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INTEGRAL WORLD: EXPLORING THEORIES OF EVERYTHING
An independent forum for a critical discussion of the integral philosophy of Ken Wilber
Publication dates of essays (month/year) can be found under "Essays".
As an economics’ student in Dublin in the late 1960’s, Peter Collins underwent a significant “scientific conversion”. Since then he has devoted considerable attention to the implications of a full spectrum developmental approach for radical new interpretations of mathematics and its related sciences. Though potentially of growing relevance for better understanding of our present problems, so far, he believes, these have been greatly overlooked by both the scientific and integral communities.
In this article, I will examine Ken Wilber's AQAL approach i.e. all quadrants, all levels, all lines, all states and all types with a view to enlarged understanding of these areas, which subsequently have considerable implications for the appreciation of perspectives.
Part 2: Enlarging the AQAL Framework
My personal familiarity with the quadrant notion dates back to time as a student of economics in the late 1960's. It soon became apparent to me that the theoretical approach to economics was based on consideration of the external to the almost total exclusion of its internal dimension. Even when psychological factors such as consumer expectations were acknowledged, typically they were treated in reduced fashion as “objective” variables.
Then with respect to the market mechanism, the determination of price through demand and supply was interpreted in an impersonal manner. However, this considerably misrepresented the true dynamic nature of economic behaviour, where as for example in financial markets, subjective factors can play a huge role.
Equally, I could appreciate the strong ideological implications of this attempted representation of the free market system. For once one accepts its supposedly objective nature, this thereby largely removes ethical considerations of justice with respect to the system. 
Also as regards the fundamental economics notion of scarcity, the conventional Western approach again unduly concentrated on the external aspect.
So economic growth, through the production of ever more goods and services was seen as the appropriate way of attempting to reduce scarcity.
However, in affluent Western countries this seemed somewhat self-defeating as consumer wants, largely promoted though mass advertising continued to rise beyond the ability of economies to increase production.
Thus the important (internal) psychological side of the equation in the requirement to encourage moderate consumer desires was being largely ignored.
Therefore it was clear to me that both external (objective) and interior (subjective) aspects should be promoted in a more balanced manner, which in turn needed a dynamic interactive means of viewing economic behaviour.
The two major divisions of economics are microeconomics relating to the part units of the economy and macroeconomics to its general behaviour (as a whole).
In its earlier development, an attempt was made in reduced terms to treat the overall economic system as the sum of its parts.
This led to an idealised view of free markets working efficiently in relative isolation from each other, where effectively macroeconomic behaviour was reduced to microeconomics.
However the Great Depression of the 1930's especially showed that this approach could not be sustained and that the general and particular aspects of economics (as I termed them then) both contained distinctive features that mutually interacted with each other.
So impressed was I with these polarities (external/internal and general/particular) that on completion of my degree, I proposed to do a doctorate on a new dynamic methodology for economics designed to explicitly incorporate both sets of features. 
Linear and Circular Approaches to Quadrants
However, following preparatory work for this thesis, I began to realise how they represented universal features of every system.
This then led to a deep engagement with science, philosophy, psychology and mystical spirituality that culminated through several different stages, in a new integral mathematical appreciation of the basic polarities. 
In fact the second of these stages led explicitly to a circular four quadrant geometrical interpretation, enabling the polarities to be understood in a dynamic interactive manner, in contrast to the four quadrant approach later employed by Ken Wilber (which properly allows for a limited form of differentiation).
I had been familiar with Wilber's books from the early 80's (having acquired all but “A Sociable God”) and was greatly impressed both with the range and quality of his output.
So when I then read in “Sex, Ecology, Spirituality” and “A Brief History of Everything” of his own discovery of the four quadrants, I wrote to him on three occasions (1996-1997) regarding my corresponding discovery of this notion (and extension to eight sectors) with a brief outline of its holistic mathematical rationale.
And I could readily appreciate the complementary nature of the two approaches, with Wilber's suited to extensive empirical investigation with my own more directly geared to an integral appreciation of the quadrants.
Wilber's model is customarily presented as a square diagram.
The simplest illustration can be mathematically expressed in geometrical terms as a square (with side 1 unit), which can then in turn be broken into four equal sized quadrants (also representing squares with each side half of the larger square). Though Wilber frequently shows diagonal lines bisecting the quadrants, these are simply used to represent the hierarchical nature of the holons, which he identifies with each quadrant.
And we have here the standard mathematical notion of linear dimensions (with the square linear in two dimensions). It is indeed suited to the differentiation of meanings in a multidisciplinary manner, associated with a wide range of human experience, and it has to be said that it has proved remarkably successful in this regard.
However it can only do so in a somewhat absolute fashion, where quadrant locations are given just one fixed interpretation, with holons misleadingly identified as belonging to particular quadrants. However, in dynamic relative terms, four distinct interpretations can be given, with continual switching taking place as between quadrants. And I explored this important point in my last article, which is completely overlooked in Wilber's approach.
However there is another circular notion of dimensions, where for example 2 dimensions can be geometrically expressed by the same diagram that represents the two roots of 1, i.e. + 1 and - 1 in a conventional manner.
And just as these roots have an established quantitative rationale in mathematics, I realised that these could equally be given a corresponding holistic integral interpretation, where signs now take on a qualitative rather than quantitative meaning.
This realisation proved to be vitally important, as it set the foundation for a fully fledged integral appreciation, where all mathematical symbols and relationships can be given corresponding qualitative as well as accepted quantitative meanings.
So I will just briefly explain its rationale here.
When one recognises an external phenomenon, it is thereby consciously posited in experience. Thus conscious recognition always implies the holistic mathematical operation of addition i.e. positing (+).
Then to switch polarities i.e. from external to internal, one must render the phenomenon (to a degree) unconscious, which implies dynamic negation. And this represents the corresponding holistic mathematical operation of subtraction (-). Thus to switch from external to internal, one must dynamically negate in an unconscious manner (what has externally been posited). However, the internal self then in turn is made positive i.e. conscious, in experience. So once again, in switching back to conscious recognition of the external phenomenon, one must negate conscious recognition of the (internal) self.
Thus there is a continual dynamic switching in experience, from external to internal and internal to external, where what is positive and negative, have a merely relative validity. Thus, when the external object is represented as + 1, then, relatively, the internal self is - 1. And when the conscious self is in turn posited in experience as + 1, then the related external phenomenon is now - 1.
