Logical Thinking LO21652

AM de Lange (amdelange@gold.up.ac.za)
Mon, 17 May 1999 22:42:07 +0200

Replying to LO21633 --

Dear Organlearners,

John Gunkler <jgunkler@sprintmail.com> writes:


>Please don't do this. I so often appreciate your messages,
>and enjoy learning from your thinking in part because it
>often differs from the way I've been thinking about things.
>But in your message about logical thinking you have entirely
>missed my point.

Greetings John,

I cannot speak for Winfried, but I will do so for myself.

Let me thank you for lifting this specific topic "logical thinking"
out of the general topic "junk science".


If we now think of "logical thinking", "transdiciplinary thinking"
which I introduced two weeks ago, "creative thinking" which is one of
my ongoing themes between the lines of many of my contributions and
"systems thinking", the fifth discipline of LOs, what is the
relationship between all these kinds of "thinking". As for me,
"systems thinking" is the umbrella involving all these kinds of
thinking and many more.

>It simply is not true that the logical fallacy of denying the
>antecedent depends upon other "facts." Nor does my example
>depend upon other facts. It really doesn't matter whether there
>actually is a corner drug store where I could have purchased a
>toy. The point is that logically (not empirically) there could
>have been one.

You are right -- based on the assumption that logic has to stand on
its own legs.


But you know by now my own kind of systems thinking. No system can
stand forever on its own legs. All systems are connected in a
super-network called Creation which even itself cannot stand on its
own legs like the Creator. Further I do have affinity any more to the
fragmentation of academical subjects, including logic. How we get to
facts is just as important to me as dealing with the logical
relationship between facts.

>I know this is sometimes difficult for people to understand, but
>there is a difference between a statement's logical status and
>its empirical status. To object to a statement on logical grounds
>is to object to the FORM of the statement, not its content.
>If the form of a statement is fallacious (such as the form
>described as denial of the antecedent) it doesn't matter what the
>"facts" are -- the statement is fallacious.

I agree with you. But I want to point out something further. The FORM
of logical arguments is not a subject for only logics. Here is an

Almost all systems (Frege, Russel, Hilbert, Ackerman, Post or Rosser,
etc.) of classical logic uses
p=>q; p :. q
or "modus ponens" as inference rule. It does not matter what the
propositions p and q are. So long as p is true and p=>q is true, we
may conclude that q is true. Unfortunately, quantum mechanics has
thrown a spanner in the workings of classical logic. The statements p
and q may concerns two so-called complementary quantities. They are
complementary because of a Heisenberg uncertainty relationship between
them. In that case it is impossible to set up an "implication" p=>q.
Thus we cannot apply classical logic to quantum mechanics all the way
since quantum mechanics defy the FORM of logical arguments when it
concerns complementary quantities. In other words, the "so long as
p=>q is true" have little sense when p and q concerns complementarity

One way to get around this restriction, is to extend classical logic
into fuzzy logic as I have indicated before. But is this the way to
go -- generalising when the formal system fails?

The "uncertainty complementarity priciple" of quantum mechanics sort
of divide all independently measurable physical quantities in half.
But I have shown many times that in entropy production we have another
completely different complementary duality operating on FORM and not
CONTENT, namely that between extensive and intensive quantities --
extensive quantities leading to entropic fluxes and intensive
quantities to entropic forces. Again this "entropy complementarity
principle" sort of divide all physical quantities in two. What effect
does it have on "implication" p=>q? Perhaps we should go a little bit
into this issue. I will try to show that p=>q is ineffective dealing
with p and q when they concern intensive/extensive quantities.

What about other complementary dualities which do not know enough of
(like the one leading to the distictinction between the plant and
animal kingdoms of life) or and those which we are not even aware of
(so that I cannot give even an example.) Are we going to generalise
classical logic for each of these complementary dualities? Where are
we going to end up with this formalism -- complexity or

But first I want to discuss once more what you have written:

>The only valid way to argue against what I just wrote is the way
>At argued - -- that there are other systems of logic (in particular,
>ones that do not include the law of the excluded middle) in which
>the form named "denial of the antecedent" is not fallacious. So,
>if we agree that our discourse is to be ruled by this other system
>of logic, then I can't say what I said validly. But if we do agree to
>"abide" by standard logic (as even At admits holds in most ordinary
>discourse), then I can justify all that I wrote in the original
>about logical fallacies.

