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''This is a description of techniques for conceptual integration. Look for articles on [[Conceptual integration]] and [[Plausible science]].''
==Introduction==
==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.
The process of integration, leading to the formulation of a new, more plausible hypothesis, is part of the induction process, which is still unconscious and inaccessible for conscious reasoning.


Apart from its contributions to deductive thinking, this approach is misleading in at least three of its explicitly or implicitly suggested conclusions:
The integration process is the elaboration of a new, more general hypothesis out of some particular hypotheses with limited applicability.


(1) there is no category between true and false;
Because it is still largely unconscious, this process can not yet 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.
(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.
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.


==Definition==
==Spontaneous induction==


As defined elsewhere, integration can be defined as [1,2]
Our brain enables us, and, in fact, stimulates us, to make spontaneous generalizations, i.e. formulating explanatory hypotheses generated from the observation of analogous or related phenomena. Why and how the brain does so is discussed elsewhere. But two factors are limiting the probability for spontaneous generalizations to be exact and scientifically true:


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.
(1) our normal observations are mostly limited to restricted number of applications


Symbolically this process could be represented by:
(2) in the field of alpha sciences ( = Arts and Philosophy, Law, Economics and Business Administration, Psychology and Educational Sciences, Political and Social Sciences) we still lack tools for exact measurement and the possibility to do experiments, two essential conditions for classical science.


        (A,B) Æ [A>>A'] & [B>>B'] Æ {A'B'}
We can expect that most of those spontaneously induced hypotheses are highly vague, incorrect, and indeed subjective (closely linked to our limited observation position).


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}.
This inability to observe details that could render the hypothesis more correct, yields hypotheses that, apart from a true (but unobservable) essence or '''kernel''', consist of too generalized or too specific exaggerations. These superfluous aspects are called '''eductions'''.
       
We would like to introduce the function of Y (Psi) meaning "to be reduced to its essential core", so that:


        Y(A) = A'
<blockquote>'''Example'''. A teacher observes a pupil that is often absent-minded, and even plays during the course. He concludes that this pupil is not enough mature for this class, and should be helped by doing the year over. But should the teacher know that this pupil is highly gifted, he should better understand why he is so often absent-minded, and should rather be helped by jumping one year. In this example, the eduction consists in the assumption that this pupil will be absent-minded in all circumstances.</blockquote>


and v  as the inverse function, the "eduction"
But if several observers perceive the same phenomena from different experiential observation points, we could expect that their eductions should be different, and that by a laborious work of comparison and reformulation, they could extract the kernel, the essence, thus developing a much more refined and plausible hypothesis.


        A = v(A')
<blockquote>'''Example'''. One of the teachers in the class is giving rather difficult lessons about a very demanding topic, and observes that the often absent-minded pupil becomes very interested and participating and excels in resolving difficult problems. He concludes, equally inexactly, that this a very excellent pupil, well adapted to the intellectual level of the teachings.</blockquote>


so that A is an eduction of A', meaning that we can come from A' to A by making A' less general.
The integration technique tries intelligently to combine apparently irreconcilable hypotheses, by reformulating and adding nuances, decreasing the eductions (i.e. performing a '''retroduction'''), thus enabling the elaboration of a more plausible hypothesis.


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


        W (A,B)= {A'B'}
We can describe the integration procedure symbolically


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".
[[Image:Integrationscheme.jpg|frame|Preparing integration]]
[[Image:IntegrationschemeDone.jpg|frame|Succeeded integration]]


Symbolically, the above statements can be written as
Let's consider two statements, A en B. They seem irreconcilable, and <> symbolizes this incongruence:


        (A,B) Æ [A>>A#]& [B>>B#]Æ {A#B#}
<blockquote>A <> B</blockquote>


        Y(A) = A#
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 behaviors 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.


        A = v (A#)
The solution is that both observers retroduce their statements, by adding nuances or limiting conditions, making an integration possible.
 
