Mark Newman (Rhodes College)
According to some philosophers of science, our understanding of a scientific theory is reflected by our ability to solve problems using that theory (see for instance de Regt and Dieks (2005), de Regt (2009), de Regt and Gijsbers (2017) and Newman (2017a, 2017b)). If this is so, then it follows that the degree of understanding someone has of a theory could in principle be measured by the maximum difficulty levels of the problems they can solve. I raise five problems for this view. I then look at two models from cognitive science that claim to measure and rank physics problems by their level of difficulty. I raise four problems for these models, and argue that even if they could provide an objective measure of problem difficulty they cannot provide a measure of someone's degree of theoretical understanding. I argue that what all these problems show is that we need a more fine-grained measure? one that works at the fundamental level of individual beliefs and inferences, not at the abstract level of problems.
