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Beyond Method

engaging opposition in psycho-social organization

-- / --

Prepared for the meeting on methodology of the Goals, Processes and Indicators of Development Project (GPID) of the United Nations University. Organized by the Division of System Studies of the University of Bucuresti, Bucharest, 1-4 December 1981 [searchable PDF version]


Abstract: Various manifestations of "disagreement-phobia" are reviewed to show the current importance of disagreement in a society narrowly focused on superficial agreement-promoting processes. Arguments of Paul Feyerabend relating to the suppression of disagreement in science are examined, together with his views on the significance of incommensurability for development. The absence of adequate approaches to the art of disagreement is noted and it is argued that the present level of disagreement in society is not yet great enough to sustain more than an undifferentiated, mass-conscious version of the desired level of agreement. An ordered series of 210 mutually-incompatible, transformation-oriented statements is generated on the basis of a variety of existing multi-set integrated concept schemes. This is intended as an initial stop towards a guide to more realistic psycho-social organization.

Scientific suppression of disagreement
Significance of incommensurability
Approaches to the art of disagreement
Constraints on method

[Presentation | Disagreement |
Underlying relationship
| Completeness |
Number uniqueness
| Number pattern | Transformation operator | Self-constraint | Containment of unpredictable | Inter-set consistency | Operational relevance | Inter-set harmony |
Annex 1: Review of concept schemes included
Annex 2: Results of experiment

Cutting Up an Ox

Prince Wen Hui's cook
Was cutting up an ox.
Out went a hand,
Down went a shoulder,
He planted a foot,
He pressed with a knee.
The ox fell apart
With a whisper.
The bright cleaver murmured
Like a gentle wind.
Rhythm! Timing!
Like a sacred dance.
Like "The Mulberry Grove,"
Like ancient harmonies!

"Good work ! " the Prince exclaimed,
"Your method is "faultless ! "
"Method ? " said the cook
Laying aside his cleaver.
"What I follow is Tao
Beyond all methods ! "

The Way of Chuang Tzu.
Translated by Thomas Merton. 1970


1. The basic point of this paper is that our society has proved itself unable to design any frameworks, whether conceptual or organizational, in which disagreement is an accepted, permanent integral feature. The frameworks now used era all based on the assumption that agreement and consensus is the essential element an which any viable organization depends. As a consequence disagreement can never be tolerated except through processes designed to eliminate it (e.g. conflict resolution, mediation, arbitration). These of course include competition and violent conflict, in which victory, through the downfall of the opponent, is sought.

2. It would seem that all intellectual and political effort is directed either toward achieving some measure of agreement or toward manipulating any disagreement to the advantage of one party so that the disagreement is suppressed and a particular "agreement" prevails. Even arguments for a "moral equivalent of war" are based on the necessity of believing that a victor can emerge and eliminate the disagreement.

3. Perhaps the most tragic consequence is the amount of effort devoted to the illusion of "peace" in which disagreement is somehow absent, inactive or without functional significance. This is the simplistic ideal that "all men will be brothers", which ignores the basic issue of how to structure a society in which brothers disagree - as they do with great frequency and for extended periods of time. The significance of the "peace movement" lies not in the essentially fragile ad hoc agreement to demonstrate on particular occasions, but rather in the disagreement with other power groups.

4. At this point in time much hope is placed on reaching agreement on a set of values or ethical standards an the key to any action strategy. There is no evidence whatsoever that thin hope is well-founded for the foreseeable future.. Every item of evidence indicates the contrary - unless strategies based or the imposition of a set of values are considered acceptable, whether or not they are viable as a result of the imposition process.

5. The immediate relevance of this argument can be seem from the following quotations concerning the recent Cancun conference.

Before: "The obvious needs saying, because the biggest threat to next week's summit of rich and poor countries in Cancun, Mexico, comes not from apathy but from too-high hopes., So start with two things that Cancun will not achieve. First, it will shun the sort of Rubik-cube completeness in which industrial countries agree, eg. to reduce tariffs on third-world imports in return for, eg., oil producers' promises to maintain a steady supply of oil. That was the painstaking approach of the Brandt Commission, which originally proposed this summit. Its members took more than two years to agree upon a package that bound none of them and changed net a line of legislation nor a decimal point on tariffs. The Cancun summiteers are in power and short of time. .They will rightly go for something less ambitious. That means, second, that Cancun will produce few, if any, commitments that presidents and Prime ministers can wave in the air". (Economist, 17 Oct 1961)

After: "Leaders of 22 industrialized and developing nations have ended two clays of talks with a detailed analysis of problems of world poverty but without an agreement on a global strategy to alleviate them". (International Herald Tribune, 26 Oct 1981)

Great hopes are once again placed on the slender possibility that something of major significance could emerge from the new round of "global negotiations" which it was tentatively' "agreed should be held in the future. This possibility diverts attention from the essential problems of disagreement which have undermined the significance of all previous initiatives of this kind.

6. The fear of situations in which disagreement prevails is such that they are shunned, whether unconsciously of, by well-ration alized processes. Where they cannot be avoided, much effort is devoted to amplifying the significance of whatever minor items can be discovered on which agreement in achieved. A Veneer of agreement is thus generated to disguise fundamental disagreement. Agreement then becomes an essentially superficial pretence of little operational significance. A tragic example is the vast body of resolutions generated by United Nations bodies and almost immediately forgotten. According to the International Herald Tribune (24 Nov 1981):

'Many envoys here, however, complain that this year's UN General Assembly is notable chiefly for its overly familiar debates. Virtually all 126 items on the agenda have produced almost identical resolutions and votes for three or more years. Some of the deepest concerns here are discussed only in corridors, not on the assembly floor.' (International Herald Tribune)

In the case of UNESCO, these are now being generated by "consensus voting" to avoid the problems of disagreement.

7. A strange feature of the preoccupation with seldom-achieved agreement is that little attention is given to the processes which are able to occur once that condition has been achieved. To the extent that it is not superficial, agreement involves a degree of homogeneity in approach which is rapidly repudiate as constricting and alienating. Dynamism of any sort is associated with disagreement.

8. In a very meaningful sense, the present is in basic disagreement with the past and with the seeds of the future as they emerge. Again it is not the continuity from past-to-present-to-future which provides significant information, but rather the dynamics arising from the disagreement of past and present positions (as epitomized by generation "gaps") The nostalgia occasionally encountered for a "golden age" in the past, and the hopes projected onto some utopian ideal in the future have a common weakness. In both cases their significance lies in their contrast with the tensions and disagreements of the present. Such ideal settings are seen as disagreement free and, consequently, there in great difficulty in describing their processes in an attractive manner.

9. An obvious feature of academic or even political life is the relative lack of significance attached to agreement with a particular thesis - except in terms of the essentially "mechanical" process of marshalling support to ensure that a particular position triumphs and maintains its position. Of much greater interest to those involved is the process of responding to the challenge of those who manifest disagreement. It is this which is the stimulus which energizes many psycho-social processes. Associating for any length of time with a group of people in basic agreement is of very little interest - unless a new level disagreement can be discovered.

10. It is useful, in the light of the previous points, to view the development process as one based on disagreement rather then agreement. Little "happens' if everyone agrees. With the introduction of disagreement comes the possibility of development. To stress consensus as a key to development, is to come dangerously close to destroying the basis for its dynamism. Development can only occur if there is disagreement with the current state of affairs.

11. The previous point suggests that there is a fundamental weakness in the "liberal goodwill" viewpoint which has encouraged the favourable attitude towards solving all the "nasty" world problems. This has effectively generated a kind of conspiracy of consensus, based an mutual tolerance, and a horror of disagreement which has progressively under- the original thrust. Indeed, once every issue becomes a "motherhood" type issue, namely one which calls for unthinking, universal agreement, then no further progress is possible. The "mutual tolerance" mentioned is counter-productive to the extent that it de-activates disagreement and the dynamics associated with diversity.

12. Because a sense of dynamism would seem to be a fundamental nee,!, the reality of groups making up the "peace movement", for example, is one of extensive fragmentation. Sadly to some, the constituent groups are usually extremely hostile to one another. Since disagreement is an anathema, each group turns in upon itself or towards its special. constituency and avoids any reflection on the significance of that disagreement for the future of "peace". But the identity of each group is clarified by dynamics which reinforce for it the understanding of why it cannot possibly associate or agree (other than te m- under special circumstances) with any of the other groups. A similar point could be made with regard to the "ecology movement".

