from the top down toward unity as significance.
Evolution is the interference pattern between them.




What
necessary logic turns a nuclear chain reaction (addition and
multiplication) into a nursery for problem solving sentience?

The same logic making tiny system Turing universal. Usually some
small
part of classical logic is enough.

Why would any kind of universality or logic entail the automatic
development of sentience? What is logical about sentience?

The illogicality of sentience. From the point of view of numbers, when
they look at themselves, they discover, for logical reason, that there
is something non logical about them.

If there is something non logical about numbers (which are really the
embodiment of pure logic), why does that truth have to be 'discovered'
by them?

Because truth extend logics, and number are constrained by truth, before what they can believe.

You are treating numbers as if they are conscious entities themselves. I am OK with that, but I require that there be a common world wherein we can determine the continuous transformation of one form of entity into another, an unbroken chain from these numbers to us, such that their properties are not just some appearance that pops in and out randomly.



In our development as children, do we not discover logic out
of the chaos of infancy rather than the other way around? Do we not
learn numbers rather than learn feelings?

Because we have brains which sum up millions years of teaching in nine month, making us believe that walking and seeing is simpler than trigonometry. Later we can understand that is the contrary.

    OK, but this really does not explain anything.




Then the comp act of faith
appears to be the simplest way to restore logic, except for that act
of faith and the belief in addition and multiplication.

What kind of faith does a Turing machine have?

If she is correct, it looks like it is plotinian sort of faith. But a machine can also develop a faith in mechanism, by surviving back-up, and be led, with occam, to a more pythagorean sort of faith.

Bruno


http://iridia.ulb.ac.be/~marchal/



You must admit that you are merely speculating Bruno. Unless you can physically demonstrate the Turing machine, it is nothing more than patterns of chalk marks on a board.

--
Onward!

Stephen

"Nature, to be commanded, must be obeyed."
~ Francis Bacon


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