An epistemological study of material models from practical mathematics in early-modern natural philosophical debates

Een epistemologische studie van materiële modellen uit praktische wiskunde binnen vroegmoderne natuurfilosofische debatten
Start - End 
2013 - 2017 (ongoing)
Department of Philosophy and moral sciences
Other institution(s) 
Museum for history of science
Research Focus 
Additional tags 
History of science



In the first half of the seventeenth century natural philosophers looking for alternatives to the then dominant Aristotelian physics often took simple material objects and contrivances to offer important lessons about wider natural phenomena. One way to express this is by stating that they took such objects to be models for these phenomena. An example is Descartes’ use of a spherical glass filled with water as a model for a raindrop, which allowed him to reason and experiment with reflection, refraction and the separation of light. We will study what is involved in this particular type of modeling activity. We want to understand both why these natural philosophers took particular objects to be models for certain phenomena, and how they tried to extract the relevant information from these models. 

On the first question, it is important to notice that for many of these objects and contrivances, there already existed fairly developed knowledge concerning their behavior in the field known as ‘practical mathematics’. This consists of practices like engineering in which mathematics was applied to solve practical problems. In a first stage of our project, we will investigate how objects known from practical mathematics reappear in the writings of natural philosophers to serve as models for natural inquiry. In this process practical knowledge thus became ‘appropriated’ to serve different ends. 

To answer the second question, we will select some cases of such appropriation for a detailed analysis. We will look at how natural philosophers isolated relevant aspects of the objects’ behavior that they considered crucial for understanding the phenomena they were interested in. Not surprisingly, direct manipulations of the objects often played an important role to achieve this. To fully understand this aspect of the modeling process, we will not only look at the texts of the natural philosophers, but we will also engage in the reconstruction of some of these experiments.