Can we go further than our 3 approaches to classical BI?

Smolin: dimension, topology, differential structure and signature are fixed in GR and do count as background.

(Wuthrich – some of these (like dimension) aren’t usually thought of as varying between models of GR! … so we need to bear in mind that we’re thinking about a bigger class of GR-like models than we might think.)

So Mark wants to ask if we can create an approach to QG that’s  more background independent than GR.