3.2. The symbol

The symbol is a sign that informs by convention. Alternatively, like WHITTICK (1960) put it: ‘A symbol includes all that is meant by a sign, mark or token.’ Such an appealing definition pinpoints, in its shortness, to the different directions of its meaning. The main constituencies are the sign and the convention. The first (sign) is a static description of reality, finding its place (in a quadralectic environment) in the empirical visibility (of the Third Quadrant). The second (convention) is a dynamic, swerving and swaying entity in the multitudes of a domain, which is later identified as that of a language (in the Fourth Quadrant). The original Greek meaning of the word ‘symbol’ as a ‘bringing together’ is applicable here.

The given definition lacks, unfortunately, an important element of the character of the symbol. The convention – or communis opinio – must have a specific intention, which is different from the apparent meaning. The sign is not what it really is (a cross, a car or whatever), but it stands for something else (a Christian faith, wealth or some other substitution value). This transitory quality is the hallmark of the symbol-sign.

The conclusion of the above given definition would be – in a linear and hierarchical line of thinking – that the symbol only finds its reason of being in the things to come. Its ‘Second Quadrant’ identity is based on a ‘Third Quadrant’ entity, which gets another (double or multiple) meaning by the interpretation in the ‘Fourth Quadrant’. Another possibility would be, that the association of the sequence (signal, symbol, sign, language) with the quadrants is invalid and should be arranged in another way.

The solution to this sequential problem is a transposition from a linear (and hierarchic) to a cyclical (and non-hierarchical) way of thinking. Everything is in everything, not only at the very beginning – like the linear view often prescribes – but also during the whole process of data exchange. There is no ‘before’ or ‘after’ in a general overview, only on a local and limited scale. The essence of the whole quadralectic communication lies embedded in every single moment and every single place.

The position of the symbol in the dynamic Second Quadrant is well earned, because the transitory nature is typical for this phase, just after the first division took place. It is the world of ideas, non-coherent connections and preliminary interpretations, which might substantiate itself after some form of a convention (in the fourth (sub)division of the Second Quadrant) has taken place.

This symbol-forming course is, in many ways, a proficient reflection of the communication-as-a-whole because the observer has to go through all the various stages to get the picture (of a symbol) right. The initial signal manifests itself in an invisible visibility (after its diffusion in an array). This array is picked up by an observer, interpreted (symbolized), established and communicated (compared) with the findings of other observers. The first full round along the observational stands yields a personal symbolism, based on an individual impression (which was, in essence, already explored in the second phase of interpretation).

The last stage in the path of signal processing, i.e. the actual participation in a communal comparison, gives the communication a sudden ‘human touch’ (and associated subjectivism). The newly experienced reality (for the observer) is no longer noncommittal, but assimilates in a group and mingles as a component in a language (defined here as the collective construction of the visible invisibility).

The language-entity has the capacity to become a new signal. The array of this (language) signal makes a second round (along the observational stages of the language group), which results in a group symbolism. Interaction between different (cultural) groups can result in a third round, a fourth, and so on.

Symbols, as a particular expression of understanding, are very versatile. They can be manifest as a separate presence, like a down-to-earth sign in the Third Quadrant or cluster together as an icon in the Fourth Quadrant (fig. 14). The various meanings (and operational places within a communication) have to be fully understood to grasp the intention of a symbol within a language.


Fig. 14 – The symbol is a sign, which informs by convention and points to something else. The Hitler Jugend of Zernikow (100 kms north of Berlin) planted these larch trees just before the Second World War. The yellow foliage formed in autumns a swastika pattern amidst the other trees. The swastika itself is an ancient sun-sign, which became a symbol in Nazi Germany. The pattern was discovered from the air in 1992. The trees were cut down in December 2000 in fear of becoming a place of pilgrimage for extreme-right wing groups.

3.3. The sign

The sign is a familiar point of visibility. The main characteristics of the sign are its limitation (as an object) and its capability of establishing a connection. The sign brings the signal to its destination: the understanding by an observer. The study of the sign is a ‘Third Quadrant’ venture, initially ruled by the two- and three divisions.

The American mathematician Charles Sanders PIERCE (1839 – 1914) caught the spirit of this new field of psychological investigation, which he labelled semeiotic (in the current use and spelling the word semiotics includes all the various studies of signs). He emphasized the subjective character of the sign (in: PIERCE, 1963; par. 2.308) by saying that ‘nothing is a sign, unless it is interpreted as a sign’.

The three-division became a central point of departure in his mathematical or symbolic logic. The process of signification, for instance, consisted of three stages. Firstly, the sign in itself (representamen, Third Quadrant), secondly the object (the sign as used by its observer, Second Quadrant) and thirdly, the sign as an image as created by itself (interpretant, Fourth Quadrant). These three connections were again placed in trichotomies. The object was divided by Pierce in:

The icon is a representation of an object shaped after nature,

The index  is a reference to an object (a gesture): anything that focuses attention is an index;

The symbol rules about the use of an object as a representamen, and can be expressed in words and sentences.

The threefold division of signs as a sign vehicle, designatum and interpreter (at present rendered as respectively second, third and fourth quadrant expressions of the sign) was further advanced by Charles Morris (1901 – 1979) in his book ‘Foundations of the Theory of Signs’ (1938).

Van SCHALKWIJK (1989), in his eminent study of the sign of the cross, gave a more elaborate division of communication-elements, which is closer to the modern, quadralectic way of thinking:

Signals    ———————–  extrinsic

Signs —————————– intrinsic

Symbols ———————— analogy, metaphor

   subdivided in:

  —————     Icons             –       clusters of ‘symbols’

   ————–      Gestures      –       sign language

   ————–      Proxemics   –       silent language of non-verbal communication

The quadralectic sequence (of quadrants) can be reduced from these given distinctions, but some ‘juggling’ is necessary. Signs (III) and symbols (II) have to change places. The icons remain with the symbols, but the gestures belong more to the world of signs and can even bridge the gap to a language (the sign language as a way of expression).

Finally, the proxemics – cultural interaction, the feel of distance, smell, or the angle of vision – is a genuine expression of a Fourth Quadrant ‘language’, based on subjective intervention and a collective construction of the visible invisibility (IV).

The sign is – in a quadralectic communication – not only a simple visible visibility (positioned in the Third Quadrant), but also an interactive element in the (third part) of the Second Quadrant and in the (third part) of the Fourth Quadrant. It acts as an object with a certain content and is a constituent in several regimes. The various positions, seen as a centre of significance, have a specific formalization of expression. The sign is the ‘decoder’ in the communication process. The interaction can be divided in:

1. a source, sending a signal (or array of signals),

2. which can be regarded as encoded messages (symbols)

3. to a receiver, who tries to understand them (as a decoder) and

4. leading them to the destination (of understanding).

This sequence is derived from the coding theory (a branch of mathematics concerned with transmitting data across noisy channels and recovering the message). The various positions are given in fig. 15.


Fig. 15 – The sign is a receiver in a communication, which translates a message (or an array of signals) from a sender (using these encoded messages as symbols) to a destination. The destination can be described as a language, capturing the understanding of the original signals to the participants in the communication. Its use and meaning can become a new message source for another (communication) cycle.


Radio telescope Kootwijk (1948 – 1955). The Netherlands – An example of a receiver (of cosmic signals).

3.4. The language

The language is the most complicated form of a communication, because it employs all the previous communication elements at the same time. The word ‘language’ is used here in a general sense, as the denominator of any form of communication in which signals, symbols and signs are combined in a meaningful set of rules to articulate thoughts.

Language deals, firstly, with signals, which are emitted from any given source. Secondly, there are a meaning and setting of such signals transferred by man to symbols. These symbols can have several meanings and are joint together in a concept. Thirdly, there are the actual signs (words), which are used to visualize (and/or make audible) the message. Finally, there is the knowledge of the whole process, expressed in such terms as ‘speaking the language’.

The understanding of (any) language means, when conceived in its most complete manifestation, a knowledge and mastering of all the meaningful elements of a particular communication under the given circumstances. Experience gives an insight in the bond between primary knowledge, language and a fruitful understanding within a communication specter.


Fig. 16 – The English philosopher John Locke (1632 – 1704) studied the nature and development of knowledge in the heydays of oppositional thinking. He reached conclusions, which had – at some points – a resemblance with the quadralectic philosophy.

The English philosopher John Locke (1632 – 1704) traced the intellectual development of knowledge in his book ‘An Essay Concerning Human Understanding’ (first published in 1689; he worked on the book for almost twenty years). He was a rationalist and dualist at heart, just like his major sources of influences, René Descartes (1591 – 1650) and Robert Boyle (1627 – 1691). It is remarkable, that his strict and often sceptical approach to knowledge opened up an occasional glimpse in the world of higher division thinking. One may wonder if such insights were just a coincidence, born in a creative mind, or that they are part and parcel of any inquisitive reasoning power at the boundaries of two-fold thinking.

The division of his ‘Essay’ in four books reflected perspicuously the present quadralectic approach of understanding. The contents of the book will be briefly discussed here:

Book 1. Introduction

The object of Locke’s book was an enquiry into understanding, with the idea (defined as the object of the understanding when a man thinks) at the centre of attention. The bounds between opinion and knowledge were of special interest. Locke employed a threefold method to reach his goal:

 A search for the original of those ideas (or notions), which a man has in mind;

  1. The extent and limits of knowledge gained by such ideas; and
  2. The foundations of faith or opinion.

He regarded the origin of ideas as two-fold: there were speculative and practical principles. The former propositions were self-evident and logic. The latter gave guidance for conduct and moral duties in everyday life. There were, according to Locke, in contrast to the Cartesians, no innate (or preconceived) ideas: his ‘First Quadrant’ was seen as a complete empty place. Any idea of cyclicity (and division thinking), that gives a different view on the character of the First Quadrant, was unknown to Locke.

Book 2. Ideas

Locke moved in the second book to the ‘great and principal actions of the mind, which are most frequently considered, and which are so frequent that everyone that pleases may take notice of them in himself: perception or thinking, and volition or willing’. The power of thinking was called the Understanding, and the power of volition called the Will’ (Book II, Ch. 6).

Locke considered sense experience (sensation) and reflection as the primary sources of ideas. Again, an immediate, two-fold division followed: simple ideas (derived from one sense only, which also included the results of sensation and reflection – like pleasure and pain, power, existence and unity) and complex ideas (of substances).

The interpretation of the ‘Second Quadrant’ of Ideas is, from a modern, quadralectic point of view, rather hodgepodge. Sensation is a ‘Fourth Quadrant’ feature. Reflection takes place mainly in the ‘Second Quadrant’ (and also in the ‘Fourth Quadrant’). Unity and existence are ‘First Quadrant’ items. And the source of power and various oppositions (such as pleasure/pain, heat/cold, light/darkness, white/black and motion/rest) have their home ground in the ‘Third Quadrant’.

The dualism of Locke did not arrange the products of his simple ideas any further in a comprehensive way, but it must be granted that the mere mentioning of these diverse items under one heading (identified as the Second Quadrant) touches the tetradic perception of a communication.

Book 3. Substance

There is no clear idea of substance in general, concluded Locke (still in Book II, Ch. 23). He referred to the Platonic line of thinking that our observation of physical things (like a horse or a stone) is interwoven with the idea we have of such substances. There can hardly be, in other words, a clear-cut ‘horse’ or ‘stone’. The differentiation between the ‘real thing’ (realist) and ‘the idea of a thing’ (nominalism) has kept philosophers busy for a long time after Plato. The efforts always boiled down to the eternal question: What is real?

The controversy found a new lease of life in the Middle Ages, with William of Ockham (c. 1285 – 1347/49) as a major pioneer on the ‘via moderna’ (rejecting the universals). He maintained that science had to do with propositions, not with things as such. Things are always singular, while science was concerned with general concepts. The last word on the subject (of ideas) was still not said in the middle of the seventeenth century and in the lifetime of Locke.

John Locke compared the physical things with the substance of spirit: ‘It is plain, then, that the idea of corporeal substance in matter is as remote from our conceptions and apprehensions as that of spiritual substance or spirit’. He used a three-division to connect the complex ideas of corporeal substances with the senses:

1. The ideas of primary qualities are discovered by our senses (like bulk, figure, number, situation etc.)

2. The sensible secondary qualities are nothing but the powers those substances have to produce several ideas in us by our senses.

3. The alterations of primary qualities can be noticed (active) or unnoticed (passive powers), but are – in the end – always traceable to sensible simple ideas.

This celebration of the senses – in the end of Book II and prior to the subject of their substratum (substance or visible visibility) – is an indication of the unconscious use of a higher division model. A modern interpretation would place his thoughts in the fourth (sub)quadrant of the Second Quadrant (II, 4) or in the Fourth Quadrant (IV, which Locke could not grasp in his life and times).

Book III of the ‘Essay’ dealt directly with words or language in general. The capacity to make general signs (expressed in words) was retraced to common sensible ideas. ‘Words stands for nothing but the ideas in the mind of him that uses them’ (Book III, Ch. 2). There is, again, a pointing finger to the Second Quadrant.

