When I returned to grad school for the third time around, this time in a systems engineering program, I had in mind integrating many of my old projects investigating the dynamics of information, inquiry, learning, and reasoning, considering these processes as they evolve their trajectories through the media of sign relations that give them their concrete embodiments.
Up until that time I don’t believe I’d ever given much thought to sign relations that had anything smaller than infinite domains of objects, signs, and interpretant signs. Countably infinite domains are what come natural in logic, since that is the norm for the formal languages it uses. Continuous domains come first to mind when turning to physical systems, despite the fact that systems with a discrete or quantized character often enter the fray.
So it was a bit of a novelty to me when my advisor, following the motto of engineers the world over to “Keep It Simple, Stupid!” — affectionately known by the acronym KISS — asked me to construct the simplest, non-trivial, finite example of a sign relation that I could possibly devise. The outcome of that exercise I wrote up in the following primer on sign relations.