Re: The role of logic, & planning ...

[Russell Standish]

Marchal wrote:
> 
> Russell Standish wrote (to George):
> 
> >I don't think Bruno's conclusion is weird. I come to essentially the
> >same conclusion in "Occam", without the need for formalising
> >"Knowledge", nor the need to use Modal logic.
> 
> The fact that you come to the same conclusion does not mean these
> conclusions are not weird. I hope you realise these conclusions run
> against the average materialistic aristotelian current scientific
> paradigm.

Naturally. But then, that's part of its appeal!

> 
> >I would like to think that my exposition is easier to follow than
> >Bruno's, but this could simply be a biased viewpoint on my part. I
> >welcome comment and criticism on that paper.
> 
> I still believe my general remarks apply to your "why Occam's razor".
> (I reprint it and I will reread it once I have more time).
> You put to much for me in the hypothesis. Like all physicist you seem
> not to be aware of the mind body problem. 

You are right! What is the mind-body problem?

> With comp, what the UDA shows
> (and what the graph movie or Maudlin works "proves") is that it is
> not possible to attach awareness to worlds or histories.

I'm not really sure what you mean by this. In essence, I say that an
awareness must experience a history in order to be aware. The Time and
Projection postulates of my paper.

> The reversal
> means really that you need first a theory of consciousness, or a 
> psychology for deriving the existence of physical beliefs.
> I agree that there are similarities in some of our conclusion, but
> I am not sure we mean the same by "psychology".

I'm reasonably sure we don't, at the level of fine detail. However,
that debate can be postponed until other issues have been resolved,
such as whether my argument stands up to further scrutiny.

> 
> >Incidently, I didn't mean to imply that this sort of modeling of
> >Knowlegde was inappropriate, only that there was no discussion as to
> >why one would want to model it in this particular way.
> 
> 
> The word "model" is tricky. It means different things for logician
> and painters (who are using it in the sense of reality) and physicist
> and toys builder (who are using it as "theory" or approximation, or 
> reduction). 
> Soemtimes I use it in the physicist sense ...
> But my approach is more axiomatic. I hope I will be able to give 
> enough illustrations to help understanding ...
> 
> >Its really the
> >same as when Hal Ruhl (and I admit I'm putting words in his mouth
> >here, although its consistent with my understanding of his position)
> >models the universe by cellular automata.
> 
> Hal Ruhl, like Toffoli, and even like Schmidhuber-2, seems indeed
> to search for such "modelisation".
> But I do not (and apparently Schmidhuber-1 don't do it either).
> 
> The UD does NOT depend on the choice of a particular formal systems.
> The UDA really shows that my "awareness" will be linked with all
> implementation of my computationnal extension.
> By implementation here I just mean the giving of a program and its
> relative UTM interpretation.
> 
> And the provability logics (G and G*) is correct and complete for ALL 
> sound
> classical Universal Machines. In that sense there is no modelisation
> at all. And comp is not the hypothesis that my brain can be modelised
> by a Turing Machine, it is the act of faith of telling "yes" to the
> (mad) surgeon.
> 
> >I notice Bruno has posted a more detailed discourse on this issue,
> >which I will digest in due course.
> 
> It is an important one, but it will be fully clear only after 
> I explain Godel and Lob theorem with enough rigor.
> 
> >Perhaps all he was doing was
> >assuming a cultural background of philosophy I have not been exposed
> >to. Just as an example, he says most philosophers would agree that
> >[]A->A, where []A is interpreted as knowing A. This is clearly a
> >different meaning of the word "to know" that we use here in
> >Australia. I know of plenty of people who know that God exists. And I
> >know of a number of other people who know that God doesn't exist. So,
> >by this application of Modal logic, we can conclude that God both
> >exists and doesn't exist at the same time, which seems kind of 
> >illogical.
> 
> To say the least. I must say that I am quite astonished that 
> Australian can "know" falsities. What is the difference between
> knowledge and belief for an Australian ?
> 

A matter of degree, as far as I can tell.

> >Perhaps the way out of this mess is to say that I'me really talking
> >about belief, ...
> 
> Yes, I think indeed you were talking of "belief". The nice thing
> with axiomatic approach is that we will "define" knowledge or 
> knowability by axiom like K, T, 4. Except that formal provability
> will be defined in arithmetic and then we will look at which
> formula it obeys. And It does not obeys to knowledge axiom (see
> below).
> 
> >...rather than knowledge, however that would imply that
> >knowledge is devoid of meaning, since it is impossibl

Re: Belief & Knowledge

[Scott D. Yelich]

On Wed, 2 May 2001, Brent Meeker wrote:
> A true belief that has a casual connection with the fact that makes it
> true.

Knowledge is when predicted.