Locke gave, in the same chapter, an example of words, which stand on their own (i.e. as ‘Third Quadrant’ entities). Words can be learned before the ideas are known for which they stand. He referred to the parrot, as the symbol of ignorant repetition, but he did not realize the weakening of his prior argument (saying that words were solely derived from ideas). Words may, in their primordial existence, also have been the building stones of a language in their own right.

The next remark on the real existence of things (in Book III, Ch. 3) was the rejection of the general and universal. These features do not belong to things themselves, he stated, but are invented by man and are creatures of his understanding. He proved himself here a follower of the nominalism of William of Ockham. Universality belongs not to things themselves. Things are always particular in their existence.

This clearness of thinking denies a unity to be capable of harboring a multiplicity (in itself). This fundamental difference of insight can be traced back to the expressions of lower and higher division thinking. A dualistic thinker is not willing to see more in a unity than there is: the opposition of a multiplicity. Unity – in the quadralectic mind – is, on the other hand, seen as a transitory position within a given interaction. It includes all the aspects of the whole communication, being either visible (matter or substance) or invisible (spirit and idea), being it either single or multiple.

Locke’s view of substance, as a Third Quadrant issue, was a mirror image of his notion of the First Quadrant, which could not hold innate ideas. Unity is unity. It is only in higher forms of division thinking that such basic statements are put in perspective.

Book 4. Knowledge in general

The author of the ‘Essay’ reached his zenith in Book 4, which investigated knowledge, as the ultimate proof of understanding. He regarded this commodity as ‘nothing but the perception of the connexion and agreement, or disagreement and repugnancy of any of our ideas.’ (Book IV, Ch. I). Such an opposition can be reduced, in Locke’s view, to four sorts:

1. The identity  or diversity – the first act of the mind to know what an idea is;

2. The relation – the perception of the relation between two ideas;

3. The coexistence or necessary connexion – the notion of substance. There is a complete ignorance of the substance either of spirit or of body;

4. The real existence – the conformity between our ideas and the reality of things.

Again, he followed a ‘quadralectic’ scheme, with a typical sequence of static-dynamic-static-dynamic phases, which is a reminder to the unity and separation (love and strife) cycle of Empedocles. However, Locke gave his credentials away in the choice of identity as the first act of the mind. The understanding is not the primary (quadralectic) division-principle, but a choice between two members of a duality: identity and diversity. Locke found, as a good dualist, his security in the safe haven of visible visibility (predominant in the Third Quadrant).

This choice was not surprising, since John Locke (1632 – 1704) witnessed during his lifetime the apex of European oppositional thinking. Bertrand Russell called Locke ‘the most fortunate of philosophers’, because his ideas were understood and welcomed by many of his contemporaries (COLLINSON, 1998). The present indication of the venturing of his critical and methodical mind in the realms of some sort of tetradic setting is a curious phenomenon.

Locke introduced, in addition to the reduction of knowledge into four varieties, also a hierarchy of knowledge. He proved himself here, again, a faithful thinker-in-opposites applying a trifold scheme. The hierarchy was based on ‘a different clearness of our knowledge’ with regards to ‘the different way of perception of the mind in the agreement of disagreement of any of its ideas’ and consisted of three ‘degrees’.

The dualistic theme (of dis/agreement) was used here to define a certain ‘clearness’. This transparency can be transferred to the quadralectic way of thinking and restated as ‘visibility’ and the awareness of distance. Locke’s linear differentiation of knowledge is then substituted, in modern thinking, by the ‘intensio’ and ‘remissio’ in a cyclic setting.

The division (of knowledge), as given in the ‘Essay’ (Book IV, Ch. 2) corresponds with the characteristics of the First, Third and Fourth Quadrant in the quadralectic way of thinking. They are:

  1. Intuitive knowledge (I)

The mind (in the ‘First Quadrant’) has ‘no other immediate object but its own ideas, which it alone does or can contemplate, it is evident that our knowledge is only conversant about them.’ Sometimes the mind perceives the agreement or disagreement of two ideas immediately by themselves, without the intervention of any other. This is the most basic and clearest kind of understanding: the intuitive knowledge.

The ‘First Quadrant’ of Locke is, at scrutiny, not as empty as he described it earlier (in the introduction) as a place without any innate ideas. Apparently, agreement and disagreement (of ideas) – or in other words: division – are present in the whole specter of communication. Which is fair enough, and in agreement with the quadralectic approach, but it did not enhance his statement on the absence of innate ideas. If ideas have the power to ignite themselves as intuition, seemingly without our intervention, why should there be no innate (or preconceived) ideas?

The type of division thinking and environment might hold, again, the key here. In a rational world of opposites is no place for innate ideas, because they point to an area before the actual existence. Preconceived ideas are no real problem in a cyclic framework. They might be the remnants of an earlier communication cycle, passed through before the present one. Intuition is, in a cyclic outlook, just the assemblage of the invisible in-visibility (I), bearing the full history and future of a communication in it.

 2. Demonstrative knowledge (II/III)

This second type of knowledge is much more imperfect than the intuitive knowledge. There is no immediate recognition, instead the mind had to proceed by reasoning (understood as an interchange of ideas). Some work has to be done, before results can be obtained.

Locke pointed out that the intermediate ideas had to be found and brought to agreement or disagreement, i.e. proof. Once this dynamic process was completed, it was called a demonstration. The method of intervening proofs did not deliver its certainty so easily as intuitive knowledge.

The dynamic development and use of ideas find – in a modern, quadralectic understanding – its basis in the Second Quadrant. The main cognitive setting of this quadrant is the invisible visibility. The primary division sparks off an intellectual action, characterized by the introduction of a value system. Locke’s demonstration is the outcome of such an active operation. It carries the initial (intuitive) ideas through the Second Quadrant into the Third Quadrant, where the visible visibility (or proof) is fabricated. The demonstrative knowledge (of Locke) covers therefore two quadrants.

  1. Sensitive knowledge (of particular existence) (IV)

This knowledge is again narrower, reaching no further than the existence of things actually present to our senses. Locke is not very clear on this type of knowledge, even to the extend of being evasive (pointing to sidelines of faith and opinion). The existence of ‘particular finite beings without us’ goes, in his view, beyond bare probability. However, he has no idea, as an oppositional thinker, how to imagine such a world-outside-ideas. There simply is no place for the effects of senses in relation to a real existence other than ‘ideas’.

The nature of sensitive knowledge is much more understandable in a quadralectic approach. Here a situation is visualized in which the senses have their own ‘ideas’ transferred to ‘knowledge’ in the second quarter of the Fourth Quadrant (IV, 2).

His conclusion that knowledge (IV) comes short of the reality of things (III) but even of the extent of our own ideas (II), is in line with his hierarchical view. The notion that knowledge is narrower than our ideas is, in essence, an assumption, based on the subjective preconception that ideas are the ‘highest’ contributors to a communication.

It is remarkable that Locke, despite his lack of a wider frame of mind, came close to many viewpoints of the quadralectic way of thinking. One may wonder about the connection between an in-depth two-fold study (like Locke did) and a proper four-fold approach (in a modern quadralectic analysis). They seem to come very close at a certain point, despite an a priori difference in initial division. Somewhere in the mind seems to be a cognitive bridge connecting a (double) duality with a (quadralectic) quaternity. Further psychological research will be necessary at this point.

His four degrees in reason (Book IV, Ch. 17), for instance, summarized near the end of the ‘Essay’, are just another indication of this curious tendency.

 1. First and highest is the discovering and finding of proofs;

  1. The regular and methodical disposition of them;
  1. Laying them in a clear and fit order to make their connection and force be plainly and easily perceived;
  1. The making of the right conclusion.

Proof – use – order – conclusion is a familiar sequence. Locke ended his book, rather conventionally, in a triple-division mood and conform to the basic oppositional ideas at the end of the seventeenth century (of the European cultural history). The three stages or ‘the first division of the objects of knowledge’ (Book IV, Ch. 21), in his view, are:

  1. The nature of things (as they are in themselves knowable);
  1. The actions to reach a goal (especially happiness) and
  1. The use of signs (in which knowledge can be attained).

These entities are the major constituencies of John Locke’s philosophy, or ‘the three great provinces of the intellectual world’. Locke’s frantic emphasis on ideas and the senses seemed to be a reflection of his need to bring the human understanding in areas of multiplicity (in a tetradic view identified as positions in the Second and Fourth Quadrant).

Locke’s contribution to the knowledge of an intellectual ‘language’ – used here as an expression for ways in which a communication is performed – was considerable. The links between an unwavering dualistic framework and a (partly unconscious?) understanding of the tetradic way of thinking are instructive in their own way.

The English philosopher will be left behind here, but the investigation into the development of an intellectual interaction (defined as a language) will be continued in his spirit. The actual mechanisms of a communication will be described in a rationalistic and comprehensive way. It implies that facts are primary rooted in an oppositional substratum and are transported from there into areas of greater expansion.

The dual way of thinking distinguishes two basic kinds of argument in a communication: the inductive and the deductive way. The former manner of reasoning (induction) is usually pictured as moving from the specific to the general (from one to many). A specific delineation – the one – is compared with other delineations – the many – in order to reach a conclusion based on similarities. The latter kind of reasoning (deduction) begins with the general and ends with the specific (from many to one). The observer compares the quantity – the many – with itself in order to deduct a generality – the one.

Inductive arguments are usually based on experience or observation and are comparisons between two or more sets of events, ideas or things. The importance of the comparison gave rise to the use of the name analogical argument as an equivalent expression of inductive reasoning. The strength of inductive arguments depends upon the genuine nature of the comparison between the particular and the items chosen from a generalization.

The major premise of deductive arguments is based on a rule, law, principle or generalization. A deductive argument can be expressed as a syllogism or as a conditional. Both forms deal with the same logic reasoning, but use another way to reach its conclusion. The technicalities of logic are here of no concern to us, but it is important to note that the deduction uses various methods to reach the same goal.

The difference between inductive and deductive of reasoning is mostly in the way the arguments are expressed. Any inductive argument can also be formulated in a deductive way, and vice versa. This reversal is a logic consequence of the oppositional environment (one versus many) in which the arguments were positioned in the first place.

The quadralectic mind – as may be expected – differentiates between four forms of argumentation. The wider view includes the above-mentioned pair of inductive-deductive reasoning, but is joined by two other operational means. The first addition, better known as trial-and-error reasoning, is a very basic form of argumentation. Certain elements are joined together without any preconceived ideas or intentions. The results can be weird and devoid of all common sense. The method is unsuitable, due to its volatile and transient nature, to be productive in a dualistic (or scientific) environment. It is, for this very reason, in the past largely neglected as a viable option for a logical sequence.

The second addendum, the analogical argument, is mentioned before as part of the inductive method. This amalgamation is a simplification born in lower division thinking. The use of analogies is instrumental in all types of argumentation, but also has a coordinating function on its own.

The four basic argumentations in a quadralectic communication are given here:

  1. The Trial-and-error method (TE):

Catching haphazard elements and join them together to some new form. No plan or fixed idea is used to select the individual elements, even the outline of these units is not considered. This form was never favored in scientific circles, because of its transcendental nature.

  1. The Inductive method (IN):

Using specifics to reach generalities. By choosing a distinct element and compare it with a multitude in order to find a general expression. This is a long established and respected scientific method, starting with the Pre-Socratici like Thales, Anaximander, Parmenides and Pythagoras. There is a distinct a priori element (the choice of a part) in this way of reasoning.

3. The Deductive method (DE):

Using generalities to reach specifics. Selection in a dynamic multitude will give a static limitation. The terms of certain laws or rules are compared with the multitude. It is considered the more advanced scientific method, already used by Aristotle and his followers. The nature of an a priori choice is hidden away behind the acceptance and use of the law or rule as a (temporary) truth.

4. The Analogy method (AN):

A combination of the previous methods with a special emphasis in the mechanism of the argumentation in the context of a language (the term language is used here as a summary of all the elements used in the data exchange between communication partners). Analogy is a tentative method. NORTH (1989, p. 285) said, in his essay on ‘Science and Analogy’: ‘Analogy is the basis for much scientific conjecture, but even conjecture is an art, which can be done rationally, that is, even though it might prove in the end to have yielded a false conclusion’.

These four ways of understanding fit in the context of multiple division thinking. Every mode of inquiry is connected with a particular quadrant. This implies – in a reciprocal way – also an indication of the position of the communicator when a specific method is used. The way of reasoning is a structural part of the communication as a whole (fig. 17).


Fig. 17 – This summary gives the four ways of argumentation and their relation to the various positions in a quadralectic communication. The type of action is an approximation of the movement in a particular quadrant.

The conclusion of the preliminary movements in the quadralectic field is faithful to its own starting-point: each division-component (quadrant) has its process (method), but also its own world of expression and typification. This conceptual step implies a move from the Second Quadrant (the process) to a Third Quadrant environment. A distinct form (of division thinking) can be narrowed down in this latter field to an opposition of unity versus plurality.

