redefining my definitions

By Monday afternoon I'd reached the conclusion that somewhere along the way, my formal system in chapter 7 had really gone awry. The natural language system presented in the anonymous text I'm looking at is really quite straightforward and intuitive, and the fact my formal system had ended up so clunky and unintuitive, and that I was still coming up with not only new subcases for the definitions I already had, but even wholly new definitions (which then manifested a need for new subcases that I hadn't already considered), was a pretty good indication that this way of formalizing things was probably not the right way to go. So I emailed what I had to Benedikt and we set up a meeting to talk about things tomorrow. I took two days off and didn't try working on the chapter any more, but that just meant no active writing, just lots of thinking going on on the background. By last night I'd sort of convinced myself that I had a vague idea of a better way to do things, so I spent most of today trying to make that vagueness more precise. Which meant redefining all my definitions...and the end result was about 1/3 of page longer than what I had to start with. So what does this say about my attempt to simplify things? I don't know. I leave the answer to you, dear reader, and so I present to you, the totally redefined chapter 7.