Seb Henagulph's 'Three Pillars of Transdisciplinarity'

Montréal, April 22, 2000

Seb Henagulph's essay, ... 'The Three Pillars of Transdisciplinarity' [appended below], ... provides a lucid framing of the geometry of relational versus rational perception and inquiry. The transdisciplinary framing he weaves in the essay gives insights into the natural 'possibility-based' order in the 'containing environment', ... an ordering which is essentially relativistic and relational, ... and beyond the reach of material causal- and rational thought- based inquiry. The key multivalent 'connector' between the domains of the relational and rational which Seb utilizes in weaving this tapestry of understanding is Stéphane Lupasco's notion of 'the included middle'.

In the Aristotelian logic of 'the excluded middle', the mainstay of our western culture, a subject 'A' is viewed as being fully independent from all other objects in the containing ensemble ( i.e. in the reciprocal constituency, 'non-A'). In other words, the space which envelopes and 'contains' ('includes') the overall ensemble constituency is seen as 'empty' by the logic of 'the excluded middle' ; i.e. the 'middle' is seen as non-connective and non-participatory. In the language of logic, the 'middle'- ground between the subject and its reciprocal (the containing medium) is 'excluded' from participation in the logical construct.

Meanwhile, 'excluded middle' logic is not the only strain of logical reasoning in the world as the citations in the essay indicate, "... the logic of the included middle is a true logic, formalizable and formalized, multivalent (with three values: A, non-A, and T) and non-contradictory. Our understanding of the axiom of the included middle -- there exists a third term T which is at the same time A and non-A -- is completely clarified once the notion of 'levels of Reality' is introduced."

'T', in effect, in the geometry of the essay, plays the role of a mediating and containing 'ether' between subject and object, facilitating interaction across multiple levels of reality (multiple levels of subjective focus). This 'mediation' is shown, in the essay, to give rise to both 'complexity' in the domain of the explicit and to 'relational intelligence' in humans in the domain of the implicit in association with a fractal or holonic geometry. The multi-reality 'communion' facilitating role of 'T' is congruent with the connective role of 'evolutionary space' (container-constituent ontogenetic space) in the material domain and to 'intuitive intellection' in the cognitive domain. The geometry, in these cases, is one where a given 'subject' 'A', not only relates to other objects 'non-A' through direct interaction, ... but is also related implicitly through 'reciprocal disposition' (as a sandgrain in a dune relates to its brother grains not only through direct interactions but also by its positioning within the potential energy configuration characterizing the dune and its continuing metamorphosis). In this geometric visualization, 'T' represents the possibility space or 'potential energy space' 'container', ... the broad 'supra-landscape within which specific linear material-causal and 'rational intelligence' sub-spaces are 'included' as small, subsidiary features.

Relating 'T' to the geometries discussed in the series of essays on this website, we could say that 'T' has a 'spatial role' (since it represents the connective ground between 'things') which corresponds to relativistic, curved-space 'reciprocal disposition'. That is, while 'non-A' stands for the reciprocal material constituency within a given mechanical ensemble (system) in the physical domain (and/or 'non-A' stands for the reciprocal immaterial constituency within an ensemble (system) of rational propositions in the cognitive domain), 'T' is the relational, mediating medium which facilitates 'communion' across multiple mechanical systems and multiple 'systems of rational propositions'. An example may help here;

Imagine a mountainous topography in a temperate climate (subject to fluvial erosion). We can describe the natural phenomena we see in terms of 'kinetic' or 'material-causal' effects, such as are incurred by a rock tumbling down the mountain side. This type of material-causal description is 'covered' by Aristotelian 'excluded middle' logic which underpins Newton's laws and the western scientific tradition. But such 'excluded middle' type of perception and inquiry does not 'cover' (i.e. is incapable of 'including') the fact that the rock is also, and at the same time, a full-fledged constituent of the mediating containing space, ... a space which is at the same time undergoing 'induced' reciprocal effects as a result of the kinetics of its constituent, ... induced reciprocal effects which transform the containing landscape and its potential energy endowed configuration constituted by its constituency. Each constituent of the landscape, each rock, sandgrain, plant and animal has an identity by virtue of its 'place' in the containing space and the opportunities which that 'place' give access to, such as the opportunity for a rock to roll down into the valley. The opportunity or 'possibility' given by the positioning of the constituent within the constituency is the relativistic quality which opens the door explicit material causal kinetics. The kinetic actuality of an object is the endowment of its 'place' within the containing brotherhood of objects which comprise the multi-reality topography of opportunity.

For example, the rock may roll down into a stream, and in the place where it formerly sat, seeds long pressed down into the dirt and darkness may now start to grow, ... and the stream in which the rock comes to rest may, as a result, be bottlenecked to such a degree that it overflows its banks and changes the topography. Thus the rock's movement induces transformation in its containing landscape by virtue of its 'place' within the geometrically configured potentia of its multireality space-time container, ...i.e. it induces transformation which is beyond the descriptive capability of 'excluded middle' or 'rational' perception and inquiry because it involves SIMULTANEOUS COMMUNION amongst and across multiple realities.

