In the literature, there have been several methods and definitions for working out if two theories are equivalent (essentially the same) or not. In this article, we do something subtler. We provide means to measure distances (and explore connections) between formal theories. We introduce two main notions for such distances. The first one is that of textit{axiomatic distance}, but we argue that it might be of limited interest. The more interesting and widely applicable notion is that of textit{conceptual distance} which measures the minimum number of concepts that distinguish two theories. For instance, we use conceptual distance to show that relativistic and classical kinematics are distinguished by one concept only. We also develop further notions of distance, and we include a number of suggestions for applying and extending our project.
Download