Greetings to you all.
A number of fellow learners have written privately to me about some
difficulties they experience with logic since this topic became explored
in our LO-dialogue. These difficulties have to be expected. Even logicians
who have proceeded far into logics experience difficulties daily.
It brought me deeply under the impression that it is useless to have a
dialogue on logics if we do not understand why we need logic, whatever the
system of logic we will be using. Why do we need logic when more and more
people begin to claim that logic is primarily responsible for the present
predicament of humankind and thus should be scrapped?
I am sure that most of us, if not all, want a "healthy mind". But what is
a "healthy mind"? Let us think about our bodies. What makes a healthy
body? Excercises, food and rest, among other things. Let us focus of the
food. The past century physiologists in collaboration with chemists have
discovered that a healthy body requires definite "bricks" in the food in
amounts between definite limits. The collaborative effort of these
scientists is known as nutrition science.
These "bricks" can be classified into groups like inorganic elements,
carbohydrates, aminoacids, proteins and vitamins. Each such a group can
be further classified itself. For example, in the inorganic elements we
can have macro-elements, micro- elements and trace-elements according to
our daily need for each element. The vitamins, for example, can be divided
into the water soluble and the oil soluble vitamins. When we move our mind
over all these "nutritional bricks", the variety among them is stunning.
I do not like to use the word "bricks". A better word to use, is
"elements" (from the Latin for "first things"). But the chemists have
already used the word "element" in a definitive sense as I have indicated
above. For example, carbohydrates consist of three elements: carbon C,
hydrogen H and oxygen O. Aminoacids usually consists of four elements:
carbon C, hydrogen H, oxygen O and nitrogen N. So we cannot use the the
name "element" for something like carbon C like the chemists do and and
also for a nutrional "brick", say an aminoacid, as we now want to do.
We can now try anyone of several solutions. In my own mother tongue we
will speak of such a "brick" or "building block" in any system as a
"grondstof" ("ground-stuff"). Perhaps we can call it "understuff" too. But
we can also take the noun "element", convert into the adjective
"elemental" and then use it again as the noun "elemental". This is a kind
of "looped thinking", telling us to think deeper than merely the
"element". We can apply this "looped thinking" once more to the noun
"essence", get to the adjective "essential" and then make it the noun
"essential". Let us try the "elemental" solution and see how far we get
When any one of these "nutrition elementals" are absent, our body will
definitely become ill. It does not matter whether the daily requirement of
a "nutritional elemental" is large or minute. When less than the minimum
is taken up, the body will lose its health.
More important, what will happen when we take the daily requirement of a
"nutritional elemental", multiply it by 30 and then eat only once a month
that kind of food or supplement which contain this "nutritional
elemental"? Before the month is over, we will most probably have developed
severe symptoms for the deficiency in this "nutritional elemental".
What will happen when we take in each day 30 times the daily requirement
of a "nutritional elemental"? Many things can happen. Our body can take up
only the 1/30th which it needs. It can take up all 30/30 and then will
have to battle to get rid of the other 29/30 parts not needed. It can even
get poisoned to the point of death!
Let us compare the "healthy mind" with the "healthy body". Just as the
body needs daily "nutritional elementals" to sustain its health, the mind
also needs daily "mental elementals" to sustain its own health! Just as
there is an astounding diversity in the "nutritional elementals", there is
also an astounding diversity in the "mental elementals".
The "mental elementals" range from almost simple to very complex in their
internal organisation. They also range in the daily amount required from
minute to large quantities. In each "mental elemental" the daily
requirement is between a minimum and maxinimum level, a sort of "window".
Thus we can think of the "window of a mental elemental". With daily
uptakes below the "window of a mental elemental" we will experience
deficiency symptoms while uptakes above the "window" will cause profusion
Making daily use of all these "mental elementals" can be thought of as
"interdiciplinary thinking". Following the full course of each of these
"mental elementals" in the mind, what it leads to and what becomes of
itself, can be thought of as "transdisciplinary thinking". This tells us
that "interdiciplinary thinking" alone is not sufficient. Its like eating
a variety of food, but never taking care that the variety of foods are
eaten in harmonius amounts so as to avoid deficiencies or profusions. To
seek for this harmony and keep alert for any symptoms of deficiency or
profusion, we need "transdiciplinary thinking". "Disciplinary" thinking
itself is like eating one kind of food such as bread for breakfast, lunch,
dinner and snacks in between.