In terms of physics, the rock can be said to have changed the 'potential energy topography' by unburdening the seeds, and by bottlenecking the stream. Newton's laws, however, are incomplete when it comes to describing the reciprocal relationship between the 'kinetics of objects' and their 'reciprocal effect' on the topography of potentials (i.e. their effect on the 'possibility space' which the seed and the flowing water in the stream 'sees'). The reciprocal interplay between kinetic behaviors of things and the topography of potentia (energy-related possibility) leads one into a higher dimensional (than kinetic) 'outer-inner', container-constituent 'wave' view.

The relevance of the incompleteness in the 'excluded middle' inquiry can be further highlighted if we continue to 'study' the mountainous terrain and the kinetic movements of the objects within it. After some time, the mountains will be eroded and we will be left with a flat, fertile plane irrigated by a meandering river. The 'potentials' or 'energy-related possibilities' will be much different in this new environment, but nothing in our 'excluded middle' inquiry, no matter in how much detail we have studied the material-causal behavior of each and every atom in the topography, will inform us about this changed landscape of possibility, since the excluded middle denies (i.e. specifically precludes) consideration of a containing and connecting 'T' medium.

This point is critical to an understanding of complex systems and consciousness; i.e. ...

... There is an obvious natural order in the induced transformation of 'possibilities' in any containing space reciprocally related to the kinetic behaviors of its constituents and constituent systems. An understanding of this order is beyond the capability of logical (excluded-middle) and material-causal (kinetic) inquiry except in the degenerate numerical sense of 'probabilities'. An understanding of this relativistic 'potential energy related' or 'possibility based' order requires the logic of 'the INCLUDED middle', ... a logic which goes hand in hand with the theory of relativity and its self-referential space-time continuum, geometrically visualizable by the non-euclidian spherical space convention.

The philosophical implications of the logical treatment of transdisciplinarity in Seb Henagulph's essay, 'Three Pillars of Transdisciplinarity' is consistent with the philosophical propositions of Lao Tsu; i.e, .... in association with every object and its material causal kinetics, is a reciprocal 'utility' which is a function of a multivalent (multi-reality) containing space;

"Thirty spokes share the wheel's hub;
It is the center hole that makes it useful.
Shape clay into a vessel;
It is the space within that makes it useful.
Cut doors and windows for a room;
It is the holes which make it useful.
Therefore profit comes from what is there;
Usefulness from what is not there."

While the clay vessel 'A' appears to be excluded from the reciprocal constituency, 'non-A', of all other things in its containing space, ... its kinetic actvities are reciprocally bound up in the kinetic activities of those other constituents through the mediating role of the containing space or 'ether'. The ether participates relativistically in the morphogenetic transformation of the landscape composed of the constituency of 'A' and 'non-A', just as the potential energy configuration of a mountainous topography participates in the evolution of its material constituents. The logic of the excluded middle is 'blind' to such participation, ... and it is the logic of 'the INCLUDED middle', ... the multi-reality participation of the containing space, ... which extends our understanding from a flatspace voyeur view of the mechanics of life 'out there', to an immersed volumetric experiencing of multivalent dynamic equilibria between the 'out there' and the 'in here'.

Seb's essay opens up yet another portal of opportunity for us to enter into this deeper realm of implicit understanding which comes from systems perception and inquiry based on the presence of an implicit, relativistic mediating space or 'included middle'.


The Three Pillars of Transdisciplinarity

by Seb Henagulph


The three pillars of transdisciplinarity -- levels of Reality, the logic of the included middle, and complexity -- determine the methodology of transdisciplinary research.

Basarab Nicolescu [8]

There is much to suggest that when human beings acquired the powers of conscious attention and rational thought they became so fascinated with these new tools that they forgot all else, like chickens hypnotized with their beaks to a chalk line.

Our difficulty is not that we have developed conscious attention but that we have lost the wider style of feeling which should be its background, the feeling which would lets us know what nature is from the inside.

Alan Watts [14]


A recent editorial in Nature Neuroscience speaks of the growing problem of experts who are no longer able to understand one another:

"In Darwin's time, it was possible to write a book that was both a primary scientific report and a popular bestseller. Today, however, that seems like a remote ideal. Not only is it difficult to communicate scientific ideas to the general public, but scientists seem to have increasing difficulty communicating with each other. Even within biology, researchers in different areas of specialization are often unable to understand each other's papers." [7]

One of the main reasons for this 'disciplinary big bang' (and its resulting breakdown in communication) is the predominantly reductive binary or exclusionary bivalent logic approach which science has taken since discovering these new tools of rational thought. This type of thought attempts to remove the observer from the observation. The great insight from quantum theory is that this is impossible, the presence of the observer or subject can be reduced to a minimum, but it cannot be removed altogether. In order to navigate this exponentially growing complexity we need to develop tools of thought which use different logics, ones that include the subject and allow a wider view which can be used across all disciplines, allowing strategic points and knots of communication to be located. As Edgar Morin exhorts us: "Our effort, then, will not be directed at the totality of knowledge in each sphere, but on crucial knowledge, strategic points, knots of communication, organizational articulation between disjointed spheres." [5]

