**Introduction** During more than
25 centuries western thinking was dominated by the dualistic paradigm described
by Aristotle's syllogism. A statement is true or false, exclusively one
of both, and all of intellectual activity consists of evaluating, arguing
or refuting the statement. This approach got a boost during Renaissance,
where "cartesian" deductive logical and mathematical thinking was considered
as the absolute requisite for any kind of scientific, "experimental", reliable
thinking.

Apart from its contributions
to deductive thinking, this approach is misleading in at least three of
its explicitly or implicitly suggested conclusions:

(1) there
is no category between true and false;

(2) science and
technology are making progress thanks to logical deductions and experimental
procedures;

(3) "sciences" which
so far are unable to apply the exact, experimental procedure can't be rated
as scientifically reliable, and remain in the realm of mythical, obscure,
fictitious and unreliable thinking.

During the second part
of the 20th century, after the umpteenth deception about the blessings
of scientific progress, tentatives towards a more holistic, non-aristotelic
approach of reality were launched. This trend is masterly pictured by authors
as Fritjof Capra. Many approaches, from postmodernism to New Age,
recommend a less dualistic, mutually-exclusive way of thinking. But up
to now a central paradigm was not clearly defined. In this essay, integration is proposed as such a paradigm. **Definition**

As defined elsewhere,
integration can be defined as [1,2]

a process
of combination of elements that, at first approach, seem to be incompatible
or even conflictuous, but, after a bit of analysis and re-synthesis (leading
to reformulation or re-orientation), prove to be rather complementary. Symbolically this
process could be represented by:

(A,B) Æ [A>>A'] & [B>>B']
Æ
{A'B'}

where A en B are
elements in their primary, "unintegrable" state, that are "retroduced"
to their "essential core" [AÆA']
& [BÆB'],
what makes them "integrable", and then combined into a new unity {A'B'}.
Æ
here
means "to provoke a certain fact or transformation". and >>here means "to
transform into". We use the three kinds of brackets in a different sense:
(collection of elements), [process], {integration}.

We would like to
introduce the function of Y (Psi) meaning "to be reduced to its essential core", so that:

Y(A)
= A'

and v
as the inverse function, the "eduction"

A = v(A')

so that A is an eduction
of A', meaning that we can come from A' to A by making A' less general.

Likewise we propose
to introduce the fundamental function W (Omega) to describe the integrative process in short:

W (A,B)=
{A'B'}

To make the indication
"a more integrative version" more precise than A' relative to A (A' meaning
just "vaguely related to") we propose to introduce the index # meaning
"more integrative".

Symbolically, the
above statements can be written as

(A,B) Æ [A>>A_{#}]& [B>>B_{#}]Æ
{A_{#}B_{#}}

Y(A)
= A_{#}

A = v
(A_{#})

W (A,B)
= {A_{#}B_{#}}

**Assumptions** The **paradigm of
integration** is based upon some assumptions, postulates, some of them
conflictuous with the fundamental logical postulates.

**1. The probability
that a theory is completely true/false, is practically nill**

The **probability
that a theory**, an insight, a concept, a hypothesis, an idea, etc. **is** completed, completely exact and **true**, **is practically inexistent**.
Each idea, etc. will probably be improved some day. So between "true" and
"false" a third category has to be intercalated, being defined as "theories
that are far more better than previous theories, but not as perfect as
the final theory".

The classical, dualistic,
aristotelian-cartesian categories:

In the integrative
approach we discern three categories:

In practice, we could
probably put all existing theories, concepts, etc., in the middle category,
making both classical logical extreme categories obsolete, i.e. only existing
as a theoretical concept, unless we're working with extremely simple data,
e.g. natural numbers and other conventional concepts.

Inspired
by the diagram, we could, perhaps, represent the presence of the plausibility
factor, in discursive intellection, as forming an important part of a sort
of continuum as follows: "FPPPPPPPPPPPPPPPPPPT",

where "F" stands
for "false", "P" stands for "more or less plausible" and "T" stands for
"true".