I admit that classical logic holds in ordinary discourse where the
"academical apartheid" (fragmentation and demarcation of academical
subjects) flourishes. But I will never admit that it holds when the
seven essentialities begin to play the decisive role in distinguishing
between constructive and destructive outcomes, revolutionary or
evolutionary. It does not fit me -- it does not work for me ;-)
Fragmentation denies wholeness and demarcation denies sureness. Since
classical logic is impaired in each of the seven essentialities of
creativity, it is no wonder that classical logic cannot serve
creativity as might have done.

Furthermore, the kind of logic which I am interested in, is one that
serves "deep creativity". I have already explained how my concept of
"deep creativity" differs form the common concept of creativity. The
two main differences are:
(1) The common concept of creativity is that it is a property which
only humans have. Other kinds of living organisms are not creative and
also not inanimate nature. In "deep creativity" there are varying
degrees of creativity among self-organising systems with humans at the
top of the ladder.
(2) The common concept of creativity is concerned with revolutionary
invention, the emergence of something novel. The evolutionary growth
from invention to innovation is not considered to be particularly
creative. In "deep creativity" revolutionary emergences at the adge of
chaos and evolutionary digestions close to equilibrium are the wto
asymptotes between which creative actions meander.

I think you must not be too harsh on Winfried. He seems to be very
interested on the seven essentialities and has written (except for me)
more on them than anybody else on this list. Maybe he did not have
sufficient learning time to contemplate on their role in logics. But
when he begins to think about the possible connections between logical
facts and empirical facts, he is in my point of view on a hot trail
into transdisciplinary thinking. On the other hand, he must also
realise that his trail and your trail are not the same. Thus he cannot
expect you to think as he thinks, trying to uncover the connections
between "logic" and "empiric".


Ok, let me try to explain why I am of opinion how classical logic
fails creative thinking. First of all, I consider Classical Logic to
be Proof Theory (propositional and qualificational). (The
"qualification" can involve "predicate qualifiers" or "class
qualifiers" -- the result is technically known as "first order
logic".) I do not consider Classical Logic to include Model Theory.
See also my contribution ""Junk" Science LO21558" where I discuss in
short the main difference between Proof Theory and Model Theory.

In that contribution I model the monary logical function NOT by:
The truth table for NOT is:
p NOT(p)
The truth table for the other three monary functions are not important
now. There are 2^2=4 monary truth functions.

There are (2^2)^2=16 binary truth functions. I have model FIVE of them
as follows:
The truth table for AND (conjunction) is:
p q AND(p,q)
1 T T T
2 T F F
3 F T F
4 F F F
The truth table for OR (disjunction) is:
p q OR(p,q)
1 T T T
2 T F T
3 F T T
4 F F F
The truth table for EQUIV (equivalency) is:
p q EQUIV(p,q)
1 T T T
2 T F F
3 F T F
4 F F T
The truth table for IMPLY (implication) is:
p q IMPLY(p,q)
1 T T T
2 T F F
3 F T T
4 F F T
The truth table for LAST (consequent projection) is:
p q LAST(p,q)
1 T T T
2 T F F
3 F T T
4 F F F

Classical logic is not concerned with the fifth one, namely LAST. But
in another contribution I tried to make it plausible that it concerns
people who, despite the development of the argument, want to "get the
last word in", whether q is true or not. We ought to be able to
identify this kind of LAST arguments in any LO if we want to emerge
from an ordinary organisation to a LO. As a dual to the LAST, we can
get also get FIRST.
The truth table for FIRST (antecedent projection) is:
p q LAST(p,q)
1 T T T
2 T F T
3 F T F
4 F F F
It concerns people who, despite the development of the argument, want
to "get the first word in", whether p is true or not.

