Version française
Home     About     Download     Resources     Contact us    

This site is updated infrequently. For up-to-date information, please visit the new OCaml website at

Browse thread
JoCaml Released.
[ Home ] [ Index: by date | by threads ]
[ Search: ]

[ Message by date: previous | next ] [ Message in thread: previous | next ] [ Thread: previous | next ]
Date: 2007-06-06 (11:02)
From: Oliver Bandel <oliver@f...>
Subject: polycontextural logic (Re: [Caml-list] JoCaml Released.)
On Wed, Jun 06, 2007 at 10:40:57AM +0100, Jon Harrop wrote:
> On Wednesday 06 June 2007 10:00:38 Oliver Bandel wrote:
> > ...I will collect both mails and send it to the list today...
> On Wednesday 06 June 2007 10:00:38 Oliver Bandel wrote:
> > it interests other people...
> On Wednesday 06 June 2007 10:31:25 Oliver Bandel wrote:
> > ...I will try my best.... it follows today...
> The suspense is killing. ;-)

heheh :)

I'm not the only unpatient person, it seems ;-)

OK, here it comes:



I mentioned that polycontextural logic seems to be the only
thingy that can describe / formalize parallelism and
self-reference (e.g. liar-paradoxon) and other interesting things
in a complete, non-contradictional, non-reductional way.

First the disclaimer: no, I'm not knowing this stuff as good as that
I might write papers about it. I've just looked inside a littlebid.

What does this term "polycontextural logics" mean?

It means that the logic can not only be used in one
logical context (true / false), but also can be used between
different contexts. Using logic in many context is nothing new.
But that *between* these contexts there can also be logical operators
be used, this is very uncommon / unusual.
This is a kind of enhancement of logics. People who are fluent
in using PCL would say, that it's the more general (generic?)
form of logics, because the logic we use, is a subsystem,
only be used in one context.

To decribe self-reference there were many attempts in logic.
One is George Spencer Brown's "calculus of indications".
Francisco Varela enhanced it to the "calculus of self-reference".
But both are monocontextural. For example, the "calculus of indications"
can't describe self-reference in a non-timely (non-toggling)
way betweeen true-false-true-false... (liar-paradoxon for example).

The problem is, that the subject (observer) does not only talk about
it's observations and does say something about them in the same
context; in the liar-paradoxon the subject (observer) talks about
itself, and this means a context-switch between the observer
saying something about his observations (the subject tells something
about the so called objective world).

To say it with Heinz von Foerster's words:

      "Objectivity is a subject's delusion that
       observing can be done without him."
                              (Heinz von Foerster)

This is not possible with clasical logic, because it is based on
a philosophy, that avoids self-reference. Hence the liar-paradoxon:
You can't describe something that is spread about more than one
logical context with a logic that is bound to one context!

It seems to be that there must be a contradiction in what the lying
subject tells us, and we go into a timely toggling function:

  let toggle = function true -> false | false -> true

To have a time-independent description of the liar-problem
(no longer a paradox), there must be a way to explicitly
introduce the subject that says something into the logic.

The subject that says something about the so called objective
world (which it is part of!) must be included in the philosophic
base, so that it also can be included in a formal system.
If you do this, than there is a possibility to also describe
the liar-problem (liar-paradoxon in monocontextural explanation).

The way to do this, is not to insist on ONE logical place (contexture)
and to do a timely toggling, but to accept MORE THAN ONE logical place.
Include the subject in the logic, and the problem is gone!

This might seem frightening to the objectivity-based worldview
of today's science, because the last some-hundred years the
last exit to absolutism was to have the logic.

The sun is not the center of the world anymore, we also
had to see that ratio is not all (Freud often will be mentioned at this point),
computers are calculating much faster then we can,
and now the whole logic, the formal base of our ratio seems to be
the problem.

