Definitions and Learning. LO25845

From: AM de Lange (
Date: 01/05/01

Replying to LO25817 --

Dear Organlearners,

Winfried Dressler <> writes under
Subject: Polanyi, The Tacit Dimension LO25817

>Two questions may depict my current thinking:
>What does 'define' mean? This is a self-referential question
>and requires the most abstract levels of general systems
>theory, which is something in the making.
>What is a 'term'? This is also a selfreferential question.
>I stress this, because it is this selfreferential property
>which is in my understanding at the roots of why the tacit
>dimension exists at all. (O-H-d/Tacit-Dimension-Win ;-)
>Terms can be understood as elements with relations:
>This is where definitions make sense. Definitions are then
>a collection of the relations of one term to others. This
>understanding is somewhat pre-systemic, and one may
>have difficulties in seeing the point of my two questions
>But terms can also be seen as systems in a context
>(surrounding). It is such systems which evolve, complexify,
>collapse creatively (or immergently) etc. This is the realm
>of painting rich pictures instead of defining.

Greetings Winfried,

Thank you for this valuable contribution.

I have changed the subject, not to escape The Tacit Dimension, but to
stress that we are into something very deep here. Part of the our dialogue
on the The Tacit Dimension has been involved with the idea of the

Definitions have served thinking humans well since Socrates more than two
millenia ago stressed that speaking about things which have not been
defined lead to fuzzy thinking at best. Let us consider your description
of definition "a definition is the relation of a term to other terms". Can
it serve us well enough as the definition of any definition for all

As you have indicated, in terms of thinking of the "system SY" alone, yes.
Observe that in simplisity thinking most, if not all, attention is on the
"system SY". The term to be defined is simply related to at least one
other term -- and preferably not too many other terms -- also belonging to
the "system SY"

However, once we have shifted mentally from the paradigm of simplicity to
complexity, this "term related definition" of any definition will not
serve us well anymore. As you have indicated, it is here where the
"painting rich picture" may serve us much better. Why?

Let me fist give an example which hopefully all of you will remember from
school mathematics. In set theory as set is "loosely defined" as "any
collection of elements". This "loosely defined" means that a plausible
description of a set is given, but that actually it is considered as a
"primitive term" rather than a "defined term". Or to use "Polanian
terminology", the concepts "set", "collection" and "element" are
considered as "tacit knowledge" rather than "explicated knowledge".

>From there on all other terms of set theory are related by definitions to
the "primitive terms" set, element and collection. For example, the "empty
set" is defined as "the set having collected $no$ elements". Likewise, the
"union set" is defined as "the set having collected elements from set A
$or$ set B".

But see how logic (indicated by the $$ signs as $no$ and $or$) has crept
into these definitions! Thus not only "set", "element" and "collection"
are primitive terms, but also the operators like "no" and "or" of logic.
In other words, the more we formalise the terms of set theory as our
system SY, the more we have to make use of informal terms outside SY to do
so! It seems as if the formal system SY depends on feeding on its informal
surroundings SU so as to grow itself. Among others, it feeds on "logic" as
one of the systems in the surroundings SU. Mathematicans were quick to
graps this and began to use set theory as a model for logic when logic got
deep into trouble with Goedel's (in)famous incompleteness theorem. Sadly,
most students trained in high school mathematics do not know why they had
been informed so much of set theory and so little of logic!

I say "among others" because set theory as the system SY feeds not only on
the system "logic" in the surroundings SU, but also on other systems like
"natural language". This is more difficult to perceive, but I will try to
explain it. The primitive term "collection" is not the same as "having
collected". The "collection" (noun, picture) refers to the outcome of an
action "to collect" (verb, movie). The system "logic" as it had been
created by Aristotle and improved by Venn, Boole, Frege, Russel,
Whitehead, Hilbert and Rosser, nevertheless had too much "being" and too
little "becoming" in it. Hence "set theory" as the system SY had to feed
also on the system "natural language" in the surroundings SU.

Logicians realised that whereas set theorists could use "logic" as the
unformalised dimension of "set theory", they had to do better than using
conversely "set theory" as the source of the primitive concepts in their
definition of "logic". So they began their definition of "logic" by
constructing "well formed formulae" suitable for logics. For example, they
will define "not A" as a "well formed formula" in terms of A as a "well
formed formula". Likewise they will define "A or B" as a "well formed
formula" in terms of A and B as "well formed formulae". Here the symbols A
and B represent statements in a "natural language" such as "the sun emits
light" and "Shakespear is a writer". Thus formal logic as the system SY
feeds on "natural language" as one of the systems in its surroundings SU!

