Something that came up while I was reading Pragmatism. If we turn Pragmatism on its head and ask: what THEORETICAL (instead of practical) difference would something have?

For instance, there are cases where notions that are entirely different practically are the same theoretically, abstractly, structurally.

Two notable examples are:

  • Topologically same 3-D structures: Like the famous example of the torus, a coffee mug and a doughnut are theoretically the exact same structure.
  • Music transposition: Playing the same melody in another key might be practically very different, e.g. much harder/easier to play on the organ and much different feeling relative to how low/high pitch it is. But theoretically it is exactly the same.