  1. Unity- and part-thinking, centered around the One (Unity), and

2.   Muun– and multiplicity thinking, centered around the Many (Plurality)

The term muun is introduced here as a neologism. The word is an amalgamation of the word multiplicity (mu) and unity (un). It wants to express the connection between these two items in a single, cognitive component.

The muun is a symbolic unity in multiplicity.

Its closest conceptual neighbor is perhaps the ‘Idea’, used in a Platonic sense. Plato was, despite his pioneering contemplative activities, never an accomplished four-fold thinker. This specific disposition came to the foreground in the interpretation of his beloved idea. Although a division-thinker by heart, he did not recognize the vital importance of the first division.

Examples of mind-constructions like value, category, abstraction, concept, attitude, stability, variable, mechanism, opinion, behavior, trust, power, freedom (and many more) are covered by the definition of a muun. These terms present themselves as a unity – and are used as such in a language – but they are composed of many different subunits. Their unity is symbolic.

A classification of the quadralectic system can be based on the previous qualifications. The various characteristics are placed in the quadrants in which they have their major field of influence (fig. 18).


Fig. 18 – A quadralectic scheme to indicate the environment of the various quadrant and the associated mind constructions and their representation.

This scheme should not be treated as a fixed entity but rater as a guideline to the dynamics of quadralectic thinking. This means that none of the entities mentioned in fig. 18 are limited to the positions as given above.

Creativeness plays an important part in the quadralectic epistemology as a criterion of visibility. The act of creation is, in a modern view, a movement from one (sub) quadrant into another. This conceptual transpose means, implicit, a change in the type of visibility. Creation as ‘making something’ (creativity) is closely related and interchangeable with ‘seeing something’ (visibility).

The Italian philosopher Giambattista Vico (1668 – 1744; fig. 19) communicated, early in the eighteenth century, the same relation between the origin and the actual appearance in his dictum verum et factumconvertuntur.


Fig. 19 – Giambatista Vico (1668 – 1744) – ‘a prophet without honor in his own country in his own day’ (BURKE, 1985) – proposed at the first quarter of the eighteenth century a ‘New Science’, based on a triple-division. The beginning of the twentieth century saw a revaluation of his ideas, starting with a footnote in Karl Marx ‘Das Kapital’ to a full reinstatement by the Italian philosopher Bernedetto Croce (1866 – 1952).

The verum-factum theory, as it became later known (MORRISON, 1978), stated that the Truth (of knowing) could only be reached in an act of making. ‘Vico’s doctrine required that one make, collect, order, or generally do something with (the elements of) a thing in order to know it’ (HENDERSON, 1985). Or, as Vico put it himself: ‘But in the night of thick darkness enveloping the earliest antiquity, so remote from ourselves, there shines the eternal and never failing light of a truth beyond all question: that the world of civil society has certainly been made by men, and that its principles are therefore to be found within the modifications of our own mind’ (Scienza Nuova, Book I, Section III).

Vico idea’s were fully developed in his book Scienza Nuova (1725/1744) or ‘Principles of a New Science concerning the Common Nature of the Nations…’ (BERGIN & FISCH, 1948/1968). He presented – at the age of fifty-seven – a universal historical model, his ‘New Science’, of which the three fundamental components were given in the title of the book: principles – nature – nations. These catchwords will be briefly mentioned here, in order to place the phenomenon of ‘creativity’ (as related to division) in a historic perspective.


Book 1 of the ‘New Science’ started with the establishment of principles. ‘We might expect that the term ‘principles’ should mean not merely the principles as such’, said Vico in his introduction, ‘but the science and the world of nations as constructed from those principles’. He mentioned Euclid’s Elements as an example, in which ‘we understand not merely the elements in the strict sense – that is the definitions, axioms and postulates – but the system of geometry constructed from those elements.’

Vico was full of great intentions. He was determined to place the traditional sciences, like history, law and philology, on the same footage as the new, analytical sciences, promoted by the philosopher René Descartes (1596 – 1650) in his ‘Discours de la méthode’ (1637).

There are three different types of ‘principles’ in Vico’s view. They are the building stones of his intellectual construction.

A. The principle of science. Any inquiry should start with a chronological table in which the materials are set in order (Book I, Section I). An example is provided in a folded chart based on the principle of the three ages (gods, heroes, men), which gives, in seven parallel columns, the chief events of Hebrew, Chaldean, Scythian (with only one entry), Phoenician, Egyptian, Greek, and Roman history, from the Universal Flood to the Second Punic War. The same seven-division is encountered (in Book II, Section I, Chapter II) in the corollaries (consequences) concerning the principal aspects of his ‘New Science’. It started with the divine providence and ended with the principles of universal history.

B. The principle of the elements (with axioms, definitions and postulates) was dealt with in Section II of Book I. In this passage he formally introduced his famous triple division of history. ‘Two great remnants of Egyptian antiquity have come down to us. One of them is that the Egyptians reduced all preceding world time to three ages; namely, the age of gods, the age of heroes, and the age of men. The other is that during these three ages three languages had been spoken, corresponding in order to the three aforesaid ages; namely, the hieroglyphic or sacred language, the symbolic or figurative (which is the heroic) language, and the epistolary or vulgar language of men employing conventional signs for communicating the common needs of their life.’ And finally,

C. The principle of the three primary institutions of religion, marriage and burial (Section III of Book I). These social foundations provide divine providence, moderation of the passions and the immortality of human souls. These institutions, upon all men agree and always have agreed, give us the universal and eternal principles. Vico saw the ‘terror of Jove’ (the wielder of the thunderbolt) as the instigator of frightful ideas of God. ‘The idea’, he said (Book II, Section III), ‘was of course not shaped by reasoning, for they were not yet capable of that, but by the senses, which, however false in the matter, were true enough in their form’. The god-fearing giants created a moral virtue from impulse by checking their bestial habits. They became the founders of the nations and the lords of the first commonwealths.

The introduction of marriage was ‘a chaste carnal union consummated under the fear of some divinity’. Vico rated the unbroken companionship of life very high as a stabilizing factor in human society. The solemn matrimony was a heritage of the innocence of the golden age observed in the first gentile nations.

‘Afterwards, the god-fearing giants, those settled in the mountains, must have become sensible of the stench from the corpses of their dead rotting on the ground near by, and must have begun to bury them.’ The universal belief in the immortality of human souls is the third basic principle in society.

 2.  Nature

Nature is, in Vico’s vision, the process of being born. The nature (natura) of nations is nothing but their birth (nascimento). ‘Whenever the time and guise are thus and so, such and not otherwise are the institutions that come into being’ (Book I, Section II). Vico offers here a very clean-cut definition of ‘visibility’ (in the modern sense): something is visible if it becomes visible.

The very beginning (of a nation) is characterized by the birth of a religion. Some wandering people, reduced to bestiality, were frightened by thunder and lightning and called for help to the gods. In the meantime, ‘the act of copulation and frightened copulating pairs in nearby caves’ resulted in the beginning of matrimony and of settled life. The institutions of religion and matrimony have a common birth.

The nature of peoples goes, according to Vico, through various (5) stages: first crude, then severe, then benign, then delicate, and finally dissolute. The human race first appears huge and grotesque (like the Cyclopes). Next are the proud and magnanimous men (like Achilles), then we have the valorous and just (like Aristides and Scipio Africanus or Alexander and Caesar). They were followed by tendencies of melancholy and reflectiveness (like Tiberius) and finally, the dissolute and shameless madmen take power (like Caligula, Nero and Domitian).

The stages are linked to different (6) forms of power distribution: the transfer from a family- to a city-state, an aristocratic commonwealth (based on families), popular liberty, the start of monarchies, the establishment of monarchies and finally, their overthrow.

This sequence seems a rather haphazard use of human virtues and vices, mainly following the Greek and Roman history as a guideline. However, Vico regarded these regional successions as ‘the principle of the ideal eternal history traversed in time by every nation in its rise, development, maturity, decline and fall’ (a five-division again).

Later on, Vico returned to the ‘three languages of the Egyptians’ and the triple division of a divine, heroic and human nature (Book II, Section II, Chapter III). His emphasis on a ‘language’ as the symbol of communication was widely appreciated in the early decennia of the twentieth centuries by linguists such as Noam Chomsky.

The first language was the language of the gods. It consisted of the first true hieroglyphs, or sacred or divine characters. Vico saw the Divine Providence as the founder of the commonwealth and so the true God instituted the natural law of the gentes.

Secondly, the heroes founded the heroic or poetic language. They used symbols and symbolic emblems as a kind of speech. ‘They must have been metaphors, images, similitudes or comparisons, which, having passed into articulate speech, supplied all the resources of poetic expression.’ The nature of the politics in the heroic age was basic indeed.

The effective power had nothing to do with the refined ideas of the philosophers about ‘people’, ‘king’ and ‘liberty’, as they were associated with (later) plebeian, monarchistic and popular institutions. On the contrary: Achilles, ‘the greatest of the Greek heroes’, did not have any respect of the dead. He (Achilles) was quite clear to his opponent Hector: ‘If I kill you, I shall drag you naked, bound by my chariot, three days around the walls of Troy and finally I shall give your body to my hunting dogs to eat’.

Thirdly, there was – in the age of men – the epistolary speech of the Egyptians, which was suitable for expressing the needs of everyday life. ‘This language must be understood as having sprung up by their free consent, by this eternal property, that vulgar speech and writing are a right of the people’. And Vico continued: ‘The vulgar languages were introduced by the vulgar, who were the plebs of the heroic people.’ They were not fixed by convention, but must have had natural significations. ‘In general metaphor makes up the great body of the language among all nations.’

3. Nations

Vico stated that doctrines or theories must begin where the matters they treat begin. A nation is etymologically a birth or a being born, being characterized by a common language. Vico did not have a modern national state in mind and made no reference to a particular political institution. However, three conditions must – ideally – be met in order to qualify as a nation:

  1. it is a system of institution

 2. a nation is isolated from other nations

 3. the institutions are continually changing due to internal stresses

These major entities can be reduced to the ultimate constituents of Vico’s thoughts: a unity – a boundary (limitation) – and a change (movement). Vico aimed, in a modern view, to identify a communication unit within a large civil world. ‘The world of nations’ (il mondo delle nazioni) must be understood as a collection of visibilities within a Greek kosmos or a Latin mundus.

The last part of his book (of the New Science) was devoted to ‘the course the nations run’. Vico started in the introduction with a recapitulation of the main (four)-division of its contents: Book I is concerned with the principles. Book II investigated the origin of all the divine and human institutions. Book III discovered the poems of Homer as the treasure stores of the natural law of the gentes of Greece’. Finally, Book IV follows the course of the nations, ’again in constant uniformity upon the division of the three ages which the Egyptians said had elapsed before them in their world, namely, the successive ages of gods, heroes, and men.’

Giambattista Vico concluded his book with eleven triadic entities. There are, in his view, three kinds of natures (divine, heroic, human), customs (religion/ piety, choleric/punctilious, dutiful/civil duty) and natural law. Furthermore, he recognized three governments, three languages and three characters (divine hieroglyphics, imaginative universals, vulgar words). They were followed by a three division of jurisprudence, authority, reason, judgements, and three sects of times (religious, punctilious, civil).

It is clear, from this list of examples, that Vico approach to creativity was based on a (numerical) three-fold division. This type of division is characterized by a dynamic component. There is an element of play between two opposites and their middle part. Thoughts can go back-and-fro and a ‘heroic’ compromise can be found. ‘Knowing for Vico is never passive but always requires some creative activity of the knower’ (HENDERSON, 1985). Only what is made can be seen: it is a world view that still holds it values, because – in a way – it is true (from the human perspective). But the picture changes in a move away from the anthropocentric perception. It is only in the four-fold way of thinking that (human) creativity gets a new meaning, as part of a new visibility.

A creation can be defined, in a modern approach, as a border-crossing event within a communication cycle. Creativity, as a move from one (sub)division of a quadrant into another, is not only a form of ‘making’ (like it was in Vico’s drift towards the Third Quadrant). In the quadralectic view, it might include a ‘not-making’, and a move into an environment of lesser visibility (like the First Quadrant). Four-fold thinking provides, in the end – which is also a beginning (T.S. Eliot) – a greater freedom of conceptual interpretation.  

4. Modern knowledge and new names

The tetradic way of thinking is probably just as old as mankind itself. Signs on the wall of the cave of Lascaux in Southern France, drawn by Stone Age people some fifteen thousand years ago, show the combination of circles and crosses. This universal graphic symbolism points to a four-fold division of space, which can only be visualized if there is also a mental division at the same time.

This historic setting seems logic: the individual development of man – starting with birth and growth and ending with old age and death – is a re-enactment of the development of mankind as a whole. BRONOWSKI (1973/1977) sketched in his book ‘The Ascent of Man’ a picture of man as a unique animal climbing to the top of its intellectual capacities. The title was a direct reference to Darwin’s book, which was written a century earlier and was called ‘The Descent of Man’ (1871).