Classical logic is quite concerned about the EQUIV (equivalency)
function, but in a rather complex manner, making use of phrases
such as "if and only if" and "a necessary and sufficient condition".
I still remember as a pregraduate student in mathematics how
these phrases in some theorems baffled me, forcing me
to memorise those theorems. But actually, it is much simpler
that I have imagined. The singular function EQUIV(p,q) and the
complex function AND(IMPLY(p,q),IMPLY(q,p)) has exactly the
same truth table. The usual way to write

Here is the truth table for both: (I hope it gets out all in one
p q EQUIV(p,q) IMPLY(p,q) IMPLY(q,p) (p=>q)AND(q=>p)
1 T T T T T T
2 T F F F T F
3 F T F T F F
4 F F T T T T
Compare the third and sixth columns with each other. Their outputs are
the same for each of the four rows.

This correspondence between EQUIV(p,q) and "(p=>q)and(q=>p)" is not
exactly a failure of Classical Logic. It is a failure of At de Lange
as a student to realise that they have the same outcome -- nobody
explained it to him.

But here is another failure of Classical Logic. It concerns the
logical function XOR (exclusive disjuction)
The truth table for XOR (exclusive disjunction) is:
p q XOR(p,q)
1 T T F
2 T F T
3 F T T
4 F F F
It concerns two people who oppose each other in every possible
argument. They are fundamentalists who simply believe that there
cannot ever be any agreement between some of their assumptions. When
the one believe an assumption to be true, the other one has to believe
the assumption to be false, and vice versa. It is usually
characterised by sentences such as "either p or q but not both". It is
easily constructed in Classical Logic as (pORq)AND(NOT(pANDq)

Here is the truth table for both: (I hope it gets out all in one
p q XOR(p,q) OR(p,q) NOT(AND(p,q)) (pORq)AND(NOT(pANDq)

1 T T T T F F
2 T F F T T T
3 F T F T T T
4 F F T F T F
Compare columns 3 and 6 to see how they correspond. But also compare 3
and 4 to se how XOR (exclusive disjunction) and OR (inclusive
disjuction) differ. They differ in the sense that XOR, unlike OR, do
not acept truth when all statements concerned are false (the fourth

Now what is the failure of Classical Logic? It cannot show logical
thinkers how futile exclusive thinking in innovative (revolutionary,
at the edge of chaos) thinking is. The reason is simple. Classical
Logic keeps away from the fourth line in all its carefully developed
forms of argumentation -- the fourth line where everything is false.
How is this possible?

To explain it, I must make use of a parable.


Think of a marsh which covers completely a layer of "quick sand" or
"quick bog". If we want to meander through such a marsh, we will
simply fail with death. This is how the people (Frankone and
Sachsers -- Belgians to the Romans) in the Lowlands region of Northern
Europe defied the Roman armies. They meandered into the marshes and
somehow got through. The Romans followed them, but with deadly
consequences for themselves. How was this possible? The Belgians put
stepping stones in the marshes in a meandering course. The stones were
so deep under the surface that they could not be seen. Only the
Belgians knew the meandering course of these stepping stones.

(In my own mother tongue Afrikaans we still have this ancient Germanic
word "bog" to refer to all around falsities. When an Afrikaner says
"dit is 'n klomp bog" -- it is a lot of tripe -- then no Classical
Logic in all the world can reach such a person. This is how the mind
work of many of those who made the practice of classes (castes) into
the ideology and policy of apartheid. They were a bunch of creative
people -- sadly creating destructively rather than constructively.
When the rest of the world tried to convince them with Classical Logic
what a horrendous system they were creating, they simply said "dit is
'n klomp bog". Are they the only ones guilty persisting with
apartheid. What about those who tried to convince them with Classical
Logic -- did they not also contribute to apartheid in terms of the
failure of Classical Logic?)

In Classical Logic (CL) reality is the marsh, containing propositions
of which some are true and others are false. CL itself is a meandering
course of stepping stones. They cannot be seen empirically, a point
which John makes very good. Thanks John. Every axiom of CL is a
stepping stone -- a true statement. They are close to the edge of the
marsh so that we can step into the marsh. The first stride that we
give inside the marsh is Modus Ponens of CL. Each step stone further
inside the marsh is a derived theorem -- also a true statement. We can
have the same stride (Modus Ponens) all the way. But we can also
change the length and direction of the strides from one stepping stone
(true statement) to another. They are called derived inference rules.