The more an outlook
is implausible, the closer it stands to the "F" or "false" end of the continuum,
and the more an outlook is plausible, the closer it is the "T" or "true"
end of the continuum. [Brian Cowan]

As the "plausibility"
category is very extended, it seems useful to introduce a measure of plausibility
(P). This
measure can only be used in a relative sense, i.e. by comparing two or
more theories. *Example*. If
we define T_{E} as the Theories of Einstein, and T_{N} as the Theories of Newton, we can state that:

P(T_{E})
> P (T_{N})

Or:

Y(T_{N})
= T_{E} T_{N} = v
(T_{E})

As explained in the
General
Systems Theory, and Logics, knowledge of
any rather complex system presents a progressive development: as with a
spiral, each new experience or intellectual confrontation may lead to a
more comprehensive conceptualization.

E_{1}(A)
Æ a_{1}

a_{1} + E_{2}(A)
Æ a_{2}

a_{2} + E_{3}(A)
Æ a_{3}

generally described
as

a_{n-1} +
E_{n}(A) Æ a_{n}

*A* is a phenomenon,
a part of reality to be conceptualized. *E* is an experience and/or
an intellectual communication. *E(A)* is an experience with phenomenon
A , and E_{1}(A), E_{2}(A)... are consecutive experiences.
*a*_{1},
a_{2}, ..., a_{n}are consecutive visions, hypotheses
about phenomenon A , becoming progressively more integrative. A cyclic
scheme could also represent this procedure:

This means that at
each given moment, each concept may become more complete, more realistic,
more comprehensive, more integrative.

The **historically
most significant example** is the theory of Newton, improved by Einstein.
This example is particularly striking because during centuries the theories
of Newton were quoted as the illustration
*par excellence* of scientific,
aristotelic-cartesian thinking. Let's take Newton's Law of the Addition
of Speeds:

Einstein proposed
an elaborated formula:

This means that at
relatively slow speeds (v << c), the denominator practically equals
1, so we find back Newton's formula. But at high speeds the denominator
increases, making the total speed significantly lower than what Newton
predicted, and limiting even the maximal speed at the speed of light, c.
Newton's formula appears to be a reduction a simplification of Einstein's
elaborated formula, but at "normal" speeds on earth it was impossible to
discover the inaccuracy of Newton's "simple" formula.

**2. The 'complements'
operator - the non-existence of contradictions**

As there exists more
than one category of exactness, the opposition and mutual exclusion of
two statements (about the same phenomenon) that are not similar or reduceable
to each other, disappear. Besides the fundamental categories **equals
(=)** and **is unequal (<>)** we should like to introduce a third,
much more useful operator: **complements (****¿)**

Where in the traditional
approach statements as

psychoanalysis <>
behaviourTheory

science <> religion

theoryOfNewton <>
unexplainableEvidence

seem very justified,
in an integrative approach they are... false, because:

psychoanalysis ¿ behaviourTheory

science ¿ religion

theoryOfNewton ¿ unexplainableEvidence

Hence:

W (psychoanalysis,
behaviourTheory, ...) = integrativePsychology

W (science,
religion, ... ) = hyperphysics

W (theoryOfNewton,
unexplainableEvidence ) = theoryOfEinstein ("Hyperphysics" being
the name that Teilhard and Wildiers used as the scientific label for their evolutionary, cosmic and integrative
approach).

This second postulate
can be formulated another way: *the probability that in two statements,
which seem mutually exclusive of paradoxical, one is true and the other
is false, is much lower than the probibility that both pseudo-conflicting
statements are complementary*, i.e. true in certain circumstances. Practically
speaking: all so called contradictions are most probably complements.

