Mathematization

This chapter conceives mathematization as a modeling process in which the modeler attempts to find an answer to a specific question about a target system. Each answer has to meet specific requirements to be satisfactory. These requirements can come from specific theoretical frameworks, methodological demands, and what is already known about the subject matter. Even if the mathematical framework is set in advance, it still does not tell which of its mathematical forms is most appropriate. The selection of these mathematical forms is similar to the selection of materials in mechanical design: one has to take into account the properties of the considered materials and their combinations. These materials are not only selected for enabling correspondence with the target system, but also chosen to achieve the model’s goal. Modeling is an attempt to integrate various kinds of specific ingredients, such as theoretical notions, facts and data about the phenomenon in question, and (mathematical) analogies. Finding the appropriate mathematical forms is crucial for successful integration. Although material knowledge and knowledge of the target system are essential, finding the right combination of materials remains an experimental, inductive process.