**1. Presentation**

(a) 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 that fail to take this constraint into account tend to give rise to methods which are poorly understood and rarely used, whatever their merits.

(b) 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.

(c) The intent is therefore to establish a constraint framework such that different kinds of development discussed can be effectively distinguished whilst at the same time clarifying why those we do no happen to favour appear disagreeable and essentially unjustifiable, if not incomprehensible.

(d) 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**

(a) Any text on method can be further elaborated by introducing statements in agreement with the initial statement. There is no well-defined limit to this expansion process.

(b) 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 and compensate for its weaknesses. 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.

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

(d) 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 (*ie* debate) are described by a probability wave function. When a particular probability is actualized (*ie* debate position is taken), the wave function "collapses" (*ie* no other statements are relevant in that context).

**3. Underlying relationship**

(a) 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 that contain elements in maximal disagreement.

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

(c) The disagreement becomes especially 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 one 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.

(d) 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**

(a) 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.

(b) 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).

(c) 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**

(a) 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.

(b) 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.

(c) A new constraint is therefore introduced which requires that only one set be allowed with a given number of matching statements as elements.

(d) This constraint highlights the essential "management" issue of handling the set elements and maintaining the integrity of the set. This is the challenge of **managing contradictions** 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.

(e) 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. Some of the sets may instead be reflected in the sets of principles, values, strategies, or procedures of that organization - or even in informal factions concerned with particular policies.

(f) 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 to be elucidated, as well as the set elements "activated" as role stereotypes for "players" implementing the method.

**6. Number pattern**

(a) 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.

(b) 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.

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

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

(e) 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 integrated set of transformative operations that require a complete pattern of checks and balances. As an illustration of the non-trivial role of numbers in the organization of information, the database software through which this book is produced distributes information more efficiently on the storage disk if the file size is determined using a prime number. Otherwise information is not distributed so evenly, leading to performance degradation. This suggests the possibility that more fruitful patterns of disagreement can be organized when a set spreads the weight of the incompatible positions more evenly using a number of set elements based on a prime number.

**7. Transformation operator**

(a) 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.

(b) 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.

(c) 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 mutually counteracting.

(d) 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 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 of Requisite Variety, *also the gene pool concept).

**8. Self-constraint**

(a) 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.

(b) Whilst the statements could be oriented toward many domains of action, the one which introduces the greatest constraint and the sharpest degree of focus is that relating to the generation of statements on method and related forms. This is effectively a self-referential, self-constraining constraint.

**9. Containment of unpredictable**

(a) 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.

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

**10. Inter-set consistency**

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**

Although a previous constraint requires that the set elements have a transformative dimension, a further constraint is required to ensure that such operations are important to any isomorphic management process especially to one requiring the management of contradictions.

**12. Inter-set harmony**

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

(b) A further constraint can be usefully 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**

(a) 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 continuing refinement.

(b) 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.