13. The previous point comes even more into focus in the case of the various movements for "equality". The goal of such movements is to eliminate "inequality". However it is no exaggeration to remark that the amount of "inequality" in the world is now greater than ever before. "Equality" is well-implanted as an ideal, hut indicators of its universal non-achievement are all too evident. Society is at present primarily characterized by non-equality, except for a variety of token legal rights whose significance in practice is negligible or cosmetic. It is no longer sufficient to play out the pretence of operating in an egalitarian society - this only permits the unrecognized dynamics to reinforce the fundamental disagreement between ideal and reality. It also prevents exploration of the significance of the disagreement and the inequality.

14. There are presumably many traditional psycho-cultural reasons which reinforce the treatment of disagreement as an anathema, and in many cases as "bad" and inherently "evil". It is disagreement which banishes man from the Garden of Eden, introduces dissonance into the mythical Golden Age, and destroys the "golden age" of childhood experience. It is a denial of the spiritual union which is fundamental to many religions. As such it is necessarily the "work of the devil" or his equivalent. Even Pythagoras is supposed to have rejected the irrational disagreement associated with the square root of 2.

15. Such views strongly influence the manner in which an "enemy" is defined as a result of disagreement. "If you are not with me, you are against me" and, as such, to be contained (or eliminated, if possible). No religion, Hinduism possibly excepted, has developed a viable framework for dealing with disagreement - with well-known consequences. Equivalent problems occur with ideologies. In both cases considerable difficulty is experienced with disagreement giving rise to schisms which in the religion case may be labelled "heresies". These give rise to violent exercises in suppression.

16. Disagreement is also a major problem in mass movements such as trade unions for which the key word is "solidarity". Disagreement undermines the solidarity which is vital to successful bargaining and must therefore be violently suppressed. In societies based on the dictatorship of the proletariat, as an extension of such mass movements, the problem of handling "dissidence" remains unresolved.

17. Discontinuity is a special form of disagreement. It is only very recently that the study of discontinuity has proved -1 possible or admissible in mathematics as catastrophe theory [3], despite the general nature of the problem and the practical value of the results to natural and social sciences. Discontinuity, as a form of disagreement, has presumably been a victim of its subconscious association with death an(' accidents although birth also constitutes a discontinuity.

18. From a theoretical standpoint, disagreement generally implies invalidity or error. There is an extremely well-developed tendency to disguise error, because of the way it is related to job performance and. career evaluation. This is true of professionals, of bureaucrats, of businessmen, and of scientists. It is also true in organizational reporting procedures, whether military, business or government. Glossy "public relation," reports prevail.. It is unfortunate that it should even be necessary to make the following point:

"Changing towards long-range social planning requires that, instead of avoiding, exposure to and acknowledgement of error, it is necessary to expect it, to seek out its manifestation, and to use information derived from the failure as the basis for learning through future societal experiment. More bluntly, future-responsibility societal learning makes it necessary for individuals and organization to embrace error. It is the only way to ensure a shared self-consciousness about limited theory as to the nature of social dynamics, about limited data for testing theory, and hence about our limited ability to control our situation well enough to expect to be successful more often than not". Donald Michael ("On the requirement for embracing error". In: On Learning to Plan and Planning to Learn. Jossey-Bass, 1973, p. 131).

19. The response to disagreement between achievements as planned and as implemented introduces a special kind of blindness. Planning reinforces awareness of social reality as perceived through the system under implementation. As lived however, individuals are obliged to cross the boundaries between systems which do not "recognize" each others existence, and between new systems (possibly incomplete or already breaking down) and whatever remains of older (or even very old) systems. The lived reality is characterized by widespread incompatibility that is experienced as a kind of hubris between the various systems. A material indicator is the standardization problem of getting parts to fit or match. A bureaucratic indicator is the traditional problem of "red tape". Others are more subtle. It is very difficult to grasp these forms of disagreement.

20. The problem of handling disagreement is also evident in the design of legislative assemblies for complex societies. The traditional 2-party Westminster assembly has only proved successful in a few countries and it can be argued that its success is largely one of creating the impression that it is a success. Complex issues (e.g. defence budgets) can no longer be given more time then simpler ones and there is little time for most issues, especially new ones. Many developing countries have abandoned multi-party assemblies as being "unsuitable". This may be considered an indication that exposure to disagreement is actively avoided there: opposition is forbidden or suppressed.

Scientific suppression of disagreement

1. It is the philosopher of science Paul Feyerabend who hap recently drawn attention, dramatically to the manner in which science-as-practised suppresses disagreement in a somewhat desperate search for the single method and the ultimate theory (4). He argues that this bears a relation to how science advances (when it advances) and that this confusion Is dangerous for society.

2. Feyerabend argues that:

'Such a field study of science reveals that, while some scientists may proceed as described, the great majority follow a different path. Scepticism is at a minimum it is directed against the view of the oppositio and against minor ramifications of one's own basic ideas, never against the basic ideas themselves. Attacking the basic ideas evokes taboo reactions which are no weaker than are the taboo reactions in so-called primitive societies. Basic beliefs are protected by this reaction as well as by secondary elaborations, as we have seen, and whatever fails to fit into the established category system or is said to be incompatible with this system is either viewed as something quite horrifying or, more frequently, it is simply declared to be non-existent.' (4, p. 298)

He considers that this massive dogmatism is not just a fact but also has a most important function. Science would be ,impossible without it (4, p. 298). Furthermore:

'In the preceding chapters, which are rough sketches of an anthropological study of particular episodes, it has emerged that science is always full of lacunae and contradictions, that ignorance, pigheadedness, reliance on prejudice, lying, far from impeding the forward march of knowledge are essential presuppositions of it and that the traditional virtues of precision, consistency, "honesty", respect for facts, maximum knowledge under given circumstances, if practised with determination, may bring it to a standstill. It has also emerged that logical principles not only play a much smaller role in the (argumentative and non-argumentative) moves that advance science, but that attempt to enforce them universally would seriously impede science.' (4, p. 260)

3. He considers that the belief that science has found some special method is simply a fairy-tale.

'But the fairy-tale is false, as we have seen. There is no special method that guarantees success or makes it probable. Scientists do not solve problems because they possess a magic want-methodology, or a theory of rationality - but because they have studied a problem for a lone, time, because they know the situation fairly well, because they are not too dumb (though that is rather doubtful nowadays when almost anyone can become a scientist), and because the excesses of one scientific school are almost always balanced by the excesses of Some other school. (Besides, scientists only rarely solve their problems, they make lots of mistakes, and many of their solutions are quite useless)'. (4, p. 302)

4. Feyerabend then points out that:

'Basically there is hardly any difference between the process that leads to the announcement of a new scientific law and the process preceding passage of a new law in society: one informs either all citizens or those immediately concerned, one collects 'facts' and prejudices, one discusses the matter, and one finally votes. But while a democracy makes some effort to explain the process so that everyone can understand it, scientists either conceal it, or bend it, to make it fit their sectarian interests.' (4, p. 304)

5. Disagreement amongst sciences is in practice resolved by vote contrary to what is normally claimed:

"No scientist will admit that voting plays a role in his subject. Facts, logic, and methodology alone decide this is what the fairy-tale tells us. But how do facts decide? What is their function in the advancement of knowledge? We cannot derive our theories from them. We cannot give a negative criterion by saying, for example, that good theories are theories which can be refuted, but which are not yet contradicted by any fact... Lawyers show again and again that an expert does not know what he is talking about. Scientists, especially physicians, frequently come to different results so that it is up to the relatives of the sick person (or the inhabitants of a certain area) to decide by vote about the procedure to be adopted. How often is science improved, and turned into new directions by non-scientific influences.' (4, pp. 306-307)

6. The unity of science is itself a myth:

'Science is split into numerous disciplines, each of which may adopt a different attitude towards a given theory and single disciplines are further split into schools. Whatever unity remains is dissolved during (scientific) revolutions, when no principle remains unchallenged, no method unviolated. Even individual scientists arrive at different judgements about a proposed theory.' (4, p. 202)

7. Given this situation, the danger lies in the generalization of this myth in disguise:

'Scientists are not content with running their own playpens in accordance with what they regard as the rules of scientific method, they went to universalize these rules, they want them to become part of society at large and they use every means at their disposal - argument, propaganda, pres- tactics, intimidation, lobbying - to achieve their aims.' (4, p. 220)

'A society that is based on a set of well-defined and restrictive rules so that being a man becomes synonymous with obeying these rules, forces the dissenter into a no-man's-land of no rules at all and thus robs him of his humanity.' (4, p. 218)

8. It is ironical that, the avoidance by scientists disagreement, as described above, and the scientific dedication to the elimination of discrepancies in theory, are complemented by the deep disagreement amongst philosophers of science concerning the nature of the scientific process itself.