        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",
 
here "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 TE as the Theories of Einstein, and TN as the Theories of Newton, we can state that:
 
    P(TE) > P (TN)
 
    Or:
    Y(TN) = TE
 
    TN = v (TE)
 
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.
 
    E1(A) Æ a1
 
    a1 + E2(A) Æ a2
 
    a2 + E3(A) Æ a3
 
generally described as


    an-1 + En(A) Æ an
Let's symbolize the kernel by #, and symbolize the retroducing process by &Psi;


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 E1(A), E2(A)... are consecutive experiences. a1, a2, ..., anare consecutive visions, hypotheses about phenomenon A , becoming progressively more integrative. A cyclic scheme could also represent this procedure:
<blockquote>&Psi;(A) = A#<br/>
&Psi;(B) = B#</blockquote>


This means that at each given moment, each concept may become more complete, more realistic, more comprehensive, more integrative.
Let's symbolize integration by &Omega;, than


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:
<blockquote>&Omega;(A,B) = {A#B#}</blockquote>


Einstein proposed an elaborated formula:
==The integration techniques==


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.
A practical description of tools to perform conceptual integrations.


2. The 'complements' operator - the non-existence of contradictions
===Direct techniques===


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 (¿)
Ideally we should have an operationalized integration paradigm to our disposal, to perform direct integrations starting with conflicting hypotheses. Unfortunately, at this point in the development of science, such direct integrative tools are still lacking. Integration remains a procedure, performed by our Unconscious. Examples are the creation of Art, and inventions in general, even scientific. The traditional scientific tools are only able to check or to falsify proposed hypotheses, that were developed unconsciously. Science is the conscious control of hypotheses, developed by the unconscious.


Where in the traditional approach statements as
Of course, ''afterwards'' we can try to ''reconstruct'' the way intellectual creations were made. E.g. we can make theories about the music of Bach, Mozart, and the way these musical styles developed, often from other sources and influences. Or the development of jazz, from Afro-American  musical traditions and European classical music. But even that is usually very difficult. Even Einstein, making an integration of Newton's theories and recent observations conflicting with those theories, was unable to explain ''how'' he made his new theory.


    psychoanalysis <> behaviourTheory
===Indirect techniques===
    science <> religion
    theoryOfNewton <> unexplainableEvidence


seem very justified, in an integrative approach they are... false, because:
The unavailability of direct techniques doesn't mean we are unable to forge integrations. We have a large number of methods to our disposal, that '''enhance the probability''' that our Unconscious will spontaneously develop new integrative hypotheses, and even applications based upon those unconscious hypotheses.


    psychoanalysis ¿ behaviourTheory
We will discuss here (A) some '''basic principles''', and (B) some '''applied techniques'''
    science ¿ religion
    theoryOfNewton ¿ unexplainableEvidence


Hence:
====Basic Principles====
    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).
Those principles can be grouped in at least two sections: (1) '''Mental attitudes''', (2) '''Feeding inspiration'''


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.
'''(1) Mental attitudes enhancing spontaneous integration'''


3. An integrative theory is more plausible than its non-integrative elements
These are kind of beliefs, i.e. not yet proved (and hence easily refutable) convictions that new and better hypotheses can be developed, by us and by others. Of course, each conviction has to be formulated in a statistical way. These convictions don't necessarily ensure successful integrations, but maximize the probability to perform ones.  


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.
*(Nearly) always, even here and now, better insights and inventions can be realized
*I am (very often) able to perform such new insights
*A hypothesis, made by someone else and apparently conflicting with mine, has (nearly always) a valuable and irrefutable kernel
* Every conflict is a false conflict. An integration can (nearly) always be made (even if this consumes sometimes much effort and time)
* Experience, age, hierarchical position, academic degree and formerly made inventions (nearly) never coincide with creative productivity.
* Inspiration by observing other people performing creative work not only gives us new ideas, but boosts our mental attitudes
* A number of psychological factors doubtlessly contribute to develop a creative, integrative attitude. Even the IQ doesn't seem the major factor, as illustrated by Emotional Intelligence.  


