General Model Theory by Stachowiak

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

  1. Mapping: Models are always models of something, i.e. mappings from, representations of natural or artificial originals, that can be models themselves.
  2. 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.
  3. 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.


  1. 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.
  2. 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. […]
  3. 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 fulfil their 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.

Have fun

Part II: Stachowiak’s K-System of Modelling

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24 Responses to General Model Theory by Stachowiak

  1. TY says:

    Hi! Good introduction. Do you have the full book? Is there a definition to model in the book, including the “K-System”?

    • TY says:

      Sorry, the comment lost the key message, I wanted to say:
      Is there a definition with to model in the book, including the “K-System”?

    • TY says:

      with (M, O, K, t, Z)
      ( I see: In the previous comments, used a pair of ANGLE brackets, so, be eaten with the site :p )

      • Hi TY
        I don’t own the book, I’ve just made some copies of the essentials, and yes the “K-System” is amongst these, too. So, I’ll have a look the next days. Perhaps it should be translated as well.

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  4. TY says:

    There is a question: is there any direct definition of the term model in the
    And I have a feeling, though not quite sure:
    Stachowiak’s GMT is very model-as-use.
    On the perspective of model-as-use, you can’t define the concept model as a
    type of entities, as said by Marx W. Wartofsky (1966): "anything can be a model
    of anything else!" May be this is indeed one of the reasons behind this: in
    Stachowiak’s book, it seems not a special definition in common form to model
    (such as: A model is a …)? as you’ve introduced on this bolg, one is the three
    attributes of model ("three criteria" by Ludewig, J., 2003), another is the
    5-tuple, a system with model in use (in my word: situation; it perhaps can be
    called a Use Case of models, and in Gelbmann (2002), it denoted by Th
    ("Theory in non-statement view").
    There is another document on Stachowiak’s GMT, "An Outline of Pragmatologic
    Model-Theory (sec. Stachowiak). Semiotic Subjectivity II", a Lecture by Dr.
    Gerhard Gelbmann, June 2002.
    In this document, stated that
      The pragmatologic conception of model means a "functional" (or
    "operational") mapping of attributes (of the same sort) of a so-called original onto attributes of a model This shall serve as a first, but not
    ultimate or exhaustive definition.
    I don’t know if it is Stachowiak’s; I see, it’s basically that so-called homomorphic
    model, and said "not ultimate or exhaustive".
    (Just to share my thoughts. Have fun 🙂 )
    (Sorry, please delete the comment above: it is messed up because I used some
    of angle brackets)

  5. Yes, Stachowiak actually avoids the term definition, however the properties he defines are considered necessary by him.

    Thx for the link to the document. It makes an important point: Stachowiak’s main focus is actually more on modellING then on model. His view includes the “organism” k and has a special focus on describing (i.e. formalising) the “pragmatic” property.

    Thus, it it a specialisation of “Model as use”, since it requires reduction, however it’s strong focus on the modelling operation makes it quite close to “Model as use”. Perhaps “Model in use” would be the corresponding term for Stachowiak’s position?


    • TY says:

      “Stachowiak actually avoids the term definition” is an important comment.
      The three attributes (properties) is necessary to the type of models studied by Stachowiak: models on mapping (the attr. 2, with 1); the attr. 3 is a reflection from the essence of “model as use”: it is meaningless that define a model without the uses.

      “modeLLING”: I think I understand what are you emphasis.
      And the words “model as use” is more directly pointed to the basic question “what is a model”, relatively, “model in use” is more involved in the question “how does a model work”.

      • added a little introduction to the K-System article. Also changed some wording that made it look like a definiton before.

        Stachowiak’s explications (1-12) follow pretty much the cognitive modelling ‘process’, seems very much like “how does a model work”.


  6. TY says:

    Hi, |=
    I got this: “a compilation with some illustrations” on Stackowiak but in German

  7. yes, I know, the Müller site is great in general, unfortunately mostly it’s german language, however he has some pages in english as well. This one is great, for example:


  8. TY says:

    You know, Stachowiak was a mathematician and logician, I’m curious that how did he treate the model theory in his general model theory?

    • Just scanned through the book again, to find some clues. Think the only point where his math background shines through is in the “explication” of the model concept, I mean the more formal one.

      He also builds essentially upon the work of Frege. Perhaps this is due to his past as logician, too?


      • TY says:

        Is that implied, I think, he actually avoid (or ignored) the model theory in his general model theory?
        Of course, that should be in fact very natural matter.

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