Dear Organlearners,
Greetings to you all.
In my reply to Richard Karash <Richard@Karash.com> who wrote:
>>But, I think repeated negation will suppress.
I showed that repeated negation leads to the following truth table:
(1) (2) (3) (4)
prop NOT prop NOT NOT prop NOT NOT NOT prop
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
TRUE FALSE TRUE FALSE
FALSE TRUE FALSE TRUE
In column (1) are the two possible values (true or false) of any
proposition (abbreviated to "prop") which a person A makes. If the "prop"
happens to be true, the upper row of the table applies, but if the "prop"
happens to be false, the bottom row of the table applies.
The negation of "prop" (indicated by NOT prop) by person B brings us to
column (2), either the upper or the bottom row. The negation of A of B's
negation (indicated by NOT NOT prop) brings us to column (3).
When persons A and B keep on negating each other, we have in effect a
progress from left to right in the table, either in the upper or in the
bottom row. Person A jumps along columns (1), (3) , (5), .... and person
B jumps along columns (2), (4), (6), ..... With such repeated negation
there is no hope that they will ever land on the same column.
I then wrote:
>They indeed have progress since they jump columns form left to
>right while skipping one column in each jump. But this progress
>has no other change than itself. This is another example of linear
>thinking.
(You will remember some time ago I articulated in words what we can learn
from mathematics about linear activities. One insight is that any linear
activity is a change without any further changes in such a change. In
other words, the change has no dance.)
>How can we escape this pattern of linear thinking?
>
>It is impossible to escape it with analytical or destructive thinking
>so typical of debates.
(snip)
>It is possible to escape the pattern with constructive thinking.
>
>But constructive thinking is not simplistic thinking. I will
>demonstrate
>it by merely asking you fellow learners to construct a way how to
>escape the pattern of linear thinking illustrated in the table above.
>Should Rick get four different constructive ways in less than a week,
>then I will negate my proposition with "constructive thinking is
>indeed
>simplistic thinking".
A week has gone by and not even one fellow learner came up with a
construction which will allow us to escape the linear thinking of repeated
negation. Perhaps constructive thinking is not so simplistic after all.
So how will we join the uneven columns of person A's thinking with the
even columns of person B's thinking? Let us allow our minds to meander.
My grandaughter Jessica is fond of playing a game with her friends. It is
called HOP SCOTCH. I do not know if this game is also played in other
countries. A string of circles is drawn on a pavement, each circle just
large enough to stand in with one leg. After every two to three circles,
the string is broken by two squares so that one can stand with both leags,
one in each square. The first kid place a stone in the first circle. Then
the kid begin to jump with one leg, skipping the circle with the stone in
it. The kid may land with both legs when reaching two adhacent squares.
After reaching the end of the string and coming back all the way, the kid
may displace the stone from the first to the second circle and repeat the
process.
However, once the kid's foot touches any line, the game is terminated for
that kid until the next round. The stone is left alone. The second kid
does the same as the first kid, but now has to deal with two stones. It
means that this kid has two places in which he/she cannot land. For the
third kid it becomes three places, two fixed (for that round) and the
last one movable. For the fourth kid it becomes four places, three fixed
(for that round) and the last one movable.
The progress in the truth table above is similar to the game HOP SCOTCH,
but without double squares breaking the monotony of circle after circle,
all in a line. The progress in the truth table is like each debater
jumping on one leg. What we need, are places where each debater can land
with both legs.
Truth itself has progress along the arrow of time. We may think of it as
the "evolution of truth". It involves, among other things, propositions
having two truth values, TRUE and FALSE. I will now try to articulate an
intuitive belief which all people have when thinking (even when it happens
tacitly) about the "evolution of truth". The belief is that all
propositions with values TRUE and only those propositions are connected
into one gigantic network. Thus not even one proposition with value TRUE
is all on its own, neither is any proposition with the value FALSE
connected to this network. This belief may also be called the "wholeness
of truth". (Another belief is that each true proposition corresponds to an
empirically verifiable fact.)