Belief & Knowledge

[Brent Meeker]

On 02-May-01, rwas rwas wrote:

>> Just as an example, he says most philosophers
>> would agree that
>> []A->A, where []A is interpreted as knowing A. This
>> is clearly a
>> different meaning of the word "to know" that we use
>> here in
>> Australia.
> 
> I get the impression folks here assume that when one
> person knows something, that only that person knows
> that something. For other people to know the same
> something, they have to discover and assimilate it for
> themselves. It also seems that folks here assume
> knowledge is some kind of pattern that exists separate
> from the truth of surrounding it's existence.
> 
>> From a mystic standpoint, this can't be. To know
> something is closer to the analogy of a subscriber
> line. When one *knows* something, anything, they
> subscribe this pattern.

Correct me if I'm wrong, but the usual definition of knowledge is:

A true belief that has a casual connection with the fact that makes it
true.

The standard example is that I may believe that Tom has bought a blue
car because I saw him drive up in it.  And Tom has bought a blue car -
so the belief is true.  But it isn't knowledge because the car I saw
him drive up in is a rental car, not the one he bought.  So in this
example there is no casual connection between my belief and the fact
that Tom bought a blue care, and hence my true belief is not knowledge.

Brent Meeker

Re: The role of logic, & planning ...

[rwas rwas]

> 

> Just as an example, he says most philosophers
> would agree that
> []A->A, where []A is interpreted as knowing A. This
> is clearly a
> different meaning of the word "to know" that we use
> here in
> Australia.

I get the impression folks here assume that when one
person knows something, that only that person knows
that something. For other people to know the same
something, they have to discover and assimilate it for
themselves. It also seems that folks here assume
knowledge is some kind of pattern that exists separate
from the truth of surrounding it's existence.

>From a mystic standpoint, this can't be. To know
something is closer to the analogy of a subscriber
line. When one *knows* something, anything, they
subscribe this pattern.

Another issue is how folks seem to thing knowledge is
inanimate until someone acts on it, like words on a
paper being meaningless until someone read them. From
a mystic standpoint, that isn't so. Knowledge and
expression is simply manifest from one place to
another. The knowledge itself is not constrained to
the limits of those that would interpret it. Those
entities interpret and then express that understanding
wherever they happen to be existing.

For someone to try to form the basis for existence
based on what one thinks others can know in terms of
what I've tried to counter, I feel intuitively that
they would fail, or not succeed completely. 

One analogy to explain this is someone caught in an
event horizon of a black-hole. The realm formed by
this Event-Horizon can be vast, but is still by
definition, limited. I see people trying to define
existence by illusionary data like someone trying to
understand the universe by what he can see from his
vantage point in the Event-Horizon. Drawn out, it
would look like someone walking in a circle.
Eventually, he'd come back to where he started. He
might vary his path slightly to see different things,
but he'd simply be make the circle bigger. He can
never know what lay outside the circle with his given
modus operandi.

>From my perspective, true knowing, is being what you
know. Which implies a great deal on what is truly
knowable. If you look at what we're used to here, we
have belief and knowing implicitly understood in
statistical terms. We know we can walk, we've done it
so often, so we don't doubt we can. Belief seems to be
predicated on the existence of doubt. True knowing has
no constraints of doubt. To know is to be one with
that knowledge. This from a mystic standpoint, is true
faith. Faith is *not* belief. Faith is knowing.




 I know of plenty of people who know that
> God exists. And I
> know of a number of other people who know that God
> doesn't exist. So,
> by this application of Modal logic, we can conclude
> that God both
> exists and doesn't exist at the same time, which
> seems kind of illogical.
> 
> Perhaps the way out of this mess is to say that I'me
> really talking
> about belief, rather than knowledge, however that
> would imply that
> knowledge is devoid of meaning, since it is
> impossible to establish
> with certainty whether any particular fact is true.
> Even Mathematical
> proof is contingent upon belief of the efficacy of
> the formal proof,

Again, I had thought the point of these threads were
to try to describe consciousness with the idea in mind
of trying to synthesize consciousness in software or
some other artificial means.

I propose the best way to do this is to know what one
is after specifically, then solve the problem of
achieving it.

If one attempts to use a limited thinking style to
implement something interpreted with that same
thinking style, the end result would seem to
necessarily be limited to perceptional constraints of
that thinking style. I get the intuitive sense, that
linear or sequential thinking will not result in the
kind of achievement we're talking about.

Robert W.


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Program for UD

[hal]

Has anyone proposed a specific implementation for the Universal Dovetailer
(UD)?  This is a program which runs all possible programs, a little bit
at a time, making progress in all of them.

For something close, here is Greg Chaitin's program to calculate Omega,
the probability that a random program will halt.  It comes from from
http://www.cs.auckland.ac.nz/CDMTCS/chaitin/omega.l, and is written in
his dialect of Lisp.

