On the modelling relation

Abstract

Some conceptual problems which are related to the way data (i.e. empirical information) are represented in model building are discussed. Elements of a framework for modelling are proposed in which a constructive relationship between the data and the modelling relation itself is incorporated. The main novelty of this approach is the use of the notion of information set, which is defined as the set of observed values of those observables which are actually available as data sources for a given model, as contrasted to a complete set of observations where questions of restricted availability cannot be raised. This permits the application of complexity theory in a new way. Some examples are given where, as a consequence, essential differences between descriptions, otherwise considered equivalent, will be revealed. One application, showing the existence of fundamentally inequivalent forms of dynamics which belong to different information sets, is elaborated in more detail. la science occidentale est fondée sur la doctrine monastique d'un univers ordonné, créé par un Dieu qui reste hors de la nature et la gouverne par des lois accessibles á la raison humaine.

Different forms of causation in dynamical systems: Determinism, pattern generation, and information

“…In our case, the main ideas come from the side-products of the research the author is doing jointly with Prof. V. Csányi. Results of the work are reported in several publications (e.g., Csányi, 1982aCsányi, , 1982bCsányi, , 1989Csányi and Kampis, 1985;Kampis and Csányi, 1987a, 1987b, 1988. Some of the linkage points between those works and the present one will be clarified later in this paper.…”

Biological Evolution as a Process Viewed Internally

“…Zeno was the first to compare the properties of a mathematical description of motion to the very motion itself. 14 In the spirit of Eleatic philosophy, we can now associate "motion" or "change" with an "endo"-viewpoint and a "no motion" state or "static" state with an "exo" -viewpoint. The motivation is that processes viewed internally can show Whiteheadian or Heraclitean phenomena of change, whereas those operations of decoupling that result in an "exo" -picture were found to render this picture static, just as the "One" of the Eleatics was conceived.…”

“…The motivation is that processes viewed internally can show Whiteheadian or Heraclitean phenomena of change, whereas those operations of decoupling that result in an "exo" -picture were found to render this picture static, just as the "One" of the Eleatics was conceived. Using a few other concepts in a similar way, the following 14 A detailed discussion of the paradoxes and their various solutions is given in [7]. ll>Whitehead's famous bon mot "The history of philosophy consists of a series of footnotes to Plato" is not the reason why this footnote was inserted.…”

“…A non-classical modelling methodology, as introduced in [14], is based on a particular constructive definition, the concept of information sets. An information set I is a record of observations I = 01, 02, •.…”

An invitation to cognitive science: Justin Leiber, Oxford, Eng. and Cambridge, Mass., Basil Blackwell, 1991

“…We will teview Casti's books first. I first encountered Casti's writings in an interesting piece written by Kampis (1988) on model building to which I referred in my latest text (van Gigch, 1991). In the three books reviewed here, Casti discusses, in an approachable style, many of the riddles and paradoxes of modem physics.…”