A logic of systems

Excerpt from chapter 8 of [A. Angyal](https://en.wikipedia.org/wiki/Andras_Angyal), _Foundations for a Science of Personality_, Harvard University Press, 1941, pp. 243-61. [[on the Internet Archive](https://archive.org/details/20200311foundationsforascienceofpersonality)] Snippets of text (from the beginning, maybe the middle, and the end) appear below, to give a sense of the content for the chapter. For more depth, the original source is cited, above. ---

### The Structure of Wholes The problem of the integration of part processes in the total organism is the most important and at the same time the most difficult problem for a science of personality. The difficulty lies not alone in the paucity of usable factual data, but to an even greater extent in the inadequacy of our logical tools. Such a handicap is felt not only in the study of personality, but in the study of wholes in general. An attempt will be made to develop some concepts which may be useful for the understanding of the structure of wholes. Our scientific thinking consists prevalently in the logical manipulation of relationships. That the structure of wholes cannot be described in terms of relationships has, however, been repeatedly pointed out by many writers. While accepting the premise that holistic connexions cannot be resolved into relationships, some authors have implied that the pattern or structure of wholes does not lend itself at all to logical manipulation. We suggest, however, that the structure of wholes is perhaps amenable to logical treatment after all, that, though it may not be described in terms of relations, it may be described in terms of some more adequate logical unit, representing an entirely different logical genus. Here the attempt will be made to demonstrate that there is a logical genus suitable to the treatment of wholes. We propose to call it _system_. [p. 17] [....]

The differences between relationships and systems may be formulated as follows: * 1\. A relation requires two and only two members (relata) between which the relation is established. [....] [p. 18] * 2\. A relation requires an aspect out of which the relationship is formed. [....] \ \ The system is dimensional. _A system is a distribution of the members in a dimensional domain_. [p. 20] * 3\. In establishing a relationship between objects and in arranging objects in a system, the separation of the objects is presupposed. [....] * 4\. In a relationship the connectedness between the relata is a _direct_ one. [....] [p. 21] \ \ _In a system the members are, from the holistic viewpoint, not significantly connected with each other except with reference to the whole_ [....] [p. 22].

## System and Gestalt In the course of the past two decades it has been almost generally recognized by biologists and psychologists that the clarification of the problem of wholes is essential for progress in the study of the organism. The increasing awareness of the problem of wholes led to the discovery of certain general principles, best formulated perhaps by the Gestalt psychologists. It will be useful to examine briefly these formulations in the light of the previous discussion. [pp. 25-26] The most generally known thesis with regard to wholes is the following: 'The whole is more than the sum of its parts.' This is not a very felicitous formulation since -- contrary to the concept of Gestalt psychologists -- it may suggest that a summation of parts takes place and that, besides the summation, a new additional factor enters into the constitution of wholes. In Ehrenfels' _Gestaltqualit├Ąt_ such an additional factor actually has been suggested. Wholes, however, cannot be compared to additive aggregations at all. [....] The formation of wholes is therefore not additional to the aggregation of parts, but something of an entirely different order. _In aggregates it is significant that the parts are added; in a system it is significant that the parts are arranged_. [....] [p. 26] [....]

This brief discussion of some holistic principles and concepts suggests the possibility of the logical formulation of some principles and concepts. Only a strict logical formulation can dispel the vagueness and obscurity which have been so common in the early holistic theories. [p. 29]