Thus in dynamic relative terms, both internal and external aspects continually switch between + 1 and - 1 (and - 1 and + 1).
To the extent that dynamic negation takes place, there is likewise an unconscious merging of positive and negative polarities leading to the qualitative experience of interdependence. This is akin to the manner in which matter and anti-matter particles fuse, thereby creating physical energy.
Thus the qualitative experience of interdependence relates directly to a corresponding form of psycho-spiritual energy, which is customarily referred to as holistic intuition. And again this in turn reflects the degree to which the unconscious recognition of complementary opposite poles enters experience.
In analytic quantitative terms, + 1 - 1 = 0. Likewise, in a complementary holistic manner, + 1 - 1 = 0, where 0 now relates to the nondual notion of emptiness (or nothingness).
And this is directly related to the appreciation of perspectives, where external and internal (and internal and external) are always in dynamic relation to each other. Likewise in analytic terms, we can view perspectives as objective or subjective or alternatively, in more holistic terms - where the unconscious is directly involved - as interobjective or intersubjective. So again, when little interaction as between opposite poles takes place, the unconscious largely serves to switch experience in a somewhat rigid manner from external to internal (and internal to external).
However, when the quality of interaction increases (through implicit recognition of the opposite unrecognised pole), then the unconscious union of opposites through intuition (as the recognition of qualitative interdependence) thereby occurs.
Now this initial breakthrough with respect to integral mathematical appreciation occurred by 1970, and was directly related to the personal stage of spiritual development unfolding at that time.
It then took a further 10 years, corresponding to a new stage of development, to make the next big breakthrough, in the (circular) holistic appreciation of 4-dimensional understanding. And this is expressed through the geometrical representation of the four roots of unity, which literally divide the unit circle (in the complex plane) into four quadrants.
However, this introduces imaginary as well as real mathematical notions.
Suffice it to say that in analytic terms, the imaginary notion has utterly transformed the quantitative appreciation of mathematics, with numbers now understood in more comprehensive complex terms, as comprising both real and imaginary parts.
What however is not at all yet realised is that the corresponding integral mathematical appreciation of the imaginary notion has likewise the power to utterly transform understanding of all qualitative type relationships. And deeply relevant to such appreciation is the relationship between parts and wholes (and wholes and parts), which when correctly understood in holistic mathematical terms, is real and imaginary (and imaginary and real) with respect to each other.
So properly understood, holons (and onhols) should be viewed in a complex rational manner, explicitly incorporating both conscious and unconscious aspects of understanding. In this context, conscious understanding represents what is real, suited to appreciation of reality as composed of parts in a quantitative manner. Therefore, when as in conventional science, only the real (conscious) aspect is formally recognised, the whole is viewed in a necessarily reduced manner as the sum of its constituent parts.
The unconscious aspect cannot directly enter understanding but rather is indirectly projected in imaginary terms (now using the term in its precise holistic mathematical manner). And it is this indirect relationship of the unconscious to objects, in an imaginary manner, thereby providing a quality of relationship with other objects, that properly defines them as wholes (as distinct from parts).
So, when Ken Wilber says that we don't see the square root of - 1 (i.e. i, the imaginary unit), out there in the empirical world, in a crucially important sense, he is very mistaken. For when one acquires the integral mathematical appreciation of this notion, one clearly realises that it is always implicitly present, whenever the qualitative recognition of wholeness (as interdependence) is involved.
I would say that perhaps the single most important integral mathematical insight to be appreciated is this qualitative recognition of the imaginary notion. 
And just as with two dimensions, we have (horizontal) real polarities that are + 1 and - 1 with respect to each other, likewise with four dimensions, we have the two additional (vertical) polarities + i and - i.
And this implies, as I highlighted in a previous article, that there are two complementary notions of wholeness i.e. the collection notion of qualitative wholeness (as holarchy) that ultimately transcends all parts and the individual notion of wholeness (as onarchy), where ultimately the whole is seen as deeply immanent within each part.
And this latter emphasis is greatly missing from Ken Wilber's work, leading in turn to a significant imbalance of his understanding of how development unfolds with respect to each of his quadrants.
So the circular approach directly focuses on the complementary manner in which the key opposite polarities of external and internal and whole and part are dynamically related to each other in an integral manner. And in a remarkable fashion, it manages to combine both the conscious and unconscious aspects of experience.
Therefore, the real polarities (along the x axis) relate directly to the conscious aspect as whole/parts in an analytic type manner. The imaginary polarities then, in a necessarily indirect manner, relate to the unconscious aspect as whole/parts (and part/wholes) in a qualitative holistic fashion.
So we have here the complementary relationship as between collective wholes that spiritually transcend their physical parts and individual parts, through which the spirit is correspondingly made immanent in a physical manner. And these have external and internal expressions in both analytic and holistic terms, which keep switching as between each other through the dynamic interactive nature of experience.
Thus we have a (linear) differentiated interpretation of the quadrants, where as in Wilber's approach, locations are given absolutely fixed positions.
We then have the (circular) integral appreciation, which is directly suited to how opposite poles dynamically interact with each other.
Then finally, we have the radial interpretation of quadrants that coherently combines both differentiated and integral appreciation.
Here, through recognising that quadrants locations are fixed in a relative, rather than absolute manner, 16 relatively distinct interpretations (which correspond directly with the indigenous perspectives) are identified in differentiated terms. These can then be perfectly reconciled with each other in a corresponding integral manner.
And I sought to outline the basis of this approach in my last article.
Eight Sector Approach
However, important though the 4-dimensional interpretation is for development, I have long argued that a more comprehensive integral treatment as 8-dimensional is ultimately required.
And this has significant connections with Jung's notion of mandalas, serving as symbols of integration. Though typically presented in highly ornate form, the most important mandalas are frequently based around a circle with 8 equidistant points (which in geometrical terms are expressed by the corresponding 8 roots of 1).
Then holistic mathematical appreciation can show in a precise manner why such mandalas possess their integral significance. 
Need for Two Approaches
Wilber understandably believes that development unfolds through different levels. However I would have considerable reservations regarding the nature of his treatment.
In his interpretation of levels, Wilber uses a linear asymmetrical approach, where for example, the basic stages are defined unambiguously as higher or lower in terms of each other.
So from this standpoint, the subtle realm is a higher stage of development than vision-logic, which in turn is higher than the formal rational stage. And this is consistent with his holarchic principle, where all of the lower is in the higher but not all of the higher in the lower.
