# Category Theory in Philosophy of Science

(DFG Scientific Networks Grant)

This project applies category-theoretic methods to the analysis of relations between scientific theories. Understanding such relations is a longstanding topic of interest in the philosophy of science. In particular, philosophers have been interested in questions such as when two theories are equivalent, i.e., when they say the same thing about the world; when two theories stand in a relation of reduction, i.e., when it is that one theory can be “represented” within another; and when one theory is a limit of another, i.e., when one theory may be regarded as an approximation to the other in certain physical regimes. These questions are not only of interest in themselves, but also have direct bearing on issues in philosophy of science, and indeed on scientific practice itself.

Recently, researchers in these areas have come to realise that categorical methods offer a powerful tool for addressing such questions. Roughly speaking, categorical methods involve characterising certain classes of mathematical structures (e.g. groups, smooth manifolds, or vector spaces) in terms of the morphisms between them (e.g. group homomorphisms, diffeomorphisms, or linear transformations). It has recently come to be appreciated that treating a theory as a collection of such structures (the models or solutions of the theory), together with an appropriate class of morphisms, gives a great deal of insight into the structure of the theory.

Towards investigating this topic, the project will address three specific issues. First, we will consider the relevance of these methods to judgments of equivalence between theories. Second, we will investigate the categorical foundations of such work by looking at what kinds of category-theoretic resources are required for a proper analysis of scientific theories. Finally, we will extend this analysis to cases of reduction and limits.

This project is funded by a DFG Scientific Networks Grant: for details of the members of the network, please see the "Members" page. The funding will be used to support a series of three workshops and a concluding conference. For details of these events, please see the "Events" link.

The network coordinator is Neil Dewar (neil.dewar@lrz.uni-muenchen.de).