Significance of incommensurability

1. Feyerabend clarifies his own favoured approach as follows:

'One might therefore get the impression that I recommend a new methodology which replaces induction by counter-induction and uses a multiplicity of theories, metaphysical views, fairy-tales instead of the customary pair theory/ observation. This impression would certainly be mistaken. My intention is not to replace one set of general rules by another such set: my intention is, rather, to convince the reader that all methodologies, even the most obvious ones, have their limits.' (4, p. 32)

2. For, when a new theory or methodology has been elaborated:

'It will seem that the truth has at last been arrived at. At the same time, it is evident that all contact with the world has been lost and that the stability achieved, the semblance of absolute truth, is nothing but the result of an absolute conformism. For how can we possibly test, or improve upon, the truth of a theory if it is built in such a manner that any conceivable event can be described, and explained, in terms of its principles? The only way of investigating such all-embracing principles would be to compare them with a different set of equally all-embracing principles - but this procedure has been excluded from the very beginning. The myth is, therefore, of no objective relevance; it continues to exist solely as the result of the effort of the community of believers and of their leaders, be these now priests or Nobel prize winners. This, I think, is the most decisive argument against any method that encourages uniformity, be it empirical or not. Any such method is, in the last resort, a method of deception. It enforces an unenlightened conformism, and speaks of truth; it leads to a deterioration of intellectual capabilities, of the power of imagination, and speaks of deep insight; it destroys the most precious gift of the young - their tremendous power of imagination, and speaks of education.' (4, p. 45)

3. He concludes as follows:

'To sum up: Unanimity of opinion may be fitting for a church, for the frightened or greedy victims of some (ancient, or modern) myth, or for the weak and willing followers of some tyrant. Variety of opinion is necessary for objective knowledge. And a method that encourages variety is also the only method that is compatible with a humanitarian outlook.' (4, p. 46)

4. Feyerabend takes this argument even further:

'There is no idea, however ancient and absurd that is not capable of improving our knowledge. The whole history of thought is absorbed into science and is used for improving every single theory. Nor is political interference rejected. It may be needed to overcome the chauvinism of science that resists alternatives to the status quo.' (4, p. 47)

5. On this basis he continues:

'Knowledge so conceived is not a series of self-consistent theories that converges towards an ideal view; it is not a gradual approach to the truth. It is rather an ever increasing ocean of mutually incompatible (and perhaps even incommensurable) alternatives, each single theory, each fairy tale, each myth that is part of the collection forcing the others into greater articulation and all. of them contributing, via this process of competition, to the development of our consciousness. Nothing is ever settled, no view can ever be omitted from a comprehensive account. Plutarch, or Diogenes Laertius and not Dirac, or von Neumann are the models for presenting a knowledge of this kind in which the history of a science becomes an inseparable part of the science itself - it is essential for its further development as well as for giving content to the theories it contains at any particular moment. Experts and laymen, professionals and dilettanti, truthfreaks and liars - they all are invited to participate in the contest and to make their contribution to the enrichment of our culture. The task of the scientist, however, is no longer "to search for the truth", or "to praise god", or "to systematize observations", or "to improve predictions". These are but side effects of an activity to which his attention is now mainly directed and which is "to make the weaker case the stronger" as the sophists said, and thereby to sustain the motion of the whole.' (4, p. 30)

6. In discussing incommensurability, Feyerabend draws attention to the problem of science as rational:

'Incommensurability, which I shall discuss next, is closely connected with the question of the rationality of science. Indeed one of the most general objections not merely to the use of incommensurable theories but even to the idea that there are such theories to be found in the history of science is the fear that they would severely restrict the efficacy o traditional, non-dialectical argument.' (4, p. 171)

7. He welcomes the use of apparently rational arguments to introduce revolutionary doctrines in the guise of familiar, common sense statements, as a means of transforming common sense itself (4, p. 200). Rationalists will then:

"be much less reluctant to concede that the ideology of rationalism has no intrinsic advantage, they will realize that even in science one is subjected to propaganda and involved in a struggle between opposing forces and they will agree that argument is nothing but a subtle and most effective way of paralysing a trusting opponent". (4, p. 200)

8. Feyerabend summarizes his position on incommensurability in the form of three theses:

9. Feyerabend argues against the assertion of Karl Popper's that "What is true in logic is true in psychology .... in scientific method, and in the history of science". He points out that there exist legitimate scientific statements which violate simple logical rules. He gives examples of statements which play an important role in established scientific disciplines and which are observationally adequate only if they are selfcontradictory. (4, p. 258)

10. According to Feyerabend, if many facts become available only with the help of alternatives:

"Then the refusal to consider them will result in the elimination of potentially refuting facts as well. More especially it will eliminate facts whose discovery would show the complete and irreparable inadequacy of the theory. Such facts having been made inaccessible the theory will appear to be free from blemish ... This will further reinforce the belief in the uniqueness of the accepted theory and in the futility of any account that proceeds in a different manner ... At the same time it is evident, an the basis of our considerations, that this appearance of success cannot in the least be regarded as a sign of truth and correspondence with I nature ... In other words, the suspicion arises that this alleged success is due to the fact that the theory, when extended beyond its starting point, was turned into a rigid ideology". (4, pp. 42-44)

11. Feyerabend points out that "Nobody admits that there could be various forms of knowledge and that it might be necessary to make a choice". (4, p. 213) Consequently, he argues that:

'General education should prepare a citizen to choose between the standards, or to find his way in a society that contains groups committed to various standards but it must under no condition bond his mind so that it conforms to the standards of one particular group. The standards will be considered, they will be discussed, children will be encouraged to got proficiency in the more important subjects, but only as one gets proficiency in a game, that is, without serious commitment and without robbing the mind of its ability to play other names an wall ....

It seems to me that such a change in education and, as a result in perspective will remove a great deal of the intellectual pollution Lakatos deplores. The change of perspective makes it clear that there are many ways of ordering the world that surrounds us, that the hated constraints of one set of standards may be broken by freely accepting standards of a different kind, and that there is no need to reject all order and to allow oneself to be reduced to a whining stream of consciousness.' (4, p. 218)

Approaches to the art of disagreement

1. The previous section suggests that there is a major need for a "science of disagreement" to clarify the manner in which active disagreement can be usefully structured. It appears that agreement in society is essentially superficial or token (if it prevails at all). There is a total absence of knowledge on how to disagree intelligently in an organized manner, rather then in an irrational, fear-ridden manner requiring some form of violent response to eliminate the disagreement as soon as possible.

2. It might be assumed that the methodologies of conflict resolution, mediation or arbitration would provide guidelines for a science of disagreement. This is not the case. Such methods are primarily concerned with eliminating the disagreement between the parties, or reducing it to a level at which it is not significant for their relationship.

3. In looking for a "science" of disagreement some care is necessary as the previous sections have shown. Science, as it claims to be practiced, can be usefully considered to be about agreement processes and the elimination of disagreement. "Art" may however be considered to be about disagreement processes, set against a background of the rise and fall of agreement. Agreement is not useful without disagreement. In fact it is meaningless. It is the disagreement which introduces the essence of diversity and avoids the uniformity of undifferentiated mass consciousness.

4. There is an obvious problem in using Feyerabend's "method" as a basis for any art or science of disagreement. He explicitly advances his views as epistemological anarchism and states:

'It is clear, then, that the idea of a fixed method, or of a fixed theory of rationality, rests on too naive a view of man and his social surroundings. To those who look at the rich material provided by history, and who are not intent on impoverishing it in order to please their lower instincts, their craving for intellectual security in the form of clarity, precision, "objectivity", "truth", it will become clear that there is only one principle that can be defended under all circumstances and in all stages of human development. It is the principle: anything goes.' (4, pp. 27-28)

But he goes further in arguing that science is itself anarchistic:

'To sum up: in so far as the methodology of research pro- is "rational". it does not differ from anarchism. in so far as it differs from anarchism, it is not "rational Even a complete and unquestioning acceptance of this methodology Hoes not create any problem for an anarchist who certainly does not deny that methodological rules may be and usually are enforced by threats, intimidation, deception. This, after all, is one of the reasons why he mobilizes (not counter-arguments but) counter-forces to overcome the restrictions imposed by the rules.' (4, p. 198)

But the somewhat quixotic element in his extremely valuable approach is then revealed in his remarks on its status in his own view (as the author):

'Always remember that the demonstrations and the rhetorics used do not express any "deep convictions" of mine. They merely show how easy it is to lead people by the nose in a rational way. An anarchist is like an undercover agent who plays the game of Reason in order to undercut the authority of Reason (Truth, Honesty, Justice, and so on).' (4, p. 33)

5. Feyeraband takes us to the very useful point at which it is possible to say that "disagreement is OKI' and that scientific progress might be impossible if imperfections were eliminated (41 p. 255). But, as an anarchist, he is obviously totally uninterested in the need to "organize" disagreement in any way, even if it were possible. As a result his approach provides no clues for any new way of organization which could take account of new levels of disagreement.