**3.** **An integrative
theory is more plausible than its non-integrative elements**

The **degree of
plausibility increases with integration**, at least if no logical errors
are made. This can be explained by the fact that the plausibility of the
integrative view is at least as high of the plausibility of the most plausible
of its complementary elements.

So we can state that

P(A_{#})
> P(A) and, more in detail,
if:

W (A_{1},
A_{2} , A_{3} , ...) = A_{#} then: P(A_{#})
> P(A_{1})

P(A_{#})
> P(A_{2})

P(A_{#})
> P(A_{3})

... This has a very important
consequence: to achieve the highest possible plausibility, one has to integrate.
Or, otherwise stated, the Plausibility is the highest with theories that
take into account the greatest number of phenomena, the greatest number
of arguments.

Graphically represented:

A "proof" based upon
the integration paradigm can be made by arguing, mathematically or logically,
that the former, non-integrative theories can be reached by an **eduction** (v) of the
integrative theory.

If

W (A_{1},
A_{2} , A_{3} , ...) = A_{#} then the *maximal
plausibility* for A_{#} (replacing the obsolete concepts
*true* and *exact*) is reached when

A_{1} = v
(A_{#})

A_{2} =
v
(A_{#})

A_{3} =
v
(A_{#})

i.e. if we can **(d)educe** each elementary theory from the integrative, by restricting the conditions
of applicability or observation. This is a proof, in the scientific meaning
of the word, that the integrative theory is (more) true (preferably: *plausible*)
than the non-integrative ones.

This edutive operation
can easily be done with Einstein's theory about the addition of velocity,
that mathematically can reduced to Newton's formula by putting v as extremely
low, so that the denominator practically equals 1, and can be removed in
the formula.

*Implications*.
This third assumption has many important implications for science in general,
especially for these sciences that are seemingly (still) inaccessible for
the exact-scientific method. These consequences apply as well to the **curriculum** of the studies, as to the structure of **scientific papers**. In another
article we will extend on that topic.

**The
integrative procedure**

**1. Introduction**

**Deduction and
induction**. The process of integration, leading to the formulation of
a new, more plausible hypothesis, is part of the indcution process, which
is still unconscious and inaccessible for conscious reasoning. All the
*Principles
of Logic*, from Socrates to Descartes and Leibniz, in fact are *Principles
of ***Deductive** Logic. An *Inductive Logic* is still to be
elaborated. This integrative process can be seen as the kernel of such
a paradigm.

In the next scheme
the process of thinking is depicted. In intelligent beings, Reality is,
at least in part, observed, and out from these observations some general
tendencies are abstracted. These are the hyotheses, the knowledge, general
rules and laws. The hypothesis formulation process is called **induction**.
From these abstract hypotheses, conclusions can be drawn by logical, **deductive** thinking. Generally this operation consists in replacing abstract data
by concrete numbers, and performing some mathematical transformations.
Science is a collection of conscious rules, i.e. operationalized and measurable.
Also in exact science, the elaboration of a scientific hypothesis is an
intuitive process. In fact, science only controls the "exactness" of the
intuitively formulated hypotheses.

In many cases, the
hypothesis itself remains hidden in the realm of the unconscious, and is
then called *intuition*. In this case also the deductive process is
largely unconscious and intuitive, e.g. art, musical improvisation.

The integration process
is the elaboration of a new, more general hypothesis out of some particular
hypotheses with limited applicability.

Because it is still
largely unconscious, this process can not ye be described in detail, not
yet operationalized, and not yet programmed for a computer. All computers
are still deductive up to now, although when the possibilities are limited,
a pseudo-inductive routine can be elaborated, like in computer chess programs:
a mathematical calculation of all possible reactions is made, and a quick
statistical evaluation is made of the outcome of each possibility, and
then a mathematically guided choice is automatically made.

But although we can't
yet describe the process in detail, we can identify several subphases,
making the theoretical challenge more realistic, and perhaps coming closer
to the long expected discovery of an Inductive Logic. We also will offer
some auxiliary tools to enhance this subconscious integrative process.