Both titles (and evolutionary intentions) carry the linear thought within them. Darwin’s ideas could be interpreted as an effort to pull man down from its statue at the pinnacle of creation. He proposed a decendency of mankind from the apes. Bronowski put the human race back again on the ladder of creation, culminating in a gigantic knowledge about the universe, the world and ultimately, itself.

The long journey from the forming of amino acids towards the proteins, the configuration of the four fundamental constituents into the genetic alphabet (of DNA) led eventually to the origin of life. The self-copying molecules differentiated in ever more complex forms. Hundred of millions of years ago life forms left the seas and settled on land, either in a rather stationary way as plants or in a more dynamic way as burrowing, crawling, walking or flying creatures known as animals.

It was the enormous variety of nature and the richness (of species) which puts Charles Darwin (1809 – 1882) and Alfred Wallace (1823 – 1913) on the trail of discovering the theory of evolution by natural selection. They found the key to their discovery in many field observations and the notion that the environment (geography) played a major part in the distribution of the species. Both naturalists were equipped with a new sense of multitude thinking, which could envisage the local setting of nature in a much wider context.

Darwin observed on the Galapagos Island and Wallace in the Amazon Basin and the Malay Archipelago (Borneo) that isolation, due to geographical circumstances and geological changes in time, led to a differentiation of species. Wallace drew (in 1855) the conclusion that new species arose from related, pre-existing species. Darwin wrote a ‘Sketch’ (in 1842, two years later retitled ‘Essay’) on natural selection.


Coast of Bako National Park, Serawak (N. Borneo). The ‘Sleeping Lady’ in the back ground was the peninsula where Wallace did part of his studies (on evolution) (Photo: Marten Kuilman, November 2013)


Leaping Blenny – Bako National Park – Serawak (N. Borneo). The Leaping Blenny or Alticus saliens is a saltwater fish. It gets its name from the ability to jump from place to place, outside of water. Animals like these might have inspired Wallace in his ideas about evolution (Photo: Marten Kuilman, November 2013).

The most important result of their investigations – and the subsequent popularity of their conclusions – was the return of dynamism in thinking. The visibilities of the Third Quadrant (observations) became flexible and people came to realize that a particular fragment of nature (in time and place) was not immovable, but was part of a development.

The understanding was gained that any presence in the world (including our own) is a matter of time and place and is part of a sequence of events, which are determined by the principles of visibility. The cries and joys of the early existence are followed by the first conscious experience of an outside world. Than the process of division can start to distinguish and order the outlines and features of the environment. This process starts, again, in an unconscious environment, but will develop into real visibility and an understanding of its creation. Finally, the new understanding of visibility will be celebrated and extended into all realms of life.

The present study tries to follow the implementation of the four-fold way of thinking in our personal life, the world-as-a-whole and the existence of the universe. This seems ambitious and maybe far-fetched, but it is just the consequence of a line of thinking. A complete novel world will open on the very moment we are able to comprehend the importance of higher division thinking as a means to enrich a communication. So why not follow this line of thinking into an unknown and uncharted territory?

The guided tour follows a trail, which has a close resemblance to the way of thinking itself. It aims at a familiarization with the landscape and gives an introduction to innovative terms. The exploration into the unknown will give us a variety of views, both in the country behind us (called: history) and towards a distant horizon (better known as: future). However, those are only two directions in a linear fashion. The new vision aims at all directions and includes the ground we are standing on and the sky above us. None of these four outlooks will be rated higher than another. There is in the four-fold way of thinking no hierarchical position. The past is of no more importance than the future or visa versa, and the universe might be overwhelming, but is still of the same class as the earth beneath us.

Sometimes knowledge has to find new terms to express itself. The discovery of an original set of references poses basic problems in terms of communication. Words have to be developed to catch the intentions of hitherto unknown meanings. Often the new discoveries might sound like a modern gnostic belief. The use of the term ‘invisible invisibility’, for instance, will sound as a tautology to a person, who is still trapped in oppositional thinking. And the term ‘communication factor’, abbreviated to a cryptic CF, does not mean much for someone, who is not introduced in the theory of quadralectic unification.

Hopefully, these, and other, terms will come to live during the acquaintance with the rich and colorful world of tetradic (quadralectic) thinking. The course will be run in an educational spirit. That means a repetition of the major themes at certain intervals, with a recapitulation at the end (Chapter 4.5). A shortcut to the practical side of quadralectic thinking – for those readers who are not interested in a theoretical background (which is quite excusable) – can be made to Chapter 5. A glance at the Universal Communication Sequence (UCS) in fig. 44 and the names of the inflection points of the CF-graph (in fig. 50) is then recommended to follow the line of reasoning.

A glossary with definitions and descriptions of various quadralectic terms is added at the end of this book to facilitate the understanding of the (new) names.

4.1. The First Quadrant (I)

The ultimate unity

Every communication goes through a stage of unity, even if it is not realized at that particular point in time. This is the terrain of the Greek philosopher Parmenides of Elea, who lived from around 490 – 430 BC. He argued that all existence is one, eternal and unchanging. Or, to put it shortly: What is, is. And can be nothing else. There is no existence of what is not. To imagine an empty space, either inside or outside the world destroys the unity of the One.

The universe is, in his view, a plenum, in rest with itself. Plato noticed later, that Parmenides’ world had no place in which to move. Change, as a logical consequence, is only a confusion of the senses and fictitious. The appearances of motion and time are illusions.

Parmenides was right from the point of view of the First Quadrant, because the ultimate unity of the First Quadrant (I) is ‘before’ anything else. There is no mentioning of the word ‘being’ in the work of Parmenides. He avoided the term ‘god’, because both entities point to preconceived ideas. The imaginable and the possible are equivalent in the First Quadrant. Parmenides’ expression that ‘what is, is’ (fragment 6) is right if we are able to position ourselves in the complete emptiness before a division.

However, it is important to remember that the First Quadrant is also the only place where such a statement holds true. Because the very moment a division is introduced into the (proto) communication, nothing is the same again. From that moment on, all sense data and explanations depend on the choice of division and the valuation accordingly. Much of the critique on Parmenides, of which Aristotle in his ‘Physika’ made a strong contribution, failed to distinguish between the (hypothetical) position of an observer in a communication before and after a division had taken place.

The First Quadrant (I) is the place of intuitive awareness, a walk behind the bounds of reason. We do not need an apprehension of all the complexities, because the understanding only arrives after the establishment of the limits. At this primordial phase, the communication is ambient, a keyword of the First Quadrant. Any formulation of whatever signal is received can only be a reconstruction from another quadrant, after the division-decision has been taken. This important aspect has given rise to the establishment of world religions, and many philosophers searched for new constructions in order to grasp the nature of the invisible invisibility in one way or another.

Aristotle described the potentiality of the ambient primordial state as the first of his four enteleichia (causes). He reduced all actions to four kinds of causes (fig. 20):

 ——  Final

——  Formal

——  Material

—— Efficient

The order of movement is, according to Aristotle, determined by the order of causes, which in turn depend on the place and function of each part in the whole. The telos is the expression for a superimposed movement towards the first and final cause (1). All (other) causes tend to move to and are derived from this essential state within a communication.


Fig. 20 – The four entelechia (or causes) of Aristotle are placed here in a quadralectic setting. The interpretation points to the intrinsic nature and actual ‘character’ of a specific quadrant.

The words energeia and entelecheia, which were coined by Aristotle, did not exist before his time (BLAIR, 1967). They are both related to the ‘act’ in the theory of potency (and therefore directly relevant to the First Quadrant of the quadralectic philosophy). Aristotle was the first one to ‘see’ them and needed a neologism to describe them. He used the term energeia five times more than the term enteleichia, the latter in particular in Book III and IV of the ‘Physics’ and ‘De Anima’.

Energeia points to the actual act (to do) without a reference to change. It has to be positioned in a ‘First Quadrant’ (I), in the static and fundamental part of the invisible invisibility. Motion and subsequent transition do not belong here.

Entelecheia has the meaning of ‘to be at an end’ or ‘to complete’. As such it has a richer flavor than the energeia. The field is more open, there is a view (with an end). The conception has to be placed in ‘first quarter’ of the Second Quadrant (II, 1), with its own dynamism and realization of division.

The philosopher Immanuel Kant (1724 – 1804), doggedly in search of the roots of understanding, called the first state of experience the unity of apperception. He pointed in his book ‘Kritik der reinen Vernunft’ (Critique of Pure Reason, 1781) – an unequaled study of the basic conditions and boundaries of human experience, but not recommended for light reading – to the ‘a priori’ character of cognition. By doing so, Kant paved the way to the intuitive character of the First Quadrant (in contrast to the rationalistic arguments of the Third Quadrant). He saw the ‘all’ as a preliminary step towards finding out what is (HINTON, 1904).

Kant insisted – in his ‘Kritik der Urteilskraft’ (Critique of Judgment, 1790) – that a study of the categories of mechanistic causality, which was used in the nonliving reality, could do no justice to the activities of the living realm. Human judgment was forced, in his view, to postulate an additional principle of teleological causality which Kant called ‘natural purpose’ (Naturzwecke). This ‘natural purpose’ was just a rebirth of the first quarter of the old Aristotelian entelechia tetrad. Then – within a familiar oppositional framework – the teleological judgment (of a ‘godly’ nature) was placed against an aesthetic judgment (of ‘human’ proportions). To understand such a duality it helped a great deal if the division framework – just as in Aristotle’s case – was extended to a higher type of division-thinking (like the four-fold variety).


Table with the catagories of Kant. In: KARBUSICKY, Vladimir (1990). Kosmos – Mensch – Musik. Strukturalistische Anthropologie des Musikalischen. Dr. R. Kramer, Hamburg. ISBN 3-926952-23-7

Johann Wolfgang von Goethe (1749 – 1832) was probably the most prominent of the early thinkers, who picked up this dynamic duality and used it as an antidote to the fragmentation of Newton’s universe. He saw the one-division as a distinct option: ‘A living being takes part in the Infinite (the all-encompassing Whole) and has something of infinity within itself’. His aesthetic-teleological vision of living nature became a fertile ground for later thinkers and scientists, who had an inkling of wider forms of division thinking and wanted to escape the tight bonds of the causal-mechanistic model of understanding.

When Kant died in 1804, the European consciousness was ready to throw off the oppressive bonds of oppositional (or dialectic) thinking and could accept a wider frame of mind. If Ramon Lull, in the early thirteenth century, was the first of the dualistic philosophers, than Immanuel Kant, some six hundred years later, was the last one.

The new era of understanding – and the booming of the scientific research – started when the insight dawned that the a priori element of reasoning – which still has a ring of a duality between ‘before and after’ – should be extended to the ambient. This small change in gradation is, in hindsight, an intellectual eye-opener of gigantic proportions.

Kant’s breakthrough to higher division thinking was the notion that any rational investigation must be based on the hypothesis of a random consciousness. In other words: there should be a distinct place without limits within the rationalistic cognitive framework. This assumption was fully understood by Charles Darwin, who applied the principle of randomness to the origin of species. He assumed an indefinite variability within the narrow limits of consecutive variations. The leading principle, however, was the supposition that any structure or organized being possessed features of permanence.

These postulates, the Kantian unity of apperception and the Darwinian features of permanence, were the important outcome of the new understanding. The great intellectual development of the nineteenth century in Europe became only possible after the creation of a conceptual space to accommodate the unlimited.

Contemporaneity and infinity are two distinct characteristics of the First Quadrant. The first concept points to a situation in which the division of time is eliminated (for the time being). The second state (infinity) has abandoned the influence of both the divisions of time and place. This state of non-division is hard to imagine, because our imagination is geared to think in terms of separation and division in order to ‘see’ and make it substantial. The world seems an empty place without subject matter.

The various vistas with regard to the status of the First Quadrant should be distinguished clearly. An observation (by an arbitrary observer) is always situated in a particular environment, which belongs to a chosen division. Any statement of the observer reflects that position. The name ‘First Quadrant’ is, in this respect, much clearer than many of its predecessors like monad, absolute, holon, enigma or rhizome. They aim at unity, but do not state their division environment.

The description of Unity in a four-division setting implies that the observer disposes of four positions to look at the ultimate limitation. A position in the First Quadrant (I, before any division) is fundamentally different from a location in the Second Quadrant (II, after a division is established). This latter position is, in turn, different from the ‘empirical’ view of the Third Quadrant (III). The Third Quadrant gives a temporary solution to limitation of the Unity in a binary framework. The Fourth Quadrant is different again. The insight dawns here that Unity is a form of expression, which leads to a precursory state of undividedness.

The position of an observer towards the unity of the First Quadrant is now looked at in more detail. A historical advocate of each example is given.