6. The most fruitful guide to further understanding of disagreement should be found in writings on dialectics, which were clearly of value to Fayerabend. But whether it be in the writings of Hegel Marx, Engels or Lenin, or in recent writings on dialectics as it emerges in modern science (e.g. complementarity, etc), there is little to be gleaned beyond the concept of the essential (thesis, antithesis, synthesis). Most authors emphasize the intimate relationship to the cognitive subject-object process, about which it is necessarily difficult to be "objective" without distorting comprehension of its essential dynamism. Thus: "If we try to analyze what it is that the threefold describes, we are in a bind for it is just that element of participation in life that analysis cannot, and does not even pretend to, cope with" (5, p. 57). "Since it is basically nonconceptual, it cannot be defined..." (5, p. 27). For this reason dialectics has been most favoured as a method by those capable of anchoring it in practical action a concrete material context.

7. The Marxist scholar Jean-Marie Brohm points out that neither Marx nor Engels attempted to define dialectics positively (6, p. 43). They defined it negatively by the criticism of adverse positions, as have most of their successors:

"Ce faisant ils obéissaient à un grand principe général do la dialectique: la négativité. Le positif est toujours le résidu do le négativité, un moment négatif provisoire qui attend à son tour d'être nié .... La dialectique est le produit d'une lutte ininterrompue contre les conceptions adverses. Elle se définit négativement par ce contre quoi elle s'oppose". (6, p. 43)

8. Hegel summarizes the essence of dialectics as follows (as quoted by Brohm):

"les choses finies sont, mais leur rapport à elles-mêmes est de nature négative, an ce sens qu'elles tendent à la faveur de ce rapport à se dépasser. Elles sont, mais Ia vérité de leur être est qu'elles sont finies, qu'elles ont une fin. Le fini ne se transforms pas seulement, comme toute chose en général, mais il passe, il s'évanuit; et cette disparition, cet évanouissement du fini n'est pas une simple possibilité, qui peut se réaliser ou non, mais Is nature des choses finies est telle qu'elles contiennent le germe de leur disparition, germe qui fait partie intégrante: l'heure de leur naissance est an même temps celle de leur mort". (7, p. 129)

9. In commenting on Hegel's Science of Logic (7), Lenin clarifies one of Hegel's definitions of dialectics by the following:

  1. Definition of, the concept on the basis of itself (the thing itself should be considered in its relationships and in its development)
  2. Contradiction in the thing itself, forces and contradictory tendencies in each phenomenon
  3. Union of the analysis and the synthesis.

Then he further clarifies these elements in 16 points (8, pp. 209-210):

    1. objectivité de l'examen (pas des examples, pas des digressions, mais Ia chose an elle-même).
    2. tout l'ensemble des rapports multiples at divers de cette chose aux autres.
    3. Ie développement de cette chose (respective phénomène), son mouvement propre sa vie propre.
    4. les tendances (at aspects) intérieurement contradictoires dans cette chose.
    5. Ia chose (le phénnomène, etc) comme somme et unité des contraires.
    6. la lutte respective (ou encore) le déploiement de ces contraires, aspirations contradictoires, etc.
    7. union de l'analyse at de Is synthèse, séparation des différentes parties et réunion, totalisation de ces parties ensemble.
    8. les rapports de chaque chose (phénomène, etc) non seulement sont multiples et divers, mais universels, Chaque chose (phénomène, processus, etc) est liée à chaque autre.
    9. non seulement l'unité des contraires, mais aussi les passages de chaque détermination, qualité, trait, aspect, propriété en chaque autre en son contraire.
    10. processus infini de mise à jour de nouveaux aspects, rapports, etc.
    11. processus infini d'approfondissement de la connaissance par l'homme des choses, phénomènes, processus, etc, allant des phénomènes à l'essence et d'une essence mains profonde à une essence plus profonde.
    12. Ia coexistence à la causalité et d'une forms de liaison at d'interdépendance à une autre, plus profonde, plus générale.
    13. répétition à un stade supérieur de certains traits, propriétés, etc, du star's inférieur et
    14. retour apparent à l'ancien (négation de le négation)
    15. lutte du contenu aver le forms et inversement. Rejet de la forma, remaniement du contenu.
    16. passage de la quantité en qualité et vice versa. (15 at 16 sont des examples du 9)

10. In the case of psychologist Jean Piaget, there are five characteristics of dialectics:

    1. construction of previously non-existing interdependencies between two systems considered either as opposed or as strangers to each other, and which are thus integrated into a new totality; whose properties exceed them.
    2. the interdependencies of the parts of the same object are in dialectical relationship.
    3. every new interdependency engenders properties exceeding the component parts if it results in a totality greater then that without it.
    4. intervention of circularities or spirals in the construction of interdependencies.
    5. relativisation of parts due to their interdependencies..

These five properties of dialectics are summarized by a sixth which gives its general significance: "dialectic constitutes the inferential aspect of all equilibration". This means that dialectics does not intervene at all stages of cognitive development, but only during the course of the equilibrating process. It is therefore important to distinguish carefully between the state of equilibrium corresponding to a non-dialectic moment of evolution and the dialectic processes permitting the construction of new frameworks. Piaget distinguishes eight kinds of interdependency (9, pp. 213-227). A co-author, Rolando Garcia, draws attention to similarities between Piaget's concept and that of Lenin as detailed above (9, pp. 233-237).

11. In one of the few studies that also reviews non-marxist concepts of dialectics, Paul Foulquié concludes with the following general definition:

"Est dialectique une pensée constamment tendue pour as dépasser elle-même aussi bien en allant jusqu'au bout de ce qu'elle a découvert qu'en se portent à des points de vue nouveaux qui semblent contredire ses affirmations premières". (10, p. 125)

12. Despite the relevance of dialectics to the problem of disagreement, as noted above, it does not appear to do more than explain the dynamics of the environment it constitutes. It explains the eventual future evolution beyond the stage of disagreement, but does not clarify the nature of any possible present order whilst the disagreement holds. It does not clarify the nature of the psycho-social forms to which disagreement can give rise in the present, it merely affirms that they are necessarily temporary. The question is whether there is any pattern in the present to the ancillary processes to which a dialectical confrontation gives rise. Is it possible to discover any underlying structure to disagreement? For example, evident disagreement might be considered to be structured like interference patterns from distinct interacting wave sources. Or disagreement might be compared to recent thinking on the relationship between interacting parallel universes.

13. More accessible to reflection (but spread over time) is the concept of development stages, of which the beat example is the individual human being. Development for the individual is a series of separations which give rise to a qualitatively different sense of unity. Stages include:

Each of these separations, as a form of disagreement, can be very painful. They are accompanied by changes of perspective which are difficult to communicate to younger siblings, for example. This effective secrecy is enshrined in primitive initiation rites of which equivalents still exist for apprentices, students, and soldiers. At each stage new adversaries emerge as potential enemies with whom to disagree.

14. The shock effect of such initiations has been extensively explored by psychoanalyst C G Jung in his study of the confrontation of an individual with archetypes (including adversaries) corresponding to each initiatory level (11). Of special interest is the individual's encounter with his "shadow" and its relation to creative comprehension of the significance of death as a dramatic form of disagreement. He clearly demonstrates that avoiding this confrontation is unhealthy for the development of the individual.

15. At each such development stage intense regret may be expressed for the loss of the togetherness and innocence of the preceding stages despite profound appreciation for the new insights achieved. The advantage of using such stages to model levels of disagreement is that it highlights the possibility that many of those involved in movements for "peace". "equality" and "solidarity" may be hoping to achieve a kind of womb-like of agreement within their environment. Or some childish condition of "eternal summertime" and parental security. But the more separation or disagreement that has been achieved, the greater the potential for new kinds of unity. It is the degree of disagreement which qualifies the scope and depth of the unity possible.

