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Searching the Web for "science is modeling" (Rejected by a journal.) Comparing three different approaches to explaining the nature of mathematics in my 2006 Saint Petersburg lecture (English translation in preparation), I concluded that the best way should be starting from the mathematical modeling as the most important external function of mathematics. The distinguishing feature of mathematical models - they can be investigated successfully without any reference to the modeled objects. I'm defending this point of view since 1980s, see K. Podnieks (1988: Platonism, intuition and the nature of mathematics, Abstracts of Summer School and Conf. on Math. Logic "Heyting'88", Bulgarian Acad. of Sciences, pp. 50-51). Couldn't one try generalizing this approach, and start explaining "the nature of science" from the notion of modeling? And by using the most general notion of model that has become usual in computer science - as any structure A that is used for some purpose instead of another structure B (A=B also is allowed, for some time). In this way I arrived at a somewhat extreme tentative formula that, perhaps, any branch of human activities can be qualified as scientific only to the extent to which it is building models. Of course, this formula sounds similar to the famous statement of Immanuel Kant: "Ich behaupte aber, dass in jeder besonderen Naturlehre nur soviel eigentliche Wissenschaft angetroffen werden koenne, als darin Mathematik anzutreffen ist." The first possible objection: what about philosophy? Answer of a computer scientist: one can try also meta-modeling, i.e. modeling the process of modeling itself. In computer science, modeling without a well-defined meta-model ("philosophy"), is qualified as a bad practice. Another possible objection: what about theories? Answer of a computer scientist: ontologies and theories serve as frameworks for building models, i.e. they should be considered in a meta-modeling context. For example, Newtonian mechanics is not itself a model, but it provides a framework for building models of various systems of particles. After that, I made of this topic a separate lecture "What is science? Science is modeling!" for Section of Theology, 2007 Annual Conference, University of Latvia (extended English translation available). The modeling approach seems to be especially useful in analysis of religions. If you would propose some set of concepts, then I will first try to understand it as a model of the world (or of a part of it). Do you pretend that your set of concepts is more than a model? And only recently I arrived at the idea of searching the web for "science is modeling" (and, "modelling"). The result - this formula has been used before me - more or less seriously - several times. The following authors have used it in their books, papers and presentations: 1. "I will employ the concept of the model to develop a particular view of science, namely, science as modeling (SAM). This view is held by many, perhaps most, scientists themselves. ... I claim no originality in employing the idea that science is modeling, but I do claim that it facilitates a perspicuous explication of the scientific enterprise." Jeffrey E. Foss (2000: Science and the Riddle of Consciousness. A Solution, Kluwer Academic Publishers, p. 44). 2. "Science is modeling; we derive models of Nature for the purpose of understanding how everything works." Hans Petter Langtangen, Aslak Tveito (2001: How Should We Prepare the Students of Science and Technology for a Life in the Computer Age?, Mathematics Unlimited - 2001 and Beyond, Springer, p. 809). 3. "No science without modeling or rather "science is modeling". With the help of models we try to grasp our environment and to influence it for our benefit." Ad Damen (2005: Physiological Processes and Parameter Estimation, Technical University Eindhoven, p. 3). 4. "Why model the brain? Science IS modeling." Jerome Swartz (2006: Large-Scale Brain Modeling, Computational Approaches to Cortical Functions - 2006 Workshop at Cold Spring Harbor Laboratory, The Swartz Foundation). 5. "Given that I am a mathematical biologist, it is perhaps not surprising that I am in favour of models. But it seems to me that all science is modelling. It need not to be a mathematical model, of course, ..." Hamish G.Spencer (2006: False Models as Means to Truer Theories, University of Otago, p. 1). 6. "To the grand philosophical question: "What is a man?" Aristotle answered: "Man is a rational animal." Modeling Theory offers a new answer: "Man is a modeling animal!" Homo modelus!" David Hestenes (2006: Notes for a Modeling Theory of Science, Cognition and Instruction, Modelling in Physics and Physics Education - GIREP Conference 2006, GIREP, p. 27). The very idea could be traced back to Patrick Suppes (1962: Models of Data, Logic, Methodology and Philosophy of Science: Proceedings of the 1960 International Congress. Stanford University Press, pp. 252-261). By ignoring many subtleties, one may conclude from this paper that scientific "truth" is not a correspondence between our model and the "observed reality". It is a correspondence between the model and some other models that are representing experimental data. As put by Hestenes (p. 3), this "exorcises the accumulated positivist contamination of Newtonian physics". And this answers the third possible objection: what about the "observed reality" as an external, independent and the final criterion for the "truth" of our models? Answer: no such thing is necessary. Any concept of "observed reality" is no more than element of our meta-model. For some other applications of the modeling approach (demystification of Gödel's incompleteness theorem, philosophy of mathematics as modeling mathematics) see my above-mentioned second lecture. One can read in many places about "the role of models in science", but, as we see, only few authors are using the formula "science IS modeling". Modeling is the distinguishing feature of scientific thinking (no modeling - no science). Can this thesis be maintained seriously? Personally, I would prefer an even stronger thesis: everything that is going on in human minds is modeling (music, dreaming, hallucinations, etc. included - the list due to an anonymous referee)! Because, A=B also is allowed! Karlis Podnieks |