The Dutch mathematican Lutzen Brouwer early in the twentieth century had
the astounding insight that the system "natural language" itself feeds
upon the system "intuition" so as to articulate any sentence at all in a
natural language. In other words, the system "logic" feeds on "natual
language" and through it on the system "intuition". So when we turn our
focus again to set theory, we now have to conclude that as the system SY
it feeds upon "logic", "natural language" and "intuition" as three of the
systems in the surroundings SU.

How much Brouwer's concept of "intuition" and Polanyi's concept of "tacit
knowledge" have in common, is another question. Furthermore it involves
the very concept of "definition" itself. Is it possible at all to define
intuition with words? Intuition is often defined as "instictive knowledge
from within without any prolonged conscious thinking". If intuition is so
quick, how can we even dare to articulate it because every meaningful
articulations require a careful formulation which takes time? In other
words, it does seem that intuition is tacit. In fact, the majority of
mathematicians claim emphatically that mathematical intuition cannot be
articulated -- one is either born with mathematical intuition or not! (By
the way, let me stress once again that I do not subscribe to such an
"inheritance" claim.)

Let us feed upon another system in the surroundings SU, namely
"creativity". How much have "intuition" and "tacit knowledge" to do with
"creativity"? Creativity is often defined as a novel construction of two
seemingly unrelated things. But is this definition of creativity itself
novel? The novel outcome of creativity can be descibed by holism -- it is
a whole which is more than the sum of the parts. Will creativity be
possible without a requisite level of wholeness? Furthermore, is
"wholeness" the only property requisite to creativity? What about
diversity (or "otherness" as I prefer to call it). When the two things
seems to be unrelated, it may be that we have never before considered them
together as a whole. But it may indeed also be that they are so different
from each other that we did not recognise any relationship between them
even when considering them together.

How many such "####-nesses" are prerequisite to a novel outcome for
creativity? Arthur Koestler, one of the most astounding thinkers on
creativity who personally questioned a great diversity of creative
thinkers, finally managed to articulate what he calls "bijection" as
prerequisite to all creativity. He was very excited about his contribution
in understanding creativity. Yet very few modern consultants on creativity
have even the slightest to say on "bijection". To "biject" creatively, is
not only to bring two unrelated things together and then hope for the
best, but to search and to attempt an effective connection between these
two things. For example, when Einstein connected space and time into a
four dimensional continuum, he used the constant velocity of light to fit
them together. When Planck connected the electromagnetic radiation of a
heated black body to the wavelength of the radiation, he postulated a
quantum packaging of energy proportional to the frequency and not the
amplitude of the radiation to connect energy and wavelength.

Koestler's concept of "bijection" correspond very closely to what I call
"fruitfulness". So we now have "wholeness", "otherness" and "fruitfulness"
as being requisite to creativity. How many more "###-nesses" are there?
Way above I indicated that set theory had to feed upon not only logic, but
also natural language to supplement the noun/picture ("being") with the
verb/movie ("becoming"). Now, is this "becoming-being" which I call
"liveness" not also prequisite to novel creations? Apart from the four
thus mentioned, what about "spareness"? Clearly, the system "set theory"
could not feed only upon the system "logic", but also had to feed upon the
system "natural language". Why? Is it not because a natural language also
allows us to articulate what is illogical. The system "logic" is too
restricted because it does not allow for illogical thinking.

I have now painted such rich picture that it may cause fellow learners to
become lost in what I wanted to illustrate. I wanted to illustrate with
"set theory" that in defining its terms, we have to make use of undefined
terms. In simplicity thinking defined terms belong to the system whereas
undefined terms do not belong to it. In complexity thinking each of the
undefined terms belong to its own system and thus behaves in terms of that
system. In simplicity thinking we are oblivious to the systemic behaviour
of undefined terms, but in complexity thinking we we have to open
ourselves up to the fact that they also have systemic behaviour. In fact,
the very systemic behaviour of the undefined terms will sooner or later
have profound ramifications on the systemic behaviour of the defined terms
of the system. Acknowledging this fact gives us an effective connection to
"openness", another "####-ness" prerequisite to creativity.

Opening ourselves up ("openness") to other systems which we are not
familar with is a key to authentic learning. In the illustrations above I
have opened up the system "set theory" to systems such as "logic",
"natural language", "intuition" and "creativity". Can we go further with
this opening up? Yes, think of the undefined term "element" of set theory.
Now the term "element" has profound systemic significance in the system
"chemistry"! Is it possible to define set theory in terms of chemistry
terms rather than logical terms? Yes, it is indeed possible. The set term
"union" may be defined as a "chemical mixture" whereas the term
"intersection" may be defined as a "chemical reaction". Once we do this,
exciting new insights into the system "set theory" may be gained.