For at least the last 2500 years, humankind has investigated Nature using two predominant modes of thought. Broadly these may be defined as the 'rational' and the 'relational' approach. Around 500BC in the west, associated with the Greek 'golden era of rationality', there was a shift in the mode of communication from the spoken word to the written word. This shift was driven primarily by Phoenician traders around the Mediterranean requiring a common, 'lingua franca' through which to conduct the business of trade, which itself was based on the newly introduced cultural concept of 'private property'4. With the rise of the Phoenician-Greek alphabet, there was increasing emphasis on writing and language at the expense of the direct sharing of knowledge through story-telling and myth. Accordingly, this has shaped our current conception of reality to the point that many believe that what cannot be written down, is not worth knowing.

A prime example of this can be seen in the differing views of Aristotle and Heraclitus. Aristotle was the first to formalize the linear logic upon which our current civilization is constructed: the law of the 'occluded middle' in true/false syllogistic logic. According to this a thing can be either true or false, there is no in-between. This binary logic has resulted in the perception of things possessing innate properties, such as 'absolute good' or 'absolute evil' or the 'win-lose' mentality in modern education, politics and business and the purely reductionistic dictates of much of modern science; all of which have led to the current ecological and social global crisis. Heraclitus, on the other hand, used a more organic logic and viewed Nature as a harmony of opposing tensions, "Men do not know how what is at variance agrees with itself. It is an attunement of opposite tensions, like that of the bow and the lyre." [4] This view can also be seen in pre-Aristotalian cultures, such as the Celts and American Indians, where good and evil were treated more like the north and south poles of a magnet- one cannot exist without the other. Chinese philosophy, especially Taoism, has also noted this inseparability of dualities. This is especially evident in the yin-yang formulation which describes the polarity inherent in all things. This dipolar perception is more in line with the way Nature functions: a dynamic tension between opposites. This applies to the two approaches under discussion- yang is analogous to rational thought while yin is analogous to relational thought. Although modern science claims to rely purely on rational thinking, the individual scientists (especially the innovators in any given field) actually rely on the intuitive approach when attacking difficult problems. It is only in sharing their ideas with colleagues that their thought is converted to the rational, bivalent, linear approximation.

A good example of the relation between these differing views can be seen in the game of pool. [4] The rational approach is equivalent to the amateur pool player or 'shot-meister' who concentrates merely on each individual shot; the physicist pool player can line up the cue ball exactly and tell you precisely what the balls will do: "8 ball off the side into the corner pocket" but tends to neglect the overall shape of the ball configuration and usually ends up snookered. This leads to extremely difficult shots being attempted. The Taoist pool player or 'shape-meister', on the other hand, also lines up the ball exactly and knows where the balls will go, but realizes that the overall shape of the configuration is in the primacy. As a result, the easiest or most obvious shot is not always taken, but through 'massaging' the configuration, all the shots become easy. While the 'shot-meister' is a crowd pleaser, the 'shape-meister' will always win in the end. Modern science, like the chicken with its beak to the chalk line or the 'shot-meister', in relying on the purely rational approach, is infusing dysfunction into nature at an ever greater rate, requiring more and more difficult 'shots' to get out of self-induced 'snookers'. Science needs to 'grow-up' and stop behaving like an amateur pool player. The first step in this professionalization of science is an acceptance of the logic of the included middle which allows a 'shape over shots' view rather than a reductionistic 'shots over shape' view, or even worse, a purely 'shots' view, with no consideration of shape at all.

This method of relational over rational is similar to the 'bootstrapping' approach, as advocated by Basarab Nicolescu and Ted Lumley. Nicolescu uses the word to define the method of searching for 'laws of correspondence' that cross several levels of reality, in much the same way as a crystal is created by a single law but has different facets. In essence this is transdisciplinarity: "the study of correspondences between different fields of knowledge."9 Rather than attempting to construct concepts in a rational way from the bottom-up, bootstrapping approaches from the other side, so to speak, using a top-down approach, relying more on intuition and relational patterns. Unfortunately, it is just this fact, that bootstrapping seems somehow completely removed from rationality, that many reject this intuitive approach. Lumley, in discussing his use of bootstrapping, answers this in 'Epilogue-Prologue':

".... it's the oldest of human reasoning methods, its how we learn as children, it was the mainstay of the mythopoeic peoples and of the traditional aboriginal 'learning systems'. The Greek 'golden age of rationality', wherein people began believing that abstract reasoning was more powerful than the old fuzzy and ambiguous standard of intuition, appeared to kick off with Parmenides, in 500 B.C. My point is not to knock rationality per se, but to knock the practice of putting rationality into primacy over intuition; i.e. the practice of seeing the son as having created the mother, to 'usurp' the feminine principle, if you like." [4]

What he is saying here is, we do not need to completely discard the standard logic of rational thought, it just needs to be used within the context of intuition or relational thought- in other words, the proper mother-son relationship; shape over shots not shots over shape. Article 4 of the Charter of Transdisciplinarity calls this 'open-minded rationality'; it is a way of examining Nature that has been used successfully since pre-history. Albert Einstein also noticed this inversion of the natural order: "The intuitive mind is a sacred gift and the rational mind is a faithful servant. We have created a society that honors the servant and has forgotten the gift."