4.1.1. Teilhard de Chardin (1881 – 1955)

A View from the First Quadrant (I) to the First Quadrant (I)

We have seen that the wisdom of Parmenides (What is, is) and the consequences of that vision are part of a position situated in the First Quadrant. This location and the subsequent observations are of the utmost importance for the whole bearing of the communication. It provides the scope and intentions of all interactions: geared towards a unity without boundaries. A modern representative of the idea of ‘unity thinking’ is the French Jesuit priest and paleontologist Teilhard de Chardin (1881 – 1955). He tried to integrate the religious experience with natural science by taking a ‘First Quadrant’ stance towards the world. Mankind was heading, in his view, to a convergence of systems, the Omega point.

Teilhard2Teilhard de Chardin proposed a new level of consciousness, which was called – with a neologism – the noosphere, a planetary thinking network. Human lives were, in his view, at their deepest being connected in a global communication system. Exchange of knowledge and co-operative research would result in a gathering of collective minds, with the opportunity of instantaneous feed-back and eventually leading to a world in harmony. Jennifer Cobb Kreisberg noted in 1995 that such a state was more or less reached in the Internet, with its worldwide electronic web encircling the earth. ‘Teilhard saw the Net coming more than half a century before it arrived. He believed this vast thinking membrane would ultimately coalesce into “the living unity of a single tissue” containing our collective thoughts and experiences’ (KREISBERG, 1995).

Teilhard’s work was an effort to integrate the basic Christian doctrines with science and, reciprocally, to see science from the viewpoint of faith. Such an approach puts his thoughts in the eternal struggle between science and religion, which is – in essence – a dualistic disposition. There are, in fact, numerous indications in the work of Teilhard de Chardin to bring this dual aspect to the forefront. The following passage from his book ‘The Divine Milieu’ (The Divine Ambience), written during his stay in northern China (in 1927), indicates that he had not thrown off ‘the old static dualism’ completely:

‘All around us, to right and left, in front and behind, above and below, we have only to go a little beyond the frontier of sensible appearances in order to see the divine welling up and showing through. But it is only close to us, in front of us, that the divine presence has revealed itself. It has sprung up universally, and we find ourselves so surrounded and transfixed by it, that there is no room left to fall down and adore it, even within ourselves.’

The sharp critique of British biologist and Nobel laureate Peter MEDAWAR (1915 – 1987) on ‘The Phenomenon of Man’ (1961) aimed predominantly at the extreme elements and ‘nothing-buttery’ in Teilhard’s style. In addition, the concept of consciousness and the nature of directional evolution (towards a higher cerebralisation) comes under attack.

Teilhard’s suggestion that evolution has a direction (to a ‘higher’ goal) is, indeed, a sign of lower division thinking. On the other hand, his idea that the human conscience is shaped as a specific result of an organized complexity is a viable working hypothesis. His sketch of a ‘global vision of the universe wherein matter and spirit, body and soul, nature and super-nature, science and faith find their unity in Christ’ might not be scientific, but it is – at the least – a stimulating concept.

Teilhard de Chardin envisaged the Ultimate Unity (UU) – or Omega – as a place to accommodate the opposites. The Terminal Point of Evolution acts in the same way as the medieval mystic and scientific thinker Nicolas of Cusa (1401 – 1464) did in his book ‘De docta ignorantia’: opposites are whisked away and simply denied in one-division thinking.

The chapters of his book ‘Le Phénomène Humain’ (‘The Phenomenon of Man’; written between 1938 and 1940 and published posthumously in 1955) follow a four partition: Pre-Life – Life – Thought – Survival. The foreword (p. 31) set the tone by stating that Man, as a twofold centre of the world, holds the key to the universe. The first emphasis is put on the nature and importance of seeing. It was probably this human-centered outlook, which annoyed the Roman Catholic Church. The Roman authorities prohibited the publication of his later work. What was wrong with the idea of evolution in the light of the Scriptures? It seems that the Catholic Church feared a clash of interest between the (Teilhard-invented) Point Omega and a (Church-invented) God. A quadralectic interpretation suggests a humane power struggle of the possession (and subsequent exploitation) of the invisible invisibility.

Book I: Before life came

The elemental matter – the stuff of the universe – shows three faces: plurality, unity and energy. They can be regarded respectively as a system, a totum (or whole) and a quantum (taken its full significance in duration). The transit to life (following the qualitative laws of growth) is ruled by oppositions, like the within (the psychic) and without (the material side) of things. Two types of energies, material and spiritual, are defined as tangential (linking elements) and radial (to a greater complexity, forwards). The earth is partitioned in a crystallizing world (of minerals) and a polymerizing sphere (of additive complexification) leading to organic compounds.

Book II: Life

The transit to life and the initial manifestations of life cannot be pinpointed at a particular fixed time. Somewhere a critical point of germination is reached and a cellular revolution (on an external/tangential/biological and an internal/radial/psychic level) could take place. The process is one of pluralisation in form as well as in number. A tree of life begins to grow and with it, a rise of consciousness occurs.

Book III: Thought

The ability to think resulted in man to reflection, the power acquired by a consciousness to turn in upon itself, to know that one knows. The birth of thought, like that of life, presents itself as a discontinuity in continuity, as a mutation from zero to everything. The new concepts of noogenesis (development of the mind) and the noosphere (a ‘thinking layer’) are introduced to describe the process of hominisation and civilization. The noosphere was described by Teilhard de Chardin in ‘La Vision du Passé’ (1925, p. 92) as: ‘une sphere de la reflexion, de l’invention consciente, de l’union sentie des ames‘. In ‘The Phenomenon of Man’ (1955) he called it ‘a layer or membrane on the earth’s surface, a thinking layer superposed on the living layer of the biosphere and the lifeless layer of inorganic material, the lithosphere’.

Book IV: Survival

The fourth book of ‘Le Phénomène Humain’is divided in three chapters. Firstly, we are confronted with the ‘Collective Issue’. Next is the hyper-personal positioned beyond the Collective. And finally, there is the Ultimate Earth. The mega-synthesis is, according to Teilhard, the result of a natural confluence of all grains of thought. The rise of consciousness leads to a new union of mankind or ‘planetisation’. As a result it can be observed that the domain of psychical expansion ‘is staring us in the face if we would only raise our heads to look at it’ (p. 253).

Teilhard communicated in his book a great vision, with a large degree of certainty: ‘There is now incontrovertible evidence that mankind has just entered the greatest period of change the world has ever known… The task before us now, if we would not perish, is to build the Earth’.

We will see, throughout the quadralectic philosophy, that this quotation of Teilhard is an overstatement. The reflection on the position on Earth – both as individual and as mankind – should be more humble. Chapter 6.2.3 of the present book charts the relation between Man and Planet Earth and comes to conclusions, which do not confirm Teilhard’s perception of mankind.


The CF-graph of the life of Teilhard de Chardin. The period of his visible visibility (1881 – 1955) is compared to the main periods in the Egyptian cultural history.

1. Archaïsche periode 3100 – 2600 v.C.

2. Oude Rijk 2600 – 2100 v.C.

3. Eerste Tussenperiode 2100 – 2000 v.C.

4. Midden Rijk 2000 – 1600 v.C.

5. Tweede Tussenperiode 1600 – 1500 v.C.

6. Nieuwe Rijk 1500 – 1000 v.C.

7. Late Tijd 1000 – 525 v.C

p. 228 in: Leerboek van de quadralektiek – Marten Kuilman (1990)


The CF-values of the visible life of Teilhard de Chardin (X) (1881 – 1955).

4.1.2. Carl Gustav Jung (1875 – 1961)

A view from the Second Quadrant (II) to the First Quadrant (I)

The Swiss psychiatrist and psychologist Carl Gustav Jung (1875 – 1961) is one (of the many) representatives of the thinkers who approached the First Quadrant from a Second Quadrant point of view. The most famous of his predecessors was perhaps Plato, who introduced his ‘Idea(s)’ as the archetypal representation of the (lost) unity. Since then the idea got many different names, but the process and meaning were always the same: a decision about the division was taken and the totality (of the previous First Quadrant) had to be construed from the new cognitive setting.

The question in such a cerebral operation should always be: which division was taken in the first place? Often the philosophers and researchers are not clear on their initial position and Jung is no exception to this rule. A strong line of oppositional thinking is traceable throughout his work, but the interest for the modern times lies in his distinct attention to the four-fold division as well. The idea of such a division – the actual choice – lies in the Second Quadrant and is projected on to the First Quadrant.

Jung’s interest in the alchemy might be a first indication of his sympathy in the direction of multiple division thinking. The prime object of alchemy has been the transformation of the (four) elements fire, air, earth and water. The alchemists were only able to think along these lines, because the relation between the elements (the pluriformity) was placed in the context of an Unus Mundus (the uniformity).

Alchemy, in its wide fields of study, might be a remnant of a practical form of higher division thinking. The so-called ‘mystical’ aspects were a representation of the belief in an area of invisible invisibility (which is now identified as the First Quadrant). The magician operated with his (magic) thoughts in the Second Quadrant. The alchemist, laboring with the actual chemical operations, made his observations in a Third Quadrant world. The final stage in this abstract process is the impossibility to see the woods from the trees. Feelings can be lost in a Fourth Quadrant.

Jung, although intrigued by division as such, was not always clear about his initial choices. He noticed, in his convincing psychological observations, an opposition between the ‘extravertierten’ and the ‘introvertierte’ personalities and also between ‘rationalen’ and ‘irrationalen Typen’. That is unadulterated dualistic thinking. Unfortunately, Jung does not identify his thoughts as belonging to any particular type of division. He passed straight from the obvious contraries (polarities) into a four-division of psychological types (JUNG, 1921/1967; RAZENBERG, 2000). By doing so, he gave the impression that his four-fold typology was born in a numerological context, rather than being the result of a particular type of division thinking.

‘Why did I choose the four types of basic functions is hard to say and there is no a priori reason of it, only to suggest that this view has been formed in the course of a years-long experience’ (JUNG (1921/1967, p. 470).

He stated, in this formal declaration, that the use of feelings in a practical setting – also known as experience – was the reason for the choice of (this particular) division. In other words: his (division) decision was taken in a ‘Fourth Division’ environment and was not chosen as a conscious act in the ‘Second Quadrant’.

The typology of the four basic types of persons is, nevertheless, of direct interest to the present quadralectic way of thinking, despite the possible flaw in its genetic history. The four groups of personalities – or psychological types – based on a kind of obscure data gathering (experience) – fit in with the interpretation of the cognitive situations in the quadralectic subdivisions (or quadrants):

——————— I. intuition —————— (Intuition)

——————— II. thoughts  ————— (Denken)

——————— III. reality   —————– (Empfinden)

——————— IV. feelings  —————- (Fühlen)

Every person can be classified, in Jung’s view, according to one of these four basic types and the outcome determines the way of ‘seeing the world’ and experience reality (leading to the notion of the Self).

1) Some people base their decisions on intuition, a rather enigmatic realm of the human mind, seemingly without clear rules or predictable lines of thought. The outcome of their actions has reminiscence to the trial and error-method, because there is no apparent logical scheme in the operational method. A distinct contemplative element is present, aiming at a wide (preferably infinite) field of operation.

2) Other people construct a mental picture (thoughts) from a given thought or idea and proceed from this focus point to a comparison with the multitude by means of induction. The ensuing world of general ideas is a storehouse for further action and creates the impression of a non-biased, rational foundation. Limitations and (preliminary) boundaries in the emerging communication will be accepted in order to pursue an effective and analytic research and come to certain conclusions.

3) The third type of personality uses a given, empirical reality to deduct an argument for action. The olfactory, visible or tactile experience of a material substance – which can be anything from the smell of roses to the metallic sound of a money-spewing slot machine – has a directional function in the decision taking process. Delimitation is of prime interest in this approach, and pragmatism is the name of the game.

4) Finally, there are human beings that operate according to the outcome of their feelings. The analogy is used to compare personal experiences. Feelings differ from ‘objective’ ideas in their explicit subjective nature. The boundaries are often difficult to determine in increasing multiplicity.

These distinctions of the human mind recall the same approach by the Greek philosopher Empedocles (fifth-century BC) and his division of the physical nature in four immutable elements or roots (fire, air, earth and water) (KINGSLEY,1994). The concept was used again in the application of the temperaments. All four elements (and temperaments) are present all the time, but some are more present than others. The ‘type’ is determined by the greatest visibility of one of the subdivisions at a given time.

Kees Razenberg (2000), in an interpretation of Jung, regarded the Self (with its symbolism of the circle, the quaternity and the cross) in a state of balance between the four basic functions of consciousness. The Ego reflects a state of imbalance ‘in the sense that certain functions dominate at the cost of other functions.’ The Ego (as Third Quadrant entity) and the Self (as a representation of the unity the First Quadrant) find their bond in the basic functions, leading to the fifth element (the quintessence).

