Abstract

The talk discusses the role and some features of limit objects in physical theories. The talk recalls the concept of limit object understood in the sense of (mathematical) category theory, and defines the notion of emergent property of a limit object. Examples of limit objects and emergent properties are given, and it is argued that limit objects in physical theories display a tension between two norms of theory construction in physics: one norm dictates that one should have physical theories describing all the phenomena in a certain domain. The other norm intends to restrict the entities featuring in physical theories to those that have a counterpart in the physical world, thereby not allowing imaginary objects that cannot be interpreted realistically. The tension is illustrated by how the infinite Ising model describes phase transition and a suggestion is made about how to tolerate the tension.