Patterns of Conceptual Integration

Representation, Comprehension and Communication of Sets: the Role of Number

Anthony Judge

Reproduced with the permission of the Secretary of the Commonwealth Science Council (CSR) by whom it was originally commissioned. Presented to a meeting on forms of presentation of the Goals, Processes and Indicators of Development (GPID) project of the United Nations University (Geneva, October 1978).

Originally published in 3 parts in International Classification, 5, 1978, 3, pp. 126-133; 6, 1979, 1, pp. 15-25; 6, 1979, 2, pp. 92-103. Also published by the United Nations University as working paper HSDRGPID-22/UNUP-133 in 1980.

Abstract: Examines the cognitive and other factors which tend in practice to limit the number of elements distinguished in a set, particularly for sets fundamental to social science and policy formation, such as: human needs, values, principles, problems. It is argued that the number of elements so distinguished influences significantly both the relationships perceived between the elements and the qualitative characteristics manifested by them, irrespective of the content of the set. Such effects are important in the case of the more abstract sets for which the ambiguity of verbal descriptors creates considerable problems of comprehension and communication, especially when the set of elements is used as the basis for the elaboration of a group of cooperating institutions. The representation of such sets in traditional symbol systems and in modern 2 and 3-dimensional forms, is reviewed both as a source of constraints on set formulation and as a guide to the formulation and comprehension of the more complex sets through which the problems of society can be better contained.

Sections of this Article (accessed via the links on the right)

  • Introduction
  • Context
  • Constraints on number elements in a set
  • Representation of sets: introductory comment
  • Representation of sets: review of types
  • Involvement of the observer/creator of the set
  • Number and logic
  • Comprehension and number
  • Qualitative characteristics of sets
  • Representation of multi-term sets
  • Implications
  • Annexes
  • Notes
  • References