16. This problem is well illustrated in the various levels of disagreement with which the poets of the ancient Rg Veda hymns struggled using music as a language:

"In the beginning was tone. This is the most important clu to beer in mind in our effort to understand the Rg Vedic conception and use of Language and of languages. The whole of the Rg Veda is chanted ... we have already pointed out the sophisticated musical-metrical structure of the hymns; and it is precisely an this model of musical tones that the meaning of the hymns is grounded ...

That tones recur cyclically at every doubling or halving of frequency or wave-length is the "basic miracle of music". From this acoustical phenomenon, the number 2 acquires its "female" status; it defines invariantly the octave matrix within which all tones come to birth. Here, in this initial identification of the octave with the ratio 1:2, is the root of all the problems which haunt the acoustical theorist, problems which the ancient theorist conceived as symbolizing the evil and disorder of the universe. The octave refuses to be subdivided into subordinate cycles by the only language ancient man knew -- the language of natural number, or integers, and the rational numbers derived from them. It is blunt arithmetical fact that the higher powers of 3 and 5 which define subordinate intervals of music never agree with higher powers of 2 which define octave cycles. It is man's yearning for this impossible agreement which introduced a hierarchy of values into the number field. For our ancestors, the essence of the world and of the numbers which interpreted that world was sound, not substance, and that world was rife with disagreement among an endless number of possible structures ...

Therefore, from a linguistic and cultural perspective, we have to be aware that we are dealing with a language where tonal and arithmetical relations establish the epistemological invariances... Language grounded in music is grounded thereby on context dependency; any tone can have any possible relation to other tones, and the shift from one tone to another, which alone makes melody possible, is a shift in perspective which the singer himself embodies. Any perspective (tone) must be "sacrificed" for a new one to come into bein the song is a radical activity which requires innovation while maintaining continuity, and the "world" is the creation of the singer, who shares its dimensions with the song.' (11, pp. 55-57)

17. Clearly there is a communication problem in arguing for new levels of unity, if this is comprehended as equivalent to arguing for separation of mother and child, for example. Any such argument can then only be perceived as "bad" or "evil" under present circumstances. But, at the same time, as the Rg Veda case illustrates, there is a certain level of disagreement inherent in any pattern of organization which gives rise to an "impossible yearning for agreement" that drives the search for subtler levels of agreement. But this search may be driven in either of two conflicting directions, whether towards the primordial unity (soundless, womb-like, by recovery of the past). Or towards a unity based on greater differentiation (in the future). In both cases it is necessary to live with disagreement, rather than rejecting it as "evil". As the previous quotation states:

"It is men's yearning for this impossible agreement which introduced a hierarchy of values into the number field...and that world was rife with disagreement among an endless number of possible structures".

The disagreement is only absorbed and contained, as a complementary study demonstrates, by the use of large numbers sets:

"The great expansion of the number sets in later diagrams is motivated, I believe, by the effort to approximate as exactly as possible the irrational square root of 2 which is needed to locate a tone symmetrically opposite the mean on D, that is, precisely in the middle of our octave". (14, p. 37)

An interesting study has been made of dissymetry as an anti-entropic force, This may lead to a valuable contrast between symmetry (as agreement) and dissymetry (as disagreement):

'Dans toute symétrie établie peut surgir une rupture partielle at non accidentelle qui tend à compliquer l'équilibre formé. Une telle rupture est proprement une dissymmétrie. Elle a pour effet d'enrichir la structure ou l'organisme où elle se produit, c'est-à-dire de les doter d'une propriété nouvelle ou de les faire passer à un niveau supérieur d'organisation.' (13, p. 78)


The problem of "world peace", etc needs to be seen in a similar light. As presently conceived, the level of articulated separation, disagreement or diversity is not yet great enough to sustain more than an undifferented, mass-consciousness version of the-desired level of agreement.

18. The previous point would appear to indicate that the deficiency of dialectics in understanding disagreement arises whenever some stability is required for disagreement sets higher than the threefold by which it is characterized (e.g. thesis, antithesis, synthesis). This is clearly stated by Arthur Young: "But when the stimulus causes wrong action and the result is not achieved, the (fourfold) learning cycle becomes necessary. Thus the learning cycle only becomes necessary when there is an obstacle in the larger, threefold cycle". ( 5, p. 24)

19. This suggests the need to explore more highly differentiated patterns of disagreement with higher numbers of component elements. The most interesting development in this direction is that arising from the impact of quantum theory an the conceptual bases for the classification of knowledge (15), especially that of P A Heelan (16) who is concerned with incompatible frameworks, and with complementary frameworks and dialectical development. He advocates the use of non-Boolean partially ordered lattices to interrelate such frameworks and the languages associated with them. Heelan's approach is cited by the authors of the above-mentioned studies on the Rg Veda as appropriate to the complexity with which they are dealing. Heelan relates his own work to that of Feyerabend who was extensively cited above:

'The context of assumptions in which I am working comprises those counter-positions to classical logical empiricism, established by such authors as N R Hanson, P K Feyerabend and T 5 Kuhn, such as the absence of any hard distinction between observational and theoretical language, the validity of multiple explanatory viewpoints, the existence of both continuous trajectories of theory development and discontinuous trajectories representing revolutionary episodes in the history of science or culture.' (16, p. 260)

He concludes:

'From the foregoing, it is clear that there are a variety of logical models at hand to understand inter-framework relationships and especially developmental transpositions between frameworks in history. The task of using these models practically in problems of classificationp has yet scarcely been begun.' (16, p. 272)

20. Heelan indicates the relevance of his approach to relating certain incompatible theories of physics. The question is whether, by using the term "logical", he is restricting its relevance to situations in which the disagreement is less fundamental. How irrational can disagreement be and still be organized in some way? Both Feyerabend in his book Against Method (4), and Heelan in identifying himself with "counter positions" (quotation above), are taking up positions and "disagreeing" with others. They are therefore trapping themselves in a dynamic relationship without providing any organization for that disagreement thus leaving the basic difficulty unclarified. It would seem that the difficulty lies in the .paradigm in which "positions are taken". The difficulty is less that of whether one takes a particular position and more that of the nature of the relationship to the positions one fails to understand or support (of which others, or the future, may understand more).

21. Paradox is implicit in the approach of Feyerabend and Heelan, but can it be made paradoxically explicit? Somehow any static "balance" between agreement and disagreement must be by-passed through a set of paradoxes which legitimate contradictory positions. It is strange that the absence of humour from the development of psycho-social organization is not a cause for comment given its fundamental importance to human beings, even in political life. Arthur Koestler has explored its relation to paradox and creativity ( 17 ). Can contradictory positions be mapped into a self-reflexive hierarchy of paradoxes in which dynamism is inherent? Such a context might then prove more appropriate for the dialectic process. At present this is rather like having access to the central component of an electric generator, without being able to mount it in a suitable framework so as to be able tap the energy generated to drive other psycho-social processes -- and without tearing the mounting apart as it rotates between opposing positions.

22. The remainder of this paper explores the possibility of generating a pattern of progressively more differentiated disagreements as a basis for a more appropriate manner of psycho-social organization.

Constraints on method

1. Presentation

1.1 The design of any text concerning method immediately raises the question as to whether that design will facilitate or hinder implementation of any insights embodied in the text. The form of the text is not a trivial matter and should ideally be isomorphic with the pattern of operations to which it gives rise. Texts which fail to take this constraint into account tend to give rise to methods which are poorly understood and rarely used, whatever their merits

1 .2 In recognition of this problem, the design of the "method" outlined here emerges as the result of the application of a series of constraints. Without such explicit constraints, any text on method is free to meander in an unstructured way through hundreds of paragraphs of inoperable statements.

1.3 The intent is therefore to establish a constraint framework such that different kinds of development discussed can be effectively distinguished whilst at the some time clarifying why those we do not happen to favour appear disagreeable and essentially unjustifiable, if not incomprehensible.

1.4 The aim is therefore to achieve an optimum degree of congruence or isomorphism between statements relevant to psycho-social reality, methods relevant to the transformation of that reality, and structures designed to implement such methods.

2. Disagreement

2.1 Any text an method can be further elaborated by introducing statements in agreement with the initial statement. There is no well-defined limit to this exp6nsion process.

