I've been reviewing some of this discussion, and noticed that Eliezer hasn't answered the question in your last paragraph. Here is his answer to one of my questions, which is similar to yours. But I'm afraid I still don't have a really good understanding of the answer. In other words, I'm still not really sure why we need all the extra machinery in TDT, when having a general math-counterfactual-solving module (what I called "mathematical intuition module") seems both necessary and sufficient.

I wonder if you, or anyone else, understands this well enough to try to explain it. It might help me, and perhaps others, to understand Eliezer's approach to see it explained in a couple of different ways.