For science and culture in the West to remember the gift, we need to examine the 'Three Pillars of Transdisciplinarity' as these provide a stable grounding for what F. David Peat has referred to as the 'New Science' [11] It is an approach to nature that is comfortable with ambiguity and paradox, using these as creative principles to extend the range and usefulness of the current reductionistic approach championed by science. It does not discard this most valuable contribution to humankind, but allows us to use it in a professional manner which will allow transdisciplinary communication and thus benefit all beings on this planet. The most important concept in this professionalization is the 'logic of the included middle' which formalizes the unavoidable presence of paradox and complementarity in our knowledge; this in turn allows for a realistic understanding of the presence of complexity in our world. In order to properly understand this new logic, the concept of different levels of Reality needs to be fully comprehended.

Levels of Reality

Our age is. potentially that of the abolition of the single (one logic, one language, one causality, one space-time, one reality, one knowledge) and of the emergence of the pleural (logics, languages, causalities, space-times, different levels of reality, different types of knowledge).

Basarab Nicolescu [10]

To conceive circularity is henceforth to open up the possibility of a method which, by having the terms which refer to each other interact would become, through these processes and exchanges, productive of a complex knowledge containing its own reflexivity.

The circle will be our wheel, our path will be spiral.

Edgar Morin [5]

For a pragmatic understanding of these differing modes of thought we need to begin by examining the 'levels of Reality', Nicolescu's first pillar of transdisciplinarity. Reality here means that which resists our knowledge, experiences, representations, descriptions, images or mathematical formalizations. Mapping out the different levels of Reality is a necessary prerequisite for transdisciplinary dialogue- it is essential to know where different disciplines lie in relation to one another conceptually. The importance of this is outlined in Article 2 of the Charter of Transdisciplinarity, "The recognition of the existence of different levels of reality governed by different types of logic is inherent in the transdisciplinary attitude. Any attempt to reduce reality to one single level governed by a single form of logic is incompatible with transdisciplinarity."

The notion of Reality existing at different levels has been widespread throughout human history (and probably pre-history). From the shamans three levels of Upper, Middle and Lower, to the perennial philosophy's Body, Mind, Soul, Spirit to Wilber's recent comprehensive 13+ stages to some ancient systems proposing literally hundreds of distinct levels, there is no shortage of classification schemes. An initial distinction needs to made between levels of organization and levels of Reality. Levels of organization are those levels mapped out by the systems sciences; each level emerges from the one below it, but each level follows the same general laws. For example, molecules emerge from the behaviour of atoms. A more accurate description might be to term these emergent stages rather than levels. Levels of Reality, to be discussed below, follow fundamentally different laws. To get some perspective on the matter, I will use the concept of 'holons' as first proposed by Koestler and more recently as extended by Ken Wilber in his 'Four Quadrants of the Kosmos'15 model to outline the 'stages of organization'. Combining these insights with the 'levels of Reality' proposed by Nicolescu, I hope to reveal a useful template for transdisciplinary research.

Arthur Koestler first proposed the word "holon" over twenty-five years ago in an attempt to show that all natural systems are not made up of 'parts' and 'wholes' but part/wholes. This idea was stimulated in part by Nobel prize winner Herbert Simon's 'parable of the two watchmakers'. This parable illustrates the fact that complex systems can evolve from simple systems more easily when there are stable intermediate forms. He also showed that the resulting complex systems will tend to be hierarchic in structure.

While investigating these stable intermediate forms and hierarchies in living organisms and social organization, Koestler noted that 'wholes' and 'parts', in an absolute sense, do not actually exist; what is a whole on one level of a natural hierarchy is simultaneously part of a larger whole on another level and vice versa. Thus he proposed the word holon to describe the relationship existing between the parts and the wholes. A classic example is that of letters being parts of whole words, while words are parts of whole sentences and sentences are the parts of whole paragraphs etc. This relationship can also be seen to exist, infinitely, in fractals such as the Madelbrot set. Koestler further noted that these chains of holons, rather than forming heirarchies, exist as, what he called, holarchies.