The big problem is that he thereby uses an approach that is solely suited for the differentiation of stage development to likewise include the integral aspect. So there is a confusion of two distinct notions, with the integral effectively reduced to differentiated appreciation.
This then leads to Wilber employing a top-down form of integration. However I explained at considerable length in a previous article why this will not suffice as it is very unbalanced.
Integration takes place in a complementary manner in horizontal, vertical and diagonal terms.
So in vertical complementary terms, the highest is paired with the lowest and the lowest with the highest stage (and 2nd highest with 2nd lowest and so on). However, when one approaches development from a differentiated perspective, one may be tempted to think that the 1st stage is completed following initial differentiation of the bodyself, thereby allowing progress to the next stage.
However, differentiation is not integration. So the continuous problem in development remains of achieving satisfactory bottom-up integration of the first level with other levels and in turn top-down integration of all these with the first level.
The holarchical approach therefore in fact offers no satisfactory explanation as to how integration, as opposed to differentiation, takes place. And as successful integration ultimately involves all other levels, this implies that it remains an ongoing process throughout one's entire development, never reaching final completion.
So though a certain differentiation of the body/mind does indeed take place at the 1st of the lower levels, a great deal of instinctive confusion necessarily remains. And this can only be directly accessed much later in development, through a complementary relationship with the corresponding “highest” stage. 
Therefore an all-level balanced approach should combine both linear and circular notions.
In earlier development, circular notions, relating to a greatly confused form of integration, are more relevant with the linear emphasis on differentiation, through successive stages, taking time to properly establish.
Then when development reaches the fully fledged personal levels (where the differentiated aspect reaches its zenith), linear asymmetrical notions now appear largely appropriate for the study of development.
As in our culture, intellectual life is predominantly conducted using the specialised reason of the middle levels, it is not surprising that this linear view is then subsequently imposed - though inappropriate for proper interpretation - on the earlier stages.
Then at the “higher” stages, linear notions start to gradually break down with mature contemplative understanding becoming increasingly circular in a paradoxical manner.
And because of their mutual complementarity, it is only now that one can properly return to the corresponding “lower” stages with a view to unravelling earlier primitive confusion.
Finally, at the radial stages, both linear and circular aspects can both be combined to their optimum effect, where the relative independence of each stage can seamlessly interpenetrate with the combined interdependence of all stages.
Discontinuity as between West and East
A considerable discontinuity marks Wilber's treatment of recognised Western stages up to the centaur and “higher” esoteric Eastern stages beyond this stage.
Though he makes considerable use of the specialised terminology of these mystical traditions in describing the advanced meditative states that occur - though not properly suited to a Western style intellectual treatment - remarkably little content is provided as to the equally important dynamic structures (cognitive, affective and volitional) that unfold at all these various stages.
This discontinuity in Wilber's approach can be conveniently expressed by stating that his intellectual treatment of the recognised Western stages over-emphasises structures of form, whereas his treatment of spiritual stages, beyond the centaur, equally over-emphasises corresponding states of emptiness.
However the considerable task, in successfully marrying East with West, which is not really addressed by Wilber, is to show how structures and states are dynamically related with each other throughout all stages of development.
Intellectual discourse, as we know it, is largely conducted from just the middle levels of the spectrum. And this will remain until it can be shown how these are coherently connected with all other levels.
So even with Ken Wilber, intellectual discourse is largely confined to the middle levels, while readily admitting that his use of vision-logic represents the advanced expression of these levels.
Therefore I believe that a truly important task for our time is the clarification (in cognitive, affective and volitional terms) of the multidimensional structures that unfold at the more advanced levels. And I have found that this task can be greatly facilitated through the appropriate use of integral mathematical notions.
Perhaps, the greatest finding of all that stems from this approach is that mathematics itself undergoes a complete transformation with respect to understanding, where its symbols can be given a coherent qualitative as well as quantitative interpretation.
And as this new understanding gradually encompasses all perspectives (relating to both the arts and sciences), the realisation eventually dawns that reality itself, as regards all its aspects, is intrinsically encoded in a mathematical manner (where once more its symbols are appreciated in both quantitative and qualitative terms).
Wilber maintains that phenomenal reality is composed of (sentient) perspectives.
However, I would rather say that all phenomenal reality is encoded in mathematical terms. So perspectives implicitly entail, as soon as they arise, fundamental mathematical notions.
Mathematics in this inherent sense is thereby the language of all reality.
Need to Balance Dual and Nondual
Another notion of Wilber's that I would strongly contest is his apparent view that the most advanced level of development is nondual.
So when one looks at his typical outline of stage levels, overall development is portrayed as ascending in linear asymmetrical fashion to a “highest stage” that is termed nondual reality.
However properly understood, both dual and nondual aspects are equally important in experience.
In development, the initial specialisation of dual understanding culminates with the vision-logic (of the centaur).
Then the following phase of transcendent spiritual development (understood as the spiritual ascent) culminates with the experience of nondual reality, where emptiness is beyond any phenomenal notion of form.
However in itself this represents an extreme position, which if sustained, is potentially unhealthy for development.
So the next phase of the spiritual descent is then designed to come down from the heights, as it were, in the realisation that both dual and nondual are complementary notions that are equally necessary.
Thus when the marriage of dual and nondual takes place - what I term - radial reality can then properly commence. Here one is continually aware of the nondual as the present moment at the centre of one's being, with all dual activity then seamlessly emanating from the centre as temporary phenomenal expressions of this reality.
Therefore in this final stage, which is better represented I believe in Western mysticism, activity (dual) and contemplation (nondual) are seen as mutually serving each other.
Thus the most advanced experience is not that of the nondual, but rather the exquisitely balanced interaction of both dual and nondual aspects.
And I believe there is a significant failure to properly represent this in Wilber's work, apart from the fact that such omission leaves many advanced stages of development, especially at the radial levels, completely unaddressed.
Extended Model of Development
So in an attempt to clarify, I will briefly outline my own model of development, which is designed to properly recognise differentiation (dual), integration (nondual) and irradiation (which is the balanced specialised combination of both dual and nondual). This latest model, which can be found in various contributions at Spectrum of Development, includes 8 bands (with 3 main levels in each band).
So for example, the more cautious contemplative person may be especially required here to become much more prominent in supporting an active cause. To a certain extent everyone enjoys continuous access to all these bands. However mature development requires proper differentiation in terms of each level in a discrete sense combined with continual sustained integration of all levels.