2.2 In the present social context a statement on method only acquires significance through the manner in which it disagrees with other extant statements. This may be used as an explicit technique for limiting the further expansion of sets of statements in agreement with one another. Each statement must therefore be matched with other opposing, or mutually disagreeable, statements. Instead of emerging only in the dynamics of the debate between adherents of methods, disagreement is thus "internalized" as an explicit structuring device in the design of the text. Unless such disagreement is internalized, the method described is always essentially inadequate and must always assume the existence of other methods to complement it. Since adherents of a particular method tend to have difficulty in acknowledging the significance of other methods, failure to internalize strongly reinforces application of inadequate methods without any device for their reconciliation.

2.3 Disagreement is usually conceived as being a condition prevailing between two elements which together constitute a set, whether of : people, values, principles, concepts, methods, or facts. The condition may however exist between a larger number of elements.

2.4 In the absence of a suitable constraint framework embodying the complete pattern of potential disagreement, statements and counter-statements in any debate twist into predictable and essentially pre-determined patterns. There is In fact an interesting parallel to the description of energy states in fundamental physics. The possible energy states (i.e. debate statements) are described by a probability wave function. When a particular probability is actualized (i.e. debate position is taken), the wave function "collapses" (ie no other statements are relevant in that context).

3. Underlying relationship

3.1 Unless they are identical, members of a set necessarily differ and this difference may be interpreted as "disagreement". In order to understand how such disagreement may be organized, a search must first be made for sets which contain elements in maximal disagreement.

3.2 If such sets are meaningful, then the elements of the set retain some degree of commonality which binds them together despite the high level disagreement between them. The qualitative characteristic of the bond is what needs to be understood.

3.3 The disagreement becomes specially interesting when the elements are such that the disagreement is somehow "active". The elements are then complementary in that each is a vehicle for a particular perception of an underlying condition which cannot be adequately conveyed through any of them (cf. the complementarity between wave and particle descriptions of light). This complementarity may of course be denied and then the set elements are perceived as opposed The set as such may then not be considered a meaningful grouping device for those elements.

3.4 It is the presence of this combination of maximal disagreement with an underlying commonality, or relationship between set elements, which constitutes the third constraint.

4. Completeness

4.1 The previous constraints do not in any way limit the expansion of a set of matched statements. A new constraint is therefore introduced to limit a particular set of matched statements to a given number of elements.

4.2 This is done on the assumption that once established the set constitutes a complete pattern of incompatible positions and cannot be enlarged or reduced (although the individual statements may of course be reworded).

4.3 If further matching statements are required to clarify the methods, these should be combined in one or more other sets each complete in its own way.

5. Number uniqueness

5.1 In the practical use of sets of elements such as those it is intended to generate here, there is an important constraint relating to the uniqueness of any given set. For example, the concept of the method or approach as implemented constitutes a fundamental 1-element set. Furthermore, if in applying the method a balance has to be maintained between two conflicting considerations, this constitutes a 3-element set. In both cases, the dynamics it is intended to encompass will also be present when dealing with some sub-component of the method -- where the sub-component approach then itself again constitutes a 1-element set, for example.

5.2 The previous constraints do not prevent the emergence of sets for which the pattern of disagreement between the elements is effectively a replication or a qualification of that in other sets.

5.3 A new constraint is therefore introduced which requires the only one set be allowed with a given number of matching statements as elements.

5.4 This constraint highlights the essential "management" issue of handling the set elements and maintaining the integrity of the set. It is not possible to apply a method without having a 1-element set, for example. It may even be explicitly stated that there is no single central concept but that is then itself the one governing central concept. It is highly probable that the application of the method will also, for example, at some point involve an explicit polarization between two complementary approaches or considerations, thus constituting a 2-element set requiring some form of mediation governed by statements in a 3-element set.

5.5 These questions become clearer when considered in the light of any organizational structure created to implement the method. A hierarchy necessarily emerges with concerns relating to the 1-element set "at the top". Note however that this conceptual hierarchy does not have to be matched in a one-to-one relationship with the organizational structure of roles and departments. S e of the sets may instead be reflected in the sets of principles, values, strategies, or procedures of that organization -- or even i informal factions concerned with particular policies.

5.6. The set associated with a given number N effectively gives rise to a range of N-"person" games as an organizational, management, coordination or strategy problem. It is the qualitative characteristic of the range of games that is t be elucidated as well as the set elements "activated" as role stereotypes for "players" implementing the method.

6. Number pattern

6.1 The previous constraints do not prevent the usual situation in which sets of elements are treated independently, each set being embedded wherever convenient within an arbitrarily structured text which supposedly provides the connecting links between them.

6.2 To the extent that the text constitutes a complete explication of a method, of which the essential items are formulated as set elements, some degree of order should emerge from the relationship between those sets. The various Sets in effect constitute some kind of hierarchy of N-person games within which disagreement or contradictions are handled.

6.3 A new constraint is therefore introduced which requires that the numbers whereby the sets are labeled should themselves fall into a pattern (not necessarily complete) which can be used to elucidate the relationships between the methodological significance of the sets.

6.4 A pattern of numbers can be considered as a "minimal form". The question is what pattern of numbers is most appropriate as a constraint. In terms of number theory, the conventional number series 0, 1, 2, 3, ... is arbitrarily based on the number 10 (written N10). It is preferable to avoid possible distortion arising from this particular choice of pattern. The hybrid number pattern which appears to avoid this problem in the most balanced manner can be obtained by taking the series in which each succeeding number in the series is taken with itself as base, namely

00, 11, 22, 33, 44, 55...1010, 11ll...

As indicated above, a set corresponding to any number in the series is then composed of elements equal to that number (e.g. at level 5, there are 5 elements or matching statements.

6.5 The imposition of any such numbering pattern may appear totally unnecessary. Why is any such device required ? A response is that most social science texts avoid the issue of how systematically their arguments need to be structured to render explicit as many relationships between statements as is feasible. There is no implication that such texts should be structured other than arbitrarily for editorial purposes. It is not surprising that insights emerging from such texts cannot be easily geared into any set of transformative operations.

7. Transformation operator

7.1 The set elements in academic texts tend to be unsatisfactory because they are primarily descriptive. A descriptive set is essentially static and de-emphasizes transformation.

7.2 The problem is therefore to generate a set in which the elements are essentially dynamic or have an operative dimension, namely a set of operators. This requirement constitutes the seventh constraint on set design.

7.3 Such operators are effectively methods or methodological operations. However, given the design of the set, each operator would be in maximal opposition to the other operators in the same set. The operators would therefore be counteracting.

7.4 If such sets of counteracting methods are to be designed, the question is how much incompatibility can be effectively built into operators without destroying the basis for grouping them as a set ? And yet the more they are incompatible, the greater the probability that they will be able to "contain" the complexity of conditions to which they are applied (cf. Ashby's Law, also the gene pool concept).

8. Self-constraint

8.1 Whilst the operational emphasis introduced by the previous constraint ensures a degree of action entailment, such action lacks focus. Statements can be sharpened by introducing a suitable focus.

8.2 Whilst the statements could be oriented towards many domains of action. The one which introduces the greatest constraint and the sharpest degree of focus is that relatinq to the generation of statements on method and related forms. This is effectively a self-reflexive, self-constraining constraint.

9. Containment of unpredictable

9.1 Although previous constraints have emphasized the importance of maximal-incompatibility consistent with set formation, they fail to allow for a specific openness to the risks and hazards of real-world processes.

9.2 A further constraint is therefore introduced to ensure such responsiveness to the possibility of unforeseen conditions.

10. Inter-set consistency

10.1 Although the number pattern ensures a formal relationship between the sets, a further constraint is introduced to ensure that there is consistency between the contents of different sets.

11. Operational relevance

11.1 Although a previous constraint requires that the set element have a transformative dimension, a further constraint is required to ensure that such operations are important to any isomorphic management process.

12. Inter-set harmony

12.1 Although a previous constraint requires that there be consistency between sets contents, this is only a neutral "mechanical" condition.

12. 2 A further constraint can be useful, introduced to require that the set elements be conceived in such a way, that there is harmonic reinforcement between elements in different sets. Such harmony would also be significant to any isomorphic management process

13. Non-definitive

13.1 The previous constraints leave open the possibility that the set elements may be generated with the conventional, idea of producing a definitive, finished product. This would close the set elements to any process of conti nuing refinement.

