Topological Structure on Scientific Theories

Samuel Fletcher (Munich Center for Mathematical Philosophy)

Topological Structure on Scientific Theories

Abstract  

I review and amplify on some of the many uses of representing a scientific theory in a particular context not just as a collection of models, but as a topological space.  Topological structure on a set encodes among that set’s elements a notion of similarity, which proves fruitful in the analysis of a variety of issues central to the philosophy of science.  These include intertheoretic reduction, idealization and approximation, emergence, the epistemic connection between modeling and knowledge, and modality in science. The morals are twofold: first, the further adoption of topological (and related) methods has the potential to aid decisive progress in philosophy of science; and second, the selection and justification of a topology is not a matter of technical convenience, but rather often involves great conceptual and philosophical subtlety.