So Wilber's model is certainly not all-level as I would understand it. Also, even insofar as it recognises the levels of Band 3 (in terms of the spiritual ascent) it is gravely deficient with respect to proper recognition of structures.
Also there is no distinct Band 5 (regarding the corresponding spiritual descent) and no proper recognition of the radial levels (Bands 6, 7 and 8).
And the importance of this for perspectives is that it means that properly we have several metaperspectives of perspectives (that I briefly referred to in the last article).
So we can distinguish two differentiated types (of which Wilber's approach represents the second of these), two integral types (the 1st of which I hope to develop in a future article) and then three radial metaperspectives.
Limited Nature of Lines
Wilber uses the term “lines of development” to refer to the multiple intelligences that can unfold in development, such as interpersonal and intrapersonal skills, needs, self identity, aesthetics, artistic talent such as musical and design, kinisthetic abilities, moral and ethical and so on.
Now Wilber's view is that many of these unfold in a relatively independent manner, which explains his use of the term “lines”.
However, once again this only serves to highlight the differentiated aspect of development to the exclusion of the corresponding integral aspect, for clearly from the latter perspective, one should be focusing on the manner in which these “lines” are likewise relatively interdependent with each other. And regarding this latter aspect the very use of the terms “lines” is somewhat inappropriate.
So I personally prefer the use of the terms “modes” in this context, which can be defined in linear terms (with respect to their relative independence) and in a circular manner (regarding their corresponding relative interdependence).
I have been always surprised that Wilber, even in his own terms, has never properly considered the implications of introducing these many lines (Wilber 3), as it threatens to undermine any coherent notion of his basic stages in development.
Wilber freely accepts that the lines can undergo very unequal development. Thus someone, who is advanced with respect to a cognitive, could be at a comparatively early level of development regarding a corresponding affective line. This then begs the question as to whether the basic stages, which presumably encompass a number of lines, can be given any strict meaning. For example how would holarchic development now apply to a basic stage as opposed to an individual line of development?
In the terms that I describe it, we have modes of development that can exhibit both linear aspects (as relatively independent) and circular aspects (as relatively interdependent) respectively.
And indeed the circular aspect is very important in many contexts (though largely ignored by Wilber).
Cyclical Patterns of Behaviour
It has always fascinated me as to how development can become very much tied to a favoured mode.
I remember in particular reflecting on this issue when reading a biography of Johnny Cash, which provided a fascinating study of a man, where the potential for true greatness and many human frailties were combined in equal measure.
So Cash attempted to express his desire for spiritual transcendence through his undoubted ability as a singer and performer.
However sudden success in this regard can then easily lead to a premature form of transcendence, where with new found fame, successful hit records and adoring audiences, the sky is seemingly the only limit.
Therefore in reaching out for ever more success, one quickly discovers that one is not ready to cope with the many new responsibilities that it brings. So this can lead to the strong exposure of the raw shadow, which one is equally unprepared to face. Then in the attempt to restore the glory and avoid the shadow, one may be led into increasingly damaging behaviours such as alcoholism, drug taking, promiscuous sex and the abuse of power and celebrity.
So there can now be a prolonged period of time, where behaviour keeps swinging in an unstable fashion as between trans and pre (and pre and trans) states with neither attaining their developed expression.
And this cyclical pattern is very common in a great many situations, as for example where a special talent is expressed through artistic and sporting endeavours.
In fact the role of sport as a unique secular form of religion has been greatly overlooked. I once listened to a programme where Irish fans of remote clubs in the lower English and Scottish leagues were invited to come on air and speak about their allegiance. What I found remarkable is that this allegiance, initially made on very arbitrary grounds, often remained a life long commitment irrespective of the playing fortune of the clubs. This commitment as the supporter of a football club can be even greater than to a person's marriage or religious affiliation and clearly expresses the need to belong to a certain type of community, which exercises a far more significant meaning in people's lives than commonly recognised.
However when one examines more closely, sport in many ways provides the immanent dimension of felt emotional experience that formal religion so often fails to provide.
So when one's chosen team eventually achieves the holy grail of winning that long awaited cup or championship, it can spark remarkable displays of genuine joy among supporters. If one was to ask them many years later what was the happiest moment of their lives, many would point to that special day when their team won the coveted trophy.
Returning to musical ability, I have often wondered regarding its dual nature.
So from one perspective, this ability clearly relates to the person displaying the talent.
However the corresponding appreciation of say, a gifted singer may relate to a person without such a gift. So in a sense the talent of the individual singer only has meaning in the context of a wider community of listeners who can appreciate that talent.
And then when we inquire into the possible stages of development of such a mode, there are two sides regarding both the singer and supportive audience.
I remember being deeply moved by the singing of Charlotte Church, who as a 12 year old issued an album entitled “Voice of an Angel”.
On reflection, though she undoubtedly possessed the capacity to significantly move others at a mature level of development, she herself could not possibly have attained this maturity at such a tender age. So this points once more in yet another context to the complementary nature of pre and trans notions. As we know, some of the most famous artists lived chaotic lives displaying a high level of emotional immaturity. However their creative work e.g. through great paintings and music, could communicate with others at the most exalted level of feeling.
There is another important point here in that modes are often subject to a very limited range of stage development. So for example, it is not really meaningful to speak of a sporting talent, say for golf as unfolding through all stages, though indirectly, the implications of golfing success may have repercussions for one's further psychological development.
One especially important mode that I believe has been greatly ignored relates to the capacity for humour.
And once again humour does not rightly develop in an independent manner (as distinct from other modes) but in many ways is interdependent with them contributing to their more dynamic cyclical nature. In particular, humour can be used to achieve a rapid alteration in mood, whereby one can switch for example from a “low” to a “high” state.
In fact, many comedians have basically depressive personalities and have become practiced in the use of humour as an escape from this condition. However it generally only works as a temporary solution to their problem, which then often emerges in a more pronounced fashion in later life.
Primary and Secondary Modes
However, with respect to modes, I believe it is very important to distinguish as between primary and secondary manifestations.
Now the primary modes are cognitive (reason), affective (emotion) and volitional (will).
We should perhaps distinguish a 4th mode i.e. kinesthetic, which properly represents the instinctive combination of both affective and cognitive. So, for example the critical sporting intelligence of a sensori-motor nature that enables a player to be in the right place at the right time to score that crucial winning goal, really represents an instinctive combination of affective and cognitive aspects (operating at an optimum level).