  BTW: that the ratio is not all, was already told us by Shakyamuni Buddha.... :)
   he also told us that subject and object can't be cutted apart ... or
   in other words, that the ratio is, what makes the cut, splitting
   the subject (which is part of the world) apart from the world
   (which will be sawn as the opposite of the subject, and not it's
    embedding environment),
   or in George Spencer Brown's words: the ratio is, what "draw(s) a distinction"

Gotthard Guenther, who has created the polycontextural logics (PCL),
has started differently: he said: the subject is there at the same time
as the obecjtive world is here. He said, we do not have to start
with either the subject, and create the world from it, nor do we have
to start with the world and have to create the subject from it.

We have to start with both thingys at the same time: the subject as well as
what we call the world (as being apart from the world) are there
at the same time. We accept both right from the beginning on and then
we are not constricted to the one or the other thingy.

And that's the starting point of where the liar-paradox turns to
a liar-problem, turns to only a description of a subject saying something
about istelf. :)

The polycontextural logic is based on morphogramatics, kenogramatics, ...
which is a pre-linguistical approach.

Here are some links:

But be aware, as you CAN'T derive that stuff from your science and logic
you are already have in use, learning this might be more difficult than
only switching from imperative programming to functional programming. ;-)

It's the other way around: the logic you use and even the numbers you use,
can be derived from PCL (or kenogrammatics / morphogrammatics / ...)
so that throwing away your many calculi would be a good idea. ;-)
At least throw them away for a certain period of time.

When you look ta the PKL-pages from thinkart-lab,
in the graphics/animation you can see the term "P-combinator".
Following the first link google shows,  you can find this:

There is a PLisp (parallelized Lisp), which uses the
They also refer back to Polycontextural logics.

One paper about the parallelizsation, and how to
describe it with PCL (german text), you can find here:

As far as I understand (which seems not to be far enough ;-))
the "dissemination" (truest parallelism one even can't imagine ;-))
is "more parallel than parallel".

(Let's call it "independent processes"?? But how can they be independent,
 if all proceeds in this one world? Is this a contradiction of the PCL?
 Or a limitation of my PCL-knowledge?)

There is also a german book "mg-book.pdf"
which explains the morphogrammatik and kenogrammatic and PCL.

(It's written in LaTeX, and called "book", but is only singlesided,
 not layouted in book-format. But maybe not all people are
 typographic fetishists like me and don't have a problem
 with this ;-))

Gothard Guenther btw. has worked together with McCulloch at
the BCL (Biological Computr laboratory)  (which was lead by Heinz von Foerster).

The paper "A heterarchy of values determeined by the topology of nervous nets"
by McCulloch has inspired Gotthard Gunther.

To the BCL:
 "A Brief History of the BCL
   Heinz von Foerster and the Biological Computer Laboratory":

Hope this gives an impression of what I meant, when mentioning the PCL.
As I'm also new to this kind of thinking and didn't had a longer time
to jump inside, this only is a slight overview on an interesting theme.
I hope this can motivate more people to try to think in new ways.


P.S.: Using the classical mathematics / logics for describing self-referential
      processes, as the cyberneticians use it, there is the same problem with
      the time-toggling in the liar-paradoxon: you have to use iterative
      or endless recursive functions (hello lazy evaluation ;-)) but there
      is no way to describe the things without such an infinite approach.
      (See self-reference, chaos theory and so on: always infinite calculations.)

      This again is the time-based approach. If we could (can we?) go and
      spread the calculaions in space instead of reiterating / recursively
      doing onedimenasional (monocontextural) calculations (because we
      first take the hammer and making the world a flat plane), then many
      problems might be solved easier and elegantly.
      (If we will have the computers to calculate this, is a different question ;-)
       The complexity might be the same; but it's spread over space not over time...
       ...possibly massive parallel computing (bio-computers?)might help a littlebid here))

      For at least some of these problems the PCL (and kenogrammatics / morphpogrammatics)
      might be fruitful.

      In the german interview of Ruolf Kaehr

     he said, that the numbers do not begin with 1 but with 4.
     Don't take that literally, because the 4 is bound to the kenogramatics
     and the multiplicity of formal systems, necessary to create things like numbers...