13.2 A further "constraint" is therefore introduced which requires that each statement be subject to ongoing reformulation. The pattern of statements thus itself becomes a domain for necessary further action, in the light of experience and insight.


1. In order to generate such an integrated multi-set grouping of operational statements it is of course vital to have a rich variety of source material an possible content. Such material was collected for an earlier paper (18) and tentatively ordered there according to the number of elements in the sets in question. The contents of that paper are given here as Annex 1, as an indication of the variety of material. As pointed out in that paper, this ordering permitted useful comparisons between sets in different schemes having an equal number of elements.

2. Such material can only be useful if care is taken to treat the morphological characteristics as independent of the special properties of the substrate with which a given set is particularly concerned. This point has been clearly by Rene Thom in his study of morphogenesis:

'L'indépendance du substrat: L'idée essentielle de notre théorie, à savoir qu'une certaine compréhension des processus morphogénétiques est possible sans avoir recours aux propriétés spéciales au substrat des formes, ou à la nature des forces agissantes, pourra sembler difficile à admettre, surtout de Is part d'expérimentateurs habitués à tailler dans le vif, et continuellement en lutte avec une réalité qui leur résiste. L'idée cependant n'est pas nouvelle, et on Ia trouve, formulée presque explicitement, dans le traité classique de d'Arcy Thompson On Growth and Form; mais les idées de ce grand visionnaire étaient trop an avance sur leur temps pour s'imposer; exprimées souvent d'une manière trop naivement géométrique, il leur manquait d'ailleurs une justification mathématique et dynamique que seules les recherches récentes pourront leur donner ... On m'objectera qu'ici j'ai comparé l'incomparable, an mettant sur Ie même plan un processus biologique d'une part, et un processus de la nature inanimée d'autre part. Précisément, cette comparaison fera sentir un point important, dont peu de gens sont conscients: à savoir que la morphogenèse en nature inanimée est moins bien connue at tout aussi peu comprise que la morphogenèse des êtres vivants; cette dernière a attiré l'attention des biologistes depuis plusieurs siècles ...

Le dédain des physico-chimistes pour ce genre de questions s'explique aisément: c'est qu'il s'agit là de phénomènes extrêmement instables, difficilement reproductibles, et rebelles à toute mathématisation: en effet, Ie propre de toute forms, de toute morphologie est de s'exprimer par une discontinuité des propriétés du milieu: or, rien ne met plus mal à l'aise un mathématicien qu'une discontinuité, car tout modéle quantitatif utilisable repose sur l'emploi de fonctions analytiques, donc continues.' (19, pp 10-12, emphasis added)

The point is also made in relation to one of documents included in the material collected:

'This study will develop the hypothesis that the "lattice logic" which de Nicolas perceives in the Rg Veda was grounded on a proto-science of number and tone. The numbers Rgvedic man cared about define alternate tunings for the musical scale. The hymns describe the numbers poetically, distinguish "sets" by classes of gods and demons, and portray tonal and arithmetical relations with graphic sexual and spatial metaphor. Vedic concerns were with those invariances which became the focus of attention in Greek tuning theory. Because the poets limited themselves to integers, or natural numbers, and consistently used the smallest integers possible in every tonal context, they made it possible for us to rediscover their constructions by the methods of Pythagorean mathematical harmonics.' (14, p. 3)

3. Using equivalent sets from the source material as a guideline, a new set for the number in question was "generated" taking into account the constraints. Given the variety of emphases of sets of an equivalent number of elements, this process of generation necessarily involved non-logical operations, especially since the intention was to maximize the incompatibility between the elements in any given set. The results are given in Annex 2

4. Two interesting and related difficulties emerged in comparing equivalent items from the source material.

5. For each set an underlying relationship or theme is common to each element. The incompatibility is embedded in the qualification on that theme.

The only similar exercise detected is a doctoral thesis in philosophy (20) which was composed directly onto a word processor (to facilitate experiments with alternative structures) using the poetic power of the German language to full effect


1. The ordered collection of statements presented in Annex 2 raises a number of interesting questions. It is necessarily imperfect, and is even more so as a first draft. Its current status can best be compared to an unituned musical instrument. Only when it is tuned, to the extent possible, will it be possible to determine whether it can be realistically applied as a guide to operations.

2. Prior to, or during, the tuning process itself it will be necessary to sharpen up the sets to a greater extent. This is due to the weakness of some of them in terms of the constraint requirements for:

In this sense it is necessary to "charge up" each set and render it inherently more dynamic. The generated sets can be confronted with new source material to assist in this process. (For example the 16-point definition of dialectics by Lenin, quoted above).

3. The "tuning" process may be envisaged as follows. The different sets need to be compared to highlight the pattern of relationships between them. For example, the sets with common numerical factors (e.g. 2, 4, 8, etc) have commonalities which can be highlighted. This will help to clarify the contents of each set and to increase the degree of order prevailing between them.

4. The tuning process is necessary to overcome the problem of the awkwardness of the individual statements. Such awkwardness, is to be expected in a first draft, given the manner in which the sets were generated. There is a basic dilemma in formulating such statements in order to avoid an impression of jargon. But the problem is really that a "general, neutral" set of statements is inconsistent with the underlying philosophy of this approach. No particular wording is adequate.

5. Efforts to produce an exhaustive "definition" merely result in an exhausting amount of text. The study of the significance of some of the sets has in fact been a life work for some people, resulting in many volumes of commentary (as is the case with Carl Jung and the 4-set). The very quantity of information quickly becomes counter-productive in terms of operational criteria.

6. One may around this problem of awkwardness and length is to use the "artificial" statement scheme as generated here as a basis for generating other schemes, corresponding to the difficulties initially encountered:

By combining these different possibilities sets of "more readable" statements can be produced which will presumably be closer in terminology to particular source material sets. Sets may thus be generated according to application.

7. The problem of the lack of sufficiently general words needs to he seen in the light of the previous point and the use of synonyms. In effect by shifting the emphasis according to any of the above scales, there is a shift through the set of synonyms used to generate the set. The tuning process and the generation of sets could be better studied using an on-line synonym database, which could also permit alternation between noun, adjective and verb.

8. It is possible that the problem of lack of general words would disappear in sets having an even higher number of elements where the emergent concerns would become much more specific.

9. At this preliminary stage, it is preferable to assess the value of the approach an the basis of the internal structure and consistency of the scheme. Specific references from each generated element to source material have been omitted because of the quantity of such material and the complexity of the decision process leading to a particular choice of words. In some cases, for example, 20 source sets were compared to produce the generated set.

10. It will be noticed that the attributes of the higher number sets are aspects of those associated with their lower number factors and "condensed" into those associated with their prime number factors. In affect each set "tells the same resource management story", but in the lower number sets the story is highly compacted. In the higher number sets, the attributes associated with elements are simplified, and more easily comprehensible, at the cost of making the relationship pattern more complex. In the lower number sets, these qualities are absorbed into more complex set elements, at the cost of comprehensibility, although the relationship pattern is simpler.

11. It will be noticed that sets which are multiples of 2 do not result in new information. The 2-operator merely dichotomizes each element in a set, elaborating on a common point. However a set with 2 as a factor establishes an unresolved polarity which can only be handled in an operational setting by introducing a new perspective (the set elements + 1) from which the polarity can be viewed and balanced. In this sense such polarized sets can effectively "give birth to" a new perspective as pointed out in one of the source documents:

'A vibrating string of any reference length can be halved to sound the octave higher or doubled to sound the octavo lower... The number 2 is "female" in the sense that it creates the matrix, the octave, in which all other tones are born. By itself, however, it can only create "cycles of barrenness", in Socrates metaphor, for multiplication and division by 2 can never introduce new tones ...' (14, pp. 19-20)

12. As structured the scheme supports the view that a monolithic structure of any kind inhibits development. The tension of a polarity is necessary to engender any development. It is useful to distinguish growth or elaboration (in which no new pattern is introduced, by a 2-factor, for example) from new development (in which a new pattern is introduced as a result of balancing a polarity). This suggests that any of the classic polarities are very healthy, if they can give birth to a new pattern: capitalism/communism, governmental/nongovernmental, rationalism/empiricism, etc. It suggests that a monolithic "world government" would be a total inhibitor of development. In an earlier paper (21), it was suggested that oscillation or resonance between two or more polar positions was essential to significant integration or qualitative transformation. The extreme example of brainwashing (stick and carrot) techniques (22) was given there as an example of oscillatory operations which have there constructive equivalent. This emerges more clearly here.