CL is the meandering through the marsh on stepping stones of truth. CL
avoid stepping with both legs in the "quick bog" of all around false
statements -- row 4 of all truth tables. Some times it looks as of CL
steps into rows 2 and 3, ie. with one leg on a stepping stone and the
other leg in the "quick bog". But this is not the case. It was merely
a change in stride -- length and direction. The Romans did not know
it. I, as a student up to my MSc, also did not know how CL works. I
fear that the far majority of post graduate students today still do
not know it. I dare not even speak of pregraduate students.

Sadly, the Romans were not so INNOVATIVE with technology as they
believed themselves to be. (They did not know how the Brusselator
worked -- two millenia had to elapse.) Furthermore, with their immense
technology for those days, they SCARED THE WITS out of their
opponents. (They knew intuitively how the Digestor worked --
competition, predation and intimidation) Thus they never thought of
inventing stilts. The Belgians were also very careful not to let the
Romans see how they themselves used stilts in the marshes so that the
Romans could copy them. The Belgians also used the stilts to collect
the "bitters" for their famous beers from vines high up in the
trees -- but never showed the Romans the trick of their trade.

CL does not allow for the inventing of stilts to meander through the
"quick bog" of marshes without the use of stepping stones.


I am now probably going to stick my head into a bee hive, but I will
have to do it. Why sticking my head my head into a bee hive? The
majority of people in Western Civilisation believe in the "win/loose"
situation. In other words, most of their tacit knowledge concerns the
workings of the Digestor. It is how politics and religion have
operated in Western Civilisation for two millenia since the days of
the Romans. They have little, if any, inclination towards a "win/win"
situation. In other words, very little of their tacit knowledge
concerns the Brusselator. In fact, up to WWII the far great majority
of them belived that creative innovation (classical creativity) is a
trait which only the few geniusses have. Only after WWII did they
begin to use the word creativity (in the sense of innovation).

Very few thinker before WWII gave attention to the notion of
emergence -- people like S Alexander, H Bergson, L E J Brouer, L
Kronecker, C L Morgan, C S Peirce, H Poincare', E Post, W V O Quine
and A N Whitehead. The endeavours of these people trying to develop
their notions into consistent concepts were completely alien to people
thinking along the lines of Classical logic. Why? Because Classical
Logic or Proof Theory was designed and used to aid evolutionary
thinking close to equilibrium -- digestive thinking. It was not
designed to to aid revolutionary thinking at the edge of chaos --
bifurcative thinking.

Even many mathematicans say that the discovery of a theorem is
inspiration, but fonding its proof is perspiration. Only when
Prigogine in the seventies broke through the ceiling of evolutionary
thinking by formulating his theory of dissipative self-organisng
systems, did more and more scientists take notice of the concept of an
emergence. Strangely enough, he himself seldom, if ever, used the word
emergence, but rather stopped at the word bifurcation.

It is beneficial to read the works of the incredible American thinker
Charles Peirce. He was probably first to begin thinking outside
deduction and induction. Among other things, he was probably the first
to make use of the logical connective which I now will call the
STROKE(p,q) (contrary conjunction or alternative denial). I will now
use Model Theory of Logic to describe it.

The truth table for STROKE (contrary disjunction) is:
p q STROKE(p,q)
1 T T F
2 T F T
3 F T T
4 F F T
Why "contrary conjunction"? Compare it with
the truth table for AND (conjunction) which is:
p q AND(p,q)
1 T T T
2 T F F
3 F T F
4 F F F
They work contrary to each other.

The STROKE does what we require from any emergence to truth. How? Let
us compare it with Classical Logic (CL). CL works only with truth
which already has emerged -- row (1) of truth tables. It does not work
with truth which still has to emerge. Why? It avoids row (2) by using
as principal "logical becoming" the ancient (Aristotle) inference rule
of Modus Ponens. See row (2) of IMPLY(p,q). CL also avoids rows (3)
and (4) by using as principal "logical beings" axioms (antecedents p
which are only true). In other words, CL meander through the marsh on
"true steppings stones" by giving "true strides". It avoids using even
one leg to step in the "quick bog" of the marsh. But the STROKE
function does the contrary. It keeps to the "quick bog" with one or
even both legs. As soon as it emerge to truth -- hit a true stepping
stone -- it looses its interest in the course of logic. The emergence
has been accomplished -- what about a new one rather than digesting
the old one.