Insofar as integration is concerned, the primary modes (like the primary colours in printing) are especially important. Therefore, to a considerable extent, balanced development must take place with respect to the 3 primary modes, especially at more advanced stages, though a great amount of variation is possible regarding the precise manner in which they are subsequently combined.
The primary modes then have a direct bearing on perspectives.
Therefore, we can distinguish as between external and internal on the one hand and personal (subjective) and impersonal (objective) perspectives on the other corresponding to both affective (emotional) and cognitive (rational) modes.
Then the volitional mode is essentially geared to maintaining a successful balance as between these complementary perspectives, thereby enabling their coherent integration, which in the most general sense defines the true nature of morality.
Bi-directional Nature of States
Wilber likewise defines his model as all states.
And in referring to states, he customarily uses the familiar language of waking, dream and sleep states.
Whereas he maintains a sharp divide as between prepersonal and transpersonal stages, he does concede that a temporary relationship can however exist as between pre and trans in terms of states.
Therefore, because he maintains that sleep, dream and waking states are open to everyone, a person, say at the mythical stage of development could obtain access to the subtle stage through a temporary peak of the spiritual state relating to that corresponding stage.
However, even in this respect there are certain problems with Wilber's approach.
For example, he does not distinguish as between the peaking of a transcendent as opposed to an immanent state.
Due to his linear asymmetrical treatment of stages (based on holarchy), this would only properly allow for the peaking of transcendent states.
However, to likewise accommodate the peaking of immanent states, one would require a true bi-directional approach, with all stages given interpretations from two opposite directions.
Just as one can temporarily obtain a peak view of a “higher” more developed state from a customary “lower” less developed stage, likewise one can also obtain a valley experience of a “lower” less developed state from a customary “higher” developed stage, with which it is paired in a complementary manner.
So for example, it would be quite common for someone who has attained mature contemplative development with respect to the subtle, to sometimes experience states associated with the earlier mythical stage, especially where traditional religious teaching has played an important earlier role in development.
Also, Wilber does not sufficiently emphasise the remarkably lucid experience of temporary states that sometimes can arise.
These can occur even in early childhood with those gifted, for example, with a special mystical talent, which can then act as a substantial catalyst for subsequent spiritual development.
Even more significantly, he largely ignores the hugely disturbing phenomenon of how some charismatic spiritual leaders, who may indeed have attained to a high level of transcendence, later succumb to sexual temptation and the desire for unfettered power, relating to instinctive states of the lower primitive self.
These then can lead to an accelerated form of corrupt development, through uncontrolled exposure to the raw shadow, with potentially devastating consequences for followers.
So I would consider this lack of sufficient recognition of the true dynamic complementarity of “higher” and “lower” stages of development (from both directions) as a significant failing regarding Wilber's writings.
Reconciling States with Structures
And then Wilber, in his attempt to maintain the holarchic nature of basic stage development, separates in an untenable manner the behaviour of states from their corresponding structures.
In is true that in some cases, development may be led more by states than structures. For example, Evelyn Underhill highlights the remarkably fluid experience of the French mystic Madame Guyon and refers - perhaps unkindly - to her feeble surface intelligence. So when the fluctuation between affective states is unduly rapid, the corresponding development of cognitive structures cannot sufficiently take place.
The opposite case, which is perhaps more common in our culture, arises when structure development becomes unduly rigid, thereby hampering the development of authentic spiritual states. I remember becoming especially aware of this when studying the German philosopher Hegel. His dialectical understanding represents a valid expression of the cognitive structures properly associated with the subtle realm. However, though initially present to a degree in his early writing, the corresponding contemplative state, dynamically appropriate to these structures, became largely depleted in later work. This then led Hegel to the misleading claim that philosophy was above religion and towards an increasingly turgid use of his dialectic.
Thus when there is too much emphasis on structures, it becomes increasingly difficult to attain to the highest states (associated with the advanced spiritual stages).
So, properly understood, both structures and states are dynamically related to each other throughout development.
Therefore a change in relation to states implies a corresponding change in relation to structures and likewise a change in structures implies a corresponding change in states.
However this necessary interaction can be explicitly ignored at the rational stages of the middle levels (which completely dominate conventional intellectual discourse).
One could validly maintain that the understanding of a scientific hypothesis, for example, requires the waking state for comprehension. However here, the cognitive structures are considered neutral with respect to this state. Therefore the state is effectively ignored altogether.
However at all other stages, the dynamic interaction as between states and structures assumes a much greater importance. So it is vital to properly portray this interaction in stage development. Indeed I would attain that a key reason why so few in our culture develop in any sustained manner beyond the middle stages is precisely because of the totally dominant influence of structures at these stages, which thereby greatly hinders the development of higher intuitive states.
I have never been especially impressed with Wilber's treatment of the more advanced spiritual levels. He clothes these, far too heavily with the terminology - largely unfamiliar to the Western mind - of the various Eastern spiritual traditions relating to meditative states. However, again he provides remarkably little content on the corresponding structures (affective, cognitive and volitional) associated with these levels.
In fact he seems, somewhat misleadingly, to associate their structures with the attainment of permanent states. However just as one would not define the structures of the middle levels as the permanent waking state, equally one should not refer to structures at the “higher” levels as permanent states.
And it is simply not true that one can only temporarily peak a “higher” state from the customary experience of a “lower” stage. One can equally peak a “higher” structure, and one can perhaps even peak a “higher” structure in a very lucid manner at a comparatively early age. And indeed this is necessarily the case, when one accepts the dynamic complementary nature of both states and structures.
In my own case, I remember at an early age, getting a very lucid insight into the reduced interpretation of multiplication and even then became convinced of a hidden dimension to mathematics that I was determined to unravel. And some 60 years later, I am still inspired by that same insight.
So again there is a massive area to be investigated in properly relating the states and structures associated with each stage and the complementary manner (in horizontal, vertical and diagonal terms) that they interact throughout development, which has remained largely unaddressed. 
Also, I would suggest that the waking, dream, and sleep terminology, though indeed valuable in certain respects, needs to be invigorated with fresh insights that might offer more precision as to the various types of states that unfold throughout development.
For example, in holistic mathematical terms, I now refer to a number spectrum of states and structures. Here, each number is associated with a distinctive holistic dimension, with a corresponding structure and state (that can be precisely defined in a qualitative manner).