So we can state that
<blockquote>'''Application.''' Statistically speaking younger, non-academic etc. people make more (integrative) inventions than people supposed to do so by their age, diploma, etc. Perhaps partly because these mental attitudes are part of their natural confidence.</blockquote>
    P(A#) > P(A)


and, more in detail, if:
'''(2) Feeding inspiration by contrasting experiences'''
    W (A1,  A2 ,  A3 , ...) = A#
    then:
    P(A#) > P(A1)
    P(A#) > P(A2)
    P(A#) > P(A3)
    ...


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.
Although most probably several inspiring factors contribute to the occurrence of integration and progress, one of the major factors seems to be the exposure to contrasting experiences. Explanations for this phenomenon include
* discovering the relativity of local traditions, considered as universal and eternal
* discovering the explanation for the limits of one's own system, by observing the possibilities of unexpected variants
* the invitation to combine "the best of two worlds"


Graphically represented:
Some traditional examples are
*Hippocrates, who traveled years through the neighboring countries to study local medical treatments, before starting developing his own theories and practices
* Antique Alexandria, a meeting point of Egyptian mysticism and Greek rationalism, Jewish confidence and Babylonian science, developing an impressive amount of progressive sciences, ranging form philosophy and mathematics to geometry and applied physics
* The invention of jazz by a cultural crossing of Afro-American rhythm and improvisation, with European musical harmony


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.
====Some applied techniques====


If
* '''Brainstorming'''
    W (A1,  A2 ,  A3 , ...) = A#


then the maximal plausibility for  A# (replacing the obsolete concepts true and exact) is reached when
The classical technique of [http://en.wikipedia.org/wiki/Brainstorming Brainstorming] is an excellent application of the above principles, on condition that is doesn't be limited to one session, and if the final aim is not to find the ''best'' idea, but a formulation with which ''everybody'' could agree.


    A1 = v (A#)
* '''Classification method'''
    A2 = v (A#)
    A3 = 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.
## First as much elements, ideas, variants etc. are collected, and put into a document
## One tries to make a logical classification of all elements, brainstorming about the name of new categories. In this logical classification, symmetry in subdivisions has to be pursued.  
## Each time a list with more than 3 items subsists, a new division has to be created and a regrouping of items has to be performed
## With such logical schemes, several holes or empty categories might be discovered. These act as (creative) inspiration for new elements.


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.
* '''The Matrix method'''


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.
This is a variation of the Classification method. But in stead of logical categories, ''dimensions'' are taken to classify. Elements that are difficult to classify with the present dimensions, suggest a new dimension yet to create. With few dimensions (e.g. two or three) a graphical schema (table) can be used.


The integrative procedure
<blockquote>'''Example.''' Looking for the ideal music we could try to classify existing musical styles e.g. Gregorian, jazz, baroque, country, classical. We could take two dimensions into account, e.g. riches of harmony, and riches of rhythm


1. Introduction
{| class="wikitable"
|-
! Poor rhythm
! Medium rhythm
! Rich rhythm
|-
! Rich harmony
| Classical
|
|
|-
! Medium harmony
| Baroque
| Country
| Jazz
|-
!Poor harmony
| Gregorian
|
| African
|}


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.
The empty boxes could inspire for creations. </blockquote>


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.
* '''A Corpus'''


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.
A ''Corpus'' is a bigger logical scheme, a logical collection of structured texts, covering all important aspects. An encyclopedia is not a Corpus, because it's not a logical frame, but an alphabetical.


The integration process is the elaboration of a new, more general hypothesis out of some particular hypotheses with limited applicability.
Such a corpus grows constantly, as new insights develop, but requires from the contributors (authors, editors) that every new contributor should fit in the existing corpus. If this is not possible, the corpus has to be elaborated. Conflicts to fit are rich inspiration sources for new insights.


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.
The notion of [[Web 3.0]] employs this corpus method as one of its essential techniques.


