1. In a system with P terms, it should be possible to identify by analysis (with computer assistance and graphic output) configurations of the P terms (linked by Q relationships), selected in order of their degree of symmetry for a given value of P. Constraints on the maximum and minimum value of Q in each case could also be partially determined in terms of symmetry requirements. Tables of such configurations, without considering symmetry, have been produced by Frank Harary ( 124).
Patterns of Conceptual Integration
1. Eliciting subordinate sets: relating distinctions
If a set is named (e.g. "development"), the question may be asked in how many ways possible elements may be distinguished by subdividing the set.
The series below was developed by J. G. Bennett (45) to replace the Aristotelian and Kantian categories, with their dualistic characteristic. His definitions of systematic features are given in Annex 1. The characteristics given here summarize the extensive descriptions of Bennett (vol. 1, pp. 31-48, vol. 3, pp. 14-75).
The definitions given below are those of J. G. Bennett ((45), vol. 3, pp. 10 11) and are given as a basis for his elaboration of a multi-term sequence in Annex 2. In the main part of this article "set" has been used to signify what Bennett defines as "system", although the two terms have been used interchangeably.
"1. A system is a set of independent but mutually relevant terms. The relevance of the terms requires them to be compatible. No one term of the system can be understood without reference to all the others.
11.1 The purpose of this paper is to demonstrate the importance of number in the complete sets fundamental to social science and policy formulation. It is fairly obvious that formulation of a 2-term set of concepts (values, problems, etc.) establishes a dynamic for the advocates of each term, or those involved in any institutionalization of the dyad--namely a dynamic having any or all such aspects as: active/passive, right/wrong, we/ they, dominant/subordinate, conflict, complementarily. For example:
10.1 The above sections have identified: the constraints on set formulation imposed by number: the importance for comprehensibility of representation in 3 dimensions; the impact of particular number choices on the consciousness of those exposed to such sets; the problems of comprehension and the role of memory; and the properties exemplified by sets of a given number of terms. These are brought into focus by the problems of representing and comprehending multi-term sets. The problems have been strongly emphasized.
9.1. Characteristics of multi-term systems: The remarks of the previous section provide a context within which efforts at establishing the characteristics of multi-term systems can be considered as defined in Annex 1 . This question cannot be explored here. It serves as an indication only therefore, that the results of J. G. Bennett's exercise are summarized in Annex 2. This suffers from the disadvantage of not establishing explicit links to the rich variety of cultural and mathematical material reviewed by von Franz in her study of the first four integers.
8.1 Problems of comprehension: It is appropriate to note that work in the well-defined field of "multi-valued logic" does not seem to have had any impact on these concerns37. Nor does that on the "theory of numbers"33. It is only more recently in studies which face up to non-quantitative considerations with propositions for 3 or 4-valued logics that the nature of the link begins to emerge (48, 49).
7.1 Beyond 2-term logic: multi-term systems: In the above argument the terms "set" and "system" have been used interchangeably since one of the characteristics of the sets of elements under consideration was identified as the complementarily of their elements. In discussing multi-term systems, a mathematician and director of industrial research J. G. Bennett clarifies further the kinds of sets to which these arguments apply (45, vol. 2, pp. 3-10). A set of elements taken without reference to any internal connections is called a class.
6.1. Whenever it is convenient, there is a widespread tendency to avoid consideration of the impact of those involved on research or on the policy-making process in which they participate. Researchers correct for bias in experiments and aim for reproducible results. Efforts are made to balance the interests represented at policy meetings. Consequently, when sets of basic values, problems, concepts, or principles are generated by either, they are conceived to be objective.