Another important concept in relation to the First Quadrant (as seen from the Second Quadrant) is the process of synchronicity or ‘meaningful coincidence’. Jung developed this idea around 1920 after his contact with Einstein and study of the ‘I Ching’ (HAMAKER-ZONTAG, 1976/2000). The word was coined in Jung’s publication ‘Synchronizität als ein Prinzip akausaler Zusammenhänge’ (in: JUNG & PAULI, 1971). The term indicates the coincidence in time of two or more non-causal events that have a similar intention and meaning. A curious book by Paul KAMMERER (1919), called ‘Das Gesetz der Serie’, was published about that same time and its appearance fits into the very definition of the word synchronicity. Kammerer called the phenomenon ‘seriality’ and described many amazing events and weird coincidences.







Attraction (A) and repulsion (R) as working parameters of synchronicity given by the German naturalist Paul Kammerer.

In: KAMMERER, Paul (1939). Das Gesetz der Serie. Eine Lehre von den Wiederholungen im Lebens- und im Weltgeschehen. Deutsche Verlagsanstalt Stuttgart und Berlin.


The Dutch psychologist Jan Hendrik VAN DEN BERG elaborated on the theme of the contemporaneity (synchronicity) of historical phenomena. His interest came as part of a theory of changes, which he called – with a neologism – the metabletic method. The book on this subject ‘Metabletica of leer der veranderingen’ was translated as ‘The Changing Nature of Man’, and appeared in 1956.

Van den Berg took ‘contemporaneity’ (as a First Quadrant-feature of unity and eternity) out of its context and placed it in the Second Quadrant (of multiplicity and actuality). His basic statement is that there is always some sort of connection between (historic) events, which occur simultaneously.

The metabletic method consisted of four stages. Firstly, the notion of the change. Secondly, the moment of its first appearance, which has to be traced. Time has obliterated or diffused the actual change in thought, but an epoch-making book or event often remains as a visible trace. The choice of this book (the third step) holds the key to deeper understanding. The fourth and final action is a study of the effects of the noted change followed in time. These steps in the ‘metabletic approach’ fit in with the quadralectic approach.

Van den Berg (1963) described examples of the metabletic approach. He noted, for instance, the growing importance of the (two) division as a leading mental feature in the early eighteenth century. The year 1740 was boldly labeled as ‘the Year of the Division’. The key-books to give an insight in the new sense of division were, according to van den Berg, David Hume’s ‘A Treatise of Human Nature’ (1739) and Samuel Richardson’s ‘Pamela or Virtue Rewarded’ (1740).

Three events were singled out by VAN DEN BERG (1963) to show the importance of division and polarity in the first half of the eighteenth century:

1. The discovery of two types of electricity (vitreous and resinous) by Charles Francois du Fay (1698 – 1739). He was the superintendent of the gardens of the king of France and discovered that rubbing two different objects together produced two types of electric charge. Matter contained two types of fluid, in his view, which were normally in exact balance. This equilibrium was disturbed when two bodies were rubbed together.

The dual character of electricity (positive and negative) has never been challenged since its introduction in the eighteenth century, although there is a strong ‘philosophical’ component in its existence. It is possible, from the quadralectic point of view, to regard the dualistic electrical properties of attraction and repulsion as the result of an internal shift of particles of a higher division order, rather than of ‘charged’ particles (protons and ions), as seen in modern physics. It is a challenging thought to explain the intensio (attraction) and remissio (repulsion) which originate in the atomic model in terms of a dynamic shift in stead of an electrical charge.

2. An attack on the fifth theorem of Euclid by Giovanni Girolamo Saccheri (1667 – 1733), which resulted (later) in a non-Euclidean geometry. Saccheri was a professor of philosophy in Turin and taught mathematics at the University of Pavia (1697). Euclid assumed – around 300 BC in his book ‘The Elements’ – that straight lines were infinite, and parallel lines never meet. The crossing of an infinite straight line with two parallel (infinite) straight lines, as in Euclid’s fifth postulate, gave a conflict of understanding. Saccheri sensed that problem (of two infinities) and worked on its solution. The quadrilateral (fig. 21) was used for better comprehension.


Fig. 21 – A drawing of the Saccheri quadrilateral to explain the problem of Euclid’s fifth postulate. The Saccheri quadrilateral has equal summit angles at D and C. Giovanni Girolamo Saccheri (1667 – 1733) was a professor of philosophy in Turin and taught mathematics at the University of Pavia (1697). Euclid assumed – around 300 BC in his book The Elements – that straight lines were infinite, and parallel lines never meet. The crossing of an infinite straight line with two other parallel (infinite) straight lines, as in Euclid’s fifth postulate, gave a conflict of understanding. Saccheri sensed that problem (of two infinities) and worked on its solution. GREENBERG, Marvin J. (1972/74). Euclidean and Non-Euclidean Geometries. Development and History. W.H. Freeman & Co,. San Francisco.

Saccheri considered a number of non-Euclidean theorems without completely realizing the revolutionary nature of his investigations. ‘It was as if a man had discovered a rare diamond, but, unable to believe what he saw, announced it was glass’ (GREENBERG, 1972).

The non-Euclidean geometry gained momentum in the early nineteenth century. Carl Friedrich Gauss (1777 – 1855) studied the fifth postulate, but never published, because he disliked controversy (with the Kantian spirit of the time that Euclidean geometry was the inevitable necessity of thought). The Transylvanian-born Jonos Bolyai (1802 – 1860) was on the same mathematical track as Gauss. He wrote to his mathematician father Farkas Bolyai in 1823, that ‘I have discovered things so wonderful that I was astounded …out of nothing I have created a strange new world.’

Bolyai prepared, between 1820 and 1823, a treatise on the complete system of non-Euclidean geometry, but he discovered even before publication that Gauss had anticipated much of his work. Non-Euclidean geometry reached another peak with the introduction Einstein’s theory of relativity and the assumption of a curved time-space.

3. The development of the binominal nomenclature of plants by Carl Linneaus (1707 – 1778; fig. 22) was seen by Van den Berg (1983) as the third major indication of oppositional division thinking. The Swedish biologist was described by Tore FRÄNGSMYR et al. (1983) as a ‘perceptive observer but also a troubled individual with a deeply pessimistic outlook on life.’ He believed that everything had to be arranged to give it discipline and order. Without a system, chaos would reign. He published his ‘Systema naturae’ in 1735, introducing a binominal nomenclature, which is still in use today.

Linnaeus .

Fig. 22 – An oil painting of Linnaeus (Carl von Linné) by Alexander Roslin (1775), now in the portrait collection at Gripsholm Castle (Mariefred, Södermanland, Sweden).




A société linnéenne was even founded in France (in 1787), despite a firm opposition towards Linnaeus’ artificial system by such notable scholars like Georges-Louis Leclerc, Comte de Buffon (1707 – 1788; in his ‘Histoire Naturelle’ (1749/1767), Michel Adanson (1727 – 1806) and Bernard de Jussieu (1699 – 1777) (DURIS, 1994; STAFLEU, 1971). Only recently the taxonomical system has come under renewed attack from scientists, who want to include the genetic history in the name and propose a system based on phylogenese (comprising the evolutionary background).

Later in life, Linnaeus developed curious speculations, for instance, of a five division (numero quinquenario) in the ‘Clavis Medicinae’ (1766) and a twelve-division in the ‘Metamorphosis Humana’ (1767) in which the ages of man were discussed. Furthermore, he used a climacteric scale of seven (teeth/7; puberty/14; apex of life/42; sexual drive extinguished/63; child again/70). He was influenced by Andreas Caesalpinus (1519 – 1603), who brought the first botanical system in the modern sense in his book ‘De Plantis’ (1583). He also believed that ‘plants should be arranged like armies arranged for battle’.

The metabletic approach (van den Berg) and the notion of synchronicity (Jung) and/or seriality (Kammerer) are, in a practical sense, explorations in the world of analogy. The search for the ‘timeless time’ or the coincidentia oppositorum is the sincere effort to exclude the subjectivity (of a choice) from a communication.

However, that fully unattached state is hard to imagine in the real world. The very realization of synchronicity or seriality – as subjective events – makes it clear that coincidences find their origin in the criteria, which are constructed ‘to let it happen’. And the choice of the division environment is probably the most important touchstone in that process. The more limited an initial division, the more often ‘things will happen’. In the ultimate unity (UU), all things will happen all the time, at the same time.

The conscious acknowledgement of this situation points to the Second Quadrant, as the designated place where the initial division took place. The circle closes in. The analogy, as a process of the Fourth Quadrant, is just as intertwined with the generation of ideas in the Second Quadrant as vice versa. The subjective intervention takes place in both quadrants to limit the field of observation. The ancestry of unity, with its hind of infinity, is incorporated in the muun, the (human) construction of that unity in a multiple world (after a conscious division has taken place in the Second Quadrant).


4.1.3. Giordiano Bruno (1546 – 1600)

View from the Third Quadrant (III) to the First Quadrant (I)

The Italian Dominican friar and scholar Giordano Bruno (1546 – 1600) gave a thorough philosophical treatment of the First Quadrant from a Third Quadrant perspective. Bruno lived in turbulent times, and his life seemed a permanent flight from reality, running from his birthplace Nola (near Naples) to Rome (inquisition trial), Genua (pest), Noli, Venice, Geneva (in jail) and Paris.

His stay in Paris (1582/1583) was, in hindsight, the most rewarding. Bruno taught at the Collège Royal and was sent to London for a diplomatic mission. Again, conflict broke out and a return to Paris followed. The political situation, however, had changed, and he had to find refuge in Germany. More travels followed. He stayed in Prague and returned to Venice. Here, the Inquisition caught him again and a trial resulted in a deportation to Rome (and seven years in jail). He ended his life by burning at the stake on the 17th February of 1600 (WILDGEN, 1998).

Bruno’s frame of mind was dualistic and oppositional. However, a distinct extension into the triadic world provided him with the tools to embark in the dynamic aspects of a communication. His interest in the works of Raymond Lull (and a comprehensive publication of his doctrine in several works; see p. 17) had to do with the same intellectual dynamism with could be generated in a triadic system. The difference may be that Lull was acting to limit the four-division (BONNER, 1985; Vol. 1, p. 56 – 57), while Bruno tried to reach the latter from a two-division. Both men took these actions in order to develop a ‘metaphysics of unity’ (HENTSCHEL, 1988) in using the three-division as a steppingstone to an unity-in-multiplicity. The triangle consisted of:

1. The original unity is the place where the ‘immanence’ is seen as a unity of materia and forma. The oppositional nature of matter and form is neutralized here.

2. The multiplicity provides the extension, where transcendence can be achieved.

3. The harmonic unity is the area where a controversy is solved.

Bruno elaborated in his book ‘Von der Ursach’ (Of the Cause) on these different settings within a human relationship. He joined the formal and final causes together. This action brought Aristotle’s entelechia (see p. 60/61; fig. 20) back from four to three. Furthermore, Bruno joined the efficient cause and the form in the substratum (the material cause) together. By doing so, there was only a duality left in the causes (Ursachen): the First (final) and Second (formal) Quadrant coupled as the representation of the inside and the Third (material) and Fourth (efficient) Quadrant were connected as the outside.

Now the limited, oppositional stage was set to reach for the universal substance, which was the last, absolute and original unity. This goal could only be reached – in a dualistic mind – by taking a definite stance in the choice between the inside and outside. Bruno opted wholeheartedly for the latter.


A cryptic woodcut from the work of Bruno, 1591. P. 170, Abb. 38 in: WILDGEN, Wolfgang (1998). Das Kosmische Gedachtnis. Kosmologie, Semiotik und Gedachtnistheorie im Werke Giordano Brunos (1548 – 1600). Peter Lang, Frankfurt am Main. ISBN 3-363-3295

Bruno’s line of thought started – in a quadralectic interpretation – with the material (Third Quadrant), went through transcendental translations and ended with a nearly godly and eternal substance, which he called Dio (First Quadrant). The latter location makes it impossible to distinguish any difference between (formal) being and potential (final) being. He used the word natura naturans, to express the educational aspect of nature, towards this ultimate state of everything, which is or could become.

Because everything is possible in the absolute (of the First Quadrant), everything is real. There is no nothingness, only a complete reality of all being (be it material or spiritual). Everything is substantial. The plurality of worlds and the infinity of space are real and not creations of thought. The created world uses all possibilities of being and there is no choice made by a God, as Thomas of Aquinas proposed. It is the completion of the potentia absoluta, seen from the human perspective.

The inversion of the observational orientation – turning the vantage point from the First to the Third Quadrant – might be his main heresy. This shift implied a natural surrender to conscious subjectivism, which was not tolerated by the Church. The journey through Bruno’s path of division thinking was brilliantly recorded by MICHEL (1962/1973).

He described several stages of discours (ways of reasoning) in Bruno’s life. Bruno started in a Neo-Platonic mood with nine components (influenced by Raymond Lull). This initial number was reduced to five in 1583, then con-sisting of: sensus, imaginatio, ratio, intellectus, and mens. Another reduction (to four) took place in his book De l’Infinito universo e mondi (On the Infinite Universe and Worlds, 1584). The remaining four were earlier determined by Pythagoras and presented by Aristotle in his De Anima (On the Soul) (fig. 23):


Fig. 23 – A scheme of the ways of reasoning (discours) and the associated methods placed in a quadralectic environment (of quadrants).