So just what are all these "mental elementals" and how much of each is
needed daily? I do not want to go into all of them. However, I think a
LO-dialogue on the topic "mental elementals" in full will be delightful.
I would rather propose that "logic" (hard core) and "science" (hard core)
are two of these "mental elementals" so as to illustrate how they function
in the mind.
Two very important "nutritional elementals" needed for a healthy body are
the macro-elements calcium Ca and phosphoros P. They are combinded
together (with oxygen) as almost insoluble Calcium Phosphate (CP). This CP
is the white stuff with which our bones and teeth are made up. Without CP
our body will become like that of a jelly fish. Most important to regulate
the uptake and balance of CP is vitamin K. Broccolli and tomatoes are very
rich in vitamin K. Too little vitamin K will lead to a loss of CP from our
bones and teeth, making them brittle.
When we compare the skeleton of an elephant with that of a rat, there are
many, many correspondences in form. This is so because both are, after
all, mammals. However, in one aspect they differ remarkedly, namely
content. The skeleton of an elephant has much, much more mass. But let us
think of the ratio of skeleton mass to total body mass for an animal. By
taking the ratio, we sort of remove the difference because of mere size.
This ratio is not the same for the elephant and the rat, but somewhat
larger for the elephant. The reason is the extra mechanical strength
needed when scaling up the size.
Logic and science are also two important "mental elementals" for a
healthy mind. According to my own experiences with them, I prefer to
compare them with calcium and phosphoros. Together they form the "bones
and teeth" of our mind, giving it a firm skeleton. Some people are like
elephants do that they need massive amounts of logic and science to keep
them firm and going. Other people are like rats. To claim that all people
must have minds like elephants is simply foolish. The minds of some
people, after all, are like rats ;-)
The function of the calcium phsphate based skeleton is to make the body
frim and to allow certain motions within the limtes of theis firmness. The
function of the skeleton is not to act also, for example, as the blood
circulation system or the neurological system. Forcing it to act outside
the limitations which its own functionality has brought upon it, is sheer
madness. In other words, we have to become aware of the advantages
(functionality) of the skeleton as well as its shortcomings (limitations).
It is the same with logic and science as two of the many "mental
elementals". Each on its own as a whole and together as a whole greater
than their sum, we have to to know their functionality and their
limitations. To use logic or science for phenomenological purposes, would
be a grave misunderstanding. Likewise, to use another "mental elementals"
like cybernetics to replace, say, logic would be also a mental blunder.
When the "mental elemental" is something so complex as psychology, we may
unconsciouly try such a replacement with devastating consequences.
It is the formidable task of the psychologist to investigate the whole
movie of thoughts and thinking in any person. Some mind produce horror
movies, others produce home movies and some even epic movies The
psychologist not only study the "what" of the movie, but also the "how".
This is to find out what should be prevented to make less horror movies
and what should be promoted to make more epic movies. When the task of the
psychologist shifts to prevention and promotion, the domain of psychiatry
is entered. The psychiatrist not only must have superior knowledge of
psychology, but also has to operate with utmost responsibility.
It is alarming how many people take notice of only a few psychological
patterns and then immediately begin to act left, right and centre as
"quack psychiatrists". This is nothing else than a severe deficiency in
psychology as a "mental elemental". It not only makes these "quack
psychiatrists" in dire need of psychiatry self, but also the innocent
victims of their quackery.
The same kind of deficiency can happen with any other "mental elemental"
including logic and science. A "quack logician" will take notice of a few
logical patterns and then immediately begin to command people how to set
up their truth. Thus they become "quack pseudo-psychiatrists", something
worse than even "quack psychiatrists". This happens far too much in the
teaching of mathematics.
On the other hand, some people intuitively resist acting as "quack
pseudo-psychiatrists" as a result of knowing too little of a particular
"mental elemental". This is very responsible of them. But this responsible
restraint may get out of control and develop into a fear for the very
"mental elemental" of which they know too little. It usually happens when
they have become the victims of a quack employing that "mental elemental".
Thus they begin to resist knowing more of that very "mental elemental".
This deliberate self-inflicted deficiency in a "mental elemental" can
become most dangerous to that person's "mental health". In other words, to
follow up someone else's hurting quackery with one's own quackery can
become mortally unhealthy. unfortunately, in the case of logic as such a
"mental elemental" it happens far too often. So many people have been hurt
by "quack logicians", especially in the teaching of mathematics, that they
are driven self to the point of commiting "suicidal logic".