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.
* '''Analogies'''


2. Eduction (v)
The intuitive integration probably will be inspired by analogies, and especially by analogies with fundamental features of reality described by the [http://en.wikipedia.org/wiki/Systems_theory Systems Theory], and assisted by inductive Logics.


Let's consider two statements, A en B. They seem irreconcilable:
==Primitive forms of Integrative Thinking==


    A <> B
Scientific research often gives us the impression that real science started at the end of the Medieval times, and that the so called Alpha Sciences (social and psychological sciences) still don't comply with scientific criteria, But how to explain the fact that pre-renaissance science yielded so many impressive scientific insights, including Greek mathematics and science, Egyptian and Assyrian geometry, architecture and astronomy, and... modern science itself?


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.
===Unconscious integration===


3. Retroduction (Y)
One could perhaps consider that those "primitive", "unscientific" forms of thinking were in fact kinds of '''intuitive 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,<ref>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</ref> 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.


The solution is that both observers retroduce their statements, by adding nuances or limiting conditions, making an integration possible.
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" intuitively that his creations are "right", i.e. an integration between a series of good separate ideas.


We postulate that A ¿ B, and we retroduce A and B to A# and B# by
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 integrations as plausible, but as absolutely true, because God can't lie.


    Y(A) = A#  and Y(B) = B#
===The scientific method of Pierre Teilhard de Chardin and Alfred North Whitehead===


4. Combination (+)
''(With thanks to Brian Cowan)''


At this point an integration, now nothing more than a simple combination, will be possible:
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.' <ref>P. Teilhard de Chardin, 'The Evolution of Chastity', in 'Toward the Future' (Harvest Book, 1975), p. 60.</ref> 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.' <ref>P. Teilhard de Chardin, 'The Phenomenon of Man' (Fountain Books, 1977), p. 35.</ref> Whether these eyes are those of the body or of the mind, their function is always 'to try to see more and better' <ref>P. Teilhard de Chardin, 'Phenomenon', p. 35.</ref>. 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.
 
    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:
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]
'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.' <ref>P. Teilhard de Chardin, 'The New Spirit', in 'The Future of Man' (Harper & Row, 1969), p. 85</ref>


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.
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.


===Plausible science===


An important application of the Conceptual Integration is [[Plausible science]], discussed in another article.


    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.
==References==
 
   


    [1] Roose, K., 1980, Ontwerp voor een Integratieve Psychologie, Gent.
<references/>
    [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

Revision as of 03:55, 6 August 2007

This is a description of techniques for conceptual integration. Look for articles on Conceptual integration and Plausible science.

Introduction

The process of integration, leading to the formulation of a new, more plausible hypothesis, is part of the induction process, which is still unconscious and inaccessible for conscious reasoning.

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 yet 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.

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.

Spontaneous induction

Our brain enables us, and, in fact, stimulates us, to make spontaneous generalizations, i.e. formulating explanatory hypotheses generated from the observation of analogous or related phenomena. Why and how the brain does so is discussed elsewhere. But two factors are limiting the probability for spontaneous generalizations to be exact and scientifically true:

(1) our normal observations are mostly limited to restricted number of applications

(2) in the field of alpha sciences ( = Arts and Philosophy, Law, Economics and Business Administration, Psychology and Educational Sciences, Political and Social Sciences) we still lack tools for exact measurement and the possibility to do experiments, two essential conditions for classical science.

We can expect that most of those spontaneously induced hypotheses are highly vague, incorrect, and indeed subjective (closely linked to our limited observation position).

This inability to observe details that could render the hypothesis more correct, yields hypotheses that, apart from a true (but unobservable) essence or kernel, consist of too generalized or too specific exaggerations. These superfluous aspects are called eductions.

Example. A teacher observes a pupil that is often absent-minded, and even plays during the course. He concludes that this pupil is not enough mature for this class, and should be helped by doing the year over. But should the teacher know that this pupil is highly gifted, he should better understand why he is so often absent-minded, and should rather be helped by jumping one year. In this example, the eduction consists in the assumption that this pupil will be absent-minded in all circumstances.