Bruno brought the number further down in 1591 to three (sensus, ratio, and intellectus). The triptych ‘De Minimo’, ‘De Monade’ (‘A Pythagorean reverie’) and ‘De Immenso’ were a tribute to the three-division. Finally, the number was back again to four in his last work ‘Summa terminorum metaphysicorum’ (Zürich, 1591 – 1595). This development and change of vision during a human life might hint to more general rules, which can be applied to every intellectual presence.


The (historic-visible) life of Giordano Bruno (1546 – 1600) expressed in a universal CF-graph. The line of the CF-graph of the European cultural period is indicated. The encircled numbers refer to the periods in his life which were ruled by a particular form of division thinking (number of discourses/way of reasoning).


4.1.4. Jan Christiaan Smuts (1870 – 1950)

View from the Fourth Quadrant (IV) to the First Quadrant (I)

A more psychological version of the idea of unity was proposed by the South African general and statesman in his challenging book ‘Holism and Evolution’ (SMUTS, 1926/1936). He sees matter and life as structures or patterns. There is, in his view, a fundamental whole-making tendency in nature. This idea was earlier expressed by Plato (in a dictum taken from the Sophist): ‘That which comes to be always does so as a whole; so that if a man does not count the whole among realities, he ought not to speak of substance or of coming-to-be as real.’

Smuts invented the word holism to express ‘a blending and ordering of multiple elements into new unities’ (p. 228). Its character is both general and specific or concrete. The holistic paradigm is characterized by a pluralism of approach and interpretation, but aims at a synthesis leading to unity. Holism is, in a modern interpretation, a delimited, ‘Fourth-Quadrant’ view on the First Quadrant. It is, at scrutiny, a highly interesting unfolding of human thoughts, because it reveals the deeper mechanisms of higher division thinking.

‘Holism as a process is not only creative but self-creative’ said Smuts (p. 86), ‘and its final structures are far more holistic than its initial structures. Natural wholes are always composed of parts; in fact, the whole is not some entity additional to the parts, but is just the parts in their synthesis, which may be physico-chemical or organic or physical or personal. As Holism is a process of creative synthesis, the resulting wholes are not static but dynamic, evolutionary, creative.’ He distinguished five main levels (grades) of holistic synthesis in nature:

———————- physical mixture

———————- chemical compounds

———————- organisms

———————- minds (or psychical organs)

———————- personality

We will follow Smuts in this subdivision of holistic thinking, in order to understand his intentions with regards to the Whole. The aim is to establish a position of the Whole within the quadralectic framework. The leading hierarchical agent in the division is a growing ‘humanization’ of matter, revealing a two-fold base (of material versus non-material or mechanic versus human/life). Smuts’s outlook had, in that respect, an anthropocentric nature: Man is the ultimate creation in the universe.

The various steps in this hierarchic ladder will now be examined to find the main elements in this line of thinking.

1. Physical mixture

The lowest (or earlier) order consisted of a mere physical mixture, ‘where the structure is almost negligible, and the parts largely preserve their separate characters and activities or functions.’ Matter is, as described in Chapter III of ‘Holism and Evolution’, ‘a structure of energy units revolving with immense velocities in Space-Time, and the various elements arise from the number and arrangement of the units in an atom.’

Smuts was fascinated by the discovery of radioactivity (by Becquerel in 1896) and its implications for the nature of matter. The atom was no longer indivisible and could break up spontaneously. The ‘physical mixture with a negligible structure’ provided the ‘soup’ in which chemistry (as a study of qualitative and quantitative proportions of matter) and biology (as the study of life) became really possible.

The internal activity of (physical) matter holds the key to its self-creation.

The recent knowledge (of radioactivity) pointed – for Smuts – to the physical nature of matter. He mentioned that carbon, for instance, could be found as either coal or graphite or diamond. The modern molecular approach learned that these appearances were caused by a different internal arrangement in the spacing of the atoms.

The structure of physical matter became even more important in organic chemistry. The chemical formula will no longer be sufficient to indicate a particular compound. Its representation often needs a diagrammatic and/or three-dimensional model to make a sensible distinction between atom configurations with the same formula.

2. Chemical compounds

The following level in the holistic evolution comprised the chemical amalgamates, ‘where the structure is more synthetic and the activities and functions are strongly influenced by the new structure and can only with difficulty be traced to the individual parts.’ Apparently, the physical soup had brought out a different arrangement, due to an internal order. Energy units arranged themselves into a chemical compound or a crystal or a colloid. By doing so, it displayed an element of creativity that supports Smuts’ ideas about a tendency towards wholeness.

Unfortunately, at this crucial moment in his line of thinking, Smuts did not elaborate on the principle of division. How is it possible to recognize the emerging structures without a definition of the setting in which the observation takes place? He accepted the ‘new order’ as an innate property of the (physical) material, rather than the result of a change in division-thinking. Instead, he placed all the emphasis on direction and movement (towards the whole). ‘This capacity of direction is as a phenomenon and as a fact of universal observation beyond dispute.’ Rightly so, but this dynamic capacity is meaningless without a clear statement of the conceptual (division) environment.

3. Organisms

Organisms, as the next step in the (hierarchic) ladder of humanization, mark the crossing of the boundary between dead material and life. Smuts focused on the cell as the elementary unit. It is ‘the second fundamental structure of the universe’ (after the atoms) and the origin of life.

There is, in many ways, a resemblance between the behavior of cells and atoms. They accumulate and divide, grow and break. Cells develop into multi-cellular organisms and the division of cells, as it occurs in growth and reproduction, may find its origin in the breakdown of cells or groups, which had become too complex to be stable.

The step from the primordial physical brine to the colloidal fluid with biological life is, in fact, a logical one. Smuts was clear in the discussion of his fundamental concepts (p. 11): ‘We have to return to the fluidity and plasticity of nature and experience in order to find the concepts of reality’. And, on the next page: ‘The hard and abrupt contours of our ordinary conceptual system do not apply to reality and make reality inexplicable, not only in the case of causation, but in all cases of relations between things, qualities, and ideas.’

The quintessence of this vision lies in the appeal to think about a higher division level and to see ‘unity’ as an element of a greater universe, which includes itself (as a ‘whole’). ‘Wholes are not mere artificial constructions of thought; they actually exist; they point to something real in the universe, and Holism is a real operative feature, a vera causa’ (p. 85).

However, a cell differs from an atom or molecule. The cell has a system of co-operation among its parts, which make them function for the whole. An organic body often consists of an indefinite number and variety of cells, which all have to work together in order to sustain the ‘life’ of the individual. In itself, they are immensely complex organizations, which match ‘the wonders of the astronomical universe at the other end’. The protoplasm in the cell is the basis in a process of constant growth and renewal, whereby material is transformed and assimilated. But at the same time there is a breakdown of substances. This process of metabolism, with its form of control, marks a borderline between the living and non-living matter.

The origin of life is in the cell. It could be found in the division of the first cell. ‘This original haphazard division would gradually become stabilized and standardized, so to speak, until cell-division becomes the regular basis not only of all growth but also of all reproductive processes in both plant and animal’ (p. 71). Smuts was eager to apply his holistic theory to the development of life. He found in Darwin’s conception of evolution or organic descent (in Chapter VIII: Darwinism and Holism) a challenging lead.

Smuts’ approach to Darwin’s theory of ‘Organic Descent’ – as he called the evolutionary process – was in the spirit of the dual way of thinking. Darwin’s doctrine on the origin of species was, for instance, broken down into two major operative factors:

  1. Variation in the reproduction and inheritance of living beings, and
  2. Natural Selection, or the survival of the fittest

Darwin was, according to Smuts, rather vague on the first aspect (of variation or inner creativity). It included, in Darwin’s opinion, not only inborn variations, but also individually acquired modifications, which turned in time to specific characters. The inner factor of variation had in general a positive and creative direction.

The external factor of natural selection, which operates selectively on slight variations, was much more familiar to Darwin. The meticulous description of examples of this natural discrimination was the backbone of his book ‘The Origin of Species’ (published in 1859). The inevitable conclusion was drawn, in particular, by later followers, that natural selection was essentially a negative and destructive process.

Smuts suggested another option to sidestep the opposition between variation and selection. He called it a ‘Holistic Selection’, which acted within each organism and ‘is much more subtle in its operation, and is much more social and friendly in its activity’ (p. 209). ‘The whole is all the time on the scene as an active friendly arbiter and regulator, and its favours go to those variations which are along the road of its own development, efficiency and perfection.’ The whole is ‘higher’ than the part, ‘there is something wider and deeper at work in Evolution than the factors as found by Darwin and his successors, something of which those factors are themselves but an expression.’

4. Minds (or physical organs)

The mind is, after the atom and the cell, the third great fundamental structure of Holism. Smuts regarded the mind as a holistic structure, which performs the organic regulation and has a relation to other earlier holistic structures. It is the supreme organ which controls all the other structures and mechanisms. ‘Mind is not yet the master, but it is the key in the hands of the master, Personality.’ (p. 225). It holds the secret to freedom.

The approach to the source of the Mind is, again, explicitly dualistic. It finds its earliest beginnings, according to Smuts, in the inorganic structures of nature when a disturbance of the equilibrium leads to a state of tension. This tension leads to a compensation and a selective action and is ‘without doubt the original stimulus and source of Mind as well as of life.’

It seems as if some sort of early pleasure-and-pain principle rules the subsequent development of the Mind in the living bodies. The evolution started as a vague sense of irritation, which was counterbalanced. The removal of strain subsequently led to a sense of ease and comfort. And the experience of a positive response became finally the generator for a further development of life, in Smuts’ view. Feelings (of comfort and discomfort) were seen as the critical components in this process.

This oppositional line of thinking echoes the influential doctrine of the Greek philosopher Epicures (341 – 270 BC). He did not specifically search for truth (in philosophy and/or in life), but for a state of well being (searching for the positive response). Truth, in his opinion, was a matter of sensation: whatever we experience is true (BAKER, 1947). This statement puts a major emphasis on our feelings as an instrument to generate happiness. Any discomfort (or pain) could be neutralized in the reestablishment of the equilibrium of pleasure and pain. The ideal situation was called ataraxia, a state of sufficiency and satisfaction.

The discussion on the early beginning of evolution continued in the same oppositional spirit. The reaction on the tension goes from passive to active. ‘The passive tension became an active ad-tension or attention, and in this transformation, we reach the most primitive, most characteristic function of Mind.’

Next there is a universal side of the Mind, which participates in a wider setting of multiplicity. But there is also an individual aspect, in which the mind is part of ‘a harmonious co-operative ordered structural unity.’ The conscious Mind is as an organ of wholes, which is geared towards co-ordination. It ‘runs through the psychological functions from the beginnings of attention and passing through sensation, perception, imagination, conception and on to judgement or reasoning’. The yardstick in this gradual progress is an increase in order. Regulation, co-ordination and control are the instruments to make that order more effective.

5. Personality

The personality is the final step in the progressive phases of reality: the crown of humanization, or the last link in the chain from matter, life and mind to personality. This new entity is groping backwards in the mental or spiritual sphere and further into the organic and material world, but it also adds something more to the chain. It can be noted that the previous four stages were described as multiplicities while the fifth and final item in the chain of holistic progress is a singularity.

This time the road of dualism seems to be abandoned. Smuts insisted that it is wrong to see the human personality in terms of separate spiritual and material entities. The division leads to an erroneous attention to one of the parts, as many examples in the history of philosophy can prove. The interrelation between the Mind and the Body gave rise to all sorts of theories, but they missed the point, because their initial setting within an oppositional framework was wrong.

Obviously, the greatest culprit was Descartes, suggesting an anima dwelling in a corpus. According to the French philosopher, there are two distinct separate res or entities, the res cogitans and the res extensa. The tension between these two states causes the problems and contradictions in life. Smuts also pointed to Berkeley and Geulincx, who tried to bridge the gap by proposing God as a medium. Gottfried Leibniz suggested a pre-established harmony, and Spinoza came up with one substance underlying the mind and the body. They are all solutions to a problem that does not exist in the eyes of a holistic observer.

What we do need, is a new relativism of our own arguments. There should be no Cartesian inclination to assume that the order we make of events and the interpretation we give them is ‘correct or incorrect’. In fact, it has now to be understood, that the very concept of correctness belongs to the realm of oppositional thinking and dualism. The holistic paradigm is born in an environment of multiplicity. Many options are open all the time, and the most convincing one is chosen. Selectiveness is the fundamental property of all organisms. It is the most primitive property of life because it is so close to the selective power of matter.

‘When we focus on our own culture’s process of making order’, CRAIGE (1988, p. 111) stated: ‘in our ‘reconnection’ of res cogitans and res extensa, we may acknowledge that since the understanding we have of our world depends upon our particular processes of investigation, we need a multitude of interpretations.’ Any personality that can find its way through the staggering variety of multiplicity, in freedom and purity, can be called holistic.

