A Category Theoretic Framework for Physical Representation
A Category Theoretic Framework for Physical Representation
This work was presented to the ANU philosophy department seminar, and was scheduled as a presentation at the Sydney University (March 2020)
It is increasingly popular for philosophers of science to use category theory, the mathematical theory of structure, to adjudicate debates about the (in)equivalence of formal physical theories. In this talk, I discuss the theoretical foundations of this strategy. I introduce concept of a “representation diagram" as a way to scaffold narrative accounts of how mathematical gadgets represent target systems, and demonstrate how their content can be effectively summarised by what I call a “structure category". I argue that the narrative accounts contain the real content of an act of physical representation, and the category theoretic methodology serves only to make that content precise and conducive to further analysis. In particular, one can use tools from category theory to assess whether one physical formalism thus presented has more "properties", "structure", or "stuff" than another.While this presentation emphasised applications to physics, this framework is also extremely promising for helping us understand computational representation. I believe many issues in AI ethics boil down to a discrepancy between beliefs and intentions about a computation system, and its real world manifestation. By clarifying the ways in which formal structures represent the world, and how these representations can break down, we can better understand how to tie our technologies to our values.