In his 1973 book “Allgemeine Modelltheorie” (General Model Theory) Herbert Stachowiak describes the fundamental properties that make a Model. Unfortunately this is still only available in german language, so I thought why not try a translation of the essential bits:
Fundamental Model Properties
- Mapping: Models are always models of something, i.e. mappings from, representations of natural or artificial originals, that can be models themselves.
- Reduction: Models in general capture not all attributes of the original represented by them, but rather only those seeming relevant to their model creators and/ or model users.
- Pragmatism: Models are not uniquely assigned to their originals per se. They fulfill their replacement function a) for particular – cognitive and/ or acting, model using subjects, b) within particular time intervals and c) restricted to particular mental or actual operations.
- Mapping: Such originals can evolve in a natural way, be produced technically or can be given somehow else. They can belong to the areas of symbols, the world of ideas and terms, or the physical world. [...] Actually, every entity, that can be experienced (more general: ‘built’) by a natural or mechanical cognitive subject, can in this sense be considered an original of one or many models. Originals and models are interpreted here solely as attribute classes [representable by predicate classes], that often achieve the shape of attributive systems [interrelated attributes that constitute a uniform orderly whole]. The concept of mapping coincides with the concept of assigning model attributes to original attributes in the sense of a mathematical (set theoretical, algebraic) mapping.
- Reduction: To know once that not all attributes of the original are covered by the corresponding model, as well as which attributes of the original are covered by the model, requires the knowledge of all attributes of the original as well as of the model. This knowledge is present especially in those who created the original as well as the model , i.e. produced it mentally, graphically, technically, linguistically, etc in a reproducible way. Only then an attribute class is determined the way intended by the creator/ user of the original and the model. Here, an attribute class is an aggregation of attributes of the original as well as of the model side, out of the overall unique attribute repertoire. Thus, the original-model comparison is uniquely realisable. [...]
- Pragmatism: Beyond mapping and reduction the general notion of model needs to be relativised in three ways. Models are not only models of something. They are also models for someone, a human or an artificial model user. At this, they fulfill they function over time, within a time interval. Finally, they are models for a certain purpose. Alternatively this could be expressed as: a pragmatic complete determination of the notion of model has not only to consider the question ‘what of‘ something is a model, but also ‘whom for‘, when, and ‘what for‘ it is a model, wrt. its specific function. [...]
- Stachowiak, Herbert (1973) (in german (DE)). Allgemeine Modelltheorie [General Model Theory]. Springer. ISBN 3-211-81106-0.
Part II: Stachowiak’s K-System of Modelling