Logic is neither psychology nor even psychiatry. Logic and psychology are
simply two vastly different "mental elementals". Yet they correspond
remarkedly in one and only one feature -- in logic it is tacitly assumed
that the same "mental movie" exists which is also studied by
psychologists. But otherwise logic takes this movie and cut it up in a
series of pictures (screens) so as to trace step by step "patterns of
truth". This step-step nature is inherent to logic to get its
functionality. Thus this functionality also induces limitations into
logic. For example, should the logical sequences themselves be replayed as
a movie, it will appear to be erratic or marionette-like.
Often the psychologist will also cut the "mental movie" into separate,
successive pictures so as to analyze each of them. When they become
replayed as a movie, the same erratic or marionette-like effect will
result. Whereas it is typical of logic and in particular one of its
limitations, it should never be done in psychology because then the
psychologist becomes also a "quack logician".
Most people are aware that they need logic as a "mental elemental". But
most of them make a serious blunder by assuming that "logic" is
prerequisite to plan and make a "mental movie" which they specifically
afterwards want to analyze logically. What they actually need to plan and
make the "mental movie" is creativity and neither logic nor even
psychology. Some logicicians are tacitly aware of this and will try to
articulate it in one or other manner, for example, "intuitive logic" is
used to plan and make the "mental movie" which afterwards can be analyzed
by "formal logic".
Psychologists have studied human creativity perhaps more than any other
discipline since the early 1950s. But this does not make creativity a part
of psychology. In fact, without creativity themselves, psychologists would
not have advanced one step in psychology. People who thus want to learn
how to plan and make "mental movies" will have to explore beyond what
psychologists have uncovered on human creativity.
A most important question is whether "creativity" is a "mental elemental"
too? As I have studied the thinking of others on creativity, they would
intuitively say yes. I think differently. When we take all the "mental
elementals" together, it will afford us with a whole more than their sum.
This whole is not creativity, but the closest articulation we will get on
creativity. To use a NLP maxim, the whole of all the "mental elementals"
is the map of which the territory is creativity.
What happens when we do use the logic in the output
of the "mental movie" to plan and make the movie, i.e.
use the logic of the output as input to the "mental movie"?
In other words, what happens when we set up a "feed back
loop in logic" for the "mental movie"? In most people it
causes the mind to grind into a standstill. In other words,
when they use logic so as to think logically, they cease
thinking at all. This frightens them very much, so much that
they again deny themselves logic as a "mental elemental".
This has to do with one of the most puzzling truths in
logic, called the Law of the Excluded Middle. As soon as
they adhere to LEM, come rain or sushine, they grind
to a standstill. They cannot move one step forward from
the proposition "p" to which LEM has been applied to a
new proposition "q" which they want to introduce. In
symbolic logic applying LEM to p will result into the
To move one step forward to q (whether true or false) will
result in the expression
This latter expression is NOT a theorem of logic. In other
words, it is not true for all possible propositions p and q
whether they each is true or false. It is because this expression
is not a theorem that you cannot move even one step forward.
However, denying for the moment LEM on p which will then
results in the expression (note the abscence of the first NOT)
will result one step forward to q in the expression
This latter expression is INDEED a theorem of logic. It
also has profound implications. The q may, for example,
be the emerging result of a bifurcation in which p is one
of the components needed in the bifurcation. This means
that logic is indeed friendly to emerging phenomena. Yet I
have read hundreds of times the past few years that we must
scrap logic if we want to emerge to a new level of complexity
in our thinking. I wonder where all the quackery will end.
I can only beg you fellow learners two things
* be cautious of "logical quackery".
* learn from logic itself how to avoid "logical quackery"
I have used above four logical expressions
Do they then give us an indication what logic is about?