More recently Ken Wilber has taken up this idea of 'holons' and 'holarchies' and incorporated it into his 'Four Quadrants of the Kosmos' model. The individual holons at each stage, he points out, exist in groups or communities of similar holons. Then taking an insight from Jantch he shows that, at every stage, each 'micro' event or individual holon exists embedded in a 'macro' event or group (or society) of holons. He has further extended the idea by pointing out that each holon, starting at the most basic level, has both an interior and an exterior. He claims this is not an emergent quality, but "exists from the first moment a boundary is drawn; exists, that is, from the moment of creation."(SES p538), Of interest here are what Wilber refers to as the 'deep structure' of holons. He provides twenty tenents describing the behaviour of holons in general. The first tenent states that reality is not made up of 'things' or 'processes' but of holons, arranged holarchially. The second tenent describes the 'deep structure' or fundamental capacities of holons, which are self-preservation or autopoiesis, self-adaptation or allopoiesis, self-transcendence and self-dissolution. Wilber designates the first as 'agency' which is related to yang as described in Taoism and the second as 'communion', related to yin properties. The third deep structure is self-transcendence (after Jantch & Waddington) or self-transformation. This is related to Whitehead's concept of 'creativity'. It relates to the emergence of new properties via breaks in symmetry, as studied in the new discipline of non-linear science (after Prigogine). Emergent properties have been observed in many domains and include vortices, lasers, chemical oscillations (in vitro and in vivo), genetic networks, developmental patterns, population genetics, immune networks, ecology and geophysics, to name a few. As Wilber(SES p47) says, "In fact, it seems difficult for any densely connected aggregate to escape emergent properties."

Gerhard Grössing has independently described a similar scheme which he calls the 'logic of evolution': symmetry - asymmetry - integration = meta-symmetry etc. [2] All systems (including intellectual ones) can be seen to follow this logic. He relates this to the development of human understanding of nature in that it has progressed from (i) subjective schema in Aristotelian physics and alchemy to (ii) asymmetry between space and time on the one hand, and matter on the other in Newtonian physics and (iii) integration by means of reciprocal influencing of space-time and matter in the general theory of relativity. He further extends this to a new understanding of causality:

"The way is opened, with the development of the notion of causality in describing natural phenomena, which leads to the notion of integrative, circular co-dependency, not only in the general theory of relativity but also in the quantum theory; (i) subjective 'explanation' through the personification of nature (mother, spirit, god etc.); (ii) 'linear' objective description of nature (for example, observer-independent planetary orbits in Newtonian physics); (iii) circular, 'wholeness-like' causality (for example the connection between space-time and matter in the general theory of relativity) Only with circular causality does an essential characteristic of quantum theory become understandable: now we can no longer (in the metaphorically extended sense of 'linear') describe an 'object', unless we put the hermeneutical circle between 'object' and 'observational instrument' in the centre of our awareness (whereby the detachedness in these two components shall be understood merely as thought-props.)"

Alwyn Scott has provided some further examples of this circular co-dependency in non-linear systems which is reminiscent of the mythological ouroboros [12]. There are many examples of these "closed causal loops" which depend on the balance between two opposing forces. For example in solitons, or coherent waves of energy which emerge as independent dynamic entities, there are two balanced tendencies: dispersion (spreading of energy) and non-linearity (concentration of energy), respectively yin (communion) and yang (agency). Another example at the molecular level in crystals is the interaction between local vibrational energy and lattice distortion. A simple and well known example is a candle. The flame exists due to a balance between "the yin of thermal diffusion" and "the yang of nonlinear energy release." Interestingly the nerve fibers in animals also display this nonlinear diffusion. Similar patterns can be observed at each level of emergence in all non-linear dynamic holarchies.

It is this circular co-dependancy which is of utmost importance in understanding the complexity which exists in all natural systems. Holons exhibit this in the relationship between whole and parts. Morin points out the same circularity exists between unity and diversity (or the one and the many) and also between the subject and object. [6] Alan Watts illustrates this by indicating the inseperability of figure and ground in our perception, although it seems possible in our use of words: "Things are separable in words which are inseparable in nature because words are counters and classifiers which can be arranged in any order. The word 'being' is formally separate from the word 'nothing', as 'pleasure' from 'pain.' But in nature being and nothing, or solid and space, constitute a relationship as inseperable as back and front." [14]

The preceding paragraphs have described levels of organization, as revealed by the systems sciences. Nicolecu makes the point that these are different from what he terms 'levels of Reality'. That is, the levels of organization all exist at a single level of Reality. He defines a level of Reality as "an ensemble of systems which are invariant under the action of certain general laws." [8] Quantum theory describes a completely different level of Reality in that fundamental laws are not the same as those at the macrophysical level. For example, at the quantum level, notions of local causality breakdown and are replaced by a global causality. The passage from the quantum level to the classical level can be seen in terms of a phase transition, such as when water changes phase from solid to liquid. This idea can be extended to perhaps provide a more accurate understanding of the transpersonal stages of the psyche. Wilber's model has these stages emerging directly from the vision-logic or Centaur level, which many authors have disagreed with. Given an understanding of Nicolecu's concept of levels of Reality, these transpersonal stages should perhaps be understood as existing at a separate level of Reality; that is, the movement beyond the stage of vision-logic is akin to the phase transition going from quantum to classical levels. The laws governing these levels do seem to depart radically from the laws of the macrophysical world. These phase transitions of Reality can be described by the logic of the included middle, as formalized by Lupasco.

