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(2017) Springer handbook of model-based science, Dordrecht, Springer.
Model-based reasoning in mathematical practice
Joachim Frans, Isar Goyvaerts, Bart Van Kerkhove
pp. 537-549
The nature of mathematical reasoning has been the scope of many discussions in philosophy of mathematics. This chapter addresses how mathematicians engage in specific modeling practices. We show, by making only minor alterations to accounts of scientific modeling, that these are also suitable for analyzing mathematical reasoning. In order to defend such a claim, we take a closer look at three specific cases from diverse mathematical subdisciplines, namely Euclidean geometry, approximation theory, and category theory. These examples also display various levels of abstraction, which makes it possible to show that the use of models occurs at different points in mathematical reasoning. Next, we reflect on how certain steps in our model-based approach could be achieved, connecting it with other philosophical reflections on the nature of mathematical reasoning. In the final part, we discuss a number of specific purposes for which mathematical models can be used in this context. The goal of this chapter is, accordingly, to show that embracing modeling processes as an important part of mathematical practice enables us to gain new insights in the nature of mathematical reasoning.
Publication details
DOI: 10.1007/978-3-319-30526-4_24
Full citation:
Frans, J. , Goyvaerts, I. , Van Kerkhove, B. (2017)., Model-based reasoning in mathematical practice, in L. Magnani & T. Bertolotti (eds.), Springer handbook of model-based science, Dordrecht, Springer, pp. 537-549.
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