The Chern-Simons interpretation you mentioned is not directly related to the family resemblance theory. Allow me to explain each of these concepts separately:
Family Resemblance Theory: The family resemblance theory is a concept proposed by the philosopher Ludwig Wittgenstein. It suggests that categories or concepts do not have a single defining feature but instead have a collection of overlapping similarities, much like the members of a family who share certain traits but may not have a single characteristic in common. According to this theory, the meaning of a category or concept is derived from the similarities between its various instances rather than from a specific set of defining features.
Chern-Simons Theory: Chern-Simons theory is a mathematical and theoretical physics framework named after mathematicians Shiing-Shen Chern and James Harris Simons. It originated in the field of differential geometry and has found applications in theoretical physics, particularly in the study of topological quantum field theories.
Chern-Simons theory focuses on certain mathematical quantities called Chern-Simons forms, which are associated with three-dimensional manifolds. These forms have significance in the study of gauge theories, knot theory, and quantum field theory. Chern-Simons theory has been used to understand various phenomena in condensed matter physics, high-energy physics, and gravitational physics.
To the best of my knowledge, there is no direct connection between the Chern-Simons interpretation and the family resemblance theory. They belong to different domains, with the former being a mathematical and physical framework, while the latter is a philosophical concept.