The Logic of the Included Middle

The highest skills are contingent upon the unification of opposites, the co-ordination of relatively independent parts . . .

Straus, E.W. The upright posture, Psychiat. Quart. 26: 529-561, 1952

Classical logic, as introduced by Aristotle, is founded on three axioms:
1. The axiom of identity : A is A.
2. The axiom of non-contradiction : A is not non-A.
3. The axiom of the excluded middle : There exists no third term T which is
at the same time A and non-A.

Classical thought, with its' single level of Reality has assumed that the second and third axioms are equivalent. With the notion of different levels of Reality, as discussed above, this notion is no longer valid.

Multivalent logics, for example fuzzy logic, tend to attack the second axiom, claiming that the difference between A and not-A is not absolute but a matter of degree (shades of grey rather than black and white). While this is applicable to a single level of Reality and is the logic that Wilber's holons obey, it is inadequate for a multi-level reality as quantum theory has made necessary. This can be seen in Kosko's theory of Subsethood which describes the relationship between the parts and the whole, using fuzzy logic. [3]

Stéphane Lupasco in the 1940s, through contact with quantum physicist Louis de Broglie developed what he called "le principe d'antagonisme", which is a logic of contradiction and complementarity. His ideas are currently undergoing a revival in France, where several of his works have been re-released. His theory formalizes the 'logic of the included middle' and allows for a complete integration of the different levels of Reality, both on the side of the subject and that of the object. Basarab Nicolescu in Gödelian Aspects of Nature and Knowledge says of the logic of the included middle:

"History will credit Stéphane Lupasco with having shown that the logic of the included middle is a true logic, formalizable and formalized, multivalent (with three values: A, non-A, and T) and non-contradictory. Our understanding of the axiom of the included middle -- there exists a third term T which is at the same time A and non-A -- is completely clarified once the notion of 'levels of Reality' is introduced." [8]

The centrality of this logic to transdisciplinarity inquiry is evident in the following comment by Nicolescu, "The logic of the included middle is perhaps the privileged logic of complexity, privileged in the sense that it allows us to cross the different areas of knowledge in a coherent way, by enabling a new kind of simplicity." [8]

Lupasco's logic keeps the first two axioms as they are, but introduces a third term T - thus allowing for an included middle, but at a different level of Reality. Many of the paradoxes revealed by quantum theory are thus resolved. For example, what appears as either a wave (A) or a particle (non-A) at the classical level, becomes a quanton (T) at the quantum level. This term T, in turn generates another pair of contradictories at its own level (A1 and non-A1), which are resolved by another T at another level of Reality (T1). This process can occur for all designated levels, those currently known and those yet to be discovered. Nature can thus be seen as an open unity of levels, with a coherence existing between each of them. Not only does this occur for Nature or the transdisciplinary Object, but also for the human or transdisciplinary Subject- humans have different levels of perception analogous to the differing levels of Reality, the two sides of the same coin. The logic of the included middle, once included in the Transdisciplinary model of Reality, also helps to resolve many other contradictory dualities: subject/object, matter/consciousness, nature/divine, simplicity/complexity, reductionism/holism, diversity/unity. In the case of simplicity and complexity, the infinite simplicity of the transdisciplinary Subject corresponds with the infinite complexity of the transdisciplinary Object. [9]

This new logic corresponds to what Wilber describes as vision-logic [15]. Similar intuitions of this have been put forward by several authors. Two of particular interest are Nishida Kitaro and Matte Blanco [1]. Nishida, coming from a background in Zen, was attempting to find a logic with which to account for the satori experience. He realised that ordinary logic could not accomplish this task because "for any judgement to take place, there has to be a whole in which the subject and the predicate are contained." Blanco, working in psychiatry and psychoanalysis and having studied Russell and Whitehead's Principia Mathematica, arrived at very similar conclusions in trying to formalize the logic of the unconscious as put forward by Freud. He noted that our thought (especially pre-conscious or mythic) does not always use the exclusionary bivalent 'either-or' logic. This is most evident in the use of metaphor and imaginary thinking, which tend to exhibit a 'both-and' logic. Blanco's epistemology relied on the terms asymmetry and symmetry, which he initially referred to as homogeneity and heterogeneity. Curiously, Lupasco also used these terms, saying that homogeneity is a state of simplicity or equilibrium whereas heterogeneity leads to complexity. The parallels with Wilber's agency and communion and Grössing's logic of evolution are quite striking. The yang-yin polarity is apparent in all four.


To cover all the earth with sheets of hide-
Where could such amounts of skin be found ?
But simply wrap some leather round your feet,
And it's as if the whole earth had been covered !

Shantideva [13]

The system paradigm demands that we master, not nature, but the desire for mastery, which opens up for us forms of action which necessarily entail self-consciousness and self-control.