No, never. They are only four pictures which I have cut out from a "mental
movie" which I have carefully planned and made between ~~~BEGIN~~~ and
~~~~END~~~ (see above). All along this "mental movie" there is logical
thinking which you can uncover using "logic"
So what then is is logic, other than saying that it is one of many "mental
Aristotle was perhaps the first person who made formally room in human
thinking for logic. Logic was for him the study of correct reasoning. But
he actually used the word good ("eu") rather than correct, thinking
("noeo") rather than reasoning and organisation ("organon") rather than
"study". In other words, he thought of logic as how to organise good
When Charles Peirce early in the 20th century tried to find the best
definition for logic, he found in literature already some hundred
definitions which have seen the light since Aristotle's first definition
more than two millenia ago. This, I think, tells us something very
important about logic which was not realised in Peirce's time. Logic
itself is a complex "mental elemental" rather than simple. This why it
allowed each definition to zoom in on some facet of the complexity in
I think that Aristotle's definition gives us an extremely important
pointer -- the ORANISATION of good thinking. We may think in terms of a
Learning Individual that using "organisation" rather than "study" or
"training" is not the best way of articulating logic. But when we think in
terms of Senge's Learning Organisation, is Aristotle's definition not one
of brilliant insight already more than two millenia ago?
Let us jump two millenia to the nineties of the 20th century. I was
studying the various interpretations given for "entropy" during the
course of history, comparing them with the one which I wanted to give it.
Here is some interpretations -- dissipation, maximization, nature's
propensity, disorder, probability, information, arrow of time,
complexions, order and chaos -- to illustrate the immense diversity in
these interpretations. So I felt not too out of line when I wanted to
articulate it as a "measure of organisation".
But I knew intuitively that should I relate entropy to measure the
organisation of any system while Aristotle related logic to the
organisation of thinking that sooner or later all these things will have
to be connected to each other. This connection is not simple. Aristotle
already indicated that he was not interested in logic how the mind often
thought crazilly, but to make sure that even when thinking crazy, the
outcome is reliable after careful scrutiny. I was interested how my mind
could make such crazy connections.
Logicians are forever, since Aristotle, interested in how the past of
truth (indicated by what they call premisses) are related (which they call
inferences) to the future of truth (indicated by what they call the
conclusion). The permisses are always one picture in a "mental movie" and
the conclusion is the next picture following it.
Logicians were often worried about the seemingly crazy dance of the mind
to which they had to apply logic, but in their wisdom they did not try to
prescribe logic for this dance. So it seems that I am foolish rather than
wise in saying that logic is one of many "mental elementals" need to keep
the mind healthy and dancing. Perhaps I am making a grave error here. But
as I see it, all these "mental elementals" are needed to complete what I
call the "ordinate cybernetic loop" of the mind. Creativity, for example,
gives rise to logic in a higher level of complexity in thinking. But this
logic has a back action which enriches creativity lower down. The same
with all the other "mental elementals".
In this "mental movie" logicians tried to uncover the evolution of truth.
Anybody who explores some or other kind of evolution, whether it is the
evolution of chemical compounds like the chemist, the evolution of
biological species like the biologist, the evolution of languages like the
entymologist or the evolution of knowledge like epistemologist, has my
deepest admiration. For me that person is trying to fathom some
manifestation of the one-to-many-mapping of Creation -- the continuous
increasing in organisation of Creation.
How can I ever exclude the logician in me because some people, trying to
find a scapegoat for the predicament of modern humankind, pointed the
finger to logic?
The "metal movie" which I used so much above as metaphor, is for me the
"evolution of the mind". That which sustain this "evolution of the mind"
is for me nothing else than "human creativity" That which sustains all
kinds of evolution in Creation is for me "deep creativity". That which
sustains "deep creativity" itself is LEC and LEP from below and love from
above. The principal process in which I become aware of Creation and all
evolution it, is for me "authentic learning".
I need logic in my learning so as to pay closer attention to thruth. Truth
manifests itself as an ever increasing organisation in this ever
increasing organisation of Creation itself.
In conclusion, I want to advise strongly fellow learners to begin to learn
more of logic so as to enrich your learning. Do it like eating an apple a
day which keeps the doctor away. Do not indulge in eating as much apples
as possible in one day. Also, do not restrain yourself from ever eating
apples because it might have beeen the forbidden fruit.
Let us help each other in learning logic as well as all the other "mental
elementals". My help to you is that emergent learning is the "mental
awakening" to each of these "mental elementals". Digestive learning is the
"mental eating" of each of these "mental elementals" after having become
aware of them.
Is it not amazing -- the "body and mind" and "doing and thinking" are all
one whole. Let us respect this truth when using logic with its LEM.
With care and best wishes
At de Lange <email@example.com> 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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