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

From: Marchal <marchal.domain.name.hidden>
Date: Wed May 2 08:53:31 2001

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 "idealist" use it also.
The beauty of comp is that it gives a non solispsistic idealism.


>Even Mathematical
>proof is contingent upon belief of the efficacy of the formal proof,
>something that has been called into doubt, particularly for more
>complex proofs like Fermat's last theorem, or the 4 colour theorem.


I definitely and infinitely agree. And *that* is part of the big
Godelian surprise. Godel's result is that there is no possible
formal proof of the fact that a formal proof of p entails p.
"p" being arbitrary.
The formula (with [] representing formal provability):

                            []([]p ->p)

cannot be proved formaly for all sentences p.
With p equal to the constant sentence FALSE, it is a direct
consequence of Godel's second theorem. It says that a consistent
machine cannot prove its consistency. A machine cannot
prove "not provable FALSE", that is: -[]FALSE, that is:
[]FALSE->FALSE. Remember that -p <-> (p -> FALSE).
A formal proof acts indeed like a belief, for the formal
system.

>I don't mean to be picky, but its just these sorts of considerations
>and misunderstandings that throw me off the track every time.

All that will be transparent with G and G*, ... It is because
such matter is not obvious *at all* that the modal detour is
useful.

      Self-reference is really the land of counter-intuition and
      surprise.

Bruno


PS Apology for my anomalous multiple last post sending.
Received on Wed May 02 2001 - 08:53:31 PDT