Edgar Morin [6]

Along with the emergence of different levels of Reality and alternatives to bivalent logic (including Lupasco's Antagonistic Principle), this century has seen the rise of chaos, complexity and the non-linear sciences. These systems paradigms have finally dashed all hopes of describing and controlling Nature in simple terms. While these concepts are revolutionizing our understanding in different disciplines in science, their fundamental knowledge of Nature has not yet made its way to the social and political spheres. Indeed, the concept of a uni-dimensional reality governed by a bivalent logic and linear simplicity seems more entrenched than ever as people search for firm ground on which to stand in a rapidly changing world. The rise of fundamentalist movements and increasingly punitative laws are a reaction to the increasing complexification of societies all over the planet.

Complex Nature demands complex thought. Edgar Morin has been calling for a new complex thinking for over twenty years now. It is more relevant today than ever. In a recent article he has repeated his call for a radical reformulation in our organization of knowledge. [6] In order to organize the increasingly complex nature of knowledge we need to develop a form of recursive thinking. This is a mode of thought "capable of establishing a dynamic and generative feedback loop between terms or concepts (such as whole and part, order and disorder, observer and observed, system and ecosystem etc.) that remain both complementary and antagonistic." Although this initially seems impossible, once one has comprehended the different levels of Reality and their associated logic of the included middle (Lupasco's Antagonistic Principle), it becomes much clearer how to proceed. What he is calling for is a knowledge that does not try and separate out the opposing poles of the many dipolar relationships in nature- in a manner of speaking, to cut the ouroboros in half. While this separation is possible using rational thinking, this is exactly the root of the current global crisis. Nature does not (and cannot) function using monopolar relationships. It is this amateur attempt at simplifying our knowledge of nature that results in our infusing more and more dysfunction into the many complex, interrelated systems that make up our ecosystem. To this end, he introduces a macro-concept for our notion of system that consists of three related and inseparable parts- System, Organization and Interaction. This principle of system organization is an irreducible explanatory principle- it cannot be simplified further. In fact he goes on to show that this macro-concept is related (again inseparably) to another triad of Organization, Order and Disorder. This relation can be visualised as two triangles meeting at a common vertex of organization (or more correctly auto-[geno-pheno]-eco-re-organization). There is a recursive feedback loop between all five. Rather than an atomistic notion of order, this is a molar, recursive macro-concept or as Alwyn Scott would describe it "a slithering nest of ourobori."12

Further insights into this new organization of knowledge can be derived from the attractor concept in dynamical systems theory.11 An attractor is a solution to a set of equations towards which a dynamical system tends. Attractors are not real physical objects, they exist in phase space. A phase space is a mathematical plot which is a collection of all possible states in a dynamical system. So a single point in phase space describes the entire system completely. The study of phase space was initially limited to 2 dimensions (that is a representation of two first order differential equations), and since chaos cannot exist in a 2D flow, the only known attractors, proved by the famous Poincare-Bendixson theorem, were point attractors, periodic attractors (or limit cycles) and quasi-periodic attractors (or invariant tori). This all changed with Lorenz' s study of the weather. Using three differential equations, he found an attractor which was not one of the standard three. It was chaotic because of its sensitivity to initial conditions and it was also 'strange', which actually means it exhibited fractal structure. The general (but incorrect) understanding of strange attractors is that they are chaotic, but there also exist chaotic attractors that are not strange and strange attractors that are not chaotic ! So the term 'strange' should be reserved for attractors that exhibit fractal structure (i.e. are geometrically strange).

An interesting comparison can be made between the differing logics discussed previously and the concept of attractors. The standard bivalent logic is analogous to the point or cyclic attractor- their behaviour is predictable and regular. Just as these were assumed to be the only possible attractors, bivalent logic was assumed to be the only possible logic. With the addition of a third dimension, the strange attractor was discovered; similarly, with the discovery of another level of Reality, the 'logic of the included middle' became possible. Strange attractors are deterministic but unpredictable; in effect they constrain chaos to a limited domain. The same can be said for complex thought relying on the logic of the included middle- it can be infinitely subtle and complex, even fractal in structure, but it is still constrained to specific areas, allowing it to be useful in understanding complex systems. In this way, thought can remain coherent while being free to be unpredictable, thus allowing for the emergence of creative ideas.


"Disciplinary research concerns, at most, one and the same level of Reality ; moreover, in most cases, it only concerns fragments of one level of Reality. On the contrary, transdisciplinarity concerns the dynamics engendered by the action of several levels of Reality at once . The discovery of these dynamics necessarily passes through disciplinary knowledge. While not a new discipline or a new superdiscipline, transdisciplinarity is nourished by disciplinary research; in turn, disciplinary research is clarified by transdisciplinary knowledge in a new, fertile way. In this sense, disciplinary and transdisciplinary research are not antagonistic but complementary."