Smuts’ introduction of the personality-as-a-whole is full of good intentions. He believed in the possibility to establish a science of Personality. In fact, ‘the science of Personality may be the very keystone of the arch, and serve to complete the full growing circle of organised human knowledge.’ The new discipline of Personology should combine the analytical contributions of psychology and physiology with other human sciences in order to place the individual character in a wider scope. This might include, but is certainly not equivalent to, the present interpretation of this neologism by the Beverly Hill-based psychic George Roman, who applied the term for face reading and the interpretation of face language.

The study of biographies, as examples of personal Holism, is recommended by Smuts to discover the laws of personal evolution. These descriptions of interesting people should not be ‘the empirical unsatisfactory patch-work affair which biography now mostly is’, but provide a theory of personality. The lives for such a study, as may be expected in a holistic environment, should be chosen with care.

The type of personality without the capacity for inner growth and with an arrested development is not suitable for a treatment in the Personology. Also the class of persons with only an external character do not provide good material. The absence of inwardness and an inner spiritual life by many public men, administrators and businessmen absorbed in the practical site of their affairs, make them poor study objects.

However, people with real inner histories and a continuous development do have the necessary ingredients to reconstruct their lives in the light of a holistic context. Smuts pointed to poets, artists and writers as the most suitable persons to employ in a holistic study. In addition, religious and social innovators, with a more or less faithful record of their actions, offer the opportunity to study the laws of growth and development.

Finally, the personality, as the most holistic entity in the universe, is put into action, as an active shaping factor in the life of the human individual. The main characteristic of the personality is its self-realisation: ‘the end of a whole is more wholeness, in other words, more of its creative self, more self-realisation.’ The personality aims for an inward spiritual grace and unity. The principal operator in this process is the will.

The personality is compared with a well-organized society. There is a central legislative and executive authority, which controls activities in certain directions. Some of them are consciously taken, but many more are the result of some subconscious decision level. The final aim is a wholeness and harmony, in which the contraries disappear.

Smuts’ concept of holism has attractive sides. However, his journey through the development of life is – in its final conclusions – a dualistic construction. The definition of the holistic movement as essentially an effort ’to eliminate what is alien and adventitious and to conserve and develop what is pure and relevant to its ideal, and so to reach perfection’ is nothing but oppositional thinking. Efficiency and purity are noble and even modern characteristics to aim for, but they are subjective and time-bound. As final aims in life they are bound to restrain the mind in an oppositional cadre.

The hierarchic scale of humanization, as proposed by Smuts, places the lower and earlier position of mechanism against a higher and later rank of holism. This pellucid development (or evolution) from the physical brine to the understanding human personality is, in his view, an all-compassing trend towards a self-development. However, a critical observer can pose the question why holism is a more fundamental concept, which ‘in its most far-reaching reactions tends to transform, transcend and absorb the concept of mechanism’?

It was Smuts who gave the answer and showed himself – at this particular point – to be an advocate of higher division thinking. He introduced a deeper harmony, in which ‘the earlier, cruder notes of the physico-chemical order become a new music of being’. This new tunefulness sounds rather patronising, but that is not his intention (p. 175/176):

‘The structural march of Holism has only proceeded one step, one great step forward; but the system and character of its advance remain fundamentally the same. The new is a greater complication, a deeper intensification; there is more selectiveness, more quality, more direction, more control; there is more of the whole, of the character of the wholeness, in the new structure than in the old. But there is no switching off from the old to the new; the one is a continuation of the other, a continuation indeed of a novel and creative character, but not a denial of and a going back on the other.’

It may well be, that Smuts described here, in a somewhat different setting, the very transition from dualistic to quadralectic thinking. That one great conceptual step is an enormous one, reaching for vast horizons.

An analysis of the holistic line of thought reveals a distinct four-fold nature, despite the five stages as mentioned above:

1. The physico-chemical stage ———— related to —————- matter

2. The organic stage ———————– related to —————- life

3. The psychical stage ——————— related to —————- mind

4. The personal stage ———————- related to —————-  personality

The holistic evolution from matter to personality seems to reflect the characteristics of an evolution in division thinking from one to four.

The physico-chemical soup is comparable to the one-division, in which everything is in everything. Matter is present in an amalgamated form, but is not materialized in a context, because there are no distinctions yet.

The subsequent organic separation from this primary brine is similar to the first (two) division, in which a boundary line is established. Matter and life are the same entities, but the fundamental difference is in the notion of division. The former is a concentration of atoms bound by physical force. The latter is a concentration of cells, held together by a holistic force.

The psychical factor adds a dimension to the primary division of cells. It can be compared with the thinking in a three-division, operated by a mind. Organic units are able to devise a system of an internal shift and a subsequent valuation thereof.

Finally, the personal stage represents the world of the four division, in which the valuation system is balanced and geared towards the covering of large fields of information and an effective use thereof.

Holism, in a modern sense, should not be seen in Smuts’ original intention as a way to higher self-fulfillment. The emphasis on the anthropocentric element in his philosophic viewpoint leads to ourselves, but at the same time to nowhere. The intention of a subjective approach to life – fueled by the personality – is much more realistic.

The whole, as a philosophical entity, has a distinct place in a quadralectic world view. It fits in the four-fold sequence of I. unity – II. muun – III. part – IV. whole, describing the same area of the universe from a different point of view.

The whole is the representative of unity in the Fourth Quadrant.  

The whole merges in the unity of the (following) First Quadrant. The cycle can start anew (fig. 24). Only the description of the road of being remains open, said Parmenides. That is exactly what the teaching of Lao Tzu tried to convey in the longing for completeness and spontaneity of the origin. The Tao (meaning the immeasurable ta) of being, is a living and creative totality without a form or name. It encompasses the great emptiness, the one, and the nameless origin of heaven and earth. In the beginning is nothing, just a dimensionless unity (LÜHRS, 1986).


Fig. 24 – This scheme gives the thinking path (or Tao) of a cyclic-quadralectic communication through the quadrants. The first and third quadrant have only one conceptual position (unity). The second and fourth quadrants are divided into four-divisions, which reflect the major division.

‘The Western mind has no word for Tao’, said Carl Jung in his ‘Commentary on ‘The Secret of the Golden Flower’ (the ‘Tai Yi Jin Hua Zong Zhi’, a Chinese book of life). ‘The Chinese character is made up of the sign for ‘head’ and the sign for ‘going’. ‘Head’ can be taken as consciousness and ‘going’ as traveling a way, and the idea would then be: to go consciously, or the conscious way… If we take the Tao to be the method or conscious way by which to unite what is separated, we have probably come close to the psychological meaning of the concept.’

This testimony was Jung’s explanation, translating the meaning of the ‘head’ into consciousness and ‘going’ into ‘a way’. However, another explanation is possible if the basic two signs of the Chinese character for tao are explained in a different way. The signs might refer to the fundamental elements in a communication: division and movement (see p. 15; fig. 4). The ‘head’ is, in that situation, the initiator of division (thinking) and the ‘going’ is the equivalent of movement. The concept of Tao is, from the quadralectic point of view, a representation of the ‘Ultimate Communication’ in which a (conscious) sense of division is paired with an abstract mechanism of movement.

The notion of this ‘Ultimate Communication’ is very much a First Quadrant topic perceived in the Fourth Quadrant. ‘The Tao that can be talked about is not the true Tao’ is a quotation from the book Tao Te Ching, written around 500 BC. ‘It is nothing, and yet in everything. What is it? Thirty spokes on a cartwheel. Go towards the hub that is the centre – but look, there is nothing at the centre. And that is precisely how it works!’

The Tao is explained as being within all things. It can be seen as a dialectical synthesis, superseding the contradictions (of oppositional thinking). It is also important in the ‘wu-wei’ (actionless-action) attitude towards the environment, by accepting and not interfering with the movement of nature, on the one hand, while using at the same time its advance towards action on the other.

This two-fold aspect was pushed forward by another founder of Taoism called Chung Tzu. He saw – some hundred years after the explanations of the Tao Te Ching by Lao Tzu – the object of cognition in the dialectic of the single and the plural, the absolute and the relative and the constant and the changing. This element of contradiction is present in all things (yin-yang) and a movement of something towards its opposite is a strong convention in Taoism.

A repositioning of Neo-Taoism, which took place around 250 BC, was in itself a split in two oppositional direction: the revisionists (led by Wang Pi and Kuo Hsing) moved towards Confucianism, explaining it as the fulfillment of Taoism in a practical sense and the hedonists (or romantic Taoists). The latter were known as the ‘Seven Sages of the Bamboo Grove’ (led by Chi K’ang), teaching an evasion of duty, a critical attitude towards conformity and a general following of impulses and stimulants.

Modern Taoism can still be divided into two categories. Either the materialist philosophy of its three founders (Lao Tzu, Chuang Tzu and Lieh Tzu) or the later conversion of the revisionist movement into a religion (Tao-chiao). The contemporary (quadralectic) perspective considers the materialists- and spiritual sides of Taoism to be expressions of two different ‘holistic’ viewpoints in the Fourth Quadrant (aiming at the invisible invisibility of the preceding or following First Quadrant). The materialists find their place in the third division of the Fourth Quadrant (IV, 3), while the spiritual minds are gathered in the fourth division (of the Fourth Quadrant; IV, 4).

It seems that different cultures find ways to express the same journey through life in the concept of what Smuts’ called the Whole. Holism and (original) taoism have their dedication to describe the invisible in common.

4.2. The Second Quadrant (II)

The first multiplicity

The Second Quadrant (II) comprises the primary division and marks a break with the static and undivided nature of the First Quadrant. The division-principle, which is ‘potentially’ present in the First, becomes active in the Second Quadrant. It means a transfer of information between partners within a particular frame of division.

This situation changes with the realization of the mechanism of division in combination with movement. The disintegration of the original unity prompts a primal communication. The arrival of multiplicity enables an interaction based on differences, which have been created and noted for the first time. The shift between parts of a division leads to transformations within the validation process. They are generally known as forms of ‘visibility’: the possibility to record differences and order them in a logic fashion.

The boundary between the First and Second Quadrant is clear and sharp. Both division and movement start their functional existence at the same time and place here. It is a moment of choice, not of development. Suddenly, when a certain stage of approach is reached within the First Quadrant, the nature of the unity changes dramatically.

Parts are recognized and motion is envisaged. At once, the number of the primary division and the nature of motion (linear or cyclic) is ‘seen’. In hindsight, when a higher form of division thinking is taken, it is possible to project some sort of ‘evolution’ in the creation of divisions – in the sequence from 1 – 2 – 3 – 4, etc. – but this is not the case. There is no ‘development’ in division thinking, nor in the choice of motion at the boundary of the First Quadrant, only an a priori. This brings us to a very important law in the understanding of a communication:

The division, which destroys the original unity, is set to govern the whole of the communication.

A communication which ‘opens’ in a two-division will continue in a mood of dualistic thinking, even if one of the partners tries to employ higher division thinking. Which brings us to another, equally important rule, which will later be of crucial significance in the calculations of communication values in a cyclic setting, namely that:

The level of division thinking within a communication is set by the partner employing the lowest division.

So the events at the boundary of unity are of vital consequence for the rest of the communication. There might be a particular growth or regression within the communication, but the highest level of insight will always be determined by the initial division at the boundary of the First and Second Quadrant. With this knowledge in mind – admittedly derived at in higher division thinking – it is better, if possible, to set the stakes as high as possible and aim at the highest division.

The principle of displacement opens a second possibility to a further visibility. A movement within the context of the newly found division gives various perspectives, which can be validated in a process of comparison. This valuation is, in its bare essence, the visibility itself.

Four mental steps are distinguished in the Second Quadrant, reflecting the quadralectic model of communication-as-a-whole:

——————— 4.2.1. A proto-communication

——————— 4.2.2. The first division

——————— 4.2.3. The valuation

——————— 4.2.4. The implementation

The numbers refer to the ensuing sub-chapters in which the various characteristics will be shortly described. The proto-communication carries the features of the First Quadrant (I), with the (invisible) invisibility as the main feature. The first division is the hallmark of the Second Quadrant (II), setting a communication in motion. The valuation is the achievement of the Third Quadrant (III). Boundaries are marked in the process, and the differences between parts are calculated. Finally, if all the tools are at hand, there is the implementation that keeps the mind going in the Fourth Quadrant (IV). The communication is at a level of its greatest understanding.

The major events of the Second Quadrant herald the nature of things to come. The whole communication (cycle) is already represented in the Second Quadrant (see also the ‘Tao of quadralectic thinking’ in the previous chapter). The layout of an interaction is known that very moment a division-decision has been taken. The situation can be compared with a person looking in a mirror with another mirror under a certain angle and discovering an endless repetition of images. Visibility looses itself in a perpetual repetition. The observer seems to disappear in a tunnel of infinite images.

The following short description of the four cognitive positions in the Second Quadrant is an introduction in the quadralectic way of thinking as a whole.