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The Modeling Relation


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I wish that someone had shown me this about 20 years ago. This resides at the philosophical roots of science. So I am going to throw it out here and open it for discussion. I'm still trying to grasp certain aspects of it myself. So hopefully any questions or comments will force me to think and I will learn something here too. This is taken from the work of theoretical biologist Robert Rosen and can be found in his books Anticipatory Systems and Life Itself.


Let me present a figure and then outline its features.




A natural system N is a set of perceptions that seem to us to belong together. A formal system F is a sublanguage of natural language defined by syntactical qualities alone (i.e. axiomatic systems). Phenomena are the observables of a natural system. Propositions are the statements of a formal language.


There are four arrows here and they are...


measurement: phenomena ----> propositions

inference: propositions ----> propositions

prediction: propositions ----> phenomena

causality: phenomena ----> phenomena


The thing to note here is that if we follow the path of measurement followed by inference followed by prediction then this path takes us from phenomena of N to phenomena of N. And causality also takes us from phenomena to phenomena. If measurement followed by inference followed by prediction = causality then the modeling relation holds and F is a model of N. If F is a model of N then it provides an explanation for the behavior of N.


However in general will find that most measurements, inferences, and predictions do not commute with causality. This strikes me as one way of saying that misunderstanding is more likely than understanding.


Well that's it for the first installment of this thread. There will likely be others forthcoming. Again I welcome any criticisms, questions, comments, etc.

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