Basarab Nicolescu [8]

The 'Three Pillars of Transdisciplinarity' allow for a more comprehensive understanding of complexity. This in turn allows for a radical reformation in our organization of knowledge. The investigation of the dynamics engendered by the action of several levels of Reality at once- the essence of transdisciplinarity- will allow fresh insights into all disciplines, and these insights will in turn feedback into transdisciplinary research allowing further insights to be generated for the disciplines. This dynamic feedback in an open unity of levels of Reality, making use of the logic of the included middle and, where necessary, the logic of the occluded middle, should allow humankind to gain some measure of control on the currently overwhelming deluge of information being generated by the present disciplinary big bang. With greater understanding of the knowledge so generated, this should allow for a more comprehensive ability to tackle the multifarious and inter-related problems facing our planet. This is not a panacea which will banish all our problems, but at least it will allow us to stop infusing further dysfunction into the ecosystem and perhaps leave a somewhat habitable earth for the generations to come.

***** A last word from Alan Watts: [on the 'T' (for Tao) in the logic of the included middle]

"There is nothing for it, then, but to trust and go with the Tao as the source and ground of our own being which 'may be attained but not seen.'

Is there any clear way of distinguishing organic pattern from mechanical and linear pattern, between nature and artifice, growing and making ? Obviously, no animal or plant is 'made' in the same way that a table is made of wood. A living creature is not an assemblage of parts, nailed, screwed, or glued together. Its members and organs are not assembled from distant sources and gathered into a center. A tree is not made of wood; it is wood. A mountain is not made of rock; it is rock. The seed grows into the plant by an expansion from within, and its parts or distinguishable organs develop simultaneously as it expands. Certainly, the growing seed is gathering nourishment from its environment, but the process is no mere sticking together of nutritive elements, for it absorbs and transforms them, and one sees nothing like this is the manufacture of an electric motor or computer.

Though we talk about mechanisms of organisms, surely this is no more than analogy. In studying organisms by the analytic way of breaking them down into parts we are simply using a mechanical image of their structure. Such analysis is the linear, bit-by-bit method of conscious attention, whereas in the living organism the so-called "parts" are exfoliated simultaneously throughout its body. Nature has no "parts" except those which are distinguished by human systems of classification, and it is only by elaborate surgery that any part of a body can be replaced. The body is not a surgical constuct put together with scalpels, clamps, and sutures. We must make a distinction between an organism which is differentiated and a machine which is partitive. Machines generating other machines will always do so by assemblage and the linear method, although we are coming to the point of combining such machines as computers with organic elements. In fact the computer was always combined with an organic element-- man himself, for man is the boss and creator of the computer.

But the Tao is not considered the boss and creator of our organic universe. It may reign but does not rule. It is the pattern of things but not the enforced law. Thus we read in the Han Fei Tzu book (early -3rd century):

'Tao is that whereby all things are so, and with which all principles agree. Principles (li) are the markings (wen) of completed things. Tao is that whereby all things become complete. Therefore it is said that Tao is what gives principles. When things have their principles, the one (thing) cannot be the other. . . . All things have each their own different principle, whereas Tao brings the principles of all things into single agreement. Therefore it can be both one thing and another, and is not in one thing only.'"

Watts, Alan.(1975) Tao: The Watercourse Way. Pantheon Books, NY


1. Finkenthal, M.(1998) Rethinking Logic : Lupasco, Nishida and Matte Blanco. Bulletin Interactif du Centre International de Recherches et Études transdisciplinaires n

2. Grössing, G.(2000) Quantum Cybernetics : Towards a Unification of Relativity and Quantum Theory Via Circularly Causal Modeling, Springer Verlag

3. Kosko, B. (1993) Fuzzy Thinking: The New Science of Fuzzy Logic. Hyperion, New York

4. Lumley, T. (1999) Epilogue-Prologue: The 'Inside Story'

5. Morin, E. (1977) La Méthode. 1. La Nature de la Nature. Seuil, Paris

6. Morin, E. (1992) From the Concept of System to the Paradigm of Complexity. Journal of Social and Evolutionary Systems 15(4):371-385, JAI Press

7. Nature Neuroscience Editorial February 2000 Volume 3 Number 2 p 97

8. Nicolescu, B.(1998) Gödelian Aspects of Nature and Knowledge. Bulletin Interactif du Centre International de Recherches et Études transdisciplinaires n

9. Nicolescu, B. (1996) La transdisciplinarité , manifeste, Le Rocher, Paris, coll. "Transdisciplinarité" Translated by Karen-Claire Voss and Rob Baker

10. Nicolescu, B.(1991) Science, meaning and evolution - The cosmology of Jakob Boehme , Parabola Books, New York.

11. Peat, F. D.(1999) New Science, New Vision

12. Scott, A C (1999) Nonlinear Science: Emergence & Dynamics of Coherent Structures. Oxford University Press, Oxford

13. Shantideva (1997) The Way of the Bodhisattva. Shambala Publications Inc., Massachusetts

14. Watts, A W (1958) Nature, Man, Woman. Pantheon Books Inc. Republished 1991: Vintage Books, New York

15. Wilber, K (1995) Sex, Ecology, Spirituality: The Spirit of Evolution.

Shambala Publications Inc., Massachusetts

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