But if several observers perceive the same phenomena from different experiential observation points, we could expect that their eductions should be different, and that by a laborious work of comparison and reformulation, they could extract the kernel, the essence, thus developing a much more refined and plausible hypothesis.

Example. One of the teachers in the class is giving rather difficult lessons about a very demanding topic, and observes that the often absent-minded pupil becomes very interested and participating and excels in resolving difficult problems. He concludes, equally inexactly, that this a very excellent pupil, well adapted to the intellectual level of the teachings.

The integration technique tries intelligently to combine apparently irreconcilable hypotheses, by reformulating and adding nuances, decreasing the eductions (i.e. performing a retroduction), thus enabling the elaboration of a more plausible hypothesis.

Symbolic description

We can describe the integration procedure symbolically

Preparing integration
Succeeded integration

Let's consider two statements, A en B. They seem irreconcilable, and <> symbolizes this incongruence:

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 behaviors 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.

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

Let's symbolize the kernel by #, and symbolize the retroducing process by Ψ

Ψ(A) = A#
Ψ(B) = B#

Let's symbolize integration by Ω, than

Ω(A,B) = {A#B#}

The integration techniques

A practical description of tools to perform conceptual integrations.

Direct techniques

Ideally we should have an operationalized integration paradigm to our disposal, to perform direct integrations starting with conflicting hypotheses. Unfortunately, at this point in the development of science, such direct integrative tools are still lacking. Integration remains a procedure, performed by our Unconscious. Examples are the creation of Art, and inventions in general, even scientific. The traditional scientific tools are only able to check or to falsify proposed hypotheses, that were developed unconsciously. Science is the conscious control of hypotheses, developed by the unconscious.

Of course, afterwards we can try to reconstruct the way intellectual creations were made. E.g. we can make theories about the music of Bach, Mozart, and the way these musical styles developed, often from other sources and influences. Or the development of jazz, from Afro-American musical traditions and European classical music. But even that is usually very difficult. Even Einstein, making an integration of Newton's theories and recent observations conflicting with those theories, was unable to explain how he made his new theory.

Indirect techniques

The unavailability of direct techniques doesn't mean we are unable to forge integrations. We have a large number of methods to our disposal, that enhance the probability that our Unconscious will spontaneously develop new integrative hypotheses, and even applications based upon those unconscious hypotheses.

We will discuss here (A) some basic principles, and (B) some applied techniques

Basic Principles

Those principles can be grouped in at least two sections: (1) Mental attitudes, (2) Feeding inspiration

(1) Mental attitudes enhancing spontaneous integration

These are kind of beliefs, i.e. not yet proved (and hence easily refutable) convictions that new and better hypotheses can be developed, by us and by others. Of course, each conviction has to be formulated in a statistical way. These convictions don't necessarily ensure successful integrations, but maximize the probability to perform ones.

  • (Nearly) always, even here and now, better insights and inventions can be realized
  • I am (very often) able to perform such new insights
  • A hypothesis, made by someone else and apparently conflicting with mine, has (nearly always) a valuable and irrefutable kernel
  • Every conflict is a false conflict. An integration can (nearly) always be made (even if this consumes sometimes much effort and time)
  • Experience, age, hierarchical position, academic degree and formerly made inventions (nearly) never coincide with creative productivity.
  • Inspiration by observing other people performing creative work not only gives us new ideas, but boosts our mental attitudes
  • A number of psychological factors doubtlessly contribute to develop a creative, integrative attitude. Even the IQ doesn't seem the major factor, as illustrated by Emotional Intelligence.

Application. Statistically speaking younger, non-academic etc. people make more (integrative) inventions than people supposed to do so by their age, diploma, etc. Perhaps partly because these mental attitudes are part of their natural confidence.