The trouble with this belief is that it is conceptual (i.e. being) and not
procedural (i.e becoming). It does not tell us how false propositions
immerge, nor how we can emmerge from false to true propositions. It does
not even tell us how to proceed on this network of true propositions. Thus
we are not able to infer from it that the
THE PROGRESS FROM TRUE TO TRUE IS TRUE
Worst of all, it does not tell us what to do when we find a single true
proposition standing all on its owns. They emerge as a result of
experience and even experiment. They stand alone because the thinking in
terms of the present paradigm disable their connection to the network of
true propositions. To hook one or more of them to the network requires a
paradigm shift -- a new more complex way of connecting true propositions
which seems to defy the "wholeness of truth". I have written in past
contributions how these paradigm shifts happen in terms of "deep
creativity". The present paradigm is driven to the edge of chaos as a
result of much and fast entropy production. At the edge lies the ordinate
bifurcation.
The new paradigm is its constructive emergence which requires a certain
level of maturity in all seven essentialities. But if one or more of them
are impaired, the bifurcation will keep on resulting in destructive
immergences to paradigms of lower order. In other words, before the new
paradigm emerge from the present paradigm, many inferior paradigms will
immerge from it as a result of impaired essentialities. They each give
rise to a deluge of seemingly true propositions in terms of such an
immerged paradigm, but false with respect to the present paradigm (now
under stress) or the new emerging paradigm.
It should now be clear that the "evolution of truth" does not only involve
the expanding network of true propositions, but also an underlying "garden
of paradigms". It is because of this "garden of paradigms" that progress
from false to false propositions do happen. It happens as a progress in
"true" propositions in terms of some or other lower order paradigm.
Consequently, whatever construction we now make to break the monotonous
pattern of repeated negations, it has to acknowledge that
THE PROGRESS FROM FALSE TO FALSE IS TRUE.
It is most important for us to reconnect all these immerged lower order
paradigms into the new emerging paradigm of higher order. This is the
"healing process" very important to the "evolution of truth". It does not
reverse destructive immergences since they happened irreversibly. It
rather recognises that they immerged as a result of immature or impaired
essentialities at the edge of chaos. This usually happens when a person's
thinking is pushed to the edge of chaos by a deluge of entropy produced
externally -- the bifurcation forced by surrounding systems like other
people rather than self accomplished. So the healing and growth of these
impaired essentialities need to be of highest priority by way of
irreversible, authentic learning. Consequently our construction needed
also has to acknowledge that
THE PROGRESS FROM FALSE TO TRUE IS TRUE
Since this last progress for authentic learning is irreversible, the
opposite "progress" from true to false cannot be true. Any action which
leads true propositions into false propsitions is a retrogression rather
than than a progression. Such actions, even destructive immergences have
to be avoided. They are very, very real. But they are never true to the
"evolution of truth". Consequently our construction needed also has to
acknowledge that
THE PROGRESS FROM TRUE TO FALSE IS FALSE
Please study the four capitalised sentences which I have constructed
by carefully motivating them. They are
THE PROGRESS FROM TRUE TO TRUE IS TRUE
THE PROGRESS FROM TRUE TO FALSE IS FALSE
THE PROGRESS FROM FALSE TO TRUE IS TRUE
THE PROGRESS FROM FALSE TO FALSE IS TRUE.
They contribute together to the "evolution of truth" as follows
(I hope the schematic diagram comes out right. The T stands
for a true proposition and the F for a false proposition.)
T => T => T => T => T => T => T => T => T => T => T .... TRUE
\\ //
\\ //
\ \......FALSE / /......TRUE
\\ //
\\ //
F => F => F => F => F => F => F => F => F => F => F ....TRUE
In other words, both horizontal as well as the upward progress are true,
but the downward progress is false.
Do we have anything in our system of thinking which embodies these four
kinds of activities of which three are true progresses? Yes, indeed.
It is the "what if" technique so powerful in dialogue. But we will have to
articulate this "what if" technique more fully so that we can clearly see
the different propositions in it playing a role. Its full description is:
WHAT conclusion B can be made IF prosition A is the premiss.