**2. Eduction (v)**

Let's consider two
statements, A en B. They seem irreconcilable:

A <> B But let's suppose that,
most probably, both observers were sufficiently intelligent not to be completely
wrong, and were observing different situations: different factors elicited
different behaviours in the same object. So the different perceptions of
the same object are in fact compatible, save for the exaggerate generalization
(**eduction**), unconsciously made in the absence of correcting phenomena,
thus making the statements unnecessarily incompatible. **3. Retroduction
(Y)**

The solution is that
both observers **retroduce** their statements, by adding *nuances* or *limiting conditions*, making an integration possible.

We postulate that
A ¿ B, and we retroduce A and B to A_{#} and B_{#} by

Y(A)
= A_{# }and Y(B)
= B_{#}

**4. Combination
(+)**

At this point an
integration, now nothing more than a simple **combination**, will be
possible:

W (A,
B) = {A_{#}B_{#}}

To perform this integration,
several methods seem useful:

- Each observer
can be placed in the situation of the other observer, and discover that
his statement needs some more nuance.

- The observers
can communicate their different approach to each other, believe each other,
and by empathy understand the limits of their own experience, and make
together an integrative hypothesis satisfying both of them.

- One observer can
accept the apparent contradictory statements as complementary, and try
to formulate an integration.

**5. Auxiliary methods** The intuitive integration
probably will be inspired by analogies, and especially by analogies with
fundamental features of reality described by the General
Systems Theory, and assisted by inductive Logics.

In another
article, several auxiliary tools to enhance intuitive integration,
are described.

**Primitive
forms of Integrative Thinking**

**1. Introduction**

If we consider the
ways of thinking humans used in history, some difficult questions arise

- During
Renaissance, the scientific method of thinking emerged, claiming that a
hypothesis only could be accepted as "true" if experimental ebidence cam
to support it. How do we explain that, before this time, so much exact
science was developed, including Greek mathematics and science, Egyptian
and Assyrian geometry, architecture and astronomy. How could, ironically,
such a inexact way of thinking, typical for the so-called *Dark Middle
Ages*, develop the laws of exact scientific reasoning? - What's the difference
between Aristotelian dualism and Cartesian dualism?

- Was thinking with
revelated insight really so naive and so stupid?

These questions could
perhaps receive a beginning of an answer with the following considerations. **2. Intuition and
"Revelation" as a primitive form of integration**

One could perhaps
consider that those "primitive", "unscientific" forms of thinking were
in fact kinds of integrative thinking. The most important condition for
integrative thinking, i.e. a general knowledge of multiple fields of human
experience, was fulfilled. The ancient philosphers, unless nowadays scientists,
appeared to be experienced in many diverse "sciences", ranging from mathematics
to architecture and the art of war making, from music to medicine, passing
through law, politics and astronomy, all in one person. The notion of *homo
universalis*,[3] i.e. someone who knows "everything", was a high ranking
qualification until the 17th and even the 18th century. Blaise Pascal (1623-62)
is renown as the "last" *homo universalis*, although I should tend
to qualify Teilhard as a modern *homo universalis*.

This very general,
universal intellectual development is a fertile source for integrative
thinking. From such a diversified experience and knowledge, the philosopher-scientist
tries to formulate for himself hypotheses that fit with his experiences.
The control for the validity of such a hypothesis is his intuitive certitude
that all important data are explained. The same phenomenon probably occurs
with a successful artist: he "feels" that his creations are "right", i.e.
an intregration between a series of good separate ideas.

The step from such
an intuition towards the honest conviction that one is enlighted by divine
revelation, is not far.

The thinking error
is not that one conceives such intuitive integartions as *plausible*,
but as *absolutely true*, because *God can't lie*.