It is quite possible to follow the course of Classical Logic, i.e if
we want to make further digestions on our revolutionary creations. The
following correspondences (I will indicate them by a double equality
==) shows why. I will use the direct notation P|Q rather than
functional notation STROKE(p,q) because the expressions are easuer to
read for all of used to natural languages.
Check them by creating your own truth tables for comparison.
NOT(p) == p|p
AND(p,q) == (p|q)|(p|q)
OR(p,q) == (p|p)|(q|q)
IMPLY(p,q) == p|(q|q)

Here is an example for NOT(p)
p q NOT(p) p|p
*T *F *F *T
*F *T *T *T
Only in rows (1) and (4) do p and q correspond, the rows not marked by
an aterisk *. Now compare columns 3 and 4 for rows 1 and 4. They

The question now arises, how many initial steps in the marsh do a
logical system based on STROKE to formulate its inference rule, need?
Classical Logic using IMPLY to formulate its inference rule Modus
Ponens, needs three axioms. However, already in 1916 J G P Nicod
produced in a brillaint paper a logical "proof system" which uses only
"inference" rule (logical becoming), namely
>From p and p|(r|q) to infer q
and only one
"axiom" (logical being), namely

Interesting, is it not? Whereas Classical Logic needs only three
"atomic" propositions p,q,r, Nicod's Logic uses five of them! It gains
in one thing (less "axioms"), but ooses in other things namely more
"elements" needed and a much longer compound (axiom) to start with.
Compare the length of Law of the Excluded Middle (LEM) of Classical
logic, namely
p=>p == NOT(pANDp)

Furthermore, "proving theorems" in the NICOD system is EXTREMELY
COMPLEX when compared with proving theorems in the systems (Frege,
Russel, Hilbert, Ackerman, Post or Rosser, etc.) of Classical Logic.
No wonder that when Nicod published his system, people from the world
of Proof Theory shuddered.

However, some fourty years later when James Watson and Francis Crick
announced their brilliant work on the structure of DNA, competing with
other equally brilliant people like Maurice Wilkens and Linus Pauling
in race of intelligence, nobody took notice of Nicod's system anymore.
Why should they because fragmentarism and demarcationism rule the
academical world. Crick and Watsin received the Nobel Prize for their

Now what is DNA? It is the vital molecule of heredity in all living
organisms. Every professional geneticist and biologist can list the
elemenst used in DNA. They are: carbon C, hydrogen H, nitrogen N,
oxygen O and phosporous P. Count them -- five. Count the number of
elements in Nicod's incredibly complex axiom -- five. What is going on
here -- serendipity -- blind chance?

What about the elementary sustainers of creativity which I have
written about a couple of times. How many are they? I list them for
problem solving
exemplar studying
game playing
art expressing


Please remember that I am the last one to say that we must take over
Nicod's system lock, stock and barrel. This will be a most uncreative
thing to do. But what we can do, is to learn digestively from him
while pursuing also our own emergent learning.

I tried desperately in this contribution to get you interested in
looking at all the disciplines (subjects) of academy and not merely
one or two of them. That is why this contribution has become so
lengthy. It seems as if I have focused only on Logic. But fellow
learners who have followed my meanderings on entropy production,
creativity and learning, will realise how much this contribution
connects to the immense network of complexity which I have tried to
paint the past few years. It is this network of life, no, it is this
web of reality which we have to bear in mind if we want to succeed
with our Learning Organisations. What we should not allow, is this
complexity to scare the wits out of us.

On the other hand, John issues a solemn warning for each of us:

>So the point is that, given the information provided by the
>person making the argument, we should not be led to believe
>that the conclusion (q is not true) must be true, because it
>may not be.

I cannot agree more.

The only positive hope which I can offer to each of us, including
myself, is that we each have to emergence further in Truth by first
becoming grafted onto Truth. The grafting is individual, but the
further emergences are organisational.

I salute all the great thinkers in Logic who taught me to think more
logical and not merely classical.

Best wishes


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

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