As we have seen, some of these numbers i.e. 2, 4 and 8 are especially important in integral terms. Then odd numbered dimensions such as 1 and 3 are more significant from a differentiated perspective. However, ultimately all numbers can be given a distinctive holistic meaning.
Importance for Perspectives
States have a direct relevance to perspectives in this important respect.
The qualitative recognition of interdependence (which is necessary for both intersubjective and interobjective understanding) always implies the intervention of a psychological state. At the earlier levels, this occurs in a largely instinctive manner, where both objective and subjective can still remain confused with each other.
Then at the middle stages, even though one can still make interdependent connections (that implicitly require intuition), no formal recognition of this takes place in a rational manner. And this leads to the substantial reduction of wholes (in every context) to parts at these stages.
So, it is only at the more advanced stages that one can properly interpret in an explicit fashion the true unconscious basis of intersubjective and interobjective meaning. So spiritual intuition now becomes so refined that one can clearly differentiate it from both the objective and subjective structures with which it is associated.
In my experience, the spiritual ascent was strongly related to the potential nature of intersubjective (and interobjective) meaning associated directly with intuition. Here, holistic connections that literally went beyond the various subjective (and objective) events that occurred in experience, pointed directly to the creative possibilities inherent in these events.
However I was only later to realise that the corresponding spiritual descent is likewise associated with the actual nature of intersubjective and interobjective connections.
At earlier stages of development, such connections are made instinctively in a merely implicit manner. So it requires the considerable refinement of understanding (in what Jung refers to as sense as opposed to intuition) to then make explicit the holistic nature of these actual connections (which are inherent in all relationships). 
This also implies for example whenever the interrelationship of phenomena takes place in nature, that intervention through a state is required.
And we commonly refer to this state as physical energy, which thereby complements the psychological notion of a state as spiritual energy.
Wilber uses the notion of types to refer to various elements not included in his other categories. In particular he refers to the distinctions as between masculine and feminine, while also referring to well known psychological typologies such as the Myers-Briggs Type Indicator (MBTI) based on Jungian notions, The Enneagram and the Big Five (OCEAN) typology.
Masculine and feminine
The Chinese refer to masculine and feminine principles. Though these can in no way be exclusively identified with either sex, it is however perhaps more typical for male behaviour to be associated with the masculine principle of reason and female behaviour with the feminine principle of feeling respectively.
And this can in turn lead to two approaches to spirituality, which are relatively distinct from each other.
In this context, I would see the traditional emphasis on the ascent with respect to development as reflecting an undue male bias (where spirituality develops through the refined rational function).
So to properly accommodate both approaches, where emphasis on the ascent can be properly balanced with corresponding emphasis on the descent, a dynamic bi-directional interpretation is required.
Therefore, typically from a male perspective, the earlier focus regarding contemplative development is largely on transcendence. And I liken this to a steep mountain climb, where one believes that nondual reality can be attained on completion of the ascent.
However in gradually being exposed to the shadow side of personality, one recognises that a corresponding descent, requiring a prolonged return to the earlier stages of development (so as to properly unravel their instinctive nature) is likewise required. And I liken this to a deep subterranean sea voyage.
So, as ones “higher” spiritual self continues with the transcendent ascent, one's “lower” shadow self becomes increasingly submerged in the primitive unconscious (relating to the immanent nature of spiritual experience).
Thus when the ascent to the nondual has been completed (insofar as this is possible) one is then faced with the corresponding descent from the mountain so as to reach the plains below, where one can embrace dual reality without possessive attachment.
Likewise when the subterranean descent is completed, so that one can finally unwind all earlier repression and confusion, a corresponding ascent from the depths is now required so that one can step out again on dry land. And here, where both selves meet, the true marriage of masculine and feminine takes place in a new found balancing of spontaneous emotional with refined rational appreciation.
And this represents the harmonious relationship of both the spiritual and physical aspects of the self.
I believe that there can be an important difference in the typical male and female routes to this spiritual marriage.
For the male, predominant emphasis is likely to be placed initially on the “higher” transpersonal ascent (and corresponding descent), with only later a significant correction taking place through a corresponding equal emphasis on the “lower” prepersonal descent (and ascent).
However in female terms, it is likely to work somewhat in reverse, with more emphasis initially placed on the prepersonal descent (and ascent) with the transpersonal ascent (and descent) only properly completed somewhat later in the spiritual journey.
Personality Types and Perspectives
However it is the MBTI that I particularly want to concentrate on in this section as it can equally be described as a system of perspectives that in many ways complements Wilber's own work in this respect.
Indeed I would see it as having certain advantages over the Wilberian approach.
For example, because it has been extensively adopted, there is now a great amount of research relating to all the perspectives which it contains. And whereas Wilber focuses on intellectual methodologies associated with perspectives, the MBTI allows for a wider range in a manner, where the methodology directly relates to the perspective in question.
Secondly, in terms of the four functions (intuition, sense, thinking and feeling) and four attitudes (extraversion, introversion, perception and judgement), which can be applied to each of the functions, one can equally incorporate both the conscious and unconscious dimensions of experience. Jung termed intuition and sense the irrational (unconscious) and thinking and feeling the rational (conscious) functions respectively.
Thus in using the terms rational and irrational, which equally can apply to number types, Jung implicitly came close to the holistic mathematical appreciation of the four functions.
Following considerable reflection, I came to the position that the two rational (thinking and feeling) properly represented the real, whereas the two irrational functions (sense and intuition) represented the corresponding imaginary aspects of understanding with both now understood in a precise qualitative mathematical fashion.
Likewise extraversion and introversion can be identified in relative terms with both the positive (+) and negative (-) expression of these qualitative numbers, whereas perception and judgement relate to their understanding both as individual numbers (within given dimensions) or to the collective dimensions (which contain the individual numbers).
In this way, the Jungian model gives way to a 4-dimensional complex mathematical approach (in holistic terms) that can be geometrically represented by the unit circle in the complex plane (as the 4 roots of 1). This naturally divides the circle into 4 quadrants.
And just as the linear representation of the quadrants is directly associated with the differentiated aspect, the circular representation is suited to their corresponding integration.
And again in the last article, I showed that to reconcile the differentiated with the integral interpretations, one must define the four (linear) quadrants in a relative - rather than absolute - manner where they now become associated with 16 distinctive interpretations, which correspond directly with the indigenous (primary) perspectives.
Likewise the 16 personality types in the Myers-Briggs system correspond to 16 indigenous perspectives (now understood in a holistic integral, rather than partially differentiated manner).