**3. The scientific
method of Pierre Teilhard de Chardin**

The notion of thought
or consciousness moving along a continuum of ever increasing plausibility
seems to be compatible with Teilhard de Chardin's view that thought or
consciousness gropes its way forward from one approximate conception of
reality to another with, on average, later cognitional approximations being
more accurate that earlier ones. In this regard, the French Jesuit writes:
*'Consciousness,
we know, does no more than grope its way forward, one approximation following
upon another.'* [4] And elsewhere, in a not dissimilar vein, he remarks
that '*the history of the living world can be summarised as the elaboration
of ever more perfect eyes within a cosmos in which there is always something
more to be seen.'* [5] Whether these eyes are those of the body or of
the mind, their function is always *'to try to see more and better'* [6]. So, Teilhard, here, does seem to be, at least in part, talking about
consciousness at the thinking level, ever groping it's way, by means of
increasingly plausible cognitions, away from falsity towards truth.

Hence I believe that
Teilhard was, in large measure, an integrative thinker and theoriser. In
this connection, in an essay of his, we read:

'What I
wish to offer here is the outcome of my own thinking, expressed in a simple
and clarified form so that everyone may be able to understand it without
ambiguity, and may criticise and (this is my great hope) correct and amplify
it.' [7]

So, to all appearances,
the French Jesuit was open to having his outlook, on an ongoing basis,
criticised, corrected and amplified with a view to having it continuously
nudged forward along the plausibility continuum in the hope that it would
ever move closer and closer to the truth. **4. Teilhard and
Revelation**

**His approach.** I have, above, used the expression "in large measure" advisedly. My reason
for doing so is that that, in my opinion, as regards one area of his outlook,
Père Teilhard does, in some measure, and in some sense, believe
he stands, from a knowledge standpoint, at the truth end of the plausibility
continuum. And this one area, as I have said elsewhere,
is that of his religious **faith** which, to his mind, contains indubitable
certitudes revealed by God to humanity by way of scripture and the Church.

Thus we find Teilhard
referring to '*the revealed knowledge' *which is* 'afforded us by
the Catholic faith' *and* 'which is richer and more exact' *than
knowledge* 'in the field of pure empirical science.' *[8] In the expression
"richer and more exact", we can probably read "truer and more accurate".
So, in the mind of the French Jesuit, the knowledge that comes to us by
way of **divine revelation** is, in some sense, a kind of knowledge
that outranks ordinary knowledge in terms of its truth value.

For Teilhard, when,
by way of divine revelation, we receive 'from on high', from God, 'a reply'
to our religious questioning, 'we in some way enter the order of certainty'
and leave behind 'the scientific framework of "hypothesis".' [9] So, once
again we encounter the notion that divinely revealed knowledge significantly
surpasses ordinary knowledge as regards its truth value.

One 'lesson of revelation',
in the eyes of the French Jesuit, is the religious teaching that there
is a cosmic Christ, *'a Word who makes himself incarnate.'* [10] The
knowledge which this religious teaching affords, in the opinion of Teilhard,
is a knowledge which is at the truth end of the plausibility continuum.

So, for Teilhard,
how would his certainty about the reality of a cosmic Christ square with
Kris' s first postulate that there is very little probability, in the overwhelming
majority of cases, that a theory is entirely true. My suspicion is that
the French Jesuit would agree with the postulate, but also maintain that
his knowledge of the cosmic Christ is a sort of special knowledge, a knowledge
that transcends theory because it is revealed knowledge. Further, my hunch
is that Teilhard would also claim that because this knowledge is a special,
transcendent kind of knowledge it is exempt from the normal condition of
ongoing self-correction that is invariably associated with theory.

**Criticism. **What
are we to think of Teilhard's view about these two levels of knowledge,
an ordinary and perpetually self-correcting level based on experience,
and a super-ordinary changelessly true level based on divine revelation?
Is this view viable over the long term? No doubt these questions are among
those that are being pondered by those who concern themselves with carrying
out the task, set to them by the French Jesuit, of criticising, correcting
and amplifying his thought.