    Omega in the limit from below! 

   define (all-bit-strings-of-size k)
   if = 0 k '(())
   (extend-by-one-bit (all-bit-strings-of-size - k 1))
   define (extend-by-one-bit x)
   if atom x nil
   cons append car x '(0)
   cons append car x '(1)
   (extend-by-one-bit cdr x)
   define (count-halt p)
   if atom p 0
   +
   if = success car try t 'eval read-exp car p
  1 0
   (count-halt cdr p)
   define (omega t) cons (count-halt (all-bit-strings-of-size t))
cons /
cons ^ 2 t
 nil

Examples of calling it:

   (omega 0)
   (omega 1)
   (omega 2)
   (omega 3)
   (omega 8)

To read it, keep in mind that Lisp is a prefix style language, so that
the syntax is "operator operands".  Also, the single quote means that
the following argument is quoted rather than evaluated.  The built-in
functions car and cdr return the 1st element of a list and the remainder
of the list, respectively, and cons puts car and cdr back together to
form the original list.

The first two functions just return a list of all bit strings of size k.
These will be the programs that run.  The first function tests if k = 0
and returns (()), otherwise it calls itself on k-1 to get all k-1 bit
strings, then calls extend-by-one-bit.  The latter takes the first
element (car of x) and appends both 0 and 1 to it.  Then it recurses on
the remainder of the list.  So calling all-bit-strings-of-size-k with 1
gives ( (0) (1) ), with 2 gives ( (0 0) (0 1) (1 0) (1 1) ) and so on.
These are the possible programs which will be run.

The count-halt function will return the number of programs in list p
which halt within t steps.  If p is an atom (not a list) it returns 0,
else it tries running car p (the first element of p) for t steps and
counts 1 or 0 based on halt/no-halt.  It recurses on the remainder of
p and adds that result to the 1 or 0.

The key to this function is Chaitin's operator "try", which takes a number
of steps and a program.  It runs the program for that many steps and
returns a success/still-running flag, plus the output from the program
if any.  Above Chaitin is only using the success flag to count whether
the program has halted.

Last we have omega itself, which for parameter t calls count-halt
on all strings of length t. It then shows that this needs to be
divided by 2^t to get the halting probability.  (BTW Chaitin
has actual Lisp interpreters which can run this program at
http://www.cs.auckland.ac.nz/CDMTCS/chaitin/lm.html.)

You could get the effect of a UD, then, by calling omega with successively
larger numbers.  It would run all 1-bit programs for 1 step, then all
2-bit programs for 2 steps, all 3-bit programs for 3 steps, and so on.
It might appear that this will not, for example, run 2-bit programs for
10 steps.  However Chaitin's programs are self-delimiting.  When you
have all 10-bit programs, some of those are 2-bit programs with 8 ignored
bits at the end.  So in running N-bit programs for N steps, we are also
running all K bit programs for N steps, where K < N.

This way of doing a UD is wasteful in that we keep restarting each program
from the beginning.  I think in most conceptions of the UD we assume that
each program's state is retained, so that when its turn comes up again,
it continues from where it left off.  However I think it would be difficult
to manage the storage space for this to work.

Doing it Chaitin's way might appear to change the frequency with
which a program ones so that it departs from the universal measure.
If we have two programs of length K and L, where K << L but both are
large, it should be that the first program gets running time 2^(L-K)
greater than the second program.  However program K actually gets in
addition L-K runs before we even start running program L, as we build
up to programs of size L.  In the end this should not matter though
as this constant factor will decrease in importance as the size of
programs approaches infinity.  Running programs of size N >> L >> K,
K will get running time 2^(L-K) more than L due to its smaller size,
which corresponds to the universal measure.

This leads to three questions:

 - Would all UD programs would correspond to the universal measure,
asymptotically?

 - Is there a way to retain state for all the programs so that you don't
have to start over from the beginning?  (Although Chaitin's way may
be simpler, and if it gives the same probability distribution then we
couldn't tell the difference).

 - Is it necessary 

Re: The role of logic, & planning ...

[Marchal]

Russell Standish wrote (to George):

>I don't think Bruno's conclusion is weird. I come to essentially the
>same conclusion in "Occam", without the need for formalising
>"Knowledge", nor the need to use Modal logic.

The fact that you come to the same conclusion does not mean these
conclusions are not weird. I hope you realise these conclusions run
against the average materialistic aristotelian current scientific
paradigm.

>I would like to think that my exposition is easier to follow than
>Bruno's, but this could simply be a biased viewpoint on my part. I
>welcome comment and criticism on that paper.