So in Wilberian terms, one can indeed legitimately attempt to individually differentiate the key primary perspectives (in an analytic manner). However in integral terms, as Wilber realises, all personal perspectives are involved. Now my own modification, as suggested in the last article is that we should include an additional 4th person perspective (along with 1st, 2nd and 3rd persons).
What is fascinating is that the MBTI approach to personality types can be given a corresponding interpretation through these four person perspectives, with each personality type corresponding to a unique configuration of the four perspectives in a very coherent manner. Perhaps in a future contribution I will show precisely how this can be achieved.
Finally just a quick comment on the Enneagram! This has become like the MBTI a widely used system of personality (with 9 basic types).
One fascinating feature of the Enneagram is the fact that number itself is used in a holistic integral manner.
So the 9 numbers i.e. 1, 2, 3, …,8, 9, are broken into two groups with one containing the 6 digits 1, 4, 2, 8, 5, 7 and the other the 3 digits 3, 9, 6.
The 6 digits 142857 are well known in mathematics as the most cited example of a cyclic prime, which is obtained through obtaining the reciprocal of the prime number 7.
So 1/7 = .142857… with these 6 digits continually repeating in the same order.
Here is where the integral aspect comes in! A prime, such as 7, is a good example of a linear independent number, which contains no factors (other than 1 and the number in question). However the reciprocal 7 then leads to the opposite extreme of cyclical or circular interdependence, where the same digits keep recurring in its decimal sequence. And if we multiply 142857 by 2, 3, 4, 5 and 6 respectively, we keep generating the same cyclic sequence of digits i.e. 285714, 428571, 571428, 714285 and 857142.
Independence can be associated with the masculine and interdependence with the feminine principles respectively.
And in the Enneagram, these cyclic numbers have a holistic qualitative significance with the directions of integration (and disintegration) for each personality type given by the 6 digits, with integration moving backward and disintegration moving forward with respect to the sequence.
So for example if one is a 5 (with thinking dominant), which would be very common on a forum such as this, the direction of personality integration would move from 5 - 8 - 2 - 4 - 1 - 7, whereas the corresponding direction of disintegration for this personality type would be 5 - 7 - 1 - 4 - 2 - 8.
9 as a number has fascinating properties from the standard analytic rationale, which can then be given a corresponding holistic interpretation.
So, if one takes any number such as 030621 (based on the present date of writing this section), then the reverse number i.e. with digits in reverse order, is 126030. When we subtract these two numbers (smaller from larger) we obtain 95409.
Such a result (as the difference of the number and its reverse) is always divisible by 9 and displays marked palindromic tendencies (with the digits very similar when read from both directions). And when we divide 95409 by 9, in this case we do get a perfect palindrome i.e. 10601.
In a more holistic qualitative manner we can envisage personality integration as resulting from combining opposite tendencies, which in the context of the Enneagram numbers leads to a significant amount of balance (with both personality and shadow reflecting the same behaviour).
Just a final observation! The second sequence of numbers is 396. Now the reverse of this is 693. And when we divide 396 by 693 we generate the same recurring cycle of digits as in the first sequence i.e. 571428. 9
1. A somewhat misleading distinction is made as between positive and normative economics. Positive economics implies an objective stance with respect to economic issues, where value judgements are supposedly not meant to intrude.
Normative economics, then accepts, as for example with all political decisions regarding economic matters, that moral issues are involved.
However the mistaken belief that economic issues can be approached in a value free fashion itself implies a critical value judgement which is then often used in support of the free market ideology, where economic behaviour is viewed without consideration of its ethical consequences.
2. I wish to express here my thanks to bjm who in extended discussion on Integral World in relation to “Why Integral Theory is not Integral”, drew my attention to the fact that the sociologict/philosopher Arthur F. Bentley had in 1932 (The Linguistic Analysis of Mathematics) already discussed the notion of the four quadrants, with accompanying diagram and in fact used exactly the same terminology that I was to later employ. In contrasting it with Wilber's somewhat rigid approach (which often identifies holons with specific quadrants), bjm quotes Bentley's own words:
"In our first quadrant [UR] we can now find the objectively particularized aspects of our entire field. In the second quadrant [UL] we can find the subjectively particularized aspects. In the third [LL], the subjectively generalized (organized or socialized) aspects, and in the fourth [LR] the objectively generalized aspects. We no longer have "facts" in one region [UR], "minds" in another [UL], "ideals" and "absolutes," Platonic or other in a third [LL], and that terrible "logistics" of modern creation in a fourth [LR]. But we have the materials and meanings of all of these rigidly separated producers of paradox and confusion, represented in differential construction, in which we may see at least the hope of better understanding."
Using my own terminology this could be expressed by saying that Bentley clearly recognised that the four quadrants should be defined in a relative rather than - in contrast to Wilber - an absolute independent manner.
Then the circular approach to the quadrants, as I have suggested, can show how these relatively separate quadrants can be coherently integrated with each other.
3. Because the word “integral” has an established meaning in conventional mathematics, I generally use the term “holistic mathematics” when referring to its qualitative aspect. However “holistic mathematics” in this context equally means “integral mathematics” and when I consider it can be used in a certain context without confusion, I also employ this latter term. I then use the term “radial mathematics” to refer to the dynamic interaction of both quantitative and qualitative aspects.
4. The lack of philosophical interest in the nature of the imaginary notion among mathematicians (or anybody else apparently) has long amazed me.
For example, imaginary numbers have been hugely important in the understanding of the primes, and greater appreciation of the philosophical nature of the imaginary notion would help clarify why in fact this is the case, while helping to open up entirely new perspectives in our interpretation of their true nature.
Complex numbers (which include both real and imaginary parts) also are very important in the understanding of quantum mechanical relationships and again a better philosophical appreciation of their nature would help to explain why this is in fact the case.
Then Roger Penrose refers repeatedly to the “magic of complex numbers” due to their remarkable holistic properties, but yet without providing any clear insight into why this is the case.
And the answer is quite revealing as imaginary numbers provide an indirect analytic manner of allowing the holistic qualitative property of interdependence to be formally included in conventional mathematics (where however this interdependent property is masked through the explicit quantitative appreciation of number).
So in short, imaginary numbers are important in unveiling the secrets of the primes, because, properly understood, the primes contain both quantitative and qualitative aspects of behaviour (which cannot be directly understood in conventional mathematical terms).