My own personal opinion
is that Teilhard's "two level" approach may **not be viable over the long
term**. Why? Well, as I have said before, what was once taken to be inerrant
truth based on Scripture has turned out to be mistaken:

- Historically,
texts in the Bible, said to be divinely revealed, have been used to justify
claims that the universe was created in six days, that the universe began
to exist around the year 4000 B. C. E.,

- that the cause
of evil is a culpable trespass on the part of the first two humans on earth,

- that the sun orbits
the earth, and

- that child abuse
and slavery are morally acceptable. I think
that when slavery (and the submission of the woman to her husband) seem
to be acceptable for the Church Fathers, paedophily was considered as very
rejectable from the very beginning. Nevertheless, ons could add to this
list:

- the degradation of
sexuality, only acceptable for men "not able to vow themselves to celibacy".

- the dogm of the
Virgin-Mother, an offense for every mother and woman

- the acceptance
of death penalty, the benediction of war, the acceptance of revealed arguments
against scientific and experimental evidence, etc.

Now, if all of these
"revelations" were mistaken, I ask myself, what guarantee do we have that
the "revelation" of a **cosmic Christ** is valid, is not also mistaken? Teilhard, as he tells
us, looks largely to 'the Christogenesis of St. Paul and St. John' for
support of his view that there is a cosmic Christ. But, I ask myself, how
do I know that St. Paul and St. John were not mistaken on this matter?

It does
seem to be the case that St. Paul was mistaken on the *morality of slavery* [at Ephesians 6: 5-9 and Colossians 3: 22-24], and this mistake, on his
part, was used by pro-slavery persons and groups, in the 18th and 19th
centuries, in their disputes with the abolitionists. As we know, the abolitionists
eventually prevailed, and it is now generally admitted that, on the question
of slavery, Paul was mistaken. Might he also be mistaken as to the reality
of a cosmic Christ? I answer: "Yes, this is quite possible." Others, of
course, answer: "No, this is not possible." Perhaps, only time will tell
which response is more nearly correct.

I think that, (1) if
we consider revelation not as a direct intervention of a Superbeing into
the natural evolution, but as a message that can be "read" in nature and
reality because it was there since the very moment of Creation, and (2)
if we consider integrative thinking, including its primitive forms intuition
and "feeling a revelation" as *yielding plausibility* in stead of
absolute truth, we can still trust in integration.

[1]
Roose, K., 1980, Ontwerp voor een Integratieve Psychologie, Gent.

[2]
Roose, K. & Van Brandt, B., 1985, Het geheim van het geluk, Kluwer,
Antwerpen-Deventer

[3]
Beckers, Danny. ""Pieter Nieuwland (1764-1794): natural philosopher, mathematician,
and poet"; mathematical societies in the Netherlands and the ideal of the
Homo Universalis" De Achttiende Eeuw, 33, 1 (2001): 3-20

[4]
P. Teilhard de Chardin, 'The Evolution of Chastity', in 'Toward the Future'
(Harvest Book, 1975), p. 60.

[5]
P. Teilhard de Chardin, 'The Phenomenon of Man' (Fountain Books, 1977),
p. 35.

[6]
P. Teilhard de Chardin, 'Phenomenon', p. 35.

[7]
P. Teilhard de Chardin, 'The New Spirit', in 'The Future of Man' (Harper
& Row, 1969), p. 85

[8]
P. Teilhard de Chardin, 'The Phenomenon of Man', in ''The Vision of the
Past' (Collins, 1966), p. 161 (In footnote # 1).

[9]
P. Teilhard de Chardin, 'Outline of a Dialectic of Spirit', in 'Activation
of Energy' (Harvest Book, 1970), p. 148.

[10]
P. Teilhard de Chardin, 'Outline of a Dialectic of Spirit', in 'Activation',
p. 148. (8) 'Phenomenon', p. 325.