Winfried, I have a mixed feeling towards the use of "definitions". I
cannot deny that they, when used in a closed (rigid) manner, are very
helpful in protecting my thoughts against a deluge of information. I have
often made used of this protection when feeling close to an destructive
immergence at the edge of chaos. But just as many times I have dared to
open up such a closed definition when I became aware that my authentic
learning was stagnating into rote learning. The wierd thing is that
whereas such opening up gave me "new life", whenever I communicated this
"new life" to other people, most of them went into the protective mode by
closing the definition so as to avoid possible "death". Since I also did
so in the past and have to do it in future, how can I be indifferent or
even be annoyed by the protective mode?

>My whole point was, and is, to honor the term
>'tacit dimension' as system in context. And no
>two different minds form the same context for
>one term.

These are wise thoughts.

(Sometimes it strike me that by saying so, it may be perceived as if I am
trying to depict myself as wise too for recognising their wisdom ;)

In terms of the systems thinking I have used aboved, one person's mind
constitute the system SY while the the minds of the rest of humankind
through all ages constitute the incredible rich collection of systems
taken together as the surroundings SU. Together the system SY and the
surroundings SU form the universe UN of human thinking. This UN is very
complex, so complex that I actually use it as my defintion of complexity
. Complexity is all the perceptions
. of all humans through all ages.

All these minds commute by "information" between them and thus outside
them. However, in each of these mind there has to be "knowledge" so as to
make this "information" meaningful. Only knowledge within the mind can
produce meaning from information outside the mind.

This whole contribution up to now is just one big block of "information".
Since I have created it with my knowledge, it has a certain meaning for
me. But when any one of you fellow learners have read it up to this point
(how brave of you! ;), it will have another meaning because your
knowledge differs from mine. For me to insist that these meanings have to
be the same as mine is detrimental to your own authentic learning and thus
utterly foolish for me. But I have learned that for us to share these
different meanings in a LO-dialogue so that we can arrive at a collective
meaning, is the very key to metanoia. This collective meaning is not the
common denominator between all these different meanings, but the emerging
outcome when connecting all of them -- a whole which is more than the sum
of the parts.

Like the following:

>Surely, 'metanoia' is a not about elements in defined
>relations but about systems evolving in contexts.

Fellow learners, forgive me for elaborating so much. I have done it
because Winfried have used the word "surely". I agree completely with what
Winfired has written here. Perhaps it may seem foolish to agree here
because we would rather expect diiferent understandings. But I think that
what Winfried has written here, is a collective meaning rather than an
individualistic meaning in which both of us as well as several other
fellow learners have contributed. It is a "metanoesis" on "metanoia"!!!
This why the word "surely" is fitting. I know that I am right because I
have tried to guide him as a willing learner how to free himself from the
rigid definitions from one system by opening up to as many other systems
as possible in an ever increasing context. I have observed with growing
exitement over several years how his learning became more authentic,
culminating in this jewel of a "metanoesis" above.

However, it may not be so fitting to you. Why? You are the system SY and
we are but a few systems among many millions of other mental systems in
the surroundings SU. You need not to take us into consideration as part of
the context. But one thing is for certain -- just as animal cells cannot
live single and far apart from each other, each of us have to connect to
some mental systems in the surroundings SU so as to live mentally. Each of
us has to connect to the systems thinking of at least someone else like
Deming or Argyris. But it took a Peter Senge to realise that Systems
Thinking itself is essential to our learning, not as individuals, but
collectively as some or other organisation.

What I now want to stress is that we have to work also towards the
collective learning of humankind as the whole organisation. To accomplish
that, each of us will have to open ourselves up gradually to as many as
possible mental systems as well as their articulations into various kinds
of systems thinking. In this opening up it is only natural to go into the
protective mode (like prescribing rigid definitions) whenever the chaos
comes dangerously close to a destructive immergence. Let us not force this
protective mode on one another, but rather respect every person who have
to work in the protective mode for as long as necessay for that person.
But let us also promote the productive mode of thinking by helping all
willing to be helped.

Protection and production is a profound complementary pair in Systems
Thinking. For example, economists, linguists, ecologists and chemists have
to deal with both. Neither can replace the other. The following as well as
the preceding sentence may appear as a mystic claim, but given enough
painting of a rich picture I can substantiate it. Protection is a profound
manifestation of the Law of Energy Conservation (LEC) while production is
a profound manifestation of the Law of Entropy Production (LEP). What I
would like to see, is not a clinging of humans to either LEC or LEP, but
the dancing of humankind with LEP on LEC. In other words, what I would
like to see is productive thinking of learners enriching their protective
thinking -- creative thinking enriching traditional thinking. In order to
do that, we will have to know how to make use of our spiritual "free

With care and best wishes


At de Lange <> Snailmail: A M de Lange Gold Fields Computer Centre Faculty of Science - University of Pretoria Pretoria 0001 - Rep of South Africa

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