I still believe my general remarks apply to your "why Occam's razor".
(I reprint it and I will reread it once I have more time).
You put to much for me in the hypothesis. Like all physicist you seem
not to be aware of the mind body problem. With comp, what the UDA shows
(and what the graph movie or Maudlin works "proves") is that it is
not possible to attach awareness to worlds or histories. The reversal
means really that you need first a theory of consciousness, or a 
psychology for deriving the existence of physical beliefs.
I agree that there are similarities in some of our conclusion, but
I am not sure we mean the same by "psychology".

>Incidently, I didn't mean to imply that this sort of modeling of
>Knowlegde was inappropriate, only that there was no discussion as to
>why one would want to model it in this particular way.


The word "model" is tricky. It means different things for logician
and painters (who are using it in the sense of reality) and physicist
and toys builder (who are using it as "theory" or approximation, or 
reduction). 
Soemtimes I use it in the physicist sense ...
But my approach is more axiomatic. I hope I will be able to give 
enough illustrations to help understanding ...

>Its really the
>same as when Hal Ruhl (and I admit I'm putting words in his mouth
>here, although its consistent with my understanding of his position)
>models the universe by cellular automata.

Hal Ruhl, like Toffoli, and even like Schmidhuber-2, seems indeed
to search for such "modelisation".
But I do not (and apparently Schmidhuber-1 don't do it either).

The UD does NOT depend on the choice of a particular formal systems.
The UDA really shows that my "awareness" will be linked with all
implementation of my computationnal extension.
By implementation here I just mean the giving of a program and its
relative UTM interpretation.

And the provability logics (G and G*) is correct and complete for ALL 
sound
classical Universal Machines. In that sense there is no modelisation
at all. And comp is not the hypothesis that my brain can be modelised
by a Turing Machine, it is the act of faith of telling "yes" to the
(mad) surgeon.

>I notice Bruno has posted a more detailed discourse on this issue,
>which I will digest in due course.

It is an important one, but it will be fully clear only after 
I explain Godel and Lob theorem with enough rigor.

>Perhaps all he was doing was
>assuming a cultural background of philosophy I have not been exposed
>to. Just as an example, he says most philosophers would agree that
>[]A->A, where []A is interpreted as knowing A. This is clearly a
>different meaning of the word "to know" that we use here in
>Australia. I know of plenty of people who know that God exists. And I
>know of a number of other people who know that God doesn't exist. So,
>by this application of Modal logic, we can conclude that God both
>exists and doesn't exist at the same time, which seems kind of 
>illogical.

To say the least. I must say that I am quite astonished that 
Australian can "know" falsities. What is the difference between
knowledge and belief for an Australian ?

>Perhaps the way out of this mess is to say that I'me really talking
>about belief, ...

Yes, I think indeed you were talking of "belief". The nice thing
with axiomatic approach is that we will "define" knowledge or 
knowability by axiom like K, T, 4. Except that formal provability
will be defined in arithmetic and then we will look at which
formula it obeys. And It does not obeys to knowledge axiom (see
below).

>...rather than knowledge, however that would imply that
>knowledge is devoid of meaning, since it is impossible to establish
>with certainty whether any particular fact is true.

But, at least for a non intuitionnist, or a non constructivist, a
proposition could be true independently of our belief or knowledge.
A platonist (as I am for arithmetics) has no problem with that.
Of course the nuance between truth, provable, believable, knowable, ..
are subtil. The crazy thing is that Godel (Lob Solovay) will 
eventually put an immense light on those nuance.

In metaphysics the "royal argument" for explaining that indeed we
cannot distinguish knowledge with belief is the dream argument.
When we are awake, we cannot know for sure that we are not dreaming.
Socrate uses it in his reply to Thaetetus. Descartes, Berkeley and
almost all 

Re: The role of logic, & planning ...

[jamikes]

George wrote:: (Tuesday, May 01, 2001 3:40 PM):
> If logic (or some form of logical model) is not the vehicle for describing
> reality, then what is?
>
> George
>
Describing what?
can we "think" of anything beyond the OM (including evtl. 'memories' in it,
similarly as momentary mind-content)? Do we (in-mind) have knowledge (- what
is it?) beyond that what is IN MIND? now if we call the mechanism of mind a
"logic",  do we have anything else to use for a thing named "reality", which
exists for us only in our mind ? (And let me skip the question: "who's
mind?")
Do we have any clue to distinguish the OM-stuff from our mindcontent?
Consequent arguing curls back to solipsism, no matter how revolting it is.
So, while subscribing to George's sentence - in total, I have to question
the use of the word 'reality'. Reality is MY virtual interpretation of
thoughts about - what I believe - is the world "outside". So are the
"objective" instrumental measurements with their explanations.
As Dr. Johnson said: the only reality is a stone in my shoe, because it
hurts.
Does it really, or do I only think it is?
John Mikes
<[EMAIL PROTECTED]>
"http://pages.prodigy.net/jamikes";