To shorten it as much as possible without lossing its essences, it
becomes:
WHAT B IF A
There are 16 different binary logical functions possible between two
propositions A and B. Here are a four of the sixteen in a table
A B A and B A or B A equivalent B what B if A
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
T T T T T
T
T F F T F
F
F T F T F
T
F F F F T
T
Now compare the columns under "A", "B" and "what B if A" with the four
sentences in CAPITAL LETTERS on the progress we want in the "evolution of
truth". They are one and the same thing in form, although they differ in
content. The content of the four sentences in capital letters is a rich
SYNTHESIS in contemplations on "deep creativity" which involve concepts
like "entropy production", "bifurcations" and "paradigms". The content of
the "what B if A" is merely the result of logical ANALYSIS in terms of
function theory.
Consequently we can escape the linear thinking of repeated negation so
common to debates with the "what if" creative flow of ideas common to the
free end open dialogue.
OK. What I did, was merely to articulate what many of us intuitively know
as a result of the experiences we had. The error which we make is to think
that our intuition is something simple and that (considered as tacit
knowledge) its articulation into formal knowledge is simple as well. It
is not so simple as I have shown above.
Look at the flow of ideas in the "what if" diagram
T => T => T => T => T => T => T => T => T => T => T .... TRUE
\\ //
\\ //
\ \......FALSE / /......TRUE
\\ //
\\ //
F => F => F => F => F => F => F => F => F => F => F ....TRUE
For some people the upper horizontal flow is most important. However,
because of considering it important, they may easily exclude the other
three kinds of flow. Again, this monotonous exclusion is most dangerous
linear thinking. But in the free, open dialogue we rather accept all four
kinds of flow as real. The one kind of flow which each of us as an
INDIVIDUAL has to avoid SELF, is the production of false propositions by
employing true propositions. If some other individual does it, it is not
for us to command that he/she should not do it. If that individual does
not want to avoid such destructive immergences, there is nothing which we
can do about it. We each can only try to avoid doing it self.
For me as a teacher the most important flow is the one branching from the
flow of false propositions back to the flow of true propositions. The
decisive lesson which I have learned after six months of teaching is that
it is contraproductive for me as the source of external work and control
to try and force such a flow in the learner. Sometimes I succeed, but this
success exist only by my efforts. As soon as I stop pressurising the
learner, this flow stops and the flow from true to false takes its place.
My task as a teacher is rather to act as midwife, to guide the learner how
to self make that flow. This is only possible when the learner has the
free energy to do it and the seven essentialities are mature enough for
such a flow. My task as a teacher is to help the learner how to improve on
these requirements.
My task as a scientist is to follow the upper horizontal flow by logical
and empirical means.
My task as a fellow learner is to follow the lower horizontal flow, trying
to understand what appears to me as a flow of false propisitions, is a
flow of true propsitions to someone else.
My task as an artist in "deep creativity" is to break through these four
kinds of slow into a fifth flow, exploring what is unknown to me and other
people. The closest which I can express this task, is to extend the "what
if" diagram into
????????????????????????????????????????????????
//
//
/ /......TRUE
//
//
T => T => T => T => T => T => T => T => T => T => T .... TRUE
\\ //
\\ //
\ \......FALSE / /......TRUE
\\ //
\\ //
F => F => F => F => F => F => F => F => F => F => F ....TRUE
What (which I have indicated by ??????) lies beyond the conventional?
What emergences can I experience which I cannot even imagine? How can I
break free of a linear thinking which I am not even aware of? Can I do it
all alone as "dassein", or do I also need "mitsein"? How much is my task
as an artist of "deep creativity" related to the well being of a learning
organisation? Can I really live without God?
Dear fellow learners, this is perhaps my last contribution before I head
of for the deserts to fill my spiritual fuel tank once again.
Perhaps the new millenium may bring lots of new thoughts to us.
(Or do I have to wait another year? When Gregorius commanded the
calculation of the present calender long ago, his arithmaticians did not
knew of the existence of the number zero 0. Worse, when it was finally
introduced, the clergy considered it to be the number of the devil and
thus tried to prevent its usage. What a lovely confusion ;-)
I wish you all unlimited and unconditional love for the new millenium.
--At de Lange <amdelange@gold.up.ac.za> Snailmail: A M de Lange Gold Fields Computer Centre Faculty of Science - University of Pretoria Pretoria 0001 - Rep of South Africa
Learning-org -- Hosted by Rick Karash <rkarash@karash.com> Public Dialog on Learning Organizations -- <http://www.learning-org.com>