Likewise, complex numbers are important in quantum mechanics because the behaviour of sub-atomic particles cannot be understood in an independent manner, but rather in the context of dynamic interactions containing both aspects of (quantitative) independence and (qualitative) interdependence respectively.
And “the magic of complex numbers” is due to the fact that though again not yet directly appreciated regarding their qualitative aspect, they provide an indirect quantitative means of unlocking many of the holistic secrets of number behaviour.
5. The eight sectors correspond geometrically to the eight roots of unity which can be shown on a circular diagrams where the 8 equidistant points on the circle are connected by horizontal, vertical and diagonal lines drawn through the centre of the circle.
The additional diagonal lines bisecting each of the 4 quadrants of the circle, now represents a new set of complementary polarities relating to (fundamental) form and emptiness.
From one perspective, as experience approaches nondual reality, form and emptiness become so closely related as to be indistinguishable. At the other extreme of early infant development, psychological and physiological reactions again are so confused as to be indistinguishable.
So if we are to properly understand the two extremes of development, then these additional polarities are required.
In particular, I would see that Wilber confuses the psychophysical interactions (relating to instinctive behaviour) where physical and psychological cannot be yet clearly separated, with more developed conscious development, where physical and psychological aspects can now be distinguished.
So this necessary distinction as between primitive instinctive and the most refined conscious understanding (approaching emptiness) respectively, cannot be properly incorporated within his four quadrants.
Again Jung's mandalas represent ornate images based on equidistant points on a circular circumference, which geometrically represent the various roots of unity. And in this context the arrangements based on 8 points are perhaps given the greatest emphasis as pictorial symbols of integration. Equally, in holistic mathematical terms, the eight-dimensional approach represents the most refined level of integration (incorporating horizontal, vertical and diagonal polarities). In fact the diagonal lines, which are recognised as null lines in physics, can be easily shown to have a magnitude = 0. So equally, in holistic terms, these lines can be shown to equate with nothingness or emptiness.
6. I refer to the initial substantial differentiation that takes place as the default development of that stage. However as further stages unfold, one keeps revisiting that earlier stage (while in turn also revisiting “higher” stages from that stage), hopefully leading to continual enhancement with respect to its understanding (in both a differentiated and integral manner).
Likewise, one can form a diminished impression of stages that have not yet undergone their initial default development from the perspective of “lower” stages that have undergone this process.
Thus in a certain restricted sense all stages of the spectrum are continuously present in experience (though often in a greatly diminished manner). Then through the continual dynamics of visiting all stages, both their enhanced differentiation and integration can thereby take place.
7. I attempted this in detail some years ago in my Stages of Development, where I adopted a question and answer type format in dealing with the key issues raised. Though I have since extended the spectrum to 8 rather than 7 bands, I would still largely stand over the views expressed at that time.
8. I have referred before to my own deep immersion in understanding the true nature of the Riemann Hypothesis, which is generally accepted as the outstanding unsolved problem in mathematics today.
Basically there are two ways to construct the natural number system known as the additive and multiplicative approaches respectively. The former operates through the successive addition of 1 to the previous number (that starts with 0). The latter operates through the unique multiplication of primes which generates all the natural numbers (other than 0 and 1). Though seemingly independent, neither can be properly understood in the absence of the other.
So, the Riemann Hypothesis can be fruitfully stated as the basic condition required so that both number systems can be perfectly reconciled with each other.
However, what I found fascinating when interpreting this Hypothesis from a holistic mathematical perspective is that the two number systems became remarkably closely associated with both the ascent and descent respectively of the spiritual contemplative journey. Therefore, in this important holistic sense, I could see the Riemann Hypothesis equally as the condition for the integration of both the “higher” spiritual and “lower” physical aspects of self, where both refined reason and instinctive desire can be fully harmonised with each other.
And I now see this marriage, which can be given a full integral mathematical explanation, as the basic condition for the unfolding of the radial stages of development.
In fact when we speak about a “Theory of Everything”, I would see the Riemann Hypothesis, when given its true radial expression that coherently relates in a dynamic interactive manner both the quantitative and qualitative aspects of its mathematical symbols, as constituting its supreme expression.
9. I include here some other interesting number observations regarding 9.
When one obtains the reciprocal of 9 i.e. 1/9, the result is .11111… (with 1 continually recurring).
If we now obtain the square of 9 i.e. 92 = 81, its reciprocal is thereby 1/81. And 1/81 = .0123456789 …, where all 10 digits continually recur in an ordered ascending fashion.
So in obtaining the reciprocal of 9 and the square of 9 respectively, we move from one extreme, where only one digit recurs to the other extreme, where all 10 digits recur (in ordered fashion).
Incidentally the same form of behaviour (as with the number 9) applies when we obtain the difference of a number and its reverse and divide by 11.
However there is an interesting distinction. When the numbers contain an even number of digits we must add both with the result then divisible by 11. However when they contain and odd number of digits, we subtract both numbers before dividing the result by 11. So there is a dualistic distinction here as between numbers which have an even (feminine) and odd (masculine) number of digits.
The example used in the article 126030 has 6 digits (which is even). Therefore in this case we add the number to its reverse i.e. 126030 + 030621 =156651. And when we divide by 11, we obtain 14241. Note that in this case we generate two palindromes!
And finally we can perhaps throw some light on why 9 itself is so fitting as an integral number. To do this, we represent it its simplest base 2 form as 1001 (where it naturally exists as a palindrome, showing a harmonious balance as between opposite sides).
Then we form the two extreme numbers i.e. the first descending from the highest digits, and the second ascending from the lowest digits we have 1100 and 0011. And when we subtract these two numbers we once again get 1001.
In this way 9 is seen as particularly appropriate in reconciling opposite number tendencies in a balanced manner.
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Ken Wilber: A Brief History of Everything; Shambhala Publications, 20th Anniversary Edition 20th May 2017
Ken Wilber: A Sociable God: Towards a New Understanding of Religion (with foreward by Roger Walsh); Shambhala, First Printing edition, Feb, 22nd, 2005
Ken Wilber; Integral Psychology: Consciousness, Spirit, Psychology, Therapy; Shambhala Publications, 1st Paperback Edition, New Edition 1st May, 2000
Arthur Fisher Bentley; Linguistic Analysis of Mathematics; The Principia Press inc. 1932
Underhill, Evelyn; Mysticism: The Nature and Development of Spiritual Consciousness: Oneworld Publications Ltd 1993
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