It’s been a while since I started this thread, with many sidetrips and tangents, so let me go back to the top and expand on the motivations I expressed there, addressing a few issues that have arisen in the meantime.
People interested in category theory as applied to systems may wish to check out the following article, reporting work I carried out while engaged in a systems engineering program at Oakland University.
This article develops a differential extension of propositional calculus and applies it to a context of problems arising in dynamic systems. The work pursued here is coordinated with a parallel application that focuses on neural network systems, but the dependencies are arranged to make the present article the main and the more self-contained work, to serve as a conceptual frame and a technical background for the network project.
Category theory, as working mathematicians understand it, is one of the chief conceptual frameworks for the development of mathematics today, the other being set theory. Every graduate math course I ever took began with a two- or three-week review of set theory and category theory before launching into the main subject matter. From a logical point of view, however, category theory has a history stretching back to Aristotle.
I once started writing a sketch on the “Precursors of Category Theory”, collecting a sample of historical landmarks through the centuries, from Aristotle to category theory’s modern mathematical avatars. Here’s a link to a survey page on my blog.
To be continued …
- Differential Propositional Calculus • Part 1 • Part 2
- Differential Logic • Part 1 • Part 2 • Part 3
- Differential Logic and Dynamic Systems
• Part 1 • Part 2 • Part 3 • Part 4 • Part 5