13. "Disagreement" as it has been discussed here, and allowed to emerge in the generated sets has not been clearly defined. This is because the definition is implicit in the 2-level set. At that level the subtleties of any distinction between opposition and complementarity, for example, do not emerge. "Disagreement" therefore also covers its synonyms, namely: disaccord, dissent, unconformity, controversy, disunion, discrepancy, difference, oppo4ition, dissonance, irrelation, inequality, incompatibility, irreconcilability, etc (Roget's Thesaurus).

14. There is a progressive "dilution" of the degree of disagreement between elements in a set as the number of elements increases. In affect the basic maximal disagreement of the 2-level is spread between the elements. This suggests that using sets with a higher number of elements as operators makes it progressively easier to contain the disagreement.

15. Each set is a container for a different kind of disagreement. Each can also be used to highlight what can go wrong when working with operators at that level, namely the characteristic errors for that level of operation.


1. By deliberately internalizing disagreement, the scheme moves beyond the stage of being a "cook book for potted wisdom" or a set of "bloodless categories". Each set can be tuned to constitute a set of challenging operations -- challenging because of the difficulty of maintaining them in equilibrium. The question is how effectively the sets can be tuned to take the scheme beyond the status of being simply an interesting exercise.

2. The scheme is valuable because of the way it interrelates incompatibilities at different levels '. It is significant also because of the way each set is embedded in a context of interdependent sets.

3. Given its relation to the source material of diverse cultural origin and specialization, the scheme is also valuable to the extent that interfaces can be provided to such specialized sets. It offers a way of interrelating and engaging groups working through apparently different concept schemes.

4. The awkwardness of the statements at present draws attention to the basic problem of how to condense qualitative complexes. The solution in traditional cultures of projecting them onto gods or demons (about whom stories could be told to bring out those qualities) was a good way of transforming the problem.

5. As designed the scheme is not "ideal" in the sense which is now so easily condemned. No set element is imposed, since as a hierarchy of paradoxes the problem of comprehension is central. A distinction may even be usefully made between:

6. The generation of these sets has been approached as a design problem in which constraints are necessary and must be creatively selected ( ). It is possible that the constraints could be refined as part of the tuning process.

7. It might be supposed that the use of any number pattern as a constraint on the ordering of social relations is quite arbitrary. There are however number-bound constraints as psychologists and psychoanalysts have shown. It would be interesting to explore their relation to the well-defined number-bound constraints on certain concrete mechanical operations (e.g. number of constraints to immobilize an object, or number of possible space relations)

8. The basic question raised, as to whether there was any pattern in the present to the ancillary processes to which a dialectical confrontation gives rise, is answered affirmatively. The sets show how the level of articulated disagreement can be increased to produce the level of differentiation capable of sustaining a non-homogenized society.

9. Any commentary and criticism of the gets could itself be usefully organized as an ordered breakdown using an analogous number pattern.

10. The pattern of sets opens the way to distinguishing very precisely various kinds of development. For example, one kind is associated with activating in a societies sets with a given factor (e.g. 7, 14, 21, etc). The decay of a culture (or an individual) may well correspond to the loss could well go undetected for some time. The loss of sets of exceptional operators, corresponding to the isolated prime numbers, be extremely difficult to detect, despite their importance for development. Such sets "stabilize" operators which are elusive in normal discourse.

11. This scheme suggests a much healthier approach to "positivity" as a slogan and "negativity" as an anathema in society today. The more responsible approach is well-illustrated by the following:

'What does it mean, to be whole? It means that we must be willing to conceive of, to contain within ourselves, whatever is "other than" any limited idea. It means knowing that when we emphasize a positive, we are at the same time creating a negative. When we choose an ideal of knowledge, then we must deal with the ignorance that is other than the knowledge. When we emphasize an ideal of holiness, then we must live with the sin that is its companion, and accept our responsibility for having created it. If we deny doing so, that is a contraction of awareness ... If we allow that ugliness is always within us, then we are free to create beauty. If we know that stupidity is always within us, then we are free to emphasize this intelligence' (24, pp. 24-25).


The material forming the basis of this experiment (and used to construct Annex 2) was originally presented in a document entitled: Patterns of N-foldness; comparison of integrated multiset concept schemes as forms of presentation (14). The annexes, containing the conceptual schemes derived according to this 'method', formed the bulk of the document, and were as follows:

Annex 0: UNU/GPID Project: It is appropriate to employ the same presentation method to the GPID concept scheme as It is now emerging.

Annex 1: Geometry of Meaning: This Is a modern effort to order a complex pattern of information on change and development In the light of physical concepts of dimensionality and control.

Annex 2: Book of Changes: This is the 3000-year old Chinese I Ching which is conceived as encoding the complex pattern of changes in physical and social phenomena. It has been of considerable Interest to Leibniz (philosopher), Jung I psycho- analyst) and western mathematicians, and its poetic expression has proved highly acceptable to a segment of western society.

Annex 3: Catastrophe theory: This is a now controversial way of thinking about change in all kinds of phenomena In the light of the mathematics of differential topology.

Annex 4: Tibetan Buddhism: This is a highly structured traditional scheme of concepts sets which, because of both illiteracy and the absence of paper, uses powerful imagery to facilitate memorability and communicability

Annex 5: Genetic code: This recent fundamental breakthrough in the biological sciences groups a number of concept sets in a highly integrated pattern.

Annex 6: Chinese Communist terminology: This is included because it illustrates the importance in one non-western political systems of concept sets governed by number.

Annex 7: Tonal patterns of Rg Veda chanted poetry: The Rg Veda is, in terms of survival over 4000 years, the most successful active communication vehicle. The concept scheme interlinks many concept sets in a very powerful way.

Annex 8: Movement and dance notation: This concept scheme is one of the most widely accepted frameworks of understanding of dance Is ordered.

Annex 9: Chinese art of war: This traditional scheme Is even row considered basic to ordering perceptions of strategy and tactics

Annex 10. Art of colour: Artists achieve certain visual effects by selecting Intuitively amongst a range governed by a perception-oriented concept scheme distinct from the colour preoccupations of physicists and chemists.

Annex 11: Islamic cosmological doctrine: As In the case of Tibetan Buddhism, this concept scheme has been of special significance to Islamic culture for an extended period.

Annex 12: Language and transformational-generative grammars: Language itself should be rich in concept schemes which are themselves a form of language. This annex, unlike the others, considers aspects of current thinking which have rendered superficial the traditional concept sets in this area.

Annex 13: Thermodynamics: This fundamental discipline is concerned with the description of change In physical processes. It has been applied by analogy to social processes. Its pattern of concepts is very well integrated. Unlike the other concept schemes, the concept sets are not explicitly set out. An attempt is made in this annex to show how they might emerge for comparison with other schemes.

Annex 14: Periodic classification of chemical elements: This fundamental scheme is included because of the comprehensibility of the pattern goverrning the complexity of the information ordered.

Annex 15: Systematics: This modern scheme, formulated by a philosopher, is included because of the variety of phenomena it encompasses and the leads It offers to understanding number-governed patterning complexity.

Annex 16: Periodic coordinate system: This ambitious modern scheme is included because it purports to order patterns of interaction in a variety of complex systems.

Annex 17: Synergetics: geometry of thinking: This highly original and well-integrated scheme is included because of the multiplicity of concept sets it includes and the leads it provides as to how transformations between them may be accomplished.

Annex 18: Polygons and polyhedra: This annex indicates the sets of polygons and polyhedra. It is significant in the light of the previous annex as indicating how set elements can be interrelated in an integrated whole.

Annex 19: Topological features of polyhedra: Again, in the light of Annex 17, the number-governed sets. associated with this material offer useful indications as to how such sets are interrelated In patterns.

Annex 20: Chladni patterns: This is included as a systematic study of the range of patterns arising form the vibration of a surface area. It Is significant in that it indicates how a zone Is "broken up" into sub-zones.

Annex 2: Results of experiment

The material forming the basis for this experiment were originally presented in a document entitled: Patterns of N-foldness; comparison of integrated multiset concept schemes as forms of presentation (14). The results have been presented as Annex 2 of this paper, but now appear as two separate documents. The first version has been used to highlight the relevance to articulation of sets of principles, charters or declarations:

Distinguishing Levels of Declarations of Principles

The second version has been adapted to highlight the challenge of dialogue with 'aliens', notably those on this planet who are experienced as alien -- especially those of different cultures:

Distinguishing Patterns of Assumption in Dialogue with Aliens


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