(2) Feeding inspiration by contrasting experiences

Although most probably several inspiring factors contribute to the occurrence of integration and progress, one of the major factors seems to be the exposure to contrasting experiences. Explanations for this phenomenon include

  • discovering the relativity of local traditions, considered as universal and eternal
  • discovering the explanation for the limits of one's own system, by observing the possibilities of unexpected variants
  • the invitation to combine "the best of two worlds"

Some traditional examples are

  • Hippocrates, who traveled years through the neighboring countries to study local medical treatments, before starting developing his own theories and practices
  • Antique Alexandria, a meeting point of Egyptian mysticism and Greek rationalism, Jewish confidence and Babylonian science, developing an impressive amount of progressive sciences, ranging form philosophy and mathematics to geometry and applied physics
  • The invention of jazz by a cultural crossing of Afro-American rhythm and improvisation, with European musical harmony

Some applied techniques

  • Brainstorming

The classical technique of Brainstorming is an excellent application of the above principles, on condition that is doesn't be limited to one session, and if the final aim is not to find the best idea, but a formulation with which everybody could agree.

  • Classification method
    1. First as much elements, ideas, variants etc. are collected, and put into a document
    2. One tries to make a logical classification of all elements, brainstorming about the name of new categories. In this logical classification, symmetry in subdivisions has to be pursued.
    3. Each time a list with more than 3 items subsists, a new division has to be created and a regrouping of items has to be performed
    4. With such logical schemes, several holes or empty categories might be discovered. These act as (creative) inspiration for new elements.
  • The Matrix method

This is a variation of the Classification method. But in stead of logical categories, dimensions are taken to classify. Elements that are difficult to classify with the present dimensions, suggest a new dimension yet to create. With few dimensions (e.g. two or three) a graphical schema (table) can be used.

Example. Looking for the ideal music we could try to classify existing musical styles e.g. Gregorian, jazz, baroque, country, classical. We could take two dimensions into account, e.g. riches of harmony, and riches of rhythm

Poor rhythm Medium rhythm Rich rhythm
Rich harmony Classical
Medium harmony Baroque Country Jazz
Poor harmony Gregorian African

The empty boxes could inspire for creations.

  • A Corpus

A Corpus is a bigger logical scheme, a logical collection of structured texts, covering all important aspects. An encyclopedia is not a Corpus, because it's not a logical frame, but an alphabetical.

Such a corpus grows constantly, as new insights develop, but requires from the contributors (authors, editors) that every new contributor should fit in the existing corpus. If this is not possible, the corpus has to be elaborated. Conflicts to fit are rich inspiration sources for new insights.

The notion of Web 3.0 employs this corpus method as one of its essential techniques.

  • Analogies

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

Primitive forms of Integrative Thinking

Scientific research often gives us the impression that real science started at the end of the Medieval times, and that the so called Alpha Sciences (social and psychological sciences) still don't comply with scientific criteria, But how to explain the fact that pre-renaissance science yielded so many impressive scientific insights, including Greek mathematics and science, Egyptian and Assyrian geometry, architecture and astronomy, and... modern science itself?

Unconscious integration

One could perhaps consider that those "primitive", "unscientific" forms of thinking were in fact kinds of intuitive 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,[1] 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" intuitively that his creations are "right", i.e. an integration 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 integrations as plausible, but as absolutely true, because God can't lie.

The scientific method of Pierre Teilhard de Chardin and Alfred North Whitehead

(With thanks to Brian Cowan)

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.' [2] 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.' [3] Whether these eyes are those of the body or of the mind, their function is always 'to try to see more and better' [4]. 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.' [5]

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.

Plausible science

An important application of the Conceptual Integration is Plausible science, discussed in another article.

References

  1. 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
  2. P. Teilhard de Chardin, 'The Evolution of Chastity', in 'Toward the Future' (Harvest Book, 1975), p. 60.
  3. P. Teilhard de Chardin, 'The Phenomenon of Man' (Fountain Books, 1977), p. 35.
  4. P. Teilhard de Chardin, 'Phenomenon', p. 35.
  5. P. Teilhard de Chardin, 'The New Spirit', in 'The Future of Man' (Harper & Row, 1969), p. 85